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fft_constants.go
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fft_constants.go
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package fft
/*
Constants (complex roots of cyclotomic polynomials) for the NTT.
These were computed using scripts/generate_constants.sage.
If this module is loaded with fft_short, we only need the first half of each phi*_roots table.
*/
// The roots of phi_4 = x^2 + 1
// The second root is the conjugates of the first one.
var phi4_roots = []complex128{1.00000000000000i, -1.00000000000000i}
// The roots of phi_8 = x^4 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi8_roots = []complex128{
complex128(0.707106781186548 + 0.707106781186547i),
complex128(-0.707106781186548 - 0.707106781186547i),
complex128(0.707106781186548 - 0.707106781186547i),
complex128(-0.707106781186548 + 0.707106781186547i),
}
// The roots of phi_16 = x^8 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi16_roots = []complex128{
complex128(0.923879532511287 + 0.38268343236509i),
complex128(-0.923879532511287 - 0.38268343236509i),
complex128(0.38268343236509 - 0.923879532511287i),
complex128(-0.38268343236509 + 0.923879532511287i),
complex128(0.923879532511287 - 0.38268343236509i),
complex128(-0.923879532511287 + 0.38268343236509i),
complex128(0.38268343236509 + 0.923879532511287i),
complex128(-0.38268343236509 - 0.923879532511287i),
}
// The roots of phi_32 = x^16 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi32_roots = []complex128{
complex128(0.98078528040323 + 0.195090322016128i),
complex128(-0.98078528040323 - 0.195090322016128i),
complex128(0.195090322016128 - 0.98078528040323i),
complex128(-0.195090322016128 + 0.98078528040323i),
complex128(0.831469612302545 - 0.555570233019602i),
complex128(-0.831469612302545 + 0.555570233019602i),
complex128(0.555570233019602 + 0.831469612302545i),
complex128(-0.555570233019602 - 0.831469612302545i),
complex128(0.98078528040323 - 0.195090322016128i),
complex128(-0.98078528040323 + 0.195090322016128i),
complex128(0.195090322016128 + 0.98078528040323i),
complex128(-0.195090322016128 - 0.98078528040323i),
complex128(0.831469612302545 + 0.555570233019602i),
complex128(-0.831469612302545 - 0.555570233019602i),
complex128(0.555570233019602 - 0.831469612302545i),
complex128(-0.555570233019602 + 0.831469612302545i),
}
// The roots of phi_64 = x^32 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi64_roots = []complex128{
complex128(0.995184726672197 + 0.0980171403295606i),
complex128(-0.995184726672197 - 0.0980171403295606i),
complex128(0.0980171403295606 - 0.995184726672197i),
complex128(-0.0980171403295606 + 0.995184726672197i),
complex128(0.773010453362737 - 0.634393284163646i),
complex128(-0.773010453362737 + 0.634393284163646i),
complex128(0.634393284163645 + 0.773010453362737i),
complex128(-0.634393284163645 - 0.773010453362737i),
complex128(0.956940335732209 - 0.290284677254462i),
complex128(-0.956940335732209 + 0.290284677254462i),
complex128(0.290284677254462 + 0.956940335732209i),
complex128(-0.290284677254462 - 0.956940335732209i),
complex128(0.881921264348355 + 0.471396736825998i),
complex128(-0.881921264348355 - 0.471396736825998i),
complex128(0.471396736825998 - 0.881921264348355i),
complex128(-0.471396736825998 + 0.881921264348355i),
complex128(0.995184726672197 - 0.0980171403295606i),
complex128(-0.995184726672197 + 0.0980171403295606i),
complex128(0.0980171403295606 + 0.995184726672197i),
complex128(-0.0980171403295606 - 0.995184726672197i),
complex128(0.773010453362737 + 0.634393284163646i),
complex128(-0.773010453362737 - 0.634393284163646i),
complex128(0.634393284163645 - 0.773010453362737i),
complex128(-0.634393284163645 + 0.773010453362737i),
complex128(0.956940335732209 + 0.290284677254462i),
complex128(-0.956940335732209 - 0.290284677254462i),
complex128(0.290284677254462 - 0.956940335732209i),
complex128(-0.290284677254462 + 0.956940335732209i),
complex128(0.881921264348355 - 0.471396736825998i),
complex128(-0.881921264348355 + 0.471396736825998i),
complex128(0.471396736825998 + 0.881921264348355i),
complex128(-0.471396736825998 - 0.881921264348355i),
}
// The roots of phi_128 = x^64 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi128_roots = []complex128{
complex128(0.998795456205172 + 0.049067674327418i),
complex128(-0.998795456205172 - 0.049067674327418i),
complex128(0.049067674327418 - 0.998795456205172i),
complex128(-0.049067674327418 + 0.998795456205172i),
complex128(0.740951125354959 - 0.671558954847018i),
complex128(-0.740951125354959 + 0.671558954847018i),
complex128(0.671558954847018 + 0.740951125354959i),
complex128(-0.671558954847018 - 0.740951125354959i),
complex128(0.941544065183021 - 0.33688985339222i),
complex128(-0.941544065183021 + 0.33688985339222i),
complex128(0.33688985339222 + 0.941544065183021i),
complex128(-0.33688985339222 - 0.941544065183021i),
complex128(0.903989293123443 + 0.427555093430282i),
complex128(-0.903989293123443 - 0.427555093430282i),
complex128(0.427555093430282 - 0.903989293123443i),
complex128(-0.427555093430282 + 0.903989293123443i),
complex128(0.989176509964781 - 0.146730474455362i),
complex128(-0.989176509964781 + 0.146730474455362i),
complex128(0.146730474455362 + 0.989176509964781i),
complex128(-0.146730474455362 - 0.989176509964781i),
complex128(0.803207531480645 + 0.595699304492433i),
complex128(-0.803207531480645 - 0.595699304492433i),
complex128(0.595699304492433 - 0.803207531480645i),
complex128(-0.595699304492433 + 0.803207531480645i),
complex128(0.970031253194544 + 0.242980179903264i),
complex128(-0.970031253194544 - 0.242980179903264i),
complex128(0.242980179903264 - 0.970031253194544i),
complex128(-0.242980179903264 + 0.970031253194544i),
complex128(0.857728610000272 - 0.514102744193222i),
complex128(-0.857728610000272 + 0.514102744193222i),
complex128(0.514102744193222 + 0.857728610000272i),
complex128(-0.514102744193222 - 0.857728610000272i),
complex128(0.998795456205172 - 0.049067674327418i),
complex128(-0.998795456205172 + 0.049067674327418i),
complex128(0.049067674327418 + 0.998795456205172i),
complex128(-0.049067674327418 - 0.998795456205172i),
complex128(0.740951125354959 + 0.671558954847018i),
complex128(-0.740951125354959 - 0.671558954847018i),
complex128(0.671558954847018 - 0.740951125354959i),
complex128(-0.671558954847018 + 0.740951125354959i),
complex128(0.941544065183021 + 0.33688985339222i),
complex128(-0.941544065183021 - 0.33688985339222i),
complex128(0.33688985339222 - 0.941544065183021i),
complex128(-0.33688985339222 + 0.941544065183021i),
complex128(0.903989293123443 - 0.427555093430282i),
complex128(-0.903989293123443 + 0.427555093430282i),
complex128(0.427555093430282 + 0.903989293123443i),
complex128(-0.427555093430282 - 0.903989293123443i),
complex128(0.989176509964781 + 0.146730474455362i),
complex128(-0.989176509964781 - 0.146730474455362i),
complex128(0.146730474455362 - 0.989176509964781i),
complex128(-0.146730474455362 + 0.989176509964781i),
complex128(0.803207531480645 - 0.595699304492433i),
complex128(-0.803207531480645 + 0.595699304492433i),
complex128(0.595699304492433 + 0.803207531480645i),
complex128(-0.595699304492433 - 0.803207531480645i),
complex128(0.970031253194544 - 0.242980179903264i),
complex128(-0.970031253194544 + 0.242980179903264i),
complex128(0.242980179903264 + 0.970031253194544i),
complex128(-0.242980179903264 - 0.970031253194544i),
complex128(0.857728610000272 + 0.514102744193222i),
complex128(-0.857728610000272 - 0.514102744193222i),
complex128(0.514102744193222 - 0.857728610000272i),
complex128(-0.514102744193222 + 0.857728610000272i),
}
// The roots of phi_256 = x^128 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi256_roots = []complex128{
complex128(0.999698818696204 + 0.0245412285229123i),
complex128(-0.999698818696204 - 0.0245412285229123i),
complex128(0.0245412285229123 - 0.999698818696204i),
complex128(-0.0245412285229123 + 0.999698818696204i),
complex128(0.724247082951467 - 0.689540544737067i),
complex128(-0.724247082951467 + 0.689540544737067i),
complex128(0.689540544737067 + 0.724247082951467i),
complex128(-0.689540544737067 - 0.724247082951467i),
complex128(0.932992798834739 - 0.359895036534988i),
complex128(-0.932992798834739 + 0.359895036534988i),
complex128(0.359895036534988 + 0.932992798834739i),
complex128(-0.359895036534988 - 0.932992798834739i),
complex128(0.914209755703531 + 0.40524131400499i),
complex128(-0.914209755703531 - 0.40524131400499i),
complex128(0.40524131400499 - 0.914209755703531i),
complex128(-0.40524131400499 + 0.914209755703531i),
complex128(0.985277642388941 - 0.170961888760301i),
complex128(-0.985277642388941 + 0.170961888760301i),
complex128(0.170961888760301 + 0.985277642388941i),
complex128(-0.170961888760301 - 0.985277642388941i),
complex128(0.817584813151584 + 0.575808191417845i),
complex128(-0.817584813151584 - 0.575808191417845i),
complex128(0.575808191417845 - 0.817584813151584i),
complex128(-0.575808191417845 + 0.817584813151584i),
complex128(0.975702130038529 + 0.21910124015687i),
complex128(-0.975702130038529 - 0.21910124015687i),
complex128(0.21910124015687 - 0.975702130038529i),
complex128(-0.21910124015687 + 0.975702130038529i),
complex128(0.844853565249707 - 0.534997619887097i),
complex128(-0.844853565249707 + 0.534997619887097i),
complex128(0.534997619887097 + 0.844853565249707i),
complex128(-0.534997619887097 - 0.844853565249707i),
complex128(0.99729045667869 - 0.0735645635996674i),
complex128(-0.99729045667869 + 0.0735645635996674i),
complex128(0.0735645635996674 + 0.99729045667869i),
complex128(-0.0735645635996674 - 0.99729045667869i),
complex128(0.757208846506485 + 0.653172842953777i),
complex128(-0.757208846506485 - 0.653172842953777i),
complex128(0.653172842953777 - 0.757208846506485i),
complex128(-0.653172842953777 + 0.757208846506485i),
complex128(0.949528180593037 + 0.313681740398892i),
complex128(-0.949528180593037 - 0.313681740398892i),
complex128(0.313681740398892 - 0.949528180593037i),
complex128(-0.313681740398892 + 0.949528180593037i),
complex128(0.893224301195515 - 0.449611329654607i),
complex128(-0.893224301195515 + 0.449611329654607i),
complex128(0.449611329654607 + 0.893224301195515i),
complex128(-0.449611329654607 - 0.893224301195515i),
complex128(0.99247953459871 + 0.122410675199216i),
complex128(-0.99247953459871 - 0.122410675199216i),
complex128(0.122410675199216 - 0.99247953459871i),
complex128(-0.122410675199216 + 0.99247953459871i),
complex128(0.788346427626606 - 0.615231590580627i),
complex128(-0.788346427626606 + 0.615231590580627i),
complex128(0.615231590580627 + 0.788346427626606i),
complex128(-0.615231590580627 - 0.788346427626606i),
complex128(0.96377606579544 - 0.266712757474898i),
complex128(-0.96377606579544 + 0.266712757474898i),
complex128(0.266712757474898 + 0.96377606579544i),
complex128(-0.266712757474898 - 0.96377606579544i),
complex128(0.870086991108711 + 0.492898192229784i),
complex128(-0.870086991108711 - 0.492898192229784i),
complex128(0.492898192229784 - 0.870086991108711i),
complex128(-0.492898192229784 + 0.870086991108711i),
complex128(0.999698818696204 - 0.0245412285229123i),
complex128(-0.999698818696204 + 0.0245412285229123i),
complex128(0.0245412285229123 + 0.999698818696204i),
complex128(-0.0245412285229123 - 0.999698818696204i),
complex128(0.724247082951467 + 0.689540544737067i),
complex128(-0.724247082951467 - 0.689540544737067i),
complex128(0.689540544737067 - 0.724247082951467i),
complex128(-0.689540544737067 + 0.724247082951467i),
complex128(0.932992798834739 + 0.359895036534988i),
complex128(-0.932992798834739 - 0.359895036534988i),
complex128(0.359895036534988 - 0.932992798834739i),
complex128(-0.359895036534988 + 0.932992798834739i),
complex128(0.914209755703531 - 0.40524131400499i),
complex128(-0.914209755703531 + 0.40524131400499i),
complex128(0.40524131400499 + 0.914209755703531i),
complex128(-0.40524131400499 - 0.914209755703531i),
complex128(0.985277642388941 + 0.170961888760301i),
complex128(-0.985277642388941 - 0.170961888760301i),
complex128(0.170961888760301 - 0.985277642388941i),
complex128(-0.170961888760301 + 0.985277642388941i),
complex128(0.817584813151584 - 0.575808191417845i),
complex128(-0.817584813151584 + 0.575808191417845i),
complex128(0.575808191417845 + 0.817584813151584i),
complex128(-0.575808191417845 - 0.817584813151584i),
complex128(0.975702130038529 - 0.21910124015687i),
complex128(-0.975702130038529 + 0.21910124015687i),
complex128(0.21910124015687 + 0.975702130038529i),
complex128(-0.21910124015687 - 0.975702130038529i),
complex128(0.844853565249707 + 0.534997619887097i),
complex128(-0.844853565249707 - 0.534997619887097i),
complex128(0.534997619887097 - 0.844853565249707i),
complex128(-0.534997619887097 + 0.844853565249707i),
complex128(0.99729045667869 + 0.0735645635996674i),
complex128(-0.99729045667869 - 0.0735645635996674i),
complex128(0.0735645635996674 - 0.99729045667869i),
complex128(-0.0735645635996674 + 0.99729045667869i),
complex128(0.757208846506485 - 0.653172842953777i),
complex128(-0.757208846506485 + 0.653172842953777i),
complex128(0.653172842953777 + 0.757208846506485i),
complex128(-0.653172842953777 - 0.757208846506485i),
complex128(0.949528180593037 - 0.313681740398892i),
complex128(-0.949528180593037 + 0.313681740398892i),
complex128(0.313681740398892 + 0.949528180593037i),
complex128(-0.313681740398892 - 0.949528180593037i),
complex128(0.893224301195515 + 0.449611329654607i),
complex128(-0.893224301195515 - 0.449611329654607i),
complex128(0.449611329654607 - 0.893224301195515i),
complex128(-0.449611329654607 + 0.893224301195515i),
complex128(0.99247953459871 - 0.122410675199216i),
complex128(-0.99247953459871 + 0.122410675199216i),
complex128(0.122410675199216 + 0.99247953459871i),
complex128(-0.122410675199216 - 0.99247953459871i),
complex128(0.788346427626606 + 0.615231590580627i),
complex128(-0.788346427626606 - 0.615231590580627i),
complex128(0.615231590580627 - 0.788346427626606i),
complex128(-0.615231590580627 + 0.788346427626606i),
complex128(0.96377606579544 + 0.266712757474898i),
complex128(-0.96377606579544 - 0.266712757474898i),
complex128(0.266712757474898 - 0.96377606579544i),
complex128(-0.266712757474898 + 0.96377606579544i),
complex128(0.870086991108711 - 0.492898192229784i),
complex128(-0.870086991108711 + 0.492898192229784i),
complex128(0.492898192229784 + 0.870086991108711i),
complex128(-0.492898192229784 - 0.870086991108711i),
}
// The roots of phi512 = x^256 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi512_roots = []complex128{
complex128(0.999924701839145 + 0.0122715382857199i),
complex128(-0.999924701839145 - 0.0122715382857199i),
complex128(0.0122715382857199 - 0.999924701839145i),
complex128(-0.0122715382857199 + 0.999924701839145i),
complex128(0.715730825283819 - 0.698376249408973i),
complex128(-0.715730825283819 + 0.698376249408973i),
complex128(0.698376249408973 + 0.715730825283819i),
complex128(-0.698376249408973 - 0.715730825283819i),
complex128(0.928506080473216 - 0.371317193951837i),
complex128(-0.928506080473216 + 0.371317193951837i),
complex128(0.371317193951837 + 0.928506080473216i),
complex128(-0.371317193951837 - 0.928506080473216i),
complex128(0.919113851690058 + 0.393992040061048i),
complex128(-0.919113851690058 - 0.393992040061048i),
complex128(0.393992040061048 - 0.919113851690058i),
complex128(-0.393992040061048 + 0.919113851690058i),
complex128(0.983105487431216 - 0.183039887955141i),
complex128(-0.983105487431216 + 0.183039887955141i),
complex128(0.183039887955141 + 0.983105487431216i),
complex128(-0.183039887955141 - 0.983105487431216i),
complex128(0.824589302785025 + 0.565731810783613i),
complex128(-0.824589302785025 - 0.565731810783613i),
complex128(0.565731810783613 - 0.824589302785025i),
complex128(-0.565731810783613 + 0.824589302785025i),
complex128(0.978317370719628 + 0.207111376192219i),
complex128(-0.978317370719628 - 0.207111376192219i),
complex128(0.207111376192219 - 0.978317370719628i),
complex128(-0.207111376192219 + 0.978317370719628i),
complex128(0.838224705554838 - 0.545324988422046i),
complex128(-0.838224705554838 + 0.545324988422046i),
complex128(0.545324988422046 + 0.838224705554838i),
complex128(-0.545324988422046 - 0.838224705554838i),
complex128(0.996312612182778 - 0.0857973123444399i),
complex128(-0.996312612182778 + 0.0857973123444399i),
complex128(0.0857973123444399 + 0.996312612182778i),
complex128(-0.0857973123444399 - 0.996312612182778i),
complex128(0.765167265622459 + 0.643831542889791i),
complex128(-0.765167265622459 - 0.643831542889791i),
complex128(0.643831542889791 - 0.765167265622459i),
complex128(-0.643831542889791 + 0.765167265622459i),
complex128(0.953306040354194 + 0.302005949319228i),
complex128(-0.953306040354194 - 0.302005949319228i),
complex128(0.302005949319228 - 0.953306040354194i),
complex128(-0.302005949319228 + 0.953306040354194i),
complex128(0.887639620402854 - 0.46053871095824i),
complex128(-0.887639620402854 + 0.46053871095824i),
complex128(0.46053871095824 + 0.887639620402854i),
complex128(-0.46053871095824 - 0.887639620402854i),
complex128(0.993906970002356 + 0.110222207293883i),
complex128(-0.993906970002356 - 0.110222207293883i),
complex128(0.110222207293883 - 0.993906970002356i),
complex128(-0.110222207293883 + 0.993906970002356i),
complex128(0.780737228572094 - 0.624859488142386i),
complex128(-0.780737228572094 + 0.624859488142386i),
complex128(0.624859488142386 + 0.780737228572094i),
complex128(-0.624859488142386 - 0.780737228572094i),
complex128(0.960430519415566 - 0.278519689385053i),
complex128(-0.960430519415566 + 0.278519689385053i),
complex128(0.278519689385053 + 0.960430519415566i),
complex128(-0.278519689385053 - 0.960430519415566i),
complex128(0.876070094195407 + 0.482183772079123i),
complex128(-0.876070094195407 - 0.482183772079123i),
complex128(0.482183772079123 - 0.876070094195407i),
complex128(-0.482183772079123 + 0.876070094195407i),
complex128(0.99932238458835 - 0.0368072229413588i),
complex128(-0.99932238458835 + 0.0368072229413588i),
complex128(0.0368072229413588 + 0.99932238458835i),
complex128(-0.0368072229413588 - 0.99932238458835i),
complex128(0.732654271672413 + 0.680600997795453i),
complex128(-0.732654271672413 - 0.680600997795453i),
complex128(0.680600997795453 - 0.732654271672413i),
complex128(-0.680600997795453 + 0.732654271672413i),
complex128(0.937339011912575 + 0.348418680249435i),
complex128(-0.937339011912575 - 0.348418680249435i),
complex128(0.348418680249435 - 0.937339011912575i),
complex128(-0.348418680249435 + 0.937339011912575i),
complex128(0.909167983090522 - 0.416429560097637i),
complex128(-0.909167983090522 + 0.416429560097637i),
complex128(0.416429560097637 + 0.909167983090522i),
complex128(-0.416429560097637 - 0.909167983090522i),
complex128(0.987301418157858 + 0.158858143333861i),
complex128(-0.987301418157858 - 0.158858143333861i),
complex128(0.158858143333861 - 0.987301418157858i),
complex128(-0.158858143333861 + 0.987301418157858i),
complex128(0.810457198252595 - 0.585797857456439i),
complex128(-0.810457198252595 + 0.585797857456439i),
complex128(0.585797857456439 + 0.810457198252595i),
complex128(-0.585797857456439 - 0.810457198252595i),
complex128(0.97293995220556 - 0.231058108280671i),
complex128(-0.97293995220556 + 0.231058108280671i),
complex128(0.231058108280671 + 0.97293995220556i),
complex128(-0.231058108280671 - 0.97293995220556i),
complex128(0.851355193105265 + 0.524589682678469i),
complex128(-0.851355193105265 - 0.524589682678469i),
complex128(0.524589682678469 - 0.851355193105265i),
complex128(-0.524589682678469 + 0.851355193105265i),
complex128(0.998118112900149 + 0.0613207363022086i),
complex128(-0.998118112900149 - 0.0613207363022086i),
complex128(0.0613207363022086 - 0.998118112900149i),
complex128(-0.0613207363022086 + 0.998118112900149i),
complex128(0.749136394523459 - 0.662415777590172i),
complex128(-0.749136394523459 + 0.662415777590172i),
complex128(0.662415777590172 + 0.749136394523459i),
complex128(-0.662415777590172 - 0.749136394523459i),
complex128(0.945607325380521 - 0.325310292162263i),
complex128(-0.945607325380521 + 0.325310292162263i),
complex128(0.325310292162263 + 0.945607325380521i),
complex128(-0.325310292162263 - 0.945607325380521i),
complex128(0.898674465693954 + 0.438616238538528i),
complex128(-0.898674465693954 - 0.438616238538528i),
complex128(0.438616238538528 - 0.898674465693954i),
complex128(-0.438616238538528 + 0.898674465693954i),
complex128(0.99090263542778 - 0.134580708507126i),
complex128(-0.99090263542778 + 0.134580708507126i),
complex128(0.134580708507126 + 0.99090263542778i),
complex128(-0.134580708507126 - 0.99090263542778i),
complex128(0.795836904608884 + 0.605511041404325i),
complex128(-0.795836904608884 - 0.605511041404325i),
complex128(0.605511041404326 - 0.795836904608883i),
complex128(-0.605511041404326 + 0.795836904608883i),
complex128(0.966976471044852 + 0.254865659604515i),
complex128(-0.966976471044852 - 0.254865659604515i),
complex128(0.254865659604515 - 0.966976471044852i),
complex128(-0.254865659604515 + 0.966976471044852i),
complex128(0.863972856121587 - 0.503538383725718i),
complex128(-0.863972856121587 + 0.503538383725718i),
complex128(0.503538383725718 + 0.863972856121587i),
complex128(-0.503538383725718 - 0.863972856121587i),
complex128(0.999924701839145 - 0.0122715382857199i),
complex128(-0.999924701839145 + 0.0122715382857199i),
complex128(0.0122715382857199 + 0.999924701839145i),
complex128(-0.0122715382857199 - 0.999924701839145i),
complex128(0.715730825283819 + 0.698376249408973i),
complex128(-0.715730825283819 - 0.698376249408973i),
complex128(0.698376249408973 - 0.715730825283819i),
complex128(-0.698376249408973 + 0.715730825283819i),
complex128(0.928506080473216 + 0.371317193951837i),
complex128(-0.928506080473216 - 0.371317193951837i),
complex128(0.371317193951837 - 0.928506080473216i),
complex128(-0.371317193951837 + 0.928506080473216i),
complex128(0.919113851690058 - 0.393992040061048i),
complex128(-0.919113851690058 + 0.393992040061048i),
complex128(0.393992040061048 + 0.919113851690058i),
complex128(-0.393992040061048 - 0.919113851690058i),
complex128(0.983105487431216 + 0.183039887955141i),
complex128(-0.983105487431216 - 0.183039887955141i),
complex128(0.183039887955141 - 0.983105487431216i),
complex128(-0.183039887955141 + 0.983105487431216i),
complex128(0.824589302785025 - 0.565731810783613i),
complex128(-0.824589302785025 + 0.565731810783613i),
complex128(0.565731810783613 + 0.824589302785025i),
complex128(-0.565731810783613 - 0.824589302785025i),
complex128(0.978317370719628 - 0.207111376192219i),
complex128(-0.978317370719628 + 0.207111376192219i),
complex128(0.207111376192219 + 0.978317370719628i),
complex128(-0.207111376192219 - 0.978317370719628i),
complex128(0.838224705554838 + 0.545324988422046i),
complex128(-0.838224705554838 - 0.545324988422046i),
complex128(0.545324988422046 - 0.838224705554838i),
complex128(-0.545324988422046 + 0.838224705554838i),
complex128(0.996312612182778 + 0.0857973123444399i),
complex128(-0.996312612182778 - 0.0857973123444399i),
complex128(0.0857973123444399 - 0.996312612182778i),
complex128(-0.0857973123444399 + 0.996312612182778i),
complex128(0.765167265622459 - 0.643831542889791i),
complex128(-0.765167265622459 + 0.643831542889791i),
complex128(0.643831542889791 + 0.765167265622459i),
complex128(-0.643831542889791 - 0.765167265622459i),
complex128(0.953306040354194 - 0.302005949319228i),
complex128(-0.953306040354194 + 0.302005949319228i),
complex128(0.302005949319228 + 0.953306040354194i),
complex128(-0.302005949319228 - 0.953306040354194i),
complex128(0.887639620402854 + 0.46053871095824i),
complex128(-0.887639620402854 - 0.46053871095824i),
complex128(0.46053871095824 - 0.887639620402854i),
complex128(-0.46053871095824 + 0.887639620402854i),
complex128(0.993906970002356 - 0.110222207293883i),
complex128(-0.993906970002356 + 0.110222207293883i),
complex128(0.110222207293883 + 0.993906970002356i),
complex128(-0.110222207293883 - 0.993906970002356i),
complex128(0.780737228572094 + 0.624859488142386i),
complex128(-0.780737228572094 - 0.624859488142386i),
complex128(0.624859488142386 - 0.780737228572094i),
complex128(-0.624859488142386 + 0.780737228572094i),
complex128(0.960430519415566 + 0.278519689385053i),
complex128(-0.960430519415566 - 0.278519689385053i),
complex128(0.278519689385053 - 0.960430519415566i),
complex128(-0.278519689385053 + 0.960430519415566i),
complex128(0.876070094195407 - 0.482183772079123i),
complex128(-0.876070094195407 + 0.482183772079123i),
complex128(0.482183772079123 + 0.876070094195407i),
complex128(-0.482183772079123 - 0.876070094195407i),
complex128(0.99932238458835 + 0.0368072229413588i),
complex128(-0.99932238458835 - 0.0368072229413588i),
complex128(0.0368072229413588 - 0.99932238458835i),
complex128(-0.0368072229413588 + 0.99932238458835i),
complex128(0.732654271672413 - 0.680600997795453i),
complex128(-0.732654271672413 + 0.680600997795453i),
complex128(0.680600997795453 + 0.732654271672413i),
complex128(-0.680600997795453 - 0.732654271672413i),
complex128(0.937339011912575 - 0.348418680249435i),
complex128(-0.937339011912575 + 0.348418680249435i),
complex128(0.348418680249435 + 0.937339011912575i),
complex128(-0.348418680249435 - 0.937339011912575i),
complex128(0.909167983090522 + 0.416429560097637i),
complex128(-0.909167983090522 - 0.416429560097637i),
complex128(0.416429560097637 - 0.909167983090522i),
complex128(-0.416429560097637 + 0.909167983090522i),
complex128(0.987301418157858 - 0.158858143333861i),
complex128(-0.987301418157858 + 0.158858143333861i),
complex128(0.158858143333861 + 0.987301418157858i),
complex128(-0.158858143333861 - 0.987301418157858i),
complex128(0.810457198252595 + 0.585797857456439i),
complex128(-0.810457198252595 - 0.585797857456439i),
complex128(0.585797857456439 - 0.810457198252595i),
complex128(-0.585797857456439 + 0.810457198252595i),
complex128(0.97293995220556 + 0.231058108280671i),
complex128(-0.97293995220556 - 0.231058108280671i),
complex128(0.231058108280671 - 0.97293995220556i),
complex128(-0.231058108280671 + 0.97293995220556i),
complex128(0.851355193105265 - 0.524589682678469i),
complex128(-0.851355193105265 + 0.524589682678469i),
complex128(0.524589682678469 + 0.851355193105265i),
complex128(-0.524589682678469 - 0.851355193105265i),
complex128(0.998118112900149 - 0.0613207363022086i),
complex128(-0.998118112900149 + 0.0613207363022086i),
complex128(0.0613207363022086 + 0.998118112900149i),
complex128(-0.0613207363022086 - 0.998118112900149i),
complex128(0.749136394523459 + 0.662415777590172i),
complex128(-0.749136394523459 - 0.662415777590172i),
complex128(0.662415777590172 - 0.749136394523459i),
complex128(-0.662415777590172 + 0.749136394523459i),
complex128(0.945607325380521 + 0.325310292162263i),
complex128(-0.945607325380521 - 0.325310292162263i),
complex128(0.325310292162263 - 0.945607325380521i),
complex128(-0.325310292162263 + 0.945607325380521i),
complex128(0.898674465693954 - 0.438616238538528i),
complex128(-0.898674465693954 + 0.438616238538528i),
complex128(0.438616238538528 + 0.898674465693954i),
complex128(-0.438616238538528 - 0.898674465693954i),
complex128(0.99090263542778 + 0.134580708507126i),
complex128(-0.99090263542778 - 0.134580708507126i),
complex128(0.134580708507126 - 0.99090263542778i),
complex128(-0.134580708507126 + 0.99090263542778i),
complex128(0.795836904608884 - 0.605511041404325i),
complex128(-0.795836904608884 + 0.605511041404325i),
complex128(0.605511041404326 + 0.795836904608883i),
complex128(-0.605511041404326 - 0.795836904608883i),
complex128(0.966976471044852 - 0.254865659604515i),
complex128(-0.966976471044852 + 0.254865659604515i),
complex128(0.254865659604515 + 0.966976471044852i),
complex128(-0.254865659604515 - 0.966976471044852i),
complex128(0.863972856121587 + 0.503538383725718i),
complex128(-0.863972856121587 - 0.503538383725718i),
complex128(0.503538383725718 - 0.863972856121587i),
complex128(-0.503538383725718 + 0.863972856121587i),
}
// The roots of phi1024 = x^512 + 1
// The second half of the roots are is the conjugates of the first half.
// The root at index (2 * i + 1) is the negation of the root at index (2 * i).
var phi1024_roots = []complex128{
complex128(0.999981175282601 + 0.00613588464915448i),
complex128(-0.999981175282601 - 0.00613588464915448i),
complex128(0.00613588464915448 - 0.999981175282601i),
complex128(-0.00613588464915448 + 0.999981175282601i),
complex128(0.711432195745216 - 0.702754744457225i),
complex128(-0.711432195745216 + 0.702754744457225i),
complex128(0.702754744457225 + 0.711432195745216i),
complex128(-0.702754744457225 - 0.711432195745216i),
complex128(0.926210242138311 - 0.377007410216418i),
complex128(-0.926210242138311 + 0.377007410216418i),
complex128(0.377007410216418 + 0.926210242138311i),
complex128(-0.377007410216418 - 0.926210242138311i),
complex128(0.921514039342042 + 0.388345046698826i),
complex128(-0.921514039342042 - 0.388345046698826i),
complex128(0.388345046698826 - 0.921514039342042i),
complex128(-0.388345046698826 + 0.921514039342042i),
complex128(0.981963869109555 - 0.189068664149806i),
complex128(-0.981963869109555 + 0.189068664149806i),
complex128(0.189068664149806 + 0.981963869109555i),
complex128(-0.189068664149806 - 0.981963869109555i),
complex128(0.828045045257756 + 0.560661576197336i),
complex128(-0.828045045257756 - 0.560661576197336i),
complex128(0.560661576197336 - 0.828045045257756i),
complex128(-0.560661576197336 + 0.828045045257756i),
complex128(0.979569765685441 + 0.201104634842092i),
complex128(-0.979569765685441 - 0.201104634842092i),
complex128(0.201104634842092 - 0.979569765685441i),
complex128(-0.201104634842092 + 0.979569765685441i),
complex128(0.83486287498638 - 0.550457972936605i),
complex128(-0.83486287498638 + 0.550457972936605i),
complex128(0.550457972936605 + 0.83486287498638i),
complex128(-0.550457972936605 - 0.83486287498638i),
complex128(0.99576741446766 - 0.0919089564971327i),
complex128(-0.99576741446766 + 0.0919089564971327i),
complex128(0.0919089564971327 + 0.99576741446766i),
complex128(-0.0919089564971327 - 0.99576741446766i),
complex128(0.76910333764558 + 0.639124444863776i),
complex128(-0.76910333764558 - 0.639124444863776i),
complex128(0.639124444863776 - 0.76910333764558i),
complex128(-0.639124444863776 + 0.76910333764558i),
complex128(0.955141168305771 + 0.296150888243624i),
complex128(-0.955141168305771 - 0.296150888243624i),
complex128(0.296150888243624 - 0.955141168305771i),
complex128(-0.296150888243624 + 0.955141168305771i),
complex128(0.884797098430938 - 0.465976495767966i),
complex128(-0.884797098430938 + 0.465976495767966i),
complex128(0.465976495767966 + 0.884797098430938i),
complex128(-0.465976495767966 - 0.884797098430938i),
complex128(0.994564570734255 + 0.104121633872055i),
complex128(-0.994564570734255 - 0.104121633872055i),
complex128(0.104121633872055 - 0.994564570734255i),
complex128(-0.104121633872055 + 0.994564570734255i),
complex128(0.776888465673232 - 0.629638238914927i),
complex128(-0.776888465673232 + 0.629638238914927i),
complex128(0.629638238914927 + 0.776888465673233i),
complex128(-0.629638238914927 - 0.776888465673233i),
complex128(0.958703474895871 - 0.284407537211272i),
complex128(-0.958703474895871 + 0.284407537211272i),
complex128(0.284407537211272 + 0.958703474895871i),
complex128(-0.284407537211272 - 0.958703474895871i),
complex128(0.879012226428633 + 0.476799230063322i),
complex128(-0.879012226428633 - 0.476799230063322i),
complex128(0.476799230063322 - 0.879012226428634i),
complex128(-0.476799230063322 + 0.879012226428634i),
complex128(0.999077727752645 - 0.0429382569349408i),
complex128(-0.999077727752645 + 0.0429382569349408i),
complex128(0.0429382569349408 + 0.999077727752645i),
complex128(-0.0429382569349408 - 0.999077727752645i),
complex128(0.73681656887737 + 0.676092703575316i),
complex128(-0.73681656887737 - 0.676092703575316i),
complex128(0.676092703575316 - 0.73681656887737i),
complex128(-0.676092703575316 + 0.73681656887737i),
complex128(0.93945922360219 + 0.342660717311994i),
complex128(-0.93945922360219 - 0.342660717311994i),
complex128(0.342660717311994 - 0.93945922360219i),
complex128(-0.342660717311994 + 0.93945922360219i),
complex128(0.906595704514915 - 0.4220002707998i),
complex128(-0.906595704514915 + 0.4220002707998i),
complex128(0.4220002707998 + 0.906595704514915i),
complex128(-0.4220002707998 - 0.906595704514915i),
complex128(0.988257567730749 + 0.152797185258443i),
complex128(-0.988257567730749 - 0.152797185258443i),
complex128(0.152797185258443 - 0.988257567730749i),
complex128(-0.152797185258443 + 0.988257567730749i),
complex128(0.806847553543799 - 0.590759701858874i),
complex128(-0.806847553543799 + 0.590759701858874i),
complex128(0.590759701858874 + 0.806847553543799i),
complex128(-0.590759701858874 - 0.806847553543799i),
complex128(0.971503890986252 - 0.237023605994367i),
complex128(-0.971503890986252 + 0.237023605994367i),
complex128(0.237023605994367 + 0.971503890986252i),
complex128(-0.237023605994367 - 0.971503890986252i),
complex128(0.854557988365401 + 0.51935599016559i),
complex128(-0.854557988365401 - 0.51935599016559i),
complex128(0.51935599016559 - 0.854557988365401i),
complex128(-0.51935599016559 + 0.854557988365401i),
complex128(0.998475580573295 + 0.0551952443496899i),
complex128(-0.998475580573295 - 0.0551952443496899i),
complex128(0.0551952443496899 - 0.998475580573295i),
complex128(-0.0551952443496899 + 0.998475580573295i),
complex128(0.745057785441466 - 0.666999922303638i),
complex128(-0.745057785441466 + 0.666999922303638i),
complex128(0.666999922303637 + 0.745057785441466i),
complex128(-0.666999922303637 - 0.745057785441466i),
complex128(0.94359345816196 - 0.331106305759876i),
complex128(-0.94359345816196 + 0.331106305759876i),
complex128(0.331106305759876 + 0.94359345816196i),
complex128(-0.331106305759876 - 0.94359345816196i),
complex128(0.901348847046022 + 0.433093818853152i),
complex128(-0.901348847046022 - 0.433093818853152i),
complex128(0.433093818853152 - 0.901348847046022i),
complex128(-0.433093818853152 + 0.901348847046022i),
complex128(0.990058210262297 - 0.140658239332849i),
complex128(-0.990058210262297 + 0.140658239332849i),
complex128(0.140658239332849 + 0.990058210262297i),
complex128(-0.140658239332849 - 0.990058210262297i),
complex128(0.799537269107905 + 0.600616479383869i),
complex128(-0.799537269107905 - 0.600616479383869i),
complex128(0.600616479383869 - 0.799537269107905i),
complex128(-0.600616479383869 + 0.799537269107905i),
complex128(0.968522094274417 + 0.24892760574572i),
complex128(-0.968522094274417 - 0.24892760574572i),
complex128(0.24892760574572 - 0.968522094274417i),
complex128(-0.24892760574572 + 0.968522094274417i),
complex128(0.860866938637767 - 0.508830142543107i),
complex128(-0.860866938637767 + 0.508830142543107i),
complex128(0.508830142543107 + 0.860866938637767i),
complex128(-0.508830142543107 - 0.860866938637767i),
complex128(0.999830581795823 - 0.0184067299058048i),
complex128(-0.999830581795823 + 0.0184067299058048i),
complex128(0.0184067299058048 + 0.999830581795823i),
complex128(-0.0184067299058048 - 0.999830581795823i),
complex128(0.720002507961382 + 0.693971460889654i),
complex128(-0.720002507961382 - 0.693971460889654i),
complex128(0.693971460889654 - 0.720002507961382i),
complex128(-0.693971460889654 + 0.720002507961382i),
complex128(0.930766961078984 + 0.365612997804774i),
complex128(-0.930766961078984 - 0.365612997804774i),
complex128(0.365612997804774 - 0.930766961078984i),
complex128(-0.365612997804774 + 0.930766961078984i),
complex128(0.916679059921043 - 0.399624199845647i),
complex128(-0.916679059921043 + 0.399624199845647i),
complex128(0.399624199845647 + 0.916679059921043i),
complex128(-0.399624199845647 - 0.916679059921043i),
complex128(0.984210092386929 + 0.177004220412149i),
complex128(-0.984210092386929 - 0.177004220412149i),
complex128(0.177004220412149 - 0.984210092386929i),
complex128(-0.177004220412149 + 0.984210092386929i),
complex128(0.821102514991105 - 0.570780745886967i),
complex128(-0.821102514991105 + 0.570780745886967i),
complex128(0.570780745886967 + 0.821102514991105i),
complex128(-0.570780745886967 - 0.821102514991105i),
complex128(0.977028142657754 - 0.213110319916091i),
complex128(-0.977028142657754 + 0.213110319916091i),
complex128(0.213110319916091 + 0.977028142657754i),
complex128(-0.213110319916091 - 0.977028142657754i),
complex128(0.841554977436898 + 0.540171472729893i),
complex128(-0.841554977436898 - 0.540171472729893i),
complex128(0.540171472729893 - 0.841554977436898i),
complex128(-0.540171472729893 + 0.841554977436898i),
complex128(0.996820299291166 + 0.0796824379714301i),
complex128(-0.996820299291166 - 0.0796824379714301i),
complex128(0.0796824379714301 - 0.996820299291166i),
complex128(-0.0796824379714301 + 0.996820299291166i),
complex128(0.761202385484262 - 0.648514401022113i),
complex128(-0.761202385484262 + 0.648514401022113i),
complex128(0.648514401022112 + 0.761202385484262i),
complex128(-0.648514401022112 - 0.761202385484262i),
complex128(0.951435020969008 - 0.307849640041535i),
complex128(-0.951435020969008 + 0.307849640041535i),
complex128(0.307849640041535 + 0.951435020969008i),
complex128(-0.307849640041535 - 0.951435020969008i),
complex128(0.890448723244758 + 0.455083587126344i),
complex128(-0.890448723244758 - 0.455083587126344i),
complex128(0.455083587126344 - 0.890448723244758i),
complex128(-0.455083587126344 + 0.890448723244758i),
complex128(0.993211949234795 - 0.116318630911905i),
complex128(-0.993211949234795 + 0.116318630911905i),
complex128(0.116318630911905 + 0.993211949234795i),
complex128(-0.116318630911905 - 0.993211949234795i),
complex128(0.784556597155575 + 0.620057211763289i),
complex128(-0.784556597155575 - 0.620057211763289i),
complex128(0.620057211763289 - 0.784556597155575i),
complex128(-0.620057211763289 + 0.784556597155575i),
complex128(0.962121404269042 + 0.272621355449949i),
complex128(-0.962121404269042 - 0.272621355449949i),
complex128(0.272621355449949 - 0.962121404269042i),
complex128(-0.272621355449949 + 0.962121404269042i),
complex128(0.87309497841829 - 0.487550160148436i),
complex128(-0.87309497841829 + 0.487550160148436i),
complex128(0.487550160148436 + 0.87309497841829i),
complex128(-0.487550160148436 - 0.87309497841829i),
complex128(0.999529417501093 + 0.0306748031766366i),
complex128(-0.999529417501093 - 0.0306748031766366i),
complex128(0.0306748031766366 - 0.999529417501093i),
complex128(-0.0306748031766366 + 0.999529417501093i),
complex128(0.728464390448225 - 0.6850836677727i),
complex128(-0.728464390448225 + 0.6850836677727i),
complex128(0.6850836677727 + 0.728464390448225i),
complex128(-0.6850836677727 - 0.728464390448225i),
complex128(0.935183509938948 - 0.35416352542049i),
complex128(-0.935183509938948 + 0.35416352542049i),
complex128(0.35416352542049 + 0.935183509938948i),
complex128(-0.35416352542049 - 0.935183509938948i),
complex128(0.91170603200543 + 0.410843171057904i),
complex128(-0.91170603200543 - 0.410843171057904i),
complex128(0.410843171057904 - 0.91170603200543i),
complex128(-0.410843171057904 + 0.91170603200543i),
complex128(0.986308097244599 - 0.16491312048997i),
complex128(-0.986308097244599 + 0.16491312048997i),
complex128(0.16491312048997 + 0.986308097244599i),
complex128(-0.16491312048997 - 0.986308097244599i),
complex128(0.814036329705948 + 0.580813958095765i),
complex128(-0.814036329705948 - 0.580813958095765i),
complex128(0.580813958095765 - 0.814036329705948i),
complex128(-0.580813958095765 + 0.814036329705948i),
complex128(0.974339382785576 + 0.225083911359793i),
complex128(-0.974339382785576 - 0.225083911359793i),
complex128(0.225083911359793 - 0.974339382785576i),
complex128(-0.225083911359793 + 0.974339382785576i),
complex128(0.848120344803297 - 0.529803624686295i),
complex128(-0.848120344803297 + 0.529803624686295i),
complex128(0.529803624686295 + 0.848120344803297i),
complex128(-0.529803624686295 - 0.848120344803297i),
complex128(0.997723066644192 - 0.0674439195636641i),
complex128(-0.997723066644192 + 0.0674439195636641i),
complex128(0.0674439195636641 + 0.997723066644192i),
complex128(-0.0674439195636641 - 0.997723066644192i),
complex128(0.753186799043613 + 0.657806693297079i),
complex128(-0.753186799043613 - 0.657806693297079i),
complex128(0.657806693297079 - 0.753186799043613i),
complex128(-0.657806693297079 + 0.753186799043613i),
complex128(0.947585591017741 + 0.319502030816016i),
complex128(-0.947585591017741 - 0.319502030816016i),
complex128(0.319502030816016 - 0.947585591017741i),
complex128(-0.319502030816016 + 0.947585591017741i),
complex128(0.895966249756185 - 0.444122144570429i),
complex128(-0.895966249756185 + 0.444122144570429i),
complex128(0.444122144570429 + 0.895966249756185i),
complex128(-0.444122144570429 - 0.895966249756185i),
complex128(0.9917097536691 + 0.128498110793793i),
complex128(-0.9917097536691 - 0.128498110793793i),
complex128(0.128498110793793 - 0.9917097536691i),
complex128(-0.128498110793793 + 0.9917097536691i),
complex128(0.792106577300212 - 0.610382806276309i),
complex128(-0.792106577300212 + 0.610382806276309i),
complex128(0.610382806276309 + 0.792106577300212i),
complex128(-0.610382806276309 - 0.792106577300212i),
complex128(0.965394441697689 - 0.260794117915276i),
complex128(-0.965394441697689 + 0.260794117915276i),
complex128(0.260794117915276 + 0.965394441697689i),
complex128(-0.260794117915276 - 0.965394441697689i),
complex128(0.867046245515693 + 0.498227666972782i),
complex128(-0.867046245515693 - 0.498227666972782i),
complex128(0.498227666972782 - 0.867046245515693i),
complex128(-0.498227666972782 + 0.867046245515693i),
complex128(0.999981175282601 - 0.00613588464915448i),
complex128(-0.999981175282601 + 0.00613588464915448i),
complex128(0.00613588464915448 + 0.999981175282601i),
complex128(-0.00613588464915448 - 0.999981175282601i),
complex128(0.711432195745216 + 0.702754744457225i),
complex128(-0.711432195745216 - 0.702754744457225i),
complex128(0.702754744457225 - 0.711432195745216i),
complex128(-0.702754744457225 + 0.711432195745216i),
complex128(0.926210242138311 + 0.377007410216418i),
complex128(-0.926210242138311 - 0.377007410216418i),
complex128(0.377007410216418 - 0.926210242138311i),
complex128(-0.377007410216418 + 0.926210242138311i),
complex128(0.921514039342042 - 0.388345046698826i),
complex128(-0.921514039342042 + 0.388345046698826i),
complex128(0.388345046698826 + 0.921514039342042i),
complex128(-0.388345046698826 - 0.921514039342042i),
complex128(0.981963869109555 + 0.189068664149806i),
complex128(-0.981963869109555 - 0.189068664149806i),
complex128(0.189068664149806 - 0.981963869109555i),
complex128(-0.189068664149806 + 0.981963869109555i),
complex128(0.828045045257756 - 0.560661576197336i),
complex128(-0.828045045257756 + 0.560661576197336i),
complex128(0.560661576197336 + 0.828045045257756i),
complex128(-0.560661576197336 - 0.828045045257756i),
complex128(0.979569765685441 - 0.201104634842092i),
complex128(-0.979569765685441 + 0.201104634842092i),
complex128(0.201104634842092 + 0.979569765685441i),
complex128(-0.201104634842092 - 0.979569765685441i),
complex128(0.83486287498638 + 0.550457972936605i),
complex128(-0.83486287498638 - 0.550457972936605i),
complex128(0.550457972936605 - 0.83486287498638i),
complex128(-0.550457972936605 + 0.83486287498638i),
complex128(0.99576741446766 + 0.0919089564971327i),
complex128(-0.99576741446766 - 0.0919089564971327i),
complex128(0.0919089564971327 - 0.99576741446766i),
complex128(-0.0919089564971327 + 0.99576741446766i),
complex128(0.76910333764558 - 0.639124444863776i),
complex128(-0.76910333764558 + 0.639124444863776i),
complex128(0.639124444863776 + 0.76910333764558i),
complex128(-0.639124444863776 - 0.76910333764558i),
complex128(0.955141168305771 - 0.296150888243624i),
complex128(-0.955141168305771 + 0.296150888243624i),
complex128(0.296150888243624 + 0.955141168305771i),
complex128(-0.296150888243624 - 0.955141168305771i),
complex128(0.884797098430938 + 0.465976495767966i),
complex128(-0.884797098430938 - 0.465976495767966i),
complex128(0.465976495767966 - 0.884797098430938i),
complex128(-0.465976495767966 + 0.884797098430938i),
complex128(0.994564570734255 - 0.104121633872055i),
complex128(-0.994564570734255 + 0.104121633872055i),
complex128(0.104121633872055 + 0.994564570734255i),
complex128(-0.104121633872055 - 0.994564570734255i),
complex128(0.776888465673232 + 0.629638238914927i),
complex128(-0.776888465673232 - 0.629638238914927i),
complex128(0.629638238914927 - 0.776888465673233i),
complex128(-0.629638238914927 + 0.776888465673233i),
complex128(0.958703474895871 + 0.284407537211272i),
complex128(-0.958703474895871 - 0.284407537211272i),
complex128(0.284407537211272 - 0.958703474895871i),
complex128(-0.284407537211272 + 0.958703474895871i),
complex128(0.879012226428633 - 0.476799230063322i),
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