Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(419,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.3 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.419 |
Dual form | 462.2.g.a.419.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.61803 | − | 0.618034i | −0.934172 | − | 0.356822i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −3.23607 | −1.44721 | −0.723607 | − | 0.690212i | \(-0.757517\pi\) | ||||
−0.723607 | + | 0.690212i | \(0.757517\pi\) | |||||||
\(6\) | 0.618034 | − | 1.61803i | 0.252311 | − | 0.660560i | ||||
\(7\) | 0.381966 | − | 2.61803i | 0.144370 | − | 0.989524i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | − | 3.23607i | − | 1.02333i | ||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 1.61803 | + | 0.618034i | 0.467086 | + | 0.178411i | ||||
\(13\) | 6.00000i | 1.66410i | 0.554700 | + | 0.832050i | \(0.312833\pi\) | ||||
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 2.61803 | + | 0.381966i | 0.699699 | + | 0.102085i | ||||
\(15\) | 5.23607 | + | 2.00000i | 1.35195 | + | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.23607 | 1.75500 | 0.877502 | − | 0.479573i | \(-0.159208\pi\) | ||||
0.877502 | + | 0.479573i | \(0.159208\pi\) | |||||||
\(18\) | −2.00000 | + | 2.23607i | −0.471405 | + | 0.527046i | ||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 3.23607 | 0.723607 | ||||||||
\(21\) | −2.23607 | + | 4.00000i | −0.487950 | + | 0.872872i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 1.23607i | 0.257738i | 0.991662 | + | 0.128869i | \(0.0411347\pi\) | ||||
−0.991662 | + | 0.128869i | \(0.958865\pi\) | |||||||
\(24\) | −0.618034 | + | 1.61803i | −0.126156 | + | 0.330280i | ||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | −6.00000 | −1.17670 | ||||||||
\(27\) | −2.38197 | − | 4.61803i | −0.458410 | − | 0.888741i | ||||
\(28\) | −0.381966 | + | 2.61803i | −0.0721848 | + | 0.494762i | ||||
\(29\) | 0.472136i | 0.0876734i | 0.999039 | + | 0.0438367i | \(0.0139581\pi\) | ||||
−0.999039 | + | 0.0438367i | \(0.986042\pi\) | |||||||
\(30\) | −2.00000 | + | 5.23607i | −0.365148 | + | 0.955971i | ||||
\(31\) | 0.763932i | 0.137206i | 0.997644 | + | 0.0686031i | \(0.0218542\pi\) | ||||
−0.997644 | + | 0.0686031i | \(0.978146\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −0.618034 | + | 1.61803i | −0.107586 | + | 0.281664i | ||||
\(34\) | 7.23607i | 1.24098i | ||||||||
\(35\) | −1.23607 | + | 8.47214i | −0.208934 | + | 1.43205i | ||||
\(36\) | −2.23607 | − | 2.00000i | −0.372678 | − | 0.333333i | ||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 3.70820 | − | 9.70820i | 0.593788 | − | 1.55456i | ||||
\(40\) | 3.23607i | 0.511667i | ||||||||
\(41\) | 12.1803 | 1.90225 | 0.951125 | − | 0.308807i | \(-0.0999297\pi\) | ||||
0.951125 | + | 0.308807i | \(0.0999297\pi\) | |||||||
\(42\) | −4.00000 | − | 2.23607i | −0.617213 | − | 0.345033i | ||||
\(43\) | 10.9443 | 1.66899 | 0.834493 | − | 0.551019i | \(-0.185761\pi\) | ||||
0.834493 | + | 0.551019i | \(0.185761\pi\) | |||||||
\(44\) | 1.00000i | 0.150756i | ||||||||
\(45\) | −7.23607 | − | 6.47214i | −1.07869 | − | 0.964809i | ||||
\(46\) | −1.23607 | −0.182248 | ||||||||
\(47\) | 1.52786 | 0.222862 | 0.111431 | − | 0.993772i | \(-0.464457\pi\) | ||||
0.111431 | + | 0.993772i | \(0.464457\pi\) | |||||||
\(48\) | −1.61803 | − | 0.618034i | −0.233543 | − | 0.0892055i | ||||
\(49\) | −6.70820 | − | 2.00000i | −0.958315 | − | 0.285714i | ||||
\(50\) | 5.47214i | 0.773877i | ||||||||
\(51\) | −11.7082 | − | 4.47214i | −1.63948 | − | 0.626224i | ||||
\(52\) | − | 6.00000i | − | 0.832050i | ||||||
\(53\) | 7.70820i | 1.05880i | 0.848371 | + | 0.529402i | \(0.177584\pi\) | ||||
−0.848371 | + | 0.529402i | \(0.822416\pi\) | |||||||
\(54\) | 4.61803 | − | 2.38197i | 0.628435 | − | 0.324145i | ||||
\(55\) | 3.23607i | 0.436351i | ||||||||
\(56\) | −2.61803 | − | 0.381966i | −0.349850 | − | 0.0510424i | ||||
\(57\) | 1.23607 | − | 3.23607i | 0.163721 | − | 0.428628i | ||||
\(58\) | −0.472136 | −0.0619945 | ||||||||
\(59\) | 3.23607 | 0.421300 | 0.210650 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210650 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(60\) | −5.23607 | − | 2.00000i | −0.675973 | − | 0.258199i | ||||
\(61\) | − | 3.52786i | − | 0.451697i | −0.974162 | − | 0.225848i | \(-0.927485\pi\) | ||
0.974162 | − | 0.225848i | \(-0.0725154\pi\) | |||||||
\(62\) | −0.763932 | −0.0970195 | ||||||||
\(63\) | 6.09017 | − | 5.09017i | 0.767289 | − | 0.641301i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 19.4164i | − | 2.40831i | ||||||
\(66\) | −1.61803 | − | 0.618034i | −0.199166 | − | 0.0760747i | ||||
\(67\) | 1.52786 | 0.186658 | 0.0933292 | − | 0.995635i | \(-0.470249\pi\) | ||||
0.0933292 | + | 0.995635i | \(0.470249\pi\) | |||||||
\(68\) | −7.23607 | −0.877502 | ||||||||
\(69\) | 0.763932 | − | 2.00000i | 0.0919666 | − | 0.240772i | ||||
\(70\) | −8.47214 | − | 1.23607i | −1.01261 | − | 0.147738i | ||||
\(71\) | − | 6.18034i | − | 0.733471i | −0.930325 | − | 0.366736i | \(-0.880475\pi\) | ||
0.930325 | − | 0.366736i | \(-0.119525\pi\) | |||||||
\(72\) | 2.00000 | − | 2.23607i | 0.235702 | − | 0.263523i | ||||
\(73\) | 14.1803i | 1.65968i | 0.557999 | + | 0.829842i | \(0.311569\pi\) | ||||
−0.557999 | + | 0.829842i | \(0.688431\pi\) | |||||||
\(74\) | − | 4.47214i | − | 0.519875i | ||||||
\(75\) | −8.85410 | − | 3.38197i | −1.02238 | − | 0.390516i | ||||
\(76\) | − | 2.00000i | − | 0.229416i | ||||||
\(77\) | −2.61803 | − | 0.381966i | −0.298353 | − | 0.0435291i | ||||
\(78\) | 9.70820 | + | 3.70820i | 1.09924 | + | 0.419871i | ||||
\(79\) | 7.23607 | 0.814121 | 0.407061 | − | 0.913401i | \(-0.366554\pi\) | ||||
0.407061 | + | 0.913401i | \(0.366554\pi\) | |||||||
\(80\) | −3.23607 | −0.361803 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 12.1803i | 1.34509i | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 2.23607 | − | 4.00000i | 0.243975 | − | 0.436436i | ||||
\(85\) | −23.4164 | −2.53987 | ||||||||
\(86\) | 10.9443i | 1.18015i | ||||||||
\(87\) | 0.291796 | − | 0.763932i | 0.0312838 | − | 0.0819021i | ||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −12.9443 | −1.37209 | −0.686045 | − | 0.727559i | \(-0.740655\pi\) | ||||
−0.686045 | + | 0.727559i | \(0.740655\pi\) | |||||||
\(90\) | 6.47214 | − | 7.23607i | 0.682223 | − | 0.762749i | ||||
\(91\) | 15.7082 | + | 2.29180i | 1.64667 | + | 0.240246i | ||||
\(92\) | − | 1.23607i | − | 0.128869i | ||||||
\(93\) | 0.472136 | − | 1.23607i | 0.0489582 | − | 0.128174i | ||||
\(94\) | 1.52786i | 0.157587i | ||||||||
\(95\) | − | 6.47214i | − | 0.664027i | ||||||
\(96\) | 0.618034 | − | 1.61803i | 0.0630778 | − | 0.165140i | ||||
\(97\) | − | 2.47214i | − | 0.251007i | −0.992093 | − | 0.125504i | \(-0.959945\pi\) | ||
0.992093 | − | 0.125504i | \(-0.0400547\pi\) | |||||||
\(98\) | 2.00000 | − | 6.70820i | 0.202031 | − | 0.677631i | ||||
\(99\) | 2.00000 | − | 2.23607i | 0.201008 | − | 0.224733i | ||||
\(100\) | −5.47214 | −0.547214 | ||||||||
\(101\) | −6.76393 | −0.673036 | −0.336518 | − | 0.941677i | \(-0.609249\pi\) | ||||
−0.336518 | + | 0.941677i | \(0.609249\pi\) | |||||||
\(102\) | 4.47214 | − | 11.7082i | 0.442807 | − | 1.15928i | ||||
\(103\) | 9.70820i | 0.956578i | 0.878203 | + | 0.478289i | \(0.158743\pi\) | ||||
−0.878203 | + | 0.478289i | \(0.841257\pi\) | |||||||
\(104\) | 6.00000 | 0.588348 | ||||||||
\(105\) | 7.23607 | − | 12.9443i | 0.706168 | − | 1.26323i | ||||
\(106\) | −7.70820 | −0.748687 | ||||||||
\(107\) | 8.94427i | 0.864675i | 0.901712 | + | 0.432338i | \(0.142311\pi\) | ||||
−0.901712 | + | 0.432338i | \(0.857689\pi\) | |||||||
\(108\) | 2.38197 | + | 4.61803i | 0.229205 | + | 0.444371i | ||||
\(109\) | 8.76393 | 0.839432 | 0.419716 | − | 0.907655i | \(-0.362130\pi\) | ||||
0.419716 | + | 0.907655i | \(0.362130\pi\) | |||||||
\(110\) | −3.23607 | −0.308547 | ||||||||
\(111\) | 7.23607 | + | 2.76393i | 0.686817 | + | 0.262341i | ||||
\(112\) | 0.381966 | − | 2.61803i | 0.0360924 | − | 0.247381i | ||||
\(113\) | − | 8.00000i | − | 0.752577i | −0.926503 | − | 0.376288i | \(-0.877200\pi\) | ||
0.926503 | − | 0.376288i | \(-0.122800\pi\) | |||||||
\(114\) | 3.23607 | + | 1.23607i | 0.303086 | + | 0.115768i | ||||
\(115\) | − | 4.00000i | − | 0.373002i | ||||||
\(116\) | − | 0.472136i | − | 0.0438367i | ||||||
\(117\) | −12.0000 | + | 13.4164i | −1.10940 | + | 1.24035i | ||||
\(118\) | 3.23607i | 0.297904i | ||||||||
\(119\) | 2.76393 | − | 18.9443i | 0.253369 | − | 1.73662i | ||||
\(120\) | 2.00000 | − | 5.23607i | 0.182574 | − | 0.477985i | ||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 3.52786 | 0.319398 | ||||||||
\(123\) | −19.7082 | − | 7.52786i | −1.77703 | − | 0.678765i | ||||
\(124\) | − | 0.763932i | − | 0.0686031i | ||||||
\(125\) | −1.52786 | −0.136656 | ||||||||
\(126\) | 5.09017 | + | 6.09017i | 0.453468 | + | 0.542555i | ||||
\(127\) | −17.7082 | −1.57135 | −0.785675 | − | 0.618640i | \(-0.787684\pi\) | ||||
−0.785675 | + | 0.618640i | \(0.787684\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −17.7082 | − | 6.76393i | −1.55912 | − | 0.595531i | ||||
\(130\) | 19.4164 | 1.70293 | ||||||||
\(131\) | −9.41641 | −0.822715 | −0.411358 | − | 0.911474i | \(-0.634945\pi\) | ||||
−0.411358 | + | 0.911474i | \(0.634945\pi\) | |||||||
\(132\) | 0.618034 | − | 1.61803i | 0.0537930 | − | 0.140832i | ||||
\(133\) | 5.23607 | + | 0.763932i | 0.454025 | + | 0.0662413i | ||||
\(134\) | 1.52786i | 0.131987i | ||||||||
\(135\) | 7.70820 | + | 14.9443i | 0.663417 | + | 1.28620i | ||||
\(136\) | − | 7.23607i | − | 0.620488i | ||||||
\(137\) | 6.47214i | 0.552952i | 0.961021 | + | 0.276476i | \(0.0891666\pi\) | ||||
−0.961021 | + | 0.276476i | \(0.910833\pi\) | |||||||
\(138\) | 2.00000 | + | 0.763932i | 0.170251 | + | 0.0650302i | ||||
\(139\) | − | 10.0000i | − | 0.848189i | −0.905618 | − | 0.424094i | \(-0.860592\pi\) | ||
0.905618 | − | 0.424094i | \(-0.139408\pi\) | |||||||
\(140\) | 1.23607 | − | 8.47214i | 0.104467 | − | 0.716026i | ||||
\(141\) | −2.47214 | − | 0.944272i | −0.208191 | − | 0.0795220i | ||||
\(142\) | 6.18034 | 0.518643 | ||||||||
\(143\) | 6.00000 | 0.501745 | ||||||||
\(144\) | 2.23607 | + | 2.00000i | 0.186339 | + | 0.166667i | ||||
\(145\) | − | 1.52786i | − | 0.126882i | ||||||
\(146\) | −14.1803 | −1.17357 | ||||||||
\(147\) | 9.61803 | + | 7.38197i | 0.793282 | + | 0.608854i | ||||
\(148\) | 4.47214 | 0.367607 | ||||||||
\(149\) | − | 2.00000i | − | 0.163846i | −0.996639 | − | 0.0819232i | \(-0.973894\pi\) | ||
0.996639 | − | 0.0819232i | \(-0.0261062\pi\) | |||||||
\(150\) | 3.38197 | − | 8.85410i | 0.276136 | − | 0.722934i | ||||
\(151\) | 12.1803 | 0.991222 | 0.495611 | − | 0.868545i | \(-0.334944\pi\) | ||||
0.495611 | + | 0.868545i | \(0.334944\pi\) | |||||||
\(152\) | 2.00000 | 0.162221 | ||||||||
\(153\) | 16.1803 | + | 14.4721i | 1.30810 | + | 1.17000i | ||||
\(154\) | 0.381966 | − | 2.61803i | 0.0307797 | − | 0.210967i | ||||
\(155\) | − | 2.47214i | − | 0.198567i | ||||||
\(156\) | −3.70820 | + | 9.70820i | −0.296894 | + | 0.777278i | ||||
\(157\) | 13.4164i | 1.07075i | 0.844616 | + | 0.535373i | \(0.179829\pi\) | ||||
−0.844616 | + | 0.535373i | \(0.820171\pi\) | |||||||
\(158\) | 7.23607i | 0.575671i | ||||||||
\(159\) | 4.76393 | − | 12.4721i | 0.377804 | − | 0.989105i | ||||
\(160\) | − | 3.23607i | − | 0.255834i | ||||||
\(161\) | 3.23607 | + | 0.472136i | 0.255038 | + | 0.0372095i | ||||
\(162\) | −8.94427 | + | 1.00000i | −0.702728 | + | 0.0785674i | ||||
\(163\) | 18.4721 | 1.44685 | 0.723425 | − | 0.690403i | \(-0.242567\pi\) | ||||
0.723425 | + | 0.690403i | \(0.242567\pi\) | |||||||
\(164\) | −12.1803 | −0.951125 | ||||||||
\(165\) | 2.00000 | − | 5.23607i | 0.155700 | − | 0.407627i | ||||
\(166\) | 6.00000i | 0.465690i | ||||||||
\(167\) | 13.8885 | 1.07473 | 0.537364 | − | 0.843350i | \(-0.319420\pi\) | ||||
0.537364 | + | 0.843350i | \(0.319420\pi\) | |||||||
\(168\) | 4.00000 | + | 2.23607i | 0.308607 | + | 0.172516i | ||||
\(169\) | −23.0000 | −1.76923 | ||||||||
\(170\) | − | 23.4164i | − | 1.79596i | ||||||
\(171\) | −4.00000 | + | 4.47214i | −0.305888 | + | 0.341993i | ||||
\(172\) | −10.9443 | −0.834493 | ||||||||
\(173\) | 7.70820 | 0.586044 | 0.293022 | − | 0.956106i | \(-0.405339\pi\) | ||||
0.293022 | + | 0.956106i | \(0.405339\pi\) | |||||||
\(174\) | 0.763932 | + | 0.291796i | 0.0579135 | + | 0.0221210i | ||||
\(175\) | 2.09017 | − | 14.3262i | 0.158002 | − | 1.08296i | ||||
\(176\) | − | 1.00000i | − | 0.0753778i | ||||||
\(177\) | −5.23607 | − | 2.00000i | −0.393567 | − | 0.150329i | ||||
\(178\) | − | 12.9443i | − | 0.970214i | ||||||
\(179\) | − | 12.9443i | − | 0.967500i | −0.875206 | − | 0.483750i | \(-0.839274\pi\) | ||
0.875206 | − | 0.483750i | \(-0.160726\pi\) | |||||||
\(180\) | 7.23607 | + | 6.47214i | 0.539345 | + | 0.482405i | ||||
\(181\) | 3.52786i | 0.262224i | 0.991368 | + | 0.131112i | \(0.0418548\pi\) | ||||
−0.991368 | + | 0.131112i | \(0.958145\pi\) | |||||||
\(182\) | −2.29180 | + | 15.7082i | −0.169879 | + | 1.16437i | ||||
\(183\) | −2.18034 | + | 5.70820i | −0.161175 | + | 0.421963i | ||||
\(184\) | 1.23607 | 0.0911241 | ||||||||
\(185\) | 14.4721 | 1.06401 | ||||||||
\(186\) | 1.23607 | + | 0.472136i | 0.0906329 | + | 0.0346187i | ||||
\(187\) | − | 7.23607i | − | 0.529154i | ||||||
\(188\) | −1.52786 | −0.111431 | ||||||||
\(189\) | −13.0000 | + | 4.47214i | −0.945611 | + | 0.325300i | ||||
\(190\) | 6.47214 | 0.469538 | ||||||||
\(191\) | 11.7082i | 0.847176i | 0.905855 | + | 0.423588i | \(0.139230\pi\) | ||||
−0.905855 | + | 0.423588i | \(0.860770\pi\) | |||||||
\(192\) | 1.61803 | + | 0.618034i | 0.116772 | + | 0.0446028i | ||||
\(193\) | −2.94427 | −0.211933 | −0.105967 | − | 0.994370i | \(-0.533794\pi\) | ||||
−0.105967 | + | 0.994370i | \(0.533794\pi\) | |||||||
\(194\) | 2.47214 | 0.177489 | ||||||||
\(195\) | −12.0000 | + | 31.4164i | −0.859338 | + | 2.24978i | ||||
\(196\) | 6.70820 | + | 2.00000i | 0.479157 | + | 0.142857i | ||||
\(197\) | 14.9443i | 1.06474i | 0.846513 | + | 0.532368i | \(0.178698\pi\) | ||||
−0.846513 | + | 0.532368i | \(0.821302\pi\) | |||||||
\(198\) | 2.23607 | + | 2.00000i | 0.158910 | + | 0.142134i | ||||
\(199\) | 20.1803i | 1.43055i | 0.698845 | + | 0.715273i | \(0.253698\pi\) | ||||
−0.698845 | + | 0.715273i | \(0.746302\pi\) | |||||||
\(200\) | − | 5.47214i | − | 0.386938i | ||||||
\(201\) | −2.47214 | − | 0.944272i | −0.174371 | − | 0.0666038i | ||||
\(202\) | − | 6.76393i | − | 0.475909i | ||||||
\(203\) | 1.23607 | + | 0.180340i | 0.0867550 | + | 0.0126574i | ||||
\(204\) | 11.7082 | + | 4.47214i | 0.819738 | + | 0.313112i | ||||
\(205\) | −39.4164 | −2.75296 | ||||||||
\(206\) | −9.70820 | −0.676403 | ||||||||
\(207\) | −2.47214 | + | 2.76393i | −0.171825 | + | 0.192107i | ||||
\(208\) | 6.00000i | 0.416025i | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 12.9443 | + | 7.23607i | 0.893240 | + | 0.499336i | ||||
\(211\) | 9.41641 | 0.648252 | 0.324126 | − | 0.946014i | \(-0.394930\pi\) | ||||
0.324126 | + | 0.946014i | \(0.394930\pi\) | |||||||
\(212\) | − | 7.70820i | − | 0.529402i | ||||||
\(213\) | −3.81966 | + | 10.0000i | −0.261719 | + | 0.685189i | ||||
\(214\) | −8.94427 | −0.611418 | ||||||||
\(215\) | −35.4164 | −2.41538 | ||||||||
\(216\) | −4.61803 | + | 2.38197i | −0.314217 | + | 0.162072i | ||||
\(217\) | 2.00000 | + | 0.291796i | 0.135769 | + | 0.0198084i | ||||
\(218\) | 8.76393i | 0.593568i | ||||||||
\(219\) | 8.76393 | − | 22.9443i | 0.592212 | − | 1.55043i | ||||
\(220\) | − | 3.23607i | − | 0.218176i | ||||||
\(221\) | 43.4164i | 2.92050i | ||||||||
\(222\) | −2.76393 | + | 7.23607i | −0.185503 | + | 0.485653i | ||||
\(223\) | − | 23.5967i | − | 1.58016i | −0.613007 | − | 0.790078i | \(-0.710040\pi\) | ||
0.613007 | − | 0.790078i | \(-0.289960\pi\) | |||||||
\(224\) | 2.61803 | + | 0.381966i | 0.174925 | + | 0.0255212i | ||||
\(225\) | 12.2361 | + | 10.9443i | 0.815738 | + | 0.729618i | ||||
\(226\) | 8.00000 | 0.532152 | ||||||||
\(227\) | −22.0000 | −1.46019 | −0.730096 | − | 0.683345i | \(-0.760525\pi\) | ||||
−0.730096 | + | 0.683345i | \(0.760525\pi\) | |||||||
\(228\) | −1.23607 | + | 3.23607i | −0.0818606 | + | 0.214314i | ||||
\(229\) | − | 2.00000i | − | 0.132164i | −0.997814 | − | 0.0660819i | \(-0.978950\pi\) | ||
0.997814 | − | 0.0660819i | \(-0.0210498\pi\) | |||||||
\(230\) | 4.00000 | 0.263752 | ||||||||
\(231\) | 4.00000 | + | 2.23607i | 0.263181 | + | 0.147122i | ||||
\(232\) | 0.472136 | 0.0309972 | ||||||||
\(233\) | 25.4164i | 1.66508i | 0.553962 | + | 0.832542i | \(0.313115\pi\) | ||||
−0.553962 | + | 0.832542i | \(0.686885\pi\) | |||||||
\(234\) | −13.4164 | − | 12.0000i | −0.877058 | − | 0.784465i | ||||
\(235\) | −4.94427 | −0.322529 | ||||||||
\(236\) | −3.23607 | −0.210650 | ||||||||
\(237\) | −11.7082 | − | 4.47214i | −0.760530 | − | 0.290496i | ||||
\(238\) | 18.9443 | + | 2.76393i | 1.22797 | + | 0.179159i | ||||
\(239\) | 21.8885i | 1.41585i | 0.706287 | + | 0.707926i | \(0.250369\pi\) | ||||
−0.706287 | + | 0.707926i | \(0.749631\pi\) | |||||||
\(240\) | 5.23607 | + | 2.00000i | 0.337987 | + | 0.129099i | ||||
\(241\) | − | 18.1803i | − | 1.17110i | −0.810637 | − | 0.585549i | \(-0.800879\pi\) | ||
0.810637 | − | 0.585549i | \(-0.199121\pi\) | |||||||
\(242\) | − | 1.00000i | − | 0.0642824i | ||||||
\(243\) | 3.90983 | − | 15.0902i | 0.250816 | − | 0.968035i | ||||
\(244\) | 3.52786i | 0.225848i | ||||||||
\(245\) | 21.7082 | + | 6.47214i | 1.38689 | + | 0.413490i | ||||
\(246\) | 7.52786 | − | 19.7082i | 0.479959 | − | 1.25655i | ||||
\(247\) | −12.0000 | −0.763542 | ||||||||
\(248\) | 0.763932 | 0.0485097 | ||||||||
\(249\) | −9.70820 | − | 3.70820i | −0.615232 | − | 0.234998i | ||||
\(250\) | − | 1.52786i | − | 0.0966306i | ||||||
\(251\) | −1.70820 | −0.107821 | −0.0539104 | − | 0.998546i | \(-0.517169\pi\) | ||||
−0.0539104 | + | 0.998546i | \(0.517169\pi\) | |||||||
\(252\) | −6.09017 | + | 5.09017i | −0.383645 | + | 0.320651i | ||||
\(253\) | 1.23607 | 0.0777109 | ||||||||
\(254\) | − | 17.7082i | − | 1.11111i | ||||||
\(255\) | 37.8885 | + | 14.4721i | 2.37267 | + | 0.906280i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.944272 | 0.0589021 | 0.0294510 | − | 0.999566i | \(-0.490624\pi\) | ||||
0.0294510 | + | 0.999566i | \(0.490624\pi\) | |||||||
\(258\) | 6.76393 | − | 17.7082i | 0.421104 | − | 1.10246i | ||||
\(259\) | −1.70820 | + | 11.7082i | −0.106143 | + | 0.727512i | ||||
\(260\) | 19.4164i | 1.20415i | ||||||||
\(261\) | −0.944272 | + | 1.05573i | −0.0584490 | + | 0.0653479i | ||||
\(262\) | − | 9.41641i | − | 0.581748i | ||||||
\(263\) | 21.5279i | 1.32746i | 0.747970 | + | 0.663732i | \(0.231029\pi\) | ||||
−0.747970 | + | 0.663732i | \(0.768971\pi\) | |||||||
\(264\) | 1.61803 | + | 0.618034i | 0.0995831 | + | 0.0380374i | ||||
\(265\) | − | 24.9443i | − | 1.53231i | ||||||
\(266\) | −0.763932 | + | 5.23607i | −0.0468397 | + | 0.321044i | ||||
\(267\) | 20.9443 | + | 8.00000i | 1.28177 | + | 0.489592i | ||||
\(268\) | −1.52786 | −0.0933292 | ||||||||
\(269\) | 23.5967 | 1.43872 | 0.719360 | − | 0.694638i | \(-0.244435\pi\) | ||||
0.719360 | + | 0.694638i | \(0.244435\pi\) | |||||||
\(270\) | −14.9443 | + | 7.70820i | −0.909479 | + | 0.469106i | ||||
\(271\) | − | 23.7082i | − | 1.44017i | −0.693885 | − | 0.720085i | \(-0.744103\pi\) | ||
0.693885 | − | 0.720085i | \(-0.255897\pi\) | |||||||
\(272\) | 7.23607 | 0.438751 | ||||||||
\(273\) | −24.0000 | − | 13.4164i | −1.45255 | − | 0.811998i | ||||
\(274\) | −6.47214 | −0.390996 | ||||||||
\(275\) | − | 5.47214i | − | 0.329982i | ||||||
\(276\) | −0.763932 | + | 2.00000i | −0.0459833 | + | 0.120386i | ||||
\(277\) | −24.1803 | −1.45286 | −0.726428 | − | 0.687243i | \(-0.758821\pi\) | ||||
−0.726428 | + | 0.687243i | \(0.758821\pi\) | |||||||
\(278\) | 10.0000 | 0.599760 | ||||||||
\(279\) | −1.52786 | + | 1.70820i | −0.0914708 | + | 0.102267i | ||||
\(280\) | 8.47214 | + | 1.23607i | 0.506307 | + | 0.0738692i | ||||
\(281\) | − | 25.4164i | − | 1.51622i | −0.652129 | − | 0.758108i | \(-0.726124\pi\) | ||
0.652129 | − | 0.758108i | \(-0.273876\pi\) | |||||||
\(282\) | 0.944272 | − | 2.47214i | 0.0562306 | − | 0.147214i | ||||
\(283\) | 14.9443i | 0.888345i | 0.895941 | + | 0.444172i | \(0.146502\pi\) | ||||
−0.895941 | + | 0.444172i | \(0.853498\pi\) | |||||||
\(284\) | 6.18034i | 0.366736i | ||||||||
\(285\) | −4.00000 | + | 10.4721i | −0.236940 | + | 0.620316i | ||||
\(286\) | 6.00000i | 0.354787i | ||||||||
\(287\) | 4.65248 | − | 31.8885i | 0.274627 | − | 1.88232i | ||||
\(288\) | −2.00000 | + | 2.23607i | −0.117851 | + | 0.131762i | ||||
\(289\) | 35.3607 | 2.08004 | ||||||||
\(290\) | 1.52786 | 0.0897193 | ||||||||
\(291\) | −1.52786 | + | 4.00000i | −0.0895650 | + | 0.234484i | ||||
\(292\) | − | 14.1803i | − | 0.829842i | ||||||
\(293\) | 18.1803 | 1.06211 | 0.531053 | − | 0.847338i | \(-0.321796\pi\) | ||||
0.531053 | + | 0.847338i | \(0.321796\pi\) | |||||||
\(294\) | −7.38197 | + | 9.61803i | −0.430525 | + | 0.560935i | ||||
\(295\) | −10.4721 | −0.609711 | ||||||||
\(296\) | 4.47214i | 0.259938i | ||||||||
\(297\) | −4.61803 | + | 2.38197i | −0.267966 | + | 0.138216i | ||||
\(298\) | 2.00000 | 0.115857 | ||||||||
\(299\) | −7.41641 | −0.428902 | ||||||||
\(300\) | 8.85410 | + | 3.38197i | 0.511192 | + | 0.195258i | ||||
\(301\) | 4.18034 | − | 28.6525i | 0.240951 | − | 1.65150i | ||||
\(302\) | 12.1803i | 0.700900i | ||||||||
\(303\) | 10.9443 | + | 4.18034i | 0.628732 | + | 0.240154i | ||||
\(304\) | 2.00000i | 0.114708i | ||||||||
\(305\) | 11.4164i | 0.653702i | ||||||||
\(306\) | −14.4721 | + | 16.1803i | −0.827317 | + | 0.924968i | ||||
\(307\) | 3.52786i | 0.201346i | 0.994920 | + | 0.100673i | \(0.0320996\pi\) | ||||
−0.994920 | + | 0.100673i | \(0.967900\pi\) | |||||||
\(308\) | 2.61803 | + | 0.381966i | 0.149176 | + | 0.0217645i | ||||
\(309\) | 6.00000 | − | 15.7082i | 0.341328 | − | 0.893609i | ||||
\(310\) | 2.47214 | 0.140408 | ||||||||
\(311\) | −10.4721 | −0.593820 | −0.296910 | − | 0.954905i | \(-0.595956\pi\) | ||||
−0.296910 | + | 0.954905i | \(0.595956\pi\) | |||||||
\(312\) | −9.70820 | − | 3.70820i | −0.549619 | − | 0.209936i | ||||
\(313\) | 8.00000i | 0.452187i | 0.974106 | + | 0.226093i | \(0.0725954\pi\) | ||||
−0.974106 | + | 0.226093i | \(0.927405\pi\) | |||||||
\(314\) | −13.4164 | −0.757132 | ||||||||
\(315\) | −19.7082 | + | 16.4721i | −1.11043 | + | 0.928100i | ||||
\(316\) | −7.23607 | −0.407061 | ||||||||
\(317\) | − | 12.2918i | − | 0.690376i | −0.938534 | − | 0.345188i | \(-0.887815\pi\) | ||
0.938534 | − | 0.345188i | \(-0.112185\pi\) | |||||||
\(318\) | 12.4721 | + | 4.76393i | 0.699403 | + | 0.267148i | ||||
\(319\) | 0.472136 | 0.0264345 | ||||||||
\(320\) | 3.23607 | 0.180902 | ||||||||
\(321\) | 5.52786 | − | 14.4721i | 0.308535 | − | 0.807756i | ||||
\(322\) | −0.472136 | + | 3.23607i | −0.0263111 | + | 0.180339i | ||||
\(323\) | 14.4721i | 0.805251i | ||||||||
\(324\) | −1.00000 | − | 8.94427i | −0.0555556 | − | 0.496904i | ||||
\(325\) | 32.8328i | 1.82124i | ||||||||
\(326\) | 18.4721i | 1.02308i | ||||||||
\(327\) | −14.1803 | − | 5.41641i | −0.784175 | − | 0.299528i | ||||
\(328\) | − | 12.1803i | − | 0.672547i | ||||||
\(329\) | 0.583592 | − | 4.00000i | 0.0321745 | − | 0.220527i | ||||
\(330\) | 5.23607 | + | 2.00000i | 0.288236 | + | 0.110096i | ||||
\(331\) | 8.94427 | 0.491622 | 0.245811 | − | 0.969318i | \(-0.420946\pi\) | ||||
0.245811 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | −10.0000 | − | 8.94427i | −0.547997 | − | 0.490143i | ||||
\(334\) | 13.8885i | 0.759947i | ||||||||
\(335\) | −4.94427 | −0.270134 | ||||||||
\(336\) | −2.23607 | + | 4.00000i | −0.121988 | + | 0.218218i | ||||
\(337\) | 13.4164 | 0.730838 | 0.365419 | − | 0.930843i | \(-0.380926\pi\) | ||||
0.365419 | + | 0.930843i | \(0.380926\pi\) | |||||||
\(338\) | − | 23.0000i | − | 1.25104i | ||||||
\(339\) | −4.94427 | + | 12.9443i | −0.268536 | + | 0.703036i | ||||
\(340\) | 23.4164 | 1.26993 | ||||||||
\(341\) | 0.763932 | 0.0413692 | ||||||||
\(342\) | −4.47214 | − | 4.00000i | −0.241825 | − | 0.216295i | ||||
\(343\) | −7.79837 | + | 16.7984i | −0.421073 | + | 0.907027i | ||||
\(344\) | − | 10.9443i | − | 0.590076i | ||||||
\(345\) | −2.47214 | + | 6.47214i | −0.133095 | + | 0.348448i | ||||
\(346\) | 7.70820i | 0.414396i | ||||||||
\(347\) | − | 16.9443i | − | 0.909616i | −0.890589 | − | 0.454808i | \(-0.849708\pi\) | ||
0.890589 | − | 0.454808i | \(-0.150292\pi\) | |||||||
\(348\) | −0.291796 | + | 0.763932i | −0.0156419 | + | 0.0409511i | ||||
\(349\) | − | 22.0000i | − | 1.17763i | −0.808267 | − | 0.588817i | \(-0.799594\pi\) | ||
0.808267 | − | 0.588817i | \(-0.200406\pi\) | |||||||
\(350\) | 14.3262 | + | 2.09017i | 0.765770 | + | 0.111724i | ||||
\(351\) | 27.7082 | − | 14.2918i | 1.47895 | − | 0.762840i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | 0.944272 | 0.0502585 | 0.0251293 | − | 0.999684i | \(-0.492000\pi\) | ||||
0.0251293 | + | 0.999684i | \(0.492000\pi\) | |||||||
\(354\) | 2.00000 | − | 5.23607i | 0.106299 | − | 0.278294i | ||||
\(355\) | 20.0000i | 1.06149i | ||||||||
\(356\) | 12.9443 | 0.686045 | ||||||||
\(357\) | −16.1803 | + | 28.9443i | −0.856354 | + | 1.53189i | ||||
\(358\) | 12.9443 | 0.684126 | ||||||||
\(359\) | − | 18.8328i | − | 0.993958i | −0.867763 | − | 0.496979i | \(-0.834443\pi\) | ||
0.867763 | − | 0.496979i | \(-0.165557\pi\) | |||||||
\(360\) | −6.47214 | + | 7.23607i | −0.341112 | + | 0.381374i | ||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | −3.52786 | −0.185420 | ||||||||
\(363\) | 1.61803 | + | 0.618034i | 0.0849248 | + | 0.0324384i | ||||
\(364\) | −15.7082 | − | 2.29180i | −0.823334 | − | 0.120123i | ||||
\(365\) | − | 45.8885i | − | 2.40192i | ||||||
\(366\) | −5.70820 | − | 2.18034i | −0.298373 | − | 0.113968i | ||||
\(367\) | − | 26.6525i | − | 1.39125i | −0.718406 | − | 0.695624i | \(-0.755128\pi\) | ||
0.718406 | − | 0.695624i | \(-0.244872\pi\) | |||||||
\(368\) | 1.23607i | 0.0644345i | ||||||||
\(369\) | 27.2361 | + | 24.3607i | 1.41785 | + | 1.26817i | ||||
\(370\) | 14.4721i | 0.752371i | ||||||||
\(371\) | 20.1803 | + | 2.94427i | 1.04771 | + | 0.152859i | ||||
\(372\) | −0.472136 | + | 1.23607i | −0.0244791 | + | 0.0640871i | ||||
\(373\) | −7.81966 | −0.404887 | −0.202443 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202443 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(374\) | 7.23607 | 0.374168 | ||||||||
\(375\) | 2.47214 | + | 0.944272i | 0.127661 | + | 0.0487620i | ||||
\(376\) | − | 1.52786i | − | 0.0787936i | ||||||
\(377\) | −2.83282 | −0.145897 | ||||||||
\(378\) | −4.47214 | − | 13.0000i | −0.230022 | − | 0.668648i | ||||
\(379\) | −12.3607 | −0.634925 | −0.317463 | − | 0.948271i | \(-0.602831\pi\) | ||||
−0.317463 | + | 0.948271i | \(0.602831\pi\) | |||||||
\(380\) | 6.47214i | 0.332014i | ||||||||
\(381\) | 28.6525 | + | 10.9443i | 1.46791 | + | 0.560692i | ||||
\(382\) | −11.7082 | −0.599044 | ||||||||
\(383\) | 20.0000 | 1.02195 | 0.510976 | − | 0.859595i | \(-0.329284\pi\) | ||||
0.510976 | + | 0.859595i | \(0.329284\pi\) | |||||||
\(384\) | −0.618034 | + | 1.61803i | −0.0315389 | + | 0.0825700i | ||||
\(385\) | 8.47214 | + | 1.23607i | 0.431780 | + | 0.0629959i | ||||
\(386\) | − | 2.94427i | − | 0.149859i | ||||||
\(387\) | 24.4721 | + | 21.8885i | 1.24399 | + | 1.11266i | ||||
\(388\) | 2.47214i | 0.125504i | ||||||||
\(389\) | − | 17.2361i | − | 0.873903i | −0.899485 | − | 0.436952i | \(-0.856058\pi\) | ||
0.899485 | − | 0.436952i | \(-0.143942\pi\) | |||||||
\(390\) | −31.4164 | − | 12.0000i | −1.59083 | − | 0.607644i | ||||
\(391\) | 8.94427i | 0.452331i | ||||||||
\(392\) | −2.00000 | + | 6.70820i | −0.101015 | + | 0.338815i | ||||
\(393\) | 15.2361 | + | 5.81966i | 0.768558 | + | 0.293563i | ||||
\(394\) | −14.9443 | −0.752882 | ||||||||
\(395\) | −23.4164 | −1.17821 | ||||||||
\(396\) | −2.00000 | + | 2.23607i | −0.100504 | + | 0.112367i | ||||
\(397\) | − | 14.9443i | − | 0.750032i | −0.927018 | − | 0.375016i | \(-0.877637\pi\) | ||
0.927018 | − | 0.375016i | \(-0.122363\pi\) | |||||||
\(398\) | −20.1803 | −1.01155 | ||||||||
\(399\) | −8.00000 | − | 4.47214i | −0.400501 | − | 0.223887i | ||||
\(400\) | 5.47214 | 0.273607 | ||||||||
\(401\) | − | 2.47214i | − | 0.123453i | −0.998093 | − | 0.0617263i | \(-0.980339\pi\) | ||
0.998093 | − | 0.0617263i | \(-0.0196606\pi\) | |||||||
\(402\) | 0.944272 | − | 2.47214i | 0.0470960 | − | 0.123299i | ||||
\(403\) | −4.58359 | −0.228325 | ||||||||
\(404\) | 6.76393 | 0.336518 | ||||||||
\(405\) | −3.23607 | − | 28.9443i | −0.160802 | − | 1.43825i | ||||
\(406\) | −0.180340 | + | 1.23607i | −0.00895012 | + | 0.0613450i | ||||
\(407\) | 4.47214i | 0.221676i | ||||||||
\(408\) | −4.47214 | + | 11.7082i | −0.221404 | + | 0.579642i | ||||
\(409\) | − | 5.23607i | − | 0.258907i | −0.991586 | − | 0.129453i | \(-0.958678\pi\) | ||
0.991586 | − | 0.129453i | \(-0.0413223\pi\) | |||||||
\(410\) | − | 39.4164i | − | 1.94664i | ||||||
\(411\) | 4.00000 | − | 10.4721i | 0.197305 | − | 0.516552i | ||||
\(412\) | − | 9.70820i | − | 0.478289i | ||||||
\(413\) | 1.23607 | − | 8.47214i | 0.0608229 | − | 0.416887i | ||||
\(414\) | −2.76393 | − | 2.47214i | −0.135840 | − | 0.121499i | ||||
\(415\) | −19.4164 | −0.953114 | ||||||||
\(416\) | −6.00000 | −0.294174 | ||||||||
\(417\) | −6.18034 | + | 16.1803i | −0.302653 | + | 0.792355i | ||||
\(418\) | 2.00000i | 0.0978232i | ||||||||
\(419\) | −9.12461 | −0.445766 | −0.222883 | − | 0.974845i | \(-0.571547\pi\) | ||||
−0.222883 | + | 0.974845i | \(0.571547\pi\) | |||||||
\(420\) | −7.23607 | + | 12.9443i | −0.353084 | + | 0.631616i | ||||
\(421\) | 4.47214 | 0.217959 | 0.108979 | − | 0.994044i | \(-0.465242\pi\) | ||||
0.108979 | + | 0.994044i | \(0.465242\pi\) | |||||||
\(422\) | 9.41641i | 0.458384i | ||||||||
\(423\) | 3.41641 | + | 3.05573i | 0.166111 | + | 0.148575i | ||||
\(424\) | 7.70820 | 0.374343 | ||||||||
\(425\) | 39.5967 | 1.92072 | ||||||||
\(426\) | −10.0000 | − | 3.81966i | −0.484502 | − | 0.185063i | ||||
\(427\) | −9.23607 | − | 1.34752i | −0.446965 | − | 0.0652113i | ||||
\(428\) | − | 8.94427i | − | 0.432338i | ||||||
\(429\) | −9.70820 | − | 3.70820i | −0.468717 | − | 0.179034i | ||||
\(430\) | − | 35.4164i | − | 1.70793i | ||||||
\(431\) | − | 5.88854i | − | 0.283641i | −0.989892 | − | 0.141821i | \(-0.954704\pi\) | ||
0.989892 | − | 0.141821i | \(-0.0452956\pi\) | |||||||
\(432\) | −2.38197 | − | 4.61803i | −0.114602 | − | 0.222185i | ||||
\(433\) | 26.4721i | 1.27217i | 0.771619 | + | 0.636085i | \(0.219447\pi\) | ||||
−0.771619 | + | 0.636085i | \(0.780553\pi\) | |||||||
\(434\) | −0.291796 | + | 2.00000i | −0.0140067 | + | 0.0960031i | ||||
\(435\) | −0.944272 | + | 2.47214i | −0.0452744 | + | 0.118530i | ||||
\(436\) | −8.76393 | −0.419716 | ||||||||
\(437\) | −2.47214 | −0.118258 | ||||||||
\(438\) | 22.9443 | + | 8.76393i | 1.09632 | + | 0.418757i | ||||
\(439\) | − | 17.2361i | − | 0.822633i | −0.911493 | − | 0.411316i | \(-0.865069\pi\) | ||
0.911493 | − | 0.411316i | \(-0.134931\pi\) | |||||||
\(440\) | 3.23607 | 0.154273 | ||||||||
\(441\) | −11.0000 | − | 17.8885i | −0.523810 | − | 0.851835i | ||||
\(442\) | −43.4164 | −2.06511 | ||||||||
\(443\) | 29.8885i | 1.42005i | 0.704178 | + | 0.710024i | \(0.251316\pi\) | ||||
−0.704178 | + | 0.710024i | \(0.748684\pi\) | |||||||
\(444\) | −7.23607 | − | 2.76393i | −0.343409 | − | 0.131170i | ||||
\(445\) | 41.8885 | 1.98571 | ||||||||
\(446\) | 23.5967 | 1.11734 | ||||||||
\(447\) | −1.23607 | + | 3.23607i | −0.0584640 | + | 0.153061i | ||||
\(448\) | −0.381966 | + | 2.61803i | −0.0180462 | + | 0.123690i | ||||
\(449\) | − | 31.4164i | − | 1.48263i | −0.671156 | − | 0.741316i | \(-0.734202\pi\) | ||
0.671156 | − | 0.741316i | \(-0.265798\pi\) | |||||||
\(450\) | −10.9443 | + | 12.2361i | −0.515918 | + | 0.576814i | ||||
\(451\) | − | 12.1803i | − | 0.573550i | ||||||
\(452\) | 8.00000i | 0.376288i | ||||||||
\(453\) | −19.7082 | − | 7.52786i | −0.925972 | − | 0.353690i | ||||
\(454\) | − | 22.0000i | − | 1.03251i | ||||||
\(455\) | −50.8328 | − | 7.41641i | −2.38308 | − | 0.347687i | ||||
\(456\) | −3.23607 | − | 1.23607i | −0.151543 | − | 0.0578842i | ||||
\(457\) | −2.00000 | −0.0935561 | −0.0467780 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467780 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(458\) | 2.00000 | 0.0934539 | ||||||||
\(459\) | −17.2361 | − | 33.4164i | −0.804511 | − | 1.55974i | ||||
\(460\) | 4.00000i | 0.186501i | ||||||||
\(461\) | −41.2361 | −1.92056 | −0.960278 | − | 0.279047i | \(-0.909982\pi\) | ||||
−0.960278 | + | 0.279047i | \(0.909982\pi\) | |||||||
\(462\) | −2.23607 | + | 4.00000i | −0.104031 | + | 0.186097i | ||||
\(463\) | −26.4721 | −1.23026 | −0.615132 | − | 0.788424i | \(-0.710897\pi\) | ||||
−0.615132 | + | 0.788424i | \(0.710897\pi\) | |||||||
\(464\) | 0.472136i | 0.0219184i | ||||||||
\(465\) | −1.52786 | + | 4.00000i | −0.0708530 | + | 0.185496i | ||||
\(466\) | −25.4164 | −1.17739 | ||||||||
\(467\) | −22.6525 | −1.04823 | −0.524116 | − | 0.851647i | \(-0.675604\pi\) | ||||
−0.524116 | + | 0.851647i | \(0.675604\pi\) | |||||||
\(468\) | 12.0000 | − | 13.4164i | 0.554700 | − | 0.620174i | ||||
\(469\) | 0.583592 | − | 4.00000i | 0.0269478 | − | 0.184703i | ||||
\(470\) | − | 4.94427i | − | 0.228062i | ||||||
\(471\) | 8.29180 | − | 21.7082i | 0.382066 | − | 1.00026i | ||||
\(472\) | − | 3.23607i | − | 0.148952i | ||||||
\(473\) | − | 10.9443i | − | 0.503218i | ||||||
\(474\) | 4.47214 | − | 11.7082i | 0.205412 | − | 0.537776i | ||||
\(475\) | 10.9443i | 0.502158i | ||||||||
\(476\) | −2.76393 | + | 18.9443i | −0.126685 | + | 0.868309i | ||||
\(477\) | −15.4164 | + | 17.2361i | −0.705869 | + | 0.789185i | ||||
\(478\) | −21.8885 | −1.00116 | ||||||||
\(479\) | −0.944272 | −0.0431449 | −0.0215724 | − | 0.999767i | \(-0.506867\pi\) | ||||
−0.0215724 | + | 0.999767i | \(0.506867\pi\) | |||||||
\(480\) | −2.00000 | + | 5.23607i | −0.0912871 | + | 0.238993i | ||||
\(481\) | − | 26.8328i | − | 1.22347i | ||||||
\(482\) | 18.1803 | 0.828092 | ||||||||
\(483\) | −4.94427 | − | 2.76393i | −0.224972 | − | 0.125763i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 8.00000i | 0.363261i | ||||||||
\(486\) | 15.0902 | + | 3.90983i | 0.684504 | + | 0.177353i | ||||
\(487\) | 1.52786 | 0.0692341 | 0.0346171 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346171 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(488\) | −3.52786 | −0.159699 | ||||||||
\(489\) | −29.8885 | − | 11.4164i | −1.35161 | − | 0.516268i | ||||
\(490\) | −6.47214 | + | 21.7082i | −0.292381 | + | 0.980677i | ||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 19.7082 | + | 7.52786i | 0.888514 | + | 0.339382i | ||||
\(493\) | 3.41641i | 0.153867i | ||||||||
\(494\) | − | 12.0000i | − | 0.539906i | ||||||
\(495\) | −6.47214 | + | 7.23607i | −0.290901 | + | 0.325237i | ||||
\(496\) | 0.763932i | 0.0343016i | ||||||||
\(497\) | −16.1803 | − | 2.36068i | −0.725787 | − | 0.105891i | ||||
\(498\) | 3.70820 | − | 9.70820i | 0.166169 | − | 0.435035i | ||||
\(499\) | 19.0557 | 0.853052 | 0.426526 | − | 0.904475i | \(-0.359737\pi\) | ||||
0.426526 | + | 0.904475i | \(0.359737\pi\) | |||||||
\(500\) | 1.52786 | 0.0683282 | ||||||||
\(501\) | −22.4721 | − | 8.58359i | −1.00398 | − | 0.383487i | ||||
\(502\) | − | 1.70820i | − | 0.0762409i | ||||||
\(503\) | −4.58359 | −0.204372 | −0.102186 | − | 0.994765i | \(-0.532584\pi\) | ||||
−0.102186 | + | 0.994765i | \(0.532584\pi\) | |||||||
\(504\) | −5.09017 | − | 6.09017i | −0.226734 | − | 0.271278i | ||||
\(505\) | 21.8885 | 0.974027 | ||||||||
\(506\) | 1.23607i | 0.0549499i | ||||||||
\(507\) | 37.2148 | + | 14.2148i | 1.65277 | + | 0.631301i | ||||
\(508\) | 17.7082 | 0.785675 | ||||||||
\(509\) | 17.1246 | 0.759035 | 0.379518 | − | 0.925185i | \(-0.376090\pi\) | ||||
0.379518 | + | 0.925185i | \(0.376090\pi\) | |||||||
\(510\) | −14.4721 | + | 37.8885i | −0.640837 | + | 1.67773i | ||||
\(511\) | 37.1246 | + | 5.41641i | 1.64230 | + | 0.239608i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 9.23607 | − | 4.76393i | 0.407782 | − | 0.210333i | ||||
\(514\) | 0.944272i | 0.0416500i | ||||||||
\(515\) | − | 31.4164i | − | 1.38437i | ||||||
\(516\) | 17.7082 | + | 6.76393i | 0.779560 | + | 0.297766i | ||||
\(517\) | − | 1.52786i | − | 0.0671954i | ||||||
\(518\) | −11.7082 | − | 1.70820i | −0.514429 | − | 0.0750542i | ||||
\(519\) | −12.4721 | − | 4.76393i | −0.547466 | − | 0.209113i | ||||
\(520\) | −19.4164 | −0.851466 | ||||||||
\(521\) | 19.0557 | 0.834847 | 0.417423 | − | 0.908712i | \(-0.362933\pi\) | ||||
0.417423 | + | 0.908712i | \(0.362933\pi\) | |||||||
\(522\) | −1.05573 | − | 0.944272i | −0.0462080 | − | 0.0413297i | ||||
\(523\) | − | 29.7771i | − | 1.30206i | −0.759052 | − | 0.651031i | \(-0.774337\pi\) | ||
0.759052 | − | 0.651031i | \(-0.225663\pi\) | |||||||
\(524\) | 9.41641 | 0.411358 | ||||||||
\(525\) | −12.2361 | + | 21.8885i | −0.534026 | + | 0.955294i | ||||
\(526\) | −21.5279 | −0.938659 | ||||||||
\(527\) | 5.52786i | 0.240798i | ||||||||
\(528\) | −0.618034 | + | 1.61803i | −0.0268965 | + | 0.0704159i | ||||
\(529\) | 21.4721 | 0.933571 | ||||||||
\(530\) | 24.9443 | 1.08351 | ||||||||
\(531\) | 7.23607 | + | 6.47214i | 0.314019 | + | 0.280867i | ||||
\(532\) | −5.23607 | − | 0.763932i | −0.227012 | − | 0.0331207i | ||||
\(533\) | 73.0820i | 3.16553i | ||||||||
\(534\) | −8.00000 | + | 20.9443i | −0.346194 | + | 0.906347i | ||||
\(535\) | − | 28.9443i | − | 1.25137i | ||||||
\(536\) | − | 1.52786i | − | 0.0659937i | ||||||
\(537\) | −8.00000 | + | 20.9443i | −0.345225 | + | 0.903812i | ||||
\(538\) | 23.5967i | 1.01733i | ||||||||
\(539\) | −2.00000 | + | 6.70820i | −0.0861461 | + | 0.288943i | ||||
\(540\) | −7.70820 | − | 14.9443i | −0.331708 | − | 0.643099i | ||||
\(541\) | −23.5967 | −1.01450 | −0.507252 | − | 0.861798i | \(-0.669339\pi\) | ||||
−0.507252 | + | 0.861798i | \(0.669339\pi\) | |||||||
\(542\) | 23.7082 | 1.01835 | ||||||||
\(543\) | 2.18034 | − | 5.70820i | 0.0935673 | − | 0.244962i | ||||
\(544\) | 7.23607i | 0.310244i | ||||||||
\(545\) | −28.3607 | −1.21484 | ||||||||
\(546\) | 13.4164 | − | 24.0000i | 0.574169 | − | 1.02711i | ||||
\(547\) | 24.8328 | 1.06177 | 0.530887 | − | 0.847442i | \(-0.321859\pi\) | ||||
0.530887 | + | 0.847442i | \(0.321859\pi\) | |||||||
\(548\) | − | 6.47214i | − | 0.276476i | ||||||
\(549\) | 7.05573 | − | 7.88854i | 0.301131 | − | 0.336675i | ||||
\(550\) | 5.47214 | 0.233333 | ||||||||
\(551\) | −0.944272 | −0.0402273 | ||||||||
\(552\) | −2.00000 | − | 0.763932i | −0.0851257 | − | 0.0325151i | ||||
\(553\) | 2.76393 | − | 18.9443i | 0.117534 | − | 0.805592i | ||||
\(554\) | − | 24.1803i | − | 1.02732i | ||||||
\(555\) | −23.4164 | − | 8.94427i | −0.993971 | − | 0.379663i | ||||
\(556\) | 10.0000i | 0.424094i | ||||||||
\(557\) | − | 9.05573i | − | 0.383704i | −0.981424 | − | 0.191852i | \(-0.938551\pi\) | ||
0.981424 | − | 0.191852i | \(-0.0614493\pi\) | |||||||
\(558\) | −1.70820 | − | 1.52786i | −0.0723140 | − | 0.0646796i | ||||
\(559\) | 65.6656i | 2.77736i | ||||||||
\(560\) | −1.23607 | + | 8.47214i | −0.0522334 | + | 0.358013i | ||||
\(561\) | −4.47214 | + | 11.7082i | −0.188814 | + | 0.494321i | ||||
\(562\) | 25.4164 | 1.07213 | ||||||||
\(563\) | −23.5279 | −0.991581 | −0.495791 | − | 0.868442i | \(-0.665122\pi\) | ||||
−0.495791 | + | 0.868442i | \(0.665122\pi\) | |||||||
\(564\) | 2.47214 | + | 0.944272i | 0.104096 | + | 0.0397610i | ||||
\(565\) | 25.8885i | 1.08914i | ||||||||
\(566\) | −14.9443 | −0.628155 | ||||||||
\(567\) | 23.7984 | + | 0.798374i | 0.999438 | + | 0.0335286i | ||||
\(568\) | −6.18034 | −0.259321 | ||||||||
\(569\) | − | 6.00000i | − | 0.251533i | −0.992060 | − | 0.125767i | \(-0.959861\pi\) | ||
0.992060 | − | 0.125767i | \(-0.0401390\pi\) | |||||||
\(570\) | −10.4721 | − | 4.00000i | −0.438630 | − | 0.167542i | ||||
\(571\) | −26.9443 | −1.12758 | −0.563791 | − | 0.825917i | \(-0.690658\pi\) | ||||
−0.563791 | + | 0.825917i | \(0.690658\pi\) | |||||||
\(572\) | −6.00000 | −0.250873 | ||||||||
\(573\) | 7.23607 | − | 18.9443i | 0.302291 | − | 0.791408i | ||||
\(574\) | 31.8885 | + | 4.65248i | 1.33100 | + | 0.194191i | ||||
\(575\) | 6.76393i | 0.282075i | ||||||||
\(576\) | −2.23607 | − | 2.00000i | −0.0931695 | − | 0.0833333i | ||||
\(577\) | 37.5279i | 1.56231i | 0.624340 | + | 0.781153i | \(0.285368\pi\) | ||||
−0.624340 | + | 0.781153i | \(0.714632\pi\) | |||||||
\(578\) | 35.3607i | 1.47081i | ||||||||
\(579\) | 4.76393 | + | 1.81966i | 0.197982 | + | 0.0756225i | ||||
\(580\) | 1.52786i | 0.0634411i | ||||||||
\(581\) | 2.29180 | − | 15.7082i | 0.0950797 | − | 0.651686i | ||||
\(582\) | −4.00000 | − | 1.52786i | −0.165805 | − | 0.0633320i | ||||
\(583\) | 7.70820 | 0.319241 | ||||||||
\(584\) | 14.1803 | 0.586787 | ||||||||
\(585\) | 38.8328 | − | 43.4164i | 1.60554 | − | 1.79505i | ||||
\(586\) | 18.1803i | 0.751023i | ||||||||
\(587\) | 27.5967 | 1.13904 | 0.569520 | − | 0.821978i | \(-0.307129\pi\) | ||||
0.569520 | + | 0.821978i | \(0.307129\pi\) | |||||||
\(588\) | −9.61803 | − | 7.38197i | −0.396641 | − | 0.304427i | ||||
\(589\) | −1.52786 | −0.0629545 | ||||||||
\(590\) | − | 10.4721i | − | 0.431131i | ||||||
\(591\) | 9.23607 | − | 24.1803i | 0.379921 | − | 0.994646i | ||||
\(592\) | −4.47214 | −0.183804 | ||||||||
\(593\) | 1.70820 | 0.0701475 | 0.0350738 | − | 0.999385i | \(-0.488833\pi\) | ||||
0.0350738 | + | 0.999385i | \(0.488833\pi\) | |||||||
\(594\) | −2.38197 | − | 4.61803i | −0.0977332 | − | 0.189480i | ||||
\(595\) | −8.94427 | + | 61.3050i | −0.366679 | + | 2.51326i | ||||
\(596\) | 2.00000i | 0.0819232i | ||||||||
\(597\) | 12.4721 | − | 32.6525i | 0.510451 | − | 1.33638i | ||||
\(598\) | − | 7.41641i | − | 0.303279i | ||||||
\(599\) | 15.7082i | 0.641820i | 0.947110 | + | 0.320910i | \(0.103989\pi\) | ||||
−0.947110 | + | 0.320910i | \(0.896011\pi\) | |||||||
\(600\) | −3.38197 | + | 8.85410i | −0.138068 | + | 0.361467i | ||||
\(601\) | 9.23607i | 0.376747i | 0.982097 | + | 0.188374i | \(0.0603216\pi\) | ||||
−0.982097 | + | 0.188374i | \(0.939678\pi\) | |||||||
\(602\) | 28.6525 | + | 4.18034i | 1.16779 | + | 0.170378i | ||||
\(603\) | 3.41641 | + | 3.05573i | 0.139127 | + | 0.124439i | ||||
\(604\) | −12.1803 | −0.495611 | ||||||||
\(605\) | 3.23607 | 0.131565 | ||||||||
\(606\) | −4.18034 | + | 10.9443i | −0.169815 | + | 0.444581i | ||||
\(607\) | − | 1.23607i | − | 0.0501705i | −0.999685 | − | 0.0250852i | \(-0.992014\pi\) | ||
0.999685 | − | 0.0250852i | \(-0.00798571\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | −1.88854 | − | 1.05573i | −0.0765277 | − | 0.0427803i | ||||
\(610\) | −11.4164 | −0.462237 | ||||||||
\(611\) | 9.16718i | 0.370865i | ||||||||
\(612\) | −16.1803 | − | 14.4721i | −0.654051 | − | 0.585001i | ||||
\(613\) | −4.18034 | −0.168842 | −0.0844212 | − | 0.996430i | \(-0.526904\pi\) | ||||
−0.0844212 | + | 0.996430i | \(0.526904\pi\) | |||||||
\(614\) | −3.52786 | −0.142373 | ||||||||
\(615\) | 63.7771 | + | 24.3607i | 2.57174 | + | 0.982317i | ||||
\(616\) | −0.381966 | + | 2.61803i | −0.0153898 | + | 0.105484i | ||||
\(617\) | 11.0557i | 0.445087i | 0.974923 | + | 0.222543i | \(0.0714359\pi\) | ||||
−0.974923 | + | 0.222543i | \(0.928564\pi\) | |||||||
\(618\) | 15.7082 | + | 6.00000i | 0.631877 | + | 0.241355i | ||||
\(619\) | 21.2361i | 0.853550i | 0.904358 | + | 0.426775i | \(0.140350\pi\) | ||||
−0.904358 | + | 0.426775i | \(0.859650\pi\) | |||||||
\(620\) | 2.47214i | 0.0992834i | ||||||||
\(621\) | 5.70820 | − | 2.94427i | 0.229062 | − | 0.118150i | ||||
\(622\) | − | 10.4721i | − | 0.419894i | ||||||
\(623\) | −4.94427 | + | 33.8885i | −0.198088 | + | 1.35772i | ||||
\(624\) | 3.70820 | − | 9.70820i | 0.148447 | − | 0.388639i | ||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | −8.00000 | −0.319744 | ||||||||
\(627\) | −3.23607 | − | 1.23607i | −0.129236 | − | 0.0493638i | ||||
\(628\) | − | 13.4164i | − | 0.535373i | ||||||
\(629\) | −32.3607 | −1.29030 | ||||||||
\(630\) | −16.4721 | − | 19.7082i | −0.656266 | − | 0.785194i | ||||
\(631\) | −32.9443 | −1.31149 | −0.655745 | − | 0.754982i | \(-0.727646\pi\) | ||||
−0.655745 | + | 0.754982i | \(0.727646\pi\) | |||||||
\(632\) | − | 7.23607i | − | 0.287835i | ||||||
\(633\) | −15.2361 | − | 5.81966i | −0.605579 | − | 0.231311i | ||||
\(634\) | 12.2918 | 0.488170 | ||||||||
\(635\) | 57.3050 | 2.27408 | ||||||||
\(636\) | −4.76393 | + | 12.4721i | −0.188902 | + | 0.494552i | ||||
\(637\) | 12.0000 | − | 40.2492i | 0.475457 | − | 1.59473i | ||||
\(638\) | 0.472136i | 0.0186920i | ||||||||
\(639\) | 12.3607 | − | 13.8197i | 0.488981 | − | 0.546697i | ||||
\(640\) | 3.23607i | 0.127917i | ||||||||
\(641\) | 32.3607i | 1.27817i | 0.769136 | + | 0.639085i | \(0.220687\pi\) | ||||
−0.769136 | + | 0.639085i | \(0.779313\pi\) | |||||||
\(642\) | 14.4721 | + | 5.52786i | 0.571170 | + | 0.218167i | ||||
\(643\) | − | 32.0689i | − | 1.26467i | −0.774694 | − | 0.632337i | \(-0.782096\pi\) | ||
0.774694 | − | 0.632337i | \(-0.217904\pi\) | |||||||
\(644\) | −3.23607 | − | 0.472136i | −0.127519 | − | 0.0186048i | ||||
\(645\) | 57.3050 | + | 21.8885i | 2.25638 | + | 0.861861i | ||||
\(646\) | −14.4721 | −0.569399 | ||||||||
\(647\) | 5.88854 | 0.231503 | 0.115751 | − | 0.993278i | \(-0.463072\pi\) | ||||
0.115751 | + | 0.993278i | \(0.463072\pi\) | |||||||
\(648\) | 8.94427 | − | 1.00000i | 0.351364 | − | 0.0392837i | ||||
\(649\) | − | 3.23607i | − | 0.127027i | ||||||
\(650\) | −32.8328 | −1.28781 | ||||||||
\(651\) | −3.05573 | − | 1.70820i | −0.119763 | − | 0.0669498i | ||||
\(652\) | −18.4721 | −0.723425 | ||||||||
\(653\) | 21.2361i | 0.831032i | 0.909586 | + | 0.415516i | \(0.136399\pi\) | ||||
−0.909586 | + | 0.415516i | \(0.863601\pi\) | |||||||
\(654\) | 5.41641 | − | 14.1803i | 0.211798 | − | 0.554495i | ||||
\(655\) | 30.4721 | 1.19064 | ||||||||
\(656\) | 12.1803 | 0.475562 | ||||||||
\(657\) | −28.3607 | + | 31.7082i | −1.10646 | + | 1.23705i | ||||
\(658\) | 4.00000 | + | 0.583592i | 0.155936 | + | 0.0227508i | ||||
\(659\) | − | 9.88854i | − | 0.385203i | −0.981277 | − | 0.192601i | \(-0.938308\pi\) | ||
0.981277 | − | 0.192601i | \(-0.0616925\pi\) | |||||||
\(660\) | −2.00000 | + | 5.23607i | −0.0778499 | + | 0.203814i | ||||
\(661\) | 44.4721i | 1.72977i | 0.501974 | + | 0.864883i | \(0.332607\pi\) | ||||
−0.501974 | + | 0.864883i | \(0.667393\pi\) | |||||||
\(662\) | 8.94427i | 0.347629i | ||||||||
\(663\) | 26.8328 | − | 70.2492i | 1.04210 | − | 2.72825i | ||||
\(664\) | − | 6.00000i | − | 0.232845i | ||||||
\(665\) | −16.9443 | − | 2.47214i | −0.657071 | − | 0.0958653i | ||||
\(666\) | 8.94427 | − | 10.0000i | 0.346583 | − | 0.387492i | ||||
\(667\) | −0.583592 | −0.0225968 | ||||||||
\(668\) | −13.8885 | −0.537364 | ||||||||
\(669\) | −14.5836 | + | 38.1803i | −0.563834 | + | 1.47614i | ||||
\(670\) | − | 4.94427i | − | 0.191014i | ||||||
\(671\) | −3.52786 | −0.136192 | ||||||||
\(672\) | −4.00000 | − | 2.23607i | −0.154303 | − | 0.0862582i | ||||
\(673\) | −11.3050 | −0.435774 | −0.217887 | − | 0.975974i | \(-0.569916\pi\) | ||||
−0.217887 | + | 0.975974i | \(0.569916\pi\) | |||||||
\(674\) | 13.4164i | 0.516781i | ||||||||
\(675\) | −13.0344 | − | 25.2705i | −0.501696 | − | 0.972662i | ||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 2.76393 | 0.106227 | 0.0531133 | − | 0.998588i | \(-0.483086\pi\) | ||||
0.0531133 | + | 0.998588i | \(0.483086\pi\) | |||||||
\(678\) | −12.9443 | − | 4.94427i | −0.497122 | − | 0.189884i | ||||
\(679\) | −6.47214 | − | 0.944272i | −0.248378 | − | 0.0362378i | ||||
\(680\) | 23.4164i | 0.897978i | ||||||||
\(681\) | 35.5967 | + | 13.5967i | 1.36407 | + | 0.521029i | ||||
\(682\) | 0.763932i | 0.0292525i | ||||||||
\(683\) | − | 33.8885i | − | 1.29671i | −0.761339 | − | 0.648355i | \(-0.775457\pi\) | ||
0.761339 | − | 0.648355i | \(-0.224543\pi\) | |||||||
\(684\) | 4.00000 | − | 4.47214i | 0.152944 | − | 0.170996i | ||||
\(685\) | − | 20.9443i | − | 0.800239i | ||||||
\(686\) | −16.7984 | − | 7.79837i | −0.641365 | − | 0.297743i | ||||
\(687\) | −1.23607 | + | 3.23607i | −0.0471589 | + | 0.123464i | ||||
\(688\) | 10.9443 | 0.417246 | ||||||||
\(689\) | −46.2492 | −1.76196 | ||||||||
\(690\) | −6.47214 | − | 2.47214i | −0.246390 | − | 0.0941126i | ||||
\(691\) | − | 29.5967i | − | 1.12591i | −0.826486 | − | 0.562957i | \(-0.809664\pi\) | ||
0.826486 | − | 0.562957i | \(-0.190336\pi\) | |||||||
\(692\) | −7.70820 | −0.293022 | ||||||||
\(693\) | −5.09017 | − | 6.09017i | −0.193360 | − | 0.231346i | ||||
\(694\) | 16.9443 | 0.643196 | ||||||||
\(695\) | 32.3607i | 1.22751i | ||||||||
\(696\) | −0.763932 | − | 0.291796i | −0.0289568 | − | 0.0110605i | ||||
\(697\) | 88.1378 | 3.33846 | ||||||||
\(698\) | 22.0000 | 0.832712 | ||||||||
\(699\) | 15.7082 | − | 41.1246i | 0.594139 | − | 1.55548i | ||||
\(700\) | −2.09017 | + | 14.3262i | −0.0790010 | + | 0.541481i | ||||
\(701\) | − | 17.4164i | − | 0.657809i | −0.944363 | − | 0.328904i | \(-0.893321\pi\) | ||
0.944363 | − | 0.328904i | \(-0.106679\pi\) | |||||||
\(702\) | 14.2918 | + | 27.7082i | 0.539409 | + | 1.04578i | ||||
\(703\) | − | 8.94427i | − | 0.337340i | ||||||
\(704\) | 1.00000i | 0.0376889i | ||||||||
\(705\) | 8.00000 | + | 3.05573i | 0.301297 | + | 0.115085i | ||||
\(706\) | 0.944272i | 0.0355381i | ||||||||
\(707\) | −2.58359 | + | 17.7082i | −0.0971660 | + | 0.665986i | ||||
\(708\) | 5.23607 | + | 2.00000i | 0.196783 | + | 0.0751646i | ||||
\(709\) | −22.5836 | −0.848145 | −0.424072 | − | 0.905628i | \(-0.639400\pi\) | ||||
−0.424072 | + | 0.905628i | \(0.639400\pi\) | |||||||
\(710\) | −20.0000 | −0.750587 | ||||||||
\(711\) | 16.1803 | + | 14.4721i | 0.606810 | + | 0.542748i | ||||
\(712\) | 12.9443i | 0.485107i | ||||||||
\(713\) | −0.944272 | −0.0353633 | ||||||||
\(714\) | −28.9443 | − | 16.1803i | −1.08321 | − | 0.605534i | ||||
\(715\) | −19.4164 | −0.726132 | ||||||||
\(716\) | 12.9443i | 0.483750i | ||||||||
\(717\) | 13.5279 | − | 35.4164i | 0.505207 | − | 1.32265i | ||||
\(718\) | 18.8328 | 0.702834 | ||||||||
\(719\) | −17.5279 | −0.653679 | −0.326840 | − | 0.945080i | \(-0.605984\pi\) | ||||
−0.326840 | + | 0.945080i | \(0.605984\pi\) | |||||||
\(720\) | −7.23607 | − | 6.47214i | −0.269672 | − | 0.241202i | ||||
\(721\) | 25.4164 | + | 3.70820i | 0.946556 | + | 0.138101i | ||||
\(722\) | 15.0000i | 0.558242i | ||||||||
\(723\) | −11.2361 | + | 29.4164i | −0.417874 | + | 1.09401i | ||||
\(724\) | − | 3.52786i | − | 0.131112i | ||||||
\(725\) | 2.58359i | 0.0959522i | ||||||||
\(726\) | −0.618034 | + | 1.61803i | −0.0229374 | + | 0.0600509i | ||||
\(727\) | − | 2.29180i | − | 0.0849980i | −0.999097 | − | 0.0424990i | \(-0.986468\pi\) | ||
0.999097 | − | 0.0424990i | \(-0.0135319\pi\) | |||||||
\(728\) | 2.29180 | − | 15.7082i | 0.0849396 | − | 0.582185i | ||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 45.8885 | 1.69841 | ||||||||
\(731\) | 79.1935 | 2.92908 | ||||||||
\(732\) | 2.18034 | − | 5.70820i | 0.0805877 | − | 0.210981i | ||||
\(733\) | 26.5836i | 0.981887i | 0.871191 | + | 0.490944i | \(0.163348\pi\) | ||||
−0.871191 | + | 0.490944i | \(0.836652\pi\) | |||||||
\(734\) | 26.6525 | 0.983761 | ||||||||
\(735\) | −31.1246 | − | 23.8885i | −1.14805 | − | 0.881142i | ||||
\(736\) | −1.23607 | −0.0455621 | ||||||||
\(737\) | − | 1.52786i | − | 0.0562796i | ||||||
\(738\) | −24.3607 | + | 27.2361i | −0.896729 | + | 1.00257i | ||||
\(739\) | 9.41641 | 0.346388 | 0.173194 | − | 0.984888i | \(-0.444591\pi\) | ||||
0.173194 | + | 0.984888i | \(0.444591\pi\) | |||||||
\(740\) | −14.4721 | −0.532006 | ||||||||
\(741\) | 19.4164 | + | 7.41641i | 0.713280 | + | 0.272449i | ||||
\(742\) | −2.94427 | + | 20.1803i | −0.108088 | + | 0.740844i | ||||
\(743\) | 1.52786i | 0.0560519i | 0.999607 | + | 0.0280259i | \(0.00892210\pi\) | ||||
−0.999607 | + | 0.0280259i | \(0.991078\pi\) | |||||||
\(744\) | −1.23607 | − | 0.472136i | −0.0453165 | − | 0.0173093i | ||||
\(745\) | 6.47214i | 0.237121i | ||||||||
\(746\) | − | 7.81966i | − | 0.286298i | ||||||
\(747\) | 13.4164 | + | 12.0000i | 0.490881 | + | 0.439057i | ||||
\(748\) | 7.23607i | 0.264577i | ||||||||
\(749\) | 23.4164 | + | 3.41641i | 0.855617 | + | 0.124833i | ||||
\(750\) | −0.944272 | + | 2.47214i | −0.0344799 | + | 0.0902696i | ||||
\(751\) | −32.3607 | −1.18086 | −0.590429 | − | 0.807090i | \(-0.701041\pi\) | ||||
−0.590429 | + | 0.807090i | \(0.701041\pi\) | |||||||
\(752\) | 1.52786 | 0.0557155 | ||||||||
\(753\) | 2.76393 | + | 1.05573i | 0.100723 | + | 0.0384729i | ||||
\(754\) | − | 2.83282i | − | 0.103165i | ||||||
\(755\) | −39.4164 | −1.43451 | ||||||||
\(756\) | 13.0000 | − | 4.47214i | 0.472805 | − | 0.162650i | ||||
\(757\) | −1.41641 | −0.0514802 | −0.0257401 | − | 0.999669i | \(-0.508194\pi\) | ||||
−0.0257401 | + | 0.999669i | \(0.508194\pi\) | |||||||
\(758\) | − | 12.3607i | − | 0.448960i | ||||||
\(759\) | −2.00000 | − | 0.763932i | −0.0725954 | − | 0.0277290i | ||||
\(760\) | −6.47214 | −0.234769 | ||||||||
\(761\) | −33.1246 | −1.20077 | −0.600383 | − | 0.799713i | \(-0.704985\pi\) | ||||
−0.600383 | + | 0.799713i | \(0.704985\pi\) | |||||||
\(762\) | −10.9443 | + | 28.6525i | −0.396469 | + | 1.03797i | ||||
\(763\) | 3.34752 | − | 22.9443i | 0.121189 | − | 0.830638i | ||||
\(764\) | − | 11.7082i | − | 0.423588i | ||||||
\(765\) | −52.3607 | − | 46.8328i | −1.89310 | − | 1.69324i | ||||
\(766\) | 20.0000i | 0.722629i | ||||||||
\(767\) | 19.4164i | 0.701086i | ||||||||
\(768\) | −1.61803 | − | 0.618034i | −0.0583858 | − | 0.0223014i | ||||
\(769\) | 51.4853i | 1.85661i | 0.371823 | + | 0.928304i | \(0.378733\pi\) | ||||
−0.371823 | + | 0.928304i | \(0.621267\pi\) | |||||||
\(770\) | −1.23607 | + | 8.47214i | −0.0445448 | + | 0.305315i | ||||
\(771\) | −1.52786 | − | 0.583592i | −0.0550247 | − | 0.0210176i | ||||
\(772\) | 2.94427 | 0.105967 | ||||||||
\(773\) | 1.12461 | 0.0404495 | 0.0202247 | − | 0.999795i | \(-0.493562\pi\) | ||||
0.0202247 | + | 0.999795i | \(0.493562\pi\) | |||||||
\(774\) | −21.8885 | + | 24.4721i | −0.786767 | + | 0.879633i | ||||
\(775\) | 4.18034i | 0.150162i | ||||||||
\(776\) | −2.47214 | −0.0887445 | ||||||||
\(777\) | 10.0000 | − | 17.8885i | 0.358748 | − | 0.641748i | ||||
\(778\) | 17.2361 | 0.617943 | ||||||||
\(779\) | 24.3607i | 0.872812i | ||||||||
\(780\) | 12.0000 | − | 31.4164i | 0.429669 | − | 1.12489i | ||||
\(781\) | −6.18034 | −0.221150 | ||||||||
\(782\) | −8.94427 | −0.319847 | ||||||||
\(783\) | 2.18034 | − | 1.12461i | 0.0779190 | − | 0.0401903i | ||||
\(784\) | −6.70820 | − | 2.00000i | −0.239579 | − | 0.0714286i | ||||
\(785\) | − | 43.4164i | − | 1.54960i | ||||||
\(786\) | −5.81966 | + | 15.2361i | −0.207580 | + | 0.543453i | ||||
\(787\) | − | 43.5279i | − | 1.55160i | −0.630978 | − | 0.775800i | \(-0.717346\pi\) | ||
0.630978 | − | 0.775800i | \(-0.282654\pi\) | |||||||
\(788\) | − | 14.9443i | − | 0.532368i | ||||||
\(789\) | 13.3050 | − | 34.8328i | 0.473669 | − | 1.24008i | ||||
\(790\) | − | 23.4164i | − | 0.833118i | ||||||
\(791\) | −20.9443 | − | 3.05573i | −0.744693 | − | 0.108649i | ||||
\(792\) | −2.23607 | − | 2.00000i | −0.0794552 | − | 0.0710669i | ||||
\(793\) | 21.1672 | 0.751669 | ||||||||
\(794\) | 14.9443 | 0.530352 | ||||||||
\(795\) | −15.4164 | + | 40.3607i | −0.546764 | + | 1.43145i | ||||
\(796\) | − | 20.1803i | − | 0.715273i | ||||||
\(797\) | 49.7082 | 1.76075 | 0.880377 | − | 0.474274i | \(-0.157289\pi\) | ||||
0.880377 | + | 0.474274i | \(0.157289\pi\) | |||||||
\(798\) | 4.47214 | − | 8.00000i | 0.158312 | − | 0.283197i | ||||
\(799\) | 11.0557 | 0.391124 | ||||||||
\(800\) | 5.47214i | 0.193469i | ||||||||
\(801\) | −28.9443 | − | 25.8885i | −1.02270 | − | 0.914727i | ||||
\(802\) | 2.47214 | 0.0872942 | ||||||||
\(803\) | 14.1803 | 0.500413 | ||||||||
\(804\) | 2.47214 | + | 0.944272i | 0.0871855 | + | 0.0333019i | ||||
\(805\) | −10.4721 | − | 1.52786i | −0.369094 | − | 0.0538501i | ||||
\(806\) | − | 4.58359i | − | 0.161450i | ||||||
\(807\) | −38.1803 | − | 14.5836i | −1.34401 | − | 0.513367i | ||||
\(808\) | 6.76393i | 0.237954i | ||||||||
\(809\) | − | 16.8328i | − | 0.591810i | −0.955217 | − | 0.295905i | \(-0.904379\pi\) | ||
0.955217 | − | 0.295905i | \(-0.0956212\pi\) | |||||||
\(810\) | 28.9443 | − | 3.23607i | 1.01700 | − | 0.113704i | ||||
\(811\) | 46.7214i | 1.64061i | 0.571927 | + | 0.820304i | \(0.306196\pi\) | ||||
−0.571927 | + | 0.820304i | \(0.693804\pi\) | |||||||
\(812\) | −1.23607 | − | 0.180340i | −0.0433775 | − | 0.00632869i | ||||
\(813\) | −14.6525 | + | 38.3607i | −0.513885 | + | 1.34537i | ||||
\(814\) | −4.47214 | −0.156748 | ||||||||
\(815\) | −59.7771 | −2.09390 | ||||||||
\(816\) | −11.7082 | − | 4.47214i | −0.409869 | − | 0.156556i | ||||
\(817\) | 21.8885i | 0.765783i | ||||||||
\(818\) | 5.23607 | 0.183075 | ||||||||
\(819\) | 30.5410 | + | 36.5410i | 1.06719 | + | 1.27685i | ||||
\(820\) | 39.4164 | 1.37648 | ||||||||
\(821\) | 1.63932i | 0.0572127i | 0.999591 | + | 0.0286063i | \(0.00910692\pi\) | ||||
−0.999591 | + | 0.0286063i | \(0.990893\pi\) | |||||||
\(822\) | 10.4721 | + | 4.00000i | 0.365258 | + | 0.139516i | ||||
\(823\) | −38.2492 | −1.33328 | −0.666642 | − | 0.745378i | \(-0.732269\pi\) | ||||
−0.666642 | + | 0.745378i | \(0.732269\pi\) | |||||||
\(824\) | 9.70820 | 0.338201 | ||||||||
\(825\) | −3.38197 | + | 8.85410i | −0.117745 | + | 0.308260i | ||||
\(826\) | 8.47214 | + | 1.23607i | 0.294783 | + | 0.0430083i | ||||
\(827\) | 16.9443i | 0.589210i | 0.955619 | + | 0.294605i | \(0.0951881\pi\) | ||||
−0.955619 | + | 0.294605i | \(0.904812\pi\) | |||||||
\(828\) | 2.47214 | − | 2.76393i | 0.0859127 | − | 0.0960533i | ||||
\(829\) | − | 23.8885i | − | 0.829683i | −0.909894 | − | 0.414842i | \(-0.863837\pi\) | ||
0.909894 | − | 0.414842i | \(-0.136163\pi\) | |||||||
\(830\) | − | 19.4164i | − | 0.673953i | ||||||
\(831\) | 39.1246 | + | 14.9443i | 1.35722 | + | 0.518411i | ||||
\(832\) | − | 6.00000i | − | 0.208013i | ||||||
\(833\) | −48.5410 | − | 14.4721i | −1.68185 | − | 0.501430i | ||||
\(834\) | −16.1803 | − | 6.18034i | −0.560279 | − | 0.214008i | ||||
\(835\) | −44.9443 | −1.55536 | ||||||||
\(836\) | −2.00000 | −0.0691714 | ||||||||
\(837\) | 3.52786 | − | 1.81966i | 0.121941 | − | 0.0628967i | ||||
\(838\) | − | 9.12461i | − | 0.315204i | ||||||
\(839\) | −48.9443 | −1.68974 | −0.844872 | − | 0.534969i | \(-0.820323\pi\) | ||||
−0.844872 | + | 0.534969i | \(0.820323\pi\) | |||||||
\(840\) | −12.9443 | − | 7.23607i | −0.446620 | − | 0.249668i | ||||
\(841\) | 28.7771 | 0.992313 | ||||||||
\(842\) | 4.47214i | 0.154120i | ||||||||
\(843\) | −15.7082 | + | 41.1246i | −0.541019 | + | 1.41641i | ||||
\(844\) | −9.41641 | −0.324126 | ||||||||
\(845\) | 74.4296 | 2.56045 | ||||||||
\(846\) | −3.05573 | + | 3.41641i | −0.105058 | + | 0.117459i | ||||
\(847\) | −0.381966 | + | 2.61803i | −0.0131245 | + | 0.0899567i | ||||
\(848\) | 7.70820i | 0.264701i | ||||||||
\(849\) | 9.23607 | − | 24.1803i | 0.316981 | − | 0.829867i | ||||
\(850\) | 39.5967i | 1.35816i | ||||||||
\(851\) | − | 5.52786i | − | 0.189493i | ||||||
\(852\) | 3.81966 | − | 10.0000i | 0.130859 | − | 0.342594i | ||||
\(853\) | 6.94427i | 0.237767i | 0.992908 | + | 0.118884i | \(0.0379316\pi\) | ||||
−0.992908 | + | 0.118884i | \(0.962068\pi\) | |||||||
\(854\) | 1.34752 | − | 9.23607i | 0.0461113 | − | 0.316052i | ||||
\(855\) | 12.9443 | − | 14.4721i | 0.442685 | − | 0.494937i | ||||
\(856\) | 8.94427 | 0.305709 | ||||||||
\(857\) | 18.2918 | 0.624836 | 0.312418 | − | 0.949945i | \(-0.398861\pi\) | ||||
0.312418 | + | 0.949945i | \(0.398861\pi\) | |||||||
\(858\) | 3.70820 | − | 9.70820i | 0.126596 | − | 0.331433i | ||||
\(859\) | 4.65248i | 0.158740i | 0.996845 | + | 0.0793702i | \(0.0252909\pi\) | ||||
−0.996845 | + | 0.0793702i | \(0.974709\pi\) | |||||||
\(860\) | 35.4164 | 1.20769 | ||||||||
\(861\) | −27.2361 | + | 48.7214i | −0.928203 | + | 1.66042i | ||||
\(862\) | 5.88854 | 0.200565 | ||||||||
\(863\) | − | 25.5967i | − | 0.871323i | −0.900110 | − | 0.435662i | \(-0.856514\pi\) | ||
0.900110 | − | 0.435662i | \(-0.143486\pi\) | |||||||
\(864\) | 4.61803 | − | 2.38197i | 0.157109 | − | 0.0810361i | ||||
\(865\) | −24.9443 | −0.848131 | ||||||||
\(866\) | −26.4721 | −0.899560 | ||||||||
\(867\) | −57.2148 | − | 21.8541i | −1.94312 | − | 0.742204i | ||||
\(868\) | −2.00000 | − | 0.291796i | −0.0678844 | − | 0.00990420i | ||||
\(869\) | − | 7.23607i | − | 0.245467i | ||||||
\(870\) | −2.47214 | − | 0.944272i | −0.0838133 | − | 0.0320138i | ||||
\(871\) | 9.16718i | 0.310618i | ||||||||
\(872\) | − | 8.76393i | − | 0.296784i | ||||||
\(873\) | 4.94427 | − | 5.52786i | 0.167338 | − | 0.187090i | ||||
\(874\) | − | 2.47214i | − | 0.0836212i | ||||||
\(875\) | −0.583592 | + | 4.00000i | −0.0197290 | + | 0.135225i | ||||
\(876\) | −8.76393 | + | 22.9443i | −0.296106 | + | 0.775215i | ||||
\(877\) | 55.0132 | 1.85766 | 0.928831 | − | 0.370503i | \(-0.120815\pi\) | ||||
0.928831 | + | 0.370503i | \(0.120815\pi\) | |||||||
\(878\) | 17.2361 | 0.581689 | ||||||||
\(879\) | −29.4164 | − | 11.2361i | −0.992191 | − | 0.378983i | ||||
\(880\) | 3.23607i | 0.109088i | ||||||||
\(881\) | −23.4164 | −0.788919 | −0.394459 | − | 0.918913i | \(-0.629068\pi\) | ||||
−0.394459 | + | 0.918913i | \(0.629068\pi\) | |||||||
\(882\) | 17.8885 | − | 11.0000i | 0.602339 | − | 0.370389i | ||||
\(883\) | −12.9443 | −0.435609 | −0.217805 | − | 0.975992i | \(-0.569890\pi\) | ||||
−0.217805 | + | 0.975992i | \(0.569890\pi\) | |||||||
\(884\) | − | 43.4164i | − | 1.46025i | ||||||
\(885\) | 16.9443 | + | 6.47214i | 0.569575 | + | 0.217558i | ||||
\(886\) | −29.8885 | −1.00413 | ||||||||
\(887\) | −0.944272 | −0.0317055 | −0.0158528 | − | 0.999874i | \(-0.505046\pi\) | ||||
−0.0158528 | + | 0.999874i | \(0.505046\pi\) | |||||||
\(888\) | 2.76393 | − | 7.23607i | 0.0927515 | − | 0.242827i | ||||
\(889\) | −6.76393 | + | 46.3607i | −0.226855 | + | 1.55489i | ||||
\(890\) | 41.8885i | 1.40411i | ||||||||
\(891\) | 8.94427 | − | 1.00000i | 0.299644 | − | 0.0335013i | ||||
\(892\) | 23.5967i | 0.790078i | ||||||||
\(893\) | 3.05573i | 0.102256i | ||||||||
\(894\) | −3.23607 | − | 1.23607i | −0.108230 | − | 0.0413403i | ||||
\(895\) | 41.8885i | 1.40018i | ||||||||
\(896\) | −2.61803 | − | 0.381966i | −0.0874624 | − | 0.0127606i | ||||
\(897\) | 12.0000 | + | 4.58359i | 0.400668 | + | 0.153042i | ||||
\(898\) | 31.4164 | 1.04838 | ||||||||
\(899\) | −0.360680 | −0.0120293 | ||||||||
\(900\) | −12.2361 | − | 10.9443i | −0.407869 | − | 0.364809i | ||||
\(901\) | 55.7771i | 1.85820i | ||||||||
\(902\) | 12.1803 | 0.405561 | ||||||||
\(903\) | −24.4721 | + | 43.7771i | −0.814382 | + | 1.45681i | ||||
\(904\) | −8.00000 | −0.266076 | ||||||||
\(905\) | − | 11.4164i | − | 0.379494i | ||||||
\(906\) | 7.52786 | − | 19.7082i | 0.250097 | − | 0.654761i | ||||
\(907\) | −55.4164 | −1.84007 | −0.920036 | − | 0.391834i | \(-0.871841\pi\) | ||||
−0.920036 | + | 0.391834i | \(0.871841\pi\) | |||||||
\(908\) | 22.0000 | 0.730096 | ||||||||
\(909\) | −15.1246 | − | 13.5279i | −0.501652 | − | 0.448691i | ||||
\(910\) | 7.41641 | − | 50.8328i | 0.245852 | − | 1.68509i | ||||
\(911\) | − | 16.2918i | − | 0.539771i | −0.962892 | − | 0.269886i | \(-0.913014\pi\) | ||
0.962892 | − | 0.269886i | \(-0.0869859\pi\) | |||||||
\(912\) | 1.23607 | − | 3.23607i | 0.0409303 | − | 0.107157i | ||||
\(913\) | − | 6.00000i | − | 0.198571i | ||||||
\(914\) | − | 2.00000i | − | 0.0661541i | ||||||
\(915\) | 7.05573 | − | 18.4721i | 0.233255 | − | 0.610670i | ||||
\(916\) | 2.00000i | 0.0660819i | ||||||||
\(917\) | −3.59675 | + | 24.6525i | −0.118775 | + | 0.814096i | ||||
\(918\) | 33.4164 | − | 17.2361i | 1.10291 | − | 0.568875i | ||||
\(919\) | −21.1246 | −0.696837 | −0.348418 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348418 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(920\) | −4.00000 | −0.131876 | ||||||||
\(921\) | 2.18034 | − | 5.70820i | 0.0718446 | − | 0.188092i | ||||
\(922\) | − | 41.2361i | − | 1.35804i | ||||||
\(923\) | 37.0820 | 1.22057 | ||||||||
\(924\) | −4.00000 | − | 2.23607i | −0.131590 | − | 0.0735612i | ||||
\(925\) | −24.4721 | −0.804639 | ||||||||
\(926\) | − | 26.4721i | − | 0.869928i | ||||||
\(927\) | −19.4164 | + | 21.7082i | −0.637719 | + | 0.712991i | ||||
\(928\) | −0.472136 | −0.0154986 | ||||||||
\(929\) | 0.944272 | 0.0309806 | 0.0154903 | − | 0.999880i | \(-0.495069\pi\) | ||||
0.0154903 | + | 0.999880i | \(0.495069\pi\) | |||||||
\(930\) | −4.00000 | − | 1.52786i | −0.131165 | − | 0.0501006i | ||||
\(931\) | 4.00000 | − | 13.4164i | 0.131095 | − | 0.439705i | ||||
\(932\) | − | 25.4164i | − | 0.832542i | ||||||
\(933\) | 16.9443 | + | 6.47214i | 0.554731 | + | 0.211888i | ||||
\(934\) | − | 22.6525i | − | 0.741212i | ||||||
\(935\) | 23.4164i | 0.765798i | ||||||||
\(936\) | 13.4164 | + | 12.0000i | 0.438529 | + | 0.392232i | ||||
\(937\) | − | 46.1803i | − | 1.50865i | −0.656504 | − | 0.754323i | \(-0.727965\pi\) | ||
0.656504 | − | 0.754323i | \(-0.272035\pi\) | |||||||
\(938\) | 4.00000 | + | 0.583592i | 0.130605 | + | 0.0190550i | ||||
\(939\) | 4.94427 | − | 12.9443i | 0.161350 | − | 0.422420i | ||||
\(940\) | 4.94427 | 0.161264 | ||||||||
\(941\) | −32.2918 | −1.05268 | −0.526341 | − | 0.850273i | \(-0.676437\pi\) | ||||
−0.526341 | + | 0.850273i | \(0.676437\pi\) | |||||||
\(942\) | 21.7082 | + | 8.29180i | 0.707292 | + | 0.270161i | ||||
\(943\) | 15.0557i | 0.490282i | ||||||||
\(944\) | 3.23607 | 0.105325 | ||||||||
\(945\) | 42.0689 | − | 14.4721i | 1.36850 | − | 0.470779i | ||||
\(946\) | 10.9443 | 0.355829 | ||||||||
\(947\) | − | 32.0000i | − | 1.03986i | −0.854209 | − | 0.519930i | \(-0.825958\pi\) | ||
0.854209 | − | 0.519930i | \(-0.174042\pi\) | |||||||
\(948\) | 11.7082 | + | 4.47214i | 0.380265 | + | 0.145248i | ||||
\(949\) | −85.0820 | −2.76188 | ||||||||
\(950\) | −10.9443 | −0.355079 | ||||||||
\(951\) | −7.59675 | + | 19.8885i | −0.246341 | + | 0.644930i | ||||
\(952\) | −18.9443 | − | 2.76393i | −0.613987 | − | 0.0895796i | ||||
\(953\) | 2.36068i | 0.0764699i | 0.999269 | + | 0.0382350i | \(0.0121735\pi\) | ||||
−0.999269 | + | 0.0382350i | \(0.987826\pi\) | |||||||
\(954\) | −17.2361 | − | 15.4164i | −0.558038 | − | 0.499125i | ||||
\(955\) | − | 37.8885i | − | 1.22604i | ||||||
\(956\) | − | 21.8885i | − | 0.707926i | ||||||
\(957\) | −0.763932 | − | 0.291796i | −0.0246944 | − | 0.00943243i | ||||
\(958\) | − | 0.944272i | − | 0.0305080i | ||||||
\(959\) | 16.9443 | + | 2.47214i | 0.547159 | + | 0.0798294i | ||||
\(960\) | −5.23607 | − | 2.00000i | −0.168993 | − | 0.0645497i | ||||
\(961\) | 30.4164 | 0.981174 | ||||||||
\(962\) | 26.8328 | 0.865125 | ||||||||
\(963\) | −17.8885 | + | 20.0000i | −0.576450 | + | 0.644491i | ||||
\(964\) | 18.1803i | 0.585549i | ||||||||
\(965\) | 9.52786 | 0.306713 | ||||||||
\(966\) | 2.76393 | − | 4.94427i | 0.0889281 | − | 0.159079i | ||||
\(967\) | −38.0689 | −1.22421 | −0.612106 | − | 0.790775i | \(-0.709678\pi\) | ||||
−0.612106 | + | 0.790775i | \(0.709678\pi\) | |||||||
\(968\) | 1.00000i | 0.0321412i | ||||||||
\(969\) | 8.94427 | − | 23.4164i | 0.287331 | − | 0.752243i | ||||
\(970\) | −8.00000 | −0.256865 | ||||||||
\(971\) | −8.76393 | −0.281248 | −0.140624 | − | 0.990063i | \(-0.544911\pi\) | ||||
−0.140624 | + | 0.990063i | \(0.544911\pi\) | |||||||
\(972\) | −3.90983 | + | 15.0902i | −0.125408 | + | 0.484017i | ||||
\(973\) | −26.1803 | − | 3.81966i | −0.839303 | − | 0.122453i | ||||
\(974\) | 1.52786i | 0.0489559i | ||||||||
\(975\) | 20.2918 | − | 53.1246i | 0.649858 | − | 1.70135i | ||||
\(976\) | − | 3.52786i | − | 0.112924i | ||||||
\(977\) | 21.3050i | 0.681606i | 0.940135 | + | 0.340803i | \(0.110699\pi\) | ||||
−0.940135 | + | 0.340803i | \(0.889301\pi\) | |||||||
\(978\) | 11.4164 | − | 29.8885i | 0.365056 | − | 0.955730i | ||||
\(979\) | 12.9443i | 0.413701i | ||||||||
\(980\) | −21.7082 | − | 6.47214i | −0.693443 | − | 0.206745i | ||||
\(981\) | 19.5967 | + | 17.5279i | 0.625676 | + | 0.559622i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.0557 | 0.480203 | 0.240102 | − | 0.970748i | \(-0.422819\pi\) | ||||
0.240102 | + | 0.970748i | \(0.422819\pi\) | |||||||
\(984\) | −7.52786 | + | 19.7082i | −0.239980 | + | 0.628275i | ||||
\(985\) | − | 48.3607i | − | 1.54090i | ||||||
\(986\) | −3.41641 | −0.108801 | ||||||||
\(987\) | −3.41641 | + | 6.11146i | −0.108745 | + | 0.194530i | ||||
\(988\) | 12.0000 | 0.381771 | ||||||||
\(989\) | 13.5279i | 0.430161i | ||||||||
\(990\) | −7.23607 | − | 6.47214i | −0.229977 | − | 0.205698i | ||||
\(991\) | −0.944272 | −0.0299958 | −0.0149979 | − | 0.999888i | \(-0.504774\pi\) | ||||
−0.0149979 | + | 0.999888i | \(0.504774\pi\) | |||||||
\(992\) | −0.763932 | −0.0242549 | ||||||||
\(993\) | −14.4721 | − | 5.52786i | −0.459259 | − | 0.175421i | ||||
\(994\) | 2.36068 | − | 16.1803i | 0.0748762 | − | 0.513209i | ||||
\(995\) | − | 65.3050i | − | 2.07031i | ||||||
\(996\) | 9.70820 | + | 3.70820i | 0.307616 | + | 0.117499i | ||||
\(997\) | − | 32.4721i | − | 1.02840i | −0.857669 | − | 0.514201i | \(-0.828088\pi\) | ||
0.857669 | − | 0.514201i | \(-0.171912\pi\) | |||||||
\(998\) | 19.0557i | 0.603199i | ||||||||
\(999\) | 10.6525 | + | 20.6525i | 0.337029 | + | 0.653415i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 462.2.g.a.419.3 | yes | 4 | |
3.2 | odd | 2 | 462.2.g.d.419.2 | yes | 4 | ||
7.6 | odd | 2 | 462.2.g.d.419.4 | yes | 4 | ||
21.20 | even | 2 | inner | 462.2.g.a.419.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.g.a.419.1 | ✓ | 4 | 21.20 | even | 2 | inner | |
462.2.g.a.419.3 | yes | 4 | 1.1 | even | 1 | trivial | |
462.2.g.d.419.2 | yes | 4 | 3.2 | odd | 2 | ||
462.2.g.d.419.4 | yes | 4 | 7.6 | odd | 2 |