Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(316,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bu (of order \(6\), degree \(2\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.4 | ||
Root | \(1.20036 + 0.747754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.316 |
Dual form | 585.2.bu.c.361.4 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16117 | + | 1.24775i | 1.52818 | + | 0.882295i | 0.999438 | + | 0.0335125i | \(0.0106693\pi\) |
0.528742 | + | 0.848783i | \(0.322664\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.11378 | + | 3.66117i | 1.05689 | + | 1.83059i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.64996 | + | 0.952606i | −0.623627 | + | 0.360051i | −0.778280 | − | 0.627918i | \(-0.783907\pi\) |
0.154653 | + | 0.987969i | \(0.450574\pi\) | |||||||
\(8\) | 5.55889i | 1.96536i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.24775 | + | 2.16117i | −0.394574 | + | 0.683423i | ||||
\(11\) | −0.926118 | − | 0.534695i | −0.279235 | − | 0.161217i | 0.353842 | − | 0.935305i | \(-0.384875\pi\) |
−0.633077 | + | 0.774089i | \(0.718208\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.40072 | + | 3.32235i | 0.388490 | + | 0.921453i | ||||
\(14\) | −4.75447 | −1.27069 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.70857 | + | 4.69138i | −0.677142 | + | 1.17284i | ||||
\(17\) | −0.318632 | − | 0.551886i | −0.0772795 | − | 0.133852i | 0.824796 | − | 0.565431i | \(-0.191290\pi\) |
−0.902075 | + | 0.431579i | \(0.857957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.96410 | − | 2.86603i | 1.13884 | − | 0.657511i | 0.192699 | − | 0.981258i | \(-0.438276\pi\) |
0.946144 | + | 0.323747i | \(0.104943\pi\) | |||||||
\(20\) | −3.66117 | + | 2.11378i | −0.818663 | + | 0.472655i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.33433 | − | 2.31114i | −0.284481 | − | 0.492736i | ||||
\(23\) | −1.90893 | + | 3.30636i | −0.398039 | + | 0.689423i | −0.993484 | − | 0.113973i | \(-0.963642\pi\) |
0.595445 | + | 0.803396i | \(0.296976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.11827 | + | 8.92792i | −0.219311 | + | 1.75091i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.97531 | − | 4.02720i | −1.31821 | − | 0.761069i | ||||
\(29\) | 4.72756 | − | 8.18837i | 0.877886 | − | 1.52054i | 0.0242288 | − | 0.999706i | \(-0.492287\pi\) |
0.853657 | − | 0.520836i | \(-0.174380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.46410i | − | 0.262960i | −0.991319 | − | 0.131480i | \(-0.958027\pi\) | ||
0.991319 | − | 0.131480i | \(-0.0419730\pi\) | |||||||
\(32\) | −2.07908 | + | 1.20036i | −0.367534 | + | 0.212196i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.59030i | − | 0.272733i | ||||||
\(35\) | −0.952606 | − | 1.64996i | −0.161020 | − | 0.278895i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.655970 | + | 0.378725i | 0.107841 | + | 0.0622619i | 0.552950 | − | 0.833214i | \(-0.313502\pi\) |
−0.445110 | + | 0.895476i | \(0.646835\pi\) | |||||||
\(38\) | 14.3044 | 2.32048 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.55889 | −0.878938 | ||||||||
\(41\) | 0.232051 | + | 0.133975i | 0.0362402 | + | 0.0209233i | 0.518011 | − | 0.855374i | \(-0.326673\pi\) |
−0.481770 | + | 0.876297i | \(0.660006\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.318632 | + | 0.551886i | 0.0485909 | + | 0.0841618i | 0.889298 | − | 0.457328i | \(-0.151194\pi\) |
−0.840707 | + | 0.541490i | \(0.817860\pi\) | |||||||
\(44\) | − | 4.52091i | − | 0.681552i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.25104 | + | 4.76374i | −1.21655 | + | 0.702375i | ||||
\(47\) | − | 9.44613i | − | 1.37786i | −0.724828 | − | 0.688930i | \(-0.758081\pi\) | ||
0.724828 | − | 0.688930i | \(-0.241919\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.68508 | + | 2.91865i | −0.240726 | + | 0.416950i | ||||
\(50\) | −2.16117 | − | 1.24775i | −0.305636 | − | 0.176459i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −9.20287 | + | 12.1510i | −1.27621 | + | 1.68504i | ||||
\(53\) | 6.99102 | 0.960290 | 0.480145 | − | 0.877189i | \(-0.340584\pi\) | ||||
0.480145 | + | 0.877189i | \(0.340584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.534695 | − | 0.926118i | 0.0720982 | − | 0.124878i | ||||
\(56\) | −5.29543 | − | 9.17196i | −0.707632 | − | 1.22565i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 20.4341 | − | 11.7977i | 2.68313 | − | 1.54911i | ||||
\(59\) | 0.641756 | − | 0.370518i | 0.0835495 | − | 0.0482373i | −0.457643 | − | 0.889136i | \(-0.651306\pi\) |
0.541193 | + | 0.840899i | \(0.317973\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.09928 | − | 3.63606i | −0.268785 | − | 0.465550i | 0.699763 | − | 0.714375i | \(-0.253289\pi\) |
−0.968548 | + | 0.248825i | \(0.919956\pi\) | |||||||
\(62\) | 1.82684 | − | 3.16418i | 0.232009 | − | 0.401851i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.84325 | 0.605406 | ||||||||
\(65\) | −3.32235 | + | 1.40072i | −0.412086 | + | 0.173738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.01029 | − | 4.04739i | −0.856443 | − | 0.494468i | 0.00637624 | − | 0.999980i | \(-0.497970\pi\) |
−0.862820 | + | 0.505512i | \(0.831304\pi\) | |||||||
\(68\) | 1.34703 | − | 2.33313i | 0.163352 | − | 0.282934i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 4.75447i | − | 0.568268i | ||||||
\(71\) | −8.45663 | + | 4.88244i | −1.00362 | + | 0.579439i | −0.909317 | − | 0.416105i | \(-0.863395\pi\) |
−0.0943010 | + | 0.995544i | \(0.530062\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.71649i | 0.434982i | 0.976062 | + | 0.217491i | \(0.0697873\pi\) | ||||
−0.976062 | + | 0.217491i | \(0.930213\pi\) | |||||||
\(74\) | 0.945110 | + | 1.63698i | 0.109867 | + | 0.190295i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20.9860 | + | 12.1163i | 2.40726 | + | 1.38983i | ||||
\(77\) | 2.03741 | 0.232185 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.31937 | −1.04851 | −0.524255 | − | 0.851561i | \(-0.675656\pi\) | ||||
−0.524255 | + | 0.851561i | \(0.675656\pi\) | |||||||
\(80\) | −4.69138 | − | 2.70857i | −0.524512 | − | 0.302827i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.334335 | + | 0.579085i | 0.0369211 | + | 0.0639492i | ||||
\(83\) | − | 5.11778i | − | 0.561749i | −0.959744 | − | 0.280875i | \(-0.909376\pi\) | ||
0.959744 | − | 0.280875i | \(-0.0906245\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.551886 | − | 0.318632i | 0.0598605 | − | 0.0345605i | ||||
\(86\) | 1.59030i | 0.171486i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.97231 | − | 5.14819i | 0.316849 | − | 0.548799i | ||||
\(89\) | 10.8932 | + | 6.28917i | 1.15467 | + | 0.666650i | 0.950021 | − | 0.312185i | \(-0.101061\pi\) |
0.204651 | + | 0.978835i | \(0.434394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.47602 | − | 4.14741i | −0.574043 | − | 0.434767i | ||||
\(92\) | −16.1402 | −1.68273 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.7864 | − | 20.4147i | 1.21568 | − | 2.10562i | ||||
\(95\) | 2.86603 | + | 4.96410i | 0.294048 | + | 0.509306i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.65597 | + | 2.11078i | −0.371208 | + | 0.214317i | −0.673986 | − | 0.738744i | \(-0.735419\pi\) |
0.302778 | + | 0.953061i | \(0.402086\pi\) | |||||||
\(98\) | −7.28351 | + | 4.20514i | −0.735746 | + | 0.424783i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.11378 | − | 3.66117i | −0.211378 | − | 0.366117i | ||||
\(101\) | 7.62379 | − | 13.2048i | 0.758595 | − | 1.31393i | −0.184972 | − | 0.982744i | \(-0.559219\pi\) |
0.943567 | − | 0.331181i | \(-0.107447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5269 | 1.33285 | 0.666423 | − | 0.745574i | \(-0.267824\pi\) | ||||
0.666423 | + | 0.745574i | \(0.267824\pi\) | |||||||
\(104\) | −18.4686 | + | 7.78645i | −1.81099 | + | 0.763524i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.1088 | + | 8.72307i | 1.46750 | + | 0.847259i | ||||
\(107\) | −3.68137 | + | 6.37632i | −0.355891 | + | 0.616422i | −0.987270 | − | 0.159053i | \(-0.949156\pi\) |
0.631379 | + | 0.775475i | \(0.282489\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0760i | 0.965103i | 0.875868 | + | 0.482551i | \(0.160290\pi\) | ||||
−0.875868 | + | 0.482551i | \(0.839710\pi\) | |||||||
\(110\) | 2.31114 | − | 1.33433i | 0.220358 | − | 0.127224i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 10.3208i | − | 0.975223i | ||||||
\(113\) | −3.34403 | − | 5.79203i | −0.314580 | − | 0.544868i | 0.664768 | − | 0.747050i | \(-0.268530\pi\) |
−0.979348 | + | 0.202181i | \(0.935197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.30636 | − | 1.90893i | −0.308320 | − | 0.178008i | ||||
\(116\) | 39.9721 | 3.71131 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.84926 | 0.170238 | ||||||||
\(119\) | 1.05146 | + | 0.607061i | 0.0963872 | + | 0.0556492i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.92820 | − | 8.53590i | −0.448018 | − | 0.775991i | ||||
\(122\) | − | 10.4775i | − | 0.948592i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.36033 | − | 3.09479i | 0.481372 | − | 0.277920i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.744750 | − | 1.28994i | 0.0660859 | − | 0.114464i | −0.831089 | − | 0.556139i | \(-0.812282\pi\) |
0.897175 | + | 0.441675i | \(0.145616\pi\) | |||||||
\(128\) | 14.6253 | + | 8.44391i | 1.29270 | + | 0.746343i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −8.92792 | − | 1.11827i | −0.783030 | − | 0.0980789i | ||||
\(131\) | −4.12676 | −0.360557 | −0.180278 | − | 0.983616i | \(-0.557700\pi\) | ||||
−0.180278 | + | 0.983616i | \(0.557700\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.46039 | + | 9.45767i | −0.473476 | + | 0.820084i | ||||
\(134\) | −10.1003 | − | 17.4942i | −0.872533 | − | 1.51127i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.06787 | − | 1.77124i | 0.263068 | − | 0.151882i | ||||
\(137\) | −17.4155 | + | 10.0548i | −1.48790 | + | 0.859041i | −0.999905 | − | 0.0138029i | \(-0.995606\pi\) |
−0.487999 | + | 0.872844i | \(0.662273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.4126 | − | 18.0352i | −0.883189 | − | 1.52973i | −0.847776 | − | 0.530355i | \(-0.822059\pi\) |
−0.0354130 | − | 0.999373i | \(-0.511275\pi\) | |||||||
\(140\) | 4.02720 | − | 6.97531i | 0.340360 | − | 0.589521i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −24.3683 | −2.04494 | ||||||||
\(143\) | 0.479208 | − | 3.82584i | 0.0400734 | − | 0.319933i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.18837 | + | 4.72756i | 0.680007 | + | 0.392602i | ||||
\(146\) | −4.63726 | + | 8.03198i | −0.383783 | + | 0.664731i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.20216i | 0.263216i | ||||||||
\(149\) | −11.5768 | + | 6.68388i | −0.948410 | + | 0.547565i | −0.892587 | − | 0.450876i | \(-0.851112\pi\) |
−0.0558233 | + | 0.998441i | \(0.517778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.2984i | − | 1.48910i | −0.667567 | − | 0.744550i | \(-0.732664\pi\) | ||
0.667567 | − | 0.744550i | \(-0.267336\pi\) | |||||||
\(152\) | 15.9319 | + | 27.5949i | 1.29225 | + | 2.23824i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.40320 | + | 2.54219i | 0.354820 | + | 0.204856i | ||||
\(155\) | 1.46410 | 0.117599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.42229 | 0.193320 | 0.0966599 | − | 0.995317i | \(-0.469184\pi\) | ||||
0.0966599 | + | 0.995317i | \(0.469184\pi\) | |||||||
\(158\) | −20.1408 | − | 11.6283i | −1.60231 | − | 0.925096i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.20036 | − | 2.07908i | −0.0948968 | − | 0.164366i | ||||
\(161\) | − | 7.27382i | − | 0.573258i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.8416 | + | 7.99144i | −1.08416 | + | 0.625938i | −0.932015 | − | 0.362421i | \(-0.881950\pi\) |
−0.152142 | + | 0.988359i | \(0.548617\pi\) | |||||||
\(164\) | 1.13277i | 0.0884545i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.38573 | − | 11.0604i | 0.495629 | − | 0.858454i | ||||
\(167\) | 12.4648 | + | 7.19658i | 0.964558 | + | 0.556888i | 0.897573 | − | 0.440866i | \(-0.145329\pi\) |
0.0669853 | + | 0.997754i | \(0.478662\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.07597 | + | 9.30735i | −0.698151 | + | 0.715950i | ||||
\(170\) | 1.59030 | 0.121970 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.34703 | + | 2.33313i | −0.102710 | + | 0.177900i | ||||
\(173\) | 12.1745 | + | 21.0868i | 0.925608 | + | 1.60320i | 0.790581 | + | 0.612358i | \(0.209779\pi\) |
0.135027 | + | 0.990842i | \(0.456888\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.64996 | − | 0.952606i | 0.124725 | − | 0.0720103i | ||||
\(176\) | 5.01691 | − | 2.89651i | 0.378164 | − | 0.218333i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.6947 | + | 27.1840i | 1.17636 | + | 2.03752i | ||||
\(179\) | −1.89414 | + | 3.28075i | −0.141575 | + | 0.245215i | −0.928090 | − | 0.372356i | \(-0.878550\pi\) |
0.786515 | + | 0.617571i | \(0.211883\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48794 | 0.630904 | 0.315452 | − | 0.948942i | \(-0.397844\pi\) | ||||
0.315452 | + | 0.948942i | \(0.397844\pi\) | |||||||
\(182\) | −6.65968 | − | 15.7960i | −0.493649 | − | 1.17088i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −18.3797 | − | 10.6115i | −1.35497 | − | 0.782291i | ||||
\(185\) | −0.378725 | + | 0.655970i | −0.0278444 | + | 0.0482279i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.681482i | 0.0498349i | ||||||||
\(188\) | 34.5839 | − | 19.9670i | 2.52229 | − | 1.45625i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.3044i | 1.03775i | ||||||||
\(191\) | −2.72155 | − | 4.71386i | −0.196924 | − | 0.341083i | 0.750605 | − | 0.660751i | \(-0.229762\pi\) |
−0.947530 | + | 0.319668i | \(0.896429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5288 | + | 6.07880i | 0.757879 | + | 0.437562i | 0.828534 | − | 0.559939i | \(-0.189176\pi\) |
−0.0706548 | + | 0.997501i | \(0.522509\pi\) | |||||||
\(194\) | −10.5349 | −0.756363 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.2476 | −1.01768 | ||||||||
\(197\) | −3.79172 | − | 2.18915i | −0.270149 | − | 0.155970i | 0.358807 | − | 0.933412i | \(-0.383184\pi\) |
−0.628955 | + | 0.777442i | \(0.716517\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.4186 | + | 18.0456i | 0.738558 | + | 1.27922i | 0.953144 | + | 0.302516i | \(0.0978265\pi\) |
−0.214586 | + | 0.976705i | \(0.568840\pi\) | |||||||
\(200\) | − | 5.55889i | − | 0.393073i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32.9526 | − | 19.0252i | 2.31854 | − | 1.33861i | ||||
\(203\) | 18.0140i | 1.26434i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.133975 | + | 0.232051i | −0.00935719 | + | 0.0162071i | ||||
\(206\) | 29.2340 | + | 16.8783i | 2.03683 | + | 1.17596i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19.3803 | − | 2.42749i | −1.34378 | − | 0.168316i | ||||
\(209\) | −6.12979 | −0.424007 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.32684 | − | 9.22635i | 0.366715 | − | 0.635168i | −0.622335 | − | 0.782751i | \(-0.713816\pi\) |
0.989050 | + | 0.147583i | \(0.0471492\pi\) | |||||||
\(212\) | 14.7775 | + | 25.5953i | 1.01492 | + | 1.75789i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.9121 | + | 9.18688i | −1.08773 | + | 0.628002i | ||||
\(215\) | −0.551886 | + | 0.318632i | −0.0376383 | + | 0.0217305i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.39471 | + | 2.41571i | 0.0946792 | + | 0.163989i | ||||
\(218\) | −12.5723 | + | 21.7759i | −0.851505 | + | 1.47485i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.52091 | 0.304799 | ||||||||
\(221\) | 1.38724 | − | 1.83164i | 0.0933161 | − | 0.123210i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.4804 | − | 10.6697i | −1.23754 | − | 0.714494i | −0.268949 | − | 0.963155i | \(-0.586676\pi\) |
−0.968591 | + | 0.248661i | \(0.920010\pi\) | |||||||
\(224\) | 2.28694 | − | 3.96110i | 0.152803 | − | 0.264662i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 16.6901i | − | 1.11021i | ||||||
\(227\) | −13.5842 | + | 7.84283i | −0.901613 | + | 0.520547i | −0.877723 | − | 0.479168i | \(-0.840938\pi\) |
−0.0238900 | + | 0.999715i | \(0.507605\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.62085i | 0.503600i | 0.967779 | + | 0.251800i | \(0.0810225\pi\) | ||||
−0.967779 | + | 0.251800i | \(0.918977\pi\) | |||||||
\(230\) | −4.76374 | − | 8.25104i | −0.314112 | − | 0.544058i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 45.5182 | + | 26.2800i | 2.98842 | + | 1.72536i | ||||
\(233\) | −19.0550 | −1.24833 | −0.624166 | − | 0.781292i | \(-0.714561\pi\) | ||||
−0.624166 | + | 0.781292i | \(0.714561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.44613 | 0.616198 | ||||||||
\(236\) | 2.71306 | + | 1.56639i | 0.176605 | + | 0.101963i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.51493 | + | 2.62393i | 0.0981980 | + | 0.170084i | ||||
\(239\) | − | 12.7535i | − | 0.824954i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) | ||
0.910968 | − | 0.412477i | \(-0.135336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.4550 | + | 12.9644i | −1.44646 | + | 0.835111i | −0.998268 | − | 0.0588285i | \(-0.981263\pi\) |
−0.448187 | + | 0.893940i | \(0.647930\pi\) | |||||||
\(242\) | − | 24.5967i | − | 1.58114i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.87483 | − | 15.3717i | 0.568153 | − | 0.984069i | ||||
\(245\) | −2.91865 | − | 1.68508i | −0.186466 | − | 0.107656i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.4752 | + | 12.4780i | 1.04829 | + | 0.793954i | ||||
\(248\) | 8.13878 | 0.516813 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.24775 | − | 2.16117i | 0.0789149 | − | 0.136685i | ||||
\(251\) | −3.80593 | − | 6.59207i | −0.240228 | − | 0.416088i | 0.720551 | − | 0.693402i | \(-0.243889\pi\) |
−0.960779 | + | 0.277314i | \(0.910556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.53578 | − | 2.04139i | 0.222293 | − | 0.128341i | ||||
\(254\) | 3.21907 | − | 1.85853i | 0.201982 | − | 0.116614i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.2286 | + | 28.1087i | 1.01429 | + | 1.75680i | ||||
\(257\) | −0.167891 | + | 0.290796i | −0.0104728 | + | 0.0181394i | −0.871214 | − | 0.490903i | \(-0.836667\pi\) |
0.860742 | + | 0.509042i | \(0.170000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.44310 | −0.0896700 | ||||||||
\(260\) | −12.1510 | − | 9.20287i | −0.753572 | − | 0.570738i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.91865 | − | 5.14918i | −0.550996 | − | 0.318118i | ||||
\(263\) | −2.68795 | + | 4.65566i | −0.165746 | + | 0.287080i | −0.936920 | − | 0.349544i | \(-0.886336\pi\) |
0.771174 | + | 0.636624i | \(0.219670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.99102i | 0.429455i | ||||||||
\(266\) | −23.6017 | + | 13.6264i | −1.44711 | + | 0.835491i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 34.2212i | − | 2.09039i | ||||||
\(269\) | −0.655192 | − | 1.13483i | −0.0399478 | − | 0.0691916i | 0.845360 | − | 0.534197i | \(-0.179386\pi\) |
−0.885308 | + | 0.465005i | \(0.846052\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0851 | − | 5.82266i | −0.612629 | − | 0.353701i | 0.161365 | − | 0.986895i | \(-0.448410\pi\) |
−0.773994 | + | 0.633194i | \(0.781744\pi\) | |||||||
\(272\) | 3.45214 | 0.209317 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −50.1838 | −3.03171 | ||||||||
\(275\) | 0.926118 | + | 0.534695i | 0.0558470 | + | 0.0322433i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.1581 | − | 17.5943i | −0.610338 | − | 1.05714i | −0.991183 | − | 0.132498i | \(-0.957700\pi\) |
0.380845 | − | 0.924639i | \(-0.375633\pi\) | |||||||
\(278\) | − | 51.9697i | − | 3.11693i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.17196 | − | 5.29543i | 0.548129 | − | 0.316463i | ||||
\(281\) | − | 11.8744i | − | 0.708366i | −0.935176 | − | 0.354183i | \(-0.884759\pi\) | ||
0.935176 | − | 0.354183i | \(-0.115241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.3261 | + | 19.6173i | −0.673264 | + | 1.16613i | 0.303709 | + | 0.952765i | \(0.401775\pi\) |
−0.976973 | + | 0.213363i | \(0.931558\pi\) | |||||||
\(284\) | −35.7509 | − | 20.6408i | −2.12143 | − | 1.22481i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.80936 | − | 7.67038i | 0.343515 | − | 0.453559i | ||||
\(287\) | −0.510500 | −0.0301339 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.29695 | − | 14.3707i | 0.488056 | − | 0.845337i | ||||
\(290\) | 11.7977 | + | 20.4341i | 0.692782 | + | 1.19993i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.6067 | + | 7.85584i | −0.796272 | + | 0.459728i | ||||
\(293\) | 16.1191 | − | 9.30636i | 0.941687 | − | 0.543683i | 0.0511983 | − | 0.998689i | \(-0.483696\pi\) |
0.890489 | + | 0.455005i | \(0.150363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.370518 | + | 0.641756i | 0.0215724 | + | 0.0373645i | ||||
\(296\) | −2.10529 | + | 3.64647i | −0.122367 | + | 0.211946i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −33.3593 | −1.93245 | ||||||||
\(299\) | −13.6587 | − | 1.71083i | −0.789905 | − | 0.0989400i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05146 | − | 0.607061i | −0.0606052 | − | 0.0349904i | ||||
\(302\) | 22.8319 | − | 39.5459i | 1.31383 | − | 2.27561i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 31.0513i | 1.78091i | ||||||||
\(305\) | 3.63606 | − | 2.09928i | 0.208200 | − | 0.120204i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.14776i | − | 0.179652i | −0.995957 | − | 0.0898262i | \(-0.971369\pi\) | ||
0.995957 | − | 0.0898262i | \(-0.0286311\pi\) | |||||||
\(308\) | 4.30664 | + | 7.45932i | 0.245394 | + | 0.425034i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.16418 | + | 1.82684i | 0.179713 | + | 0.103757i | ||||
\(311\) | −3.18059 | −0.180355 | −0.0901774 | − | 0.995926i | \(-0.528743\pi\) | ||||
−0.0901774 | + | 0.995926i | \(0.528743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 35.3533 | 1.99829 | 0.999144 | − | 0.0413596i | \(-0.0131689\pi\) | ||||
0.999144 | + | 0.0413596i | \(0.0131689\pi\) | |||||||
\(314\) | 5.23499 | + | 3.02242i | 0.295427 | + | 0.170565i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.6991 | − | 34.1198i | −1.10816 | − | 1.91939i | ||||
\(317\) | 13.6357i | 0.765858i | 0.923778 | + | 0.382929i | \(0.125085\pi\) | ||||
−0.923778 | + | 0.382929i | \(0.874915\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.75656 | + | 5.05560i | −0.490273 | + | 0.283059i | ||||
\(320\) | 4.84325i | 0.270746i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.07594 | − | 15.7200i | 0.505782 | − | 0.876041i | ||||
\(323\) | −3.16344 | − | 1.82641i | −0.176018 | − | 0.101624i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.40072 | − | 3.32235i | −0.0776980 | − | 0.184291i | ||||
\(326\) | −39.8854 | −2.20905 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.744750 | + | 1.28994i | −0.0411219 | + | 0.0712253i | ||||
\(329\) | 8.99844 | + | 15.5858i | 0.496100 | + | 0.859271i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.9380 | + | 14.3980i | −1.37072 | + | 0.791383i | −0.991018 | − | 0.133727i | \(-0.957305\pi\) |
−0.379698 | + | 0.925110i | \(0.623972\pi\) | |||||||
\(332\) | 18.7371 | − | 10.8179i | 1.02833 | − | 0.593707i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.9591 | + | 31.1061i | 0.982679 | + | 1.70205i | ||||
\(335\) | 4.04739 | − | 7.01029i | 0.221133 | − | 0.383013i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7493 | −0.640026 | −0.320013 | − | 0.947413i | \(-0.603687\pi\) | ||||
−0.320013 | + | 0.947413i | \(0.603687\pi\) | |||||||
\(338\) | −31.2280 | + | 8.79023i | −1.69858 | + | 0.478125i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.33313 | + | 1.34703i | 0.126532 | + | 0.0730532i | ||||
\(341\) | −0.782847 | + | 1.35593i | −0.0423936 | + | 0.0734278i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.7574i | − | 1.06680i | ||||||
\(344\) | −3.06787 | + | 1.77124i | −0.165409 | + | 0.0954987i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 60.7630i | 3.26664i | ||||||||
\(347\) | 0.949887 | + | 1.64525i | 0.0509926 | + | 0.0883218i | 0.890395 | − | 0.455189i | \(-0.150428\pi\) |
−0.839402 | + | 0.543510i | \(0.817095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.89329 | − | 5.13454i | −0.476047 | − | 0.274846i | 0.242721 | − | 0.970096i | \(-0.421960\pi\) |
−0.718768 | + | 0.695250i | \(0.755293\pi\) | |||||||
\(350\) | 4.75447 | 0.254137 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.56730 | 0.136838 | ||||||||
\(353\) | 0.693330 | + | 0.400294i | 0.0369022 | + | 0.0213055i | 0.518338 | − | 0.855176i | \(-0.326551\pi\) |
−0.481435 | + | 0.876482i | \(0.659884\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.88244 | − | 8.45663i | −0.259133 | − | 0.448831i | ||||
\(356\) | 53.1756i | 2.81830i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.18714 | + | 4.72685i | −0.432704 | + | 0.249822i | ||||
\(359\) | 8.13272i | 0.429228i | 0.976699 | + | 0.214614i | \(0.0688494\pi\) | ||||
−0.976699 | + | 0.214614i | \(0.931151\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.92820 | − | 12.0000i | 0.364642 | − | 0.631579i | ||||
\(362\) | 18.3439 | + | 10.5909i | 0.964135 | + | 0.556643i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.60929 | − | 28.8154i | 0.189178 | − | 1.51034i | ||||
\(365\) | −3.71649 | −0.194530 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2632 | − | 17.7765i | 0.535737 | − | 0.927924i | −0.463390 | − | 0.886154i | \(-0.653367\pi\) |
0.999127 | − | 0.0417696i | \(-0.0132996\pi\) | |||||||
\(368\) | −10.3409 | − | 17.9110i | −0.539057 | − | 0.933675i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.63698 | + | 0.945110i | −0.0851025 | + | 0.0491339i | ||||
\(371\) | −11.5349 | + | 6.65968i | −0.598863 | + | 0.345754i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.90292 | + | 15.4203i | 0.460976 | + | 0.798433i | 0.999010 | − | 0.0444897i | \(-0.0141662\pi\) |
−0.538034 | + | 0.842923i | \(0.680833\pi\) | |||||||
\(374\) | −0.850322 | + | 1.47280i | −0.0439691 | + | 0.0761568i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 52.5100 | 2.70800 | ||||||||
\(377\) | 33.8266 | + | 4.23697i | 1.74216 | + | 0.218215i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.77150 | − | 1.02277i | −0.0909956 | − | 0.0525363i | 0.453812 | − | 0.891098i | \(-0.350064\pi\) |
−0.544807 | + | 0.838561i | \(0.683397\pi\) | |||||||
\(380\) | −12.1163 | + | 20.9860i | −0.621553 | + | 1.07656i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 13.5833i | − | 0.694982i | ||||||
\(383\) | 6.84611 | − | 3.95261i | 0.349820 | − | 0.201969i | −0.314786 | − | 0.949163i | \(-0.601933\pi\) |
0.664606 | + | 0.747194i | \(0.268599\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.03741i | 0.103836i | ||||||||
\(386\) | 15.1697 | + | 26.2747i | 0.772117 | + | 1.33735i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.4558 | − | 8.92343i | −0.784651 | − | 0.453018i | ||||
\(389\) | −9.21171 | −0.467052 | −0.233526 | − | 0.972351i | \(-0.575026\pi\) | ||||
−0.233526 | + | 0.972351i | \(0.575026\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.43298 | 0.123041 | ||||||||
\(392\) | −16.2244 | − | 9.36719i | −0.819458 | − | 0.473114i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.46304 | − | 9.46226i | −0.275224 | − | 0.476702i | ||||
\(395\) | − | 9.31937i | − | 0.468908i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.50305 | − | 3.17719i | 0.276190 | − | 0.159458i | −0.355507 | − | 0.934674i | \(-0.615692\pi\) |
0.631697 | + | 0.775215i | \(0.282359\pi\) | |||||||
\(398\) | 51.9996i | 2.60651i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.70857 | − | 4.69138i | 0.135428 | − | 0.234569i | ||||
\(401\) | −3.61063 | − | 2.08460i | −0.180306 | − | 0.104100i | 0.407130 | − | 0.913370i | \(-0.366530\pi\) |
−0.587437 | + | 0.809270i | \(0.699863\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.86425 | − | 2.05080i | 0.242306 | − | 0.102157i | ||||
\(404\) | 64.4600 | 3.20701 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −22.4770 | + | 38.9314i | −1.11552 | + | 1.93213i | ||||
\(407\) | −0.405004 | − | 0.701487i | −0.0200753 | − | 0.0347714i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.80580 | − | 5.08403i | 0.435419 | − | 0.251389i | −0.266234 | − | 0.963909i | \(-0.585779\pi\) |
0.701652 | + | 0.712519i | \(0.252446\pi\) | |||||||
\(410\) | −0.579085 | + | 0.334335i | −0.0285989 | + | 0.0165116i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 28.5929 | + | 49.5244i | 1.40867 | + | 2.43989i | ||||
\(413\) | −0.705915 | + | 1.22268i | −0.0347358 | + | 0.0601642i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.11778 | 0.251222 | ||||||||
\(416\) | −6.90023 | − | 5.22607i | −0.338311 | − | 0.256229i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.2475 | − | 7.64847i | −0.647959 | − | 0.374099i | ||||
\(419\) | 14.2954 | − | 24.7604i | 0.698378 | − | 1.20963i | −0.270651 | − | 0.962677i | \(-0.587239\pi\) |
0.969029 | − | 0.246948i | \(-0.0794277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.01797i | 0.0983498i | 0.998790 | + | 0.0491749i | \(0.0156592\pi\) | ||||
−0.998790 | + | 0.0491749i | \(0.984341\pi\) | |||||||
\(422\) | 23.0244 | − | 13.2932i | 1.12081 | − | 0.647101i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 38.8623i | 1.88732i | ||||||||
\(425\) | 0.318632 | + | 0.551886i | 0.0154559 | + | 0.0267704i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.92747 | + | 3.99957i | 0.335244 | + | 0.193553i | ||||
\(428\) | −31.1264 | −1.50455 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.59030 | −0.0766908 | ||||||||
\(431\) | −17.8508 | − | 10.3061i | −0.859842 | − | 0.496430i | 0.00411765 | − | 0.999992i | \(-0.498689\pi\) |
−0.863959 | + | 0.503562i | \(0.832023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.7178 | + | 25.4920i | 0.707292 | + | 1.22507i | 0.965858 | + | 0.259072i | \(0.0834168\pi\) |
−0.258566 | + | 0.965994i | \(0.583250\pi\) | |||||||
\(434\) | 6.96103i | 0.334140i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.8899 | + | 21.2984i | −1.76670 | + | 1.02001i | ||||
\(437\) | 21.8841i | 1.04686i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.47602 | − | 14.6809i | 0.404538 | − | 0.700681i | −0.589729 | − | 0.807601i | \(-0.700765\pi\) |
0.994268 | + | 0.106920i | \(0.0340988\pi\) | |||||||
\(440\) | 5.14819 | + | 2.97231i | 0.245430 | + | 0.141699i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.28351 | − | 2.22756i | 0.251311 | − | 0.105954i | ||||
\(443\) | 24.1399 | 1.14692 | 0.573461 | − | 0.819233i | \(-0.305600\pi\) | ||||
0.573461 | + | 0.819233i | \(0.305600\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.28917 | + | 10.8932i | −0.298135 | + | 0.516385i | ||||
\(446\) | −26.6262 | − | 46.1180i | −1.26079 | − | 2.18375i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.99118 | + | 4.61371i | −0.377548 | + | 0.217977i | ||||
\(449\) | −18.0679 | + | 10.4315i | −0.852676 | + | 0.492293i | −0.861553 | − | 0.507668i | \(-0.830508\pi\) |
0.00887706 | + | 0.999961i | \(0.497174\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.143271 | − | 0.248153i | −0.00674637 | − | 0.0116851i | ||||
\(452\) | 14.1371 | − | 24.4861i | 0.664952 | − | 1.15173i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −39.1437 | −1.83710 | ||||||||
\(455\) | 4.14741 | − | 5.47602i | 0.194434 | − | 0.256720i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.4708 | + | 15.2830i | 1.23825 | + | 0.714906i | 0.968737 | − | 0.248089i | \(-0.0798027\pi\) |
0.269517 | + | 0.962996i | \(0.413136\pi\) | |||||||
\(458\) | −9.50894 | + | 16.4700i | −0.444324 | + | 0.769591i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 16.1402i | − | 0.752541i | ||||||
\(461\) | −4.05146 | + | 2.33911i | −0.188695 | + | 0.108943i | −0.591372 | − | 0.806399i | \(-0.701413\pi\) |
0.402676 | + | 0.915342i | \(0.368080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0011i | 0.650688i | 0.945596 | + | 0.325344i | \(0.105480\pi\) | ||||
−0.945596 | + | 0.325344i | \(0.894520\pi\) | |||||||
\(464\) | 25.6098 | + | 44.3575i | 1.18891 | + | 2.05925i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41.1811 | − | 23.7759i | −1.90768 | − | 1.10140i | ||||
\(467\) | −6.98506 | −0.323230 | −0.161615 | − | 0.986854i | \(-0.551670\pi\) | ||||
−0.161615 | + | 0.986854i | \(0.551670\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.4223 | 0.712135 | ||||||||
\(470\) | 20.4147 | + | 11.7864i | 0.941661 | + | 0.543668i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.05967 | + | 3.56745i | 0.0948039 | + | 0.164205i | ||||
\(473\) | − | 0.681482i | − | 0.0313346i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.96410 | + | 2.86603i | −0.227769 | + | 0.131502i | ||||
\(476\) | 5.13277i | 0.235260i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.9132 | − | 27.5625i | 0.727853 | − | 1.26068i | ||||
\(479\) | 14.1065 | + | 8.14438i | 0.644542 | + | 0.372126i | 0.786362 | − | 0.617766i | \(-0.211962\pi\) |
−0.141820 | + | 0.989892i | \(0.545296\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.339423 | + | 2.70985i | −0.0154764 | + | 0.123558i | ||||
\(482\) | −64.7056 | −2.94726 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 20.8343 | − | 36.0860i | 0.947012 | − | 1.64027i | ||||
\(485\) | −2.11078 | − | 3.65597i | −0.0958454 | − | 0.166009i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3559 | − | 10.0204i | 0.786471 | − | 0.454069i | −0.0522474 | − | 0.998634i | \(-0.516638\pi\) |
0.838719 | + | 0.544565i | \(0.183305\pi\) | |||||||
\(488\) | 20.2125 | − | 11.6697i | 0.914975 | − | 0.528261i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.20514 | − | 7.28351i | −0.189969 | − | 0.329035i | ||||
\(491\) | 7.89916 | − | 13.6818i | 0.356484 | − | 0.617449i | −0.630887 | − | 0.775875i | \(-0.717309\pi\) |
0.987371 | + | 0.158426i | \(0.0506420\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.02540 | −0.271370 | ||||||||
\(494\) | 20.0364 | + | 47.5241i | 0.901481 | + | 2.13821i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.86865 | + | 3.96562i | 0.308411 | + | 0.178061i | ||||
\(497\) | 9.30208 | − | 16.1117i | 0.417255 | − | 0.722708i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.24651i | 0.0558016i | 0.999611 | + | 0.0279008i | \(0.00888226\pi\) | ||||
−0.999611 | + | 0.0279008i | \(0.991118\pi\) | |||||||
\(500\) | 3.66117 | − | 2.11378i | 0.163733 | − | 0.0945311i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 18.9955i | − | 0.847809i | ||||||
\(503\) | −3.82672 | − | 6.62808i | −0.170625 | − | 0.295532i | 0.768013 | − | 0.640434i | \(-0.221245\pi\) |
−0.938639 | + | 0.344902i | \(0.887912\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2048 | + | 7.62379i | 0.587605 | + | 0.339254i | ||||
\(506\) | 10.1886 | 0.452938 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.29695 | 0.279382 | ||||||||
\(509\) | 22.2777 | + | 12.8621i | 0.987444 | + | 0.570101i | 0.904509 | − | 0.426454i | \(-0.140237\pi\) |
0.0829345 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.54035 | − | 6.13207i | −0.156616 | − | 0.271267i | ||||
\(512\) | 47.2215i | 2.08691i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.725685 | + | 0.418974i | −0.0320086 | + | 0.0184802i | ||||
\(515\) | 13.5269i | 0.596067i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.05080 | + | 8.74824i | −0.222134 | + | 0.384747i | ||||
\(518\) | −3.11879 | − | 1.80064i | −0.137032 | − | 0.0791154i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.78645 | − | 18.4686i | −0.341458 | − | 0.809900i | ||||
\(521\) | 30.1519 | 1.32098 | 0.660490 | − | 0.750835i | \(-0.270349\pi\) | ||||
0.660490 | + | 0.750835i | \(0.270349\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.96876 | + | 3.41000i | −0.0860880 | + | 0.149109i | −0.905854 | − | 0.423589i | \(-0.860770\pi\) |
0.819766 | + | 0.572698i | \(0.194103\pi\) | |||||||
\(524\) | −8.72307 | − | 15.1088i | −0.381069 | − | 0.660031i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.6182 | + | 6.70779i | −0.506579 | + | 0.292473i | ||||
\(527\) | −0.808017 | + | 0.466509i | −0.0351978 | + | 0.0203215i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.21200 | + | 7.29539i | 0.183130 | + | 0.317191i | ||||
\(530\) | −8.72307 | + | 15.1088i | −0.378906 | + | 0.656284i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −46.1682 | −2.00165 | ||||||||
\(533\) | −0.120072 | + | 0.958614i | −0.00520088 | + | 0.0415222i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.37632 | − | 3.68137i | −0.275672 | − | 0.159159i | ||||
\(536\) | 22.4990 | − | 38.9694i | 0.971809 | − | 1.68322i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.27007i | − | 0.140983i | ||||||
\(539\) | 3.12117 | − | 1.80201i | 0.134438 | − | 0.0776180i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8881i | 0.683083i | 0.939867 | + | 0.341541i | \(0.110949\pi\) | ||||
−0.939867 | + | 0.341541i | \(0.889051\pi\) | |||||||
\(542\) | −14.5305 | − | 25.1675i | −0.624138 | − | 1.08104i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.32492 | + | 0.764945i | 0.0568057 | + | 0.0327968i | ||||
\(545\) | −10.0760 | −0.431607 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.56107 | −0.280531 | −0.140266 | − | 0.990114i | \(-0.544796\pi\) | ||||
−0.140266 | + | 0.990114i | \(0.544796\pi\) | |||||||
\(548\) | −73.6249 | − | 42.5074i | −3.14510 | − | 1.81582i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.33433 | + | 2.31114i | 0.0568962 | + | 0.0985471i | ||||
\(551\) | − | 54.1972i | − | 2.30888i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.3766 | − | 8.87769i | 0.653880 | − | 0.377518i | ||||
\(554\) | − | 50.6990i | − | 2.15399i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 44.0200 | − | 76.2450i | 1.86687 | − | 3.23351i | ||||
\(557\) | −6.79835 | − | 3.92503i | −0.288055 | − | 0.166309i | 0.349009 | − | 0.937119i | \(-0.386518\pi\) |
−0.637065 | + | 0.770810i | \(0.719852\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.38724 | + | 1.83164i | −0.0586741 | + | 0.0774702i | ||||
\(560\) | 10.3208 | 0.436133 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.8163 | − | 25.6626i | 0.624988 | − | 1.08251i | ||||
\(563\) | 7.77976 | + | 13.4749i | 0.327878 | + | 0.567901i | 0.982091 | − | 0.188410i | \(-0.0603333\pi\) |
−0.654213 | + | 0.756310i | \(0.727000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.79203 | − | 3.34403i | 0.243673 | − | 0.140684i | ||||
\(566\) | −48.9552 | + | 28.2643i | −2.05774 | + | 1.18804i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −27.1409 | − | 47.0095i | −1.13881 | − | 1.97247i | ||||
\(569\) | −1.73957 | + | 3.01303i | −0.0729267 | + | 0.126313i | −0.900183 | − | 0.435512i | \(-0.856567\pi\) |
0.827256 | + | 0.561825i | \(0.189901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.5118 | 0.900240 | 0.450120 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450120 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(572\) | 15.0200 | − | 6.33252i | 0.628018 | − | 0.264776i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.10328 | − | 0.636978i | −0.0460500 | − | 0.0265870i | ||||
\(575\) | 1.90893 | − | 3.30636i | 0.0796078 | − | 0.137885i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.97608i | 0.415310i | 0.978202 | + | 0.207655i | \(0.0665831\pi\) | ||||
−0.978202 | + | 0.207655i | \(0.933417\pi\) | |||||||
\(578\) | 35.8623 | − | 20.7051i | 1.49167 | − | 0.861218i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 39.9721i | 1.65975i | ||||||||
\(581\) | 4.87523 | + | 8.44414i | 0.202259 | + | 0.350322i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.47451 | − | 3.73806i | −0.268147 | − | 0.154815i | ||||
\(584\) | −20.6595 | −0.854898 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.4482 | 1.91876 | ||||||||
\(587\) | −20.8341 | − | 12.0286i | −0.859915 | − | 0.496472i | 0.00406862 | − | 0.999992i | \(-0.498705\pi\) |
−0.863984 | + | 0.503519i | \(0.832038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.19615 | − | 7.26795i | −0.172899 | − | 0.299471i | ||||
\(590\) | 1.84926i | 0.0761328i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.55348 | + | 2.05160i | −0.146047 | + | 0.0843203i | ||||
\(593\) | 0.940219i | 0.0386102i | 0.999814 | + | 0.0193051i | \(0.00614538\pi\) | ||||
−0.999814 | + | 0.0193051i | \(0.993855\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.607061 | + | 1.05146i | −0.0248871 | + | 0.0431057i | ||||
\(596\) | −48.9417 | − | 28.2565i | −2.00473 | − | 1.15743i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −27.3842 | − | 20.7401i | −1.11982 | − | 0.848128i | ||||
\(599\) | 11.4270 | 0.466896 | 0.233448 | − | 0.972369i | \(-0.424999\pi\) | ||||
0.233448 | + | 0.972369i | \(0.424999\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.0215 | − | 31.2142i | 0.735114 | − | 1.27325i | −0.219560 | − | 0.975599i | \(-0.570462\pi\) |
0.954674 | − | 0.297655i | \(-0.0962045\pi\) | |||||||
\(602\) | −1.51493 | − | 2.62393i | −0.0617437 | − | 0.106943i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 66.9935 | − | 38.6787i | 2.72593 | − | 1.57381i | ||||
\(605\) | 8.53590 | − | 4.92820i | 0.347034 | − | 0.200360i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.9454 | − | 34.5464i | −0.809557 | − | 1.40219i | −0.913171 | − | 0.407576i | \(-0.866374\pi\) |
0.103614 | − | 0.994618i | \(-0.466959\pi\) | |||||||
\(608\) | −6.88052 | + | 11.9174i | −0.279042 | + | 0.483315i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.4775 | 0.424223 | ||||||||
\(611\) | 31.3833 | − | 13.2314i | 1.26963 | − | 0.535285i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.299187 | + | 0.172736i | 0.0120841 | + | 0.00697673i | 0.506030 | − | 0.862516i | \(-0.331113\pi\) |
−0.493946 | + | 0.869493i | \(0.664446\pi\) | |||||||
\(614\) | 3.92763 | − | 6.80286i | 0.158506 | − | 0.274541i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3258i | 0.456328i | ||||||||
\(617\) | −33.5022 | + | 19.3425i | −1.34875 | + | 0.778700i | −0.988072 | − | 0.153991i | \(-0.950787\pi\) |
−0.360676 | + | 0.932691i | \(0.617454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.8971i | − | 0.598764i | −0.954133 | − | 0.299382i | \(-0.903219\pi\) | ||
0.954133 | − | 0.299382i | \(-0.0967805\pi\) | |||||||
\(620\) | 3.09479 | + | 5.36033i | 0.124290 | + | 0.215276i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.87381 | − | 3.96859i | −0.275615 | − | 0.159126i | ||||
\(623\) | −23.9644 | −0.960113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 76.4047 | + | 44.1123i | 3.05374 | + | 1.76308i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.12019 | + | 8.86842i | 0.204318 | + | 0.353889i | ||||
\(629\) | − | 0.482694i | − | 0.0192463i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.6408 | − | 19.4225i | 1.33922 | − | 0.773198i | 0.352526 | − | 0.935802i | \(-0.385323\pi\) |
0.986691 | + | 0.162604i | \(0.0519893\pi\) | |||||||
\(632\) | − | 51.8053i | − | 2.06071i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.0140 | + | 29.4691i | −0.675713 | + | 1.17037i | ||||
\(635\) | 1.28994 | + | 0.744750i | 0.0511899 | + | 0.0295545i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.0571 | − | 1.51022i | −0.477719 | − | 0.0598370i | ||||
\(638\) | −25.2326 | −0.998967 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.44391 | + | 14.6253i | −0.333775 | + | 0.578115i | ||||
\(641\) | −18.5908 | − | 32.2003i | −0.734293 | − | 1.27183i | −0.955033 | − | 0.296501i | \(-0.904180\pi\) |
0.220739 | − | 0.975333i | \(-0.429153\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.88410 | − | 4.55189i | 0.310918 | − | 0.179509i | −0.336419 | − | 0.941712i | \(-0.609216\pi\) |
0.647337 | + | 0.762204i | \(0.275882\pi\) | |||||||
\(644\) | 26.6307 | − | 15.3753i | 1.04940 | − | 0.605870i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.55783 | − | 7.89439i | −0.179325 | − | 0.310601i | ||||
\(647\) | 9.56118 | − | 16.5605i | 0.375889 | − | 0.651059i | −0.614571 | − | 0.788862i | \(-0.710671\pi\) |
0.990460 | + | 0.137803i | \(0.0440041\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.792455 | −0.0311066 | ||||||||
\(650\) | 1.11827 | − | 8.92792i | 0.0438622 | − | 0.350182i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −58.5161 | − | 33.7843i | −2.29167 | − | 1.32309i | ||||
\(653\) | 17.3162 | − | 29.9926i | 0.677636 | − | 1.17370i | −0.298055 | − | 0.954549i | \(-0.596338\pi\) |
0.975691 | − | 0.219152i | \(-0.0703289\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.12676i | − | 0.161246i | ||||||
\(656\) | −1.25705 | + | 0.725758i | −0.0490796 | + | 0.0283361i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 44.9114i | 1.75083i | ||||||||
\(659\) | −3.34926 | − | 5.80109i | −0.130469 | − | 0.225978i | 0.793389 | − | 0.608715i | \(-0.208315\pi\) |
−0.923857 | + | 0.382737i | \(0.874982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.22004 | + | 3.01379i | 0.203036 | + | 0.117223i | 0.598071 | − | 0.801443i | \(-0.295934\pi\) |
−0.395035 | + | 0.918666i | \(0.629268\pi\) | |||||||
\(662\) | −71.8604 | −2.79294 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.4492 | 1.10404 | ||||||||
\(665\) | −9.45767 | − | 5.46039i | −0.366753 | − | 0.211745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0491 | + | 31.2620i | 0.698865 | + | 1.21047i | ||||
\(668\) | 60.8479i | 2.35428i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.4942 | − | 10.1003i | 0.675861 | − | 0.390209i | ||||
\(671\) | 4.48990i | 0.173330i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6784 | − | 20.2276i | 0.450169 | − | 0.779715i | −0.548227 | − | 0.836329i | \(-0.684697\pi\) |
0.998396 | + | 0.0566140i | \(0.0180304\pi\) | |||||||
\(674\) | −25.3923 | − | 14.6603i | −0.978075 | − | 0.564692i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −53.2604 | − | 13.5550i | −2.04848 | − | 0.521346i | ||||
\(677\) | 45.4042 | 1.74503 | 0.872513 | − | 0.488590i | \(-0.162489\pi\) | ||||
0.872513 | + | 0.488590i | \(0.162489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.02148 | − | 6.96540i | 0.154330 | − | 0.267308i | ||||
\(680\) | 1.77124 | + | 3.06787i | 0.0679239 | + | 0.117648i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.38374 | + | 1.95360i | −0.129570 | + | 0.0748073i | ||||
\(683\) | −22.0817 | + | 12.7489i | −0.844934 | + | 0.487823i | −0.858938 | − | 0.512079i | \(-0.828875\pi\) |
0.0140045 | + | 0.999902i | \(0.495542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0548 | − | 17.4155i | −0.384175 | − | 0.665411i | ||||
\(686\) | 24.6523 | − | 42.6991i | 0.941230 | − | 1.63026i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.45214 | −0.131612 | ||||||||
\(689\) | 9.79246 | + | 23.2266i | 0.373063 | + | 0.884862i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.71257 | + | 3.29815i | 0.217316 | + | 0.125468i | 0.604707 | − | 0.796448i | \(-0.293290\pi\) |
−0.387391 | + | 0.921916i | \(0.626624\pi\) | |||||||
\(692\) | −51.4683 | + | 89.1457i | −1.95653 | + | 3.38881i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.74090i | 0.179962i | ||||||||
\(695\) | 18.0352 | − | 10.4126i | 0.684115 | − | 0.394974i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.170754i | − | 0.00646778i | ||||||
\(698\) | −12.8133 | − | 22.1933i | −0.484990 | − | 0.840028i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.97531 | + | 4.02720i | 0.263642 | + | 0.152214i | ||||
\(701\) | 29.2474 | 1.10466 | 0.552329 | − | 0.833626i | \(-0.313739\pi\) | ||||
0.552329 | + | 0.833626i | \(0.313739\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.34174 | 0.163752 | ||||||||
\(704\) | −4.48542 | − | 2.58966i | −0.169051 | − | 0.0976015i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.998937 | + | 1.73021i | 0.0375955 | + | 0.0651173i | ||||
\(707\) | 29.0499i | 1.09253i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.46865 | + | 5.46673i | −0.355603 | + | 0.205307i | −0.667150 | − | 0.744923i | \(-0.732486\pi\) |
0.311548 | + | 0.950231i | \(0.399153\pi\) | |||||||
\(710\) | − | 24.3683i | − | 0.914527i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −34.9608 | + | 60.5538i | −1.31021 | + | 2.26935i | ||||
\(713\) | 4.84084 | + | 2.79486i | 0.181291 | + | 0.104668i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.82584 | + | 0.479208i | 0.143078 | + | 0.0179214i | ||||
\(716\) | −16.0152 | −0.598516 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.1476 | + | 17.5762i | −0.378706 | + | 0.655938i | ||||
\(719\) | −8.02989 | − | 13.9082i | −0.299464 | − | 0.518688i | 0.676549 | − | 0.736398i | \(-0.263475\pi\) |
−0.976014 | + | 0.217710i | \(0.930141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3189 | + | 12.8858i | −0.831199 | + | 0.479893i | ||||
\(722\) | 29.9461 | − | 17.2894i | 1.11448 | − | 0.643444i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.9416 | + | 31.0758i | 0.666796 | + | 1.15492i | ||||
\(725\) | −4.72756 | + | 8.18837i | −0.175577 | + | 0.304108i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.3754 | −1.90541 | −0.952704 | − | 0.303900i | \(-0.901711\pi\) | ||||
−0.952704 | + | 0.303900i | \(0.901711\pi\) | |||||||
\(728\) | 23.0550 | − | 30.4406i | 0.854475 | − | 1.12820i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.03198 | − | 4.63726i | −0.297277 | − | 0.171633i | ||||
\(731\) | 0.203052 | − | 0.351697i | 0.00751016 | − | 0.0130080i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 9.82358i | − | 0.362842i | −0.983406 | − | 0.181421i | \(-0.941930\pi\) | ||
0.983406 | − | 0.181421i | \(-0.0580697\pi\) | |||||||
\(734\) | 44.3613 | − | 25.6120i | 1.63741 | − | 0.945357i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 9.16560i | − | 0.337848i | ||||||
\(737\) | 4.32824 | + | 7.49673i | 0.159433 | + | 0.276146i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.5082 | + | 24.5421i | 1.56369 | + | 0.902797i | 0.996879 | + | 0.0789487i | \(0.0251563\pi\) |
0.566811 | + | 0.823848i | \(0.308177\pi\) | |||||||
\(740\) | −3.20216 | −0.117714 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33.2386 | −1.22023 | ||||||||
\(743\) | 35.3663 | + | 20.4188i | 1.29746 | + | 0.749091i | 0.979966 | − | 0.199167i | \(-0.0638237\pi\) |
0.317499 | + | 0.948259i | \(0.397157\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.68388 | − | 11.5768i | −0.244878 | − | 0.424142i | ||||
\(746\) | 44.4346i | 1.62687i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.49503 | + | 1.44050i | −0.0912272 | + | 0.0526700i | ||||
\(749\) | − | 14.0276i | − | 0.512557i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.36340 | + | 2.36148i | −0.0497512 | + | 0.0861716i | −0.889829 | − | 0.456295i | \(-0.849176\pi\) |
0.840077 | + | 0.542467i | \(0.182510\pi\) | |||||||
\(752\) | 44.3154 | + | 25.5855i | 1.61601 | + | 0.933006i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 67.8184 | + | 51.3641i | 2.46980 | + | 1.87057i | ||||
\(755\) | 18.2984 | 0.665946 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.40301 | + | 12.8224i | −0.269067 | + | 0.466038i | −0.968621 | − | 0.248542i | \(-0.920049\pi\) |
0.699554 | + | 0.714580i | \(0.253382\pi\) | |||||||
\(758\) | −2.55234 | − | 4.42078i | −0.0927051 | − | 0.160570i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −27.5949 | + | 15.9319i | −1.00097 | + | 0.577911i | ||||
\(761\) | −9.84575 | + | 5.68445i | −0.356908 | + | 0.206061i | −0.667724 | − | 0.744409i | \(-0.732731\pi\) |
0.310815 | + | 0.950470i | \(0.399398\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.59843 | − | 16.6250i | −0.347486 | − | 0.601864i | ||||
\(764\) | 11.5055 | − | 19.9281i | 0.416255 | − | 0.720975i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.7275 | 0.712784 | ||||||||
\(767\) | 2.12991 | + | 1.61314i | 0.0769065 | + | 0.0582472i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.2352 | + | 10.5281i | 0.657579 | + | 0.379654i | 0.791354 | − | 0.611358i | \(-0.209377\pi\) |
−0.133775 | + | 0.991012i | \(0.542710\pi\) | |||||||
\(770\) | −2.54219 | + | 4.40320i | −0.0916142 | + | 0.158680i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 51.3970i | 1.84982i | ||||||||
\(773\) | −12.1961 | + | 7.04144i | −0.438664 | + | 0.253263i | −0.703031 | − | 0.711159i | \(-0.748170\pi\) |
0.264367 | + | 0.964422i | \(0.414837\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.46410i | 0.0525921i | ||||||||
\(776\) | −11.7336 | − | 20.3231i | −0.421210 | − | 0.729558i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.9081 | − | 11.4940i | −0.713740 | − | 0.412078i | ||||
\(779\) | 1.53590 | 0.0550293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.4425 | 0.373660 | ||||||||
\(782\) | 5.25809 | + | 3.03576i | 0.188029 | + | 0.108558i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.12832 | − | 15.8107i | −0.326011 | − | 0.564668i | ||||
\(785\) | 2.42229i | 0.0864552i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.5998 | + | 16.5121i | −1.01947 | + | 0.588593i | −0.913951 | − | 0.405823i | \(-0.866985\pi\) |
−0.105522 | + | 0.994417i | \(0.533651\pi\) | |||||||
\(788\) | − | 18.5095i | − | 0.659374i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.6283 | − | 20.1408i | 0.413716 | − | 0.716576i | ||||
\(791\) | 11.0350 | + | 6.37109i | 0.392361 | + | 0.226530i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.13974 | − | 12.0676i | 0.324562 | − | 0.428534i | ||||
\(794\) | 15.8574 | 0.562758 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.0454 | + | 76.2890i | −1.56115 | + | 2.70399i | ||||
\(797\) | 8.47079 | + | 14.6718i | 0.300051 | + | 0.519703i | 0.976147 | − | 0.217110i | \(-0.0696630\pi\) |
−0.676096 | + | 0.736813i | \(0.736330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.21319 | + | 3.00984i | −0.184429 | + | 0.106480i | ||||
\(800\) | 2.07908 | − | 1.20036i | 0.0735067 | − | 0.0424391i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.20213 | − | 9.01036i | −0.183694 | − | 0.318167i | ||||
\(803\) | 1.98719 | − | 3.44191i | 0.0701263 | − | 0.121462i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.27382 | 0.256369 | ||||||||
\(806\) | 13.0714 | + | 1.63726i | 0.460420 | + | 0.0576701i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 73.4039 | + | 42.3798i | 2.58234 | + | 1.49092i | ||||
\(809\) | −25.8818 | + | 44.8285i | −0.909954 | + | 1.57609i | −0.0958292 | + | 0.995398i | \(0.530550\pi\) |
−0.814125 | + | 0.580689i | \(0.802783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.6699i | 0.796047i | 0.917375 | + | 0.398023i | \(0.130304\pi\) | ||||
−0.917375 | + | 0.398023i | \(0.869696\pi\) | |||||||
\(812\) | −65.9524 | + | 38.0776i | −2.31448 | + | 1.33626i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 2.02138i | − | 0.0708494i | ||||||
\(815\) | −7.99144 | − | 13.8416i | −0.279928 | − | 0.484849i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.16344 | + | 1.82641i | 0.110675 | + | 0.0638981i | ||||
\(818\) | 25.3745 | 0.887198 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.13277 | −0.0395581 | ||||||||
\(821\) | 24.8230 | + | 14.3315i | 0.866328 | + | 0.500174i | 0.866126 | − | 0.499826i | \(-0.166603\pi\) |
0.000201482 | 1.00000i | \(0.499936\pi\) | ||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.9164 | − | 22.3718i | −0.450236 | − | 0.779831i | 0.548165 | − | 0.836371i | \(-0.315327\pi\) |
−0.998400 | + | 0.0565391i | \(0.981993\pi\) | |||||||
\(824\) | 75.1946i | 2.61953i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.05121 | + | 1.76162i | −0.106165 | + | 0.0612945i | ||||
\(827\) | − | 16.0820i | − | 0.559227i | −0.960113 | − | 0.279613i | \(-0.909794\pi\) | ||
0.960113 | − | 0.279613i | \(-0.0902063\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.2909 | + | 19.5564i | −0.392149 | + | 0.679222i | −0.992733 | − | 0.120340i | \(-0.961602\pi\) |
0.600584 | + | 0.799562i | \(0.294935\pi\) | |||||||
\(830\) | 11.0604 | + | 6.38573i | 0.383912 | + | 0.221652i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.78404 | + | 16.0910i | 0.235194 | + | 0.557854i | ||||
\(833\) | 2.14768 | 0.0744128 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.19658 | + | 12.4648i | −0.249048 | + | 0.431364i | ||||
\(836\) | −12.9570 | − | 22.4422i | −0.448128 | − | 0.776181i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61.7898 | − | 35.6744i | 2.13449 | − | 1.23235i | ||||
\(839\) | −15.4533 | + | 8.92198i | −0.533508 | + | 0.308021i | −0.742444 | − | 0.669908i | \(-0.766333\pi\) |
0.208936 | + | 0.977929i | \(0.433000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30.1996 | − | 52.3073i | −1.04137 | − | 1.80370i | ||||
\(842\) | −2.51793 | + | 4.36118i | −0.0867736 | + | 0.150296i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 45.0390 | 1.55031 | ||||||||
\(845\) | −9.30735 | − | 9.07597i | −0.320183 | − | 0.312223i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.2627 | + | 9.38927i | 0.558793 | + | 0.322619i | ||||
\(848\) | −18.9356 | + | 32.7975i | −0.650252 | + | 1.12627i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.59030i | 0.0545467i | ||||||||
\(851\) | −2.50440 | + | 1.44591i | −0.0858497 | + | 0.0495653i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.7936i | − | 0.677720i | −0.940837 | − | 0.338860i | \(-0.889959\pi\) | ||
0.940837 | − | 0.338860i | \(-0.110041\pi\) | |||||||
\(854\) | 9.98097 | + | 17.2875i | 0.341542 | + | 0.591568i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −35.4452 | − | 20.4643i | −1.21149 | − | 0.699456i | ||||
\(857\) | −11.7302 | −0.400696 | −0.200348 | − | 0.979725i | \(-0.564207\pi\) | ||||
−0.200348 | + | 0.979725i | \(0.564207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.37452 | 0.183376 | 0.0916882 | − | 0.995788i | \(-0.470774\pi\) | ||||
0.0916882 | + | 0.995788i | \(0.470774\pi\) | |||||||
\(860\) | −2.33313 | − | 1.34703i | −0.0795591 | − | 0.0459335i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.7191 | − | 44.5467i | −0.875995 | − | 1.51727i | ||||
\(863\) | 25.3234i | 0.862017i | 0.902348 | + | 0.431008i | \(0.141842\pi\) | ||||
−0.902348 | + | 0.431008i | \(0.858158\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0868 | + | 12.1745i | −0.716973 | + | 0.413944i | ||||
\(866\) | 73.4567i | 2.49616i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.89623 | + | 10.2126i | −0.200131 | + | 0.346637i | ||||
\(869\) | 8.63084 | + | 4.98302i | 0.292781 | + | 0.169037i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.62739 | − | 28.9599i | 0.122909 | − | 0.981268i | ||||
\(872\) | −56.0112 | −1.89678 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27.3060 | + | 47.2954i | −0.923640 | + | 1.59979i | ||||
\(875\) | 0.952606 | + | 1.64996i | 0.0322040 | + | 0.0557789i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.9194 | − | 10.3458i | 0.605095 | − | 0.349352i | −0.165949 | − | 0.986134i | \(-0.553069\pi\) |
0.771043 | + | 0.636783i | \(0.219735\pi\) | |||||||
\(878\) | 36.6363 | − | 21.1520i | 1.23642 | − | 0.713845i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.89651 | + | 5.01691i | 0.0976414 | + | 0.169120i | ||||
\(881\) | −24.1997 | + | 41.9150i | −0.815307 | + | 1.41215i | 0.0937999 | + | 0.995591i | \(0.470099\pi\) |
−0.909107 | + | 0.416562i | \(0.863235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.8550 | −1.54314 | −0.771572 | − | 0.636142i | \(-0.780529\pi\) | ||||
−0.771572 | + | 0.636142i | \(0.780529\pi\) | |||||||
\(884\) | 9.63829 | + | 1.20725i | 0.324171 | + | 0.0406042i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 52.1705 | + | 30.1207i | 1.75270 | + | 1.01192i | ||||
\(887\) | −0.541169 | + | 0.937332i | −0.0181707 | + | 0.0314725i | −0.874968 | − | 0.484181i | \(-0.839118\pi\) |
0.856797 | + | 0.515654i | \(0.172451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.83781i | 0.0951772i | ||||||||
\(890\) | −27.1840 | + | 15.6947i | −0.911208 | + | 0.526086i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 90.2133i | − | 3.02056i | ||||||
\(893\) | −27.0729 | − | 46.8916i | −0.905959 | − | 1.56917i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.28075 | − | 1.89414i | −0.109663 | − | 0.0633142i | ||||
\(896\) | −32.1749 | −1.07489 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.0637 | −1.73739 | ||||||||
\(899\) | −11.9886 | − | 6.92163i | −0.399842 | − | 0.230849i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.22756 | − | 3.85824i | −0.0742107 | − | 0.128537i | ||||
\(902\) | − | 0.715068i | − | 0.0238092i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.1973 | − | 18.5891i | 1.07086 | − | 0.618264i | ||||
\(905\) | 8.48794i | 0.282149i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.7653 | + | 39.4307i | −0.755910 | + | 1.30928i | 0.189010 | + | 0.981975i | \(0.439472\pi\) |
−0.944920 | + | 0.327300i | \(0.893861\pi\) | |||||||
\(908\) | −57.4279 | − | 33.1560i | −1.90581 | − | 1.10032i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.7960 | − | 6.65968i | 0.523632 | − | 0.220766i | ||||
\(911\) | −39.7417 | −1.31670 | −0.658350 | − | 0.752712i | \(-0.728745\pi\) | ||||
−0.658350 | + | 0.752712i | \(0.728745\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.73645 | + | 4.73967i | −0.0905632 | + | 0.156860i | ||||
\(914\) | 38.1387 | + | 66.0582i | 1.26152 | + | 2.18501i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.9012 | + | 16.1088i | −0.921883 | + | 0.532250i | ||||
\(917\) | 6.80900 | − | 3.93118i | 0.224853 | − | 0.129819i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.4969 | − | 40.6978i | −0.775091 | − | 1.34250i | −0.934743 | − | 0.355323i | \(-0.884371\pi\) |
0.159653 | − | 0.987173i | \(-0.448963\pi\) | |||||||
\(920\) | 10.6115 | − | 18.3797i | 0.349851 | − | 0.605960i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.6745 | −0.384481 | ||||||||
\(923\) | −28.0665 | − | 21.2569i | −0.923821 | − | 0.699680i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.655970 | − | 0.378725i | −0.0215682 | − | 0.0124524i | ||||
\(926\) | −17.4700 | + | 30.2589i | −0.574099 | + | 0.994369i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.6991i | 0.745134i | ||||||||
\(929\) | 13.1821 | − | 7.61066i | 0.432489 | − | 0.249698i | −0.267917 | − | 0.963442i | \(-0.586335\pi\) |
0.700406 | + | 0.713744i | \(0.253002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.3180i | 0.633121i | ||||||||
\(932\) | −40.2780 | − | 69.7635i | −1.31935 | − | 2.28518i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.0959 | − | 8.71564i | −0.493954 | − | 0.285184i | ||||
\(935\) | −0.681482 | −0.0222869 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.07285 | 0.198392 | 0.0991958 | − | 0.995068i | \(-0.468373\pi\) | ||||
0.0991958 | + | 0.995068i | \(0.468373\pi\) | |||||||
\(938\) | 33.3302 | + | 19.2432i | 1.08827 | + | 0.628313i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.9670 | + | 34.5839i | 0.651253 | + | 1.12800i | ||||
\(941\) | 0.0496576i | 0.00161879i | 1.00000 | 0.000809396i | \(0.000257639\pi\) | |||||
−1.00000 | 0.000809396i | \(0.999742\pi\) | ||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.885936 | + | 0.511495i | −0.0288500 | + | 0.0166566i | ||||
\(944\) | 4.01429i | 0.130654i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.850322 | − | 1.47280i | 0.0276464 | − | 0.0478849i | ||||
\(947\) | 16.1584 | + | 9.32907i | 0.525078 | + | 0.303154i | 0.739010 | − | 0.673695i | \(-0.235294\pi\) |
−0.213932 | + | 0.976849i | \(0.568627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.3475 | + | 5.20576i | −0.400816 | + | 0.168986i | ||||
\(950\) | −14.3044 | −0.464095 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.37458 | + | 5.84495i | −0.109371 | + | 0.189436i | ||||
\(953\) | 0.764764 | + | 1.32461i | 0.0247731 | + | 0.0429083i | 0.878146 | − | 0.478392i | \(-0.158780\pi\) |
−0.853373 | + | 0.521301i | \(0.825447\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.71386 | − | 2.72155i | 0.152537 | − | 0.0880673i | ||||
\(956\) | 46.6927 | − | 26.9581i | 1.51015 | − | 0.871886i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.3244 | + | 35.2028i | 0.656650 | + | 1.13735i | ||||
\(959\) | 19.1566 | − | 33.1802i | 0.618598 | − | 1.07144i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | −4.11477 | + | 5.43293i | −0.132666 | + | 0.175165i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −94.9299 | − | 54.8078i | −3.05749 | − | 1.76524i | ||||
\(965\) | −6.07880 | + | 10.5288i | −0.195683 | + | 0.338934i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.1716i | 1.03457i | 0.855813 | + | 0.517285i | \(0.173057\pi\) | ||||
−0.855813 | + | 0.517285i | \(0.826943\pi\) | |||||||
\(968\) | 47.4501 | − | 27.3953i | 1.52510 | − | 0.880519i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 10.5349i | − | 0.338256i | ||||||
\(971\) | −8.62705 | − | 14.9425i | −0.276855 | − | 0.479527i | 0.693746 | − | 0.720219i | \(-0.255959\pi\) |
−0.970601 | + | 0.240692i | \(0.922626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.3609 | + | 19.8383i | 1.10156 | + | 0.635986i | ||||
\(974\) | 50.0122 | 1.60249 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.7442 | 0.728023 | ||||||||
\(977\) | 13.6164 | + | 7.86142i | 0.435626 | + | 0.251509i | 0.701741 | − | 0.712432i | \(-0.252407\pi\) |
−0.266114 | + | 0.963942i | \(0.585740\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.72557 | − | 11.6490i | −0.214950 | − | 0.372304i | ||||
\(980\) | − | 14.2476i | − | 0.455122i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 34.1429 | − | 19.7124i | 1.08954 | − | 0.629049i | ||||
\(983\) | 38.5356i | 1.22910i | 0.788880 | + | 0.614548i | \(0.210662\pi\) | ||||
−0.788880 | + | 0.614548i | \(0.789338\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.18915 | − | 3.79172i | 0.0697521 | − | 0.120814i | ||||
\(986\) | −13.0219 | − | 7.51821i | −0.414703 | − | 0.239429i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.8590 | + | 86.6944i | −0.345469 | + | 2.75812i | ||||
\(989\) | −2.43298 | −0.0773642 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.29571 | + | 7.44040i | −0.136458 | + | 0.236352i | −0.926153 | − | 0.377147i | \(-0.876905\pi\) |
0.789696 | + | 0.613499i | \(0.210238\pi\) | |||||||
\(992\) | 1.75745 | + | 3.04399i | 0.0557991 | + | 0.0966468i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 40.2068 | − | 23.2134i | 1.27528 | − | 0.736285i | ||||
\(995\) | −18.0456 | + | 10.4186i | −0.572085 | + | 0.330293i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.2687 | + | 17.7859i | 0.325213 | + | 0.563285i | 0.981555 | − | 0.191178i | \(-0.0612308\pi\) |
−0.656343 | + | 0.754463i | \(0.727897\pi\) | |||||||
\(998\) | −1.55534 | + | 2.69393i | −0.0492335 | + | 0.0852750i | ||||
\(999\) | 0 | 0 |
(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 | 585.2.bu.c.316.4 | 8 | ||
3.2 | odd | 2 | 65.2.m.a.56.1 | yes | 8 | ||
12.11 | even | 2 | 1040.2.da.b.641.1 | 8 | |||
13.6 | odd | 12 | 7605.2.a.cf.1.1 | 4 | |||
13.7 | odd | 12 | 7605.2.a.cj.1.4 | 4 | |||
13.10 | even | 6 | inner | 585.2.bu.c.361.4 | 8 | ||
15.2 | even | 4 | 325.2.m.c.199.4 | 8 | |||
15.8 | even | 4 | 325.2.m.b.199.1 | 8 | |||
15.14 | odd | 2 | 325.2.n.d.251.4 | 8 | |||
39.2 | even | 12 | 845.2.e.m.146.1 | 8 | |||
39.5 | even | 4 | 845.2.e.m.191.1 | 8 | |||
39.8 | even | 4 | 845.2.e.n.191.4 | 8 | |||
39.11 | even | 12 | 845.2.e.n.146.4 | 8 | |||
39.17 | odd | 6 | 845.2.c.g.506.1 | 8 | |||
39.20 | even | 12 | 845.2.a.l.1.1 | 4 | |||
39.23 | odd | 6 | 65.2.m.a.36.1 | ✓ | 8 | ||
39.29 | odd | 6 | 845.2.m.g.361.4 | 8 | |||
39.32 | even | 12 | 845.2.a.m.1.4 | 4 | |||
39.35 | odd | 6 | 845.2.c.g.506.8 | 8 | |||
39.38 | odd | 2 | 845.2.m.g.316.4 | 8 | |||
156.23 | even | 6 | 1040.2.da.b.881.1 | 8 | |||
195.23 | even | 12 | 325.2.m.c.49.4 | 8 | |||
195.59 | even | 12 | 4225.2.a.bl.1.4 | 4 | |||
195.62 | even | 12 | 325.2.m.b.49.1 | 8 | |||
195.149 | even | 12 | 4225.2.a.bi.1.1 | 4 | |||
195.179 | odd | 6 | 325.2.n.d.101.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.1 | ✓ | 8 | 39.23 | odd | 6 | ||
65.2.m.a.56.1 | yes | 8 | 3.2 | odd | 2 | ||
325.2.m.b.49.1 | 8 | 195.62 | even | 12 | |||
325.2.m.b.199.1 | 8 | 15.8 | even | 4 | |||
325.2.m.c.49.4 | 8 | 195.23 | even | 12 | |||
325.2.m.c.199.4 | 8 | 15.2 | even | 4 | |||
325.2.n.d.101.4 | 8 | 195.179 | odd | 6 | |||
325.2.n.d.251.4 | 8 | 15.14 | odd | 2 | |||
585.2.bu.c.316.4 | 8 | 1.1 | even | 1 | trivial | ||
585.2.bu.c.361.4 | 8 | 13.10 | even | 6 | inner | ||
845.2.a.l.1.1 | 4 | 39.20 | even | 12 | |||
845.2.a.m.1.4 | 4 | 39.32 | even | 12 | |||
845.2.c.g.506.1 | 8 | 39.17 | odd | 6 | |||
845.2.c.g.506.8 | 8 | 39.35 | odd | 6 | |||
845.2.e.m.146.1 | 8 | 39.2 | even | 12 | |||
845.2.e.m.191.1 | 8 | 39.5 | even | 4 | |||
845.2.e.n.146.4 | 8 | 39.11 | even | 12 | |||
845.2.e.n.191.4 | 8 | 39.8 | even | 4 | |||
845.2.m.g.316.4 | 8 | 39.38 | odd | 2 | |||
845.2.m.g.361.4 | 8 | 39.29 | odd | 6 | |||
1040.2.da.b.641.1 | 8 | 12.11 | even | 2 | |||
1040.2.da.b.881.1 | 8 | 156.23 | even | 6 | |||
4225.2.a.bi.1.1 | 4 | 195.149 | even | 12 | |||
4225.2.a.bl.1.4 | 4 | 195.59 | even | 12 | |||
7605.2.a.cf.1.1 | 4 | 13.6 | odd | 12 | |||
7605.2.a.cj.1.4 | 4 | 13.7 | odd | 12 |