Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(193,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1300.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bs (of order \(12\), degree \(4\), 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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 30 x^{18} + 371 x^{16} + 2460 x^{14} + 9517 x^{12} + 21870 x^{10} + 29001 x^{8} + 20400 x^{6} + 6399 x^{4} + 666 x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 193.2 | ||
Root | \(-1.14923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.193 |
Dual form | 1300.2.bs.d.357.2 |
$q$-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 \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.387600 | + | 1.44654i | −0.223781 | + | 0.835162i | 0.759108 | + | 0.650965i | \(0.225635\pi\) |
−0.982889 | + | 0.184198i | \(0.941031\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.10545 | − | 1.21558i | −0.795787 | − | 0.459448i | 0.0462092 | − | 0.998932i | \(-0.485286\pi\) |
−0.841996 | + | 0.539484i | \(0.818619\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.655821 | + | 0.378639i | 0.218607 | + | 0.126213i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.60249 | − | 0.697334i | −0.784679 | − | 0.210254i | −0.155832 | − | 0.987784i | \(-0.549806\pi\) |
−0.628847 | + | 0.777529i | \(0.716473\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.57773 | − | 0.447059i | 0.992283 | − | 0.123992i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.05137 | + | 1.62146i | −1.46767 | + | 0.393262i | −0.902133 | − | 0.431459i | \(-0.857999\pi\) |
−0.565540 | + | 0.824721i | \(0.691332\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00046 | − | 3.73376i | −0.229521 | − | 0.856583i | −0.980543 | − | 0.196306i | \(-0.937105\pi\) |
0.751022 | − | 0.660277i | \(-0.229561\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.57447 | − | 2.57447i | 0.561795 | − | 0.561795i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.14784 | + | 0.307564i | 0.239342 | + | 0.0641315i | 0.376496 | − | 0.926418i | \(-0.377129\pi\) |
−0.137154 | + | 0.990550i | \(0.543796\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.97874 | + | 3.97874i | −0.765710 | + | 0.765710i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.29270 | + | 3.05574i | −0.982830 | + | 0.567437i | −0.903123 | − | 0.429382i | \(-0.858732\pi\) |
−0.0797063 | + | 0.996818i | \(0.525398\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.23000 | − | 6.23000i | −1.11894 | − | 1.11894i | −0.991897 | − | 0.127043i | \(-0.959451\pi\) |
−0.127043 | − | 0.991897i | \(-0.540549\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.01745 | − | 3.49432i | 0.351193 | − | 0.608283i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.69111 | − | 3.86311i | 1.10001 | − | 0.635092i | 0.163787 | − | 0.986496i | \(-0.447629\pi\) |
0.936224 | + | 0.351404i | \(0.114296\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.740038 | + | 5.34862i | −0.118501 | + | 0.856465i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.913943 | − | 3.41088i | 0.142734 | − | 0.532690i | −0.857112 | − | 0.515130i | \(-0.827744\pi\) |
0.999846 | − | 0.0175599i | \(-0.00558976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.17207 | − | 4.37424i | −0.178740 | − | 0.667066i | −0.995884 | − | 0.0906330i | \(-0.971111\pi\) |
0.817145 | − | 0.576433i | \(-0.195556\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.81282i | − | 0.993752i | −0.867822 | − | 0.496876i | \(-0.834480\pi\) | ||
0.867822 | − | 0.496876i | \(-0.165520\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.544711 | − | 0.943467i | −0.0778159 | − | 0.134781i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 9.38205i | − | 1.31375i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.88693 | − | 4.88693i | −0.671272 | − | 0.671272i | 0.286737 | − | 0.958009i | \(-0.407429\pi\) |
−0.958009 | + | 0.286737i | \(0.907429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.78882 | 0.766748 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.04287 | + | 2.42303i | −1.17728 | + | 0.315452i | −0.793848 | − | 0.608116i | \(-0.791925\pi\) |
−0.383434 | + | 0.923568i | \(0.625259\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.87808 | + | 8.44908i | −0.624574 | + | 1.08179i | 0.364049 | + | 0.931380i | \(0.381394\pi\) |
−0.988623 | + | 0.150415i | \(0.951939\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.920534 | − | 1.59441i | −0.115976 | − | 0.200877i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.507281 | − | 0.878637i | −0.0619743 | − | 0.107343i | 0.833374 | − | 0.552710i | \(-0.186406\pi\) |
−0.895348 | + | 0.445368i | \(0.853073\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.889809 | + | 1.54120i | −0.107120 | + | 0.185538i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5637 | − | 2.83054i | 1.25368 | − | 0.335924i | 0.429926 | − | 0.902864i | \(-0.358540\pi\) |
0.823759 | + | 0.566941i | \(0.191873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.06732 | 1.06125 | 0.530625 | − | 0.847607i | \(-0.321957\pi\) | ||||
0.530625 | + | 0.847607i | \(0.321957\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.63174 | + | 4.63174i | 0.527836 | + | 0.527836i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.6191i | − | 1.30725i | −0.756820 | − | 0.653623i | \(-0.773248\pi\) | ||
0.756820 | − | 0.653623i | \(-0.226752\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.07735 | − | 5.33013i | −0.341928 | − | 0.592236i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.09215i | 0.119879i | 0.998202 | + | 0.0599397i | \(0.0190909\pi\) | ||||
−0.998202 | + | 0.0599397i | \(0.980909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.36881 | − | 8.84053i | −0.253963 | − | 0.947804i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.29560 | + | 4.83523i | −0.137333 | + | 0.512533i | 0.862644 | + | 0.505811i | \(0.168807\pi\) |
−0.999977 | + | 0.00672267i | \(0.997860\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.07618 | − | 3.40777i | −0.846613 | − | 0.357231i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.4267 | − | 6.59721i | 1.18489 | − | 0.684099i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.38144 | + | 2.39272i | −0.140264 | + | 0.242944i | −0.927596 | − | 0.373585i | \(-0.878128\pi\) |
0.787332 | + | 0.616529i | \(0.211462\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.44273 | − | 1.44273i | −0.145000 | − | 0.145000i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.2722 | − | 6.50799i | 1.12162 | − | 0.647569i | 0.179808 | − | 0.983702i | \(-0.442452\pi\) |
0.941815 | + | 0.336133i | \(0.109119\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.42536 | − | 3.42536i | 0.337511 | − | 0.337511i | −0.517919 | − | 0.855430i | \(-0.673293\pi\) |
0.855430 | + | 0.517919i | \(0.173293\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.28992 | + | 0.613583i | 0.221375 | + | 0.0593173i | 0.367802 | − | 0.929904i | \(-0.380111\pi\) |
−0.146427 | + | 0.989222i | \(0.546777\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.27846 | + | 2.27846i | −0.218237 | + | 0.218237i | −0.807755 | − | 0.589518i | \(-0.799318\pi\) |
0.589518 | + | 0.807755i | \(0.299318\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.99469 | + | 11.1763i | 0.284243 | + | 1.06081i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3698 | + | 3.58242i | −1.25772 | + | 0.337006i | −0.825315 | − | 0.564672i | \(-0.809003\pi\) |
−0.432408 | + | 0.901678i | \(0.642336\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.51562 | + | 1.06148i | 0.232570 | + | 0.0981334i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.7119 | + | 3.94204i | 1.34864 | + | 0.361366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.23962 | − | 1.87040i | −0.294511 | − | 0.170036i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.57974 | + | 2.64412i | 0.412942 | + | 0.238412i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.13358 | − | 4.23059i | 0.100589 | − | 0.375404i | −0.897218 | − | 0.441587i | \(-0.854416\pi\) |
0.997807 | + | 0.0661832i | \(0.0210822\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.78183 | 0.597107 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1470 | 1.06129 | 0.530643 | − | 0.847596i | \(-0.321951\pi\) | ||||
0.530643 | + | 0.847596i | \(0.321951\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43228 | + | 9.07740i | −0.210906 | + | 0.787110i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.3932 | − | 7.15524i | −1.05883 | − | 0.611313i | −0.133719 | − | 0.991019i | \(-0.542692\pi\) |
−0.925107 | + | 0.379706i | \(0.876025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2937 | − | 7.67514i | −1.12756 | − | 0.650997i | −0.184239 | − | 0.982881i | \(-0.558982\pi\) |
−0.943320 | + | 0.331885i | \(0.892315\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.85504 | + | 2.64065i | 0.829944 | + | 0.222383i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.62273 | − | 1.33141i | −0.804694 | − | 0.111338i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.57590 | − | 0.422260i | 0.129978 | − | 0.0348274i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.861750 | − | 3.21610i | −0.0705973 | − | 0.263473i | 0.921602 | − | 0.388137i | \(-0.126881\pi\) |
−0.992199 | + | 0.124664i | \(0.960215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.6691 | + | 14.6691i | −1.19375 | + | 1.19375i | −0.217749 | + | 0.976005i | \(0.569871\pi\) |
−0.976005 | + | 0.217749i | \(0.930129\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.58257 | − | 1.22789i | −0.370479 | − | 0.0992694i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.7756 | + | 14.7756i | −1.17922 | + | 1.17922i | −0.199281 | + | 0.979942i | \(0.563861\pi\) |
−0.979942 | + | 0.199281i | \(0.936139\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.96334 | − | 5.17499i | 0.710839 | − | 0.410403i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.04286 | − | 2.04286i | −0.161000 | − | 0.161000i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.46942 | − | 7.74127i | 0.350072 | − | 0.606343i | −0.636190 | − | 0.771533i | \(-0.719490\pi\) |
0.986262 | + | 0.165190i | \(0.0528237\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.7729 | + | 9.10649i | −1.22054 | + | 0.704681i | −0.965034 | − | 0.262125i | \(-0.915577\pi\) |
−0.255510 | + | 0.966806i | \(0.582243\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6003 | − | 3.19891i | 0.969252 | − | 0.246070i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.757624 | − | 2.82749i | 0.0579370 | − | 0.216224i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.469884 | + | 1.75363i | 0.0357246 | + | 0.133326i | 0.981485 | − | 0.191539i | \(-0.0613478\pi\) |
−0.945760 | + | 0.324865i | \(0.894681\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 14.0201i | − | 1.05381i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.09987 | − | 15.7614i | −0.680156 | − | 1.17807i | −0.974933 | − | 0.222499i | \(-0.928578\pi\) |
0.294776 | − | 0.955566i | \(-0.404755\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.4351i | − | 1.29594i | −0.761667 | − | 0.647969i | \(-0.775619\pi\) | ||
0.761667 | − | 0.647969i | \(-0.224381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.3312 | − | 10.3312i | −0.763706 | − | 0.763706i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8793 | 1.23434 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.2136 | − | 3.54056i | 0.961145 | − | 0.257538i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.5403 | + | 18.2564i | −0.762672 | + | 1.32099i | 0.178796 | + | 0.983886i | \(0.442780\pi\) |
−0.941469 | + | 0.337101i | \(0.890554\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.68786 | + | 16.7799i | 0.697348 | + | 1.20784i | 0.969383 | + | 0.245554i | \(0.0789700\pi\) |
−0.272035 | + | 0.962287i | \(0.587697\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.18595 | + | 10.7144i | 0.440731 | + | 0.763368i | 0.997744 | − | 0.0671359i | \(-0.0213861\pi\) |
−0.557013 | + | 0.830504i | \(0.688053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.08783 | + | 8.81238i | −0.360667 | + | 0.624693i | −0.988071 | − | 0.154001i | \(-0.950784\pi\) |
0.627404 | + | 0.778694i | \(0.284117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.46761 | − | 0.393245i | 0.103517 | − | 0.0277373i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.8580 | 1.04283 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.636325 | + | 0.636325i | 0.0442277 | + | 0.0442277i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.4147i | 0.720400i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.67864 | + | 15.0319i | 0.597463 | + | 1.03484i | 0.993194 | + | 0.116469i | \(0.0371577\pi\) |
−0.395732 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.3780i | 1.12220i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.54388 | + | 20.6901i | 0.376343 | + | 1.40453i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.51450 | + | 13.1163i | −0.237488 | + | 0.886316i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.9253 | + | 8.50646i | −1.40759 | + | 0.572207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.0202 | + | 10.9813i | −1.27368 | + | 0.735362i | −0.975679 | − | 0.219203i | \(-0.929654\pi\) |
−0.298005 | + | 0.954564i | \(0.596321\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.06760 | − | 7.04528i | 0.269976 | − | 0.467612i | −0.698879 | − | 0.715239i | \(-0.746318\pi\) |
0.968855 | + | 0.247628i | \(0.0796510\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.1234 | + | 10.1234i | 0.668973 | + | 0.668973i | 0.957478 | − | 0.288505i | \(-0.0931582\pi\) |
−0.288505 | + | 0.957478i | \(0.593158\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.49528 | + | 4.90475i | −0.558949 | + | 0.322709i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.66935 | + | 1.66935i | −0.109363 | + | 0.109363i | −0.759671 | − | 0.650308i | \(-0.774640\pi\) |
0.650308 | + | 0.759671i | \(0.274640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.8075 | + | 4.50355i | 1.09176 | + | 0.292537i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.8726 | + | 16.8726i | −1.09140 | + | 1.09140i | −0.0960168 | + | 0.995380i | \(0.530610\pi\) |
−0.995380 | + | 0.0960168i | \(0.969390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.24155 | − | 4.63353i | −0.0799753 | − | 0.298472i | 0.914340 | − | 0.404947i | \(-0.132710\pi\) |
−0.994315 | + | 0.106475i | \(0.966043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.40216 | + | 1.98340i | −0.474849 | + | 0.127235i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.24858 | − | 12.9111i | −0.333959 | − | 0.821514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.57985 | − | 0.423319i | −0.100119 | − | 0.0268268i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.86584 | + | 2.23194i | 0.244009 | + | 0.140879i | 0.617018 | − | 0.786949i | \(-0.288341\pi\) |
−0.373009 | + | 0.927828i | \(0.621674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.77277 | − | 1.60086i | −0.174323 | − | 0.100645i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.05177 | + | 7.65731i | −0.127986 | + | 0.477650i | −0.999928 | − | 0.0119581i | \(-0.996194\pi\) |
0.871943 | + | 0.489608i | \(0.162860\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.7838 | −1.16717 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.62809 | −0.286471 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.04147 | + | 3.88683i | −0.0642200 | + | 0.239672i | −0.990573 | − | 0.136983i | \(-0.956259\pi\) |
0.926353 | + | 0.376656i | \(0.122926\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.49220 | − | 3.74827i | −0.397316 | − | 0.229391i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5636 | + | 9.56301i | 1.00990 | + | 0.583067i | 0.911163 | − | 0.412047i | \(-0.135186\pi\) |
0.0987386 | + | 0.995113i | \(0.468519\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.39786 | + | 1.98225i | 0.449388 | + | 0.120413i | 0.476413 | − | 0.879222i | \(-0.341937\pi\) |
−0.0270250 | + | 0.999635i | \(0.508603\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.05981 | − | 10.3617i | 0.487802 | − | 0.627118i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.6084 | − | 3.91430i | 0.877731 | − | 0.235187i | 0.208303 | − | 0.978064i | \(-0.433206\pi\) |
0.669428 | + | 0.742877i | \(0.266539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.72685 | − | 6.44468i | −0.103384 | − | 0.385833i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0253 | − | 13.0253i | 0.777027 | − | 0.777027i | −0.202297 | − | 0.979324i | \(-0.564841\pi\) |
0.979324 | + | 0.202297i | \(0.0648407\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.11105 | − | 2.17335i | −0.482152 | − | 0.129192i | 0.00955242 | − | 0.999954i | \(-0.496959\pi\) |
−0.491705 | + | 0.870762i | \(0.663626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.07048 | + | 6.07048i | −0.358329 | + | 0.358329i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.2675 | − | 11.1241i | 1.13338 | − | 0.654360i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.92573 | − | 2.92573i | −0.171510 | − | 0.171510i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.870229 | + | 1.50728i | −0.0508393 | + | 0.0880563i | −0.890325 | − | 0.455325i | \(-0.849523\pi\) |
0.839486 | + | 0.543382i | \(0.182856\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.1291 | − | 7.58011i | 0.761830 | − | 0.439843i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.24417 | + | 0.587226i | 0.245447 | + | 0.0339602i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.84951 | + | 10.6345i | −0.164243 | + | 0.612963i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.04500 | + | 18.8282i | 0.289827 | + | 1.08165i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.53050i | − | 0.543934i | −0.962307 | − | 0.271967i | \(-0.912326\pi\) | ||
0.962307 | − | 0.271967i | \(-0.0876742\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.62726 | + | 6.28260i | 0.206348 | + | 0.357405i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.5311i | 1.10751i | 0.832680 | + | 0.553755i | \(0.186806\pi\) | ||||
−0.832680 | + | 0.553755i | \(0.813194\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0195 | − | 17.0195i | −0.962000 | − | 0.962000i | 0.0373038 | − | 0.999304i | \(-0.488123\pi\) |
−0.999304 | + | 0.0373038i | \(0.988123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.07976 | 0.397639 | 0.198819 | − | 0.980036i | \(-0.436289\pi\) | ||||
0.198819 | + | 0.980036i | \(0.436289\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.9050 | − | 4.26174i | 0.890512 | − | 0.238612i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.77515 | + | 3.07465i | −0.0990791 | + | 0.171610i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.1083 | + | 20.9722i | 0.673723 | + | 1.16692i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.41276 | − | 4.17903i | −0.133426 | − | 0.231101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.28155 | + | 14.3441i | −0.456577 | + | 0.790814i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2412 | − | 4.08386i | 0.837730 | − | 0.224469i | 0.185647 | − | 0.982617i | \(-0.440562\pi\) |
0.652083 | + | 0.758147i | \(0.273895\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.85090 | 0.320627 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.66232 | − | 4.66232i | −0.253973 | − | 0.253973i | 0.568625 | − | 0.822597i | \(-0.307476\pi\) |
−0.822597 | + | 0.568625i | \(0.807476\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 20.7285i | − | 1.12582i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.8691 | + | 20.5579i | 0.642747 | + | 1.11327i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6667i | 1.06190i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.47707 | + | 24.1728i | 0.347707 | + | 1.29766i | 0.889417 | + | 0.457096i | \(0.151111\pi\) |
−0.541710 | + | 0.840566i | \(0.682223\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.28299 | − | 27.1805i | 0.389850 | − | 1.45494i | −0.440528 | − | 0.897739i | \(-0.645209\pi\) |
0.830378 | − | 0.557200i | \(-0.188124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.4561 | + | 16.0136i | −0.664859 | + | 0.854743i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.40368 | − | 4.85187i | 0.447283 | − | 0.258239i | −0.259399 | − | 0.965770i | \(-0.583525\pi\) |
0.706682 | + | 0.707531i | \(0.250191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.4047 | + | 19.7535i | −0.603599 | + | 1.04546i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.09591 | − | 2.09591i | −0.110618 | − | 0.110618i | 0.649631 | − | 0.760249i | \(-0.274923\pi\) |
−0.760249 | + | 0.649631i | \(0.774923\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51444 | − | 2.02906i | 0.184970 | − | 0.106793i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.96129 | − | 3.96129i | 0.207914 | − | 0.207914i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1325 | + | 2.71499i | 0.528912 | + | 0.141721i | 0.513386 | − | 0.858158i | \(-0.328391\pi\) |
0.0155260 | + | 0.999879i | \(0.495058\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.89087 | − | 1.89087i | 0.0984350 | − | 0.0984350i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.34873 | + | 16.2297i | 0.225775 | + | 0.842603i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.1023 | + | 4.04666i | −0.781969 | + | 0.209528i | −0.627653 | − | 0.778493i | \(-0.715984\pi\) |
−0.154317 | + | 0.988021i | \(0.549318\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.5697 | + | 13.2988i | −0.904888 | + | 0.684921i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4625 | + | 3.33930i | 0.640153 | + | 0.171529i | 0.564273 | − | 0.825588i | \(-0.309157\pi\) |
0.0758805 | + | 0.997117i | \(0.475823\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.68036 | + | 3.27956i | 0.291014 | + | 0.168017i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.8327 | − | 14.3371i | −1.26889 | − | 0.732594i | −0.294112 | − | 0.955771i | \(-0.595024\pi\) |
−0.974778 | + | 0.223177i | \(0.928357\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.887585 | − | 3.31251i | 0.0451185 | − | 0.168385i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 35.3120 | 1.79039 | 0.895194 | − | 0.445677i | \(-0.147037\pi\) | ||||
0.895194 | + | 0.445677i | \(0.147037\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.44474 | −0.376496 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.70817 | + | 17.5711i | −0.237496 | + | 0.886346i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.76940 | − | 4.48566i | −0.389935 | − | 0.225129i | 0.292197 | − | 0.956358i | \(-0.405614\pi\) |
−0.682132 | + | 0.731229i | \(0.738947\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.1881 | − | 7.03680i | −0.610168 | − | 0.352281i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.05240 | − | 0.281990i | −0.0525543 | − | 0.0140819i | 0.232446 | − | 0.972609i | \(-0.425327\pi\) |
−0.285000 | + | 0.958527i | \(0.591994\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.0744 | − | 19.5041i | −1.24905 | − | 0.971566i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.1074 | + | 5.38776i | −0.996686 | + | 0.267061i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.28956 | − | 27.2050i | −0.360446 | − | 1.34520i | −0.873491 | − | 0.486840i | \(-0.838150\pi\) |
0.513046 | − | 0.858361i | \(-0.328517\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.1540 | − | 15.1540i | 0.747491 | − | 0.747491i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 21.9847 | + | 5.89080i | 1.08180 | + | 0.289867i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.2551 | − | 16.2551i | 0.796014 | − | 0.796014i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.96691 | + | 2.29029i | −0.193796 | + | 0.111888i | −0.593758 | − | 0.804643i | \(-0.702357\pi\) |
0.399962 | + | 0.916532i | \(0.369023\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0987 | + | 16.0987i | 0.784602 | + | 0.784602i | 0.980604 | − | 0.196002i | \(-0.0627959\pi\) |
−0.196002 | + | 0.980604i | \(0.562796\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.57960 | − | 4.46799i | 0.125424 | − | 0.217241i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.5411 | − | 11.8594i | 0.994056 | − | 0.573918i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.65571 | − | 13.4037i | 0.273060 | − | 0.647134i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.0745698 | + | 0.278298i | −0.00359190 | + | 0.0134051i | −0.967699 | − | 0.252110i | \(-0.918875\pi\) |
0.964107 | + | 0.265515i | \(0.0855421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0790 | − | 37.6152i | −0.484364 | − | 1.80767i | −0.582909 | − | 0.812537i | \(-0.698086\pi\) |
0.0985457 | − | 0.995133i | \(-0.468581\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 4.59348i | − | 0.219736i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3895 | + | 24.9233i | 0.686771 | + | 1.18952i | 0.972877 | + | 0.231324i | \(0.0743059\pi\) |
−0.286105 | + | 0.958198i | \(0.592361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 0.824995i | − | 0.0392855i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.9217 | + | 25.9217i | 1.23158 | + | 1.23158i | 0.963357 | + | 0.268222i | \(0.0864359\pi\) |
0.268222 | + | 0.963357i | \(0.413564\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.98624 | 0.235841 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.4485 | + | 10.3023i | −1.81450 | + | 0.486193i | −0.996082 | − | 0.0884331i | \(-0.971814\pi\) |
−0.818416 | + | 0.574626i | \(0.805147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.75705 | + | 8.23944i | −0.224001 | + | 0.387980i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.5337 | − | 26.9052i | −0.729839 | − | 1.26412i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.92971 | − | 6.80646i | −0.183824 | − | 0.318393i | 0.759355 | − | 0.650676i | \(-0.225514\pi\) |
−0.943180 | + | 0.332283i | \(0.892181\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.6255 | − | 30.5282i | 0.822687 | − | 1.42494i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.4014 | + | 5.19859i | −0.903614 | + | 0.242123i | −0.680568 | − | 0.732685i | \(-0.738267\pi\) |
−0.223046 | + | 0.974808i | \(0.571600\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.60260 | 0.0744790 | 0.0372395 | − | 0.999306i | \(-0.488144\pi\) | ||||
0.0372395 | + | 0.999306i | \(0.488144\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.6094 | − | 17.6094i | −0.814864 | − | 0.814864i | 0.170495 | − | 0.985359i | \(-0.445463\pi\) |
−0.985359 | + | 0.170495i | \(0.945463\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.46657i | 0.113896i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.6465 | − | 27.1006i | −0.720955 | − | 1.24873i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 12.2012i | 0.561013i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.35457 | − | 5.05534i | −0.0620216 | − | 0.231468i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.67830 | + | 21.1917i | −0.259448 | + | 0.968273i | 0.706113 | + | 0.708099i | \(0.250447\pi\) |
−0.965562 | + | 0.260175i | \(0.916220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.2119 | − | 16.8125i | 1.01278 | − | 0.766583i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.74690 | − | 2.16328i | 0.170490 | − | 0.0984325i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.85260 | − | 11.8691i | 0.310521 | − | 0.537838i | −0.667954 | − | 0.744202i | \(-0.732830\pi\) |
0.978475 | + | 0.206364i | \(0.0661632\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.46573 | + | 9.46573i | 0.428055 | + | 0.428055i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0133 | − | 11.5547i | 0.903187 | − | 0.521455i | 0.0249539 | − | 0.999689i | \(-0.492056\pi\) |
0.878233 | + | 0.478234i | \(0.158723\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0733 | − | 27.0733i | 1.21932 | − | 1.21932i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.6822 | − | 6.88153i | −1.15200 | − | 0.308679i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.3195 | + | 15.3195i | −0.685795 | + | 0.685795i | −0.961300 | − | 0.275505i | \(-0.911155\pi\) |
0.275505 | + | 0.961300i | \(0.411155\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.05936 | − | 26.3459i | −0.315389 | − | 1.17705i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.5206 | + | 8.98181i | −1.49461 | + | 0.400479i | −0.911290 | − | 0.411765i | \(-0.864913\pi\) |
−0.583318 | + | 0.812244i | \(0.698246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.256508 | + | 19.4667i | −0.0113919 | + | 0.864549i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.1190 | − | 4.58701i | −0.758785 | − | 0.203316i | −0.141374 | − | 0.989956i | \(-0.545152\pi\) |
−0.617411 | + | 0.786641i | \(0.711819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.0908 | − | 11.0221i | −0.844528 | − | 0.487589i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.8362 | + | 10.8751i | 0.831640 | + | 0.480148i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.75081 | + | 17.7303i | −0.208940 | + | 0.779776i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.71883 | −0.119343 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.1460 | −0.575938 | −0.287969 | − | 0.957640i | \(-0.592980\pi\) | ||||
−0.287969 | + | 0.957640i | \(0.592980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.87752 | − | 21.9352i | 0.257006 | − | 0.959160i | −0.709957 | − | 0.704245i | \(-0.751286\pi\) |
0.966963 | − | 0.254915i | \(-0.0820475\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.8017 | + | 27.5983i | 2.08228 | + | 1.20220i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.6956 | − | 10.7939i | −0.812854 | − | 0.469301i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.84796 | − | 1.83491i | −0.297176 | − | 0.0796282i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.74497 | − | 12.6118i | 0.0755832 | − | 0.546277i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.3267 | − | 7.05423i | 1.13608 | − | 0.304412i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.759691 | + | 2.83521i | 0.0327222 | + | 0.122121i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.3506 | − | 12.3506i | 0.530993 | − | 0.530993i | −0.389875 | − | 0.920868i | \(-0.627482\pi\) |
0.920868 | + | 0.389875i | \(0.127482\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.2206 | + | 6.75783i | 1.08232 | + | 0.290006i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.96444 | − | 7.96444i | 0.340535 | − | 0.340535i | −0.516034 | − | 0.856568i | \(-0.672592\pi\) |
0.856568 | + | 0.516034i | \(0.172592\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.39830 | + | 3.69406i | −0.273073 | + | 0.157659i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.7045 | + | 16.7045i | 0.711637 | + | 0.711637i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.1239 | + | 24.4634i | −0.600611 | + | 1.04029i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.7800 | − | 13.1520i | 0.965219 | − | 0.557269i | 0.0674437 | − | 0.997723i | \(-0.478516\pi\) |
0.897775 | + | 0.440454i | \(0.145182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.14891 | − | 15.1259i | −0.260071 | − | 0.639756i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.54242 | + | 24.4167i | −0.276221 | + | 1.03087i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.9307 | + | 44.5258i | 0.502817 | + | 1.87654i | 0.480894 | + | 0.876779i | \(0.340312\pi\) |
0.0219234 | + | 0.999760i | \(0.493021\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.9631i | 0.628391i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3819 | + | 26.6422i | 0.644841 | + | 1.11690i | 0.984338 | + | 0.176290i | \(0.0564097\pi\) |
−0.339497 | + | 0.940607i | \(0.610257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.6467i | − | 0.864038i | −0.901865 | − | 0.432019i | \(-0.857801\pi\) | ||
0.901865 | − | 0.432019i | \(-0.142199\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.3232 | − | 22.3232i | −0.932567 | − | 0.932567i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.3744 | −0.848198 | −0.424099 | − | 0.905616i | \(-0.639409\pi\) | ||||
−0.424099 | + | 0.905616i | \(0.639409\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.0278 | + | 7.51004i | −1.16480 | + | 0.312106i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.32761 | − | 2.29948i | 0.0550783 | − | 0.0953985i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.31035 | + | 16.1260i | 0.385595 | + | 0.667870i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.5802 | − | 37.3781i | −0.890712 | − | 1.54276i | −0.839024 | − | 0.544095i | \(-0.816873\pi\) |
−0.0516879 | − | 0.998663i | \(-0.516460\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.0285 | + | 29.4942i | −0.701645 | + | 1.21529i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.8965 | + | 4.79535i | −0.736163 | + | 0.197254i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.3448 | 1.41037 | 0.705186 | − | 0.709022i | \(-0.250863\pi\) | ||||
0.705186 | + | 0.709022i | \(0.250863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.7754 | − | 10.7754i | −0.441010 | − | 0.441010i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.69200i | − | 0.355146i | −0.984108 | − | 0.177573i | \(-0.943175\pi\) | ||
0.984108 | − | 0.177573i | \(-0.0568245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.73390 | − | 3.00320i | −0.0707271 | − | 0.122503i | 0.828493 | − | 0.559999i | \(-0.189199\pi\) |
−0.899220 | + | 0.437496i | \(0.855865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 0.768305i | − | 0.0312878i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.83078 | + | 18.0287i | 0.196075 | + | 0.731764i | 0.991986 | + | 0.126349i | \(0.0403260\pi\) |
−0.795910 | + | 0.605414i | \(0.793007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.75898 | + | 21.4928i | −0.233366 | + | 0.870932i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.04573 | − | 24.3744i | −0.123217 | − | 0.986083i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.9846 | − | 12.1155i | 0.847560 | − | 0.489339i | −0.0122667 | − | 0.999925i | \(-0.503905\pi\) |
0.859827 | + | 0.510586i | \(0.170571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.94688 | + | 13.7644i | −0.319930 | + | 0.554134i | −0.980473 | − | 0.196654i | \(-0.936993\pi\) |
0.660544 | + | 0.750788i | \(0.270326\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.3555 | + | 10.3555i | 0.416225 | + | 0.416225i | 0.883900 | − | 0.467676i | \(-0.154908\pi\) |
−0.467676 | + | 0.883900i | \(0.654908\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.79070 | + | 3.34326i | −0.232373 | + | 0.134160i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.60545 | − | 8.60545i | 0.344770 | − | 0.344770i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.0653 | − | 4.03674i | −0.601651 | − | 0.161212i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −34.2265 | + | 34.2265i | −1.36470 | + | 1.36470i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7149 | − | 39.9887i | −0.426555 | − | 1.59193i | −0.760503 | − | 0.649334i | \(-0.775048\pi\) |
0.333948 | − | 0.942591i | \(-0.391619\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.1081 | + | 6.72769i | −0.997956 | + | 0.267402i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.37061 | − | 3.13195i | −0.0939271 | − | 0.124092i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.99967 | + | 2.14351i | 0.316462 | + | 0.0847958i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.26442 | − | 1.88471i | −0.128937 | − | 0.0744417i | 0.434144 | − | 0.900843i | \(-0.357051\pi\) |
−0.563081 | + | 0.826402i | \(0.690384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.8336 | − | 11.4509i | −0.782159 | − | 0.451580i | 0.0550358 | − | 0.998484i | \(-0.482473\pi\) |
−0.837195 | + | 0.546905i | \(0.815806\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.33051 | − | 23.6258i | 0.248878 | − | 0.928825i | −0.722517 | − | 0.691353i | \(-0.757015\pi\) |
0.971395 | − | 0.237471i | \(-0.0763186\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.2236 | 0.990113 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.0779 | −1.25723 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.56514 | − | 28.2335i | 0.296047 | − | 1.10486i | −0.644336 | − | 0.764743i | \(-0.722866\pi\) |
0.940383 | − | 0.340119i | \(-0.110467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.94654 | + | 3.43324i | 0.231997 | + | 0.133943i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.0616 | − | 6.38643i | −0.430900 | − | 0.248780i | 0.268830 | − | 0.963188i | \(-0.413363\pi\) |
−0.699730 | + | 0.714407i | \(0.746696\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.9009 | − | 4.52859i | −0.657370 | − | 0.176142i | −0.0853110 | − | 0.996354i | \(-0.527188\pi\) |
−0.572059 | + | 0.820213i | \(0.693855\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.19433 | − | 33.5664i | −0.162894 | − | 1.30361i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.01503 | + | 1.87967i | −0.271623 | + | 0.0727812i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.51270 | − | 31.7698i | −0.329120 | − | 1.22829i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.5870 | − | 18.5870i | 0.717542 | − | 0.717542i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.0450 | + | 6.17489i | 0.888320 | + | 0.238025i | 0.673993 | − | 0.738738i | \(-0.264578\pi\) |
0.214326 | + | 0.976762i | \(0.431244\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.9432 | + | 18.9432i | −0.728048 | + | 0.728048i | −0.970231 | − | 0.242183i | \(-0.922137\pi\) |
0.242183 | + | 0.970231i | \(0.422137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.81711 | − | 3.35851i | 0.223240 | − | 0.128888i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.61471 | + | 8.61471i | 0.330116 | + | 0.330116i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.69188 | + | 2.93042i | −0.0647380 | + | 0.112129i | −0.896578 | − | 0.442886i | \(-0.853954\pi\) |
0.831840 | + | 0.555016i | \(0.187288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.5678 | + | 10.7201i | −0.708405 | + | 0.408998i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.6689 | − | 15.2994i | −0.749324 | − | 0.582860i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.8180 | − | 47.8376i | 0.487621 | − | 1.81983i | −0.0803328 | − | 0.996768i | \(-0.525598\pi\) |
0.567954 | − | 0.823060i | \(-0.307735\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.28384 | + | 4.79135i | 0.0487690 | + | 0.182008i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.1224i | 0.837947i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.76775 | − | 3.06183i | −0.0668625 | − | 0.115809i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 5.71523i | − | 0.215861i | −0.994158 | − | 0.107931i | \(-0.965578\pi\) | ||
0.994158 | − | 0.107931i | \(-0.0344224\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.1181 | − | 21.1181i | −0.796485 | − | 0.796485i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.6440 | −1.19010 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.56101 | − | 2.56186i | 0.359071 | − | 0.0962128i | −0.0747734 | − | 0.997201i | \(-0.523823\pi\) |
0.433845 | + | 0.900988i | \(0.357157\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.39942 | − | 7.62003i | 0.164991 | − | 0.285773i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.23494 | − | 9.06719i | −0.196050 | − | 0.339569i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.8671 | − | 30.9467i | −0.667259 | − | 1.15573i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.37245 | − | 9.30535i | 0.200358 | − | 0.347031i | −0.748286 | − | 0.663377i | \(-0.769123\pi\) |
0.948644 | + | 0.316346i | \(0.102456\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.3758 | + | 3.04812i | −0.423655 | + | 0.113518i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.18383 | 0.267169 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.2084 | − | 14.2084i | −0.526961 | − | 0.526961i | 0.392704 | − | 0.919665i | \(-0.371540\pi\) |
−0.919665 | + | 0.392704i | \(0.871540\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 29.9404i | − | 1.10890i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.1853 | + | 24.5697i | 0.524663 | + | 0.908743i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.5445i | 1.38674i | 0.720582 | + | 0.693369i | \(0.243875\pi\) | ||||
−0.720582 | + | 0.693369i | \(0.756125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.707489 | + | 2.64038i | 0.0260607 | + | 0.0972598i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.64320 | − | 28.5248i | 0.281160 | − | 1.04930i | −0.670440 | − | 0.741964i | \(-0.733895\pi\) |
0.951600 | − | 0.307339i | \(-0.0994386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.7108 | − | 2.58794i | 0.760832 | − | 0.0950705i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 33.7356 | − | 19.4772i | 1.23764 | − | 0.714551i | 0.269027 | − | 0.963133i | \(-0.413298\pi\) |
0.968611 | + | 0.248582i | \(0.0799645\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.413532 | + | 0.716258i | −0.0151303 | + | 0.0262065i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.07546 | − | 4.07546i | −0.148914 | − | 0.148914i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.7530 | + | 13.1365i | −0.830270 | + | 0.479357i | −0.853945 | − | 0.520363i | \(-0.825797\pi\) |
0.0236752 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.72700 | + | 4.72700i | −0.172261 | + | 0.172261i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.7365 | − | 7.16401i | −0.971753 | − | 0.260380i | −0.262185 | − | 0.965018i | \(-0.584443\pi\) |
−0.709568 | + | 0.704637i | \(0.751110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.39044 | − | 3.39044i | 0.123065 | − | 0.123065i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.2417 | − | 38.2227i | −0.371263 | − | 1.38557i | −0.858729 | − | 0.512430i | \(-0.828745\pi\) |
0.487466 | − | 0.873142i | \(-0.337921\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.56686 | − | 2.02753i | 0.273939 | − | 0.0734017i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −31.2697 | + | 12.7116i | −1.12908 | + | 0.458991i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.642529 | + | 0.172165i | 0.0231702 | + | 0.00620843i | 0.270386 | − | 0.962752i | \(-0.412849\pi\) |
−0.247215 | + | 0.968961i | \(0.579516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.2814 | − | 5.93595i | −0.370275 | − | 0.213778i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.9854 | + | 8.07445i | 0.503018 | + | 0.290418i | 0.729959 | − | 0.683491i | \(-0.239539\pi\) |
−0.226941 | + | 0.973909i | \(0.572872\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.28059 | − | 27.1715i | 0.261190 | − | 0.974773i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.6498 | −0.489054 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.4658 | −1.05437 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.90028 | − | 33.2163i | 0.318070 | − | 1.18705i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 27.8188 | + | 16.0612i | 0.991633 | + | 0.572520i | 0.905762 | − | 0.423787i | \(-0.139299\pi\) |
0.0858710 | + | 0.996306i | \(0.472633\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.21880 | − | 3.01307i | −0.185794 | − | 0.107268i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.5042 | + | 8.70947i | 1.15572 | + | 0.309673i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.6752 | + | 32.4093i | −0.485621 | + | 1.15089i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.58199 | + | 0.423892i | −0.0560369 | + | 0.0150150i | −0.286729 | − | 0.958012i | \(-0.592568\pi\) |
0.230692 | + | 0.973027i | \(0.425901\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0467 | + | 41.2269i | 0.390805 | + | 1.45850i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.68048 | + | 2.68048i | −0.0947103 | + | 0.0947103i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −23.5976 | − | 6.32295i | −0.832740 | − | 0.223132i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20.2534 | + | 20.2534i | −0.712952 | + | 0.712952i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.27418 | + | 5.35445i | −0.326063 | + | 0.188253i | −0.654092 | − | 0.756415i | \(-0.726949\pi\) |
0.328029 | + | 0.944668i | \(0.393616\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.8784 | + | 37.8784i | 1.33009 | + | 1.33009i | 0.905283 | + | 0.424809i | \(0.139659\pi\) |
0.424809 | + | 0.905283i | \(0.360341\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.73482 | + | 9.93301i | −0.201129 | + | 0.348366i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −15.1598 | + | 8.75249i | −0.530373 | + | 0.306211i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.00622 | − | 5.29284i | −0.139989 | − | 0.184947i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.96951 | − | 22.2785i | 0.208337 | − | 0.777526i | −0.780069 | − | 0.625694i | \(-0.784816\pi\) |
0.988406 | − | 0.151832i | \(-0.0485173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.95458 | − | 7.29458i | −0.0681323 | − | 0.254273i | 0.923456 | − | 0.383704i | \(-0.125352\pi\) |
−0.991588 | + | 0.129431i | \(0.958685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 38.2354i | − | 1.32957i | −0.747033 | − | 0.664787i | \(-0.768522\pi\) | ||
0.747033 | − | 0.664787i | \(-0.231478\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.4408 | − | 42.3328i | −0.848865 | − | 1.47028i | −0.882222 | − | 0.470834i | \(-0.843953\pi\) |
0.0333566 | − | 0.999444i | \(-0.489380\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.6488i | 0.785679i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.82604 | + | 4.82604i | 0.167213 | + | 0.167213i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.5751 | 1.71357 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.6702 | − | 6.61035i | 0.851709 | − | 0.228215i | 0.193547 | − | 0.981091i | \(-0.438001\pi\) |
0.658162 | + | 0.752876i | \(0.271334\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.17511 | − | 7.23150i | 0.143969 | − | 0.249362i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.7931 | + | 23.8904i | 0.475060 | + | 0.822828i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.54725 | + | 7.87607i | 0.156245 | + | 0.270625i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.28769 | − | 10.8906i | 0.215793 | − | 0.373765i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.86851 | − | 2.37631i | 0.304008 | − | 0.0814588i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.17091 | −0.245527 | −0.122764 | − | 0.992436i | \(-0.539176\pi\) | ||||
−0.122764 | + | 0.992436i | \(0.539176\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7248 | − | 10.7248i | −0.366350 | − | 0.366350i | 0.499794 | − | 0.866144i | \(-0.333409\pi\) |
−0.866144 | + | 0.499794i | \(0.833409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.2503i | 0.929770i | 0.885371 | + | 0.464885i | \(0.153904\pi\) | ||||
−0.885371 | + | 0.464885i | \(0.846096\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.42829 | − | 11.1341i | −0.219076 | − | 0.379450i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.34796i | 0.284168i | 0.989855 | + | 0.142084i | \(0.0453803\pi\) | ||||
−0.989855 | + | 0.142084i | \(0.954620\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.62342 | + | 32.1830i | 0.292867 | + | 1.09299i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.10236 | + | 30.2384i | −0.274854 | + | 1.02577i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.20772 | − | 2.91674i | −0.0748056 | − | 0.0988299i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.81196 | + | 1.04613i | −0.0613254 | + | 0.0354062i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.3047 | − | 26.5085i | 0.516803 | − | 0.895130i | −0.483006 | − | 0.875617i | \(-0.660455\pi\) |
0.999810 | − | 0.0195127i | \(-0.00621147\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.84305 | − | 1.84305i | −0.0621644 | − | 0.0621644i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.20042 | + | 3.57981i | −0.208897 | + | 0.120607i | −0.600799 | − | 0.799400i | \(-0.705151\pi\) |
0.391901 | + | 0.920007i | \(0.371817\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1878 | − | 31.1878i | 1.04955 | − | 1.04955i | 0.0508451 | − | 0.998707i | \(-0.483809\pi\) |
0.998707 | − | 0.0508451i | \(-0.0161915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.3613 | + | 11.3507i | 1.42235 | + | 0.381118i | 0.886318 | − | 0.463077i | \(-0.153255\pi\) |
0.536035 | + | 0.844196i | \(0.319921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.52935 | + | 7.52935i | −0.252526 | + | 0.252526i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.29188 | + | 16.0175i | 0.143783 | + | 0.536607i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.4374 | + | 6.81594i | −0.851231 | + | 0.228087i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.49449 | + | 5.91177i | −0.0832887 | + | 0.197388i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 52.0108 | + | 13.9362i | 1.73466 | + | 0.464800i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.4966 | + | 21.6487i | 1.24919 | + | 0.721222i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.2788 | − | 8.24388i | −0.475169 | − | 0.274339i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.524912 | + | 1.95900i | −0.0174294 | + | 0.0650475i | −0.974093 | − | 0.226149i | \(-0.927387\pi\) |
0.956663 | + | 0.291196i | \(0.0940532\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.85671 | 0.326926 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.7972 | −0.390859 | −0.195429 | − | 0.980718i | \(-0.562610\pi\) | ||||
−0.195429 | + | 0.980718i | \(0.562610\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.761596 | − | 2.84232i | 0.0252052 | − | 0.0940669i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.5749 | − | 14.7657i | −0.844557 | − | 0.487605i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.9872 | − | 19.0452i | −1.08815 | − | 0.628242i | −0.155065 | − | 0.987904i | \(-0.549559\pi\) |
−0.933083 | + | 0.359662i | \(0.882892\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.7863 | + | 3.69402i | 0.454274 | + | 0.121722i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.5287 | − | 14.8495i | 1.20236 | − | 0.488778i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.54340 | − | 0.949451i | 0.116380 | − | 0.0311841i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.43693 | + | 9.09474i | 0.0799530 | + | 0.298389i | 0.994311 | − | 0.106519i | \(-0.0339704\pi\) |
−0.914358 | + | 0.404907i | \(0.867304\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.97772 | + | 2.97772i | −0.0975908 | + | 0.0975908i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.2527 | − | 7.57028i | −0.924951 | − | 0.247840i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.2985 | − | 39.2985i | 1.28382 | − | 1.28382i | 0.345351 | − | 0.938474i | \(-0.387760\pi\) |
0.938474 | − | 0.345351i | \(-0.112240\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.2162 | − | 18.0227i | 1.01870 | − | 0.588149i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.4526 | − | 19.4526i | −0.634137 | − | 0.634137i | 0.314966 | − | 0.949103i | \(-0.398007\pi\) |
−0.949103 | + | 0.314966i | \(0.898007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.09813 | − | 3.63406i | 0.0683244 | − | 0.118341i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.1987 | − | 8.19763i | 0.461396 | − | 0.266387i | −0.251235 | − | 0.967926i | \(-0.580837\pi\) |
0.712631 | + | 0.701539i | \(0.247503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.4404 | − | 4.05363i | 1.05306 | − | 0.131586i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.74411 | + | 10.2412i | −0.0889840 | + | 0.332093i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.57657 | − | 28.2762i | −0.245429 | − | 0.915955i | −0.973167 | − | 0.230099i | \(-0.926095\pi\) |
0.727738 | − | 0.685855i | \(-0.240572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.6592i | 0.797119i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.3956 | + | 30.1300i | 0.561733 | + | 0.972950i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 46.6257i | 1.50406i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.26945 | + | 1.26945i | 0.0409076 | + | 0.0409076i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.2534 | 1.61604 | 0.808021 | − | 0.589154i | \(-0.200539\pi\) | ||||
0.808021 | + | 0.589154i | \(0.200539\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.0303 | + | 9.38635i | −1.12534 | + | 0.301533i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.9370 | − | 41.4601i | 0.768175 | − | 1.33052i | −0.170376 | − | 0.985379i | \(-0.554498\pi\) |
0.938551 | − | 0.345139i | \(-0.112168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.6595 | + | 32.3193i | 0.598198 | + | 1.03611i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.4272 | + | 28.4527i | 0.525552 | + | 0.910283i | 0.999557 | + | 0.0297606i | \(0.00947448\pi\) |
−0.474005 | + | 0.880522i | \(0.657192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.74354 | − | 11.6802i | 0.215524 | − | 0.373299i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.35698 | + | 0.631551i | −0.0752526 | + | 0.0201639i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.3463 | −0.744631 | −0.372315 | − | 0.928106i | \(-0.621436\pi\) | ||||
−0.372315 | + | 0.928106i | \(0.621436\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −17.5394 | − | 17.5394i | −0.558285 | − | 0.558285i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.38144i | − | 0.171120i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4952 | − | 35.4988i | −0.651053 | − | 1.12766i | −0.982868 | − | 0.184312i | \(-0.940994\pi\) |
0.331815 | − | 0.943345i | \(-0.392339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.6299i | 0.749873i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.6809 | + | 39.8616i | 0.338267 | + | 1.26243i | 0.900284 | + | 0.435303i | \(0.143359\pi\) |
−0.562018 | + | 0.827125i | \(0.689975\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.2519 | + | 41.9926i | −0.355993 | + | 1.32859i |
(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 | 1300.2.bs.d.193.2 | 20 | ||
5.2 | odd | 4 | 1300.2.bn.d.557.4 | 20 | |||
5.3 | odd | 4 | 260.2.bf.c.37.2 | ✓ | 20 | ||
5.4 | even | 2 | 260.2.bk.c.193.4 | yes | 20 | ||
13.6 | odd | 12 | 1300.2.bn.d.1293.4 | 20 | |||
65.19 | odd | 12 | 260.2.bf.c.253.2 | yes | 20 | ||
65.32 | even | 12 | inner | 1300.2.bs.d.357.2 | 20 | ||
65.58 | even | 12 | 260.2.bk.c.97.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.bf.c.37.2 | ✓ | 20 | 5.3 | odd | 4 | ||
260.2.bf.c.253.2 | yes | 20 | 65.19 | odd | 12 | ||
260.2.bk.c.97.4 | yes | 20 | 65.58 | even | 12 | ||
260.2.bk.c.193.4 | yes | 20 | 5.4 | even | 2 | ||
1300.2.bn.d.557.4 | 20 | 5.2 | odd | 4 | |||
1300.2.bn.d.1293.4 | 20 | 13.6 | odd | 12 | |||
1300.2.bs.d.193.2 | 20 | 1.1 | even | 1 | trivial | ||
1300.2.bs.d.357.2 | 20 | 65.32 | even | 12 | inner |