Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), not 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Character | \(\chi\) | \(=\) | 128.17 |
Dual form | 128.4.g.a.113.5 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.729459 | + | 1.76107i | −0.140384 | + | 0.338918i | −0.978398 | − | 0.206732i | \(-0.933717\pi\) |
0.838013 | + | 0.545650i | \(0.183717\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.29822 | − | 1.78038i | 0.384444 | − | 0.159242i | −0.182087 | − | 0.983282i | \(-0.558285\pi\) |
0.566531 | + | 0.824040i | \(0.308285\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.47807 | + | 1.47807i | −0.0798085 | + | 0.0798085i | −0.745884 | − | 0.666076i | \(-0.767973\pi\) |
0.666076 | + | 0.745884i | \(0.267973\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 16.5226 | + | 16.5226i | 0.611949 | + | 0.611949i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.854325 | − | 2.06252i | −0.0234172 | − | 0.0565340i | 0.911738 | − | 0.410771i | \(-0.134741\pi\) |
−0.935156 | + | 0.354237i | \(0.884741\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 40.9706 | + | 16.9706i | 0.874092 | + | 0.362061i | 0.774203 | − | 0.632938i | \(-0.218151\pi\) |
0.0998893 | + | 0.994999i | \(0.468151\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.86818i | 0.152650i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 73.1063i | 1.04299i | 0.853253 | + | 0.521496i | \(0.174626\pi\) | ||||
−0.853253 | + | 0.521496i | \(0.825374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 18.2478 | + | 7.55849i | 0.220333 | + | 0.0912650i | 0.490120 | − | 0.871655i | \(-0.336953\pi\) |
−0.269786 | + | 0.962920i | \(0.586953\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.52480 | − | 3.68119i | −0.0158447 | − | 0.0382524i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 144.221 | + | 144.221i | 1.30748 | + | 1.30748i | 0.923228 | + | 0.384253i | \(0.125541\pi\) |
0.384253 | + | 0.923228i | \(0.374459\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −73.0834 | + | 73.0834i | −0.584667 | + | 0.584667i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −88.6990 | + | 36.7403i | −0.632227 | + | 0.261877i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 80.7690 | − | 194.994i | 0.517187 | − | 1.24860i | −0.422437 | − | 0.906392i | \(-0.638825\pi\) |
0.939624 | − | 0.342208i | \(-0.111175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 168.830 | 0.978153 | 0.489077 | − | 0.872241i | \(-0.337334\pi\) | ||||
0.489077 | + | 0.872241i | \(0.337334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.25544 | 0.0224478 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.72155 | + | 8.98462i | −0.0179731 | + | 0.0433908i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −72.0103 | + | 29.8277i | −0.319958 | + | 0.132531i | −0.536881 | − | 0.843658i | \(-0.680398\pi\) |
0.216924 | + | 0.976189i | \(0.430398\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −59.7727 | + | 59.7727i | −0.245418 | + | 0.245418i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −141.297 | − | 141.297i | −0.538215 | − | 0.538215i | 0.384789 | − | 0.923005i | \(-0.374274\pi\) |
−0.923005 | + | 0.384789i | \(0.874274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −161.344 | − | 389.519i | −0.572203 | − | 1.38142i | −0.899675 | − | 0.436560i | \(-0.856197\pi\) |
0.327472 | − | 0.944861i | \(-0.393803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 100.434 | + | 41.6013i | 0.332708 | + | 0.137812i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 239.015i | − | 0.741787i | −0.928675 | − | 0.370893i | \(-0.879052\pi\) | ||
0.928675 | − | 0.370893i | \(-0.120948\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 338.631i | 0.987261i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −128.745 | − | 53.3280i | −0.353489 | − | 0.146420i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −59.8701 | − | 144.539i | −0.155166 | − | 0.374604i | 0.827111 | − | 0.562038i | \(-0.189983\pi\) |
−0.982277 | + | 0.187435i | \(0.939983\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.34415 | − | 7.34415i | −0.0180052 | − | 0.0180052i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −26.6221 | + | 26.6221i | −0.0618627 | + | 0.0618627i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −582.808 | + | 241.407i | −1.28602 | + | 0.532686i | −0.917796 | − | 0.397051i | \(-0.870033\pi\) |
−0.368222 | + | 0.929738i | \(0.620033\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 238.297 | − | 575.301i | 0.500178 | − | 1.20754i | −0.449209 | − | 0.893427i | \(-0.648294\pi\) |
0.949387 | − | 0.314110i | \(-0.101706\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −48.8433 | −0.0976775 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 206.315 | 0.393695 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 156.090 | − | 376.834i | 0.284618 | − | 0.687129i | −0.715314 | − | 0.698804i | \(-0.753716\pi\) |
0.999932 | + | 0.0116744i | \(0.00371618\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −359.185 | + | 148.780i | −0.626679 | + | 0.259579i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −411.945 | + | 411.945i | −0.688577 | + | 0.688577i | −0.961917 | − | 0.273341i | \(-0.911871\pi\) |
0.273341 | + | 0.961917i | \(0.411871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −642.439 | − | 642.439i | −1.03003 | − | 1.03003i | −0.999535 | − | 0.0304901i | \(-0.990293\pi\) |
−0.0304901 | − | 0.999535i | \(-0.509707\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.3937 | − | 182.016i | −0.116076 | − | 0.280233i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.31132 | + | 1.78581i | 0.00638078 | + | 0.00264301i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 800.261i | − | 1.13970i | −0.821748 | − | 0.569850i | \(-0.807001\pi\) | ||
0.821748 | − | 0.569850i | \(-0.192999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 447.890i | 0.614390i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1345.29 | + | 557.236i | 1.77909 | + | 0.736923i | 0.992902 | + | 0.118933i | \(0.0379475\pi\) |
0.786187 | + | 0.617989i | \(0.212052\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 130.157 | + | 314.227i | 0.166088 | + | 0.400973i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 284.480 | + | 284.480i | 0.350568 | + | 0.350568i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 340.094 | − | 340.094i | 0.405055 | − | 0.405055i | −0.474955 | − | 0.880010i | \(-0.657536\pi\) |
0.880010 | + | 0.474955i | \(0.157536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −85.6413 | + | 35.4738i | −0.0986555 | + | 0.0408644i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −123.155 | + | 297.321i | −0.137317 | + | 0.331514i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 91.8900 | 0.0992391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 632.602 | 0.662175 | 0.331088 | − | 0.943600i | \(-0.392584\pi\) | ||||
0.331088 | + | 0.943600i | \(0.392584\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.9626 | − | 48.1940i | 0.0202658 | − | 0.0489261i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1069.17 | + | 442.863i | −1.05333 | + | 0.436303i | −0.841078 | − | 0.540913i | \(-0.818079\pi\) |
−0.212249 | + | 0.977216i | \(0.568079\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −251.287 | + | 251.287i | −0.240389 | + | 0.240389i | −0.817011 | − | 0.576622i | \(-0.804371\pi\) |
0.576622 | + | 0.817011i | \(0.304371\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.1078 | − | 13.1078i | −0.0121828 | − | 0.0121828i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 539.593 | + | 1302.69i | 0.487518 | + | 1.17697i | 0.955965 | + | 0.293481i | \(0.0948138\pi\) |
−0.468447 | + | 0.883492i | \(0.655186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 723.084 | + | 299.511i | 0.635403 | + | 0.263192i | 0.677047 | − | 0.735940i | \(-0.263260\pi\) |
−0.0416440 | + | 0.999133i | \(0.513260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 148.573i | − | 0.127045i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 118.490i | − | 0.0986425i | −0.998783 | − | 0.0493213i | \(-0.984294\pi\) | ||
0.998783 | − | 0.0493213i | \(-0.0157058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 876.659 | + | 363.124i | 0.710860 | + | 0.294448i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 396.543 | + | 957.340i | 0.313337 | + | 0.756463i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −108.056 | − | 108.056i | −0.0832397 | − | 0.0832397i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 937.635 | − | 937.635i | 0.704459 | − | 0.704459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 351.903 | − | 145.763i | 0.257968 | − | 0.106854i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −406.560 | + | 981.522i | −0.290910 | + | 0.702320i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −842.166 | −0.588427 | −0.294213 | − | 0.955740i | \(-0.595058\pi\) | ||||
−0.294213 | + | 0.955740i | \(0.595058\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 803.664 | 0.548517 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −488.895 | + | 1180.30i | −0.326069 | + | 0.787199i | 0.672808 | + | 0.739817i | \(0.265088\pi\) |
−0.998877 | + | 0.0473823i | \(0.984912\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −38.1436 | + | 15.7996i | −0.0248682 | + | 0.0103007i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −315.836 | + | 315.836i | −0.201354 | + | 0.201354i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 354.278 | + | 354.278i | 0.220934 | + | 0.220934i | 0.808892 | − | 0.587958i | \(-0.200068\pi\) |
−0.587958 | + | 0.808892i | \(0.700068\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −506.903 | − | 1223.77i | −0.309316 | − | 0.746756i | −0.999728 | − | 0.0233385i | \(-0.992570\pi\) |
0.690411 | − | 0.723417i | \(-0.257430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 420.923 | + | 174.352i | 0.251405 | + | 0.104135i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 99.0012i | − | 0.0578944i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 981.925i | − | 0.562375i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −596.352 | − | 247.017i | −0.334601 | − | 0.138596i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 263.786 | + | 636.836i | 0.145035 | + | 0.350145i | 0.979657 | − | 0.200677i | \(-0.0643142\pi\) |
−0.834623 | + | 0.550822i | \(0.814314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −963.930 | − | 963.930i | −0.519493 | − | 0.519493i | 0.397925 | − | 0.917418i | \(-0.369731\pi\) |
−0.917418 | + | 0.397925i | \(0.869731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1207.91 | + | 1207.91i | −0.638259 | + | 0.638259i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 725.668 | − | 300.581i | 0.376045 | − | 0.155763i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 439.451 | − | 1060.93i | 0.223389 | − | 0.539308i | −0.771957 | − | 0.635674i | \(-0.780722\pi\) |
0.995346 | + | 0.0963665i | \(0.0307221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 298.217 | 0.148743 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −426.337 | −0.208696 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 437.870 | − | 1057.11i | 0.210409 | − | 0.507972i | −0.783077 | − | 0.621924i | \(-0.786351\pi\) |
0.993486 | + | 0.113953i | \(0.0363512\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.2908 | − | 7.57631i | 0.00862993 | − | 0.00357464i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 856.325 | − | 856.325i | 0.396793 | − | 0.396793i | −0.480307 | − | 0.877100i | \(-0.659475\pi\) |
0.877100 | + | 0.480307i | \(0.159475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −162.925 | − | 162.925i | −0.0741580 | − | 0.0741580i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 176.616 | + | 426.388i | 0.0789832 | + | 0.190682i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2410.30 | − | 998.380i | −1.05926 | − | 0.438760i | −0.216071 | − | 0.976378i | \(-0.569324\pi\) |
−0.843189 | + | 0.537618i | \(0.819324\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 216.045i | − | 0.0933228i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1202.46i | − | 0.510636i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1526.52 | − | 632.305i | −0.637415 | − | 0.264026i | 0.0404847 | − | 0.999180i | \(-0.487110\pi\) |
−0.677900 | + | 0.735154i | \(0.737110\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1487.44 | − | 3590.99i | −0.610831 | − | 1.47468i | −0.862089 | − | 0.506756i | \(-0.830844\pi\) |
0.251258 | − | 0.967920i | \(-0.419156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 839.317 | + | 839.317i | 0.339039 | + | 0.339039i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −256.412 | + | 256.412i | −0.101901 | + | 0.101901i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 150.783 | − | 62.4565i | 0.0589646 | − | 0.0244239i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 76.7987 | − | 185.409i | 0.0295571 | − | 0.0713571i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1908.11 | −0.722858 | −0.361429 | − | 0.932400i | \(-0.617711\pi\) | ||||
−0.361429 | + | 0.932400i | \(0.617711\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3674.63 | −1.37049 | −0.685247 | − | 0.728310i | \(-0.740306\pi\) | ||||
−0.685247 | + | 0.728310i | \(0.740306\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −150.498 | + | 363.334i | −0.0552687 | + | 0.133430i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2539.28 | − | 1051.80i | 0.918356 | − | 0.380395i | 0.127107 | − | 0.991889i | \(-0.459431\pi\) |
0.791249 | + | 0.611494i | \(0.209431\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1751.18 | − | 1751.18i | 0.623809 | − | 0.623809i | −0.322694 | − | 0.946503i | \(-0.604589\pi\) |
0.946503 | + | 0.322694i | \(0.104589\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 549.771 | + | 549.771i | 0.192924 | + | 0.192924i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 168.832 | + | 407.597i | 0.0583730 | + | 0.140925i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −858.886 | − | 355.762i | −0.292620 | − | 0.121207i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4765.80i | 1.60022i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 44.0939i | − | 0.0145935i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4123.79 | − | 1708.13i | −1.34547 | − | 0.557311i | −0.410440 | − | 0.911887i | \(-0.634625\pi\) |
−0.935027 | + | 0.354577i | \(0.884625\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −424.967 | − | 1025.96i | −0.136706 | − | 0.330036i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1386.98 | − | 1386.98i | −0.439961 | − | 0.439961i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −249.543 | + | 249.543i | −0.0780649 | + | 0.0780649i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1600.01 | − | 662.747i | 0.493694 | − | 0.204495i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1240.66 | + | 2995.21i | −0.377627 | + | 0.911672i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4869.99 | 1.46242 | 0.731208 | − | 0.682155i | \(-0.238957\pi\) | ||||
0.731208 | + | 0.682155i | \(0.238957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2415.06 | −0.715573 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2187 | + | 27.0843i | −0.00328022 | + | 0.00791916i | −0.925511 | − | 0.378720i | \(-0.876364\pi\) |
0.922231 | + | 0.386639i | \(0.126364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4258.86 | − | 1764.08i | 1.22897 | − | 0.509054i | 0.328716 | − | 0.944429i | \(-0.393384\pi\) |
0.900250 | + | 0.435374i | \(0.143384\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.28986 | + | 6.28986i | −0.00179153 | + | 0.00179153i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4653.94 | + | 4653.94i | 1.30854 | + | 1.30854i | 0.922470 | + | 0.386069i | \(0.126167\pi\) |
0.386069 | + | 0.922470i | \(0.373833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −425.538 | − | 1027.34i | −0.118124 | − | 0.285176i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1409.32 | + | 583.757i | 0.386265 | + | 0.159996i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 630.197i | 0.170561i | 0.996357 | + | 0.0852805i | \(0.0271786\pi\) | ||||
−0.996357 | + | 0.0852805i | \(0.972821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1523.56i | 0.407224i | 0.979052 | + | 0.203612i | \(0.0652681\pi\) | ||||
−0.979052 | + | 0.203612i | \(0.934732\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3183.64 | − | 1318.71i | −0.840455 | − | 0.348128i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 602.891 | + | 1455.51i | 0.157214 | + | 0.379547i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 619.351 | + | 619.351i | 0.159548 | + | 0.159548i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1962.66 | + | 1962.66i | −0.499513 | + | 0.499513i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2943.19 | + | 1219.11i | −0.740129 | + | 0.306572i | −0.720707 | − | 0.693240i | \(-0.756183\pi\) |
−0.0194224 | + | 0.999811i | \(0.506183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 174.247 | − | 420.670i | 0.0432997 | − | 0.104535i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −648.320 | −0.159213 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3355.93 | 0.814541 | 0.407270 | − | 0.913308i | \(-0.366481\pi\) | ||||
0.407270 | + | 0.913308i | \(0.366481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 62.3491 | − | 150.524i | 0.0149582 | − | 0.0361124i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4556.32 | − | 1887.29i | 1.08057 | − | 0.447588i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3273.56 | − | 3273.56i | 0.767514 | − | 0.767514i | −0.210154 | − | 0.977668i | \(-0.567397\pi\) |
0.977668 | + | 0.210154i | \(0.0673966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −514.670 | − | 514.670i | −0.119305 | − | 0.119305i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 350.845 | + | 847.014i | 0.0804170 | + | 0.194144i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1523.46 | − | 631.037i | −0.345304 | − | 0.143030i | 0.203290 | − | 0.979119i | \(-0.434837\pi\) |
−0.548594 | + | 0.836089i | \(0.684837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6024.40i | 1.35039i | 0.737639 | + | 0.675196i | \(0.235941\pi\) | ||||
−0.737639 | + | 0.675196i | \(0.764059\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 176.697i | − | 0.0391729i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 213.173 | + | 88.2993i | 0.0467448 | + | 0.0193623i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 631.310 | + | 1524.12i | 0.136938 | + | 0.330597i | 0.977441 | − | 0.211210i | \(-0.0677404\pi\) |
−0.840503 | + | 0.541807i | \(0.817740\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2789.51 | + | 2789.51i | 0.598580 | + | 0.598580i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 185.259 | − | 185.259i | 0.0393296 | − | 0.0393296i | −0.687168 | − | 0.726498i | \(-0.741147\pi\) |
0.726498 | + | 0.687168i | \(0.241147\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5010.11 | − | 2075.25i | 1.05237 | − | 0.435905i | 0.211631 | − | 0.977350i | \(-0.432123\pi\) |
0.840736 | + | 0.541445i | \(0.182123\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −67.0300 | + | 161.825i | −0.0139316 | + | 0.0336339i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 417.694 | 0.0859083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −431.529 | −0.0878340 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −461.457 | + | 1114.06i | −0.0929591 | + | 0.224423i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3670.99 | + | 1520.58i | −0.731951 | + | 0.303184i | −0.717354 | − | 0.696709i | \(-0.754647\pi\) |
−0.0145978 | + | 0.999893i | \(0.504647\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2075.24 | + | 2075.24i | −0.409577 | + | 0.409577i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 151.556 | + | 151.556i | 0.0296099 | + | 0.0296099i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3461.30 | + | 8356.31i | 0.669471 | + | 1.61625i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 814.216 | + | 337.259i | 0.155916 | + | 0.0645824i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2205.93i | − | 0.418242i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2897.03i | − | 0.543880i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5184.84 | + | 2147.63i | 0.963890 | + | 0.399256i | 0.808434 | − | 0.588586i | \(-0.200315\pi\) |
0.155456 | + | 0.987843i | \(0.450315\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −259.231 | − | 625.838i | −0.0477253 | − | 0.115219i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4758.86 | − | 4758.86i | −0.867685 | − | 0.867685i | 0.124531 | − | 0.992216i | \(-0.460257\pi\) |
−0.992216 | + | 0.124531i | \(0.960257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1629.22 | − | 1629.22i | 0.294214 | − | 0.294214i | −0.544529 | − | 0.838742i | \(-0.683291\pi\) |
0.838742 | + | 0.544529i | \(0.183291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −209.939 | + | 86.9597i | −0.0375515 | + | 0.0155544i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1717.07 | + | 4145.38i | −0.304228 | + | 0.734472i | 0.695642 | + | 0.718388i | \(0.255120\pi\) |
−0.999871 | + | 0.0160838i | \(0.994880\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −471.182 | −0.0826994 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2687.74 | −0.467337 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −552.573 | + | 1334.03i | −0.0951888 | + | 0.229806i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4234.54 | + | 1754.00i | −0.722738 | + | 0.299368i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1054.92 | + | 1054.92i | −0.178401 | + | 0.178401i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 353.282 | + | 353.282i | 0.0592009 | + | 0.0592009i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3512.87 | − | 8480.82i | −0.583338 | − | 1.40830i | −0.889770 | − | 0.456410i | \(-0.849135\pi\) |
0.306432 | − | 0.951893i | \(-0.400865\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1682.63 | − | 696.969i | −0.276900 | − | 0.114696i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1897.62i | − | 0.309486i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 967.017i | − | 0.156311i | −0.996941 | − | 0.0781555i | \(-0.975097\pi\) | ||
0.996941 | − | 0.0781555i | \(-0.0249031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 208.669 | + | 86.4336i | 0.0334317 | + | 0.0138479i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −144.236 | − | 348.216i | −0.0229056 | − | 0.0552989i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1007.50 | − | 1007.50i | −0.158600 | − | 0.158600i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1278.97 | + | 1278.97i | −0.199587 | + | 0.199587i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6675.62 | − | 2765.13i | 1.03276 | − | 0.427781i | 0.199049 | − | 0.979990i | \(-0.436215\pi\) |
0.833706 | + | 0.552208i | \(0.186215\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1025.92 | − | 2476.80i | 0.157354 | − | 0.379885i | −0.825466 | − | 0.564451i | \(-0.809088\pi\) |
0.982820 | + | 0.184566i | \(0.0590878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4257.55 | −0.647440 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4340.88 | 0.654509 | 0.327254 | − | 0.944936i | \(-0.393877\pi\) | ||||
0.327254 | + | 0.944936i | \(0.393877\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1037.21 | + | 2504.05i | −0.155069 | + | 0.374370i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 269.118 | − | 111.472i | 0.0398970 | − | 0.0165259i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2662.28 | − | 2662.28i | 0.391392 | − | 0.391392i | −0.483792 | − | 0.875183i | \(-0.660741\pi\) |
0.875183 | + | 0.483792i | \(0.160741\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4574.19 | − | 4574.19i | −0.666889 | − | 0.666889i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 967.274 | + | 2335.21i | 0.139859 | + | 0.337649i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3905.13 | − | 1617.56i | −0.560011 | − | 0.231964i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11287.0i | − | 1.60539i | −0.596389 | − | 0.802695i | \(-0.703399\pi\) | ||
0.596389 | − | 0.802695i | \(-0.296601\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4669.18i | − | 0.658721i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 302.132 | + | 125.147i | 0.0422801 | + | 0.0175130i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5243 | + | 39.8932i | 0.00229382 | + | 0.00553778i | 0.925022 | − | 0.379913i | \(-0.124046\pi\) |
−0.922728 | + | 0.385451i | \(0.874046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1431.96 | − | 1431.96i | −0.197190 | − | 0.197190i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6618.31 | − | 6618.31i | 0.904138 | − | 0.904138i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10994.6 | + | 4554.09i | −1.49011 | + | 0.617224i | −0.971341 | − | 0.237689i | \(-0.923610\pi\) |
−0.518770 | + | 0.854914i | \(0.673610\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 614.326 | − | 1483.11i | 0.0826060 | − | 0.199428i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11220.8 | −1.49701 | −0.748506 | − | 0.663128i | \(-0.769229\pi\) | ||||
−0.748506 | + | 0.663128i | \(0.769229\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.7104 | 0.00287393 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3770.05 | − | 9101.71i | 0.495200 | − | 1.19552i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7872.36 | + | 3260.84i | −1.02608 | + | 0.425016i | −0.831296 | − | 0.555831i | \(-0.812400\pi\) |
−0.194783 | + | 0.980846i | \(0.562400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10543.4 | + | 10543.4i | −1.36369 | + | 1.36369i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1721.96 | − | 1721.96i | −0.221021 | − | 0.221021i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1424.77 | − | 3439.70i | −0.181488 | − | 0.438152i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12780.9 | + | 5294.04i | 1.61576 | + | 0.669270i | 0.993531 | − | 0.113565i | \(-0.0362269\pi\) |
0.622230 | + | 0.782835i | \(0.286227\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 78.6987i | − | 0.00987434i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1951.13i | − | 0.242979i | −0.992593 | − | 0.121490i | \(-0.961233\pi\) | ||
0.992593 | − | 0.121490i | \(-0.0387671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6917.06 | + | 2865.14i | 0.854996 | + | 0.354151i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 797.415 | + | 1925.13i | 0.0978368 | + | 0.236199i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 123.041 | + | 123.041i | 0.0149850 | + | 0.0149850i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3631.15 | − | 3631.15i | 0.438995 | − | 0.438995i | −0.452679 | − | 0.891674i | \(-0.649532\pi\) |
0.891674 | + | 0.452679i | \(0.149532\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −882.339 | + | 365.477i | −0.105894 | + | 0.0438629i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 504.616 | − | 1218.25i | 0.0601223 | − | 0.145148i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6774.43 | 0.801310 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2524.91 | 0.296512 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1055.57 | + | 2548.38i | −0.123074 | + | 0.297128i | −0.973394 | − | 0.229139i | \(-0.926409\pi\) |
0.850319 | + | 0.526267i | \(0.176409\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9547.06 | + | 3954.52i | −1.10521 | + | 0.457795i | −0.859287 | − | 0.511493i | \(-0.829092\pi\) |
−0.245927 | + | 0.969288i | \(0.579092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3949.16 | − | 3949.16i | 0.453936 | − | 0.453936i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5342.86 | − | 5342.86i | −0.609804 | − | 0.609804i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 498.116 | + | 1202.56i | 0.0564532 | + | 0.136290i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 174.348 | + | 72.2173i | 0.0196214 | + | 0.00812747i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 14341.1i | − | 1.60275i | −0.598162 | − | 0.801375i | \(-0.704102\pi\) | ||
0.598162 | − | 0.801375i | \(-0.295898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16123.8i | 1.78951i | 0.446554 | + | 0.894757i | \(0.352651\pi\) | ||||
−0.446554 | + | 0.894757i | \(0.647349\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1729.24 | + | 716.274i | 0.190599 | + | 0.0789487i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1541.62 | + | 3721.80i | 0.168754 | + | 0.407409i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8026.57 | + | 8026.57i | 0.872637 | + | 0.872637i | 0.992759 | − | 0.120123i | \(-0.0383288\pi\) |
−0.120123 | + | 0.992759i | \(0.538329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5595.07 | + | 5595.07i | −0.604154 | + | 0.604154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5998.55 | + | 2484.68i | −0.643340 | + | 0.266480i | −0.680409 | − | 0.732832i | \(-0.738198\pi\) |
0.0370688 | + | 0.999313i | \(0.488198\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 856.302 | − | 2067.29i | 0.0912193 | − | 0.220223i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1313.93 | −0.139031 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10135.3 | 1.06529 | 0.532646 | − | 0.846338i | \(-0.321198\pi\) | ||||
0.532646 | + | 0.846338i | \(0.321198\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −170.714 | + | 412.141i | −0.0178240 | + | 0.0430310i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2400.70 | − | 994.401i | 0.248995 | − | 0.103137i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −304.948 | + | 304.948i | −0.0314202 | + | 0.0314202i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2946.68 | − | 2946.68i | −0.301619 | − | 0.301619i | 0.540028 | − | 0.841647i | \(-0.318414\pi\) |
−0.841647 | + | 0.540028i | \(0.818414\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2685.95 | − | 6484.45i | −0.273136 | − | 0.659408i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10176.1 | − | 4215.08i | −1.02809 | − | 0.425847i | −0.196065 | − | 0.980591i | \(-0.562816\pi\) |
−0.832021 | + | 0.554743i | \(0.812816\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11097.1i | 1.11388i | 0.830552 | + | 0.556941i | \(0.188025\pi\) | ||||
−0.830552 | + | 0.556941i | \(0.811975\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1497.21i | 0.149315i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9665.86 | + | 4003.73i | 0.957779 | + | 0.396725i | 0.806149 | − | 0.591712i | \(-0.201548\pi\) |
0.151630 | + | 0.988437i | \(0.451548\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 326.277 | + | 787.701i | 0.0321238 | + | 0.0775537i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1547.81 | + | 1547.81i | 0.151421 | + | 0.151421i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −665.552 | + | 665.552i | −0.0646979 | + | 0.0646979i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1886.01 | + | 781.212i | −0.182181 | + | 0.0754620i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1398.96 | − | 3377.38i | 0.134285 | − | 0.324192i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19410.2 | 1.85151 | 0.925757 | − | 0.378119i | \(-0.123429\pi\) | ||||
0.925757 | + | 0.378119i | \(0.123429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3456.50 | −0.327656 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 310.996 | − | 750.810i | 0.0292977 | − | 0.0707309i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2719.06 | − | 1126.27i | 0.254570 | − | 0.105446i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10505.7 | + | 10505.7i | −0.977530 | + | 0.977530i | −0.999753 | − | 0.0222232i | \(-0.992926\pi\) |
0.0222232 | + | 0.999753i | \(0.492926\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1542.24 | + | 1542.24i | 0.142623 | + | 0.142623i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5195.37 | + | 12542.7i | 0.477523 | + | 1.15284i | 0.960767 | + | 0.277357i | \(0.0894586\pi\) |
−0.483243 | + | 0.875486i | \(0.660541\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14255.3 | + | 5904.72i | 1.30228 | + | 0.539422i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 242.689i | − | 0.0220365i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1217.77i | − | 0.109908i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7506.94 | + | 3109.48i | 0.673461 | + | 0.278957i | 0.693090 | − | 0.720851i | \(-0.256249\pi\) |
−0.0196297 | + | 0.999807i | \(0.506249\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 883.395 | + | 2132.70i | 0.0787768 | + | 0.190184i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2849.72 | + | 2849.72i | 0.252610 | + | 0.252610i | 0.822040 | − | 0.569430i | \(-0.192836\pi\) |
−0.569430 | + | 0.822040i | \(0.692836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3807.05 | + | 3807.05i | −0.335468 | + | 0.335468i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 405.770 | − | 168.075i | 0.0355441 | − | 0.0147229i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5853.53 | − | 14131.7i | 0.509731 | − | 1.23060i | −0.434308 | − | 0.900764i | \(-0.643007\pi\) |
0.944039 | − | 0.329834i | \(-0.106993\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1899.15 | 0.164409 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1896.26 | −0.163201 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −632.701 | + | 1527.47i | −0.0541362 | + | 0.130696i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −492.975 | + | 204.197i | −0.0419362 | + | 0.0173705i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3516.44 | − | 3516.44i | 0.297407 | − | 0.297407i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −108.330 | − | 108.330i | −0.00910949 | − | 0.00910949i | 0.702537 | − | 0.711647i | \(-0.252050\pi\) |
−0.711647 | + | 0.702537i | \(0.752050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7209.17 | − | 17404.5i | −0.602744 | − | 1.45515i | −0.870745 | − | 0.491734i | \(-0.836363\pi\) |
0.268001 | − | 0.963419i | \(-0.413637\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 380.471 | + | 157.596i | 0.0316288 | + | 0.0131011i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12342.5i | 1.02021i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29432.1i | 2.41901i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13618.2 | − | 5640.84i | −1.11296 | − | 0.461001i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3391.12 | − | 8186.89i | −0.275583 | − | 0.665317i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4638.58 | + | 4638.58i | 0.374847 | + | 0.374847i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2227.07 | − | 2227.07i | 0.178966 | − | 0.178966i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 698.434 | − | 289.301i | 0.0558138 | − | 0.0231189i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1014.09 | + | 2448.22i | −0.0805895 | + | 0.194560i | −0.959038 | − | 0.283276i | \(-0.908579\pi\) |
0.878449 | + | 0.477836i | \(0.158579\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7409.02 | 0.585546 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3641.22 | 0.286188 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 430.820 | − | 1040.09i | 0.0336755 | − | 0.0813000i | −0.906147 | − | 0.422963i | \(-0.860990\pi\) |
0.939823 | + | 0.341663i | \(0.110990\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13442.8 | − | 5568.18i | 1.04503 | − | 0.432868i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2947.71 | − | 2947.71i | 0.227907 | − | 0.227907i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1182.84 | + | 1182.84i | 0.0909578 | + | 0.0909578i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −264.517 | − | 638.601i | −0.0202309 | − | 0.0488416i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 388.391 | + | 160.877i | 0.0295452 | + | 0.0122380i | 0.397407 | − | 0.917642i | \(-0.369910\pi\) |
−0.367862 | + | 0.929880i | \(0.619910\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18696.9i | − | 1.41466i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 311.100i | 0.0234129i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12187.4 | − | 5048.19i | −0.912323 | − | 0.377897i | −0.123378 | − | 0.992360i | \(-0.539373\pi\) |
−0.788946 | + | 0.614463i | \(0.789373\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −210.957 | − | 509.296i | −0.0157080 | − | 0.0379226i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −662.015 | − | 662.015i | −0.0490335 | − | 0.0490335i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7590.98 | + | 7590.98i | −0.559280 | + | 0.559280i | −0.929102 | − | 0.369822i | \(-0.879418\pi\) |
0.369822 | + | 0.929102i | \(0.379418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19882.0 | + | 8235.38i | −1.45715 | + | 0.603573i | −0.963888 | − | 0.266306i | \(-0.914197\pi\) |
−0.493265 | + | 0.869879i | \(0.664197\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1391.89 | − | 3360.31i | 0.101478 | − | 0.244990i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21080.3 | −1.52888 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4301.60 | −0.310361 | −0.155180 | − | 0.987886i | \(-0.549596\pi\) | ||||
−0.155180 | + | 0.987886i | \(0.549596\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2680.49 | − | 6471.28i | 0.192396 | − | 0.464485i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2812.07 | + | 1164.80i | −0.200799 | + | 0.0831737i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −246.967 | + | 246.967i | −0.0175443 | + | 0.0175443i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3408.86 | + | 3408.86i | 0.240921 | + | 0.240921i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1724.60 | − | 4163.55i | −0.121264 | − | 0.292756i | 0.851578 | − | 0.524228i | \(-0.175646\pi\) |
−0.972842 | + | 0.231471i | \(0.925646\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3080.77 | + | 1276.10i | 0.215520 | + | 0.0892712i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5239.10i | 0.364649i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 19409.8i | − | 1.34412i | −0.740495 | − | 0.672062i | \(-0.765409\pi\) | ||
0.740495 | − | 0.672062i | \(-0.234591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −656.832 | − | 272.069i | −0.0452563 | − | 0.0187458i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1806.54 | + | 4361.37i | 0.123847 | + | 0.298993i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 182.514 | + | 182.514i | 0.0124496 | + | 0.0124496i | 0.713304 | − | 0.700855i | \(-0.247198\pi\) |
−0.700855 | + | 0.713304i | \(0.747198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2102.19 | + | 2102.19i | −0.142679 | + | 0.142679i | −0.774838 | − | 0.632159i | \(-0.782169\pi\) |
0.632159 | + | 0.774838i | \(0.282169\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8805.31 | − | 3647.28i | 0.594660 | − | 0.246316i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2360.81 | − | 5699.51i | 0.158646 | − | 0.383005i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13085.1 | 0.874974 | 0.437487 | − | 0.899225i | \(-0.355869\pi\) | ||||
0.437487 | + | 0.899225i | \(0.355869\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −840.964 | −0.0559566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4056.23 | − | 9792.60i | 0.268572 | − | 0.648390i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8687.78 | + | 3598.60i | −0.572424 | + | 0.237106i | −0.650069 | − | 0.759875i | \(-0.725260\pi\) |
0.0776446 | + | 0.996981i | \(0.475260\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1253.04 | − | 1253.04i | 0.0821587 | − | 0.0821587i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3141.32 | − | 3141.32i | −0.204967 | − | 0.204967i | 0.597157 | − | 0.802124i | \(-0.296297\pi\) |
−0.802124 | + | 0.597157i | \(0.796297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 808.300 | + | 1951.41i | 0.0524852 | + | 0.126710i | 0.947947 | − | 0.318427i | \(-0.103155\pi\) |
−0.895462 | + | 0.445138i | \(0.853155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18090.9 | − | 7493.51i | −1.16902 | − | 0.484226i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1005.37i | 0.0646536i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 7976.82i | − | 0.510516i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 77.6525 | + | 32.1647i | 0.00494600 | + | 0.00204870i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2180.59 | − | 5264.41i | −0.138229 | − | 0.333713i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4291.77 | − | 4291.77i | −0.270765 | − | 0.270765i | 0.558643 | − | 0.829408i | \(-0.311322\pi\) |
−0.829408 | + | 0.558643i | \(0.811322\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6016.28 | − | 6016.28i | 0.377765 | − | 0.377765i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3619.81 | + | 1499.38i | −0.226217 | + | 0.0937023i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5746.75 | + | 13873.9i | −0.357449 | + | 0.862957i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13612.8 | −0.842748 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14676.8 | −0.904365 | −0.452182 | − | 0.891925i | \(-0.649354\pi\) | ||||
−0.452182 | + | 0.891925i | \(0.649354\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11364.5 | + | 27436.3i | −0.697001 | + | 1.68271i | 0.0331742 | + | 0.999450i | \(0.489438\pi\) |
−0.730175 | + | 0.683260i | \(0.760562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3454.32 | − | 1430.83i | 0.210874 | − | 0.0873470i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10214.4 | − | 10214.4i | 0.620661 | − | 0.620661i | −0.325039 | − | 0.945701i | \(-0.605378\pi\) |
0.945701 | + | 0.325039i | \(0.105378\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 995.815 | + | 995.815i | 0.0602298 | + | 0.0602298i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −257.431 | − | 621.494i | −0.0154985 | − | 0.0374167i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3089.13 | − | 1279.56i | −0.185125 | − | 0.0766814i | 0.288195 | − | 0.957572i | \(-0.406945\pi\) |
−0.473321 | + | 0.880890i | \(0.656945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5943.60i | 0.354558i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 21229.6i | − | 1.26065i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12234.1 | − | 5067.54i | −0.723178 | − | 0.299550i | −0.00943266 | − | 0.999956i | \(-0.503003\pi\) |
−0.713745 | + | 0.700405i | \(0.753003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8849.67 | − | 21365.0i | −0.520745 | − | 1.25719i | −0.937441 | − | 0.348144i | \(-0.886812\pi\) |
0.416696 | − | 0.909046i | \(-0.363188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4369.76 | − | 4369.76i | −0.255969 | − | 0.255969i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −135.820 | + | 135.820i | −0.00792012 | + | 0.00792012i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 39770.6 | − | 16473.5i | 2.30873 | − | 0.956309i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3552.46 | + | 8576.39i | −0.205300 | + | 0.495639i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1390.16 | −0.0799797 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11132.3 | −0.637621 | −0.318811 | − | 0.947818i | \(-0.603283\pi\) | ||||
−0.318811 | + | 0.947818i | \(0.603283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3797.32 | − | 9167.53i | 0.216532 | − | 0.522753i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19266.1 | − | 7980.30i | 1.09373 | − | 0.453040i | 0.238427 | − | 0.971160i | \(-0.423368\pi\) |
0.855307 | + | 0.518121i | \(0.173368\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −935.033 | + | 935.033i | −0.0528472 | + | 0.0528472i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −39.5138 | − | 39.5138i | −0.00222345 | − | 0.00222345i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6152.93 | + | 14854.5i | 0.344708 | + | 0.832199i | 0.997227 | + | 0.0744258i | \(0.0237124\pi\) |
−0.652519 | + | 0.757773i | \(0.726288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2153.51 | + | 892.014i | 0.120119 | + | 0.0497549i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8786.97i | 0.487982i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 6937.89i | − | 0.383618i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3264.16 | + | 1352.06i | 0.179703 | + | 0.0744353i | 0.470721 | − | 0.882282i | \(-0.343994\pi\) |
−0.291018 | + | 0.956718i | \(0.593994\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 41.7281 | + | 100.740i | 0.00228733 | + | 0.00552210i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4357.56 | − | 4357.56i | −0.237830 | − | 0.237830i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10329.7 | − | 10329.7i | 0.561355 | − | 0.561355i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11590.8 | + | 4801.05i | −0.627186 | + | 0.259789i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9617.29 | + | 23218.2i | −0.518174 | + | 1.25098i | 0.420850 | + | 0.907130i | \(0.361732\pi\) |
−0.939024 | + | 0.343852i | \(0.888268\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1539.48 | −0.0825927 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2119.63 | 0.113234 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 925.723 | − | 2234.89i | 0.0492438 | − | 0.118885i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16496.9 | + | 6833.23i | −0.873841 | + | 0.361957i | −0.774105 | − | 0.633057i | \(-0.781800\pi\) |
−0.0997360 | + | 0.995014i | \(0.531800\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13222.4 | − | 13222.4i | 0.697439 | − | 0.697439i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24348.7 | + | 24348.7i | 1.27892 | + | 1.27892i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −176.260 | − | 425.529i | −0.00921922 | − | 0.0222572i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1109.82 | − | 459.703i | −0.0578062 | − | 0.0239441i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8307.83i | 0.430918i | 0.976513 | + | 0.215459i | \(0.0691247\pi\) | ||||
−0.976513 | + | 0.215459i | \(0.930875\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 742.842i | − | 0.0383702i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2683.09 | − | 1111.37i | −0.138015 | − | 0.0571679i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8347.93 | + | 20153.7i | 0.427633 | + | 1.03240i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18455.8 | − | 18455.8i | −0.941524 | − | 0.941524i | 0.0568585 | − | 0.998382i | \(-0.481892\pi\) |
−0.998382 | + | 0.0568585i | \(0.981892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3906.40 | + | 3906.40i | −0.198466 | + | 0.198466i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28476.3 | − | 11795.3i | 1.44081 | − | 0.596804i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1663.72 | − | 4016.59i | 0.0838350 | − | 0.202396i | −0.876403 | − | 0.481579i | \(-0.840064\pi\) |
0.960238 | + | 0.279183i | \(0.0900636\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3003.04 | −0.150706 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −910.581 | −0.0455111 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5023.53 | + | 12127.9i | −0.250059 | + | 0.603695i | −0.998208 | − | 0.0598348i | \(-0.980943\pi\) |
0.748149 | + | 0.663530i | \(0.230943\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1542.51 | + | 638.930i | −0.0764718 | + | 0.0316757i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2091.87 | + | 2091.87i | −0.103289 | + | 0.103289i | −0.756863 | − | 0.653574i | \(-0.773269\pi\) |
0.653574 | + | 0.756863i | \(0.273269\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2267.62 | + | 2267.62i | 0.111516 | + | 0.111516i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13020.7 | + | 31434.7i | 0.637753 | + | 1.53967i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2723.03 | − | 1127.92i | −0.132840 | − | 0.0550243i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.8821i | 0.00120900i | 1.00000 | 0.000604502i | \(0.000192419\pi\) | |||||
−1.00000 | 0.000604502i | \(0.999808\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 6072.45i | − | 0.293881i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5859.34 | − | 2427.02i | −0.282442 | − | 0.116991i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8933.37 | + | 21567.1i | 0.428915 | + | 1.03549i | 0.979632 | + | 0.200801i | \(0.0643544\pi\) |
−0.550717 | + | 0.834692i | \(0.685646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 613.722 | + | 613.722i | 0.0293501 | + | 0.0293501i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11741.7 | + | 11741.7i | −0.559311 | + | 0.559311i | −0.929111 | − | 0.369800i | \(-0.879426\pi\) |
0.369800 | + | 0.929111i | \(0.379426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1511.47 | + | 626.072i | −0.0717155 | + | 0.0297055i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3041.32 | + | 7342.39i | −0.143737 | + | 0.347012i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27974.8 | −1.31696 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31635.5 | 1.48349 | 0.741745 | − | 0.670682i | \(-0.233998\pi\) | ||||
0.741745 | + | 0.670682i | \(0.233998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2448.01 | + | 5910.02i | −0.114349 | + | 0.276063i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36991.4 | − | 15322.3i | 1.72120 | − | 0.712944i | 0.721408 | − | 0.692511i | \(-0.243495\pi\) |
0.999791 | − | 0.0204334i | \(-0.00650462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12338.7 | + | 12338.7i | −0.571894 | + | 0.571894i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 219.602 | + | 219.602i | 0.0101392 | + | 0.0101392i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1510.36 | − | 3646.34i | −0.0694665 | − | 0.167707i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1201.58 | + | 497.712i | 0.0550525 | + | 0.0228035i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20263.2i | 0.924838i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5342.49i | − | 0.242907i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26589.7 | + | 11013.8i | 1.20435 | + | 0.498857i | 0.892401 | − | 0.451243i | \(-0.149019\pi\) |
0.311946 | + | 0.950100i | \(0.399019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3377.04 | + | 8152.89i | 0.152377 | + | 0.367871i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 175.137 | + | 175.137i | 0.00787251 | + | 0.00787251i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19526.4 | − | 19526.4i | 0.874403 | − | 0.874403i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1281.80 | − | 530.939i | 0.0571833 | − | 0.0236861i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14859.3 | + | 35873.5i | −0.660406 | + | 1.59436i | 0.136763 | + | 0.990604i | \(0.456330\pi\) |
−0.797168 | + | 0.603757i | \(0.793670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17473.5 | 0.773678 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11238.5 | 0.495746 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −776.194 | + | 1873.90i | −0.0341112 | + | 0.0823517i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1832.49 | + | 759.042i | −0.0802321 | + | 0.0332332i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2222.60 | − | 2222.60i | 0.0969507 | − | 0.0969507i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11376.3 | + | 11376.3i | 0.494401 | + | 0.494401i | 0.909690 | − | 0.415288i | \(-0.136319\pi\) |
−0.415288 | + | 0.909690i | \(0.636319\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5636.60 | + | 13608.0i | 0.244054 | + | 0.589199i | 0.997678 | − | 0.0681071i | \(-0.0216960\pi\) |
−0.753624 | + | 0.657306i | \(0.771696\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10609.4 | − | 4394.55i | −0.457672 | − | 0.189574i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 5323.27i | − | 0.228793i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8327.39i | − | 0.356595i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2001.14 | − | 828.899i | −0.0853791 | − | 0.0353652i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −919.197 | − | 2219.14i | −0.0390745 | − | 0.0943343i | 0.903137 | − | 0.429352i | \(-0.141258\pi\) |
−0.942212 | + | 0.335017i | \(0.891258\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11701.5 | − | 11701.5i | −0.495612 | − | 0.495612i | 0.414457 | − | 0.910069i | \(-0.363971\pi\) |
−0.910069 | + | 0.414457i | \(0.863971\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −311.002 | + | 311.002i | −0.0131245 | + | 0.0131245i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12650.0 | − | 5239.79i | 0.531901 | − | 0.220321i | −0.100534 | − | 0.994934i | \(-0.532055\pi\) |
0.632436 | + | 0.774613i | \(0.282055\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6993.42 | − | 16883.6i | 0.292993 | − | 0.707349i | −0.707007 | − | 0.707207i | \(-0.749955\pi\) |
1.00000 | 0.000141685i | \(-4.50997e-5\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3144.59 | −0.131269 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24756.0 | −1.02971 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2156.09 | − | 5205.26i | 0.0893587 | − | 0.215731i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14975.0 | + | 6202.86i | −0.618415 | + | 0.256156i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8472.75 | − | 8472.75i | 0.348643 | − | 0.348643i | −0.510961 | − | 0.859604i | \(-0.670710\pi\) |
0.859604 | + | 0.510961i | \(0.170710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14253.2 | − | 14253.2i | −0.584413 | − | 0.584413i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 191.115 | + | 461.393i | 0.00780825 | + | 0.0188508i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −990.357 | − | 410.219i | −0.0403187 | − | 0.0167006i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2771.79i | 0.112444i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10337.0i | 0.417861i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14687.1 | − | 6083.61i | −0.591620 | − | 0.245057i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9905.44 | − | 23913.8i | −0.397603 | − | 0.959900i | −0.988233 | − | 0.152957i | \(-0.951121\pi\) |
0.590629 | − | 0.806943i | \(-0.298879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1518.26 | + | 1518.26i | 0.0607293 | + | 0.0607293i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −918.681 | + | 918.681i | −0.0366179 | + | 0.0366179i | −0.725179 | − | 0.688561i | \(-0.758243\pi\) |
0.688561 | + | 0.725179i | \(0.258243\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16817.5 | + | 6966.03i | −0.667992 | + | 0.276691i | −0.690797 | − | 0.723049i | \(-0.742740\pi\) |
0.0228054 | + | 0.999740i | \(0.492740\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −304.691 | + | 735.588i | −0.0120602 | + | 0.0291159i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30735.4 | 1.21233 | 0.606167 | − | 0.795338i | \(-0.292706\pi\) | ||||
0.606167 | + | 0.795338i | \(0.292706\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12137.5 | −0.477096 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 314.782 | − | 759.952i | 0.0123305 | − | 0.0297685i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1650.56 | + | 683.683i | −0.0644319 | + | 0.0266886i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12790.2 | − | 12790.2i | 0.497565 | − | 0.497565i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10452.2 | + | 10452.2i | 0.405218 | + | 0.405218i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −849.837 | − | 2051.69i | −0.0328340 | − | 0.0792682i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15138.1 | + | 6270.40i | 0.582870 | + | 0.241433i | 0.654580 | − | 0.755993i | \(-0.272846\pi\) |
−0.0717100 | + | 0.997426i | \(0.522846\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 7574.08i | − | 0.290634i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8980.66i | 0.343435i | 0.985146 | + | 0.171717i | \(0.0549316\pi\) | ||||
−0.985146 | + | 0.171717i | \(0.945068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16480.5 | − | 6826.45i | −0.628101 | − | 0.260168i | 0.0458448 | − | 0.998949i | \(-0.485402\pi\) |
−0.673946 | + | 0.738780i | \(0.735402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2140.84 | − | 5168.44i | −0.0813147 | − | 0.196311i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12126.2 | + | 12126.2i | 0.459029 | + | 0.459029i | 0.898337 | − | 0.439308i | \(-0.144776\pi\) |
−0.439308 | + | 0.898337i | \(0.644776\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1244.78 | − | 1244.78i | 0.0469614 | − | 0.0469614i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 923.785 | − | 382.644i | 0.0347339 | − | 0.0143873i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1806.59 | − | 4361.51i | 0.0676992 | − | 0.163440i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7687.05 | −0.287095 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17240.9 | −0.641758 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13636.2 | − | 32920.8i | 0.505888 | − | 1.22132i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10566.7 | − | 4376.88i | 0.390709 | − | 0.161837i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1187.88 | + | 1187.88i | −0.0437763 | + | 0.0437763i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12786.7 | − | 12786.7i | −0.469661 | − | 0.469661i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11478.3 | − | 27711.2i | −0.420212 | − | 1.01448i | −0.982285 | − | 0.187393i | \(-0.939996\pi\) |
0.562073 | − | 0.827087i | \(-0.310004\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24982.7 | − | 10348.2i | −0.911578 | − | 0.377588i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29181.6i | 1.06128i | 0.847596 | + | 0.530642i | \(0.178049\pi\) | ||||
−0.847596 | + | 0.530642i | \(0.821951\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 3250.75i | − | 0.117836i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5101.87 | + | 2113.26i | 0.184331 | + | 0.0763523i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1021.94 | − | 2467.19i | −0.0368021 | − | 0.0888482i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17444.3 | + | 17444.3i | 0.626151 | + | 0.626151i | 0.947097 | − | 0.320946i | \(-0.104001\pi\) |
−0.320946 | + | 0.947097i | \(0.604001\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7564.25 | + | 7564.25i | −0.270630 | + | 0.270630i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23868.6 | + | 9886.70i | −0.851186 | + | 0.352573i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3082.85 | − | 7442.67i | 0.109582 | − | 0.264555i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8303.85 | −0.294212 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2760.78 | −0.0975009 | −0.0487505 | − | 0.998811i | \(-0.515524\pi\) | ||||
−0.0487505 | + | 0.998811i | \(0.515524\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2559.54 | + | 6179.26i | −0.0901024 | + | 0.217527i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 11852.1 | − | 4909.29i | 0.415884 | − | 0.172265i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 536.904 | − | 536.904i | 0.0187793 | − | 0.0187793i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20708.4 | − | 20708.4i | −0.721998 | − | 0.721998i | 0.247014 | − | 0.969012i | \(-0.420551\pi\) |
−0.969012 | + | 0.247014i | \(0.920551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1680.72 | + | 4057.62i | 0.0584113 | + | 0.141017i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11292.0 | + | 4677.30i | 0.391189 | + | 0.162036i | 0.569603 | − | 0.821920i | \(-0.307097\pi\) |
−0.178415 | + | 0.983955i | \(0.557097\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 40755.8i | − | 1.40741i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 933.657i | − | 0.0321395i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9860.15 | − | 4084.21i | −0.338344 | − | 0.140147i | 0.207041 | − | 0.978332i | \(-0.433617\pi\) |
−0.545385 | + | 0.838186i | \(0.683617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15418.6 | − | 37223.7i | −0.527405 | − | 1.27327i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6047.77 | − | 6047.77i | −0.206217 | − | 0.206217i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18343.1 | + | 18343.1i | −0.623497 | + | 0.623497i | −0.946424 | − | 0.322927i | \(-0.895333\pi\) |
0.322927 | + | 0.946424i | \(0.395333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8201.47 | + | 3397.16i | −0.277899 | + | 0.115109i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 343.708 | − | 829.784i | 0.0116097 | − | 0.0280283i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1047.30 | −0.0352649 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1287.46 | −0.0432165 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12608.4 | + | 30439.4i | −0.421911 | + | 1.01858i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15794.4 | + | 6542.23i | −0.526879 | + | 0.218240i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31549.6 | + | 31549.6i | −1.04919 | + | 1.04919i | −0.0504630 | + | 0.998726i | \(0.516070\pi\) |
−0.998726 | + | 0.0504630i | \(0.983930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1946.24 | − | 1946.24i | −0.0645224 | − | 0.0645224i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14733.2 | − | 35569.2i | −0.486934 | − | 1.17556i | −0.956255 | − | 0.292534i | \(-0.905501\pi\) |
0.469322 | − | 0.883027i | \(-0.344499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2558.07 | + | 1059.59i | 0.0842835 | + | 0.0349114i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 8736.79i | − | 0.286976i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15596.5i | 0.510724i | 0.966845 | + | 0.255362i | \(0.0821947\pi\) | ||||
−0.966845 | + | 0.255362i | \(0.917805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −992.003 | − | 410.901i | −0.0323846 | − | 0.0134141i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6998.54 | + | 16896.0i | 0.227774 | + | 0.549894i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8671.68 | + | 8671.68i | 0.281367 | + | 0.281367i | 0.833654 | − | 0.552287i | \(-0.186245\pi\) |
−0.552287 | + | 0.833654i | \(0.686245\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9041.76 | − | 9041.76i | 0.292482 | − | 0.292482i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −879.860 | + | 364.450i | −0.0283751 | + | 0.0117534i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32907.5 | − | 79445.8i | 1.05804 | − | 2.55433i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25010.6 | 0.801705 | 0.400852 | − | 0.916143i | \(-0.368714\pi\) | ||||
0.400852 | + | 0.916143i | \(0.368714\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17497.8 | 0.559191 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4409.19 | − | 10644.7i | 0.140483 | − | 0.339156i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24578.9 | + | 10180.9i | −0.780763 | + | 0.323403i | −0.737223 | − | 0.675649i | \(-0.763864\pi\) |
−0.0435398 | + | 0.999052i | \(0.513864\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5291.37 | − | 5291.37i | 0.167579 | − | 0.167579i |
(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 | 128.4.g.a.17.5 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.13.7 | yes | 44 | ||
8.3 | odd | 2 | 256.4.g.b.33.5 | 44 | |||
8.5 | even | 2 | 256.4.g.a.33.7 | 44 | |||
32.5 | even | 8 | inner | 128.4.g.a.113.5 | 44 | ||
32.11 | odd | 8 | 256.4.g.b.225.5 | 44 | |||
32.21 | even | 8 | 256.4.g.a.225.7 | 44 | |||
32.27 | odd | 8 | 32.4.g.a.5.7 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.7 | ✓ | 44 | 32.27 | odd | 8 | ||
32.4.g.a.13.7 | yes | 44 | 4.3 | odd | 2 | ||
128.4.g.a.17.5 | 44 | 1.1 | even | 1 | trivial | ||
128.4.g.a.113.5 | 44 | 32.5 | even | 8 | inner | ||
256.4.g.a.33.7 | 44 | 8.5 | even | 2 | |||
256.4.g.a.225.7 | 44 | 32.21 | even | 8 | |||
256.4.g.b.33.5 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.225.5 | 44 | 32.11 | odd | 8 |