Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,4,Mod(129,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.129");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.44030560092\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.359712057600.22 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 17x^{6} + 82x^{4} + 96x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.8 | ||
Root | \(-1.24759i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.129 |
Dual form | 160.4.c.d.129.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 8.57295i | 1.64986i | 0.565231 | + | 0.824932i | \(0.308787\pi\) | ||||
−0.565231 | + | 0.824932i | \(0.691213\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.582576 | + | 11.1652i | −0.0521072 | + | 0.998641i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.1403i | 1.19546i | 0.801696 | + | 0.597732i | \(0.203931\pi\) | ||||
−0.801696 | + | 0.597732i | \(0.796069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −46.4955 | −1.72205 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.1347 | 0.743765 | 0.371882 | − | 0.928280i | \(-0.378712\pi\) | ||||
0.371882 | + | 0.928280i | \(0.378712\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 70.3303i | − | 1.50047i | −0.661171 | − | 0.750235i | \(-0.729940\pi\) | ||
0.661171 | − | 0.750235i | \(-0.270060\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −95.7183 | − | 4.99439i | −1.64762 | − | 0.0859698i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 73.3212i | 1.04606i | 0.852315 | + | 0.523030i | \(0.175198\pi\) | ||||
−0.852315 | + | 0.523030i | \(0.824802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 110.033 | 1.32859 | 0.664294 | − | 0.747471i | \(-0.268732\pi\) | ||||
0.664294 | + | 0.747471i | \(0.268732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −189.808 | −1.97235 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 107.870i | − | 0.977931i | −0.872303 | − | 0.488965i | \(-0.837374\pi\) | ||
0.872303 | − | 0.488965i | \(-0.162626\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −124.321 | − | 13.0091i | −0.994570 | − | 0.104073i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 167.134i | − | 1.19129i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −68.6424 | −0.439537 | −0.219769 | − | 0.975552i | \(-0.570530\pi\) | ||||
−0.219769 | + | 0.975552i | \(0.570530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −137.167 | −0.794708 | −0.397354 | − | 0.917665i | \(-0.630072\pi\) | ||||
−0.397354 | + | 0.917665i | \(0.630072\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 232.624i | 1.22711i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −247.200 | − | 12.8984i | −1.19384 | − | 0.0622922i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 60.3121i | − | 0.267980i | −0.990983 | − | 0.133990i | \(-0.957221\pi\) | ||
0.990983 | − | 0.133990i | \(-0.0427790\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 602.938 | 2.47557 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 95.1470 | 0.362426 | 0.181213 | − | 0.983444i | \(-0.441998\pi\) | ||||
0.181213 | + | 0.983444i | \(0.441998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 501.479i | 1.77848i | 0.457438 | + | 0.889241i | \(0.348767\pi\) | ||||
−0.457438 | + | 0.889241i | \(0.651233\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.0871 | − | 519.129i | 0.0897313 | − | 1.71971i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 439.305i | 1.36339i | 0.731637 | + | 0.681694i | \(0.238756\pi\) | ||||
−0.731637 | + | 0.681694i | \(0.761244\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −147.192 | −0.429132 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −628.579 | −1.72586 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 286.955i | − | 0.743703i | −0.928292 | − | 0.371851i | \(-0.878723\pi\) | ||
0.928292 | − | 0.371851i | \(-0.121277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.8080 | + | 302.963i | −0.0387555 | + | 0.742755i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 943.303i | 2.19199i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 547.175 | 1.20739 | 0.603696 | − | 0.797215i | \(-0.293694\pi\) | ||||
0.603696 | + | 0.797215i | \(0.293694\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 511.459 | 1.07353 | 0.536767 | − | 0.843730i | \(-0.319645\pi\) | ||||
0.536767 | + | 0.843730i | \(0.319645\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1029.42i | − | 2.05865i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 785.248 | + | 40.9727i | 1.49843 | + | 0.0781852i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 301.547i | − | 0.549848i | −0.961466 | − | 0.274924i | \(-0.911347\pi\) | ||
0.961466 | − | 0.274924i | \(-0.0886527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 924.762 | 1.61345 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 82.8978 | 0.138566 | 0.0692828 | − | 0.997597i | \(-0.477929\pi\) | ||||
0.0692828 | + | 0.997597i | \(0.477929\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 763.267i | − | 1.22375i | −0.790955 | − | 0.611874i | \(-0.790416\pi\) | ||
0.790955 | − | 0.611874i | \(-0.209584\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 111.526 | − | 1065.80i | 0.171706 | − | 1.64091i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 600.770i | 0.889144i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1011.45 | −1.44047 | −0.720236 | − | 0.693729i | \(-0.755966\pi\) | ||||
−0.720236 | + | 0.693729i | \(0.755966\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 177.450 | 0.243416 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 704.554i | 0.931745i | 0.884852 | + | 0.465872i | \(0.154259\pi\) | ||||
−0.884852 | + | 0.465872i | \(0.845741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −818.642 | − | 42.7152i | −1.04464 | − | 0.0545072i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 588.468i | − | 0.725177i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 743.212 | 0.885172 | 0.442586 | − | 0.896726i | \(-0.354061\pi\) | ||||
0.442586 | + | 0.896726i | \(0.354061\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1557.13 | 1.79376 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 1175.93i | − | 1.31116i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −64.1023 | + | 1228.53i | −0.0692290 | + | 1.32678i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1136.00i | 1.18911i | 0.804056 | + | 0.594553i | \(0.202671\pi\) | ||||
−0.804056 | + | 0.594553i | \(0.797329\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1261.64 | −1.28080 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 291.212 | 0.286898 | 0.143449 | − | 0.989658i | \(-0.454181\pi\) | ||||
0.143449 | + | 0.989658i | \(0.454181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 200.445i | 0.191751i | 0.995393 | + | 0.0958757i | \(0.0305651\pi\) | ||||
−0.995393 | + | 0.0958757i | \(0.969435\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 110.577 | − | 2119.23i | 0.102774 | − | 1.96967i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 754.342i | 0.681542i | 0.940146 | + | 0.340771i | \(0.110688\pi\) | ||||
−0.940146 | + | 0.340771i | \(0.889312\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −501.680 | −0.440846 | −0.220423 | − | 0.975404i | \(-0.570744\pi\) | ||||
−0.220423 | + | 0.975404i | \(0.570744\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 517.053 | 0.442130 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 497.248i | 0.413958i | 0.978345 | + | 0.206979i | \(0.0663631\pi\) | ||||
−0.978345 | + | 0.206979i | \(0.933637\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1204.38 | + | 62.8423i | 0.976602 | + | 0.0509572i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3270.04i | 2.58389i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1623.35 | −1.25053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −594.709 | −0.446814 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 815.690i | 0.597954i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 217.675 | − | 1380.49i | 0.155756 | − | 0.987796i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 915.221i | 0.639470i | 0.947507 | + | 0.319735i | \(0.103594\pi\) | ||||
−0.947507 | + | 0.319735i | \(0.896406\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4299.15 | −2.93426 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 607.419 | 0.405118 | 0.202559 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202559 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2436.15i | 1.58828i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1866.07 | + | 97.3679i | 1.18967 | + | 0.0620748i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1418.98i | − | 0.884900i | −0.896793 | − | 0.442450i | \(-0.854109\pi\) | ||
0.896793 | − | 0.442450i | \(-0.145891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3035.85 | −1.85250 | −0.926250 | − | 0.376910i | \(-0.876987\pi\) | ||||
−0.926250 | + | 0.376910i | \(0.876987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3766.14 | −2.24941 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1908.39i | − | 1.11600i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39.9894 | − | 766.403i | 0.0229030 | − | 0.438940i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1261.87i | − | 0.708011i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2649.26 | 1.45662 | 0.728308 | − | 0.685250i | \(-0.240307\pi\) | ||||
0.728308 | + | 0.685250i | \(0.240307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 283.297 | 0.152678 | 0.0763390 | − | 0.997082i | \(-0.475677\pi\) | ||||
0.0763390 | + | 0.997082i | \(0.475677\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3409.10i | − | 1.80137i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 79.9103 | − | 1531.49i | 0.0414100 | − | 0.793629i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1414.88i | 0.719235i | 0.933100 | + | 0.359617i | \(0.117093\pi\) | ||||
−0.933100 | + | 0.359617i | \(0.882907\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2460.05 | 1.22701 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2388.27 | 1.16908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1725.68i | − | 0.829239i | −0.909995 | − | 0.414619i | \(-0.863915\pi\) | ||
0.909995 | − | 0.414619i | \(-0.136085\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2597.28 | − | 135.521i | −1.22544 | − | 0.0639413i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1979.92i | − | 0.917428i | −0.888584 | − | 0.458714i | \(-0.848310\pi\) | ||
0.888584 | − | 0.458714i | \(-0.151690\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2749.35 | −1.25141 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5116.01 | −2.28790 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1468.72i | − | 0.645460i | −0.946491 | − | 0.322730i | \(-0.895399\pi\) | ||
0.946491 | − | 0.322730i | \(-0.104601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 288.025 | − | 2752.51i | 0.124415 | − | 1.18897i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4690.90i | 1.99203i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2978.59 | 1.24375 | 0.621873 | − | 0.783118i | \(-0.286372\pi\) | ||||
0.621873 | + | 0.783118i | \(0.286372\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1682.07 | −0.690760 | −0.345380 | − | 0.938463i | \(-0.612250\pi\) | ||||
−0.345380 | + | 0.938463i | \(0.612250\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4384.71i | 1.77119i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 673.394 | + | 35.1364i | 0.267616 | + | 0.0139637i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1989.55i | 0.778022i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3700.38 | 1.42414 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 274.334 | 0.103927 | 0.0519637 | − | 0.998649i | \(-0.483452\pi\) | ||||
0.0519637 | + | 0.998649i | \(0.483452\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2898.50i | − | 1.08103i | −0.841335 | − | 0.540514i | \(-0.818230\pi\) | ||
0.841335 | − | 0.540514i | \(-0.181770\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −351.257 | + | 6731.90i | −0.128995 | + | 2.47221i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2330.37i | 0.842801i | 0.906875 | + | 0.421400i | \(0.138461\pi\) | ||||
−0.906875 | + | 0.421400i | \(0.861539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1105.05 | −0.393644 | −0.196822 | − | 0.980439i | \(-0.563062\pi\) | ||||
−0.196822 | + | 0.980439i | \(0.563062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2585.15 | 0.907175 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1519.76i | − | 0.525451i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −55.4303 | + | 1062.33i | −0.0188850 | + | 0.361933i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5015.45i | 1.68405i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2985.70 | 0.988158 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4749.82 | 1.54972 | 0.774860 | − | 0.632133i | \(-0.217820\pi\) | ||||
0.774860 | + | 0.632133i | \(0.217820\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 710.679i | 0.228615i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5599.08 | − | 292.149i | −1.77607 | − | 0.0926717i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3036.92i | − | 0.950044i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6543.45 | 2.01902 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5156.70 | 1.56958 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1889.71i | 0.567462i | 0.958904 | + | 0.283731i | \(0.0915723\pi\) | ||||
−0.958904 | + | 0.283731i | \(0.908428\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5780.37 | + | 604.864i | 1.71270 | + | 0.179219i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 4154.11i | − | 1.21462i | −0.794466 | − | 0.607309i | \(-0.792249\pi\) | ||
0.794466 | − | 0.607309i | \(-0.207751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 888.642 | 0.256433 | 0.128216 | − | 0.991746i | \(-0.459075\pi\) | ||||
0.128216 | + | 0.991746i | \(0.459075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5150.37 | −1.46697 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4919.38i | 1.38317i | 0.722294 | + | 0.691586i | \(0.243088\pi\) | ||||
−0.722294 | + | 0.691586i | \(0.756912\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4904.91 | − | 255.929i | −1.36154 | − | 0.0710423i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 8671.13i | − | 2.37658i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2178.00 | 0.589468 | 0.294734 | − | 0.955579i | \(-0.404769\pi\) | ||||
0.294734 | + | 0.955579i | \(0.404769\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3156.12 | −0.843583 | −0.421792 | − | 0.906693i | \(-0.638599\pi\) | ||||
−0.421792 | + | 0.906693i | \(0.638599\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 2991.34i | − | 0.789688i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 85.7507 | − | 1643.43i | 0.0223609 | − | 0.428549i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7738.62i | − | 1.99351i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6040.10 | −1.53725 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2719.20 | 0.683801 | 0.341901 | − | 0.939736i | \(-0.388929\pi\) | ||||
0.341901 | + | 0.939736i | \(0.388929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2927.01i | − | 0.727350i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 366.195 | − | 7018.18i | 0.0899295 | − | 1.72351i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 749.067i | 0.181811i | 0.995860 | + | 0.0909056i | \(0.0289762\pi\) | ||||
−0.995860 | + | 0.0909056i | \(0.971024\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1335.33 | 0.320360 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3191.56 | 0.756907 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2546.04i | 0.596942i | 0.954419 | + | 0.298471i | \(0.0964766\pi\) | ||||
−0.954419 | + | 0.298471i | \(0.903523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3203.89 | + | 167.173i | 0.742692 | + | 0.0387522i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6371.52i | 1.46041i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7982.07 | 1.80920 | 0.904601 | − | 0.426260i | \(-0.140169\pi\) | ||||
0.904601 | + | 0.426260i | \(0.140169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1686.58 | 0.378054 | 0.189027 | − | 0.981972i | \(-0.439467\pi\) | ||||
0.189027 | + | 0.981972i | \(0.439467\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13349.2i | 2.95946i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3373.42 | − | 352.998i | −0.739726 | − | 0.0774056i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1423.07i | 0.308679i | 0.988018 | + | 0.154339i | \(0.0493249\pi\) | ||||
−0.988018 | + | 0.154339i | \(0.950675\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6377.65 | 1.36853 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5418.67 | 1.15036 | 0.575180 | − | 0.818027i | \(-0.304932\pi\) | ||||
0.575180 | + | 0.818027i | \(0.304932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8343.38i | − | 1.75252i | −0.481842 | − | 0.876258i | \(-0.660032\pi\) | ||
0.481842 | − | 0.876258i | \(-0.339968\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10532.1 | − | 549.545i | −2.18901 | − | 0.114218i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2106.58i | 0.433267i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −463.000 | −0.0942398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9738.87 | −1.96186 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2331.73i | − | 0.464919i | −0.972606 | − | 0.232459i | \(-0.925323\pi\) | ||
0.972606 | − | 0.232459i | \(-0.0746772\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −318.771 | + | 6109.29i | −0.0629137 | + | 1.20575i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4535.12i | − | 0.886041i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7586.51 | −1.46736 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11102.9 | −2.12611 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2496.55i | 0.473343i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −297.964 | + | 5710.52i | −0.0559388 | + | 1.07208i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2100.00i | 0.390401i | 0.980763 | + | 0.195200i | \(0.0625357\pi\) | ||||
−0.980763 | + | 0.195200i | \(0.937464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1718.40 | −0.316364 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8501.38 | 1.55006 | 0.775030 | − | 0.631924i | \(-0.217735\pi\) | ||||
0.775030 | + | 0.631924i | \(0.217735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7257.73i | − | 1.31064i | −0.755350 | − | 0.655321i | \(-0.772533\pi\) | ||
0.755350 | − | 0.655321i | \(-0.227467\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11493.7 | + | 599.717i | 2.05586 | + | 0.107271i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9639.14i | − | 1.70785i | −0.520397 | − | 0.853925i | \(-0.674216\pi\) | ||
0.520397 | − | 0.853925i | \(-0.325784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1862.59 | −0.326912 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6466.93 | −1.12445 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8067.72i | 1.38978i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −914.933 | + | 8743.55i | −0.156158 | + | 1.49232i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 4300.88i | − | 0.727337i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9726.34 | −1.62988 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −360.466 | −0.0598581 | −0.0299290 | − | 0.999552i | \(-0.509528\pi\) | ||||
−0.0299290 | + | 0.999552i | \(0.509528\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2804.24i | 0.461476i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3366.82 | + | 175.674i | 0.549101 | + | 0.0286510i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2820.47i | − | 0.455908i | −0.973672 | − | 0.227954i | \(-0.926796\pi\) | ||
0.973672 | − | 0.227954i | \(-0.0732036\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4262.89 | −0.682974 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3721.99 | −0.591076 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4335.24i | 0.682451i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −538.744 | + | 10325.1i | −0.0840725 | + | 1.61126i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8617.62i | 1.33319i | 0.745419 | + | 0.666597i | \(0.232250\pi\) | ||||
−0.745419 | + | 0.666597i | \(0.767750\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −735.067 | −0.112743 | −0.0563714 | − | 0.998410i | \(-0.517953\pi\) | ||||
−0.0563714 | + | 0.998410i | \(0.517953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11754.6 | −1.78750 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4535.35i | − | 0.683830i | −0.939731 | − | 0.341915i | \(-0.888924\pi\) | ||
0.939731 | − | 0.341915i | \(-0.111076\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −48.2943 | + | 925.567i | −0.00722026 | + | 0.138377i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 13916.9i | − | 2.06320i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5426.44 | −0.797762 | −0.398881 | − | 0.917003i | \(-0.630601\pi\) | ||||
−0.398881 | + | 0.917003i | \(0.630601\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5248.15 | 0.765148 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5098.41i | − | 0.737182i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8521.99 | + | 444.661i | 1.22209 | + | 0.0637660i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 609.673i | − | 0.0867157i | −0.999060 | − | 0.0433579i | \(-0.986194\pi\) | ||
0.999060 | − | 0.0433579i | \(-0.0138056\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4423.90 | −0.624117 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6353.26 | 0.889069 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5089.42i | 0.706489i | 0.935531 | + | 0.353244i | \(0.114922\pi\) | ||||
−0.935531 | + | 0.353244i | \(0.885078\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11834.8 | + | 1866.12i | 1.62973 | + | 0.256976i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4827.64i | 0.659513i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 910.876 | 0.123453 | 0.0617263 | − | 0.998093i | \(-0.480339\pi\) | ||||
0.0617263 | + | 0.998093i | \(0.480339\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7846.14 | −1.05504 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 7686.98i | − | 1.02555i | −0.858522 | − | 0.512776i | \(-0.828617\pi\) | ||
0.858522 | − | 0.512776i | \(-0.171383\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6707.68 | − | 349.994i | −0.887936 | − | 0.0463307i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 23316.5i | − | 3.06264i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4372.77 | −0.569943 | −0.284972 | − | 0.958536i | \(-0.591984\pi\) | ||||
−0.284972 | + | 0.958536i | \(0.591984\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7909.14 | 1.02297 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5207.38i | 0.668390i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 589.247 | − | 11293.0i | 0.0750589 | − | 1.43851i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12591.9i | 1.59186i | 0.605391 | + | 0.795928i | \(0.293017\pi\) | ||||
−0.605391 | + | 0.795928i | \(0.706983\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20885.0 | −2.62045 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3614.48 | 0.450122 | 0.225061 | − | 0.974345i | \(-0.427742\pi\) | ||||
0.225061 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9647.01i | 1.19244i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −103.378 | + | 1981.26i | −0.0126837 | + | 0.243085i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1636.55i | − | 0.199314i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −639.314 | −0.0772910 | −0.0386455 | − | 0.999253i | \(-0.512304\pi\) | ||||
−0.0386455 | + | 0.999253i | \(0.512304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12164.8 | 1.45997 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12114.6i | 1.44339i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7866.45 | − | 410.456i | −0.930479 | − | 0.0485506i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 26026.2i | − | 3.05637i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11018.4 | −1.28469 | −0.642346 | − | 0.766415i | \(-0.722039\pi\) | ||||
−0.642346 | + | 0.766415i | \(0.722039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16513.1 | 1.91164 | 0.955820 | − | 0.293952i | \(-0.0949707\pi\) | ||||
0.955820 | + | 0.293952i | \(0.0949707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 20425.7i | − | 2.34783i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 953.842 | − | 9115.38i | 0.108866 | − | 1.04038i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11323.9i | 1.28337i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16360.5 | 1.84124 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6106.80 | 0.682492 | 0.341246 | − | 0.939974i | \(-0.389151\pi\) | ||||
0.341246 | + | 0.939974i | \(0.389151\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1757.88i | − | 0.195100i | −0.995231 | − | 0.0975500i | \(-0.968899\pi\) | ||
0.995231 | − | 0.0975500i | \(-0.0311006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6570.33 | + | 342.827i | 0.724192 | + | 0.0377869i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 11869.2i | − | 1.29927i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1055.02 | −0.114700 | −0.0573500 | − | 0.998354i | \(-0.518265\pi\) | ||||
−0.0573500 | + | 0.998354i | \(0.518265\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6843.78 | 0.738989 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7775.51i | 0.833918i | 0.908925 | + | 0.416959i | \(0.136904\pi\) | ||||
−0.908925 | + | 0.416959i | \(0.863096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −432.977 | + | 8298.08i | −0.0461238 | + | 0.883970i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22712.0i | 2.40322i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11245.1 | 1.18194 | 0.590969 | − | 0.806694i | \(-0.298745\pi\) | ||||
0.590969 | + | 0.806694i | \(0.298745\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2581.78 | 0.269560 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2428.69i | 0.251898i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −907.148 | + | 17385.6i | −0.0934676 | + | 1.79132i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 13576.9i | − | 1.38972i | −0.719145 | − | 0.694860i | \(-0.755466\pi\) | ||
0.719145 | − | 0.694860i | \(-0.244534\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12254.4 | 1.24616 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9605.08 | −0.970397 | −0.485199 | − | 0.874404i | \(-0.661253\pi\) | ||||
−0.485199 | + | 0.874404i | \(0.661253\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3226.71i | 0.323883i | 0.986800 | + | 0.161942i | \(0.0517756\pi\) | ||||
−0.986800 | + | 0.161942i | \(0.948224\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13129.4 | + | 685.067i | 1.30938 | + | 0.0683209i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 20.6790i | − | 0.00204906i | −0.999999 | − | 0.00102453i | \(-0.999674\pi\) | ||
0.999999 | − | 0.00102453i | \(-0.000326118\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6676.34 | 0.657323 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12129.7 | −1.18664 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13607.5i | 1.32277i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13679.4 | − | 1431.42i | −1.32137 | − | 0.138270i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13342.1i | 1.28070i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12492.9 | 1.19168 | 0.595841 | − | 0.803102i | \(-0.296819\pi\) | ||||
0.595841 | + | 0.803102i | \(0.296819\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4241.77 | −0.402096 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20474.5i | 1.92882i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12683.6 | − | 661.806i | −1.18749 | − | 0.0619610i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4944.60i | 0.460084i | 0.973181 | + | 0.230042i | \(0.0738864\pi\) | ||||
−0.973181 | + | 0.230042i | \(0.926114\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14794.2 | 1.36813 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7712.73 | −0.708902 | −0.354451 | − | 0.935075i | \(-0.615332\pi\) | ||||
−0.354451 | + | 0.935075i | \(0.615332\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5032.95i | − | 0.459782i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 735.000 | − | 14086.4i | 0.0667390 | − | 1.27906i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1835.38i | 0.165650i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1492.41 | 0.133886 | 0.0669432 | − | 0.997757i | \(-0.478675\pi\) | ||||
0.0669432 | + | 0.997757i | \(0.478675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16973.7 | 1.51363 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3105.13i | − | 0.275250i | −0.990484 | − | 0.137625i | \(-0.956053\pi\) | ||
0.990484 | − | 0.137625i | \(-0.0439469\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −169.653 | + | 3251.43i | −0.0149494 | + | 0.286508i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 23570.1i | − | 2.06466i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15363.5 | −1.33787 | −0.668933 | − | 0.743322i | \(-0.733249\pi\) | ||||
−0.668933 | + | 0.743322i | \(0.733249\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16898.9 | 1.46295 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 18390.1i | − | 1.58274i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2237.99 | − | 116.774i | −0.191491 | − | 0.00999162i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11920.4i | 1.01404i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12591.2 | 1.06492 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9924.25 | −0.834529 | −0.417264 | − | 0.908785i | \(-0.637011\pi\) | ||||
−0.417264 | + | 0.908785i | \(0.637011\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 455.146i | − | 0.0380538i | −0.999819 | − | 0.0190269i | \(-0.993943\pi\) | ||
0.999819 | − | 0.0190269i | \(-0.00605681\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 23597.1 | + | 2469.22i | 1.96164 | + | 0.205268i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10057.3i | − | 0.831312i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 531.111 | 0.0436517 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −25441.1 | −2.07919 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6691.72i | − | 0.543809i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8422.34 | − | 439.461i | −0.680616 | − | 0.0355132i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25535.3i | 2.05201i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3994.02 | −0.319174 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23383.9 | 1.85832 | 0.929160 | − | 0.369678i | \(-0.120532\pi\) | ||||
0.929160 | + | 0.369678i | \(0.120532\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 14420.3i | − | 1.13966i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 292.267 | − | 5601.34i | 0.0229713 | − | 0.440248i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6908.03i | − | 0.539974i | −0.962864 | − | 0.269987i | \(-0.912981\pi\) | ||
0.962864 | − | 0.269987i | \(-0.0870195\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23780.5 | −1.84868 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7552.90 | −0.583964 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 22393.8i | − | 1.72203i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −301.222 | + | 5772.97i | −0.0230382 | + | 0.441530i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3221.81i | − | 0.245085i | −0.992463 | − | 0.122543i | \(-0.960895\pi\) | ||
0.992463 | − | 0.122543i | \(-0.0391048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 35269.1 | 2.66856 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17056.3 | −1.28363 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 14822.7i | − | 1.10959i | −0.831986 | − | 0.554796i | \(-0.812796\pi\) | ||
0.831986 | − | 0.554796i | \(-0.187204\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5551.85 | − | 289.685i | −0.413395 | − | 0.0215701i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3928.79i | 0.290994i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6434.10 | −0.474045 | −0.237022 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237022 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17760.3 | −1.30165 | −0.650827 | − | 0.759226i | \(-0.725578\pi\) | ||||
−0.650827 | + | 0.759226i | \(0.725578\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2351.85i | 0.171466i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1403.29 | + | 13410.5i | −0.101776 | + | 0.972620i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1341.96i | − | 0.0968227i | −0.998827 | − | 0.0484113i | \(-0.984584\pi\) | ||
0.998827 | − | 0.0484113i | \(-0.0154158\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24848.7 | 1.78355 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15599.0 | −1.11387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7786.42i | − | 0.553140i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −36510.5 | − | 1905.05i | −2.58038 | − | 0.134639i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12957.3i | 0.911082i | 0.890215 | + | 0.455541i | \(0.150554\pi\) | ||||
−0.890215 | + | 0.455541i | \(0.849446\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15092.8 | −1.05584 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19978.1 | −1.39051 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5966.63i | 0.413187i | 0.978427 | + | 0.206594i | \(0.0662378\pi\) | ||||
−0.978427 | + | 0.206594i | \(0.933762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 945.726 | − | 18125.0i | 0.0651613 | − | 1.24883i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 9473.56i | − | 0.649459i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10311.9 | −0.703396 | −0.351698 | − | 0.936114i | \(-0.614396\pi\) | ||||
−0.351698 | + | 0.936114i | \(0.614396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2594.60 | 0.176100 | 0.0880499 | − | 0.996116i | \(-0.471936\pi\) | ||||
0.0880499 | + | 0.996116i | \(0.471936\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14020.6i | 0.946868i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 346.463 | − | 6640.02i | 0.0232822 | − | 0.446207i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7796.08i | − | 0.521306i | −0.965432 | − | 0.260653i | \(-0.916062\pi\) | ||
0.965432 | − | 0.260653i | \(-0.0839379\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13028.9 | 0.866922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30896.5 | 2.04572 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 10443.5i | − | 0.688106i | −0.938950 | − | 0.344053i | \(-0.888200\pi\) | ||
0.938950 | − | 0.344053i | \(-0.111800\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9107.30 | − | 475.201i | −0.597141 | − | 0.0311577i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18306.1i | 1.19445i | 0.802073 | + | 0.597226i | \(0.203730\pi\) | ||||
−0.802073 | + | 0.597226i | \(0.796270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 149.857 | 0.00973066 | 0.00486533 | − | 0.999988i | \(-0.498451\pi\) | ||||
0.00486533 | + | 0.999988i | \(0.498451\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −18028.7 | −1.16500 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16454.9i | 1.05819i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15286.5 | + | 3234.61i | 0.978338 | + | 0.207015i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25596.2i | 1.63033i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4422.16 | 0.280323 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24466.5 | −1.54358 | −0.771789 | − | 0.635879i | \(-0.780638\pi\) | ||||
−0.771789 | + | 0.635879i | \(0.780638\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 40719.9i | 2.55683i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10218.6 | − | 533.185i | −0.638601 | − | 0.0333210i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10352.1i | 0.643901i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3854.37 | −0.238618 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20274.7 | −1.24930 | −0.624652 | − | 0.780903i | \(-0.714759\pi\) | ||||
−0.624652 | + | 0.780903i | \(0.714759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9167.25i | − | 0.562241i | −0.959672 | − | 0.281121i | \(-0.909294\pi\) | ||
0.959672 | − | 0.281121i | \(-0.0907061\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2504.58 | − | 48000.7i | 0.152896 | − | 2.93027i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 5459.82i | − | 0.331758i | −0.986146 | − | 0.165879i | \(-0.946954\pi\) | ||
0.986146 | − | 0.165879i | \(-0.0530462\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14847.4 | 0.898016 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26035.4 | 1.56744 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16280.5i | 0.975659i | 0.872939 | + | 0.487830i | \(0.162211\pi\) | ||||
−0.872939 | + | 0.487830i | \(0.837789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −353.868 | + | 6781.93i | −0.0211096 | + | 0.404568i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35488.4i | 2.10736i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23975.9 | 1.41725 | 0.708625 | − | 0.705585i | \(-0.249316\pi\) | ||||
0.708625 | + | 0.705585i | \(0.249316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13876.4 | −0.816532 | −0.408266 | − | 0.912863i | \(-0.633866\pi\) | ||||
−0.408266 | + | 0.912863i | \(0.633866\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 44208.2i | 2.58960i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27200.0 | − | 1419.24i | −1.58612 | − | 0.0827607i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7404.44i | 0.429837i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16200.3 | −0.936236 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13878.3 | 0.798458 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 30526.1i | − | 1.74843i | −0.485537 | − | 0.874216i | \(-0.661376\pi\) | ||
0.485537 | − | 0.874216i | \(-0.338624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2174.26 | + | 20778.2i | −0.123981 | + | 1.18482i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6992.09i | 0.396939i | 0.980107 | + | 0.198470i | \(0.0635971\pi\) | ||||
−0.980107 | + | 0.198470i | \(0.936403\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25151.4 | −1.42153 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35613.0 | 2.00395 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 22479.2i | − | 1.25936i | −0.776854 | − | 0.629681i | \(-0.783186\pi\) | ||
0.776854 | − | 0.629681i | \(-0.216814\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15843.1 | + | 826.661i | 0.883698 | + | 0.0461096i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7618.29i | 0.423080i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20181.6 | −1.11590 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5536.97 | 0.304828 | 0.152414 | − | 0.988317i | \(-0.451295\pi\) | ||||
0.152414 | + | 0.988317i | \(0.451295\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 27933.1i | − | 1.53115i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1768.61 | − | 33895.7i | 0.0965285 | − | 1.84998i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6976.29i | 0.379119i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −42173.6 | −2.28205 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16934.8 | −0.912436 | −0.456218 | − | 0.889868i | \(-0.650796\pi\) | ||||
−0.456218 | + | 0.889868i | \(0.650796\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6636.29i | − | 0.356035i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2194.06 | − | 42049.5i | 0.117210 | − | 2.24635i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6447.52i | 0.342976i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4112.16 | 0.217821 | 0.108911 | − | 0.994052i | \(-0.465264\pi\) | ||||
0.108911 | + | 0.994052i | \(0.465264\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 47027.9 | 2.48057 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14796.2i | 0.777169i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21307.5 | + | 1111.78i | 1.11448 | + | 0.0581514i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18671.9i | 0.972543i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34938.3 | −1.81221 | −0.906105 | − | 0.423053i | \(-0.860958\pi\) | ||||
−0.906105 | + | 0.423053i | \(0.860958\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4437.90 | −0.229232 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 27057.3i | − | 1.39180i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8533.71 | + | 892.976i | 0.437150 | + | 0.0457438i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 34679.2i | − | 1.76916i | −0.466389 | − | 0.884580i | \(-0.654445\pi\) | ||
0.466389 | − | 0.884580i | \(-0.345555\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 30435.7 | 1.54629 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −36769.0 | −1.86040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30802.4i | − | 1.55213i | −0.630652 | − | 0.776065i | \(-0.717213\pi\) | ||
0.630652 | − | 0.776065i | \(-0.282787\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14089.0 | + | 735.137i | 0.707049 | + | 0.0368924i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8182.38i | − | 0.408958i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16364.2 | −0.814570 | −0.407285 | − | 0.913301i | \(-0.633524\pi\) | ||||
−0.407285 | + | 0.913301i | \(0.633524\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 66342.8 | 3.28902 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4464.06i | − | 0.220418i | −0.993908 | − | 0.110209i | \(-0.964848\pi\) | ||
0.993908 | − | 0.110209i | \(-0.0351520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1543.39 | + | 29579.4i | −0.0759001 | + | 1.45464i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 32758.5i | − | 1.60451i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16701.3 | −0.814758 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17873.6 | 0.868463 | 0.434231 | − | 0.900801i | \(-0.357020\pi\) | ||||
0.434231 | + | 0.900801i | \(0.357020\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23311.5i | 1.12818i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −165.042 | + | 3163.05i | −0.00795562 | + | 0.152471i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14305.3i | 0.686834i | 0.939183 | + | 0.343417i | \(0.111584\pi\) | ||||
−0.939183 | + | 0.343417i | \(0.888416\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25093.1 | 1.20003 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21819.9 | 1.03938 | 0.519692 | − | 0.854354i | \(-0.326047\pi\) | ||||
0.519692 | + | 0.854354i | \(0.326047\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 11107.3i | − | 0.527016i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 38063.2 | + | 1986.06i | 1.79892 | + | 0.0938643i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 38483.0i | − | 1.81166i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29446.6 | 1.38085 | 0.690423 | − | 0.723406i | \(-0.257425\pi\) | ||||
0.690423 | + | 0.723406i | \(0.257425\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6421.71 | −0.299964 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 30232.4i | − | 1.40671i | −0.710840 | − | 0.703354i | \(-0.751685\pi\) | ||
0.710840 | − | 0.703354i | \(-0.248315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17052.8 | + | 1784.42i | 0.790393 | + | 0.0827075i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11447.7i | 0.528551i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10469.3 | 0.481515 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2249.41 | 0.103060 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11472.5i | 0.523617i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −15797.4 | − | 824.276i | −0.718258 | − | 0.0374773i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30871.6i | 1.39829i | 0.714980 | + | 0.699145i | \(0.246436\pi\) | ||||
−0.714980 | + | 0.699145i | \(0.753564\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21827.1 | −0.984873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11009.2 | −0.494871 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 35971.1i | − | 1.61081i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1433.16 | + | 27466.8i | −0.0639359 | + | 1.22534i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4612.35i | − | 0.204991i | −0.994733 | − | 0.102496i | \(-0.967317\pi\) | ||
0.994733 | − | 0.102496i | \(-0.0326828\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32210.4 | −1.42618 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −34556.0 | −1.52431 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 20711.0i | − | 0.910181i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1391.35 | + | 26665.4i | −0.0609174 | + | 1.16749i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 68429.8i | 2.98494i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5893.44 | 0.256122 | 0.128061 | − | 0.991766i | \(-0.459125\pi\) | ||||
0.128061 | + | 0.991766i | \(0.459125\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28114.3 | 1.21730 | 0.608648 | − | 0.793441i | \(-0.291712\pi\) | ||||
0.608648 | + | 0.793441i | \(0.291712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14459.0i | 0.623739i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19267.5 | + | 1005.34i | 0.828112 | + | 0.0432093i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 55178.9i | 2.36287i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −72399.6 | −3.08895 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28087.6 | 1.19399 | 0.596994 | − | 0.802246i | \(-0.296362\pi\) | ||||
0.596994 | + | 0.802246i | \(0.296362\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43426.8i | 1.83932i | 0.392712 | + | 0.919661i | \(0.371537\pi\) | ||||
−0.392712 | + | 0.919661i | \(0.628463\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3026.23 | − | 28920.1i | 0.127709 | − | 1.22045i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9481.07i | 0.398657i | 0.979933 | + | 0.199328i | \(0.0638760\pi\) | ||||
−0.979933 | + | 0.199328i | \(0.936124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31634.3 | 1.32534 | 0.662668 | − | 0.748913i | \(-0.269424\pi\) | ||||
0.662668 | + | 0.748913i | \(0.269424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12199.9 | −0.509278 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 10792.3i | − | 0.448898i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22106.1 | + | 1153.45i | 0.916182 | + | 0.0478046i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22925.2i | 0.946729i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24661.7 | 1.01480 | 0.507399 | − | 0.861711i | \(-0.330607\pi\) | ||||
0.507399 | + | 0.861711i | \(0.330607\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19677.2 | −0.806807 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 46454.0i | 1.89794i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1601.71 | − | 30696.9i | 0.0652075 | − | 1.24971i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13167.0i | − | 0.534149i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 71527.3 | 2.89142 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6505.86 | −0.262066 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24125.3i | 0.968386i | 0.874961 | + | 0.484193i | \(0.160887\pi\) | ||||
−0.874961 | + | 0.484193i | \(0.839113\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2980.46 | − | 57121.0i | 0.119216 | − | 2.28479i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 23911.4i | − | 0.953089i | −0.879150 | − | 0.476544i | \(-0.841889\pi\) | ||
0.879150 | − | 0.476544i | \(-0.158111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22987.8 | 0.913079 | 0.456539 | − | 0.889703i | \(-0.349089\pi\) | ||||
0.456539 | + | 0.889703i | \(0.349089\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18059.6 | −0.714832 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29565.5i | 1.16619i | 0.812404 | + | 0.583095i | \(0.198159\pi\) | ||||
−0.812404 | + | 0.583095i | \(0.801841\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16398.5 | + | 855.640i | 0.644583 | + | 0.0336331i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3969.28i | − | 0.155483i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27445.4 | −1.07137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21207.9 | −0.825031 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 52818.8i | − | 2.04771i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 30564.4 | + | 4819.39i | 1.18087 | + | 0.186200i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 10218.0i | − | 0.393427i | −0.980461 | − | 0.196714i | \(-0.936973\pi\) | ||
0.980461 | − | 0.196714i | \(-0.0630269\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19989.8 | 0.767053 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3269.43 | −0.125028 | −0.0625141 | − | 0.998044i | \(-0.519912\pi\) | ||||
−0.0625141 | + | 0.998044i | \(0.519912\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13275.6i | − | 0.505956i | −0.967472 | − | 0.252978i | \(-0.918590\pi\) | ||
0.967472 | − | 0.252978i | \(-0.0814101\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −52374.6 | − | 2732.81i | −1.98933 | − | 0.103799i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23809.7i | 0.901298i | 0.892701 | + | 0.450649i | \(0.148807\pi\) | ||||
−0.892701 | + | 0.450649i | \(0.851193\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20263.3 | −0.764463 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4815.05 | 0.181044 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48337.8i | 1.81138i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1735.26 | + | 33256.4i | −0.0648081 | + | 1.24206i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 65038.8i | − | 2.42094i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9415.49 | 0.349304 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21039.9 | 0.777957 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 95184.4i | − | 3.50780i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 979.935 | − | 18780.6i | 0.0359935 | − | 0.689821i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 39404.3i | − | 1.44255i | −0.692646 | − | 0.721277i | \(-0.743555\pi\) | ||
0.692646 | − | 0.721277i | \(-0.256445\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13540.0 | −0.494054 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48325.4 | −1.75751 | −0.878755 | − | 0.477273i | \(-0.841625\pi\) | ||||
−0.878755 | + | 0.477273i | \(0.841625\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19117.8i | 0.692999i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −48956.0 | − | 2554.43i | −1.76878 | − | 0.0922915i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13448.4i | 0.484304i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35431.2 | −1.27178 | −0.635891 | − | 0.771779i | \(-0.719367\pi\) | ||||
−0.635891 | + | 0.771779i | \(0.719367\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18003.2 | −0.644109 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 5830.23i | − | 0.207914i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −784.606 | + | 7498.08i | −0.0278894 | + | 0.266525i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 9319.76i | − | 0.330206i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40430.1 | −1.42785 | −0.713923 | − | 0.700225i | \(-0.753083\pi\) | ||||
−0.713923 | + | 0.700225i | \(0.753083\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16196.0 | −0.570141 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 72881.9i | 2.55739i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22213.6 | − | 1159.06i | −0.776965 | − | 0.0405405i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3421.64i | − | 0.119296i | −0.998219 | − | 0.0596479i | \(-0.981002\pi\) | ||
0.998219 | − | 0.0596479i | \(-0.0189978\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62220.1 | 2.16238 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33075.2 | −1.14582 | −0.572912 | − | 0.819617i | \(-0.694186\pi\) | ||||
−0.572912 | + | 0.819617i | \(0.694186\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 10263.5i | − | 0.354427i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2155.75 | + | 41315.4i | −0.0742081 | + | 1.42221i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21896.5i | 0.751364i | 0.926749 | + | 0.375682i | \(0.122591\pi\) | ||||
−0.926749 | + | 0.375682i | \(0.877409\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −53680.8 | −1.83620 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 82635.9 | 2.81772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48287.2i | 1.64132i | 0.571417 | + | 0.820660i | \(0.306394\pi\) | ||||
−0.571417 | + | 0.820660i | \(0.693606\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −159.821 | + | 3062.98i | −0.00541536 | + | 0.103786i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 15967.9i | − | 0.539361i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31416.5 | 1.05787 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10976.2 | −0.368439 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 35073.5i | − | 1.17365i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32362.2 | + | 1688.59i | 1.07956 | + | 0.0563293i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13708.7i | 0.455886i | 0.973674 | + | 0.227943i | \(0.0732000\pi\) | ||||
−0.973674 | + | 0.227943i | \(0.926800\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −69164.1 | −2.29295 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24503.4 | 0.809836 | 0.404918 | − | 0.914353i | \(-0.367300\pi\) | ||||
0.404918 | + | 0.914353i | \(0.367300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 67214.6i | − | 2.21460i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −74958.0 | − | 7843.68i | −2.46213 | − | 0.257640i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27660.1i | − | 0.905758i | −0.891572 | − | 0.452879i | \(-0.850397\pi\) | ||
0.891572 | − | 0.452879i | \(-0.149603\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20166.8 | 0.658360 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23325.9 | 0.759161 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56556.7i | 1.83507i | 0.397651 | + | 0.917537i | \(0.369825\pi\) | ||||
−0.397651 | + | 0.917537i | \(0.630175\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26018.9 | − | 1357.61i | −0.841656 | − | 0.0439159i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 83383.4i | − | 2.68908i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54094.4 | 1.73923 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47154.6 | −1.51152 | −0.755760 | − | 0.654848i | \(-0.772732\pi\) | ||||
−0.755760 | + | 0.654848i | \(0.772732\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 3090.26i | − | 0.0987578i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 643.777 | − | 12338.1i | 0.0205117 | − | 0.393109i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13606.6i | − | 0.432223i | −0.976369 | − | 0.216111i | \(-0.930663\pi\) | ||
0.976369 | − | 0.216111i | \(-0.0693375\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10080.2 | −0.319242 |
(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 | 160.4.c.d.129.8 | yes | 8 | |
3.2 | odd | 2 | 1440.4.f.k.289.6 | 8 | |||
4.3 | odd | 2 | inner | 160.4.c.d.129.2 | yes | 8 | |
5.2 | odd | 4 | 800.4.a.y.1.4 | 4 | |||
5.3 | odd | 4 | 800.4.a.z.1.1 | 4 | |||
5.4 | even | 2 | inner | 160.4.c.d.129.1 | ✓ | 8 | |
8.3 | odd | 2 | 320.4.c.j.129.7 | 8 | |||
8.5 | even | 2 | 320.4.c.j.129.1 | 8 | |||
12.11 | even | 2 | 1440.4.f.k.289.5 | 8 | |||
15.14 | odd | 2 | 1440.4.f.k.289.7 | 8 | |||
20.3 | even | 4 | 800.4.a.z.1.4 | 4 | |||
20.7 | even | 4 | 800.4.a.y.1.1 | 4 | |||
20.19 | odd | 2 | inner | 160.4.c.d.129.7 | yes | 8 | |
40.3 | even | 4 | 1600.4.a.cu.1.1 | 4 | |||
40.13 | odd | 4 | 1600.4.a.cu.1.4 | 4 | |||
40.19 | odd | 2 | 320.4.c.j.129.2 | 8 | |||
40.27 | even | 4 | 1600.4.a.cv.1.4 | 4 | |||
40.29 | even | 2 | 320.4.c.j.129.8 | 8 | |||
40.37 | odd | 4 | 1600.4.a.cv.1.1 | 4 | |||
60.59 | even | 2 | 1440.4.f.k.289.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.c.d.129.1 | ✓ | 8 | 5.4 | even | 2 | inner | |
160.4.c.d.129.2 | yes | 8 | 4.3 | odd | 2 | inner | |
160.4.c.d.129.7 | yes | 8 | 20.19 | odd | 2 | inner | |
160.4.c.d.129.8 | yes | 8 | 1.1 | even | 1 | trivial | |
320.4.c.j.129.1 | 8 | 8.5 | even | 2 | |||
320.4.c.j.129.2 | 8 | 40.19 | odd | 2 | |||
320.4.c.j.129.7 | 8 | 8.3 | odd | 2 | |||
320.4.c.j.129.8 | 8 | 40.29 | even | 2 | |||
800.4.a.y.1.1 | 4 | 20.7 | even | 4 | |||
800.4.a.y.1.4 | 4 | 5.2 | odd | 4 | |||
800.4.a.z.1.1 | 4 | 5.3 | odd | 4 | |||
800.4.a.z.1.4 | 4 | 20.3 | even | 4 | |||
1440.4.f.k.289.5 | 8 | 12.11 | even | 2 | |||
1440.4.f.k.289.6 | 8 | 3.2 | odd | 2 | |||
1440.4.f.k.289.7 | 8 | 15.14 | odd | 2 | |||
1440.4.f.k.289.8 | 8 | 60.59 | even | 2 | |||
1600.4.a.cu.1.1 | 4 | 40.3 | even | 4 | |||
1600.4.a.cu.1.4 | 4 | 40.13 | odd | 4 | |||
1600.4.a.cv.1.1 | 4 | 40.37 | odd | 4 | |||
1600.4.a.cv.1.4 | 4 | 40.27 | even | 4 |