Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,4,Mod(17,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.w (of order \(4\), degree \(2\), 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: | \(42.4813752041\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Root | \(0.347140 - 2.27426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.17 |
Dual form | 720.4.w.d.593.5 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.38994 | − | 7.38978i | 0.750419 | − | 0.660962i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 10.8652 | + | 10.8652i | 0.586664 | + | 0.586664i | 0.936726 | − | 0.350062i | \(-0.113840\pi\) |
−0.350062 | + | 0.936726i | \(0.613840\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 37.8905i | − | 1.03858i | −0.854597 | − | 0.519291i | \(-0.826196\pi\) | ||
0.854597 | − | 0.519291i | \(-0.173804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.1085 | + | 48.1085i | −1.02638 | + | 1.02638i | −0.0267344 | + | 0.999643i | \(0.508511\pi\) |
−0.999643 | + | 0.0267344i | \(0.991489\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 60.3458 | − | 60.3458i | 0.860942 | − | 0.860942i | −0.130506 | − | 0.991448i | \(-0.541660\pi\) |
0.991448 | + | 0.130506i | \(0.0416601\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 109.678i | − | 1.32430i | −0.749369 | − | 0.662152i | \(-0.769643\pi\) | ||
0.749369 | − | 0.662152i | \(-0.230357\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 39.7660 | + | 39.7660i | 0.360512 | + | 0.360512i | 0.864002 | − | 0.503489i | \(-0.167951\pi\) |
−0.503489 | + | 0.864002i | \(0.667951\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.7823 | − | 124.000i | 0.126259 | − | 0.991997i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −90.3553 | −0.578571 | −0.289285 | − | 0.957243i | \(-0.593418\pi\) | ||||
−0.289285 | + | 0.957243i | \(0.593418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 233.678 | 1.35386 | 0.676932 | − | 0.736046i | \(-0.263309\pi\) | ||||
0.676932 | + | 0.736046i | \(0.263309\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 171.449 | + | 10.8670i | 0.828007 | + | 0.0524815i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.0042 | − | 19.0042i | −0.0844399 | − | 0.0844399i | 0.663625 | − | 0.748065i | \(-0.269017\pi\) |
−0.748065 | + | 0.663625i | \(0.769017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 260.783i | − | 0.993354i | −0.867935 | − | 0.496677i | \(-0.834553\pi\) | ||
0.867935 | − | 0.496677i | \(-0.165447\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −176.216 | + | 176.216i | −0.624948 | + | 0.624948i | −0.946792 | − | 0.321845i | \(-0.895697\pi\) |
0.321845 | + | 0.946792i | \(0.395697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −145.788 | + | 145.788i | −0.452456 | + | 0.452456i | −0.896169 | − | 0.443713i | \(-0.853661\pi\) |
0.443713 | + | 0.896169i | \(0.353661\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 106.896i | − | 0.311650i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 183.285 | + | 183.285i | 0.475022 | + | 0.475022i | 0.903535 | − | 0.428513i | \(-0.140962\pi\) |
−0.428513 | + | 0.903535i | \(0.640962\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −280.002 | − | 317.899i | −0.686464 | − | 0.779373i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 279.564 | 0.616883 | 0.308441 | − | 0.951243i | \(-0.400193\pi\) | ||||
0.308441 | + | 0.951243i | \(0.400193\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −390.267 | −0.819157 | −0.409578 | − | 0.912275i | \(-0.634324\pi\) | ||||
−0.409578 | + | 0.912275i | \(0.634324\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −48.1164 | + | 759.139i | −0.0918170 | + | 1.44861i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −150.444 | − | 150.444i | −0.274324 | − | 0.274324i | 0.556514 | − | 0.830838i | \(-0.312139\pi\) |
−0.830838 | + | 0.556514i | \(0.812139\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 470.042i | − | 0.785686i | −0.919605 | − | 0.392843i | \(-0.871492\pi\) | ||
0.919605 | − | 0.392843i | \(-0.128508\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 480.765 | − | 480.765i | 0.770812 | − | 0.770812i | −0.207436 | − | 0.978249i | \(-0.566512\pi\) |
0.978249 | + | 0.207436i | \(0.0665119\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 411.687 | − | 411.687i | 0.609299 | − | 0.609299i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1322.44i | − | 1.88337i | −0.336497 | − | 0.941685i | \(-0.609242\pi\) | ||
0.336497 | − | 0.941685i | \(-0.390758\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 456.192 | + | 456.192i | 0.603296 | + | 0.603296i | 0.941186 | − | 0.337890i | \(-0.109713\pi\) |
−0.337890 | + | 0.941186i | \(0.609713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 60.3558 | − | 952.240i | 0.0770177 | − | 1.21512i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1364.85 | 1.62555 | 0.812774 | − | 0.582580i | \(-0.197957\pi\) | ||||
0.812774 | + | 0.582580i | \(0.197957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1045.41 | −1.20428 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −810.494 | − | 920.190i | −0.875315 | − | 0.993784i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −785.308 | − | 785.308i | −0.822020 | − | 0.822020i | 0.164377 | − | 0.986398i | \(-0.447439\pi\) |
−0.986398 | + | 0.164377i | \(0.947439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 111.555i | 0.109902i | 0.998489 | + | 0.0549510i | \(0.0175003\pi\) | ||||
−0.998489 | + | 0.0549510i | \(0.982500\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.8820 | + | 13.8820i | −0.0132800 | + | 0.0132800i | −0.713716 | − | 0.700436i | \(-0.752989\pi\) |
0.700436 | + | 0.713716i | \(0.252989\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 776.165 | − | 776.165i | 0.701259 | − | 0.701259i | −0.263422 | − | 0.964681i | \(-0.584851\pi\) |
0.964681 | + | 0.263422i | \(0.0848510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 410.579i | 0.360792i | 0.983594 | + | 0.180396i | \(0.0577379\pi\) | ||||
−0.983594 | + | 0.180396i | \(0.942262\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −521.328 | − | 521.328i | −0.434004 | − | 0.434004i | 0.455984 | − | 0.889988i | \(-0.349287\pi\) |
−0.889988 | + | 0.455984i | \(0.849287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 627.496 | + | 39.7725i | 0.508820 | + | 0.0322505i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1311.34 | 1.01017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −104.688 | −0.0786538 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −783.917 | − | 1156.98i | −0.560926 | − | 0.827866i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −786.555 | − | 786.555i | −0.549571 | − | 0.549571i | 0.376746 | − | 0.926317i | \(-0.377043\pi\) |
−0.926317 | + | 0.376746i | \(0.877043\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 448.364i | 0.299036i | 0.988759 | + | 0.149518i | \(0.0477722\pi\) | ||||
−0.988759 | + | 0.149518i | \(0.952228\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1191.67 | − | 1191.67i | 0.776922 | − | 0.776922i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 950.120 | − | 950.120i | 0.592512 | − | 0.592512i | −0.345797 | − | 0.938309i | \(-0.612391\pi\) |
0.938309 | + | 0.345797i | \(0.112391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 112.735i | − | 0.0687918i | −0.999408 | − | 0.0343959i | \(-0.989049\pi\) | ||
0.999408 | − | 0.0343959i | \(-0.0109507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1822.85 | + | 1822.85i | 1.06598 | + | 1.06598i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −758.076 | + | 667.706i | −0.434171 | + | 0.382413i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1492.95 | 0.820852 | 0.410426 | − | 0.911894i | \(-0.365380\pi\) | ||||
0.410426 | + | 0.911894i | \(0.365380\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2939.54 | 1.58422 | 0.792108 | − | 0.610381i | \(-0.208984\pi\) | ||||
0.792108 | + | 0.610381i | \(0.208984\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1960.54 | − | 1726.83i | 1.01597 | − | 0.894852i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 156.386 | + | 156.386i | 0.0794967 | + | 0.0794967i | 0.745737 | − | 0.666240i | \(-0.232098\pi\) |
−0.666240 | + | 0.745737i | \(0.732098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 864.129i | 0.422999i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 239.292 | − | 239.292i | 0.114986 | − | 0.114986i | −0.647272 | − | 0.762259i | \(-0.724090\pi\) |
0.762259 | + | 0.647272i | \(0.224090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −677.159 | + | 677.159i | −0.313773 | + | 0.313773i | −0.846369 | − | 0.532596i | \(-0.821216\pi\) |
0.532596 | + | 0.846369i | \(0.321216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2431.86i | − | 1.10690i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 441.523 | + | 441.523i | 0.194037 | + | 0.194037i | 0.797438 | − | 0.603401i | \(-0.206188\pi\) |
−0.603401 | + | 0.797438i | \(0.706188\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1518.76 | − | 1175.80i | 0.656041 | − | 0.507898i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4724.27 | −1.97267 | −0.986337 | − | 0.164737i | \(-0.947322\pi\) | ||||
−0.986337 | + | 0.164737i | \(0.947322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1548.35 | −0.635847 | −0.317923 | − | 0.948116i | \(-0.602985\pi\) | ||||
−0.317923 | + | 0.948116i | \(0.602985\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −299.882 | − | 19.0074i | −0.119177 | − | 0.00755378i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2286.53 | − | 2286.53i | −0.894159 | − | 0.894159i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1090.71i | 0.413200i | 0.978426 | + | 0.206600i | \(0.0662398\pi\) | ||||
−0.978426 | + | 0.206600i | \(0.933760\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2825.69 | + | 2825.69i | −1.05387 | + | 1.05387i | −0.0554112 | + | 0.998464i | \(0.517647\pi\) |
−0.998464 | + | 0.0554112i | \(0.982353\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1163.99 | − | 1163.99i | 0.420969 | − | 0.420969i | −0.464569 | − | 0.885537i | \(-0.653791\pi\) |
0.885537 | + | 0.464569i | \(0.153791\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 520.257i | 0.185327i | 0.995697 | + | 0.0926633i | \(0.0295380\pi\) | ||||
−0.995697 | + | 0.0926633i | \(0.970462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −981.726 | − | 981.726i | −0.339427 | − | 0.339427i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1927.13 | − | 2187.96i | −0.656569 | − | 0.745432i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4155.74 | −1.37540 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5524.38 | −1.80244 | −0.901219 | − | 0.433365i | \(-0.857326\pi\) | ||||
−0.901219 | + | 0.433365i | \(0.857326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −176.245 | + | 2780.65i | −0.0559062 | + | 0.882039i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2538.95 | + | 2538.95i | 0.794263 | + | 0.794263i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5806.30i | 1.76730i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −323.198 | + | 323.198i | −0.0970537 | + | 0.0970537i | −0.753967 | − | 0.656913i | \(-0.771862\pi\) |
0.656913 | + | 0.753967i | \(0.271862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2739.76 | − | 2739.76i | 0.801077 | − | 0.801077i | −0.182187 | − | 0.983264i | \(-0.558318\pi\) |
0.983264 | + | 0.182187i | \(0.0583177\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 230.334i | 0.0664667i | 0.999448 | + | 0.0332333i | \(0.0105804\pi\) | ||||
−0.999448 | + | 0.0332333i | \(0.989420\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −350.156 | − | 350.156i | −0.0984526 | − | 0.0984526i | 0.656165 | − | 0.754618i | \(-0.272178\pi\) |
−0.754618 | + | 0.656165i | \(0.772178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −145.812 | + | 2300.50i | −0.0404755 | + | 0.638587i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1013.20 | −0.274218 | −0.137109 | − | 0.990556i | \(-0.543781\pi\) | ||||
−0.137109 | + | 0.990556i | \(0.543781\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2584.30 | 0.690744 | 0.345372 | − | 0.938466i | \(-0.387753\pi\) | ||||
0.345372 | + | 0.938466i | \(0.387753\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −789.938 | − | 896.852i | −0.205989 | − | 0.233868i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5276.43 | + | 5276.43i | 1.35924 | + | 1.35924i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1708.34i | − | 0.429599i | −0.976658 | − | 0.214800i | \(-0.931090\pi\) | ||
0.976658 | − | 0.214800i | \(-0.0689099\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1506.75 | − | 1506.75i | 0.374422 | − | 0.374422i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2659.48 | − | 2659.48i | 0.645500 | − | 0.645500i | −0.306402 | − | 0.951902i | \(-0.599125\pi\) |
0.951902 | + | 0.306402i | \(0.0991252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 412.969i | − | 0.0990757i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2307.03 | + | 2307.03i | 0.540903 | + | 0.540903i | 0.923794 | − | 0.382891i | \(-0.125071\pi\) |
−0.382891 | + | 0.923794i | \(0.625071\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2892.19 | + | 183.315i | 0.670437 | + | 0.0424943i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −447.584 | −0.101449 | −0.0507243 | − | 0.998713i | \(-0.516153\pi\) | ||||
−0.0507243 | + | 0.998713i | \(0.516153\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1573.15 | −0.352627 | −0.176314 | − | 0.984334i | \(-0.556417\pi\) | ||||
−0.176314 | + | 0.984334i | \(0.556417\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4698.41 | − | 598.000i | −1.03027 | − | 0.131130i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5816.91 | + | 5816.91i | 1.26175 | + | 1.26175i | 0.950245 | + | 0.311504i | \(0.100833\pi\) |
0.311504 | + | 0.950245i | \(0.399167\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 140.032i | − | 0.0297281i | −0.999890 | − | 0.0148640i | \(-0.995268\pi\) | ||
0.999890 | − | 0.0148640i | \(-0.00473155\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4431.85 | + | 4431.85i | −0.930905 | + | 0.930905i | −0.997763 | − | 0.0668572i | \(-0.978703\pi\) |
0.0668572 | + | 0.997763i | \(0.478703\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2833.46 | − | 2833.46i | 0.582765 | − | 0.582765i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 2370.24i | − | 0.482442i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1244.45 | − | 1244.45i | −0.248127 | − | 0.248127i | 0.572074 | − | 0.820202i | \(-0.306139\pi\) |
−0.820202 | + | 0.572074i | \(0.806139\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2345.52 | − | 2065.91i | 0.462921 | − | 0.407736i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3826.17 | −0.740043 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3829.24 | −0.733269 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3274.32 | + | 2883.99i | −0.614711 | + | 0.541432i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7327.60 | + | 7327.60i | 1.36224 | + | 1.36224i | 0.871053 | + | 0.491189i | \(0.163437\pi\) |
0.491189 | + | 0.871053i | \(0.336563\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7489.38i | 1.36554i | 0.730632 | + | 0.682771i | \(0.239225\pi\) | ||||
−0.730632 | + | 0.682771i | \(0.760775\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2456.04 | + | 2456.04i | −0.443525 | + | 0.443525i | −0.893195 | − | 0.449670i | \(-0.851542\pi\) |
0.449670 | + | 0.893195i | \(0.351542\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6724.30 | + | 6724.30i | −1.19140 | + | 1.19140i | −0.214728 | + | 0.976674i | \(0.568887\pi\) |
−0.976674 | + | 0.214728i | \(0.931113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3423.60i | 0.600894i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6618.59 | − | 6618.59i | −1.14015 | − | 1.14015i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5206.18 | + | 6724.70i | 0.888574 | + | 1.14775i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3168.03 | −0.530879 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 199.080 | 0.0330586 | 0.0165293 | − | 0.999863i | \(-0.494738\pi\) | ||||
0.0165293 | + | 0.999863i | \(0.494738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2373.97 | − | 150.469i | −0.387176 | − | 0.0245403i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3308.77 | + | 3308.77i | 0.534838 | + | 0.534838i | 0.922008 | − | 0.387170i | \(-0.126547\pi\) |
−0.387170 | + | 0.922008i | \(0.626547\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8854.16i | − | 1.40610i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4888.20 | − | 4888.20i | 0.769498 | − | 0.769498i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2371.68 | + | 2371.68i | −0.366912 | + | 0.366912i | −0.866350 | − | 0.499438i | \(-0.833540\pi\) |
0.499438 | + | 0.866350i | \(0.333540\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8208.92i | 1.25906i | 0.776975 | + | 0.629532i | \(0.216753\pi\) | ||||
−0.776975 | + | 0.629532i | \(0.783247\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6800.98 | + | 6800.98i | 1.02544 | + | 1.02544i | 0.999668 | + | 0.0257707i | \(0.00820398\pi\) |
0.0257707 | + | 0.999668i | \(0.491796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3473.51 | − | 3943.63i | −0.519309 | − | 0.589594i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1778.14 | 0.261411 | 0.130705 | − | 0.991421i | \(-0.458276\pi\) | ||||
0.130705 | + | 0.991421i | \(0.458276\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5170.20 | −0.753783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 480.844 | − | 7586.34i | 0.0689549 | − | 1.08791i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4673.56 | + | 4673.56i | 0.664735 | + | 0.664735i | 0.956492 | − | 0.291757i | \(-0.0942400\pi\) |
−0.291757 | + | 0.956492i | \(0.594240\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3982.85i | 0.557357i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5729.37 | + | 5729.37i | −0.795323 | + | 0.795323i | −0.982354 | − | 0.187031i | \(-0.940114\pi\) |
0.187031 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4346.86 | − | 4346.86i | 0.593832 | − | 0.593832i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 153.883i | − | 0.0208561i | −0.999946 | − | 0.0104280i | \(-0.996681\pi\) | ||
0.999946 | − | 0.0104280i | \(-0.00331941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4297.76 | + | 4297.76i | 0.573382 | + | 0.573382i | 0.933072 | − | 0.359690i | \(-0.117118\pi\) |
−0.359690 | + | 0.933072i | \(0.617118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 411.754 | − | 6496.30i | 0.0545063 | − | 0.859954i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7833.00 | −1.02095 | −0.510474 | − | 0.859893i | \(-0.670530\pi\) | ||||
−0.510474 | + | 0.859893i | \(0.670530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4799.42 | 0.620760 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9772.54 | − | 11095.2i | −1.24484 | − | 1.41332i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10195.4 | − | 10195.4i | −1.28889 | − | 1.28889i | −0.935459 | − | 0.353435i | \(-0.885013\pi\) |
−0.353435 | − | 0.935459i | \(-0.614987\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10778.3i | 1.34226i | 0.741341 | + | 0.671128i | \(0.234190\pi\) | ||||
−0.741341 | + | 0.671128i | \(0.765810\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11241.9 | + | 11241.9i | −1.38957 | + | 1.38957i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −720.079 | + | 720.079i | −0.0876978 | + | 0.0876978i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4629.92i | 0.559743i | 0.960037 | + | 0.279872i | \(0.0902919\pi\) | ||||
−0.960037 | + | 0.279872i | \(0.909708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3037.51 | + | 3037.51i | 0.361903 | + | 0.361903i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7198.58 | + | 456.267i | 0.851480 | + | 0.0539693i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11276.5 | 1.31478 | 0.657389 | − | 0.753551i | \(-0.271661\pi\) | ||||
0.657389 | + | 0.753551i | \(0.271661\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3387.58 | 0.392163 | 0.196082 | − | 0.980588i | \(-0.437178\pi\) | ||||
0.196082 | + | 0.980588i | \(0.437178\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6530.47 | − | 8435.26i | −0.745351 | − | 0.962753i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4240.32 | − | 4240.32i | −0.480570 | − | 0.480570i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16161.7i | 1.80623i | 0.429402 | + | 0.903113i | \(0.358724\pi\) | ||||
−0.429402 | + | 0.903113i | \(0.641276\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3808.79 | + | 3808.79i | −0.422722 | + | 0.422722i | −0.886140 | − | 0.463418i | \(-0.846623\pi\) |
0.463418 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4361.44 | − | 4361.44i | 0.477428 | − | 0.477428i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1607.30i | − | 0.174744i | −0.996176 | − | 0.0873718i | \(-0.972153\pi\) | ||
0.996176 | − | 0.0873718i | \(-0.0278468\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8296.60 | + | 8296.60i | 0.889805 | + | 0.889805i | 0.994504 | − | 0.104699i | \(-0.0333880\pi\) |
−0.104699 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11451.0 | − | 10085.9i | 1.21984 | − | 1.07442i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15061.8 | −1.58309 | −0.791547 | − | 0.611108i | \(-0.790724\pi\) | ||||
−0.791547 | + | 0.611108i | \(0.790724\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9881.20 | −1.03168 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8770.97 | + | 7725.38i | −0.903713 | + | 0.795981i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2671.27 | + | 2671.27i | 0.273428 | + | 0.273428i | 0.830479 | − | 0.557050i | \(-0.188067\pi\) |
−0.557050 | + | 0.830479i | \(0.688067\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12809.1i | 1.29410i | 0.762449 | + | 0.647049i | \(0.223997\pi\) | ||||
−0.762449 | + | 0.647049i | \(0.776003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11154.1 | − | 11154.1i | 1.11960 | − | 1.11960i | 0.127804 | − | 0.991799i | \(-0.459207\pi\) |
0.991799 | − | 0.127804i | \(-0.0407927\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7905.44 | − | 7905.44i | 0.783341 | − | 0.783341i | −0.197052 | − | 0.980393i | \(-0.563137\pi\) |
0.980393 | + | 0.197052i | \(0.0631368\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3269.21i | − | 0.321872i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6676.92 | + | 6676.92i | 0.649060 | + | 0.649060i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13600.0 | − | 1730.97i | −1.31371 | − | 0.167205i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10715.8 | −1.02217 | −0.511085 | − | 0.859530i | \(-0.670756\pi\) | ||||
−0.511085 | + | 0.859530i | \(0.670756\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1828.53 | 0.173334 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12391.9 | − | 785.437i | −1.16018 | − | 0.0735358i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4489.84 | + | 4489.84i | 0.417770 | + | 0.417770i | 0.884435 | − | 0.466664i | \(-0.154544\pi\) |
−0.466664 | + | 0.884435i | \(0.654544\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15174.1i | − | 1.39470i | −0.716729 | − | 0.697352i | \(-0.754362\pi\) | ||
0.716729 | − | 0.697352i | \(-0.245638\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5452.56 | + | 5452.56i | −0.498116 | + | 0.498116i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5107.09 | − | 5107.09i | 0.460934 | − | 0.460934i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8887.20i | 0.797286i | 0.917106 | + | 0.398643i | \(0.130519\pi\) | ||||
−0.917106 | + | 0.398643i | \(0.869481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12740.5 | − | 12740.5i | −1.12936 | − | 1.12936i | −0.990281 | − | 0.139084i | \(-0.955584\pi\) |
−0.139084 | − | 0.990281i | \(-0.544416\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 824.364 | + | 935.937i | 0.0726410 | + | 0.0824726i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9257.00 | 0.806108 | 0.403054 | − | 0.915176i | \(-0.367949\pi\) | ||||
0.403054 | + | 0.915176i | \(0.367949\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10447.2 | 0.904416 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.8843 | + | 219.055i | −0.00118799 | + | 0.0187431i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5523.99 | + | 5523.99i | 0.469913 | + | 0.469913i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 13563.3i | − | 1.14054i | −0.821458 | − | 0.570268i | \(-0.806839\pi\) | ||
0.821458 | − | 0.570268i | \(-0.193161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11193.8 | + | 11193.8i | −0.935894 | + | 0.935894i | −0.998065 | − | 0.0621714i | \(-0.980197\pi\) |
0.0621714 | + | 0.998065i | \(0.480197\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14101.5 | − | 14101.5i | 1.16560 | − | 1.16560i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9004.33i | − | 0.740062i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12545.9 | + | 12545.9i | 1.01956 | + | 1.01956i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 776.293 | − | 12247.7i | 0.0627329 | − | 0.989744i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4050.34 | −0.323675 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1383.33 | 0.109934 | 0.0549668 | − | 0.998488i | \(-0.482495\pi\) | ||||
0.0549668 | + | 0.998488i | \(0.482495\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3034.09 | + | 3444.73i | 0.238470 | + | 0.270745i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2181.76 | − | 2181.76i | −0.170540 | − | 0.170540i | 0.616677 | − | 0.787217i | \(-0.288479\pi\) |
−0.787217 | + | 0.616677i | \(0.788479\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9909.96i | 0.766204i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14368.5 | − | 14368.5i | 1.10491 | − | 1.10491i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15674.9 | − | 15674.9i | 1.19240 | − | 1.19240i | 0.216007 | − | 0.976392i | \(-0.430697\pi\) |
0.976392 | − | 0.216007i | \(-0.0693035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 16955.0i | − | 1.28286i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8213.60 | + | 8213.60i | 0.614852 | + | 0.614852i | 0.944206 | − | 0.329354i | \(-0.106831\pi\) |
−0.329354 | + | 0.944206i | \(0.606831\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8226.41 | − | 521.414i | −0.612545 | − | 0.0388248i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16902.1 | 1.24530 | 0.622648 | − | 0.782502i | \(-0.286057\pi\) | ||||
0.622648 | + | 0.782502i | \(0.286057\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6507.12 | −0.476908 | −0.238454 | − | 0.971154i | \(-0.576641\pi\) | ||||
−0.238454 | + | 0.971154i | \(0.576641\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5558.57 | − | 4303.37i | 0.403145 | − | 0.312109i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7884.54 | + | 7884.54i | 0.568870 | + | 0.568870i | 0.931812 | − | 0.362942i | \(-0.118228\pi\) |
−0.362942 | + | 0.931812i | \(0.618228\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9913.20i | 0.707864i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6944.77 | − | 6944.77i | 0.493350 | − | 0.493350i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9548.44 | − | 9548.44i | 0.671390 | − | 0.671390i | −0.286646 | − | 0.958037i | \(-0.592540\pi\) |
0.958037 | + | 0.286646i | \(0.0925404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 25629.2i | − | 1.79293i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3491.97 | − | 3491.97i | −0.241818 | − | 0.241818i | 0.575784 | − | 0.817602i | \(-0.304697\pi\) |
−0.817602 | + | 0.575784i | \(0.804697\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11002.0 | − | 9690.48i | 0.758049 | − | 0.667682i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11203.0 | 0.764175 | 0.382087 | − | 0.924126i | \(-0.375205\pi\) | ||||
0.382087 | + | 0.924126i | \(0.375205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13953.5 | −0.947048 | −0.473524 | − | 0.880781i | \(-0.657018\pi\) | ||||
−0.473524 | + | 0.880781i | \(0.657018\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −878.328 | + | 773.622i | −0.0590233 | + | 0.0519871i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1292.54 | + | 1292.54i | 0.0864293 | + | 0.0864293i | 0.749000 | − | 0.662570i | \(-0.230534\pi\) |
−0.662570 | + | 0.749000i | \(0.730534\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 14027.3i | − | 0.928780i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 225.964 | − | 225.964i | 0.0148884 | − | 0.0148884i | −0.699623 | − | 0.714512i | \(-0.746649\pi\) |
0.714512 | + | 0.699623i | \(0.246649\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2717.41 | + | 2717.41i | −0.177308 | + | 0.177308i | −0.790181 | − | 0.612873i | \(-0.790014\pi\) |
0.612873 | + | 0.790181i | \(0.290014\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 8870.55i | − | 0.575989i | −0.957632 | − | 0.287995i | \(-0.907011\pi\) | ||
0.957632 | − | 0.287995i | \(-0.0929886\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 14829.3 | + | 14829.3i | 0.953650 | + | 0.953650i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15126.8 | − | 3914.00i | −0.968118 | − | 0.250496i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2293.65 | −0.145396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29762.7 | −1.87771 | −0.938853 | − | 0.344318i | \(-0.888110\pi\) | ||||
−0.938853 | + | 0.344318i | \(0.888110\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12411.6 | − | 786.685i | −0.775654 | − | 0.0491632i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5142.61 | + | 5142.61i | 0.319871 | + | 0.319871i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5168.75i | − | 0.318492i | −0.987239 | − | 0.159246i | \(-0.949094\pi\) | ||
0.987239 | − | 0.159246i | \(-0.0509063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2078.46 | − | 2078.46i | 0.127475 | − | 0.127475i | −0.640491 | − | 0.767966i | \(-0.721269\pi\) |
0.767966 | + | 0.640491i | \(0.221269\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10765.7 | − | 10765.7i | 0.654164 | − | 0.654164i | −0.299829 | − | 0.953993i | \(-0.596930\pi\) |
0.953993 | + | 0.299829i | \(0.0969297\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10592.8i | − | 0.640684i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12815.1 | − | 12815.1i | −0.767984 | − | 0.767984i | 0.209767 | − | 0.977751i | \(-0.432729\pi\) |
−0.977751 | + | 0.209767i | \(0.932729\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3313.31 | + | 3761.75i | 0.197651 | + | 0.224402i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16634.8 | −0.983307 | −0.491654 | − | 0.870791i | \(-0.663607\pi\) | ||||
−0.491654 | + | 0.870791i | \(0.663607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10835.6 | −0.637601 | −0.318800 | − | 0.947822i | \(-0.603280\pi\) | ||||
−0.318800 | + | 0.947822i | \(0.603280\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1191.86 | − | 18804.2i | 0.0695015 | − | 1.09653i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3593.07 | − | 3593.07i | −0.208582 | − | 0.208582i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14787.4i | 0.850762i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16220.3 | + | 16220.3i | −0.929045 | + | 0.929045i | −0.997644 | − | 0.0685992i | \(-0.978147\pi\) |
0.0685992 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11196.6 | − | 11196.6i | 0.635626 | − | 0.635626i | −0.313847 | − | 0.949473i | \(-0.601618\pi\) |
0.949473 | + | 0.313847i | \(0.101618\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 17065.0i | − | 0.964500i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15428.1 | + | 15428.1i | 0.864331 | + | 0.864331i | 0.991838 | − | 0.127507i | \(-0.0406975\pi\) |
−0.127507 | + | 0.991838i | \(0.540697\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 950.276 | − | 14992.6i | 0.0530046 | − | 0.836261i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17635.2 | −0.975104 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21858.6 | −1.20339 | −0.601693 | − | 0.798728i | \(-0.705507\pi\) | ||||
−0.601693 | + | 0.798728i | \(0.705507\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −833.087 | − | 945.841i | −0.0454688 | − | 0.0516227i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15737.2 | − | 15737.2i | −0.855220 | − | 0.855220i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8846.82i | 0.476662i | 0.971184 | + | 0.238331i | \(0.0766002\pi\) | ||||
−0.971184 | + | 0.238331i | \(0.923400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2084.34 | + | 2084.34i | −0.111824 | + | 0.111824i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1212.06 | + | 1212.06i | −0.0644755 | + | 0.0644755i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23189.8i | − | 1.22837i | −0.789163 | − | 0.614184i | \(-0.789485\pi\) | ||
0.789163 | − | 0.614184i | \(-0.210515\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9292.43 | + | 9292.43i | 0.488084 | + | 0.488084i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28764.1 | + | 1823.15i | 1.50450 | + | 0.0953596i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7005.29 | −0.363356 | −0.181678 | − | 0.983358i | \(-0.558153\pi\) | ||||
−0.181678 | + | 0.983358i | \(0.558153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −301.661 | −0.0155818 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1426.02 | + | 11204.0i | −0.0730495 | + | 0.573941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16025.7 | + | 16025.7i | 0.817553 | + | 0.817553i | 0.985753 | − | 0.168200i | \(-0.0537954\pi\) |
−0.168200 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21267.8i | 1.07609i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3319.43 | + | 3319.43i | −0.167266 | + | 0.167266i | −0.785777 | − | 0.618511i | \(-0.787736\pi\) |
0.618511 | + | 0.785777i | \(0.287736\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5700.41 | + | 5700.41i | −0.284908 | + | 0.284908i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19979.4i | − | 0.994526i | −0.867600 | − | 0.497263i | \(-0.834338\pi\) | ||
0.867600 | − | 0.497263i | \(-0.165662\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14574.6 | + | 14574.6i | 0.719637 | + | 0.719637i | 0.968531 | − | 0.248894i | \(-0.0800670\pi\) |
−0.248894 | + | 0.968531i | \(0.580067\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12525.7 | − | 11032.5i | 0.615983 | − | 0.542552i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16866.3 | 0.822807 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11620.1 | 0.564612 | 0.282306 | − | 0.959324i | \(-0.408901\pi\) | ||||
0.282306 | + | 0.959324i | \(0.408901\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24662.6 | − | 21722.6i | 1.18883 | − | 1.04711i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10502.0 | + | 10502.0i | 0.504229 | + | 0.504229i | 0.912749 | − | 0.408520i | \(-0.133955\pi\) |
−0.408520 | + | 0.912749i | \(0.633955\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36489.6i | 1.73817i | 0.494664 | + | 0.869085i | \(0.335291\pi\) | ||||
−0.494664 | + | 0.869085i | \(0.664709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4461.01 | + | 4461.01i | −0.211664 | + | 0.211664i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13449.4 | + | 13449.4i | −0.633154 | + | 0.633154i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30323.9i | 1.42199i | 0.703198 | + | 0.710994i | \(0.251755\pi\) | ||||
−0.703198 | + | 0.710994i | \(0.748245\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10327.2 | − | 10327.2i | −0.480522 | − | 0.480522i | 0.424777 | − | 0.905298i | \(-0.360353\pi\) |
−0.905298 | + | 0.424777i | \(0.860353\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3687.98 | − | 28976.0i | 0.170937 | − | 1.34303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28602.1 | −1.31550 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17810.1 | −0.816000 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2467.73 | + | 156.412i | 0.112200 | + | 0.00711157i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21521.8 | − | 21521.8i | −0.974802 | − | 0.974802i | 0.0248882 | − | 0.999690i | \(-0.492077\pi\) |
−0.999690 | + | 0.0248882i | \(0.992077\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11328.6i | − | 0.509229i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18775.2 | − | 18775.2i | 0.840764 | − | 0.840764i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17277.8 | − | 17277.8i | 0.767895 | − | 0.767895i | −0.209841 | − | 0.977736i | \(-0.567294\pi\) |
0.977736 | + | 0.209841i | \(0.0672945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17595.4i | 0.779076i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18216.4 | − | 18216.4i | −0.800552 | − | 0.800552i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6385.72 | + | 7249.99i | 0.279586 | + | 0.317427i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41260.2 | 1.79312 | 0.896558 | − | 0.442926i | \(-0.146059\pi\) | ||||
0.896558 | + | 0.442926i | \(0.146059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23357.1 | 1.01132 | 0.505659 | − | 0.862733i | \(-0.331249\pi\) | ||||
0.505659 | + | 0.862733i | \(0.331249\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 239.331 | − | 3775.96i | 0.0102864 | − | 0.162290i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19327.0 | + | 19327.0i | 0.827621 | + | 0.827621i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8296.46i | 0.352678i | 0.984330 | + | 0.176339i | \(0.0564254\pi\) | ||||
−0.984330 | + | 0.176339i | \(0.943575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17980.5 | + | 17980.5i | −0.761555 | + | 0.761555i | −0.976603 | − | 0.215048i | \(-0.931009\pi\) |
0.215048 | + | 0.976603i | \(0.431009\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9128.21 | − | 9128.21i | 0.383820 | − | 0.383820i | −0.488656 | − | 0.872476i | \(-0.662513\pi\) |
0.872476 | + | 0.488656i | \(0.162513\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24401.3i | 1.02231i | 0.859489 | + | 0.511154i | \(0.170782\pi\) | ||||
−0.859489 | + | 0.511154i | \(0.829218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6450.73 | − | 6450.73i | −0.268313 | − | 0.268313i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −677.271 | + | 10685.4i | −0.0280694 | + | 0.442854i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38174.8 | 1.57084 | 0.785422 | − | 0.618960i | \(-0.212446\pi\) | ||||
0.785422 | + | 0.618960i | \(0.212446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16224.9 | −0.665256 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17970.9 | − | 20403.1i | −0.731618 | − | 0.830639i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1137.45 | − | 1137.45i | −0.0461433 | − | 0.0461433i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1511.44i | − | 0.0608833i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1757.73 | − | 1757.73i | 0.0705550 | − | 0.0705550i | −0.670949 | − | 0.741504i | \(-0.734113\pi\) |
0.741504 | + | 0.670949i | \(0.234113\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7091.77 | − | 7091.77i | 0.282672 | − | 0.282672i | −0.551501 | − | 0.834174i | \(-0.685945\pi\) |
0.834174 | + | 0.551501i | \(0.185945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16842.4i | 0.668982i | 0.942399 | + | 0.334491i | \(0.108564\pi\) | ||||
−0.942399 | + | 0.334491i | \(0.891436\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33056.1 | − | 33056.1i | −1.30387 | − | 1.30387i | −0.925759 | − | 0.378114i | \(-0.876573\pi\) |
−0.378114 | − | 0.925759i | \(-0.623427\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6967.12 | + | 441.596i | 0.273860 | + | 0.0173581i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −50107.9 | −1.95603 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14475.3 | 0.563120 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4053.37 | − | 21088.2i | 0.156604 | − | 0.814754i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1780.97 | + | 1780.97i | 0.0685738 | + | 0.0685738i | 0.740562 | − | 0.671988i | \(-0.234559\pi\) |
−0.671988 | + | 0.740562i | \(0.734559\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2698.82i | − | 0.103207i | −0.998668 | − | 0.0516036i | \(-0.983567\pi\) | ||
0.998668 | − | 0.0516036i | \(-0.0164332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6744.66 | + | 6744.66i | −0.257051 | + | 0.257051i | −0.823854 | − | 0.566803i | \(-0.808180\pi\) |
0.566803 | + | 0.823854i | \(0.308180\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1302.99 | − | 1302.99i | 0.0493238 | − | 0.0493238i | −0.682015 | − | 0.731338i | \(-0.738896\pi\) |
0.731338 | + | 0.682015i | \(0.238896\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 17092.1i | − | 0.644827i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15989.7 | + | 15989.7i | 0.599189 | + | 0.599189i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39636.4 | + | 34911.3i | −1.48033 | + | 1.30386i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21114.0 | −0.783306 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22121.0 | 0.817933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12990.6 | + | 11442.0i | −0.477152 | + | 0.420271i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3070.33 | + | 3070.33i | 0.112402 | + | 0.112402i | 0.761071 | − | 0.648669i | \(-0.224674\pi\) |
−0.648669 | + | 0.761071i | \(0.724674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19102.6i | 0.694727i | 0.937731 | + | 0.347364i | \(0.112923\pi\) | ||||
−0.937731 | + | 0.347364i | \(0.887077\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17285.3 | − | 17285.3i | 0.626572 | − | 0.626572i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4871.55 | + | 4871.55i | −0.175434 | + | 0.175434i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29786.7i | 1.06917i | 0.845113 | + | 0.534587i | \(0.179533\pi\) | ||||
−0.845113 | + | 0.534587i | \(0.820467\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22613.0 | + | 22613.0i | 0.806410 | + | 0.806410i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2656.45 | + | 2056.59i | −0.0944254 | + | 0.0731029i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7724.87 | −0.272815 | −0.136407 | − | 0.990653i | \(-0.543556\pi\) | ||||
−0.136407 | + | 0.990653i | \(0.543556\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11724.1 | −0.412720 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −36080.8 | − | 2286.91i | −1.26200 | − | 0.0799892i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20722.5 | − | 20722.5i | −0.722492 | − | 0.722492i | 0.246620 | − | 0.969112i | \(-0.420680\pi\) |
−0.969112 | + | 0.246620i | \(0.920680\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 21780.7i | − | 0.754548i | −0.926102 | − | 0.377274i | \(-0.876862\pi\) | ||
0.926102 | − | 0.377274i | \(-0.123138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10370.3 | − | 10370.3i | 0.358116 | − | 0.358116i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29938.4 | + | 29938.4i | −1.02731 | + | 1.02731i | −0.0276975 | + | 0.999616i | \(0.508818\pi\) |
−0.999616 | + | 0.0276975i | \(0.991182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 46257.8i | 1.58229i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29572.1 | − | 29572.1i | −1.00518 | − | 1.00518i | −0.999987 | − | 0.00519163i | \(-0.998347\pi\) |
−0.00519163 | − | 0.999987i | \(-0.501653\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8060.12 | + | 9151.01i | 0.273109 | + | 0.310073i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20646.4 | 0.695212 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24814.3 | 0.832945 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2826.16 | + | 44588.7i | −0.0942769 | + | 1.48742i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9478.37 | + | 9478.37i | 0.315206 | + | 0.315206i | 0.846922 | − | 0.531717i | \(-0.178453\pi\) |
−0.531717 | + | 0.846922i | \(0.678453\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 8382.79i | − | 0.277051i | −0.990359 | − | 0.138525i | \(-0.955764\pi\) | ||
0.990359 | − | 0.138525i | \(-0.0442363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1224.89 | − | 1224.89i | 0.0403577 | − | 0.0403577i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24277.3 | − | 24277.3i | 0.794986 | − | 0.794986i | −0.187314 | − | 0.982300i | \(-0.559978\pi\) |
0.982300 | + | 0.187314i | \(0.0599783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 51714.8i | − | 1.68826i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14666.4 | + | 14666.4i | 0.475876 | + | 0.475876i | 0.903810 | − | 0.427934i | \(-0.140758\pi\) |
−0.427934 | + | 0.903810i | \(0.640758\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1164.18 | − | 18367.4i | 0.0376588 | − | 0.594147i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14014.8 | −0.450603 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17192.0 | −0.551080 | −0.275540 | − | 0.961290i | \(-0.588857\pi\) | ||||
−0.275540 | + | 0.961290i | \(0.588857\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3844.58 | + | 4364.92i | 0.122494 | + | 0.139073i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13617.4 | + | 13617.4i | 0.432566 | + | 0.432566i | 0.889500 | − | 0.456935i | \(-0.151053\pi\) |
−0.456935 | + | 0.889500i | \(0.651053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 720.4.w.d.17.5 | 12 | ||
3.2 | odd | 2 | inner | 720.4.w.d.17.2 | 12 | ||
4.3 | odd | 2 | 45.4.f.a.17.5 | yes | 12 | ||
5.3 | odd | 4 | inner | 720.4.w.d.593.2 | 12 | ||
12.11 | even | 2 | 45.4.f.a.17.2 | yes | 12 | ||
15.8 | even | 4 | inner | 720.4.w.d.593.5 | 12 | ||
20.3 | even | 4 | 45.4.f.a.8.2 | ✓ | 12 | ||
20.7 | even | 4 | 225.4.f.c.143.5 | 12 | |||
20.19 | odd | 2 | 225.4.f.c.107.2 | 12 | |||
60.23 | odd | 4 | 45.4.f.a.8.5 | yes | 12 | ||
60.47 | odd | 4 | 225.4.f.c.143.2 | 12 | |||
60.59 | even | 2 | 225.4.f.c.107.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.f.a.8.2 | ✓ | 12 | 20.3 | even | 4 | ||
45.4.f.a.8.5 | yes | 12 | 60.23 | odd | 4 | ||
45.4.f.a.17.2 | yes | 12 | 12.11 | even | 2 | ||
45.4.f.a.17.5 | yes | 12 | 4.3 | odd | 2 | ||
225.4.f.c.107.2 | 12 | 20.19 | odd | 2 | |||
225.4.f.c.107.5 | 12 | 60.59 | even | 2 | |||
225.4.f.c.143.2 | 12 | 60.47 | odd | 4 | |||
225.4.f.c.143.5 | 12 | 20.7 | even | 4 | |||
720.4.w.d.17.2 | 12 | 3.2 | odd | 2 | inner | ||
720.4.w.d.17.5 | 12 | 1.1 | even | 1 | trivial | ||
720.4.w.d.593.2 | 12 | 5.3 | odd | 4 | inner | ||
720.4.w.d.593.5 | 12 | 15.8 | even | 4 | inner |