Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(1,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.a (trivial) |
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: | yes |
Analytic conductor: | \(34.6931230834\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 588.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.00000 | −0.357771 | −0.178885 | − | 0.983870i | \(-0.557249\pi\) | ||||
−0.178885 | + | 0.983870i | \(0.557249\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −20.0000 | −0.548202 | −0.274101 | − | 0.961701i | \(-0.588380\pi\) | ||||
−0.274101 | + | 0.961701i | \(0.588380\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 0.0853385 | 0.0426692 | − | 0.999089i | \(-0.486414\pi\) | ||||
0.0426692 | + | 0.999089i | \(0.486414\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0000 | −0.206559 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −24.0000 | −0.342403 | −0.171202 | − | 0.985236i | \(-0.554765\pi\) | ||||
−0.171202 | + | 0.985236i | \(0.554765\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −44.0000 | −0.531279 | −0.265639 | − | 0.964072i | \(-0.585583\pi\) | ||||
−0.265639 | + | 0.964072i | \(0.585583\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 72.0000 | 0.652741 | 0.326370 | − | 0.945242i | \(-0.394174\pi\) | ||||
0.326370 | + | 0.945242i | \(0.394174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −109.000 | −0.872000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −38.0000 | −0.243325 | −0.121662 | − | 0.992572i | \(-0.538823\pi\) | ||||
−0.121662 | + | 0.992572i | \(0.538823\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −184.000 | −1.06604 | −0.533022 | − | 0.846101i | \(-0.678944\pi\) | ||||
−0.533022 | + | 0.846101i | \(0.678944\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −60.0000 | −0.316505 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −30.0000 | −0.133296 | −0.0666482 | − | 0.997777i | \(-0.521231\pi\) | ||||
−0.0666482 | + | 0.997777i | \(0.521231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.0000 | 0.0492702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 216.000 | 0.822769 | 0.411385 | − | 0.911462i | \(-0.365045\pi\) | ||||
0.411385 | + | 0.911462i | \(0.365045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −164.000 | −0.581622 | −0.290811 | − | 0.956780i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956780i | \(0.593925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −36.0000 | −0.119257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −520.000 | −1.61383 | −0.806913 | − | 0.590671i | \(-0.798863\pi\) | ||||
−0.806913 | + | 0.590671i | \(0.798863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −72.0000 | −0.197687 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −146.000 | −0.378389 | −0.189195 | − | 0.981940i | \(-0.560588\pi\) | ||||
−0.189195 | + | 0.981940i | \(0.560588\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 80.0000 | 0.196131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −132.000 | −0.306734 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −460.000 | −1.01503 | −0.507516 | − | 0.861642i | \(-0.669436\pi\) | ||||
−0.507516 | + | 0.861642i | \(0.669436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −628.000 | −1.31815 | −0.659075 | − | 0.752077i | \(-0.729052\pi\) | ||||
−0.659075 | + | 0.752077i | \(0.729052\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.0000 | −0.0305316 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 556.000 | 1.01382 | 0.506912 | − | 0.861998i | \(-0.330787\pi\) | ||||
0.506912 | + | 0.861998i | \(0.330787\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 216.000 | 0.376860 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 592.000 | 0.989542 | 0.494771 | − | 0.869023i | \(-0.335252\pi\) | ||||
0.494771 | + | 0.869023i | \(0.335252\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1024.00 | −1.64178 | −0.820891 | − | 0.571084i | \(-0.806523\pi\) | ||||
−0.820891 | + | 0.571084i | \(0.806523\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −327.000 | −0.503449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −104.000 | −0.148113 | −0.0740564 | − | 0.997254i | \(-0.523594\pi\) | ||||
−0.0740564 | + | 0.997254i | \(0.523594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 324.000 | 0.428477 | 0.214239 | − | 0.976781i | \(-0.431273\pi\) | ||||
0.214239 | + | 0.976781i | \(0.431273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 96.0000 | 0.122502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −114.000 | −0.140484 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −896.000 | −1.06714 | −0.533572 | − | 0.845755i | \(-0.679151\pi\) | ||||
−0.533572 | + | 0.845755i | \(0.679151\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −552.000 | −0.615481 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 176.000 | 0.190076 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 920.000 | 0.963009 | 0.481504 | − | 0.876444i | \(-0.340091\pi\) | ||||
0.481504 | + | 0.876444i | \(0.340091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −180.000 | −0.182734 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1108.00 | −1.09159 | −0.545793 | − | 0.837920i | \(-0.683771\pi\) | ||||
−0.545793 | + | 0.837920i | \(0.683771\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1448.00 | −1.38520 | −0.692600 | − | 0.721321i | \(-0.743535\pi\) | ||||
−0.692600 | + | 0.721321i | \(0.743535\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1316.00 | 1.18900 | 0.594498 | − | 0.804097i | \(-0.297351\pi\) | ||||
0.594498 | + | 0.804097i | \(0.297351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −86.0000 | −0.0755716 | −0.0377858 | − | 0.999286i | \(-0.512030\pi\) | ||||
−0.0377858 | + | 0.999286i | \(0.512030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −90.0000 | −0.0769588 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1778.00 | 1.48018 | 0.740089 | − | 0.672509i | \(-0.234783\pi\) | ||||
0.740089 | + | 0.672509i | \(0.234783\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −288.000 | −0.233532 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 36.0000 | 0.0284462 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −931.000 | −0.699474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 648.000 | 0.475026 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 936.000 | 0.669747 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −928.000 | −0.648399 | −0.324200 | − | 0.945989i | \(-0.605095\pi\) | ||||
−0.324200 | + | 0.945989i | \(0.605095\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −492.000 | −0.335800 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1404.00 | −0.936397 | −0.468199 | − | 0.883623i | \(-0.655097\pi\) | ||||
−0.468199 | + | 0.883623i | \(0.655097\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −108.000 | −0.0688530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1370.00 | −0.854358 | −0.427179 | − | 0.904167i | \(-0.640493\pi\) | ||||
−0.427179 | + | 0.904167i | \(0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −516.000 | −0.314867 | −0.157434 | − | 0.987530i | \(-0.550322\pi\) | ||||
−0.157434 | + | 0.987530i | \(0.550322\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1560.00 | −0.931743 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −80.0000 | −0.0467828 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 152.000 | 0.0870546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1390.00 | 0.764250 | 0.382125 | − | 0.924111i | \(-0.375192\pi\) | ||||
0.382125 | + | 0.924111i | \(0.375192\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 136.000 | 0.0732949 | 0.0366474 | − | 0.999328i | \(-0.488332\pi\) | ||||
0.0366474 | + | 0.999328i | \(0.488332\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −216.000 | −0.114134 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 736.000 | 0.381400 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 148.000 | 0.0752337 | 0.0376168 | − | 0.999292i | \(-0.488023\pi\) | ||||
0.0376168 | + | 0.999292i | \(0.488023\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −438.000 | −0.218463 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1212.00 | −0.582400 | −0.291200 | − | 0.956662i | \(-0.594054\pi\) | ||||
−0.291200 | + | 0.956662i | \(0.594054\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 240.000 | 0.113236 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1976.00 | −0.915614 | −0.457807 | − | 0.889052i | \(-0.651365\pi\) | ||||
−0.457807 | + | 0.889052i | \(0.651365\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2181.00 | −0.992717 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −396.000 | −0.177093 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2692.00 | 1.18306 | 0.591529 | − | 0.806284i | \(-0.298525\pi\) | ||||
0.591529 | + | 0.806284i | \(0.298525\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1380.00 | −0.586029 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2580.00 | −1.07731 | −0.538654 | − | 0.842527i | \(-0.681067\pi\) | ||||
−0.538654 | + | 0.842527i | \(0.681067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2036.00 | 0.836103 | 0.418052 | − | 0.908423i | \(-0.362713\pi\) | ||||
0.418052 | + | 0.908423i | \(0.362713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1884.00 | −0.761034 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 120.000 | 0.0476896 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 480.000 | 0.187706 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3960.00 | 1.50019 | 0.750093 | − | 0.661332i | \(-0.230009\pi\) | ||||
0.750093 | + | 0.661332i | \(0.230009\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | 0.000745923 0 | 0.000372962 | − | 1.00000i | \(-0.499881\pi\) | ||||
0.000372962 | 1.00000i | \(0.499881\pi\) | ||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −48.0000 | −0.0176274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3774.00 | 1.36491 | 0.682453 | − | 0.730930i | \(-0.260913\pi\) | ||||
0.682453 | + | 0.730930i | \(0.260913\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3560.00 | 1.26815 | 0.634075 | − | 0.773272i | \(-0.281381\pi\) | ||||
0.634075 | + | 0.773272i | \(0.281381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1668.00 | 0.585332 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −864.000 | −0.294363 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 648.000 | 0.217580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 880.000 | 0.291248 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2692.00 | −0.878317 | −0.439159 | − | 0.898410i | \(-0.644723\pi\) | ||||
−0.439159 | + | 0.898410i | \(0.644723\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1776.00 | 0.571312 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 656.000 | 0.208088 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3072.00 | −0.947884 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −96.0000 | −0.0292202 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4528.00 | −1.35972 | −0.679859 | − | 0.733342i | \(-0.737959\pi\) | ||||
−0.679859 | + | 0.733342i | \(0.737959\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −981.000 | −0.290667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3652.00 | 1.06781 | 0.533903 | − | 0.845546i | \(-0.320725\pi\) | ||||
0.533903 | + | 0.845546i | \(0.320725\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4804.00 | 1.38628 | 0.693138 | − | 0.720805i | \(-0.256228\pi\) | ||||
0.693138 | + | 0.720805i | \(0.256228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2758.00 | 0.775462 | 0.387731 | − | 0.921773i | \(-0.373259\pi\) | ||||
0.387731 | + | 0.921773i | \(0.373259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2080.00 | 0.577380 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −312.000 | −0.0855130 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6528.00 | 1.76678 | 0.883392 | − | 0.468635i | \(-0.155254\pi\) | ||||
0.883392 | + | 0.468635i | \(0.155254\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 56.0000 | 0.0149680 | 0.00748398 | − | 0.999972i | \(-0.497618\pi\) | ||||
0.00748398 | + | 0.999972i | \(0.497618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −176.000 | −0.0453385 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 972.000 | 0.247382 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4900.00 | −1.23221 | −0.616106 | − | 0.787663i | \(-0.711291\pi\) | ||||
−0.616106 | + | 0.787663i | \(0.711291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1440.00 | −0.357834 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 288.000 | 0.0707265 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6784.00 | 1.64659 | 0.823296 | − | 0.567612i | \(-0.192133\pi\) | ||||
0.823296 | + | 0.567612i | \(0.192133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −342.000 | −0.0811083 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4544.00 | −1.06538 | −0.532690 | − | 0.846310i | \(-0.678819\pi\) | ||||
−0.532690 | + | 0.846310i | \(0.678819\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 584.000 | 0.135377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2688.00 | −0.616116 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4052.00 | 0.918419 | 0.459210 | − | 0.888328i | \(-0.348133\pi\) | ||||
0.459210 | + | 0.888328i | \(0.348133\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2752.00 | 0.616871 | 0.308436 | − | 0.951245i | \(-0.400195\pi\) | ||||
0.308436 | + | 0.951245i | \(0.400195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2180.00 | 0.478033 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4366.00 | 0.947031 | 0.473515 | − | 0.880786i | \(-0.342985\pi\) | ||||
0.473515 | + | 0.880786i | \(0.342985\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1656.00 | −0.355348 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7734.00 | 1.64189 | 0.820946 | − | 0.571006i | \(-0.193447\pi\) | ||||
0.820946 | + | 0.571006i | \(0.193447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4052.00 | 0.851118 | 0.425559 | − | 0.904931i | \(-0.360077\pi\) | ||||
0.425559 | + | 0.904931i | \(0.360077\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 528.000 | 0.109740 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4337.00 | −0.882760 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2760.00 | 0.555993 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3420.00 | 0.681906 | 0.340953 | − | 0.940080i | \(-0.389250\pi\) | ||||
0.340953 | + | 0.940080i | \(0.389250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1840.00 | 0.363149 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −540.000 | −0.105502 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 288.000 | 0.0557039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3324.00 | −0.630227 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2512.00 | 0.471596 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7324.00 | −1.36157 | −0.680786 | − | 0.732482i | \(-0.738362\pi\) | ||||
−0.680786 | + | 0.732482i | \(0.738362\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4344.00 | −0.799746 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4192.00 | 0.764330 | 0.382165 | − | 0.924094i | \(-0.375179\pi\) | ||||
0.382165 | + | 0.924094i | \(0.375179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6840.00 | 1.23521 | 0.617603 | − | 0.786490i | \(-0.288104\pi\) | ||||
0.617603 | + | 0.786490i | \(0.288104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6630.00 | 1.17469 | 0.587347 | − | 0.809335i | \(-0.300172\pi\) | ||||
0.587347 | + | 0.809335i | \(0.300172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 760.000 | 0.133391 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3948.00 | 0.686467 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1056.00 | 0.181911 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −436.000 | −0.0744152 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −258.000 | −0.0436313 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6868.00 | −1.14048 | −0.570241 | − | 0.821478i | \(-0.693150\pi\) | ||||
−0.570241 | + | 0.821478i | \(0.693150\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −270.000 | −0.0444322 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2224.00 | −0.362717 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7378.00 | −1.19260 | −0.596299 | − | 0.802763i | \(-0.703363\pi\) | ||||
−0.596299 | + | 0.802763i | \(0.703363\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5334.00 | 0.854581 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3680.00 | 0.584408 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −864.000 | −0.134830 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2676.00 | −0.413992 | −0.206996 | − | 0.978342i | \(-0.566369\pi\) | ||||
−0.206996 | + | 0.978342i | \(0.566369\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5124.00 | 0.785907 | 0.392953 | − | 0.919558i | \(-0.371453\pi\) | ||||
0.392953 | + | 0.919558i | \(0.371453\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 108.000 | 0.0164234 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4560.00 | −0.687548 | −0.343774 | − | 0.939052i | \(-0.611705\pi\) | ||||
−0.343774 | + | 0.939052i | \(0.611705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2368.00 | −0.354029 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3656.00 | 0.537483 | 0.268741 | − | 0.963212i | \(-0.413392\pi\) | ||||
0.268741 | + | 0.963212i | \(0.413392\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4923.00 | −0.717743 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2793.00 | −0.403842 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4096.00 | 0.587382 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1616.00 | 0.229849 | 0.114924 | − | 0.993374i | \(-0.463337\pi\) | ||||
0.114924 | + | 0.993374i | \(0.463337\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1944.00 | 0.274256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2734.00 | 0.379521 | 0.189760 | − | 0.981830i | \(-0.439229\pi\) | ||||
0.189760 | + | 0.981830i | \(0.439229\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2808.00 | 0.386679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −152.000 | −0.0207650 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1380.00 | −0.187034 | −0.0935169 | − | 0.995618i | \(-0.529811\pi\) | ||||
−0.0935169 | + | 0.995618i | \(0.529811\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2784.00 | −0.374353 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6888.00 | −0.918957 | −0.459478 | − | 0.888189i | \(-0.651964\pi\) | ||||
−0.459478 | + | 0.888189i | \(0.651964\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1476.00 | −0.193874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2046.00 | −0.266674 | −0.133337 | − | 0.991071i | \(-0.542569\pi\) | ||||
−0.133337 | + | 0.991071i | \(0.542569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1728.00 | −0.223501 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4212.00 | −0.540629 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 416.000 | 0.0529905 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3116.00 | −0.393923 | −0.196962 | − | 0.980411i | \(-0.563107\pi\) | ||||
−0.196962 | + | 0.980411i | \(0.563107\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2958.00 | 0.368368 | 0.184184 | − | 0.982892i | \(-0.441036\pi\) | ||||
0.184184 | + | 0.982892i | \(0.441036\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −736.000 | −0.0909746 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −324.000 | −0.0397523 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 600.000 | 0.0730735 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7944.00 | −0.960405 | −0.480202 | − | 0.877158i | \(-0.659437\pi\) | ||||
−0.480202 | + | 0.877158i | \(0.659437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4110.00 | −0.493264 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1296.00 | −0.153297 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1548.00 | −0.181789 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4084.00 | −0.476173 | −0.238086 | − | 0.971244i | \(-0.576520\pi\) | ||||
−0.238086 | + | 0.971244i | \(0.576520\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6306.00 | −0.730013 | −0.365007 | − | 0.931005i | \(-0.618933\pi\) | ||||
−0.365007 | + | 0.931005i | \(0.618933\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4680.00 | −0.537942 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2616.00 | 0.298576 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −240.000 | −0.0270100 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11824.0 | −1.32144 | −0.660722 | − | 0.750631i | \(-0.729750\pi\) | ||||
−0.660722 | + | 0.750631i | \(0.729750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4504.00 | 0.499881 | 0.249940 | − | 0.968261i | \(-0.419589\pi\) | ||||
0.249940 | + | 0.968261i | \(0.419589\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 456.000 | 0.0502610 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3168.00 | −0.346787 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13056.0 | −1.41943 | −0.709714 | − | 0.704490i | \(-0.751176\pi\) | ||||
−0.709714 | + | 0.704490i | \(0.751176\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 132.000 | 0.0141569 | 0.00707845 | − | 0.999975i | \(-0.497747\pi\) | ||||
0.00707845 | + | 0.999975i | \(0.497747\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3584.00 | 0.381793 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4170.00 | 0.441240 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4866.00 | 0.511449 | 0.255725 | − | 0.966750i | \(-0.417686\pi\) | ||||
0.255725 | + | 0.966750i | \(0.417686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4320.00 | −0.451044 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 408.000 | 0.0423168 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10106.0 | 1.03444 | 0.517220 | − | 0.855853i | \(-0.326967\pi\) | ||||
0.517220 | + | 0.855853i | \(0.326967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −648.000 | −0.0658955 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18036.0 | 1.82217 | 0.911085 | − | 0.412219i | \(-0.135246\pi\) | ||||
0.911085 | + | 0.412219i | \(0.135246\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5288.00 | 0.530787 | 0.265393 | − | 0.964140i | \(-0.414498\pi\) | ||||
0.265393 | + | 0.964140i | \(0.414498\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2208.00 | 0.220201 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −15164.0 | −1.50258 | −0.751291 | − | 0.659971i | \(-0.770569\pi\) | ||||
−0.751291 | + | 0.659971i | \(0.770569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 444.000 | 0.0434362 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3280.00 | 0.318847 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4796.00 | 0.463275 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1314.00 | −0.126130 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7896.00 | −0.753189 | −0.376594 | − | 0.926378i | \(-0.622905\pi\) | ||||
−0.376594 | + | 0.926378i | \(0.622905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −120.000 | −0.0113753 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3680.00 | −0.344536 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2920.00 | 0.271700 | 0.135850 | − | 0.990729i | \(-0.456624\pi\) | ||||
0.135850 | + | 0.990729i | \(0.456624\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3636.00 | −0.336249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7932.00 | −0.729055 | −0.364528 | − | 0.931193i | \(-0.618770\pi\) | ||||
−0.364528 | + | 0.931193i | \(0.618770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 912.000 | 0.0833152 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 720.000 | 0.0653770 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2004.00 | −0.179782 | −0.0898911 | − | 0.995952i | \(-0.528652\pi\) | ||||
−0.0898911 | + | 0.995952i | \(0.528652\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5928.00 | −0.528630 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4496.00 | −0.398542 | −0.199271 | − | 0.979944i | \(-0.563857\pi\) | ||||
−0.199271 | + | 0.979944i | \(0.563857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4432.00 | 0.390537 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6543.00 | −0.573146 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12620.0 | −1.09896 | −0.549481 | − | 0.835506i | \(-0.685175\pi\) | ||||
−0.549481 | + | 0.835506i | \(0.685175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1188.00 | −0.102245 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5792.00 | 0.495584 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10400.0 | 0.884703 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8076.00 | 0.683039 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18008.0 | −1.51429 | −0.757145 | − | 0.653247i | \(-0.773406\pi\) | ||||
−0.757145 | + | 0.653247i | \(0.773406\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13292.0 | −1.11132 | −0.555658 | − | 0.831411i | \(-0.687534\pi\) | ||||
−0.555658 | + | 0.831411i | \(0.687534\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4416.00 | 0.365017 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4140.00 | −0.338344 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 864.000 | 0.0702139 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5264.00 | −0.425388 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7740.00 | −0.621984 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8570.00 | −0.681059 | −0.340530 | − | 0.940234i | \(-0.610606\pi\) | ||||
−0.340530 | + | 0.940234i | \(0.610606\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6108.00 | 0.482724 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 344.000 | 0.0270373 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1916.00 | −0.149766 | −0.0748832 | − | 0.997192i | \(-0.523858\pi\) | ||||
−0.0748832 | + | 0.997192i | \(0.523858\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5652.00 | −0.439383 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1672.00 | 0.129273 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 360.000 | 0.0275336 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19926.0 | 1.51578 | 0.757892 | − | 0.652380i | \(-0.226229\pi\) | ||||
0.757892 | + | 0.652380i | \(0.226229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −656.000 | −0.0496348 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1440.00 | 0.108372 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4244.00 | −0.317697 | −0.158848 | − | 0.987303i | \(-0.550778\pi\) | ||||
−0.158848 | + | 0.987303i | \(0.550778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7112.00 | −0.529565 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22794.0 | −1.67939 | −0.839696 | − | 0.543057i | \(-0.817267\pi\) | ||||
−0.839696 | + | 0.543057i | \(0.817267\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14028.0 | 1.02811 | 0.514057 | − | 0.857756i | \(-0.328142\pi\) | ||||
0.514057 | + | 0.857756i | \(0.328142\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11880.0 | 0.866133 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7848.00 | −0.569190 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8368.00 | −0.603751 | −0.301876 | − | 0.953347i | \(-0.597613\pi\) | ||||
−0.301876 | + | 0.953347i | \(0.597613\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.00000 | 0.000430659 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2920.00 | 0.207434 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −144.000 | −0.0101772 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −52.0000 | −0.00365634 | −0.00182817 | − | 0.999998i | \(-0.500582\pi\) | ||||
−0.00182817 | + | 0.999998i | \(0.500582\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8096.00 | 0.566366 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11322.0 | 0.788029 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5808.00 | −0.402202 | −0.201101 | − | 0.979570i | \(-0.564452\pi\) | ||||
−0.201101 | + | 0.979570i | \(0.564452\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10680.0 | 0.732166 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10464.0 | −0.713769 | −0.356884 | − | 0.934149i | \(-0.616161\pi\) | ||||
−0.356884 | + | 0.934149i | \(0.616161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1184.00 | −0.0803600 | −0.0401800 | − | 0.999192i | \(-0.512793\pi\) | ||||
−0.0401800 | + | 0.999192i | \(0.512793\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5004.00 | 0.337941 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3724.00 | 0.250251 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13152.0 | −0.879445 | −0.439723 | − | 0.898134i | \(-0.644923\pi\) | ||||
−0.439723 | + | 0.898134i | \(0.644923\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2080.00 | −0.137721 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18334.0 | −1.20800 | −0.603999 | − | 0.796985i | \(-0.706427\pi\) | ||||
−0.603999 | + | 0.796985i | \(0.706427\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2592.00 | −0.169950 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8122.00 | −0.529950 | −0.264975 | − | 0.964255i | \(-0.585364\pi\) | ||||
−0.264975 | + | 0.964255i | \(0.585364\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5980.00 | −0.388298 | −0.194149 | − | 0.980972i | \(-0.562195\pi\) | ||||
−0.194149 | + | 0.980972i | \(0.562195\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1944.00 | 0.125620 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9881.00 | 0.632384 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2640.00 | 0.168152 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 720.000 | 0.0456411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12528.0 | 0.790383 | 0.395192 | − | 0.918599i | \(-0.370678\pi\) | ||||
0.395192 | + | 0.918599i | \(0.370678\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8076.00 | −0.507097 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3712.00 | 0.231978 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5328.00 | 0.329847 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20798.0 | 1.28155 | 0.640773 | − | 0.767730i | \(-0.278614\pi\) | ||||
0.640773 | + | 0.767730i | \(0.278614\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1932.00 | 0.118492 | 0.0592462 | − | 0.998243i | \(-0.481130\pi\) | ||||
0.0592462 | + | 0.998243i | \(0.481130\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1968.00 | 0.120139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8424.00 | 0.511873 | 0.255936 | − | 0.966694i | \(-0.417616\pi\) | ||||
0.255936 | + | 0.966694i | \(0.417616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9200.00 | 0.556443 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17750.0 | −1.06372 | −0.531862 | − | 0.846831i | \(-0.678507\pi\) | ||||
−0.531862 | + | 0.846831i | \(0.678507\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5616.00 | 0.335016 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9216.00 | −0.547261 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27580.0 | −1.63029 | −0.815147 | − | 0.579254i | \(-0.803344\pi\) | ||||
−0.815147 | + | 0.579254i | \(0.803344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9292.00 | 0.546773 | 0.273386 | − | 0.961904i | \(-0.411856\pi\) | ||||
0.273386 | + | 0.961904i | \(0.411856\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −288.000 | −0.0168703 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2736.00 | −0.158828 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13584.0 | −0.785034 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12560.0 | 0.722613 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11486.0 | 0.657879 | 0.328940 | − | 0.944351i | \(-0.393309\pi\) | ||||
0.328940 | + | 0.944351i | \(0.393309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2943.00 | −0.167816 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7116.00 | −0.403974 | −0.201987 | − | 0.979388i | \(-0.564740\pi\) | ||||
−0.201987 | + | 0.979388i | \(0.564740\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10956.0 | 0.616498 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7612.00 | −0.426450 | −0.213225 | − | 0.977003i | \(-0.568397\pi\) | ||||
−0.213225 | + | 0.977003i | \(0.568397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5480.00 | 0.305664 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14412.0 | 0.800367 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −584.000 | −0.0322912 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21572.0 | 1.18761 | 0.593804 | − | 0.804609i | \(-0.297625\pi\) | ||||
0.593804 | + | 0.804609i | \(0.297625\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2064.00 | 0.112650 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5184.00 | −0.281719 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8274.00 | 0.447713 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1702.00 | −0.0917028 | −0.0458514 | − | 0.998948i | \(-0.514600\pi\) | ||||
−0.0458514 | + | 0.998948i | \(0.514600\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1320.00 | 0.0708176 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6240.00 | 0.333350 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6370.00 | 0.337419 | 0.168710 | − | 0.985666i | \(-0.446040\pi\) | ||||
0.168710 | + | 0.985666i | \(0.446040\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −936.000 | −0.0493709 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13248.0 | −0.695851 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 320.000 | 0.0167375 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19584.0 | 1.02005 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8808.00 | 0.456861 | 0.228430 | − | 0.973560i | \(-0.426641\pi\) | ||||
0.228430 | + | 0.973560i | \(0.426641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 168.000 | 0.00864175 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4142.00 | 0.212179 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17768.0 | −0.906436 | −0.453218 | − | 0.891400i | \(-0.649724\pi\) | ||||
−0.453218 | + | 0.891400i | \(0.649724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3936.00 | 0.199149 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5564.00 | 0.280370 | 0.140185 | − | 0.990125i | \(-0.455230\pi\) | ||||
0.140185 | + | 0.990125i | \(0.455230\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11120.0 | −0.555781 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17564.0 | −0.874293 | −0.437146 | − | 0.899390i | \(-0.644011\pi\) | ||||
−0.437146 | + | 0.899390i | \(0.644011\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −528.000 | −0.0261762 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38280.0 | −1.89012 | −0.945059 | − | 0.326901i | \(-0.893996\pi\) | ||||
−0.945059 | + | 0.326901i | \(0.893996\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5560.00 | −0.273426 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2916.00 | 0.142826 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36192.0 | 1.75854 | 0.879271 | − | 0.476322i | \(-0.158030\pi\) | ||||
0.879271 | + | 0.476322i | \(0.158030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14700.0 | −0.711418 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −544.000 | −0.0262228 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.000672178 0 | −0.000336089 | − | 1.00000i | \(-0.500107\pi\) | ||||
−0.000336089 | 1.00000i | \(0.500107\pi\) | ||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4320.00 | −0.206596 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26504.0 | 1.26251 | 0.631254 | − | 0.775576i | \(-0.282540\pi\) | ||||
0.631254 | + | 0.775576i | \(0.282540\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 864.000 | 0.0408340 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1840.00 | −0.0866213 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40184.0 | −1.88436 | −0.942180 | − | 0.335109i | \(-0.891227\pi\) | ||||
−0.942180 | + | 0.335109i | \(0.891227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20352.0 | 0.950661 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35340.0 | 1.64436 | 0.822181 | − | 0.569226i | \(-0.192757\pi\) | ||||
0.822181 | + | 0.569226i | \(0.192757\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20056.0 | 0.929591 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9504.00 | −0.437120 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11840.0 | −0.542469 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1026.00 | −0.0468279 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −592.000 | −0.0269164 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14852.0 | 0.672702 | 0.336351 | − | 0.941737i | \(-0.390807\pi\) | ||||
0.336351 | + | 0.941737i | \(0.390807\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13632.0 | −0.615098 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2512.00 | −0.112489 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1752.00 | 0.0781598 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19788.0 | −0.879457 | −0.439728 | − | 0.898131i | \(-0.644925\pi\) | ||||
−0.439728 | + | 0.898131i | \(0.644925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12480.0 | 0.552579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8064.00 | −0.355715 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20480.0 | 0.900029 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12156.0 | 0.530250 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16986.0 | 0.738190 | 0.369095 | − | 0.929392i | \(-0.379668\pi\) | ||||
0.369095 | + | 0.929392i | \(0.379668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26596.0 | 1.15156 | 0.575778 | − | 0.817606i | \(-0.304699\pi\) | ||||
0.575778 | + | 0.817606i | \(0.304699\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8256.00 | 0.356151 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4848.00 | 0.208366 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7216.00 | 0.309004 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34898.0 | −1.48349 | −0.741747 | − | 0.670680i | \(-0.766002\pi\) | ||||
−0.741747 | + | 0.670680i | \(0.766002\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12928.0 | 0.547560 | 0.273780 | − | 0.961792i | \(-0.411726\pi\) | ||||
0.273780 | + | 0.961792i | \(0.411726\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6540.00 | 0.275992 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43164.0 | −1.81494 | −0.907472 | − | 0.420112i | \(-0.861991\pi\) | ||||
−0.907472 | + | 0.420112i | \(0.861991\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41228.0 | 1.72727 | 0.863635 | − | 0.504117i | \(-0.168182\pi\) | ||||
0.863635 | + | 0.504117i | \(0.168182\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13098.0 | 0.546768 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7904.00 | 0.327580 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4968.00 | −0.205160 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1368.00 | 0.0562915 | 0.0281458 | − | 0.999604i | \(-0.491040\pi\) | ||||
0.0281458 | + | 0.999604i | \(0.491040\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22945.0 | −0.940793 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23202.0 | 0.947947 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8724.00 | 0.355165 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12156.0 | 0.491393 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2160.00 | −0.0870080 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5276.00 | −0.211778 | −0.105889 | − | 0.994378i | \(-0.533769\pi\) | ||||
−0.105889 | + | 0.994378i | \(0.533769\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1584.00 | 0.0633587 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −840.000 | −0.0334817 | −0.0167409 | − | 0.999860i | \(-0.505329\pi\) | ||||
−0.0167409 | + | 0.999860i | \(0.505329\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26028.0 | 1.03383 | 0.516917 | − | 0.856035i | \(-0.327079\pi\) | ||||
0.516917 | + | 0.856035i | \(0.327079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29448.0 | −1.16155 | −0.580777 | − | 0.814063i | \(-0.697251\pi\) | ||||
−0.580777 | + | 0.814063i | \(0.697251\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10768.0 | −0.423264 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13011.0 | −0.509662 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2080.00 | 0.0811958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2224.00 | 0.0865182 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8280.00 | 0.321003 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25866.0 | 0.995932 | 0.497966 | − | 0.867196i | \(-0.334080\pi\) | ||||
0.497966 | + | 0.867196i | \(0.334080\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10260.0 | 0.393699 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9472.00 | −0.362225 | −0.181112 | − | 0.983462i | \(-0.557970\pi\) | ||||
−0.181112 | + | 0.983462i | \(0.557970\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49372.0 | 1.88165 | 0.940827 | − | 0.338888i | \(-0.110051\pi\) | ||||
0.940827 | + | 0.338888i | \(0.110051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5520.00 | 0.209664 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11160.0 | 0.422453 | 0.211227 | − | 0.977437i | \(-0.432254\pi\) | ||||
0.211227 | + | 0.977437i | \(0.432254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1620.00 | −0.0609114 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22880.0 | 0.857391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10320.0 | 0.385430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 864.000 | 0.0321607 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6992.00 | 0.259395 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3504.00 | 0.129562 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8144.00 | −0.299133 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22708.0 | 0.831319 | 0.415660 | − | 0.909520i | \(-0.363551\pi\) | ||||
0.415660 | + | 0.909520i | \(0.363551\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9972.00 | −0.363862 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16192.0 | −0.588875 | −0.294437 | − | 0.955671i | \(-0.595132\pi\) | ||||
−0.294437 | + | 0.955671i | \(0.595132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6480.00 | −0.234892 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7536.00 | 0.272276 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46320.0 | −1.66263 | −0.831314 | − | 0.555802i | \(-0.812411\pi\) | ||||
−0.831314 | + | 0.555802i | \(0.812411\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21972.0 | −0.786104 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2368.00 | 0.0844460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3270.00 | 0.116235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13032.0 | −0.461734 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2280.00 | 0.0805214 | 0.0402607 | − | 0.999189i | \(-0.487181\pi\) | ||||
0.0402607 | + | 0.999189i | \(0.487181\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12576.0 | 0.441286 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1920.00 | −0.0671558 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49056.0 | −1.71034 | −0.855171 | − | 0.518347i | \(-0.826548\pi\) | ||||
−0.855171 | + | 0.518347i | \(0.826548\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20520.0 | 0.713147 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24876.0 | 0.861779 | 0.430890 | − | 0.902405i | \(-0.358200\pi\) | ||||
0.430890 | + | 0.902405i | \(0.358200\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15552.0 | 0.537055 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23428.0 | 0.803915 | 0.401958 | − | 0.915658i | \(-0.368330\pi\) | ||||
0.401958 | + | 0.915658i | \(0.368330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4096.00 | −0.140107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19890.0 | 0.678210 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6678.00 | −0.226990 | −0.113495 | − | 0.993539i | \(-0.536205\pi\) | ||||
−0.113495 | + | 0.993539i | \(0.536205\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15840.0 | −0.536723 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2280.00 | 0.0770135 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4065.00 | 0.136451 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11844.0 | 0.396332 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.00000 | −0.000266870 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15544.0 | 0.516920 | 0.258460 | − | 0.966022i | \(-0.416785\pi\) | ||||
0.258460 | + | 0.966022i | \(0.416785\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3168.00 | 0.105027 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31124.0 | 1.02865 | 0.514324 | − | 0.857596i | \(-0.328043\pi\) | ||||
0.514324 | + | 0.857596i | \(0.328043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1308.00 | −0.0429636 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50062.0 | 1.63933 | 0.819665 | − | 0.572843i | \(-0.194160\pi\) | ||||
0.819665 | + | 0.572843i | \(0.194160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17920.0 | 0.585011 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −774.000 | −0.0251905 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −328.000 | −0.0106425 | −0.00532125 | − | 0.999986i | \(-0.501694\pi\) | ||||
−0.00532125 | + | 0.999986i | \(0.501694\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15096.0 | −0.488323 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11808.0 | −0.379649 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20872.0 | −0.669042 | −0.334521 | − | 0.942388i | \(-0.608575\pi\) | ||||
−0.334521 | + | 0.942388i | \(0.608575\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20604.0 | −0.658457 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14240.0 | −0.453707 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46924.0 | 1.49057 | 0.745285 | − | 0.666746i | \(-0.232313\pi\) | ||||
0.745285 | + | 0.666746i | \(0.232313\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −810.000 | −0.0256529 |
(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 | 588.4.a.e.1.1 | yes | 1 | |
3.2 | odd | 2 | 1764.4.a.i.1.1 | 1 | |||
4.3 | odd | 2 | 2352.4.a.g.1.1 | 1 | |||
7.2 | even | 3 | 588.4.i.b.361.1 | 2 | |||
7.3 | odd | 6 | 588.4.i.g.373.1 | 2 | |||
7.4 | even | 3 | 588.4.i.b.373.1 | 2 | |||
7.5 | odd | 6 | 588.4.i.g.361.1 | 2 | |||
7.6 | odd | 2 | 588.4.a.b.1.1 | ✓ | 1 | ||
21.2 | odd | 6 | 1764.4.k.g.361.1 | 2 | |||
21.5 | even | 6 | 1764.4.k.j.361.1 | 2 | |||
21.11 | odd | 6 | 1764.4.k.g.1549.1 | 2 | |||
21.17 | even | 6 | 1764.4.k.j.1549.1 | 2 | |||
21.20 | even | 2 | 1764.4.a.d.1.1 | 1 | |||
28.27 | even | 2 | 2352.4.a.be.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.4.a.b.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
588.4.a.e.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
588.4.i.b.361.1 | 2 | 7.2 | even | 3 | |||
588.4.i.b.373.1 | 2 | 7.4 | even | 3 | |||
588.4.i.g.361.1 | 2 | 7.5 | odd | 6 | |||
588.4.i.g.373.1 | 2 | 7.3 | odd | 6 | |||
1764.4.a.d.1.1 | 1 | 21.20 | even | 2 | |||
1764.4.a.i.1.1 | 1 | 3.2 | odd | 2 | |||
1764.4.k.g.361.1 | 2 | 21.2 | odd | 6 | |||
1764.4.k.g.1549.1 | 2 | 21.11 | odd | 6 | |||
1764.4.k.j.361.1 | 2 | 21.5 | even | 6 | |||
1764.4.k.j.1549.1 | 2 | 21.17 | even | 6 | |||
2352.4.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
2352.4.a.be.1.1 | 1 | 28.27 | even | 2 |