Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1584,4,Mod(593,1584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1584, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1584.593");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1584.b (of order \(2\), degree \(1\), 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: | \(93.4590254491\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 593.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1584.593 |
Dual form | 1584.4.b.b.593.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(353\) | \(991\) | \(1189\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 19.7990i | 1.77088i | 0.464758 | + | 0.885438i | \(0.346141\pi\) | ||||
−0.464758 | + | 0.885438i | \(0.653859\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 16.9706i | 0.916324i | 0.888869 | + | 0.458162i | \(0.151492\pi\) | ||||
−0.888869 | + | 0.458162i | \(0.848508\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33.0000 | + | 15.5563i | 0.904534 | + | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 29.6985i | 0.633606i | 0.948491 | + | 0.316803i | \(0.102609\pi\) | ||||
−0.948491 | + | 0.316803i | \(0.897391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −126.000 | −1.79762 | −0.898808 | − | 0.438342i | \(-0.855566\pi\) | ||||
−0.898808 | + | 0.438342i | \(0.855566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 89.0955i | 1.07578i | 0.843014 | + | 0.537892i | \(0.180779\pi\) | ||||
−0.843014 | + | 0.537892i | \(0.819221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 120.208i | 1.08979i | 0.838505 | + | 0.544894i | \(0.183430\pi\) | ||||
−0.838505 | + | 0.544894i | \(0.816570\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −267.000 | −2.13600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 24.0000 | 0.153679 | 0.0768395 | − | 0.997043i | \(-0.475517\pi\) | ||||
0.0768395 | + | 0.997043i | \(0.475517\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 70.0000 | 0.405560 | 0.202780 | − | 0.979224i | \(-0.435002\pi\) | ||||
0.202780 | + | 0.979224i | \(0.435002\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −336.000 | −1.62270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 182.000 | 0.808665 | 0.404333 | − | 0.914612i | \(-0.367504\pi\) | ||||
0.404333 | + | 0.914612i | \(0.367504\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −294.000 | −1.11988 | −0.559940 | − | 0.828533i | \(-0.689176\pi\) | ||||
−0.559940 | + | 0.828533i | \(0.689176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264i | 0.0150464i | 0.999972 | + | 0.00752322i | \(0.00239474\pi\) | ||||
−0.999972 | + | 0.00752322i | \(0.997605\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 108.894i | − | 0.337955i | −0.985620 | − | 0.168978i | \(-0.945953\pi\) | ||
0.985620 | − | 0.168978i | \(-0.0540465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 55.0000 | 0.160350 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 147.078i | 0.381184i | 0.981669 | + | 0.190592i | \(0.0610407\pi\) | ||||
−0.981669 | + | 0.190592i | \(0.938959\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −308.000 | + | 653.367i | −0.755104 | + | 1.60182i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 514.774i | 1.13590i | 0.823065 | + | 0.567948i | \(0.192262\pi\) | ||||
−0.823065 | + | 0.567948i | \(0.807738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 326.683i | 0.685697i | 0.939391 | + | 0.342848i | \(0.111392\pi\) | ||||
−0.939391 | + | 0.342848i | \(0.888608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −588.000 | −1.12204 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 880.000 | 1.60461 | 0.802307 | − | 0.596912i | \(-0.203606\pi\) | ||||
0.802307 | + | 0.596912i | \(0.203606\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 337.997i | − | 0.564970i | −0.959272 | − | 0.282485i | \(-0.908841\pi\) | ||
0.959272 | − | 0.282485i | \(-0.0911587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 178.191i | 0.285694i | 0.989745 | + | 0.142847i | \(0.0456257\pi\) | ||||
−0.989745 | + | 0.142847i | \(0.954374\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −264.000 | + | 560.029i | −0.390722 | + | 0.828846i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 772.161i | − | 1.09968i | −0.835269 | − | 0.549841i | \(-0.814688\pi\) | ||
0.835269 | − | 0.549841i | \(-0.185312\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1218.00 | 1.61076 | 0.805379 | − | 0.592761i | \(-0.201962\pi\) | ||||
0.805379 | + | 0.592761i | \(0.201962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2494.67i | − | 3.18336i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1534.42i | 1.82751i | 0.406266 | + | 0.913755i | \(0.366831\pi\) | ||||
−0.406266 | + | 0.913755i | \(0.633169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −504.000 | −0.580589 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1764.00 | −1.90508 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −196.000 | −0.205163 | −0.102581 | − | 0.994725i | \(-0.532710\pi\) | ||||
−0.102581 | + | 0.994725i | \(0.532710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 546.000 | 0.537911 | 0.268956 | − | 0.963153i | \(-0.413322\pi\) | ||||
0.268956 | + | 0.963153i | \(0.413322\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 826.000 | 0.790177 | 0.395088 | − | 0.918643i | \(-0.370714\pi\) | ||||
0.395088 | + | 0.918643i | \(0.370714\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 108.000 | 0.0975771 | 0.0487886 | − | 0.998809i | \(-0.484464\pi\) | ||||
0.0487886 | + | 0.998809i | \(0.484464\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1183.70i | − | 1.04016i | −0.854117 | − | 0.520081i | \(-0.825902\pi\) | ||
0.854117 | − | 0.520081i | \(-0.174098\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1622.10i | − | 1.35039i | −0.737637 | − | 0.675197i | \(-0.764058\pi\) | ||
0.737637 | − | 0.675197i | \(-0.235942\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2380.00 | −1.92988 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2138.29i | − | 1.64720i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 847.000 | + | 1026.72i | 0.636364 | + | 0.771389i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2811.46i | − | 2.01171i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 178.191i | − | 0.124503i | −0.998060 | − | 0.0622515i | \(-0.980172\pi\) | ||
0.998060 | − | 0.0622515i | \(-0.0198281\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −588.000 | −0.392166 | −0.196083 | − | 0.980587i | \(-0.562822\pi\) | ||||
−0.196083 | + | 0.980587i | \(0.562822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1512.00 | −0.985767 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 337.997i | 0.210781i | 0.994431 | + | 0.105391i | \(0.0336093\pi\) | ||||
−0.994431 | + | 0.105391i | \(0.966391\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2880.75i | − | 1.75786i | −0.476952 | − | 0.878929i | \(-0.658259\pi\) | ||
0.476952 | − | 0.878929i | \(-0.341741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −462.000 | + | 980.050i | −0.270170 | + | 0.573118i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 475.176i | 0.272146i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2082.00 | 1.14473 | 0.572363 | − | 0.820001i | \(-0.306027\pi\) | ||||
0.572363 | + | 0.820001i | \(0.306027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1637.66i | − | 0.882588i | −0.897363 | − | 0.441294i | \(-0.854520\pi\) | ||
0.897363 | − | 0.441294i | \(-0.145480\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1385.93i | 0.718197i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2338.00 | −1.18849 | −0.594244 | − | 0.804285i | \(-0.702549\pi\) | ||||
−0.594244 | + | 0.804285i | \(0.702549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2040.00 | −0.998600 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −128.000 | −0.0615076 | −0.0307538 | − | 0.999527i | \(-0.509791\pi\) | ||||
−0.0307538 | + | 0.999527i | \(0.509791\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1176.00 | 0.544920 | 0.272460 | − | 0.962167i | \(-0.412163\pi\) | ||||
0.272460 | + | 0.962167i | \(0.412163\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1315.00 | 0.598543 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1092.00 | −0.479903 | −0.239952 | − | 0.970785i | \(-0.577132\pi\) | ||||
−0.239952 | + | 0.970785i | \(0.577132\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4531.14i | − | 1.95727i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 387.495i | 0.161803i | 0.996722 | + | 0.0809014i | \(0.0257799\pi\) | ||||
−0.996722 | + | 0.0809014i | \(0.974220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1330.00 | −0.546177 | −0.273089 | − | 0.961989i | \(-0.588045\pi\) | ||||
−0.273089 | + | 0.961989i | \(0.588045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3603.42i | 1.43205i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4158.00 | − | 1960.10i | −1.62601 | − | 0.766506i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3404.01i | 1.28956i | 0.764369 | + | 0.644779i | \(0.223051\pi\) | ||||
−0.764369 | + | 0.644779i | \(0.776949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3419.57i | − | 1.27537i | −0.770298 | − | 0.637684i | \(-0.779893\pi\) | ||
0.770298 | − | 0.637684i | \(-0.220107\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3798.00 | 1.37359 | 0.686793 | − | 0.726853i | \(-0.259018\pi\) | ||||
0.686793 | + | 0.726853i | \(0.259018\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −560.000 | −0.199484 | −0.0997421 | − | 0.995013i | \(-0.531802\pi\) | ||||
−0.0997421 | + | 0.995013i | \(0.531802\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 407.294i | 0.140820i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 5820.90i | − | 1.98317i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1386.00 | + | 2940.15i | −0.458716 | + | 0.973083i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1904.95i | 0.621525i | 0.950488 | + | 0.310763i | \(0.100584\pi\) | ||||
−0.950488 | + | 0.310763i | \(0.899416\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −84.0000 | −0.0266454 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1187.94i | 0.371625i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3742.01i | − | 1.13898i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2968.00 | 0.891264 | 0.445632 | − | 0.895216i | \(-0.352979\pi\) | ||||
0.445632 | + | 0.895216i | \(0.352979\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3444.00 | −1.00699 | −0.503494 | − | 0.863999i | \(-0.667952\pi\) | ||||
−0.503494 | + | 0.863999i | \(0.667952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −574.000 | −0.165638 | −0.0828188 | − | 0.996565i | \(-0.526392\pi\) | ||||
−0.0828188 | + | 0.996565i | \(0.526392\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5310.00 | −1.49300 | −0.746501 | − | 0.665384i | \(-0.768268\pi\) | ||||
−0.746501 | + | 0.665384i | \(0.768268\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2156.00 | 0.598476 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1236.00 | −0.334520 | −0.167260 | − | 0.985913i | \(-0.553492\pi\) | ||||
−0.167260 | + | 0.985913i | \(0.553492\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3445.02i | 0.920803i | 0.887711 | + | 0.460401i | \(0.152295\pi\) | ||||
−0.887711 | + | 0.460401i | \(0.847705\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1088.94i | 0.283960i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2646.00 | −0.681623 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5682.31i | 1.42894i | 0.699665 | + | 0.714471i | \(0.253332\pi\) | ||||
−0.699665 | + | 0.714471i | \(0.746668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1870.00 | + | 3966.87i | −0.464687 | + | 0.985751i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1494.82i | − | 0.362819i | −0.983408 | − | 0.181410i | \(-0.941934\pi\) | ||
0.983408 | − | 0.181410i | \(-0.0580660\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3088.64i | 0.741000i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4056.00 | −0.950965 | −0.475482 | − | 0.879725i | \(-0.657726\pi\) | ||||
−0.475482 | + | 0.879725i | \(0.657726\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2912.00 | −0.675029 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6256.48i | 1.41808i | 0.705167 | + | 0.709042i | \(0.250872\pi\) | ||||
−0.705167 | + | 0.709042i | \(0.749128\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1603.72i | − | 0.359479i | −0.983714 | − | 0.179740i | \(-0.942474\pi\) | ||
0.983714 | − | 0.179740i | \(-0.0575256\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8811.00 | − | 4153.55i | −1.93208 | − | 0.910793i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5019.04i | − | 1.08868i | −0.838864 | − | 0.544341i | \(-0.816780\pi\) | ||
0.838864 | − | 0.544341i | \(-0.183220\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2874.00 | −0.610137 | −0.305068 | − | 0.952330i | \(-0.598679\pi\) | ||||
−0.305068 | + | 0.952330i | \(0.598679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2167.99i | − | 0.455384i | −0.973733 | − | 0.227692i | \(-0.926882\pi\) | ||
0.973733 | − | 0.227692i | \(-0.0731179\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4989.35i | − | 1.02617i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10963.0 | 2.23143 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9240.00 | −1.84234 | −0.921172 | − | 0.389157i | \(-0.872766\pi\) | ||||
−0.921172 | + | 0.389157i | \(0.872766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10192.0 | −2.01153 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3570.00 | −0.690496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72.0000 | −0.0137874 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6468.00 | −1.21428 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3831.10i | − | 0.712224i | −0.934443 | − | 0.356112i | \(-0.884102\pi\) | ||
0.934443 | − | 0.356112i | \(-0.115898\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 287.085i | − | 0.0523444i | −0.999657 | − | 0.0261722i | \(-0.991668\pi\) | ||
0.999657 | − | 0.0261722i | \(-0.00833183\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5992.00 | −1.08207 | −0.541035 | − | 0.841000i | \(-0.681967\pi\) | ||||
−0.541035 | + | 0.841000i | \(0.681967\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6307.39i | 1.11753i | 0.829324 | + | 0.558767i | \(0.188725\pi\) | ||||
−0.829324 | + | 0.558767i | \(0.811275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 792.000 | + | 373.352i | 0.139008 | + | 0.0655289i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11226.0i | − | 1.93385i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 7929.50i | − | 1.35338i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1848.00 | 0.309676 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1708.00 | 0.283626 | 0.141813 | − | 0.989893i | \(-0.454707\pi\) | ||||
0.141813 | + | 0.989893i | \(0.454707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 17423.1i | 2.84157i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6864.59i | 1.10961i | 0.831981 | + | 0.554804i | \(0.187207\pi\) | ||||
−0.831981 | + | 0.554804i | \(0.812793\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2310.00 | + | 1088.94i | 0.366843 | + | 0.172932i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6754.28i | 1.06326i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2922.00 | 0.452050 | 0.226025 | − | 0.974122i | \(-0.427427\pi\) | ||||
0.226025 | + | 0.974122i | \(0.427427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8048.29i | − | 1.23443i | −0.786796 | − | 0.617214i | \(-0.788261\pi\) | ||
0.786796 | − | 0.617214i | \(-0.211739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8087.89i | − | 1.21948i | −0.792603 | − | 0.609738i | \(-0.791275\pi\) | ||
0.792603 | − | 0.609738i | \(-0.208725\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6692.00 | 1.00049 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5436.00 | 0.799167 | 0.399584 | − | 0.916697i | \(-0.369155\pi\) | ||||
0.399584 | + | 0.916697i | \(0.369155\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1079.00 | −0.157312 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3528.00 | −0.505929 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11536.0 | 1.64080 | 0.820401 | − | 0.571789i | \(-0.193750\pi\) | ||||
0.820401 | + | 0.571789i | \(0.193750\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2496.00 | −0.349288 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 10305.4i | − | 1.43054i | −0.698847 | − | 0.715271i | \(-0.746303\pi\) | ||
0.698847 | − | 0.715271i | \(-0.253697\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 712.764i | 0.0973719i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3724.00 | 0.504720 | 0.252360 | − | 0.967633i | \(-0.418793\pi\) | ||||
0.252360 | + | 0.967633i | \(0.418793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5098.24i | − | 0.680177i | −0.940393 | − | 0.340089i | \(-0.889543\pi\) | ||
0.940393 | − | 0.340089i | \(-0.110457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11088.0 | − | 5226.93i | −1.46778 | − | 0.691920i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 70.7107i | 0.00921638i | 0.999989 | + | 0.00460819i | \(0.00146684\pi\) | ||||
−0.999989 | + | 0.00460819i | \(0.998533\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 15146.2i | − | 1.95902i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15288.0 | 1.94740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8498.00 | 1.07431 | 0.537157 | − | 0.843482i | \(-0.319498\pi\) | ||||
0.537157 | + | 0.843482i | \(0.319498\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2614.88i | − | 0.325638i | −0.986656 | − | 0.162819i | \(-0.947941\pi\) | ||
0.986656 | − | 0.162819i | \(-0.0520587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2078.89i | 0.256965i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6006.00 | + | 2831.26i | 0.731465 | + | 0.344816i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 475.176i | 0.0574473i | 0.999587 | + | 0.0287236i | \(0.00914427\pi\) | ||||
−0.999587 | + | 0.0287236i | \(0.990856\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8736.00 | −1.04085 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24115.2i | 2.85245i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12809.9i | 1.49357i | 0.665064 | + | 0.746786i | \(0.268404\pi\) | ||||
−0.665064 | + | 0.746786i | \(0.731596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6554.00 | 0.758723 | 0.379362 | − | 0.925249i | \(-0.376144\pi\) | ||||
0.379362 | + | 0.925249i | \(0.376144\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33642.0 | 3.83971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5544.00 | −0.628321 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10692.0 | −1.19493 | −0.597466 | − | 0.801894i | \(-0.703826\pi\) | ||||
−0.597466 | + | 0.801894i | \(0.703826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7616.00 | 0.845269 | 0.422635 | − | 0.906300i | \(-0.361105\pi\) | ||||
0.422635 | + | 0.906300i | \(0.361105\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10710.0 | −1.17238 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13423.7i | − | 1.45941i | −0.683765 | − | 0.729703i | \(-0.739658\pi\) | ||
0.683765 | − | 0.729703i | \(-0.260342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 18322.6i | − | 1.96508i | −0.186050 | − | 0.982540i | \(-0.559569\pi\) | ||
0.186050 | − | 0.982540i | \(-0.440431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30380.0 | −3.23629 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 654.781i | − | 0.0688219i | −0.999408 | − | 0.0344109i | \(-0.989044\pi\) | ||
0.999408 | − | 0.0344109i | \(-0.0109555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9702.00 | − | 4573.57i | −1.01297 | − | 0.477518i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 9978.69i | − | 1.02815i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6024.55i | − | 0.616666i | −0.951278 | − | 0.308333i | \(-0.900229\pi\) | ||
0.951278 | − | 0.308333i | \(-0.0997712\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4452.00 | 0.449784 | 0.224892 | − | 0.974384i | \(-0.427797\pi\) | ||||
0.224892 | + | 0.974384i | \(0.427797\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14978.0 | −1.50343 | −0.751713 | − | 0.659490i | \(-0.770772\pi\) | ||||
−0.751713 | + | 0.659490i | \(0.770772\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9246.13i | 0.916188i | 0.888904 | + | 0.458094i | \(0.151468\pi\) | ||||
−0.888904 | + | 0.458094i | \(0.848532\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14934.1i | 1.47035i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −66.0000 | + | 140.007i | −0.00641582 | + | 0.0136100i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 23788.5i | − | 2.29787i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5124.00 | 0.488771 | 0.244386 | − | 0.969678i | \(-0.421414\pi\) | ||||
0.244386 | + | 0.969678i | \(0.421414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5405.12i | 0.512375i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3880.60i | − | 0.363318i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5096.00 | −0.474172 | −0.237086 | − | 0.971489i | \(-0.576192\pi\) | ||||
−0.237086 | + | 0.971489i | \(0.576192\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13164.0 | 1.20995 | 0.604973 | − | 0.796246i | \(-0.293184\pi\) | ||||
0.604973 | + | 0.796246i | \(0.293184\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3024.00 | −0.276256 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5736.00 | 0.517696 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4228.00 | 0.379301 | 0.189651 | − | 0.981852i | \(-0.439264\pi\) | ||||
0.189651 | + | 0.981852i | \(0.439264\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10332.0 | 0.915867 | 0.457934 | − | 0.888986i | \(-0.348590\pi\) | ||||
0.457934 | + | 0.888986i | \(0.348590\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10810.2i | 0.952574i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 5504.12i | − | 0.479304i | −0.970859 | − | 0.239652i | \(-0.922967\pi\) | ||
0.970859 | − | 0.239652i | \(-0.0770334\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3024.00 | −0.261788 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16354.0i | 1.39930i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1694.00 | − | 3593.52i | 0.144105 | − | 0.305692i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 643.467i | 0.0541090i | 0.999634 | + | 0.0270545i | \(0.00861277\pi\) | ||||
−0.999634 | + | 0.0270545i | \(0.991387\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11136.9i | 0.931136i | 0.885012 | + | 0.465568i | \(0.154150\pi\) | ||||
−0.885012 | + | 0.465568i | \(0.845850\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8820.00 | −0.729042 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2283.00 | −0.187639 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8731.35i | − | 0.709563i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2138.29i | 0.172797i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1815.00 | + | 855.599i | 0.145042 | + | 0.0683734i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16304.5i | 1.29572i | 0.761760 | + | 0.647859i | \(0.224336\pi\) | ||||
−0.761760 | + | 0.647859i | \(0.775664\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23436.0 | 1.84200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5019.04i | 0.392320i | 0.980572 | + | 0.196160i | \(0.0628471\pi\) | ||||
−0.980572 | + | 0.196160i | \(0.937153\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2138.29i | 0.165325i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13104.0 | 1.00767 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4932.00 | −0.375181 | −0.187590 | − | 0.982247i | \(-0.560068\pi\) | ||||
−0.187590 | + | 0.982247i | \(0.560068\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −126.000 | −0.00953351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17598.0 | −1.31735 | −0.658674 | − | 0.752428i | \(-0.728882\pi\) | ||||
−0.658674 | + | 0.752428i | \(0.728882\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32116.0 | 2.39138 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18546.0 | 1.36641 | 0.683206 | − | 0.730225i | \(-0.260585\pi\) | ||||
0.683206 | + | 0.730225i | \(0.260585\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20105.9i | 1.47356i | 0.676131 | + | 0.736782i | \(0.263655\pi\) | ||||
−0.676131 | + | 0.736782i | \(0.736345\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 32095.6i | − | 2.32779i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3220.00 | −0.232323 | −0.116161 | − | 0.993230i | \(-0.537059\pi\) | ||||
−0.116161 | + | 0.993230i | \(0.537059\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20670.1i | 1.47598i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2288.00 | + | 4853.58i | −0.162537 | + | 0.344794i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 18017.1i | − | 1.26686i | −0.773802 | − | 0.633428i | \(-0.781647\pi\) | ||
0.773802 | − | 0.633428i | \(-0.218353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6236.68i | 0.436295i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6426.00 | 0.444999 | 0.222499 | − | 0.974933i | \(-0.428578\pi\) | ||||
0.222499 | + | 0.974933i | \(0.428578\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 42336.0 | 2.91699 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20968.5i | 1.43030i | 0.698969 | + | 0.715152i | \(0.253642\pi\) | ||||
−0.698969 | + | 0.715152i | \(0.746358\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 9028.34i | − | 0.612768i | −0.951908 | − | 0.306384i | \(-0.900881\pi\) | ||
0.951908 | − | 0.306384i | \(-0.0991192\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20328.0 | + | 16769.7i | −1.36603 | + | 1.12692i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16809.3i | 1.12400i | 0.827136 | + | 0.562002i | \(0.189969\pi\) | ||||
−0.827136 | + | 0.562002i | \(0.810031\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3234.00 | 0.214130 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5791.20i | 0.381573i | 0.981632 | + | 0.190787i | \(0.0611039\pi\) | ||||
−0.981632 | + | 0.190787i | \(0.938896\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 57.9828i | 0.00378330i | 0.999998 | + | 0.00189165i | \(0.000602132\pi\) | ||||
−0.999998 | + | 0.00189165i | \(0.999398\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15680.0 | −1.01815 | −0.509073 | − | 0.860723i | \(-0.670012\pi\) | ||||
−0.509073 | + | 0.860723i | \(0.670012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26040.0 | −1.67459 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22289.0 | 1.42650 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22932.0 | −1.45367 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24334.0 | 1.53522 | 0.767608 | − | 0.640920i | \(-0.221447\pi\) | ||||
0.767608 | + | 0.640920i | \(0.221447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3528.00 | 0.220479 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1633.42i | 0.101599i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 22215.9i | − | 1.36892i | −0.729053 | − | 0.684458i | \(-0.760039\pi\) | ||
0.729053 | − | 0.684458i | \(-0.239961\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5096.00 | −0.312545 | −0.156273 | − | 0.987714i | \(-0.549948\pi\) | ||||
−0.156273 | + | 0.987714i | \(0.549948\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13829.6i | − | 0.840336i | −0.907446 | − | 0.420168i | \(-0.861971\pi\) | ||
0.907446 | − | 0.420168i | \(-0.138029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8008.00 | + | 16987.5i | −0.484347 | + | 1.02746i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1813.02i | − | 0.108651i | −0.998523 | − | 0.0543254i | \(-0.982699\pi\) | ||
0.998523 | − | 0.0543254i | \(-0.0173008\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 11641.8i | − | 0.694478i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16566.0 | −0.979241 | −0.489620 | − | 0.871936i | \(-0.662865\pi\) | ||||
−0.489620 | + | 0.871936i | \(0.662865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6118.00 | −0.360004 | −0.180002 | − | 0.983666i | \(-0.557610\pi\) | ||||
−0.180002 | + | 0.983666i | \(0.557610\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 29936.1i | − | 1.74567i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2885.00i | 0.167477i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5082.00 | + | 10780.5i | −0.292382 | + | 0.620236i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20933.2i | 1.19898i | 0.800381 | + | 0.599491i | \(0.204630\pi\) | ||||
−0.800381 | + | 0.599491i | \(0.795370\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12558.0 | −0.712915 | −0.356457 | − | 0.934312i | \(-0.616015\pi\) | ||||
−0.356457 | + | 0.934312i | \(0.616015\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3326.23i | − | 0.187996i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2209.00i | − | 0.123756i | −0.998084 | − | 0.0618778i | \(-0.980291\pi\) | ||
0.998084 | − | 0.0618778i | \(-0.0197089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6692.00 | −0.373267 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4368.00 | −0.241520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2828.00 | −0.155691 | −0.0778453 | − | 0.996965i | \(-0.524804\pi\) | ||||
−0.0778453 | + | 0.996965i | \(0.524804\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 57036.0 | 3.11295 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37044.0 | 2.01312 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8424.00 | 0.453880 | 0.226940 | − | 0.973909i | \(-0.427128\pi\) | ||||
0.226940 | + | 0.973909i | \(0.427128\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16215.4i | 0.869949i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9265.93i | 0.492901i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8890.00 | −0.470904 | −0.235452 | − | 0.971886i | \(-0.575657\pi\) | ||||
−0.235452 | + | 0.971886i | \(0.575657\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8414.57i | 0.441975i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19404.0 | − | 9147.13i | −1.01492 | − | 0.478438i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 23946.9i | 1.24210i | 0.783772 | + | 0.621049i | \(0.213293\pi\) | ||||
−0.783772 | + | 0.621049i | \(0.786707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14017.7i | 0.724058i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6408.00 | −0.328258 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10024.0 | 0.511375 | 0.255687 | − | 0.966759i | \(-0.417698\pi\) | ||||
0.255687 | + | 0.966759i | \(0.417698\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 534.573i | − | 0.0270477i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 6206.98i | − | 0.312770i | −0.987696 | − | 0.156385i | \(-0.950016\pi\) | ||
0.987696 | − | 0.156385i | \(-0.0499840\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29040.0 | + | 13689.6i | 1.45143 | + | 0.684210i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37331.0i | 1.85824i | 0.369772 | + | 0.929122i | \(0.379436\pi\) | ||||
−0.369772 | + | 0.929122i | \(0.620564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14340.0 | −0.708053 | −0.354027 | − | 0.935235i | \(-0.615188\pi\) | ||||
−0.354027 | + | 0.935235i | \(0.615188\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41221.5i | 2.02717i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1832.82i | 0.0894123i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33334.0 | 1.61967 | 0.809837 | − | 0.586655i | \(-0.199556\pi\) | ||||
0.809837 | + | 0.586655i | \(0.199556\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 32424.0 | 1.56295 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4354.00 | −0.209047 | −0.104524 | − | 0.994522i | \(-0.533332\pi\) | ||||
−0.104524 | + | 0.994522i | \(0.533332\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22638.0 | 1.07835 | 0.539177 | − | 0.842193i | \(-0.318736\pi\) | ||||
0.539177 | + | 0.842193i | \(0.318736\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20088.0 | 0.953125 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15288.0 | −0.719710 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27025.6i | 1.26732i | 0.773612 | + | 0.633660i | \(0.218448\pi\) | ||||
−0.773612 | + | 0.633660i | \(0.781552\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20511.8i | 0.954407i | 0.878793 | + | 0.477203i | \(0.158350\pi\) | ||||
−0.878793 | + | 0.477203i | \(0.841650\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18690.0 | −0.866277 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 26194.1i | − | 1.20475i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5258.00 | − | 11153.9i | 0.240904 | − | 0.511035i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 46290.0i | − | 2.10467i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37746.8i | 1.70969i | 0.518882 | + | 0.854846i | \(0.326348\pi\) | ||||
−0.518882 | + | 0.854846i | \(0.673652\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27528.0 | 1.23740 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9702.00 | −0.434462 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19264.4i | 0.856187i | 0.903735 | + | 0.428093i | \(0.140815\pi\) | ||||
−0.903735 | + | 0.428093i | \(0.859185\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13720.7i | 0.607514i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2772.00 | + | 5880.30i | −0.121820 | + | 0.258420i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 40389.9i | − | 1.76840i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27486.0 | 1.19451 | 0.597254 | − | 0.802052i | \(-0.296259\pi\) | ||||
0.597254 | + | 0.802052i | \(0.296259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 40894.8i | − | 1.77067i | −0.464956 | − | 0.885334i | \(-0.653930\pi\) | ||
0.464956 | − | 0.885334i | \(-0.346070\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2534.27i | − | 0.108922i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −378.000 | −0.0161867 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25770.0 | −1.09547 | −0.547734 | − | 0.836653i | \(-0.684509\pi\) | ||||
−0.547734 | + | 0.836653i | \(0.684509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42208.0 | 1.78770 | 0.893851 | − | 0.448365i | \(-0.147993\pi\) | ||||
0.893851 | + | 0.448365i | \(0.147993\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8082.00 | −0.339829 | −0.169915 | − | 0.985459i | \(-0.554349\pi\) | ||||
−0.169915 | + | 0.985459i | \(0.554349\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11914.0 | −0.499144 | −0.249572 | − | 0.968356i | \(-0.580290\pi\) | ||||
−0.249572 | + | 0.968356i | \(0.580290\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6930.00 | −0.288248 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23283.6i | 0.964985i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 27193.9i | − | 1.11900i | −0.828832 | − | 0.559498i | \(-0.810994\pi\) | ||
0.828832 | − | 0.559498i | \(-0.189006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23813.0 | −0.976383 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 26035.7i | 1.05995i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17424.0 | + | 14374.1i | −0.706843 | + | 0.583115i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21877.9i | 0.881274i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 5197.23i | − | 0.208617i | −0.994545 | − | 0.104308i | \(-0.966737\pi\) | ||
0.994545 | − | 0.104308i | \(-0.0332629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24402.0 | −0.972645 | −0.486322 | − | 0.873779i | \(-0.661662\pi\) | ||||
−0.486322 | + | 0.873779i | \(0.661662\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22232.0 | −0.883057 | −0.441529 | − | 0.897247i | \(-0.645564\pi\) | ||||
−0.441529 | + | 0.897247i | \(0.645564\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21223.1i | 0.837130i | 0.908187 | + | 0.418565i | \(0.137467\pi\) | ||||
−0.908187 | + | 0.418565i | \(0.862533\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 21620.5i | − | 0.849848i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12012.0 | − | 25481.3i | 0.468906 | − | 0.994700i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26134.7i | 1.01669i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 47712.0 | 1.84338 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 34183.0i | − | 1.31616i | −0.752946 | − | 0.658082i | \(-0.771368\pi\) | ||
0.752946 | − | 0.658082i | \(-0.228632\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 28758.0i | − | 1.09975i | −0.835246 | − | 0.549877i | \(-0.814675\pi\) | ||
0.835246 | − | 0.549877i | \(-0.185325\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8120.00 | −0.309467 | −0.154734 | − | 0.987956i | \(-0.549452\pi\) | ||||
−0.154734 | + | 0.987956i | \(0.549452\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9996.00 | 0.378391 | 0.189196 | − | 0.981939i | \(-0.439412\pi\) | ||||
0.189196 | + | 0.981939i | \(0.439412\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3024.00 | 0.114085 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9702.00 | 0.363567 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7672.00 | −0.286533 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1680.00 | 0.0623261 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 18531.9i | − | 0.685223i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 26332.7i | − | 0.967212i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37744.0 | 1.38177 | 0.690887 | − | 0.722963i | \(-0.257220\pi\) | ||||
0.690887 | + | 0.722963i | \(0.257220\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1800.29i | 0.0654735i | 0.999464 | + | 0.0327368i | \(0.0104223\pi\) | ||||
−0.999464 | + | 0.0327368i | \(0.989578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40194.0 | + | 18947.6i | 1.45698 | + | 0.686829i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 9978.69i | − | 0.359352i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 25277.7i | − | 0.907326i | −0.891173 | − | 0.453663i | \(-0.850117\pi\) | ||
0.891173 | − | 0.453663i | \(-0.149883\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10038.0 | 0.357968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48594.0 | −1.72731 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39667.3i | 1.40091i | 0.713699 | + | 0.700453i | \(0.247019\pi\) | ||||
−0.713699 | + | 0.700453i | \(0.752981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4900.25i | 0.172502i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 38808.0 | − | 82324.2i | 1.35739 | − | 2.87945i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2851.05i | 0.0994022i | 0.998764 | + | 0.0497011i | \(0.0158269\pi\) | ||||
−0.998764 | + | 0.0497011i | \(0.984173\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3990.00 | 0.138226 | 0.0691128 | − | 0.997609i | \(-0.477983\pi\) | ||||
0.0691128 | + | 0.997609i | \(0.477983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 35341.2i | − | 1.22043i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40774.6i | − | 1.39915i | −0.714558 | − | 0.699576i | \(-0.753372\pi\) | ||
0.714558 | − | 0.699576i | \(-0.246628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5292.00 | −0.181017 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11322.0 | −0.384843 | −0.192422 | − | 0.981312i | \(-0.561634\pi\) | ||||
−0.192422 | + | 0.981312i | \(0.561634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −67396.0 | −2.28365 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5736.00 | −0.193144 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24891.0 | −0.835521 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 67704.0 | 2.25852 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2791.66i | − | 0.0928373i | −0.998922 | − | 0.0464186i | \(-0.985219\pi\) | ||
0.998922 | − | 0.0464186i | \(-0.0147808\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6216.88i | 0.205468i | 0.994709 | + | 0.102734i | \(0.0327590\pi\) | ||||
−0.994709 | + | 0.102734i | \(0.967241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48888.0 | 1.61077 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 56468.1i | 1.84911i | 0.381055 | + | 0.924553i | \(0.375561\pi\) | ||||
−0.381055 | + | 0.924553i | \(0.624439\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23870.0 | + | 50635.9i | −0.779253 | + | 1.65304i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2781.76i | − | 0.0902587i | −0.998981 | − | 0.0451294i | \(-0.985630\pi\) | ||
0.998981 | − | 0.0451294i | \(-0.0143700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 75196.6i | 2.43245i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −510.000 | −0.0163974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7882.00 | 0.252654 | 0.126327 | − | 0.991989i | \(-0.459681\pi\) | ||||
0.126327 | + | 0.991989i | \(0.459681\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 11087.4i | − | 0.353262i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5910.00i | − | 0.187735i | −0.995585 | − | 0.0938674i | \(-0.970077\pi\) | ||
0.995585 | − | 0.0938674i | \(-0.0299230\pi\) | |||||||
\(998\) | 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 | 1584.4.b.b.593.2 | 2 | ||
3.2 | odd | 2 | 1584.4.b.a.593.1 | 2 | |||
4.3 | odd | 2 | 99.4.d.a.98.2 | yes | 2 | ||
11.10 | odd | 2 | 1584.4.b.a.593.2 | 2 | |||
12.11 | even | 2 | 99.4.d.b.98.1 | yes | 2 | ||
33.32 | even | 2 | inner | 1584.4.b.b.593.1 | 2 | ||
44.43 | even | 2 | 99.4.d.b.98.2 | yes | 2 | ||
132.131 | odd | 2 | 99.4.d.a.98.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.4.d.a.98.1 | ✓ | 2 | 132.131 | odd | 2 | ||
99.4.d.a.98.2 | yes | 2 | 4.3 | odd | 2 | ||
99.4.d.b.98.1 | yes | 2 | 12.11 | even | 2 | ||
99.4.d.b.98.2 | yes | 2 | 44.43 | even | 2 | ||
1584.4.b.a.593.1 | 2 | 3.2 | odd | 2 | |||
1584.4.b.a.593.2 | 2 | 11.10 | odd | 2 | |||
1584.4.b.b.593.1 | 2 | 33.32 | even | 2 | inner | ||
1584.4.b.b.593.2 | 2 | 1.1 | even | 1 | trivial |