Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,4,Mod(98,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("99.98");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.84118909057\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 98.2 | ||
Root | \(1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 99.98 |
Dual form | 99.4.d.b.98.1 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.125000 | ||||||||
\(5\) | 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 | \(0.848508\pi\) | |||||||
\(8\) | −21.0000 | −0.928078 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 59.3970i | 1.87830i | ||||||||
\(11\) | 33.0000 | − | 15.5563i | 0.904534 | − | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 29.6985i | − | 0.633606i | −0.948491 | − | 0.316803i | \(-0.897391\pi\) | ||
0.948491 | − | 0.316803i | \(-0.102609\pi\) | |||||||
\(14\) | 50.9117i | 0.971909i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | 126.000 | 1.79762 | 0.898808 | − | 0.438342i | \(-0.144434\pi\) | ||||
0.898808 | + | 0.438342i | \(0.144434\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 89.0955i | 1.07578i | 0.843014 | + | 0.537892i | \(0.180779\pi\) | ||||
−0.843014 | + | 0.537892i | \(0.819221\pi\) | |||||||
\(20\) | 19.7990i | 0.221359i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 99.0000 | − | 46.6690i | 0.959403 | − | 0.452267i | ||||
\(23\) | − | 120.208i | − | 1.08979i | −0.838505 | − | 0.544894i | \(-0.816570\pi\) | ||
0.838505 | − | 0.544894i | \(-0.183430\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −267.000 | −2.13600 | ||||||||
\(26\) | − | 89.0955i | − | 0.672041i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.9706i | 0.114541i | ||||||||
\(29\) | −24.0000 | −0.153679 | −0.0768395 | − | 0.997043i | \(-0.524483\pi\) | ||||
−0.0768395 | + | 0.997043i | \(0.524483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −70.0000 | −0.405560 | −0.202780 | − | 0.979224i | \(-0.564998\pi\) | ||||
−0.202780 | + | 0.979224i | \(0.564998\pi\) | |||||||
\(32\) | −45.0000 | −0.248592 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 378.000 | 1.90666 | ||||||||
\(35\) | −336.000 | −1.62270 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 182.000 | 0.808665 | 0.404333 | − | 0.914612i | \(-0.367504\pi\) | ||||
0.404333 | + | 0.914612i | \(0.367504\pi\) | |||||||
\(38\) | 267.286i | 1.14104i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 415.779i | − | 1.64351i | ||||||
\(41\) | 294.000 | 1.11988 | 0.559940 | − | 0.828533i | \(-0.310824\pi\) | ||||
0.559940 | + | 0.828533i | \(0.310824\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.24264i | 0.0150464i | 0.999972 | + | 0.00752322i | \(0.00239474\pi\) | ||||
−0.999972 | + | 0.00752322i | \(0.997605\pi\) | |||||||
\(44\) | 33.0000 | − | 15.5563i | 0.113067 | − | 0.0533002i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 360.624i | − | 1.15590i | ||||||
\(47\) | 108.894i | 0.337955i | 0.985620 | + | 0.168978i | \(0.0540465\pi\) | ||||
−0.985620 | + | 0.168978i | \(0.945953\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 55.0000 | 0.160350 | ||||||||
\(50\) | −801.000 | −2.26557 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 29.6985i | − | 0.0792007i | ||||||
\(53\) | 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 | ||||
\(56\) | − | 356.382i | − | 0.850420i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −72.0000 | −0.163001 | ||||||||
\(59\) | − | 514.774i | − | 1.13590i | −0.823065 | − | 0.567948i | \(-0.807738\pi\) | ||
0.823065 | − | 0.567948i | \(-0.192262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 326.683i | − | 0.685697i | −0.939391 | − | 0.342848i | \(-0.888608\pi\) | ||
0.939391 | − | 0.342848i | \(-0.111392\pi\) | |||||||
\(62\) | −210.000 | −0.430162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 433.000 | 0.845703 | ||||||||
\(65\) | 588.000 | 1.12204 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −880.000 | −1.60461 | −0.802307 | − | 0.596912i | \(-0.796394\pi\) | ||||
−0.802307 | + | 0.596912i | \(0.796394\pi\) | |||||||
\(68\) | 126.000 | 0.224702 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1008.00 | −1.72113 | ||||||||
\(71\) | 337.997i | 0.564970i | 0.959272 | + | 0.282485i | \(0.0911587\pi\) | ||||
−0.959272 | + | 0.282485i | \(0.908841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 178.191i | − | 0.285694i | −0.989745 | − | 0.142847i | \(-0.954374\pi\) | ||
0.989745 | − | 0.142847i | \(-0.0456257\pi\) | |||||||
\(74\) | 546.000 | 0.857719 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 89.0955i | 0.134473i | ||||||||
\(77\) | 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 | \(-0.185312\pi\) | |||||||
\(80\) | − | 1405.73i | − | 1.96456i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 882.000 | 1.18781 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 12.7279i | 0.0159592i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −693.000 | + | 326.683i | −0.839478 | + | 0.395734i | ||||
\(89\) | 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 | ||||||||
\(92\) | − | 120.208i | − | 0.136224i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 326.683i | 0.358455i | ||||||||
\(95\) | −1764.00 | −1.90508 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −196.000 | −0.205163 | −0.102581 | − | 0.994725i | \(-0.532710\pi\) | ||||
−0.102581 | + | 0.994725i | \(0.532710\pi\) | |||||||
\(98\) | 165.000 | 0.170077 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −267.000 | −0.267000 | ||||||||
\(101\) | −546.000 | −0.537911 | −0.268956 | − | 0.963153i | \(-0.586678\pi\) | ||||
−0.268956 | + | 0.963153i | \(0.586678\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −826.000 | −0.790177 | −0.395088 | − | 0.918643i | \(-0.629286\pi\) | ||||
−0.395088 | + | 0.918643i | \(0.629286\pi\) | |||||||
\(104\) | 623.668i | 0.588036i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 441.235i | 0.404307i | ||||||||
\(107\) | 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 | \(0.174098\pi\) | ||||
−0.854117 | + | 0.520081i | \(0.825902\pi\) | |||||||
\(110\) | 924.000 | + | 1960.10i | 0.800909 | + | 1.69898i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1204.91i | − | 1.01655i | ||||||
\(113\) | − | 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 | ||||||||
\(116\) | −24.0000 | −0.0192099 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1544.32i | − | 1.20480i | ||||||
\(119\) | 2138.29i | 1.64720i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 847.000 | − | 1026.72i | 0.636364 | − | 0.771389i | ||||
\(122\) | − | 980.050i | − | 0.727291i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −70.0000 | −0.0506950 | ||||||||
\(125\) | − | 2811.46i | − | 2.01171i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 178.191i | − | 0.124503i | −0.998060 | − | 0.0622515i | \(-0.980172\pi\) | ||
0.998060 | − | 0.0622515i | \(-0.0198281\pi\) | |||||||
\(128\) | 1659.00 | 1.14560 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1764.00 | 1.19010 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | −2640.00 | −1.70195 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2646.00 | −1.66833 | ||||||||
\(137\) | 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 | \(-0.341741\pi\) | |||||||
\(140\) | −336.000 | −0.202837 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1013.99i | 0.599241i | ||||||||
\(143\) | −462.000 | − | 980.050i | −0.270170 | − | 0.573118i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 475.176i | − | 0.272146i | ||||||
\(146\) | − | 534.573i | − | 0.303024i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 182.000 | 0.101083 | ||||||||
\(149\) | −2082.00 | −1.14473 | −0.572363 | − | 0.820001i | \(-0.693973\pi\) | ||||
−0.572363 | + | 0.820001i | \(0.693973\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1637.66i | − | 0.882588i | −0.897363 | − | 0.441294i | \(-0.854520\pi\) | ||
0.897363 | − | 0.441294i | \(-0.145480\pi\) | |||||||
\(152\) | − | 1871.00i | − | 0.998411i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 792.000 | + | 1680.09i | 0.414423 | + | 0.879124i | ||||
\(155\) | − | 1385.93i | − | 0.718197i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2338.00 | −1.18849 | −0.594244 | − | 0.804285i | \(-0.702549\pi\) | ||||
−0.594244 | + | 0.804285i | \(0.702549\pi\) | |||||||
\(158\) | − | 2316.48i | − | 1.16639i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 890.955i | − | 0.440226i | ||||||
\(161\) | 2040.00 | 0.998600 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 128.000 | 0.0615076 | 0.0307538 | − | 0.999527i | \(-0.490209\pi\) | ||||
0.0307538 | + | 0.999527i | \(0.490209\pi\) | |||||||
\(164\) | 294.000 | 0.139985 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3654.00 | 1.70847 | ||||||||
\(167\) | 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 | ||||||||
\(170\) | 7484.02i | 3.37646i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.24264i | 0.00188080i | ||||||||
\(173\) | 1092.00 | 0.479903 | 0.239952 | − | 0.970785i | \(-0.422868\pi\) | ||||
0.239952 | + | 0.970785i | \(0.422868\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4531.14i | − | 1.95727i | ||||||
\(176\) | −2343.00 | + | 1104.50i | −1.00347 | + | 0.473039i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4603.27i | 1.93837i | ||||||||
\(179\) | − | 387.495i | − | 0.161803i | −0.996722 | − | 0.0809014i | \(-0.974220\pi\) | ||
0.996722 | − | 0.0809014i | \(-0.0257799\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1330.00 | −0.546177 | −0.273089 | − | 0.961989i | \(-0.588045\pi\) | ||||
−0.273089 | + | 0.961989i | \(0.588045\pi\) | |||||||
\(182\) | 1512.00 | 0.615807 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2524.37i | 1.01141i | ||||||||
\(185\) | 3603.42i | 1.43205i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4158.00 | − | 1960.10i | 1.62601 | − | 0.766506i | ||||
\(188\) | 108.894i | 0.0422444i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5292.00 | −2.02064 | ||||||||
\(191\) | − | 3404.01i | − | 1.28956i | −0.764369 | − | 0.644779i | \(-0.776949\pi\) | ||
0.764369 | − | 0.644779i | \(-0.223051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3419.57i | 1.27537i | 0.770298 | + | 0.637684i | \(0.220107\pi\) | ||||
−0.770298 | + | 0.637684i | \(0.779893\pi\) | |||||||
\(194\) | −588.000 | −0.217608 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 55.0000 | 0.0200437 | ||||||||
\(197\) | −3798.00 | −1.37359 | −0.686793 | − | 0.726853i | \(-0.740982\pi\) | ||||
−0.686793 | + | 0.726853i | \(0.740982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 560.000 | 0.199484 | 0.0997421 | − | 0.995013i | \(-0.468198\pi\) | ||||
0.0997421 | + | 0.995013i | \(0.468198\pi\) | |||||||
\(200\) | 5607.00 | 1.98237 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1638.00 | −0.570541 | ||||||||
\(203\) | − | 407.294i | − | 0.140820i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5820.90i | 1.98317i | ||||||||
\(206\) | −2478.00 | −0.838109 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2108.59i | 0.702907i | ||||||||
\(209\) | 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 | \(0.899416\pi\) | |||||||
\(212\) | 147.078i | 0.0476480i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 324.000 | 0.103496 | ||||||||
\(215\) | −84.0000 | −0.0266454 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1187.94i | − | 0.371625i | ||||||
\(218\) | 3551.09i | 1.10326i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 308.000 | + | 653.367i | 0.0943880 | + | 0.200227i | ||||
\(221\) | − | 3742.01i | − | 1.13898i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2968.00 | −0.891264 | −0.445632 | − | 0.895216i | \(-0.647021\pi\) | ||||
−0.445632 | + | 0.895216i | \(0.647021\pi\) | |||||||
\(224\) | − | 763.675i | − | 0.227791i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 4866.31i | − | 1.43231i | ||||||
\(227\) | −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 | \(0.526392\pi\) | |||||||
\(230\) | 7140.00 | 2.04695 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 504.000 | 0.142626 | ||||||||
\(233\) | 5310.00 | 1.49300 | 0.746501 | − | 0.665384i | \(-0.231732\pi\) | ||||
0.746501 | + | 0.665384i | \(0.231732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2156.00 | −0.598476 | ||||||||
\(236\) | − | 514.774i | − | 0.141987i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6414.87i | 1.74712i | ||||||||
\(239\) | −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 | \(-0.847705\pi\) | ||
0.887711 | − | 0.460401i | \(-0.152295\pi\) | |||||||
\(242\) | 2541.00 | − | 3080.16i | 0.674966 | − | 0.818182i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 326.683i | − | 0.0857121i | ||||||
\(245\) | 1088.94i | 0.283960i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2646.00 | 0.681623 | ||||||||
\(248\) | 1470.00 | 0.376392 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 8434.37i | − | 2.13375i | ||||||
\(251\) | − | 5682.31i | − | 1.42894i | −0.699665 | − | 0.714471i | \(-0.746668\pi\) | ||
0.699665 | − | 0.714471i | \(-0.253332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1870.00 | − | 3966.87i | −0.464687 | − | 0.985751i | ||||
\(254\) | − | 534.573i | − | 0.132055i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | − | 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 | ||||||||
\(260\) | 588.000 | 0.140255 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1764.00 | −0.415955 | ||||||||
\(263\) | −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 | ||||||||
\(266\) | −4536.00 | −1.04556 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −880.000 | −0.200577 | ||||||||
\(269\) | 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 | \(-0.0575256\pi\) | |||||||
\(272\) | −8946.00 | −1.99423 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1013.99i | 0.223567i | ||||||||
\(275\) | −8811.00 | + | 4153.55i | −1.93208 | + | 0.910793i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5019.04i | 1.08868i | 0.838864 | + | 0.544341i | \(0.183220\pi\) | ||||
−0.838864 | + | 0.544341i | \(0.816780\pi\) | |||||||
\(278\) | − | 8642.26i | − | 1.86449i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7056.00 | 1.50599 | ||||||||
\(281\) | 2874.00 | 0.610137 | 0.305068 | − | 0.952330i | \(-0.401321\pi\) | ||||
0.305068 | + | 0.952330i | \(0.401321\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2167.99i | − | 0.455384i | −0.973733 | − | 0.227692i | \(-0.926882\pi\) | ||
0.973733 | − | 0.227692i | \(-0.0731179\pi\) | |||||||
\(284\) | 337.997i | 0.0706212i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1386.00 | − | 2940.15i | −0.286559 | − | 0.607884i | ||||
\(287\) | 4989.35i | 1.02617i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10963.0 | 2.23143 | ||||||||
\(290\) | − | 1425.53i | − | 0.288655i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 178.191i | − | 0.0357118i | ||||||
\(293\) | 9240.00 | 1.84234 | 0.921172 | − | 0.389157i | \(-0.127234\pi\) | ||||
0.921172 | + | 0.389157i | \(0.127234\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10192.0 | 2.01153 | ||||||||
\(296\) | −3822.00 | −0.750504 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6246.00 | −1.21416 | ||||||||
\(299\) | −3570.00 | −0.690496 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72.0000 | −0.0137874 | ||||||||
\(302\) | − | 4912.98i | − | 0.936126i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6325.78i | − | 1.19345i | ||||||
\(305\) | 6468.00 | 1.21428 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3831.10i | − | 0.712224i | −0.934443 | − | 0.356112i | \(-0.884102\pi\) | ||
0.934443 | − | 0.356112i | \(-0.115898\pi\) | |||||||
\(308\) | 264.000 | + | 560.029i | 0.0488402 | + | 0.103606i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 4157.79i | − | 0.761763i | ||||||
\(311\) | 287.085i | 0.0523444i | 0.999657 | + | 0.0261722i | \(0.00833183\pi\) | ||||
−0.999657 | + | 0.0261722i | \(0.991668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5992.00 | −1.08207 | −0.541035 | − | 0.841000i | \(-0.681967\pi\) | ||||
−0.541035 | + | 0.841000i | \(0.681967\pi\) | |||||||
\(314\) | −7014.00 | −1.26058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 772.161i | − | 0.137460i | ||||||
\(317\) | 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 | ||||
\(320\) | 8572.96i | 1.49763i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6120.00 | 1.05917 | ||||||||
\(323\) | 11226.0i | 1.93385i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7929.50i | 1.35338i | ||||||||
\(326\) | 384.000 | 0.0652386 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6174.00 | −1.03934 | ||||||||
\(329\) | −1848.00 | −0.309676 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1708.00 | −0.283626 | −0.141813 | − | 0.989893i | \(-0.545293\pi\) | ||||
−0.141813 | + | 0.989893i | \(0.545293\pi\) | |||||||
\(332\) | 1218.00 | 0.201345 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3528.00 | 0.577975 | ||||||||
\(335\) | − | 17423.1i | − | 2.84157i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6864.59i | − | 1.10961i | −0.831981 | − | 0.554804i | \(-0.812793\pi\) | ||
0.831981 | − | 0.554804i | \(-0.187207\pi\) | |||||||
\(338\) | 3945.00 | 0.634851 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2494.67i | 0.397919i | ||||||||
\(341\) | −2310.00 | + | 1088.94i | −0.366843 | + | 0.172932i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6754.28i | 1.06326i | ||||||||
\(344\) | − | 89.0955i | − | 0.0139643i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3276.00 | 0.509014 | ||||||||
\(347\) | 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 | \(0.211739\pi\) | ||||
−0.786796 | + | 0.617214i | \(0.788261\pi\) | |||||||
\(350\) | − | 13593.4i | − | 2.07600i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1485.00 | + | 700.036i | −0.224860 | + | 0.106000i | ||||
\(353\) | − | 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 | ||||||||
\(356\) | 1534.42i | 0.228439i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 1162.48i | − | 0.171618i | ||||||
\(359\) | 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 | ||||||||
\(362\) | −3990.00 | −0.579309 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 504.000 | 0.0725736 | ||||||||
\(365\) | 3528.00 | 0.505929 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11536.0 | −1.64080 | −0.820401 | − | 0.571789i | \(-0.806250\pi\) | ||||
−0.820401 | + | 0.571789i | \(0.806250\pi\) | |||||||
\(368\) | 8534.78i | 1.20898i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10810.2i | 1.51891i | ||||||||
\(371\) | −2496.00 | −0.349288 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10305.4i | 1.43054i | 0.698847 | + | 0.715271i | \(0.253697\pi\) | ||||
−0.698847 | + | 0.715271i | \(0.746303\pi\) | |||||||
\(374\) | 12474.0 | − | 5880.30i | 1.72464 | − | 0.813003i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 2286.78i | − | 0.313649i | ||||||
\(377\) | 712.764i | 0.0973719i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3724.00 | −0.504720 | −0.252360 | − | 0.967633i | \(-0.581207\pi\) | ||||
−0.252360 | + | 0.967633i | \(0.581207\pi\) | |||||||
\(380\) | −1764.00 | −0.238135 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 10212.0i | − | 1.36778i | ||||||
\(383\) | 5098.24i | 0.680177i | 0.940393 | + | 0.340089i | \(0.110457\pi\) | ||||
−0.940393 | + | 0.340089i | \(0.889543\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11088.0 | + | 5226.93i | −1.46778 | + | 0.691920i | ||||
\(386\) | 10258.7i | 1.35273i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −196.000 | −0.0256453 | ||||||||
\(389\) | 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 | ||||||
\(392\) | −1155.00 | −0.148817 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11394.0 | −1.45691 | ||||||||
\(395\) | 15288.0 | 1.94740 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8498.00 | 1.07431 | 0.537157 | − | 0.843482i | \(-0.319498\pi\) | ||||
0.537157 | + | 0.843482i | \(0.319498\pi\) | |||||||
\(398\) | 1680.00 | 0.211585 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18957.0 | 2.36963 | ||||||||
\(401\) | − | 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 | ||||||||
\(404\) | −546.000 | −0.0672389 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 1221.88i | − | 0.149362i | ||||||
\(407\) | 6006.00 | − | 2831.26i | 0.731465 | − | 0.344816i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 475.176i | − | 0.0574473i | −0.999587 | − | 0.0287236i | \(-0.990856\pi\) | ||
0.999587 | − | 0.0287236i | \(-0.00914427\pi\) | |||||||
\(410\) | 17462.7i | 2.10347i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −826.000 | −0.0987721 | ||||||||
\(413\) | 8736.00 | 1.04085 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24115.2i | 2.85245i | ||||||||
\(416\) | 1336.43i | 0.157510i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4158.00 | + | 8820.45i | 0.486542 | + | 1.03211i | ||||
\(419\) | − | 12809.9i | − | 1.49357i | −0.665064 | − | 0.746786i | \(-0.731596\pi\) | ||
0.665064 | − | 0.746786i | \(-0.268404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6554.00 | 0.758723 | 0.379362 | − | 0.925249i | \(-0.376144\pi\) | ||||
0.379362 | + | 0.925249i | \(0.376144\pi\) | |||||||
\(422\) | 5714.84i | 0.659227i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 3088.64i | − | 0.353768i | ||||||
\(425\) | −33642.0 | −3.83971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5544.00 | 0.628321 | ||||||||
\(428\) | 108.000 | 0.0121971 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −252.000 | −0.0282617 | ||||||||
\(431\) | −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 | \(0.361105\pi\) | |||||||
\(434\) | − | 3563.82i | − | 0.394168i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1183.70i | 0.130020i | ||||||||
\(437\) | 10710.0 | 1.17238 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13423.7i | − | 1.45941i | −0.683765 | − | 0.729703i | \(-0.739658\pi\) | ||
0.683765 | − | 0.729703i | \(-0.260342\pi\) | |||||||
\(440\) | −6468.00 | − | 13720.7i | −0.700795 | − | 1.48661i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 11226.0i | − | 1.20807i | ||||||
\(443\) | 18322.6i | 1.96508i | 0.186050 | + | 0.982540i | \(0.440431\pi\) | ||||
−0.186050 | + | 0.982540i | \(0.559569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30380.0 | −3.23629 | ||||||||
\(446\) | −8904.00 | −0.945329 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7348.25i | 0.774938i | ||||||||
\(449\) | − | 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 | ||||
\(452\) | − | 1622.10i | − | 0.168799i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10332.0 | −1.06807 | ||||||||
\(455\) | 9978.69i | 1.02815i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6024.55i | 0.616666i | 0.951278 | + | 0.308333i | \(0.0997712\pi\) | ||||
−0.951278 | + | 0.308333i | \(0.900229\pi\) | |||||||
\(458\) | −1722.00 | −0.175685 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2380.00 | 0.241235 | ||||||||
\(461\) | −4452.00 | −0.449784 | −0.224892 | − | 0.974384i | \(-0.572203\pi\) | ||||
−0.224892 | + | 0.974384i | \(0.572203\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14978.0 | 1.50343 | 0.751713 | − | 0.659490i | \(-0.229228\pi\) | ||||
0.751713 | + | 0.659490i | \(0.229228\pi\) | |||||||
\(464\) | 1704.00 | 0.170488 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15930.0 | 1.58357 | ||||||||
\(467\) | − | 9246.13i | − | 0.916188i | −0.888904 | − | 0.458094i | \(-0.848532\pi\) | ||
0.888904 | − | 0.458094i | \(-0.151468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14934.1i | − | 1.47035i | ||||||
\(470\) | −6468.00 | −0.634780 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10810.2i | 1.05420i | ||||||||
\(473\) | 66.0000 | + | 140.007i | 0.00641582 | + | 0.0136100i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 23788.5i | − | 2.29787i | ||||||
\(476\) | 2138.29i | 0.205900i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3708.00 | −0.354812 | ||||||||
\(479\) | 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 | ||||||
\(482\) | − | 10335.1i | − | 0.976659i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 847.000 | − | 1026.72i | 0.0795455 | − | 0.0964237i | ||||
\(485\) | − | 3880.60i | − | 0.363318i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5096.00 | 0.474172 | 0.237086 | − | 0.971489i | \(-0.423808\pi\) | ||||
0.237086 | + | 0.971489i | \(0.423808\pi\) | |||||||
\(488\) | 6860.35i | 0.636380i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3266.83i | 0.301185i | ||||||||
\(491\) | 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 | ||||||||
\(494\) | 7938.00 | 0.722971 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4970.00 | 0.449919 | ||||||||
\(497\) | −5736.00 | −0.517696 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4228.00 | −0.379301 | −0.189651 | − | 0.981852i | \(-0.560736\pi\) | ||||
−0.189651 | + | 0.981852i | \(0.560736\pi\) | |||||||
\(500\) | − | 2811.46i | − | 0.251464i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 17046.9i | − | 1.51562i | ||||||
\(503\) | 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 | ||||||
\(506\) | −5610.00 | − | 11900.6i | −0.492875 | − | 1.04555i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 178.191i | − | 0.0155629i | ||||||
\(509\) | − | 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 | ||||||||
\(512\) | −8733.00 | −0.753804 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 4484.47i | − | 0.384828i | ||||||
\(515\) | − | 16354.0i | − | 1.39930i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1694.00 | + | 3593.52i | 0.144105 | + | 0.305692i | ||||
\(518\) | 9265.93i | 0.785949i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12348.0 | −1.04134 | ||||||||
\(521\) | 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 | \(0.845850\pi\) | |||||||
\(524\) | −588.000 | −0.0490208 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12168.0 | −1.00865 | ||||||||
\(527\) | −8820.00 | −0.729042 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2283.00 | −0.187639 | ||||||||
\(530\) | −8736.00 | −0.715977 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1512.00 | −0.123221 | ||||||||
\(533\) | − | 8731.35i | − | 0.709563i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2138.29i | 0.172797i | ||||||||
\(536\) | 18480.0 | 1.48921 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18769.4i | 1.50410i | ||||||||
\(539\) | 1815.00 | − | 855.599i | 0.145042 | − | 0.0683734i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 16304.5i | − | 1.29572i | −0.761760 | − | 0.647859i | \(-0.775664\pi\) | ||
0.761760 | − | 0.647859i | \(-0.224336\pi\) | |||||||
\(542\) | − | 4811.15i | − | 0.381286i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5670.00 | −0.446874 | ||||||||
\(545\) | −23436.0 | −1.84200 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5019.04i | 0.392320i | 0.980572 | + | 0.196160i | \(0.0628471\pi\) | ||||
−0.980572 | + | 0.196160i | \(0.937153\pi\) | |||||||
\(548\) | 337.997i | 0.0263477i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26433.0 | + | 12460.6i | −2.04929 | + | 0.966042i | ||||
\(551\) | − | 2138.29i | − | 0.165325i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13104.0 | 1.00767 | ||||||||
\(554\) | 15057.1i | 1.15472i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 2880.75i | − | 0.219732i | ||||||
\(557\) | 4932.00 | 0.375181 | 0.187590 | − | 0.982247i | \(-0.439932\pi\) | ||||
0.187590 | + | 0.982247i | \(0.439932\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 126.000 | 0.00953351 | ||||||||
\(560\) | 23856.0 | 1.80018 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8622.00 | 0.647148 | ||||||||
\(563\) | −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 | ||||||||
\(566\) | − | 6503.97i | − | 0.483007i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 7097.94i | − | 0.524336i | ||||||
\(569\) | −18546.0 | −1.36641 | −0.683206 | − | 0.730225i | \(-0.739415\pi\) | ||||
−0.683206 | + | 0.730225i | \(0.739415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20105.9i | 1.47356i | 0.676131 | + | 0.736782i | \(0.263655\pi\) | ||||
−0.676131 | + | 0.736782i | \(0.736345\pi\) | |||||||
\(572\) | −462.000 | − | 980.050i | −0.0337713 | − | 0.0716398i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14968.0i | 1.08842i | ||||||||
\(575\) | 32095.6i | 2.32779i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3220.00 | −0.232323 | −0.116161 | − | 0.993230i | \(-0.537059\pi\) | ||||
−0.116161 | + | 0.993230i | \(0.537059\pi\) | |||||||
\(578\) | 32889.0 | 2.36679 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 475.176i | − | 0.0340183i | ||||||
\(581\) | 20670.1i | 1.47598i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2288.00 | + | 4853.58i | 0.162537 | + | 0.344794i | ||||
\(584\) | 3742.01i | 0.265146i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27720.0 | 1.95410 | ||||||||
\(587\) | 18017.1i | 1.26686i | 0.773802 | + | 0.633428i | \(0.218353\pi\) | ||||
−0.773802 | + | 0.633428i | \(0.781647\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6236.68i | − | 0.436295i | ||||||
\(590\) | 30576.0 | 2.13355 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12922.0 | −0.897113 | ||||||||
\(593\) | −6426.00 | −0.444999 | −0.222499 | − | 0.974933i | \(-0.571422\pi\) | ||||
−0.222499 | + | 0.974933i | \(0.571422\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42336.0 | −2.91699 | ||||||||
\(596\) | −2082.00 | −0.143091 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10710.0 | −0.732382 | ||||||||
\(599\) | − | 20968.5i | − | 1.43030i | −0.698969 | − | 0.715152i | \(-0.746358\pi\) | ||
0.698969 | − | 0.715152i | \(-0.253642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9028.34i | 0.612768i | 0.951908 | + | 0.306384i | \(0.0991192\pi\) | ||||
−0.951908 | + | 0.306384i | \(0.900881\pi\) | |||||||
\(602\) | −216.000 | −0.0146238 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 1637.66i | − | 0.110324i | ||||||
\(605\) | 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 | \(0.810031\pi\) | |||||||
\(608\) | − | 4009.30i | − | 0.267432i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 19404.0 | 1.28794 | ||||||||
\(611\) | 3234.00 | 0.214130 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5791.20i | − | 0.381573i | −0.981632 | − | 0.190787i | \(-0.938896\pi\) | ||
0.981632 | − | 0.190787i | \(-0.0611039\pi\) | |||||||
\(614\) | − | 11493.3i | − | 0.755427i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5544.00 | − | 11760.6i | −0.362620 | − | 0.769234i | ||||
\(617\) | 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 | \(-0.329988\pi\) | ||||
0.509073 | + | 0.860723i | \(0.329988\pi\) | |||||||
\(620\) | − | 1385.93i | − | 0.0897746i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 861.256i | 0.0555196i | ||||||||
\(623\) | −26040.0 | −1.67459 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22289.0 | 1.42650 | ||||||||
\(626\) | −17976.0 | −1.14771 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2338.00 | −0.148561 | ||||||||
\(629\) | 22932.0 | 1.45367 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24334.0 | −1.53522 | −0.767608 | − | 0.640920i | \(-0.778553\pi\) | ||||
−0.767608 | + | 0.640920i | \(0.778553\pi\) | |||||||
\(632\) | 16215.4i | 1.02059i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18922.2i | 1.18532i | ||||||||
\(635\) | 3528.00 | 0.220479 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1633.42i | − | 0.101599i | ||||||
\(638\) | −2376.00 | + | 1120.06i | −0.147440 | + | 0.0695039i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 32846.5i | 2.02871i | ||||||||
\(641\) | − | 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 | \(-0.450052\pi\) | ||||
0.156273 | + | 0.987714i | \(0.450052\pi\) | |||||||
\(644\) | 2040.00 | 0.124825 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33678.1i | 2.05116i | ||||||||
\(647\) | 13829.6i | 0.840336i | 0.907446 | + | 0.420168i | \(0.138029\pi\) | ||||
−0.907446 | + | 0.420168i | \(0.861971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8008.00 | − | 16987.5i | −0.484347 | − | 1.02746i | ||||
\(650\) | 23788.5i | 1.43548i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 128.000 | 0.00768845 | ||||||||
\(653\) | − | 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 | ||||||
\(656\) | −20874.0 | −1.24237 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5544.00 | −0.328461 | ||||||||
\(659\) | −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 | \(0.557610\pi\) | |||||||
\(662\) | −5124.00 | −0.300831 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25578.0 | −1.49491 | ||||||||
\(665\) | − | 29936.1i | − | 1.74567i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2885.00i | 0.167477i | ||||||||
\(668\) | 1176.00 | 0.0681150 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 52269.3i | − | 3.01394i | ||||||
\(671\) | −5082.00 | − | 10780.5i | −0.292382 | − | 0.620236i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20933.2i | − | 1.19898i | −0.800381 | − | 0.599491i | \(-0.795370\pi\) | ||
0.800381 | − | 0.599491i | \(-0.204630\pi\) | |||||||
\(674\) | − | 20593.8i | − | 1.17692i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1315.00 | 0.0748179 | ||||||||
\(677\) | 12558.0 | 0.712915 | 0.356457 | − | 0.934312i | \(-0.383985\pi\) | ||||
0.356457 | + | 0.934312i | \(0.383985\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3326.23i | − | 0.187996i | ||||||
\(680\) | − | 52388.1i | − | 2.95440i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6930.00 | + | 3266.83i | −0.389096 | + | 0.183422i | ||||
\(683\) | 2209.00i | 0.123756i | 0.998084 | + | 0.0618778i | \(0.0197089\pi\) | ||||
−0.998084 | + | 0.0618778i | \(0.980291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6692.00 | −0.373267 | ||||||||
\(686\) | 20262.9i | 1.12775i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 301.227i | − | 0.0166921i | ||||||
\(689\) | 4368.00 | 0.241520 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2828.00 | 0.155691 | 0.0778453 | − | 0.996965i | \(-0.475196\pi\) | ||||
0.0778453 | + | 0.996965i | \(0.475196\pi\) | |||||||
\(692\) | 1092.00 | 0.0599879 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8766.00 | 0.479471 | ||||||||
\(695\) | 57036.0 | 3.11295 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 37044.0 | 2.01312 | ||||||||
\(698\) | 24144.9i | 1.30931i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 4531.14i | − | 0.244659i | ||||||
\(701\) | −8424.00 | −0.453880 | −0.226940 | − | 0.973909i | \(-0.572872\pi\) | ||||
−0.226940 | + | 0.973909i | \(0.572872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16215.4i | 0.869949i | ||||||||
\(704\) | 14289.0 | − | 6735.90i | 0.764967 | − | 0.360609i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 24263.7i | − | 1.29345i | ||||||
\(707\) | − | 9265.93i | − | 0.492901i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8890.00 | −0.470904 | −0.235452 | − | 0.971886i | \(-0.575657\pi\) | ||||
−0.235452 | + | 0.971886i | \(0.575657\pi\) | |||||||
\(710\) | −20076.0 | −1.06118 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 32222.9i | − | 1.69607i | ||||||
\(713\) | 8414.57i | 0.441975i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19404.0 | − | 9147.13i | 1.01492 | − | 0.478438i | ||||
\(716\) | − | 387.495i | − | 0.0202253i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16308.0 | 0.847645 | ||||||||
\(719\) | − | 23946.9i | − | 1.24210i | −0.783772 | − | 0.621049i | \(-0.786707\pi\) | ||
0.783772 | − | 0.621049i | \(-0.213293\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 14017.7i | − | 0.724058i | ||||||
\(722\) | −3237.00 | −0.166854 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1330.00 | −0.0682722 | ||||||||
\(725\) | 6408.00 | 0.328258 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10024.0 | −0.511375 | −0.255687 | − | 0.966759i | \(-0.582302\pi\) | ||||
−0.255687 | + | 0.966759i | \(0.582302\pi\) | |||||||
\(728\) | −10584.0 | −0.538831 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10584.0 | 0.536618 | ||||||||
\(731\) | 534.573i | 0.0270477i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6206.98i | 0.312770i | 0.987696 | + | 0.156385i | \(0.0499840\pi\) | ||||
−0.987696 | + | 0.156385i | \(0.950016\pi\) | |||||||
\(734\) | −34608.0 | −1.74033 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5409.37i | 0.270913i | ||||||||
\(737\) | −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 | \(0.620564\pi\) | |||||||
\(740\) | 3603.42i | 0.179006i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7488.00 | −0.370476 | ||||||||
\(743\) | −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 | ||||||
\(746\) | 30916.1i | 1.51732i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4158.00 | − | 1960.10i | 0.203251 | − | 0.0958133i | ||||
\(749\) | 1832.82i | 0.0894123i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33334.0 | −1.61967 | −0.809837 | − | 0.586655i | \(-0.800444\pi\) | ||||
−0.809837 | + | 0.586655i | \(0.800444\pi\) | |||||||
\(752\) | − | 7731.51i | − | 0.374919i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2138.29i | 0.103278i | ||||||||
\(755\) | 32424.0 | 1.56295 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4354.00 | −0.209047 | −0.104524 | − | 0.994522i | \(-0.533332\pi\) | ||||
−0.104524 | + | 0.994522i | \(0.533332\pi\) | |||||||
\(758\) | −11172.0 | −0.535337 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 37044.0 | 1.76806 | ||||||||
\(761\) | −22638.0 | −1.07835 | −0.539177 | − | 0.842193i | \(-0.681264\pi\) | ||||
−0.539177 | + | 0.842193i | \(0.681264\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20088.0 | −0.953125 | ||||||||
\(764\) | − | 3404.01i | − | 0.161195i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15294.7i | 0.721437i | ||||||||
\(767\) | −15288.0 | −0.719710 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 27025.6i | − | 1.26732i | −0.773612 | − | 0.633660i | \(-0.781552\pi\) | ||
0.773612 | − | 0.633660i | \(-0.218448\pi\) | |||||||
\(770\) | −33264.0 | + | 15680.8i | −1.55682 | + | 0.733892i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3419.57i | 0.159421i | ||||||||
\(773\) | 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 | ||||||||
\(776\) | 4116.00 | 0.190407 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 212.132i | 0.00977545i | ||||||||
\(779\) | 26194.1i | 1.20475i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5258.00 | + | 11153.9i | 0.240904 | + | 0.511035i | ||||
\(782\) | − | 45438.7i | − | 2.07786i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3905.00 | −0.177888 | ||||||||
\(785\) | − | 46290.0i | − | 2.10467i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37746.8i | 1.70969i | 0.518882 | + | 0.854846i | \(0.326348\pi\) | ||||
−0.518882 | + | 0.854846i | \(0.673652\pi\) | |||||||
\(788\) | −3798.00 | −0.171698 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 45864.0 | 2.06553 | ||||||||
\(791\) | 27528.0 | 1.23740 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9702.00 | −0.434462 | ||||||||
\(794\) | 25494.0 | 1.13948 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 560.000 | 0.0249355 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 12015.0 | 0.530993 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 7844.64i | − | 0.345391i | ||||||
\(803\) | −2772.00 | − | 5880.30i | −0.121820 | − | 0.258420i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 40389.9i | 1.76840i | ||||||||
\(806\) | 6236.68i | 0.272553i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11466.0 | 0.499223 | ||||||||
\(809\) | −27486.0 | −1.19451 | −0.597254 | − | 0.802052i | \(-0.703741\pi\) | ||||
−0.597254 | + | 0.802052i | \(0.703741\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 40894.8i | − | 1.77067i | −0.464956 | − | 0.885334i | \(-0.653930\pi\) | ||
0.464956 | − | 0.885334i | \(-0.346070\pi\) | |||||||
\(812\) | − | 407.294i | − | 0.0176025i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18018.0 | − | 8493.77i | 0.775836 | − | 0.365733i | ||||
\(815\) | 2534.27i | 0.108922i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −378.000 | −0.0161867 | ||||||||
\(818\) | − | 1425.53i | − | 0.0609320i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5820.90i | 0.247896i | ||||||||
\(821\) | 25770.0 | 1.09547 | 0.547734 | − | 0.836653i | \(-0.315491\pi\) | ||||
0.547734 | + | 0.836653i | \(0.315491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42208.0 | −1.78770 | −0.893851 | − | 0.448365i | \(-0.852007\pi\) | ||||
−0.893851 | + | 0.448365i | \(0.852007\pi\) | |||||||
\(824\) | 17346.0 | 0.733345 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26208.0 | 1.10399 | ||||||||
\(827\) | −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 | \(0.580290\pi\) | |||||||
\(830\) | 72345.5i | 3.02548i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 12859.4i | − | 0.535843i | ||||||
\(833\) | 6930.00 | 0.288248 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23283.6i | 0.964985i | ||||||||
\(836\) | 1386.00 | + | 2940.15i | 0.0573395 | + | 0.121635i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 38429.8i | − | 1.58417i | ||||||
\(839\) | 27193.9i | 1.11900i | 0.828832 | + | 0.559498i | \(0.189006\pi\) | ||||
−0.828832 | + | 0.559498i | \(0.810994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23813.0 | −0.976383 | ||||||||
\(842\) | 19662.0 | 0.804747 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1904.95i | 0.0776907i | ||||||||
\(845\) | 26035.7i | 1.05995i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17424.0 | + | 14374.1i | 0.706843 | + | 0.583115i | ||||
\(848\) | − | 10442.6i | − | 0.422876i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −100926. | −4.07263 | ||||||||
\(851\) | − | 21877.9i | − | 0.881274i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5197.23i | 0.208617i | 0.994545 | + | 0.104308i | \(0.0332629\pi\) | ||||
−0.994545 | + | 0.104308i | \(0.966737\pi\) | |||||||
\(854\) | 16632.0 | 0.666435 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2268.00 | −0.0905592 | ||||||||
\(857\) | 24402.0 | 0.972645 | 0.486322 | − | 0.873779i | \(-0.338338\pi\) | ||||
0.486322 | + | 0.873779i | \(0.338338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22232.0 | 0.883057 | 0.441529 | − | 0.897247i | \(-0.354436\pi\) | ||||
0.441529 | + | 0.897247i | \(0.354436\pi\) | |||||||
\(860\) | −84.0000 | −0.00333067 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32076.0 | −1.26742 | ||||||||
\(863\) | − | 21223.1i | − | 0.837130i | −0.908187 | − | 0.418565i | \(-0.862533\pi\) | ||
0.908187 | − | 0.418565i | \(-0.137467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21620.5i | 0.849848i | ||||||||
\(866\) | 22848.0 | 0.896543 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 1187.94i | − | 0.0464531i | ||||||
\(869\) | −12012.0 | − | 25481.3i | −0.468906 | − | 0.994700i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26134.7i | 1.01669i | ||||||||
\(872\) | − | 24857.6i | − | 0.965350i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 32130.0 | 1.24349 | ||||||||
\(875\) | 47712.0 | 1.84338 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34183.0i | 1.31616i | 0.752946 | + | 0.658082i | \(0.228632\pi\) | ||||
−0.752946 | + | 0.658082i | \(0.771368\pi\) | |||||||
\(878\) | − | 40271.1i | − | 1.54793i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −21868.0 | − | 46389.0i | −0.837693 | − | 1.77702i | ||||
\(881\) | − | 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 | \(-0.450548\pi\) | ||||
0.154734 | + | 0.987956i | \(0.450548\pi\) | |||||||
\(884\) | − | 3742.01i | − | 0.142373i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 54967.7i | 2.08428i | ||||||||
\(887\) | 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 | ||||||||
\(890\) | −91140.0 | −3.43261 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2968.00 | −0.111408 | ||||||||
\(893\) | −9702.00 | −0.363567 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7672.00 | 0.286533 | ||||||||
\(896\) | 28154.2i | 1.04974i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 1964.34i | − | 0.0729966i | ||||||
\(899\) | 1680.00 | 0.0623261 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18531.9i | 0.685223i | ||||||||
\(902\) | 29106.0 | − | 13720.7i | 1.07442 | − | 0.506485i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 34064.2i | 1.25327i | ||||||||
\(905\) | − | 26332.7i | − | 0.967212i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37744.0 | −1.38177 | −0.690887 | − | 0.722963i | \(-0.742780\pi\) | ||||
−0.690887 | + | 0.722963i | \(0.742780\pi\) | |||||||
\(908\) | −3444.00 | −0.125874 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 29936.1i | 1.09052i | ||||||||
\(911\) | − | 1800.29i | − | 0.0654735i | −0.999464 | − | 0.0327368i | \(-0.989578\pi\) | ||
0.999464 | − | 0.0327368i | \(-0.0104223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 40194.0 | − | 18947.6i | 1.45698 | − | 0.686829i | ||||
\(914\) | 18073.6i | 0.654074i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −574.000 | −0.0207047 | ||||||||
\(917\) | − | 9978.69i | − | 0.359352i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 25277.7i | − | 0.907326i | −0.891173 | − | 0.453663i | \(-0.850117\pi\) | ||
0.891173 | − | 0.453663i | \(-0.149883\pi\) | |||||||
\(920\) | −49980.0 | −1.79108 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13356.0 | −0.477068 | ||||||||
\(923\) | 10038.0 | 0.357968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −48594.0 | −1.72731 | ||||||||
\(926\) | 44934.0 | 1.59463 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1080.00 | 0.0382034 | ||||||||
\(929\) | 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 | ||||||||
\(932\) | 5310.00 | 0.186625 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 27738.4i | − | 0.971764i | ||||||
\(935\) | 38808.0 | + | 82324.2i | 1.35739 | + | 2.87945i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2851.05i | − | 0.0994022i | −0.998764 | − | 0.0497011i | \(-0.984173\pi\) | ||
0.998764 | − | 0.0497011i | \(-0.0158269\pi\) | |||||||
\(938\) | − | 44802.3i | − | 1.55954i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2156.00 | −0.0748095 | ||||||||
\(941\) | −3990.00 | −0.138226 | −0.0691128 | − | 0.997609i | \(-0.522017\pi\) | ||||
−0.0691128 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 35341.2i | − | 1.22043i | ||||||
\(944\) | 36548.9i | 1.26013i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 198.000 | + | 420.021i | 0.00680501 | + | 0.0144356i | ||||
\(947\) | 40774.6i | 1.39915i | 0.714558 | + | 0.699576i | \(0.246628\pi\) | ||||
−0.714558 | + | 0.699576i | \(0.753372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5292.00 | −0.181017 | ||||||||
\(950\) | − | 71365.5i | − | 2.43726i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 44904.1i | − | 1.52873i | ||||||
\(953\) | 11322.0 | 0.384843 | 0.192422 | − | 0.981312i | \(-0.438366\pi\) | ||||
0.192422 | + | 0.981312i | \(0.438366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 67396.0 | 2.28365 | ||||||||
\(956\) | −1236.00 | −0.0418150 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15372.0 | 0.518420 | ||||||||
\(959\) | −5736.00 | −0.193144 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24891.0 | −0.835521 | ||||||||
\(962\) | − | 16215.4i | − | 0.543456i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 3445.02i | − | 0.115100i | ||||||
\(965\) | −67704.0 | −2.25852 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2791.66i | − | 0.0928373i | −0.998922 | − | 0.0464186i | \(-0.985219\pi\) | ||
0.998922 | − | 0.0464186i | \(-0.0147808\pi\) | |||||||
\(968\) | −17787.0 | + | 21561.1i | −0.590595 | + | 0.715909i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 11641.8i | − | 0.385357i | ||||||
\(971\) | − | 6216.88i | − | 0.205468i | −0.994709 | − | 0.102734i | \(-0.967241\pi\) | ||
0.994709 | − | 0.102734i | \(-0.0327590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48888.0 | 1.61077 | ||||||||
\(974\) | 15288.0 | 0.502935 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 23194.5i | 0.760695i | ||||||||
\(977\) | 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 | ||||
\(980\) | 1088.94i | 0.0354950i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 39492.0 | 1.28334 | ||||||||
\(983\) | 2781.76i | 0.0902587i | 0.998981 | + | 0.0451294i | \(0.0143700\pi\) | ||||
−0.998981 | + | 0.0451294i | \(0.985630\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 75196.6i | − | 2.43245i | ||||||
\(986\) | −9072.00 | −0.293014 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2646.00 | 0.0852029 | ||||||||
\(989\) | 510.000 | 0.0163974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7882.00 | −0.252654 | −0.126327 | − | 0.991989i | \(-0.540319\pi\) | ||||
−0.126327 | + | 0.991989i | \(0.540319\pi\) | |||||||
\(992\) | 3150.00 | 0.100819 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −17208.0 | −0.549099 | ||||||||
\(995\) | 11087.4i | 0.353262i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5910.00i | 0.187735i | 0.995585 | + | 0.0938674i | \(0.0299230\pi\) | ||||
−0.995585 | + | 0.0938674i | \(0.970077\pi\) | |||||||
\(998\) | −12684.0 | −0.402310 | ||||||||
\(999\) | 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 | 99.4.d.b.98.2 | yes | 2 | |
3.2 | odd | 2 | 99.4.d.a.98.1 | ✓ | 2 | ||
4.3 | odd | 2 | 1584.4.b.a.593.2 | 2 | |||
11.10 | odd | 2 | 99.4.d.a.98.2 | yes | 2 | ||
12.11 | even | 2 | 1584.4.b.b.593.1 | 2 | |||
33.32 | even | 2 | inner | 99.4.d.b.98.1 | yes | 2 | |
44.43 | even | 2 | 1584.4.b.b.593.2 | 2 | |||
132.131 | odd | 2 | 1584.4.b.a.593.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.4.d.a.98.1 | ✓ | 2 | 3.2 | odd | 2 | ||
99.4.d.a.98.2 | yes | 2 | 11.10 | odd | 2 | ||
99.4.d.b.98.1 | yes | 2 | 33.32 | even | 2 | inner | |
99.4.d.b.98.2 | yes | 2 | 1.1 | even | 1 | trivial | |
1584.4.b.a.593.1 | 2 | 132.131 | odd | 2 | |||
1584.4.b.a.593.2 | 2 | 4.3 | odd | 2 | |||
1584.4.b.b.593.1 | 2 | 12.11 | even | 2 | |||
1584.4.b.b.593.2 | 2 | 44.43 | even | 2 |