Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(244,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.244");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.b (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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 91 x^{14} + 3268 x^{12} + 59128 x^{10} + 571975 x^{8} + 2881141 x^{6} + 6555196 x^{4} + \cdots + 614656 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{12}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 244.10 | ||
Root | \(0.785333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.244 |
Dual form | 405.4.b.f.244.7 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.785333i | 0.277657i | 0.990316 | + | 0.138829i | \(0.0443337\pi\) | ||||
−0.990316 | + | 0.138829i | \(0.955666\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.38325 | 0.922907 | ||||||||
\(5\) | 3.61462 | + | 10.5799i | 0.323302 | + | 0.946296i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.9136i | 1.12923i | 0.825355 | + | 0.564614i | \(0.190975\pi\) | ||||
−0.825355 | + | 0.564614i | \(0.809025\pi\) | |||||||
\(8\) | 12.0810i | 0.533909i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.30875 | + | 2.83868i | −0.262746 | + | 0.0897671i | ||||
\(11\) | 59.3838 | 1.62772 | 0.813858 | − | 0.581064i | \(-0.197363\pi\) | ||||
0.813858 | + | 0.581064i | \(0.197363\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 45.9320i | 0.979942i | 0.871739 | + | 0.489971i | \(0.162993\pi\) | ||||
−0.871739 | + | 0.489971i | \(0.837007\pi\) | |||||||
\(14\) | −16.4241 | −0.313538 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 49.5784 | 0.774663 | ||||||||
\(17\) | − | 43.0872i | − | 0.614717i | −0.951594 | − | 0.307359i | \(-0.900555\pi\) | ||
0.951594 | − | 0.307359i | \(-0.0994451\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −140.178 | −1.69258 | −0.846292 | − | 0.532719i | \(-0.821170\pi\) | ||||
−0.846292 | + | 0.532719i | \(0.821170\pi\) | |||||||
\(20\) | 26.6877 | + | 78.1141i | 0.298377 | + | 0.873343i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 46.6360i | 0.451947i | ||||||||
\(23\) | − | 101.756i | − | 0.922501i | −0.887270 | − | 0.461251i | \(-0.847401\pi\) | ||
0.887270 | − | 0.461251i | \(-0.152599\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −98.8690 | + | 76.4848i | −0.790952 | + | 0.611878i | ||||
\(26\) | −36.0719 | −0.272088 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 154.410i | 1.04217i | ||||||||
\(29\) | 12.3918 | 0.0793486 | 0.0396743 | − | 0.999213i | \(-0.487368\pi\) | ||||
0.0396743 | + | 0.999213i | \(0.487368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 71.9790 | 0.417026 | 0.208513 | − | 0.978020i | \(-0.433138\pi\) | ||||
0.208513 | + | 0.978020i | \(0.433138\pi\) | |||||||
\(32\) | 135.583i | 0.748999i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 33.8378 | 0.170681 | ||||||||
\(35\) | −221.264 | + | 75.5948i | −1.06858 | + | 0.365081i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 150.734i | − | 0.669742i | −0.942264 | − | 0.334871i | \(-0.891307\pi\) | ||
0.942264 | − | 0.334871i | \(-0.108693\pi\) | |||||||
\(38\) | − | 110.087i | − | 0.469958i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −127.816 | + | 43.6682i | −0.505236 | + | 0.172614i | ||||
\(41\) | −51.0821 | −0.194577 | −0.0972887 | − | 0.995256i | \(-0.531017\pi\) | ||||
−0.0972887 | + | 0.995256i | \(0.531017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 34.4716i | 0.122253i | 0.998130 | + | 0.0611264i | \(0.0194693\pi\) | ||||
−0.998130 | + | 0.0611264i | \(0.980531\pi\) | |||||||
\(44\) | 438.445 | 1.50223 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 79.9121 | 0.256139 | ||||||||
\(47\) | − | 117.976i | − | 0.366139i | −0.983100 | − | 0.183069i | \(-0.941397\pi\) | ||
0.983100 | − | 0.183069i | \(-0.0586033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −94.3781 | −0.275155 | ||||||||
\(50\) | −60.0660 | − | 77.6451i | −0.169892 | − | 0.219613i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 339.128i | 0.904395i | ||||||||
\(53\) | − | 137.196i | − | 0.355573i | −0.984069 | − | 0.177787i | \(-0.943106\pi\) | ||
0.984069 | − | 0.177787i | \(-0.0568937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 214.650 | + | 628.275i | 0.526244 | + | 1.54030i | ||||
\(56\) | −252.657 | −0.602904 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.73173i | 0.0220317i | ||||||||
\(59\) | 496.314 | 1.09516 | 0.547581 | − | 0.836753i | \(-0.315549\pi\) | ||||
0.547581 | + | 0.836753i | \(0.315549\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −247.700 | −0.519914 | −0.259957 | − | 0.965620i | \(-0.583708\pi\) | ||||
−0.259957 | + | 0.965620i | \(0.583708\pi\) | |||||||
\(62\) | 56.5275i | 0.115790i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 290.149 | 0.566698 | ||||||||
\(65\) | −485.956 | + | 166.027i | −0.927315 | + | 0.316817i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 826.052i | 1.50624i | 0.657881 | + | 0.753121i | \(0.271453\pi\) | ||||
−0.657881 | + | 0.753121i | \(0.728547\pi\) | |||||||
\(68\) | − | 318.124i | − | 0.567326i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −59.3671 | − | 173.766i | −0.101367 | − | 0.296700i | ||||
\(71\) | 260.049 | 0.434677 | 0.217339 | − | 0.976096i | \(-0.430262\pi\) | ||||
0.217339 | + | 0.976096i | \(0.430262\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 372.227i | 0.596793i | 0.954442 | + | 0.298396i | \(0.0964518\pi\) | ||||
−0.954442 | + | 0.298396i | \(0.903548\pi\) | |||||||
\(74\) | 118.376 | 0.185959 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1034.97 | −1.56210 | ||||||||
\(77\) | 1241.93i | 1.83806i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −476.404 | −0.678476 | −0.339238 | − | 0.940701i | \(-0.610169\pi\) | ||||
−0.339238 | + | 0.940701i | \(0.610169\pi\) | |||||||
\(80\) | 179.207 | + | 524.535i | 0.250450 | + | 0.733060i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 40.1164i | − | 0.0540258i | ||||||
\(83\) | 313.173i | 0.414160i | 0.978324 | + | 0.207080i | \(0.0663960\pi\) | ||||
−0.978324 | + | 0.207080i | \(0.933604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 455.859 | − | 155.744i | 0.581704 | − | 0.198739i | ||||
\(86\) | −27.0717 | −0.0339444 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 717.414i | 0.869052i | ||||||||
\(89\) | −817.628 | −0.973802 | −0.486901 | − | 0.873457i | \(-0.661873\pi\) | ||||
−0.486901 | + | 0.873457i | \(0.661873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −960.603 | −1.10658 | ||||||||
\(92\) | − | 751.288i | − | 0.851382i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 92.6502 | 0.101661 | ||||||||
\(95\) | −506.692 | − | 1483.07i | −0.547216 | − | 1.60169i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 941.296i | 0.985300i | 0.870227 | + | 0.492650i | \(0.163972\pi\) | ||||
−0.870227 | + | 0.492650i | \(0.836028\pi\) | |||||||
\(98\) | − | 74.1183i | − | 0.0763987i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −729.975 | + | 564.707i | −0.729975 | + | 0.564707i | ||||
\(101\) | 1002.87 | 0.988017 | 0.494008 | − | 0.869457i | \(-0.335531\pi\) | ||||
0.494008 | + | 0.869457i | \(0.335531\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 298.834i | − | 0.285873i | −0.989732 | − | 0.142937i | \(-0.954345\pi\) | ||
0.989732 | − | 0.142937i | \(-0.0456545\pi\) | |||||||
\(104\) | −554.903 | −0.523199 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 107.745 | 0.0987275 | ||||||||
\(107\) | − | 984.533i | − | 0.889518i | −0.895650 | − | 0.444759i | \(-0.853289\pi\) | ||
0.895650 | − | 0.444759i | \(-0.146711\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 224.770 | 0.197514 | 0.0987572 | − | 0.995112i | \(-0.468513\pi\) | ||||
0.0987572 | + | 0.995112i | \(0.468513\pi\) | |||||||
\(110\) | −493.405 | + | 168.572i | −0.427675 | + | 0.146115i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1036.86i | 0.874771i | ||||||||
\(113\) | 137.764i | 0.114688i | 0.998354 | + | 0.0573440i | \(0.0182632\pi\) | ||||
−0.998354 | + | 0.0573440i | \(0.981737\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1076.57 | − | 367.809i | 0.872959 | − | 0.298246i | ||||
\(116\) | 91.4921 | 0.0732313 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 389.772i | 0.304080i | ||||||||
\(119\) | 901.109 | 0.694155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2195.43 | 1.64946 | ||||||||
\(122\) | − | 194.527i | − | 0.144358i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 531.439 | 0.384876 | ||||||||
\(125\) | −1166.58 | − | 769.561i | −0.834734 | − | 0.550653i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2742.19i | − | 1.91598i | −0.286800 | − | 0.957991i | \(-0.592591\pi\) | ||
0.286800 | − | 0.957991i | \(-0.407409\pi\) | |||||||
\(128\) | 1312.53i | 0.906347i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −130.386 | − | 381.638i | −0.0879665 | − | 0.257476i | ||||
\(131\) | 960.401 | 0.640539 | 0.320270 | − | 0.947326i | \(-0.396226\pi\) | ||||
0.320270 | + | 0.947326i | \(0.396226\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2931.63i | − | 1.91131i | ||||||
\(134\) | −648.726 | −0.418219 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 520.536 | 0.328203 | ||||||||
\(137\) | − | 726.517i | − | 0.453070i | −0.974003 | − | 0.226535i | \(-0.927260\pi\) | ||
0.974003 | − | 0.226535i | \(-0.0727397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −499.893 | −0.305039 | −0.152519 | − | 0.988300i | \(-0.548739\pi\) | ||||
−0.152519 | + | 0.988300i | \(0.548739\pi\) | |||||||
\(140\) | −1633.65 | + | 558.135i | −0.986203 | + | 0.336936i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 204.225i | 0.120691i | ||||||||
\(143\) | 2727.61i | 1.59507i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 44.7919 | + | 131.105i | 0.0256535 | + | 0.0750872i | ||||
\(146\) | −292.322 | −0.165704 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1112.90i | − | 0.618109i | ||||||
\(149\) | −19.6970 | −0.0108298 | −0.00541492 | − | 0.999985i | \(-0.501724\pi\) | ||||
−0.00541492 | + | 0.999985i | \(0.501724\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 655.417 | 0.353226 | 0.176613 | − | 0.984280i | \(-0.443486\pi\) | ||||
0.176613 | + | 0.984280i | \(0.443486\pi\) | |||||||
\(152\) | − | 1693.49i | − | 0.903686i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −975.326 | −0.510351 | ||||||||
\(155\) | 260.177 | + | 761.532i | 0.134825 | + | 0.394630i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1703.54i | − | 0.865969i | −0.901401 | − | 0.432984i | \(-0.857460\pi\) | ||
0.901401 | − | 0.432984i | \(-0.142540\pi\) | |||||||
\(158\) | − | 374.136i | − | 0.188384i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1434.46 | + | 490.083i | −0.708775 | + | 0.242153i | ||||
\(161\) | 2128.08 | 1.04171 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2606.84i | − | 1.25266i | −0.779559 | − | 0.626329i | \(-0.784557\pi\) | ||
0.779559 | − | 0.626329i | \(-0.215443\pi\) | |||||||
\(164\) | −377.152 | −0.179577 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −245.945 | −0.114994 | ||||||||
\(167\) | 1639.42i | 0.759651i | 0.925058 | + | 0.379826i | \(0.124016\pi\) | ||||
−0.925058 | + | 0.379826i | \(0.875984\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 87.2514 | 0.0397139 | ||||||||
\(170\) | 122.311 | + | 358.001i | 0.0551813 | + | 0.161514i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 254.513i | 0.112828i | ||||||||
\(173\) | − | 1174.44i | − | 0.516132i | −0.966127 | − | 0.258066i | \(-0.916915\pi\) | ||
0.966127 | − | 0.258066i | \(-0.0830852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1599.57 | − | 2067.71i | −0.690950 | − | 0.893165i | ||||
\(176\) | 2944.15 | 1.26093 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 642.110i | − | 0.270383i | ||||||
\(179\) | 2512.58 | 1.04916 | 0.524578 | − | 0.851362i | \(-0.324223\pi\) | ||||
0.524578 | + | 0.851362i | \(0.324223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3685.91 | 1.51366 | 0.756828 | − | 0.653614i | \(-0.226748\pi\) | ||||
0.756828 | + | 0.653614i | \(0.226748\pi\) | |||||||
\(182\) | − | 754.393i | − | 0.307249i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1229.31 | 0.492531 | ||||||||
\(185\) | 1594.75 | − | 544.846i | 0.633774 | − | 0.216529i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2558.68i | − | 1.00058i | ||||||
\(188\) | − | 871.044i | − | 0.337912i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1164.71 | − | 397.922i | 0.444720 | − | 0.151938i | ||||
\(191\) | 2716.35 | 1.02905 | 0.514524 | − | 0.857476i | \(-0.327969\pi\) | ||||
0.514524 | + | 0.857476i | \(0.327969\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1972.75i | − | 0.735762i | −0.929873 | − | 0.367881i | \(-0.880083\pi\) | ||
0.929873 | − | 0.367881i | \(-0.119917\pi\) | |||||||
\(194\) | −739.231 | −0.273576 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −696.818 | −0.253942 | ||||||||
\(197\) | 3406.43i | 1.23197i | 0.787758 | + | 0.615985i | \(0.211242\pi\) | ||||
−0.787758 | + | 0.615985i | \(0.788758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 981.722 | 0.349711 | 0.174855 | − | 0.984594i | \(-0.444054\pi\) | ||||
0.174855 | + | 0.984594i | \(0.444054\pi\) | |||||||
\(200\) | −924.011 | − | 1194.43i | −0.326687 | − | 0.422296i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 787.590i | 0.274330i | ||||||||
\(203\) | 259.158i | 0.0896026i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −184.642 | − | 540.444i | −0.0629073 | − | 0.184128i | ||||
\(206\) | 234.684 | 0.0793748 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2277.24i | 0.759125i | ||||||||
\(209\) | −8324.31 | −2.75505 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2017.52 | −0.658254 | −0.329127 | − | 0.944286i | \(-0.606754\pi\) | ||||
−0.329127 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(212\) | − | 1012.96i | − | 0.328161i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 773.186 | 0.246981 | ||||||||
\(215\) | −364.706 | + | 124.602i | −0.115687 | + | 0.0395246i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1505.34i | 0.470918i | ||||||||
\(218\) | 176.519i | 0.0548413i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1584.81 | + | 4638.71i | 0.485674 | + | 1.42155i | ||||
\(221\) | 1979.08 | 0.602387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 265.712i | 0.0797911i | 0.999204 | + | 0.0398956i | \(0.0127025\pi\) | ||||
−0.999204 | + | 0.0398956i | \(0.987297\pi\) | |||||||
\(224\) | −2835.53 | −0.845791 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −108.191 | −0.0318440 | ||||||||
\(227\) | 5124.95i | 1.49848i | 0.662300 | + | 0.749239i | \(0.269581\pi\) | ||||
−0.662300 | + | 0.749239i | \(0.730419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −90.7643 | −0.0261916 | −0.0130958 | − | 0.999914i | \(-0.504169\pi\) | ||||
−0.0130958 | + | 0.999914i | \(0.504169\pi\) | |||||||
\(230\) | 288.852 | + | 845.463i | 0.0828102 | + | 0.242383i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 149.706i | 0.0423649i | ||||||||
\(233\) | − | 5856.17i | − | 1.64657i | −0.567629 | − | 0.823284i | \(-0.692139\pi\) | ||
0.567629 | − | 0.823284i | \(-0.307861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1248.17 | − | 426.438i | 0.346475 | − | 0.118373i | ||||
\(236\) | 3664.41 | 1.01073 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 707.670i | 0.192737i | ||||||||
\(239\) | −6868.82 | −1.85903 | −0.929513 | − | 0.368790i | \(-0.879772\pi\) | ||||
−0.929513 | + | 0.368790i | \(0.879772\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.1374 | −0.00671886 | −0.00335943 | − | 0.999994i | \(-0.501069\pi\) | ||||
−0.00335943 | + | 0.999994i | \(0.501069\pi\) | |||||||
\(242\) | 1724.14i | 0.457984i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1828.83 | −0.479832 | ||||||||
\(245\) | −341.142 | − | 998.512i | −0.0889581 | − | 0.260378i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6438.67i | − | 1.65863i | ||||||
\(248\) | 869.577i | 0.222654i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 604.362 | − | 916.151i | 0.152893 | − | 0.231770i | ||||
\(251\) | 5765.12 | 1.44976 | 0.724882 | − | 0.688873i | \(-0.241894\pi\) | ||||
0.724882 | + | 0.688873i | \(0.241894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6042.63i | − | 1.50157i | ||||||
\(254\) | 2153.53 | 0.531986 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1290.42 | 0.315044 | ||||||||
\(257\) | − | 5609.90i | − | 1.36162i | −0.732460 | − | 0.680810i | \(-0.761628\pi\) | ||
0.732460 | − | 0.680810i | \(-0.238372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3152.38 | 0.756291 | ||||||||
\(260\) | −3587.94 | + | 1225.82i | −0.855825 | + | 0.292392i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 754.235i | 0.177850i | ||||||||
\(263\) | − | 5803.41i | − | 1.36066i | −0.732906 | − | 0.680330i | \(-0.761837\pi\) | ||
0.732906 | − | 0.680330i | \(-0.238163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1451.53 | − | 495.914i | 0.336478 | − | 0.114958i | ||||
\(266\) | 2302.31 | 0.530690 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6098.95i | 1.39012i | ||||||||
\(269\) | −7317.07 | −1.65847 | −0.829237 | − | 0.558897i | \(-0.811225\pi\) | ||||
−0.829237 | + | 0.558897i | \(0.811225\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8201.78 | −1.83846 | −0.919230 | − | 0.393722i | \(-0.871187\pi\) | ||||
−0.919230 | + | 0.393722i | \(0.871187\pi\) | |||||||
\(272\) | − | 2136.20i | − | 0.476199i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 570.558 | 0.125798 | ||||||||
\(275\) | −5871.21 | + | 4541.95i | −1.28744 | + | 0.995964i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4598.40i | − | 0.997441i | −0.866763 | − | 0.498720i | \(-0.833803\pi\) | ||
0.866763 | − | 0.498720i | \(-0.166197\pi\) | |||||||
\(278\) | − | 392.582i | − | 0.0846961i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −913.258 | − | 2673.08i | −0.194920 | − | 0.570526i | ||||
\(281\) | 3811.87 | 0.809243 | 0.404621 | − | 0.914484i | \(-0.367403\pi\) | ||||
0.404621 | + | 0.914484i | \(0.367403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4099.09i | 0.861009i | 0.902588 | + | 0.430504i | \(0.141664\pi\) | ||||
−0.902588 | + | 0.430504i | \(0.858336\pi\) | |||||||
\(284\) | 1920.00 | 0.401167 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2142.09 | −0.442882 | ||||||||
\(287\) | − | 1068.31i | − | 0.219722i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3056.49 | 0.622123 | ||||||||
\(290\) | −102.961 | + | 35.1765i | −0.0208485 | + | 0.00712289i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2748.25i | 0.550784i | ||||||||
\(293\) | − | 573.453i | − | 0.114340i | −0.998364 | − | 0.0571698i | \(-0.981792\pi\) | ||
0.998364 | − | 0.0571698i | \(-0.0182076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1793.99 | + | 5250.96i | 0.354068 | + | 1.03635i | ||||
\(296\) | 1821.01 | 0.357581 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 15.4687i | − | 0.00300698i | ||||||
\(299\) | 4673.84 | 0.903997 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −720.925 | −0.138051 | ||||||||
\(302\) | 514.721i | 0.0980757i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6949.82 | −1.31118 | ||||||||
\(305\) | −895.342 | − | 2620.64i | −0.168089 | − | 0.491992i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8610.98i | 1.60083i | 0.599447 | + | 0.800414i | \(0.295387\pi\) | ||||
−0.599447 | + | 0.800414i | \(0.704613\pi\) | |||||||
\(308\) | 9169.46i | 1.69636i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −598.056 | + | 204.326i | −0.109572 | + | 0.0374352i | ||||
\(311\) | 3049.69 | 0.556052 | 0.278026 | − | 0.960574i | \(-0.410320\pi\) | ||||
0.278026 | + | 0.960574i | \(0.410320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4105.22i | − | 0.741344i | −0.928764 | − | 0.370672i | \(-0.879127\pi\) | ||
0.928764 | − | 0.370672i | \(-0.120873\pi\) | |||||||
\(314\) | 1337.84 | 0.240442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3517.41 | −0.626170 | ||||||||
\(317\) | 5420.67i | 0.960427i | 0.877152 | + | 0.480214i | \(0.159441\pi\) | ||||
−0.877152 | + | 0.480214i | \(0.840559\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 735.874 | 0.129157 | ||||||||
\(320\) | 1048.78 | + | 3069.75i | 0.183215 | + | 0.536264i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1671.25i | 0.289239i | ||||||||
\(323\) | 6039.90i | 1.04046i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3513.10 | − | 4541.25i | −0.599605 | − | 0.775087i | ||||
\(326\) | 2047.23 | 0.347809 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 617.121i | − | 0.103887i | ||||||
\(329\) | 2467.29 | 0.413454 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5909.23 | 0.981272 | 0.490636 | − | 0.871365i | \(-0.336765\pi\) | ||||
0.490636 | + | 0.871365i | \(0.336765\pi\) | |||||||
\(332\) | 2312.24i | 0.382231i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1287.49 | −0.210923 | ||||||||
\(335\) | −8739.55 | + | 2985.87i | −1.42535 | + | 0.486971i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1324.01i | 0.214016i | 0.994258 | + | 0.107008i | \(0.0341271\pi\) | ||||
−0.994258 | + | 0.107008i | \(0.965873\pi\) | |||||||
\(338\) | 68.5214i | 0.0110268i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3365.72 | − | 1149.90i | 0.536859 | − | 0.183418i | ||||
\(341\) | 4274.39 | 0.678800 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5199.58i | 0.818515i | ||||||||
\(344\) | −416.451 | −0.0652718 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 922.324 | 0.143308 | ||||||||
\(347\) | − | 11227.7i | − | 1.73699i | −0.495697 | − | 0.868495i | \(-0.665087\pi\) | ||
0.495697 | − | 0.868495i | \(-0.334913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1042.88 | −0.159954 | −0.0799772 | − | 0.996797i | \(-0.525485\pi\) | ||||
−0.0799772 | + | 0.996797i | \(0.525485\pi\) | |||||||
\(350\) | 1623.84 | − | 1256.20i | 0.247994 | − | 0.191847i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8051.45i | 1.21916i | ||||||||
\(353\) | − | 11522.2i | − | 1.73730i | −0.495426 | − | 0.868650i | \(-0.664988\pi\) | ||
0.495426 | − | 0.868650i | \(-0.335012\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 939.978 | + | 2751.29i | 0.140532 | + | 0.411333i | ||||
\(356\) | −6036.75 | −0.898728 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1973.21i | 0.291306i | ||||||||
\(359\) | −4751.13 | −0.698482 | −0.349241 | − | 0.937033i | \(-0.613560\pi\) | ||||
−0.349241 | + | 0.937033i | \(0.613560\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12791.0 | 1.86484 | ||||||||
\(362\) | 2894.67i | 0.420277i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7092.37 | −1.02127 | ||||||||
\(365\) | −3938.13 | + | 1345.46i | −0.564743 | + | 0.192944i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11120.8i | 1.58174i | 0.611981 | + | 0.790872i | \(0.290373\pi\) | ||||
−0.611981 | + | 0.790872i | \(0.709627\pi\) | |||||||
\(368\) | − | 5044.89i | − | 0.714627i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 427.885 | + | 1252.41i | 0.0601208 | + | 0.175972i | ||||
\(371\) | 2869.27 | 0.401523 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9512.54i | 1.32048i | 0.751053 | + | 0.660242i | \(0.229546\pi\) | ||||
−0.751053 | + | 0.660242i | \(0.770454\pi\) | |||||||
\(374\) | 2009.42 | 0.277819 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1425.26 | 0.195485 | ||||||||
\(377\) | 569.182i | 0.0777570i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3029.06 | 0.410534 | 0.205267 | − | 0.978706i | \(-0.434194\pi\) | ||||
0.205267 | + | 0.978706i | \(0.434194\pi\) | |||||||
\(380\) | −3741.03 | − | 10949.9i | −0.505029 | − | 1.47821i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2133.24i | 0.285722i | ||||||||
\(383\) | 10405.3i | 1.38822i | 0.719871 | + | 0.694108i | \(0.244201\pi\) | ||||
−0.719871 | + | 0.694108i | \(0.755799\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13139.5 | + | 4489.10i | −1.73935 | + | 0.594249i | ||||
\(386\) | 1549.27 | 0.204289 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6949.83i | 0.909340i | ||||||||
\(389\) | −9049.43 | −1.17950 | −0.589748 | − | 0.807587i | \(-0.700773\pi\) | ||||
−0.589748 | + | 0.807587i | \(0.700773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4384.37 | −0.567077 | ||||||||
\(392\) | − | 1140.18i | − | 0.146908i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2675.18 | −0.342065 | ||||||||
\(395\) | −1722.02 | − | 5040.31i | −0.219353 | − | 0.642039i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 276.228i | − | 0.0349206i | −0.999848 | − | 0.0174603i | \(-0.994442\pi\) | ||
0.999848 | − | 0.0174603i | \(-0.00555807\pi\) | |||||||
\(398\) | 770.979i | 0.0970997i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4901.77 | + | 3792.00i | −0.612721 | + | 0.474000i | ||||
\(401\) | 14902.5 | 1.85585 | 0.927925 | − | 0.372767i | \(-0.121591\pi\) | ||||
0.927925 | + | 0.372767i | \(0.121591\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3306.14i | 0.408662i | ||||||||
\(404\) | 7404.47 | 0.911847 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −203.525 | −0.0248788 | ||||||||
\(407\) | − | 8951.13i | − | 1.09015i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1116.83 | 0.135021 | 0.0675104 | − | 0.997719i | \(-0.478494\pi\) | ||||
0.0675104 | + | 0.997719i | \(0.478494\pi\) | |||||||
\(410\) | 424.428 | − | 145.006i | 0.0511244 | − | 0.0174666i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 2206.36i | − | 0.263834i | ||||||
\(413\) | 10379.7i | 1.23669i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3313.35 | + | 1132.00i | −0.391918 | + | 0.133899i | ||||
\(416\) | −6227.62 | −0.733976 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 6537.36i | − | 0.764958i | ||||||
\(419\) | −5086.23 | −0.593027 | −0.296514 | − | 0.955029i | \(-0.595824\pi\) | ||||
−0.296514 | + | 0.955029i | \(0.595824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9640.06 | −1.11598 | −0.557990 | − | 0.829848i | \(-0.688427\pi\) | ||||
−0.557990 | + | 0.829848i | \(0.688427\pi\) | |||||||
\(422\) | − | 1584.42i | − | 0.182769i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1657.47 | 0.189844 | ||||||||
\(425\) | 3295.52 | + | 4259.99i | 0.376132 | + | 0.486212i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 5180.30i | − | 0.587101i | ||||||
\(428\) | − | 7269.06i | − | 0.820942i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −97.8540 | − | 286.416i | −0.0109743 | − | 0.0321214i | ||||
\(431\) | 857.490 | 0.0958326 | 0.0479163 | − | 0.998851i | \(-0.484742\pi\) | ||||
0.0479163 | + | 0.998851i | \(0.484742\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2306.40i | − | 0.255978i | −0.991776 | − | 0.127989i | \(-0.959148\pi\) | ||
0.991776 | − | 0.127989i | \(-0.0408523\pi\) | |||||||
\(434\) | −1182.19 | −0.130754 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1659.53 | 0.182287 | ||||||||
\(437\) | 14263.9i | 1.56141i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 711.237 | 0.0773246 | 0.0386623 | − | 0.999252i | \(-0.487690\pi\) | ||||
0.0386623 | + | 0.999252i | \(0.487690\pi\) | |||||||
\(440\) | −7590.17 | + | 2593.18i | −0.822380 | + | 0.280966i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1554.24i | 0.167257i | ||||||||
\(443\) | 15639.9i | 1.67737i | 0.544618 | + | 0.838684i | \(0.316675\pi\) | ||||
−0.544618 | + | 0.838684i | \(0.683325\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2955.42 | − | 8650.43i | −0.314832 | − | 0.921505i | ||||
\(446\) | −208.673 | −0.0221546 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6068.06i | 0.639931i | ||||||||
\(449\) | 8156.47 | 0.857299 | 0.428650 | − | 0.903471i | \(-0.358989\pi\) | ||||
0.428650 | + | 0.903471i | \(0.358989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3033.44 | −0.316717 | ||||||||
\(452\) | 1017.15i | 0.105846i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4024.79 | −0.416063 | ||||||||
\(455\) | −3472.22 | − | 10163.1i | −0.357759 | − | 1.04715i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 14785.2i | − | 1.51339i | −0.653766 | − | 0.756697i | \(-0.726812\pi\) | ||
0.653766 | − | 0.756697i | \(-0.273188\pi\) | |||||||
\(458\) | − | 71.2802i | − | 0.00727228i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7948.56 | − | 2715.62i | 0.805660 | − | 0.275253i | ||||
\(461\) | 8293.15 | 0.837853 | 0.418927 | − | 0.908020i | \(-0.362406\pi\) | ||||
0.418927 | + | 0.908020i | \(0.362406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14357.0i | 1.44109i | 0.693407 | + | 0.720546i | \(0.256109\pi\) | ||||
−0.693407 | + | 0.720546i | \(0.743891\pi\) | |||||||
\(464\) | 614.368 | 0.0614684 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4599.04 | 0.457181 | ||||||||
\(467\) | − | 4815.25i | − | 0.477138i | −0.971126 | − | 0.238569i | \(-0.923322\pi\) | ||
0.971126 | − | 0.238569i | \(-0.0766782\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17275.7 | −1.70089 | ||||||||
\(470\) | 334.896 | + | 980.230i | 0.0328672 | + | 0.0962014i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5995.96i | 0.584717i | ||||||||
\(473\) | 2047.05i | 0.198993i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13859.3 | − | 10721.5i | 1.33875 | − | 1.03566i | ||||
\(476\) | 6653.11 | 0.640641 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 5394.31i | − | 0.516172i | ||||||
\(479\) | 11827.7 | 1.12823 | 0.564116 | − | 0.825695i | \(-0.309217\pi\) | ||||
0.564116 | + | 0.825695i | \(0.309217\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6923.50 | 0.656308 | ||||||||
\(482\) | − | 19.7413i | − | 0.00186554i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16209.4 | 1.52230 | ||||||||
\(485\) | −9958.83 | + | 3402.43i | −0.932386 | + | 0.318549i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13087.8i | − | 1.21779i | −0.793251 | − | 0.608894i | \(-0.791613\pi\) | ||
0.793251 | − | 0.608894i | \(-0.208387\pi\) | |||||||
\(488\) | − | 2992.46i | − | 0.277586i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 784.164 | − | 267.910i | 0.0722958 | − | 0.0246998i | ||||
\(491\) | 6593.39 | 0.606019 | 0.303010 | − | 0.952988i | \(-0.402009\pi\) | ||||
0.303010 | + | 0.952988i | \(0.402009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 533.930i | − | 0.0487769i | ||||||
\(494\) | 5056.50 | 0.460532 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3568.61 | 0.323055 | ||||||||
\(497\) | 5438.55i | 0.490850i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16184.8 | 1.45196 | 0.725982 | − | 0.687713i | \(-0.241385\pi\) | ||||
0.725982 | + | 0.687713i | \(0.241385\pi\) | |||||||
\(500\) | −8613.13 | − | 5681.86i | −0.770382 | − | 0.508201i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4527.54i | 0.402537i | ||||||||
\(503\) | − | 10342.9i | − | 0.916833i | −0.888738 | − | 0.458416i | \(-0.848417\pi\) | ||
0.888738 | − | 0.458416i | \(-0.151583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3625.01 | + | 10610.3i | 0.319428 | + | 0.934956i | ||||
\(506\) | 4745.48 | 0.416921 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 20246.2i | − | 1.76827i | ||||||
\(509\) | 5648.61 | 0.491887 | 0.245943 | − | 0.969284i | \(-0.420902\pi\) | ||||
0.245943 | + | 0.969284i | \(0.420902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7784.60 | −0.673915 | ||||||||
\(512\) | 11513.7i | 0.993821i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4405.64 | 0.378063 | ||||||||
\(515\) | 3161.63 | − | 1080.17i | 0.270521 | − | 0.0924234i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 7005.84i | − | 0.595970i | ||||||
\(518\) | 2475.67i | 0.209990i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2005.77 | − | 5870.83i | −0.169151 | − | 0.495102i | ||||
\(521\) | −15511.7 | −1.30438 | −0.652188 | − | 0.758058i | \(-0.726149\pi\) | ||||
−0.652188 | + | 0.758058i | \(0.726149\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 613.845i | 0.0513223i | 0.999671 | + | 0.0256612i | \(0.00816910\pi\) | ||||
−0.999671 | + | 0.0256612i | \(0.991831\pi\) | |||||||
\(524\) | 7090.89 | 0.591158 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4557.61 | 0.377797 | ||||||||
\(527\) | − | 3101.38i | − | 0.256353i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1812.78 | 0.148992 | ||||||||
\(530\) | 389.457 | + | 1139.93i | 0.0319188 | + | 0.0934254i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 21645.0i | − | 1.76396i | ||||||
\(533\) | − | 2346.30i | − | 0.190675i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10416.3 | − | 3558.72i | 0.841747 | − | 0.287583i | ||||
\(536\) | −9979.51 | −0.804196 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 5746.34i | − | 0.460487i | ||||||
\(539\) | −5604.53 | −0.447874 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12701.1 | −1.00936 | −0.504678 | − | 0.863308i | \(-0.668389\pi\) | ||||
−0.504678 | + | 0.863308i | \(0.668389\pi\) | |||||||
\(542\) | − | 6441.12i | − | 0.510461i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5841.91 | 0.460423 | ||||||||
\(545\) | 812.459 | + | 2378.05i | 0.0638568 | + | 0.186907i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9413.79i | 0.735840i | 0.929857 | + | 0.367920i | \(0.119930\pi\) | ||||
−0.929857 | + | 0.367920i | \(0.880070\pi\) | |||||||
\(548\) | − | 5364.06i | − | 0.418141i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3566.95 | − | 4610.85i | −0.276537 | − | 0.357468i | ||||
\(551\) | −1737.07 | −0.134304 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9963.31i | − | 0.766154i | ||||||
\(554\) | 3611.27 | 0.276947 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3690.83 | −0.281522 | ||||||||
\(557\) | − | 14085.5i | − | 1.07149i | −0.844379 | − | 0.535746i | \(-0.820031\pi\) | ||
0.844379 | − | 0.535746i | \(-0.179969\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1583.35 | −0.119801 | ||||||||
\(560\) | −10969.9 | + | 3747.87i | −0.827792 | + | 0.282815i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2993.59i | 0.224692i | ||||||||
\(563\) | − | 8442.04i | − | 0.631953i | −0.948767 | − | 0.315977i | \(-0.897668\pi\) | ||
0.948767 | − | 0.315977i | \(-0.102332\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1457.53 | + | 497.965i | −0.108529 | + | 0.0370789i | ||||
\(566\) | −3219.15 | −0.239065 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3141.64i | 0.232078i | ||||||||
\(569\) | −3528.48 | −0.259968 | −0.129984 | − | 0.991516i | \(-0.541493\pi\) | ||||
−0.129984 | + | 0.991516i | \(0.541493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14738.1 | −1.08016 | −0.540078 | − | 0.841615i | \(-0.681605\pi\) | ||||
−0.540078 | + | 0.841615i | \(0.681605\pi\) | |||||||
\(572\) | 20138.7i | 1.47210i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 838.978 | 0.0610074 | ||||||||
\(575\) | 7782.76 | + | 10060.5i | 0.564458 | + | 0.729654i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17485.6i | − | 1.26159i | −0.775951 | − | 0.630793i | \(-0.782730\pi\) | ||
0.775951 | − | 0.630793i | \(-0.217270\pi\) | |||||||
\(578\) | 2400.36i | 0.172737i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 330.710 | + | 967.979i | 0.0236758 | + | 0.0692985i | ||||
\(581\) | −6549.58 | −0.467681 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 8147.24i | − | 0.578772i | ||||||
\(584\) | −4496.87 | −0.318633 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 450.352 | 0.0317472 | ||||||||
\(587\) | − | 12494.4i | − | 0.878536i | −0.898356 | − | 0.439268i | \(-0.855238\pi\) | ||
0.898356 | − | 0.439268i | \(-0.144762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10089.9 | −0.705853 | ||||||||
\(590\) | −4123.75 | + | 1408.88i | −0.287749 | + | 0.0983095i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 7473.14i | − | 0.518824i | ||||||
\(593\) | 4044.65i | 0.280091i | 0.990145 | + | 0.140046i | \(0.0447249\pi\) | ||||
−0.990145 | + | 0.140046i | \(0.955275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3257.17 | + | 9533.65i | 0.224422 | + | 0.656876i | ||||
\(596\) | −145.428 | −0.00999492 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3670.52i | 0.251001i | ||||||||
\(599\) | −21563.1 | −1.47086 | −0.735431 | − | 0.677600i | \(-0.763020\pi\) | ||||
−0.735431 | + | 0.677600i | \(0.763020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20115.9 | 1.36530 | 0.682648 | − | 0.730747i | \(-0.260828\pi\) | ||||
0.682648 | + | 0.730747i | \(0.260828\pi\) | |||||||
\(602\) | − | 566.166i | − | 0.0383309i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4839.11 | 0.325994 | ||||||||
\(605\) | 7935.65 | + | 23227.5i | 0.533273 | + | 1.56088i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17200.6i | 1.15017i | 0.818094 | + | 0.575084i | \(0.195031\pi\) | ||||
−0.818094 | + | 0.575084i | \(0.804969\pi\) | |||||||
\(608\) | − | 19005.8i | − | 1.26774i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2058.08 | − | 703.142i | 0.136605 | − | 0.0466711i | ||||
\(611\) | 5418.86 | 0.358795 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 894.343i | 0.0589269i | 0.999566 | + | 0.0294634i | \(0.00937986\pi\) | ||||
−0.999566 | + | 0.0294634i | \(0.990620\pi\) | |||||||
\(614\) | −6762.48 | −0.444481 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15003.7 | −0.981357 | ||||||||
\(617\) | 6856.71i | 0.447392i | 0.974659 | + | 0.223696i | \(0.0718122\pi\) | ||||
−0.974659 | + | 0.223696i | \(0.928188\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21165.2 | −1.37431 | −0.687157 | − | 0.726509i | \(-0.741142\pi\) | ||||
−0.687157 | + | 0.726509i | \(0.741142\pi\) | |||||||
\(620\) | 1920.95 | + | 5622.58i | 0.124431 | + | 0.364207i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2395.02i | 0.154392i | ||||||||
\(623\) | − | 17099.5i | − | 1.09964i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3925.15 | − | 15123.9i | 0.251210 | − | 0.967933i | ||||
\(626\) | 3223.96 | 0.205839 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 12577.6i | − | 0.799208i | ||||||
\(629\) | −6494.70 | −0.411702 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14889.2 | 0.939352 | 0.469676 | − | 0.882839i | \(-0.344371\pi\) | ||||
0.469676 | + | 0.882839i | \(0.344371\pi\) | |||||||
\(632\) | − | 5755.42i | − | 0.362244i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4257.03 | −0.266669 | ||||||||
\(635\) | 29012.1 | − | 9911.97i | 1.81309 | − | 0.619440i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 4334.98i | − | 0.269636i | ||||||
\(638\) | 577.906i | 0.0358613i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13886.5 | + | 4744.31i | −0.857673 | + | 0.293024i | ||||
\(641\) | −22428.3 | −1.38200 | −0.691001 | − | 0.722854i | \(-0.742830\pi\) | ||||
−0.691001 | + | 0.722854i | \(0.742830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4262.51i | 0.261426i | 0.991420 | + | 0.130713i | \(0.0417267\pi\) | ||||
−0.991420 | + | 0.130713i | \(0.958273\pi\) | |||||||
\(644\) | 15712.1 | 0.961404 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4743.33 | −0.288891 | ||||||||
\(647\) | − | 19619.7i | − | 1.19216i | −0.802924 | − | 0.596082i | \(-0.796723\pi\) | ||
0.802924 | − | 0.596082i | \(-0.203277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29473.0 | 1.78261 | ||||||||
\(650\) | 3566.39 | − | 2758.95i | 0.215208 | − | 0.166485i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 19246.9i | − | 1.15609i | ||||||
\(653\) | − | 4708.94i | − | 0.282198i | −0.989996 | − | 0.141099i | \(-0.954936\pi\) | ||
0.989996 | − | 0.141099i | \(-0.0450635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3471.49 | + | 10161.0i | 0.207088 | + | 0.606140i | ||||
\(656\) | −2532.57 | −0.150732 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1937.65i | 0.114798i | ||||||||
\(659\) | −24138.8 | −1.42688 | −0.713441 | − | 0.700715i | \(-0.752865\pi\) | ||||
−0.713441 | + | 0.700715i | \(0.752865\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31706.5 | 1.86572 | 0.932859 | − | 0.360241i | \(-0.117305\pi\) | ||||
0.932859 | + | 0.360241i | \(0.117305\pi\) | |||||||
\(662\) | 4640.72i | 0.272457i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3783.44 | −0.221123 | ||||||||
\(665\) | 31016.4 | − | 10596.7i | 1.80867 | − | 0.617931i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1260.94i | − | 0.0731991i | ||||||
\(668\) | 12104.2i | 0.701087i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2344.90 | − | 6863.46i | −0.135211 | − | 0.395759i | ||||
\(671\) | −14709.4 | −0.846272 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 277.641i | − | 0.0159023i | −0.999968 | − | 0.00795116i | \(-0.997469\pi\) | ||
0.999968 | − | 0.00795116i | \(-0.00253096\pi\) | |||||||
\(674\) | −1039.79 | −0.0594231 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 644.199 | 0.0366522 | ||||||||
\(677\) | − | 8744.57i | − | 0.496427i | −0.968705 | − | 0.248213i | \(-0.920157\pi\) | ||
0.968705 | − | 0.248213i | \(-0.0798434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19685.9 | −1.11263 | ||||||||
\(680\) | 1881.54 | + | 5507.22i | 0.106109 | + | 0.310577i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3356.82i | 0.188474i | ||||||||
\(683\) | 34097.3i | 1.91025i | 0.296210 | + | 0.955123i | \(0.404277\pi\) | ||||
−0.296210 | + | 0.955123i | \(0.595723\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7686.49 | − | 2626.09i | 0.428738 | − | 0.146478i | ||||
\(686\) | −4083.40 | −0.227267 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1709.05i | 0.0947047i | ||||||||
\(689\) | 6301.71 | 0.348441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4982.20 | −0.274286 | −0.137143 | − | 0.990551i | \(-0.543792\pi\) | ||||
−0.137143 | + | 0.990551i | \(0.543792\pi\) | |||||||
\(692\) | − | 8671.17i | − | 0.476341i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8817.50 | 0.482288 | ||||||||
\(695\) | −1806.92 | − | 5288.82i | −0.0986195 | − | 0.288657i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2200.98i | 0.119610i | ||||||||
\(698\) | − | 819.008i | − | 0.0444125i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11810.0 | − | 15266.4i | −0.637682 | − | 0.824307i | ||||
\(701\) | 16450.0 | 0.886315 | 0.443158 | − | 0.896444i | \(-0.353858\pi\) | ||||
0.443158 | + | 0.896444i | \(0.353858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21129.6i | 1.13360i | ||||||||
\(704\) | 17230.2 | 0.922423 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9048.79 | 0.482374 | ||||||||
\(707\) | 20973.7i | 1.11570i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9139.71 | 0.484131 | 0.242066 | − | 0.970260i | \(-0.422175\pi\) | ||||
0.242066 | + | 0.970260i | \(0.422175\pi\) | |||||||
\(710\) | −2160.68 | + | 738.196i | −0.114210 | + | 0.0390197i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 9877.74i | − | 0.519921i | ||||||
\(713\) | − | 7324.28i | − | 0.384707i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28857.9 | + | 9859.30i | −1.50941 | + | 0.515688i | ||||
\(716\) | 18551.0 | 0.968273 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 3731.22i | − | 0.193938i | ||||||
\(719\) | −28268.2 | −1.46624 | −0.733121 | − | 0.680098i | \(-0.761937\pi\) | ||||
−0.733121 | + | 0.680098i | \(0.761937\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6249.68 | 0.322816 | ||||||||
\(722\) | 10045.2i | 0.517787i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 27214.0 | 1.39696 | ||||||||
\(725\) | −1225.17 | + | 947.788i | −0.0627609 | + | 0.0485517i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 32221.9i | 1.64380i | 0.569632 | + | 0.821900i | \(0.307086\pi\) | ||||
−0.569632 | + | 0.821900i | \(0.692914\pi\) | |||||||
\(728\) | − | 11605.0i | − | 0.590811i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1056.63 | − | 3092.74i | −0.0535723 | − | 0.156805i | ||||
\(731\) | 1485.29 | 0.0751509 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10764.2i | − | 0.542408i | −0.962522 | − | 0.271204i | \(-0.912578\pi\) | ||
0.962522 | − | 0.271204i | \(-0.0874218\pi\) | |||||||
\(734\) | −8733.52 | −0.439183 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13796.4 | 0.690953 | ||||||||
\(737\) | 49054.0i | 2.45174i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21955.9 | −1.09291 | −0.546456 | − | 0.837488i | \(-0.684023\pi\) | ||||
−0.546456 | + | 0.837488i | \(0.684023\pi\) | |||||||
\(740\) | 11774.4 | − | 4022.73i | 0.584914 | − | 0.199836i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2253.33i | 0.111486i | ||||||||
\(743\) | 5929.17i | 0.292759i | 0.989228 | + | 0.146380i | \(0.0467621\pi\) | ||||
−0.989228 | + | 0.146380i | \(0.953238\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −71.1974 | − | 208.393i | −0.00350130 | − | 0.0102482i | ||||
\(746\) | −7470.51 | −0.366642 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 18891.4i | − | 0.923446i | ||||||
\(749\) | 20590.1 | 1.00447 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14894.6 | −0.723716 | −0.361858 | − | 0.932233i | \(-0.617857\pi\) | ||||
−0.361858 | + | 0.932233i | \(0.617857\pi\) | |||||||
\(752\) | − | 5849.05i | − | 0.283634i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −446.998 | −0.0215898 | ||||||||
\(755\) | 2369.09 | + | 6934.26i | 0.114199 | + | 0.334256i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11935.5i | 0.573058i | 0.958072 | + | 0.286529i | \(0.0925014\pi\) | ||||
−0.958072 | + | 0.286529i | \(0.907499\pi\) | |||||||
\(758\) | 2378.82i | 0.113988i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 17917.0 | − | 6121.33i | 0.855154 | − | 0.292163i | ||||
\(761\) | −28482.5 | −1.35675 | −0.678377 | − | 0.734714i | \(-0.737317\pi\) | ||||
−0.678377 | + | 0.734714i | \(0.737317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4700.75i | 0.223039i | ||||||||
\(764\) | 20055.5 | 0.949715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8171.63 | −0.385448 | ||||||||
\(767\) | 22796.7i | 1.07320i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13392.3 | −0.628009 | −0.314005 | − | 0.949421i | \(-0.601671\pi\) | ||||
−0.314005 | + | 0.949421i | \(0.601671\pi\) | |||||||
\(770\) | −3525.44 | − | 10318.9i | −0.164997 | − | 0.482943i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 14565.3i | − | 0.679039i | ||||||
\(773\) | − | 37031.6i | − | 1.72307i | −0.507696 | − | 0.861536i | \(-0.669503\pi\) | ||
0.507696 | − | 0.861536i | \(-0.330497\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7116.49 | + | 5505.30i | −0.329848 | + | 0.255169i | ||||
\(776\) | −11371.8 | −0.526060 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 7106.81i | − | 0.327496i | ||||||
\(779\) | 7160.60 | 0.329339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15442.7 | 0.707531 | ||||||||
\(782\) | − | 3443.19i | − | 0.157453i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4679.12 | −0.213152 | ||||||||
\(785\) | 18023.3 | − | 6157.65i | 0.819463 | − | 0.279969i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29263.5i | 1.32545i | 0.748862 | + | 0.662726i | \(0.230601\pi\) | ||||
−0.748862 | + | 0.662726i | \(0.769399\pi\) | |||||||
\(788\) | 25150.5i | 1.13699i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3958.32 | − | 1352.36i | 0.178267 | − | 0.0609048i | ||||
\(791\) | −2881.14 | −0.129509 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 11377.4i | − | 0.509485i | ||||||
\(794\) | 216.931 | 0.00969596 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7248.30 | 0.322750 | ||||||||
\(797\) | − | 35700.2i | − | 1.58666i | −0.608793 | − | 0.793329i | \(-0.708346\pi\) | ||
0.608793 | − | 0.793329i | \(-0.291654\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5083.24 | −0.225072 | ||||||||
\(800\) | −10370.1 | − | 13405.0i | −0.458297 | − | 0.592422i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11703.4i | 0.515290i | ||||||||
\(803\) | 22104.2i | 0.971409i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7692.20 | + | 22514.9i | 0.336788 | + | 0.985769i | ||||
\(806\) | −2596.42 | −0.113468 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12115.7i | 0.527511i | ||||||||
\(809\) | 24027.7 | 1.04421 | 0.522106 | − | 0.852881i | \(-0.325147\pi\) | ||||
0.522106 | + | 0.852881i | \(0.325147\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26426.3 | −1.14421 | −0.572104 | − | 0.820181i | \(-0.693873\pi\) | ||||
−0.572104 | + | 0.820181i | \(0.693873\pi\) | |||||||
\(812\) | 1913.43i | 0.0826948i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7029.62 | 0.302688 | ||||||||
\(815\) | 27580.1 | − | 9422.73i | 1.18538 | − | 0.404986i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4832.17i | − | 0.206923i | ||||||
\(818\) | 877.080i | 0.0374895i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1363.26 | − | 3990.23i | −0.0580575 | − | 0.169933i | ||||
\(821\) | 24496.7 | 1.04134 | 0.520669 | − | 0.853758i | \(-0.325682\pi\) | ||||
0.520669 | + | 0.853758i | \(0.325682\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14743.0i | 0.624434i | 0.950011 | + | 0.312217i | \(0.101072\pi\) | ||||
−0.950011 | + | 0.312217i | \(0.898928\pi\) | |||||||
\(824\) | 3610.20 | 0.152630 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8151.52 | −0.343375 | ||||||||
\(827\) | − | 27985.3i | − | 1.17672i | −0.808601 | − | 0.588358i | \(-0.799775\pi\) | ||
0.808601 | − | 0.588358i | \(-0.200225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39350.4 | −1.64861 | −0.824304 | − | 0.566147i | \(-0.808433\pi\) | ||||
−0.824304 | + | 0.566147i | \(0.808433\pi\) | |||||||
\(830\) | −889.000 | − | 2602.08i | −0.0371779 | − | 0.108819i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13327.1i | 0.555331i | ||||||||
\(833\) | 4066.49i | 0.169142i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17344.9 | + | 5925.87i | −0.718855 | + | 0.245597i | ||||
\(836\) | −61460.5 | −2.54265 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 3994.38i | − | 0.164658i | ||||||
\(839\) | −22700.9 | −0.934113 | −0.467057 | − | 0.884227i | \(-0.654686\pi\) | ||||
−0.467057 | + | 0.884227i | \(0.654686\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24235.4 | −0.993704 | ||||||||
\(842\) | − | 7570.65i | − | 0.309860i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14895.8 | −0.607507 | ||||||||
\(845\) | 315.381 | + | 923.112i | 0.0128396 | + | 0.0375811i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 45914.3i | 1.86261i | ||||||||
\(848\) | − | 6801.99i | − | 0.275449i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3345.51 | + | 2588.08i | −0.135000 | + | 0.104436i | ||||
\(851\) | −15338.0 | −0.617838 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34055.9i | 1.36700i | 0.729951 | + | 0.683500i | \(0.239543\pi\) | ||||
−0.729951 | + | 0.683500i | \(0.760457\pi\) | |||||||
\(854\) | 4068.26 | 0.163013 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11894.1 | 0.474921 | ||||||||
\(857\) | − | 22647.0i | − | 0.902693i | −0.892349 | − | 0.451347i | \(-0.850944\pi\) | ||
0.892349 | − | 0.451347i | \(-0.149056\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12157.1 | 0.482882 | 0.241441 | − | 0.970416i | \(-0.422380\pi\) | ||||
0.241441 | + | 0.970416i | \(0.422380\pi\) | |||||||
\(860\) | −2692.72 | + | 919.967i | −0.106769 | + | 0.0364775i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 673.415i | 0.0266086i | ||||||||
\(863\) | 11517.7i | 0.454305i | 0.973859 | + | 0.227153i | \(0.0729417\pi\) | ||||
−0.973859 | + | 0.227153i | \(0.927058\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12425.4 | − | 4245.15i | 0.488413 | − | 0.166866i | ||||
\(866\) | 1811.29 | 0.0710742 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11114.3i | 0.434613i | ||||||||
\(869\) | −28290.6 | −1.10437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37942.2 | −1.47603 | ||||||||
\(872\) | 2715.44i | 0.105455i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11201.9 | −0.433537 | ||||||||
\(875\) | 16094.3 | − | 24397.3i | 0.621813 | − | 0.942605i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27266.1i | − | 1.04984i | −0.851151 | − | 0.524921i | \(-0.824095\pi\) | ||
0.851151 | − | 0.524921i | \(-0.175905\pi\) | |||||||
\(878\) | 558.558i | 0.0214697i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10642.0 | + | 31148.9i | 0.407661 | + | 1.19321i | ||||
\(881\) | −9173.42 | −0.350806 | −0.175403 | − | 0.984497i | \(-0.556123\pi\) | ||||
−0.175403 | + | 0.984497i | \(0.556123\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8150.59i | 0.310633i | 0.987865 | + | 0.155317i | \(0.0496398\pi\) | ||||
−0.987865 | + | 0.155317i | \(0.950360\pi\) | |||||||
\(884\) | 14612.1 | 0.555947 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12282.5 | −0.465733 | ||||||||
\(887\) | 1442.34i | 0.0545986i | 0.999627 | + | 0.0272993i | \(0.00869071\pi\) | ||||
−0.999627 | + | 0.0272993i | \(0.991309\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 57348.9 | 2.16358 | ||||||||
\(890\) | 6793.47 | − | 2320.99i | 0.255862 | − | 0.0874154i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1961.82i | 0.0736398i | ||||||||
\(893\) | 16537.6i | 0.619721i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9082.03 | + | 26582.9i | 0.339194 | + | 0.992812i | ||||
\(896\) | −27449.7 | −1.02347 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6405.54i | 0.238035i | ||||||||
\(899\) | 891.953 | 0.0330904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5911.42 | −0.218577 | ||||||||
\(902\) | − | 2382.26i | − | 0.0879387i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1664.32 | −0.0612329 | ||||||||
\(905\) | 13323.2 | + | 38996.6i | 0.489368 | + | 1.43237i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5472.41i | 0.200340i | 0.994970 | + | 0.100170i | \(0.0319387\pi\) | ||||
−0.994970 | + | 0.100170i | \(0.968061\pi\) | |||||||
\(908\) | 37838.8i | 1.38296i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7981.41 | − | 2726.85i | 0.290749 | − | 0.0993342i | ||||
\(911\) | −23045.6 | −0.838130 | −0.419065 | − | 0.907956i | \(-0.637642\pi\) | ||||
−0.419065 | + | 0.907956i | \(0.637642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18597.4i | 0.674134i | ||||||||
\(914\) | 11611.3 | 0.420204 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −670.136 | −0.0241724 | ||||||||
\(917\) | 20085.4i | 0.723315i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23130.3 | 0.830247 | 0.415124 | − | 0.909765i | \(-0.363738\pi\) | ||||
0.415124 | + | 0.909765i | \(0.363738\pi\) | |||||||
\(920\) | 4443.49 | + | 13006.0i | 0.159236 | + | 0.466080i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6512.88i | 0.232636i | ||||||||
\(923\) | 11944.6i | 0.425959i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11528.8 | + | 14902.9i | 0.409801 | + | 0.529734i | ||||
\(926\) | −11275.0 | −0.400130 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1680.13i | 0.0594320i | ||||||||
\(929\) | −12258.9 | −0.432942 | −0.216471 | − | 0.976289i | \(-0.569455\pi\) | ||||
−0.216471 | + | 0.976289i | \(0.569455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13229.8 | 0.465723 | ||||||||
\(932\) | − | 43237.6i | − | 1.51963i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3781.57 | 0.132481 | ||||||||
\(935\) | 27070.6 | − | 9248.67i | 0.946849 | − | 0.323491i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37083.2i | 1.29291i | 0.762953 | + | 0.646454i | \(0.223749\pi\) | ||||
−0.762953 | + | 0.646454i | \(0.776251\pi\) | |||||||
\(938\) | − | 13567.2i | − | 0.472264i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9215.57 | − | 3148.50i | 0.319765 | − | 0.109247i | ||||
\(941\) | 2612.96 | 0.0905206 | 0.0452603 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452603 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5197.89i | 0.179498i | ||||||||
\(944\) | 24606.5 | 0.848382 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1607.62 | −0.0552518 | ||||||||
\(947\) | 34322.4i | 1.17775i | 0.808224 | + | 0.588875i | \(0.200429\pi\) | ||||
−0.808224 | + | 0.588875i | \(0.799571\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17097.1 | −0.584822 | ||||||||
\(950\) | 8419.95 | + | 10884.2i | 0.287557 | + | 0.371714i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10886.3i | 0.370616i | ||||||||
\(953\) | − | 33734.8i | − | 1.14667i | −0.819321 | − | 0.573335i | \(-0.805649\pi\) | ||
0.819321 | − | 0.573335i | \(-0.194351\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9818.58 | + | 28738.7i | 0.332693 | + | 0.973783i | ||||
\(956\) | −50714.2 | −1.71571 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9288.72i | 0.313262i | ||||||||
\(959\) | 15194.1 | 0.511619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24610.0 | −0.826089 | ||||||||
\(962\) | 5437.25i | 0.182229i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −185.596 | −0.00620088 | ||||||||
\(965\) | 20871.6 | − | 7130.77i | 0.696248 | − | 0.237873i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 27695.9i | − | 0.921033i | −0.887651 | − | 0.460517i | \(-0.847664\pi\) | ||
0.887651 | − | 0.460517i | \(-0.152336\pi\) | |||||||
\(968\) | 26522.9i | 0.880660i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2672.04 | − | 7820.99i | −0.0884475 | − | 0.258883i | ||||
\(971\) | 3160.23 | 0.104446 | 0.0522228 | − | 0.998635i | \(-0.483369\pi\) | ||||
0.0522228 | + | 0.998635i | \(0.483369\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 10454.6i | − | 0.344458i | ||||||
\(974\) | 10278.3 | 0.338128 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12280.6 | −0.402758 | ||||||||
\(977\) | − | 31041.9i | − | 1.01650i | −0.861211 | − | 0.508248i | \(-0.830293\pi\) | ||
0.861211 | − | 0.508248i | \(-0.169707\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48553.8 | −1.58507 | ||||||||
\(980\) | −2518.73 | − | 7372.27i | −0.0821000 | − | 0.240305i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5178.00i | 0.168265i | ||||||||
\(983\) | − | 7417.84i | − | 0.240684i | −0.992732 | − | 0.120342i | \(-0.961601\pi\) | ||
0.992732 | − | 0.120342i | \(-0.0383991\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36039.7 | + | 12313.0i | −1.16581 | + | 0.398298i | ||||
\(986\) | 419.313 | 0.0135433 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 47538.3i | − | 1.53076i | ||||||
\(989\) | 3507.68 | 0.112778 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13109.6 | 0.420221 | 0.210110 | − | 0.977678i | \(-0.432618\pi\) | ||||
0.210110 | + | 0.977678i | \(0.432618\pi\) | |||||||
\(992\) | 9759.16i | 0.312352i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4271.07 | −0.136288 | ||||||||
\(995\) | 3548.56 | + | 10386.5i | 0.113062 | + | 0.330930i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 35703.9i | − | 1.13416i | −0.823664 | − | 0.567079i | \(-0.808074\pi\) | ||
0.823664 | − | 0.567079i | \(-0.191926\pi\) | |||||||
\(998\) | 12710.4i | 0.403148i | ||||||||
\(999\) | 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 | 405.4.b.f.244.10 | 16 | ||
3.2 | odd | 2 | 405.4.b.e.244.7 | 16 | |||
5.2 | odd | 4 | 2025.4.a.bl.1.7 | 16 | |||
5.3 | odd | 4 | 2025.4.a.bl.1.10 | 16 | |||
5.4 | even | 2 | inner | 405.4.b.f.244.7 | 16 | ||
9.2 | odd | 6 | 45.4.j.a.4.7 | ✓ | 32 | ||
9.4 | even | 3 | 135.4.j.a.19.7 | 32 | |||
9.5 | odd | 6 | 45.4.j.a.34.10 | yes | 32 | ||
9.7 | even | 3 | 135.4.j.a.64.10 | 32 | |||
15.2 | even | 4 | 2025.4.a.bk.1.10 | 16 | |||
15.8 | even | 4 | 2025.4.a.bk.1.7 | 16 | |||
15.14 | odd | 2 | 405.4.b.e.244.10 | 16 | |||
45.2 | even | 12 | 225.4.e.g.76.7 | 32 | |||
45.4 | even | 6 | 135.4.j.a.19.10 | 32 | |||
45.14 | odd | 6 | 45.4.j.a.34.7 | yes | 32 | ||
45.23 | even | 12 | 225.4.e.g.151.10 | 32 | |||
45.29 | odd | 6 | 45.4.j.a.4.10 | yes | 32 | ||
45.32 | even | 12 | 225.4.e.g.151.7 | 32 | |||
45.34 | even | 6 | 135.4.j.a.64.7 | 32 | |||
45.38 | even | 12 | 225.4.e.g.76.10 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.j.a.4.7 | ✓ | 32 | 9.2 | odd | 6 | ||
45.4.j.a.4.10 | yes | 32 | 45.29 | odd | 6 | ||
45.4.j.a.34.7 | yes | 32 | 45.14 | odd | 6 | ||
45.4.j.a.34.10 | yes | 32 | 9.5 | odd | 6 | ||
135.4.j.a.19.7 | 32 | 9.4 | even | 3 | |||
135.4.j.a.19.10 | 32 | 45.4 | even | 6 | |||
135.4.j.a.64.7 | 32 | 45.34 | even | 6 | |||
135.4.j.a.64.10 | 32 | 9.7 | even | 3 | |||
225.4.e.g.76.7 | 32 | 45.2 | even | 12 | |||
225.4.e.g.76.10 | 32 | 45.38 | even | 12 | |||
225.4.e.g.151.7 | 32 | 45.32 | even | 12 | |||
225.4.e.g.151.10 | 32 | 45.23 | even | 12 | |||
405.4.b.e.244.7 | 16 | 3.2 | odd | 2 | |||
405.4.b.e.244.10 | 16 | 15.14 | odd | 2 | |||
405.4.b.f.244.7 | 16 | 5.4 | even | 2 | inner | ||
405.4.b.f.244.10 | 16 | 1.1 | even | 1 | trivial | ||
2025.4.a.bk.1.7 | 16 | 15.8 | even | 4 | |||
2025.4.a.bk.1.10 | 16 | 15.2 | even | 4 | |||
2025.4.a.bl.1.7 | 16 | 5.2 | odd | 4 | |||
2025.4.a.bl.1.10 | 16 | 5.3 | odd | 4 |