Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,4,Mod(8,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.8");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.f (of order \(4\), degree \(2\), 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: | \(2.65508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 16x^{10} - 14x^{8} - 512x^{6} + 3889x^{4} + 126224x^{2} + 506944 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(2.02004 - 2.30794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.17 |
Dual form | 45.4.f.a.8.3 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.287902 | + | 0.287902i | −0.101789 | + | 0.101789i | −0.756167 | − | 0.654378i | \(-0.772930\pi\) |
0.654378 | + | 0.756167i | \(0.272930\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.83422i | 0.979278i | ||||||||
\(5\) | −9.93887 | + | 5.12043i | −0.888960 | + | 0.457985i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.0557 | + | 15.0557i | 0.812931 | + | 0.812931i | 0.985072 | − | 0.172141i | \(-0.0550686\pi\) |
−0.172141 | + | 0.985072i | \(0.555069\pi\) | |||||||
\(8\) | −4.55871 | − | 4.55871i | −0.201468 | − | 0.201468i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.38724 | − | 4.33560i | 0.0438684 | − | 0.137104i | ||||
\(11\) | 27.9992i | 0.767462i | 0.923445 | + | 0.383731i | \(0.125361\pi\) | ||||
−0.923445 | + | 0.383731i | \(0.874639\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.49862 | − | 2.49862i | 0.0533071 | − | 0.0533071i | −0.679951 | − | 0.733258i | \(-0.737999\pi\) |
0.733258 | + | 0.679951i | \(0.237999\pi\) | |||||||
\(14\) | −8.66913 | −0.165494 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −60.0489 | −0.938264 | ||||||||
\(17\) | 67.9104 | − | 67.9104i | 0.968864 | − | 0.968864i | −0.0306653 | − | 0.999530i | \(-0.509763\pi\) |
0.999530 | + | 0.0306653i | \(0.00976260\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 95.2200i | − | 1.14974i | −0.818246 | − | 0.574868i | \(-0.805054\pi\) | ||
0.818246 | − | 0.574868i | \(-0.194946\pi\) | |||||||
\(20\) | −40.1146 | − | 77.8634i | −0.448495 | − | 0.870539i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.06104 | − | 8.06104i | −0.0781191 | − | 0.0781191i | ||||
\(23\) | 121.994 | + | 121.994i | 1.10598 | + | 1.10598i | 0.993674 | + | 0.112302i | \(0.0358224\pi\) |
0.112302 | + | 0.993674i | \(0.464178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 72.5624 | − | 101.783i | 0.580499 | − | 0.814261i | ||||
\(26\) | 1.43872i | 0.0108521i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −117.950 | + | 117.950i | −0.796085 | + | 0.796085i | ||||
\(29\) | −99.0852 | −0.634471 | −0.317235 | − | 0.948347i | \(-0.602755\pi\) | ||||
−0.317235 | + | 0.948347i | \(0.602755\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.7800 | −0.166743 | −0.0833716 | − | 0.996519i | \(-0.526569\pi\) | ||||
−0.0833716 | + | 0.996519i | \(0.526569\pi\) | |||||||
\(32\) | 53.7578 | − | 53.7578i | 0.296973 | − | 0.296973i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 39.1031i | 0.197239i | ||||||||
\(35\) | −226.728 | − | 72.5450i | −1.09497 | − | 0.350353i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 271.064 | + | 271.064i | 1.20439 | + | 1.20439i | 0.972816 | + | 0.231578i | \(0.0743888\pi\) |
0.231578 | + | 0.972816i | \(0.425611\pi\) | |||||||
\(38\) | 27.4140 | + | 27.4140i | 0.117030 | + | 0.117030i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 68.6509 | + | 21.9659i | 0.271367 | + | 0.0868277i | ||||
\(41\) | 453.748i | 1.72838i | 0.503166 | + | 0.864190i | \(0.332168\pi\) | ||||
−0.503166 | + | 0.864190i | \(0.667832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 30.5679 | − | 30.5679i | 0.108409 | − | 0.108409i | −0.650822 | − | 0.759230i | \(-0.725576\pi\) |
0.759230 | + | 0.650822i | \(0.225576\pi\) | |||||||
\(44\) | −219.352 | −0.751559 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −70.2445 | −0.225152 | ||||||||
\(47\) | 254.600 | − | 254.600i | 0.790153 | − | 0.790153i | −0.191365 | − | 0.981519i | \(-0.561292\pi\) |
0.981519 | + | 0.191365i | \(0.0612915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 110.348i | 0.321713i | ||||||||
\(50\) | 8.41255 | + | 50.1943i | 0.0237943 | + | 0.141971i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.5748 | + | 19.5748i | 0.0522025 | + | 0.0522025i | ||||
\(53\) | −224.021 | − | 224.021i | −0.580598 | − | 0.580598i | 0.354470 | − | 0.935068i | \(-0.384661\pi\) |
−0.935068 | + | 0.354470i | \(0.884661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −143.368 | − | 278.281i | −0.351486 | − | 0.682243i | ||||
\(56\) | − | 137.269i | − | 0.327560i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 28.5268 | − | 28.5268i | 0.0645820 | − | 0.0645820i | ||||
\(59\) | 483.263 | 1.06636 | 0.533182 | − | 0.846001i | \(-0.320996\pi\) | ||||
0.533182 | + | 0.846001i | \(0.320996\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −264.372 | −0.554908 | −0.277454 | − | 0.960739i | \(-0.589491\pi\) | ||||
−0.277454 | + | 0.960739i | \(0.589491\pi\) | |||||||
\(62\) | 8.28582 | − | 8.28582i | 0.0169726 | − | 0.0169726i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 449.437i | − | 0.877807i | ||||||
\(65\) | −12.0395 | + | 37.6275i | −0.0229740 | + | 0.0718018i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −498.817 | − | 498.817i | −0.909556 | − | 0.909556i | 0.0866805 | − | 0.996236i | \(-0.472374\pi\) |
−0.996236 | + | 0.0866805i | \(0.972374\pi\) | |||||||
\(68\) | 532.025 | + | 532.025i | 0.948788 | + | 0.948788i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 86.1614 | − | 44.3897i | 0.147118 | − | 0.0757940i | ||||
\(71\) | − | 609.904i | − | 1.01947i | −0.860332 | − | 0.509735i | \(-0.829744\pi\) | ||
0.860332 | − | 0.509735i | \(-0.170256\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.6843 | + | 74.6843i | −0.119742 | + | 0.119742i | −0.764438 | − | 0.644697i | \(-0.776984\pi\) |
0.644697 | + | 0.764438i | \(0.276984\pi\) | |||||||
\(74\) | −156.080 | −0.245188 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 745.975 | 1.12591 | ||||||||
\(77\) | −421.548 | + | 421.548i | −0.623894 | + | 0.623894i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 406.574i | 0.579027i | 0.957174 | + | 0.289513i | \(0.0934935\pi\) | ||||
−0.957174 | + | 0.289513i | \(0.906507\pi\) | |||||||
\(80\) | 596.818 | − | 307.476i | 0.834079 | − | 0.429711i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −130.635 | − | 130.635i | −0.175930 | − | 0.175930i | ||||
\(83\) | −652.278 | − | 652.278i | −0.862613 | − | 0.862613i | 0.129028 | − | 0.991641i | \(-0.458814\pi\) |
−0.991641 | + | 0.129028i | \(0.958814\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −327.223 | + | 1022.68i | −0.417556 | + | 1.30501i | ||||
\(86\) | 17.6011i | 0.0220695i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 127.640 | − | 127.640i | 0.154619 | − | 0.154619i | ||||
\(89\) | −139.860 | −0.166575 | −0.0832873 | − | 0.996526i | \(-0.526542\pi\) | ||||
−0.0832873 | + | 0.996526i | \(0.526542\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 75.2369 | 0.0866700 | ||||||||
\(92\) | −955.726 | + | 955.726i | −1.08306 | + | 1.08306i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 146.600i | 0.160857i | ||||||||
\(95\) | 487.567 | + | 946.380i | 0.526561 | + | 1.02207i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 557.633 | + | 557.633i | 0.583701 | + | 0.583701i | 0.935918 | − | 0.352217i | \(-0.114572\pi\) |
−0.352217 | + | 0.935918i | \(0.614572\pi\) | |||||||
\(98\) | −31.7693 | − | 31.7693i | −0.0327468 | − | 0.0327468i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 797.388 | + | 568.470i | 0.797388 | + | 0.568470i | ||||
\(101\) | − | 299.833i | − | 0.295391i | −0.989033 | − | 0.147695i | \(-0.952814\pi\) | ||
0.989033 | − | 0.147695i | \(-0.0471855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 577.974 | − | 577.974i | 0.552907 | − | 0.552907i | −0.374372 | − | 0.927279i | \(-0.622142\pi\) |
0.927279 | + | 0.374372i | \(0.122142\pi\) | |||||||
\(104\) | −22.7810 | −0.0214794 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 128.992 | 0.118197 | ||||||||
\(107\) | −216.994 | + | 216.994i | −0.196053 | + | 0.196053i | −0.798305 | − | 0.602253i | \(-0.794270\pi\) |
0.602253 | + | 0.798305i | \(0.294270\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 936.415i | 0.822865i | 0.911440 | + | 0.411432i | \(0.134971\pi\) | ||||
−0.911440 | + | 0.411432i | \(0.865029\pi\) | |||||||
\(110\) | 121.394 | + | 38.8417i | 0.105222 | + | 0.0336673i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −904.077 | − | 904.077i | −0.762743 | − | 0.762743i | ||||
\(113\) | −1084.00 | − | 1084.00i | −0.902428 | − | 0.902428i | 0.0932173 | − | 0.995646i | \(-0.470285\pi\) |
−0.995646 | + | 0.0932173i | \(0.970285\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1837.14 | − | 587.820i | −1.48969 | − | 0.476648i | ||||
\(116\) | − | 776.256i | − | 0.621323i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −139.132 | + | 139.132i | −0.108544 | + | 0.108544i | ||||
\(119\) | 2044.88 | 1.57524 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 547.043 | 0.411001 | ||||||||
\(122\) | 76.1133 | − | 76.1133i | 0.0564834 | − | 0.0564834i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 225.469i | − | 0.163288i | ||||||
\(125\) | −200.018 | + | 1383.15i | −0.143121 | + | 0.989705i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −915.574 | − | 915.574i | −0.639717 | − | 0.639717i | 0.310769 | − | 0.950486i | \(-0.399414\pi\) |
−0.950486 | + | 0.310769i | \(0.899414\pi\) | |||||||
\(128\) | 559.457 | + | 559.457i | 0.386324 | + | 0.386324i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.36684 | − | 14.2992i | −0.00497011 | − | 0.00964711i | ||||
\(131\) | − | 629.329i | − | 0.419731i | −0.977730 | − | 0.209865i | \(-0.932697\pi\) | ||
0.977730 | − | 0.209865i | \(-0.0673026\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1433.60 | − | 1433.60i | 0.934655 | − | 0.934655i | ||||
\(134\) | 287.221 | 0.185165 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −619.167 | −0.390391 | ||||||||
\(137\) | 660.931 | − | 660.931i | 0.412169 | − | 0.412169i | −0.470325 | − | 0.882494i | \(-0.655863\pi\) |
0.882494 | + | 0.470325i | \(0.155863\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1378.35i | − | 0.841081i | −0.907274 | − | 0.420540i | \(-0.861840\pi\) | ||
0.907274 | − | 0.420540i | \(-0.138160\pi\) | |||||||
\(140\) | 568.334 | − | 1776.24i | 0.343093 | − | 1.07228i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 175.593 | + | 175.593i | 0.103771 | + | 0.103771i | ||||
\(143\) | 69.9595 | + | 69.9595i | 0.0409112 | + | 0.0409112i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 984.795 | − | 507.359i | 0.564019 | − | 0.290578i | ||||
\(146\) | − | 43.0035i | − | 0.0243767i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2123.57 | + | 2123.57i | −1.17944 | + | 1.17944i | ||||
\(149\) | −924.719 | −0.508429 | −0.254215 | − | 0.967148i | \(-0.581817\pi\) | ||||
−0.254215 | + | 0.967148i | \(0.581817\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −401.768 | −0.216526 | −0.108263 | − | 0.994122i | \(-0.534529\pi\) | ||||
−0.108263 | + | 0.994122i | \(0.534529\pi\) | |||||||
\(152\) | −434.080 | + | 434.080i | −0.231635 | + | 0.231635i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 242.729i | − | 0.127011i | ||||||
\(155\) | 286.041 | − | 147.366i | 0.148228 | − | 0.0763659i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1305.55 | + | 1305.55i | 0.663659 | + | 0.663659i | 0.956240 | − | 0.292582i | \(-0.0945144\pi\) |
−0.292582 | + | 0.956240i | \(0.594514\pi\) | |||||||
\(158\) | −117.053 | − | 117.053i | −0.0589384 | − | 0.0589384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −259.029 | + | 809.556i | −0.127988 | + | 0.400006i | ||||
\(161\) | 3673.40i | 1.79816i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −78.8393 | + | 78.8393i | −0.0378845 | + | 0.0378845i | −0.725795 | − | 0.687911i | \(-0.758528\pi\) |
0.687911 | + | 0.725795i | \(0.258528\pi\) | |||||||
\(164\) | −3554.77 | −1.69256 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 375.585 | 0.175609 | ||||||||
\(167\) | 428.116 | − | 428.116i | 0.198375 | − | 0.198375i | −0.600928 | − | 0.799303i | \(-0.705202\pi\) |
0.799303 | + | 0.600928i | \(0.205202\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2184.51i | 0.994317i | ||||||||
\(170\) | −200.225 | − | 388.641i | −0.0903325 | − | 0.175338i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 239.476 | + | 239.476i | 0.106162 | + | 0.106162i | ||||
\(173\) | 1390.57 | + | 1390.57i | 0.611114 | + | 0.611114i | 0.943236 | − | 0.332122i | \(-0.107765\pi\) |
−0.332122 | + | 0.943236i | \(0.607765\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2624.88 | − | 439.930i | 1.13384 | − | 0.190032i | ||||
\(176\) | − | 1681.32i | − | 0.720082i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 40.2660 | − | 40.2660i | 0.0169554 | − | 0.0169554i | ||||
\(179\) | 110.674 | 0.0462131 | 0.0231065 | − | 0.999733i | \(-0.492644\pi\) | ||||
0.0231065 | + | 0.999733i | \(0.492644\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 700.593 | 0.287706 | 0.143853 | − | 0.989599i | \(-0.454051\pi\) | ||||
0.143853 | + | 0.989599i | \(0.454051\pi\) | |||||||
\(182\) | −21.6609 | + | 21.6609i | −0.00882203 | + | 0.00882203i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1112.27i | − | 0.445638i | ||||||
\(185\) | −4082.03 | − | 1306.11i | −1.62225 | − | 0.519064i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1901.44 | + | 1901.44i | 0.743567 | + | 0.743567i | ||||
\(188\) | 1994.59 | + | 1994.59i | 0.773780 | + | 0.773780i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −412.836 | − | 132.093i | −0.157633 | − | 0.0504370i | ||||
\(191\) | 2214.32i | 0.838862i | 0.907787 | + | 0.419431i | \(0.137770\pi\) | ||||
−0.907787 | + | 0.419431i | \(0.862230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1964.16 | + | 1964.16i | −0.732556 | + | 0.732556i | −0.971125 | − | 0.238569i | \(-0.923322\pi\) |
0.238569 | + | 0.971125i | \(0.423322\pi\) | |||||||
\(194\) | −321.087 | −0.118828 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −864.488 | −0.315047 | ||||||||
\(197\) | 2700.70 | − | 2700.70i | 0.976735 | − | 0.976735i | −0.0230004 | − | 0.999735i | \(-0.507322\pi\) |
0.999735 | + | 0.0230004i | \(0.00732189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 841.195i | − | 0.299652i | −0.988712 | − | 0.149826i | \(-0.952129\pi\) | ||
0.988712 | − | 0.149826i | \(-0.0478713\pi\) | |||||||
\(200\) | −794.788 | + | 133.206i | −0.281000 | + | 0.0470955i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 86.3224 | + | 86.3224i | 0.0300674 | + | 0.0300674i | ||||
\(203\) | −1491.80 | − | 1491.80i | −0.515781 | − | 0.515781i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2323.39 | − | 4509.75i | −0.791572 | − | 1.53646i | ||||
\(206\) | 332.800i | 0.112559i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −150.039 | + | 150.039i | −0.0500161 | + | 0.0500161i | ||||
\(209\) | 2666.09 | 0.882379 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3970.06 | −1.29531 | −0.647654 | − | 0.761934i | \(-0.724250\pi\) | ||||
−0.647654 | + | 0.761934i | \(0.724250\pi\) | |||||||
\(212\) | 1755.03 | − | 1755.03i | 0.568567 | − | 0.568567i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 124.946i | − | 0.0399119i | ||||||
\(215\) | −147.290 | + | 460.332i | −0.0467213 | + | 0.146020i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −433.303 | − | 433.303i | −0.135551 | − | 0.135551i | ||||
\(218\) | −269.596 | − | 269.596i | −0.0837584 | − | 0.0837584i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2180.11 | − | 1123.18i | 0.668106 | − | 0.344203i | ||||
\(221\) | − | 339.365i | − | 0.103295i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3600.34 | − | 3600.34i | 1.08115 | − | 1.08115i | 0.0847496 | − | 0.996402i | \(-0.472991\pi\) |
0.996402 | − | 0.0847496i | \(-0.0270090\pi\) | |||||||
\(224\) | 1618.72 | 0.482837 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 624.173 | 0.183714 | ||||||||
\(227\) | 1734.81 | − | 1734.81i | 0.507239 | − | 0.507239i | −0.406439 | − | 0.913678i | \(-0.633230\pi\) |
0.913678 | + | 0.406439i | \(0.133230\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3467.74i | − | 1.00067i | −0.865831 | − | 0.500337i | \(-0.833209\pi\) | ||
0.865831 | − | 0.500337i | \(-0.166791\pi\) | |||||||
\(230\) | 698.151 | − | 359.682i | 0.200151 | − | 0.103116i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 451.700 | + | 451.700i | 0.127826 | + | 0.127826i | ||||
\(233\) | 1070.17 | + | 1070.17i | 0.300899 | + | 0.300899i | 0.841365 | − | 0.540467i | \(-0.181752\pi\) |
−0.540467 | + | 0.841365i | \(0.681752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1226.78 | + | 3834.10i | −0.340536 | + | 1.06429i | ||||
\(236\) | 3785.99i | 1.04427i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −588.724 | + | 588.724i | −0.160342 | + | 0.160342i | ||||
\(239\) | −3909.44 | −1.05808 | −0.529038 | − | 0.848598i | \(-0.677447\pi\) | ||||
−0.529038 | + | 0.848598i | \(0.677447\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4787.09 | −1.27952 | −0.639759 | − | 0.768576i | \(-0.720966\pi\) | ||||
−0.639759 | + | 0.768576i | \(0.720966\pi\) | |||||||
\(242\) | −157.495 | + | 157.495i | −0.0418353 | + | 0.0418353i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2071.15i | − | 0.543409i | ||||||
\(245\) | −565.027 | − | 1096.73i | −0.147340 | − | 0.285990i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −237.919 | − | 237.919i | −0.0612891 | − | 0.0612891i | ||||
\(248\) | 131.200 | + | 131.200i | 0.0335935 | + | 0.0335935i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −340.628 | − | 455.799i | −0.0861727 | − | 0.115309i | ||||
\(251\) | − | 2337.42i | − | 0.587794i | −0.955837 | − | 0.293897i | \(-0.905048\pi\) | ||
0.955837 | − | 0.293897i | \(-0.0949523\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3415.73 | + | 3415.73i | −0.848795 | + | 0.848795i | ||||
\(254\) | 527.191 | 0.130232 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3273.36 | 0.799160 | ||||||||
\(257\) | −977.764 | + | 977.764i | −0.237320 | + | 0.237320i | −0.815740 | − | 0.578419i | \(-0.803670\pi\) |
0.578419 | + | 0.815740i | \(0.303670\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8162.10i | 1.95818i | ||||||||
\(260\) | −294.782 | − | 94.3199i | −0.0703139 | − | 0.0224980i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 181.185 | + | 181.185i | 0.0427239 | + | 0.0427239i | ||||
\(263\) | −790.690 | − | 790.690i | −0.185384 | − | 0.185384i | 0.608313 | − | 0.793697i | \(-0.291847\pi\) |
−0.793697 | + | 0.608313i | \(0.791847\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3373.60 | + | 1079.43i | 0.782034 | + | 0.250223i | ||||
\(266\) | 825.474i | 0.190275i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3907.85 | − | 3907.85i | 0.890708 | − | 0.890708i | ||||
\(269\) | −3954.49 | −0.896317 | −0.448159 | − | 0.893954i | \(-0.647920\pi\) | ||||
−0.448159 | + | 0.893954i | \(0.647920\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7863.30 | 1.76259 | 0.881295 | − | 0.472567i | \(-0.156673\pi\) | ||||
0.881295 | + | 0.472567i | \(0.156673\pi\) | |||||||
\(272\) | −4077.94 | + | 4077.94i | −0.909050 | + | 0.909050i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 380.567i | 0.0839083i | ||||||||
\(275\) | 2849.83 | + | 2031.69i | 0.624915 | + | 0.445511i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 908.009 | + | 908.009i | 0.196957 | + | 0.196957i | 0.798694 | − | 0.601737i | \(-0.205525\pi\) |
−0.601737 | + | 0.798694i | \(0.705525\pi\) | |||||||
\(278\) | 396.830 | + | 396.830i | 0.0856126 | + | 0.0856126i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 702.876 | + | 1364.30i | 0.150017 | + | 0.291187i | ||||
\(281\) | − | 7102.70i | − | 1.50787i | −0.656949 | − | 0.753935i | \(-0.728153\pi\) | ||
0.656949 | − | 0.753935i | \(-0.271847\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4721.93 | + | 4721.93i | −0.991837 | + | 0.991837i | −0.999967 | − | 0.00813014i | \(-0.997412\pi\) |
0.00813014 | + | 0.999967i | \(0.497412\pi\) | |||||||
\(284\) | 4778.13 | 0.998344 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −40.2829 | −0.00832860 | ||||||||
\(287\) | −6831.49 | + | 6831.49i | −1.40505 | + | 1.40505i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 4310.65i | − | 0.877396i | ||||||
\(290\) | −137.455 | + | 429.594i | −0.0278332 | + | 0.0869884i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −585.094 | − | 585.094i | −0.117260 | − | 0.117260i | ||||
\(293\) | 2078.57 | + | 2078.57i | 0.414442 | + | 0.414442i | 0.883283 | − | 0.468841i | \(-0.155328\pi\) |
−0.468841 | + | 0.883283i | \(0.655328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4803.09 | + | 2474.51i | −0.947955 | + | 0.488379i | ||||
\(296\) | − | 2471.40i | − | 0.485294i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 266.229 | − | 266.229i | 0.0517524 | − | 0.0517524i | ||||
\(299\) | 609.632 | 0.117913 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 920.443 | 0.176257 | ||||||||
\(302\) | 115.670 | − | 115.670i | 0.0220399 | − | 0.0220399i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5717.85i | 1.07875i | ||||||||
\(305\) | 2627.56 | − | 1353.70i | 0.493291 | − | 0.254140i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5325.58 | − | 5325.58i | −0.990056 | − | 0.990056i | 0.00989542 | − | 0.999951i | \(-0.496850\pi\) |
−0.999951 | + | 0.00989542i | \(0.996850\pi\) | |||||||
\(308\) | −3302.50 | − | 3302.50i | −0.610966 | − | 0.610966i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −39.9248 | + | 124.779i | −0.00731476 | + | 0.0228611i | ||||
\(311\) | 2005.56i | 0.365676i | 0.983143 | + | 0.182838i | \(0.0585283\pi\) | ||||
−0.983143 | + | 0.182838i | \(0.941472\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5026.49 | − | 5026.49i | 0.907713 | − | 0.907713i | −0.0883746 | − | 0.996087i | \(-0.528167\pi\) |
0.996087 | + | 0.0883746i | \(0.0281673\pi\) | |||||||
\(314\) | −751.742 | −0.135106 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3185.19 | −0.567028 | ||||||||
\(317\) | 3137.15 | − | 3137.15i | 0.555836 | − | 0.555836i | −0.372283 | − | 0.928119i | \(-0.621425\pi\) |
0.928119 | + | 0.372283i | \(0.121425\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2774.31i | − | 0.486933i | ||||||
\(320\) | 2301.31 | + | 4466.90i | 0.402022 | + | 0.780335i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1057.58 | − | 1057.58i | −0.183033 | − | 0.183033i | ||||
\(323\) | −6466.43 | − | 6466.43i | −1.11394 | − | 1.11394i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −73.0101 | − | 435.622i | −0.0124611 | − | 0.0743506i | ||||
\(326\) | − | 45.3960i | − | 0.00771243i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2068.50 | − | 2068.50i | 0.348214 | − | 0.348214i | ||||
\(329\) | 7666.35 | 1.28468 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2978.02 | 0.494523 | 0.247261 | − | 0.968949i | \(-0.420469\pi\) | ||||
0.247261 | + | 0.968949i | \(0.420469\pi\) | |||||||
\(332\) | 5110.10 | − | 5110.10i | 0.844738 | − | 0.844738i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 246.511i | 0.0403847i | ||||||||
\(335\) | 7511.84 | + | 2403.52i | 1.22512 | + | 0.391996i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5985.73 | − | 5985.73i | −0.967547 | − | 0.967547i | 0.0319428 | − | 0.999490i | \(-0.489831\pi\) |
−0.999490 | + | 0.0319428i | \(0.989831\pi\) | |||||||
\(338\) | −628.926 | − | 628.926i | −0.101210 | − | 0.101210i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8011.93 | − | 2563.54i | −1.27796 | − | 0.408904i | ||||
\(341\) | − | 805.818i | − | 0.127969i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3502.74 | − | 3502.74i | 0.551400 | − | 0.551400i | ||||
\(344\) | −278.701 | −0.0436818 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −800.693 | −0.124409 | ||||||||
\(347\) | −8183.37 | + | 8183.37i | −1.26601 | + | 1.26601i | −0.317881 | + | 0.948130i | \(0.602971\pi\) |
−0.948130 | + | 0.317881i | \(0.897029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1421.22i | − | 0.217983i | −0.994043 | − | 0.108991i | \(-0.965238\pi\) | ||
0.994043 | − | 0.108991i | \(-0.0347621\pi\) | |||||||
\(350\) | −629.053 | + | 882.366i | −0.0960694 | + | 0.134756i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1505.18 | + | 1505.18i | 0.227916 | + | 0.227916i | ||||
\(353\) | 1399.56 | + | 1399.56i | 0.211023 | + | 0.211023i | 0.804702 | − | 0.593679i | \(-0.202325\pi\) |
−0.593679 | + | 0.804702i | \(0.702325\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3122.97 | + | 6061.76i | 0.466902 | + | 0.906268i | ||||
\(356\) | − | 1095.70i | − | 0.163123i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.8632 | + | 31.8632i | −0.00470397 | + | 0.00470397i | ||||
\(359\) | 4313.98 | 0.634215 | 0.317108 | − | 0.948390i | \(-0.397288\pi\) | ||||
0.317108 | + | 0.948390i | \(0.397288\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2207.85 | −0.321891 | ||||||||
\(362\) | −201.702 | + | 201.702i | −0.0292852 | + | 0.0292852i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 589.423i | 0.0848740i | ||||||||
\(365\) | 359.862 | − | 1124.69i | 0.0516056 | − | 0.161285i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4533.34 | + | 4533.34i | 0.644792 | + | 0.644792i | 0.951730 | − | 0.306938i | \(-0.0993043\pi\) |
−0.306938 | + | 0.951730i | \(0.599304\pi\) | |||||||
\(368\) | −7325.59 | − | 7325.59i | −1.03770 | − | 1.03770i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1551.26 | − | 799.194i | 0.217962 | − | 0.112292i | ||||
\(371\) | − | 6745.59i | − | 0.943972i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2787.95 | + | 2787.95i | −0.387010 | + | 0.387010i | −0.873620 | − | 0.486609i | \(-0.838234\pi\) |
0.486609 | + | 0.873620i | \(0.338234\pi\) | |||||||
\(374\) | −1094.86 | −0.151374 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2321.29 | −0.318382 | ||||||||
\(377\) | −247.576 | + | 247.576i | −0.0338218 | + | 0.0338218i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8409.09i | 1.13970i | 0.821749 | + | 0.569849i | \(0.192998\pi\) | ||||
−0.821749 | + | 0.569849i | \(0.807002\pi\) | |||||||
\(380\) | −7414.15 | + | 3819.71i | −1.00089 | + | 0.515650i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −637.508 | − | 637.508i | −0.0853868 | − | 0.0853868i | ||||
\(383\) | 8507.38 | + | 8507.38i | 1.13500 | + | 1.13500i | 0.989333 | + | 0.145672i | \(0.0465343\pi\) |
0.145672 | + | 0.989333i | \(0.453466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2031.20 | − | 6348.22i | 0.268883 | − | 0.840351i | ||||
\(386\) | − | 1130.97i | − | 0.149132i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4368.62 | + | 4368.62i | −0.571606 | + | 0.571606i | ||||
\(389\) | −8641.23 | −1.12629 | −0.563146 | − | 0.826357i | \(-0.690409\pi\) | ||||
−0.563146 | + | 0.826357i | \(0.690409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16569.3 | 2.14308 | ||||||||
\(392\) | 503.042 | − | 503.042i | 0.0648150 | − | 0.0648150i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1555.07i | 0.198841i | ||||||||
\(395\) | −2081.83 | − | 4040.89i | −0.265186 | − | 0.514732i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1902.21 | + | 1902.21i | 0.240476 | + | 0.240476i | 0.817047 | − | 0.576571i | \(-0.195610\pi\) |
−0.576571 | + | 0.817047i | \(0.695610\pi\) | |||||||
\(398\) | 242.182 | + | 242.182i | 0.0305012 | + | 0.0305012i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4357.29 | + | 6111.93i | −0.544661 | + | 0.763991i | ||||
\(401\) | 13640.1i | 1.69864i | 0.527882 | + | 0.849318i | \(0.322986\pi\) | ||||
−0.527882 | + | 0.849318i | \(0.677014\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −71.9103 | + | 71.9103i | −0.00888860 | + | 0.00888860i | ||||
\(404\) | 2348.96 | 0.289270 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 858.982 | 0.105001 | ||||||||
\(407\) | −7589.57 | + | 7589.57i | −0.924327 | + | 0.924327i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6395.02i | − | 0.773138i | −0.922260 | − | 0.386569i | \(-0.873660\pi\) | ||
0.922260 | − | 0.386569i | \(-0.126340\pi\) | |||||||
\(410\) | 1967.27 | + | 629.458i | 0.236968 | + | 0.0758212i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4527.98 | + | 4527.98i | 0.541450 | + | 0.541450i | ||||
\(413\) | 7275.86 | + | 7275.86i | 0.866880 | + | 0.866880i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9822.86 | + | 3142.97i | 1.16189 | + | 0.371764i | ||||
\(416\) | − | 268.641i | − | 0.0316615i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −767.572 | + | 767.572i | −0.0898162 | + | 0.0898162i | ||||
\(419\) | −8474.94 | −0.988133 | −0.494067 | − | 0.869424i | \(-0.664490\pi\) | ||||
−0.494067 | + | 0.869424i | \(0.664490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9069.21 | −1.04990 | −0.524948 | − | 0.851134i | \(-0.675915\pi\) | ||||
−0.524948 | + | 0.851134i | \(0.675915\pi\) | |||||||
\(422\) | 1142.99 | − | 1142.99i | 0.131848 | − | 0.131848i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2042.49i | 0.233944i | ||||||||
\(425\) | −1984.35 | − | 11839.8i | −0.226483 | − | 1.35133i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3980.30 | − | 3980.30i | −0.451102 | − | 0.451102i | ||||
\(428\) | −1699.98 | − | 1699.98i | −0.191990 | − | 0.191990i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −90.1254 | − | 174.936i | −0.0101075 | − | 0.0196189i | ||||
\(431\) | − | 8388.11i | − | 0.937450i | −0.883344 | − | 0.468725i | \(-0.844713\pi\) | ||
0.883344 | − | 0.468725i | \(-0.155287\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4132.17 | + | 4132.17i | −0.458613 | + | 0.458613i | −0.898200 | − | 0.439587i | \(-0.855125\pi\) |
0.439587 | + | 0.898200i | \(0.355125\pi\) | |||||||
\(434\) | 249.498 | 0.0275951 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7336.08 | −0.805814 | ||||||||
\(437\) | 11616.2 | − | 11616.2i | 1.27158 | − | 1.27158i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10498.9i | − | 1.14143i | −0.821149 | − | 0.570714i | \(-0.806667\pi\) | ||
0.821149 | − | 0.570714i | \(-0.193333\pi\) | |||||||
\(440\) | −615.028 | + | 1922.17i | −0.0666370 | + | 0.208264i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 97.7038 | + | 97.7038i | 0.0105142 | + | 0.0105142i | ||||
\(443\) | 1465.93 | + | 1465.93i | 0.157220 | + | 0.157220i | 0.781333 | − | 0.624114i | \(-0.214540\pi\) |
−0.624114 | + | 0.781333i | \(0.714540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1390.05 | − | 716.144i | 0.148078 | − | 0.0762887i | ||||
\(446\) | 2073.09i | 0.220098i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6766.58 | − | 6766.58i | 0.713596 | − | 0.713596i | ||||
\(449\) | −6295.42 | −0.661691 | −0.330846 | − | 0.943685i | \(-0.607334\pi\) | ||||
−0.330846 | + | 0.943685i | \(0.607334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12704.6 | −1.32647 | ||||||||
\(452\) | 8492.32 | − | 8492.32i | 0.883728 | − | 0.883728i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 998.909i | 0.103262i | ||||||||
\(455\) | −747.770 | + | 385.245i | −0.0770462 | + | 0.0396936i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9065.09 | + | 9065.09i | 0.927893 | + | 0.927893i | 0.997570 | − | 0.0696767i | \(-0.0221968\pi\) |
−0.0696767 | + | 0.997570i | \(0.522197\pi\) | |||||||
\(458\) | 998.368 | + | 998.368i | 0.101857 | + | 0.101857i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4605.11 | − | 14392.6i | 0.466771 | − | 1.45882i | ||||
\(461\) | 13305.5i | 1.34424i | 0.740440 | + | 0.672122i | \(0.234617\pi\) | ||||
−0.740440 | + | 0.672122i | \(0.765383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3124.86 | + | 3124.86i | −0.313660 | + | 0.313660i | −0.846326 | − | 0.532666i | \(-0.821190\pi\) |
0.532666 | + | 0.846326i | \(0.321190\pi\) | |||||||
\(464\) | 5949.95 | 0.595301 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −616.210 | −0.0612562 | ||||||||
\(467\) | 4255.07 | − | 4255.07i | 0.421629 | − | 0.421629i | −0.464135 | − | 0.885764i | \(-0.653635\pi\) |
0.885764 | + | 0.464135i | \(0.153635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 15020.1i | − | 1.47881i | ||||||
\(470\) | −750.653 | − | 1457.04i | −0.0736703 | − | 0.142996i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2203.05 | − | 2203.05i | −0.214838 | − | 0.214838i | ||||
\(473\) | 855.879 | + | 855.879i | 0.0831995 | + | 0.0831995i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9691.74 | − | 6909.39i | −0.936184 | − | 0.667420i | ||||
\(476\) | 16020.0i | 1.54260i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1125.53 | − | 1125.53i | 0.107700 | − | 0.107700i | ||||
\(479\) | 10625.2 | 1.01352 | 0.506761 | − | 0.862087i | \(-0.330843\pi\) | ||||
0.506761 | + | 0.862087i | \(0.330843\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1354.57 | 0.128406 | ||||||||
\(482\) | 1378.21 | − | 1378.21i | 0.130241 | − | 0.130241i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4285.66i | 0.402485i | ||||||||
\(485\) | −8397.56 | − | 2686.92i | −0.786213 | − | 0.251560i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3269.03 | − | 3269.03i | −0.304177 | − | 0.304177i | 0.538469 | − | 0.842645i | \(-0.319003\pi\) |
−0.842645 | + | 0.538469i | \(0.819003\pi\) | |||||||
\(488\) | 1205.19 | + | 1205.19i | 0.111796 | + | 0.111796i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 478.424 | + | 153.079i | 0.0441081 | + | 0.0141130i | ||||
\(491\) | − | 18791.1i | − | 1.72715i | −0.504220 | − | 0.863575i | \(-0.668220\pi\) | ||
0.504220 | − | 0.863575i | \(-0.331780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6728.92 | + | 6728.92i | −0.614716 | + | 0.614716i | ||||
\(494\) | 136.995 | 0.0124771 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1728.21 | 0.156449 | ||||||||
\(497\) | 9182.53 | − | 9182.53i | 0.828758 | − | 0.828758i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7220.67i | 0.647778i | 0.946095 | + | 0.323889i | \(0.104990\pi\) | ||||
−0.946095 | + | 0.323889i | \(0.895010\pi\) | |||||||
\(500\) | −10835.9 | − | 1566.99i | −0.969197 | − | 0.140156i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 672.947 | + | 672.947i | 0.0598308 | + | 0.0598308i | ||||
\(503\) | 2081.38 | + | 2081.38i | 0.184501 | + | 0.184501i | 0.793314 | − | 0.608813i | \(-0.208354\pi\) |
−0.608813 | + | 0.793314i | \(0.708354\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1535.27 | + | 2980.00i | 0.135285 | + | 0.262590i | ||||
\(506\) | − | 1966.79i | − | 0.172796i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7172.81 | − | 7172.81i | 0.626461 | − | 0.626461i | ||||
\(509\) | −12624.1 | −1.09932 | −0.549659 | − | 0.835389i | \(-0.685242\pi\) | ||||
−0.549659 | + | 0.835389i | \(0.685242\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2248.85 | −0.194683 | ||||||||
\(512\) | −5418.06 | + | 5418.06i | −0.467669 | + | 0.467669i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 563.001i | − | 0.0483130i | ||||||
\(515\) | −2784.93 | + | 8703.88i | −0.238289 | + | 0.744735i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7128.60 | + | 7128.60i | 0.606413 | + | 0.606413i | ||||
\(518\) | −2349.89 | − | 2349.89i | −0.199321 | − | 0.199321i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 226.417 | − | 116.648i | 0.0190943 | − | 0.00983724i | ||||
\(521\) | 11837.5i | 0.995409i | 0.867347 | + | 0.497705i | \(0.165824\pi\) | ||||
−0.867347 | + | 0.497705i | \(0.834176\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5538.72 | + | 5538.72i | −0.463081 | + | 0.463081i | −0.899664 | − | 0.436583i | \(-0.856189\pi\) |
0.436583 | + | 0.899664i | \(0.356189\pi\) | |||||||
\(524\) | 4930.31 | 0.411033 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 455.282 | 0.0377400 | ||||||||
\(527\) | −1954.46 | + | 1954.46i | −0.161552 | + | 0.161552i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17597.9i | 1.44637i | ||||||||
\(530\) | −1282.04 | + | 660.496i | −0.105072 | + | 0.0541323i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11231.2 | + | 11231.2i | 0.915287 | + | 0.915287i | ||||
\(533\) | 1133.74 | + | 1133.74i | 0.0921349 | + | 0.0921349i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1045.57 | − | 3267.78i | 0.0844937 | − | 0.264072i | ||||
\(536\) | 4547.92i | 0.366493i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1138.51 | − | 1138.51i | 0.0912350 | − | 0.0912350i | ||||
\(539\) | −3089.65 | −0.246903 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5207.24 | 0.413820 | 0.206910 | − | 0.978360i | \(-0.433659\pi\) | ||||
0.206910 | + | 0.978360i | \(0.433659\pi\) | |||||||
\(542\) | −2263.86 | + | 2263.86i | −0.179412 | + | 0.179412i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 7301.44i | − | 0.575453i | ||||||
\(545\) | −4794.85 | − | 9306.91i | −0.376860 | − | 0.731494i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3940.59 | − | 3940.59i | −0.308021 | − | 0.308021i | 0.536121 | − | 0.844141i | \(-0.319889\pi\) |
−0.844141 | + | 0.536121i | \(0.819889\pi\) | |||||||
\(548\) | 5177.88 | + | 5177.88i | 0.403628 | + | 0.403628i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1405.40 | + | 235.545i | −0.108957 | + | 0.0182612i | ||||
\(551\) | 9434.89i | 0.729473i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6121.25 | + | 6121.25i | −0.470709 | + | 0.470709i | ||||
\(554\) | −522.836 | −0.0400959 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10798.3 | 0.823652 | ||||||||
\(557\) | −2850.64 | + | 2850.64i | −0.216850 | + | 0.216850i | −0.807170 | − | 0.590320i | \(-0.799002\pi\) |
0.590320 | + | 0.807170i | \(0.299002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 152.755i | − | 0.0115579i | ||||||
\(560\) | 13614.8 | + | 4356.25i | 1.02737 | + | 0.328723i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2044.88 | + | 2044.88i | 0.153484 | + | 0.153484i | ||||
\(563\) | −12845.3 | − | 12845.3i | −0.961569 | − | 0.961569i | 0.0377198 | − | 0.999288i | \(-0.487991\pi\) |
−0.999288 | + | 0.0377198i | \(0.987991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16324.3 | + | 5223.21i | 1.21552 | + | 0.388924i | ||||
\(566\) | − | 2718.91i | − | 0.201916i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2780.38 | + | 2780.38i | −0.205391 | + | 0.205391i | ||||
\(569\) | −25072.7 | −1.84728 | −0.923639 | − | 0.383263i | \(-0.874800\pi\) | ||||
−0.923639 | + | 0.383263i | \(0.874800\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3587.24 | −0.262909 | −0.131455 | − | 0.991322i | \(-0.541965\pi\) | ||||
−0.131455 | + | 0.991322i | \(0.541965\pi\) | |||||||
\(572\) | −548.078 | + | 548.078i | −0.0400635 | + | 0.0400635i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 3933.60i | − | 0.286037i | ||||||
\(575\) | 21269.0 | − | 3564.68i | 1.54257 | − | 0.258534i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 760.083 | + | 760.083i | 0.0548400 | + | 0.0548400i | 0.733995 | − | 0.679155i | \(-0.237654\pi\) |
−0.679155 | + | 0.733995i | \(0.737654\pi\) | |||||||
\(578\) | 1241.04 | + | 1241.04i | 0.0893091 | + | 0.0893091i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3974.76 | + | 7715.11i | 0.284557 | + | 0.552332i | ||||
\(581\) | − | 19641.0i | − | 1.40249i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6272.43 | − | 6272.43i | 0.445587 | − | 0.445587i | ||||
\(584\) | 680.928 | 0.0482483 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1196.85 | −0.0843711 | ||||||||
\(587\) | −8165.43 | + | 8165.43i | −0.574146 | + | 0.574146i | −0.933284 | − | 0.359139i | \(-0.883071\pi\) |
0.359139 | + | 0.933284i | \(0.383071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2740.43i | 0.191711i | ||||||||
\(590\) | 670.402 | − | 2095.24i | 0.0467797 | − | 0.146203i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16277.1 | − | 16277.1i | −1.13004 | − | 1.13004i | ||||
\(593\) | 9861.32 | + | 9861.32i | 0.682893 | + | 0.682893i | 0.960651 | − | 0.277758i | \(-0.0895913\pi\) |
−0.277758 | + | 0.960651i | \(0.589591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20323.8 | + | 10470.6i | −1.40032 | + | 0.721436i | ||||
\(596\) | − | 7244.46i | − | 0.497893i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −175.514 | + | 175.514i | −0.0120022 | + | 0.0120022i | ||||
\(599\) | 20769.5 | 1.41673 | 0.708363 | − | 0.705848i | \(-0.249434\pi\) | ||||
0.708363 | + | 0.705848i | \(0.249434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11642.9 | −0.790222 | −0.395111 | − | 0.918633i | \(-0.629294\pi\) | ||||
−0.395111 | + | 0.918633i | \(0.629294\pi\) | |||||||
\(602\) | −264.997 | + | 264.997i | −0.0179410 | + | 0.0179410i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 3147.54i | − | 0.212039i | ||||||
\(605\) | −5436.99 | + | 2801.09i | −0.365364 | + | 0.188232i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17174.6 | − | 17174.6i | −1.14843 | − | 1.14843i | −0.986862 | − | 0.161565i | \(-0.948346\pi\) |
−0.161565 | − | 0.986862i | \(-0.551654\pi\) | |||||||
\(608\) | −5118.82 | − | 5118.82i | −0.341440 | − | 0.341440i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −366.748 | + | 1146.21i | −0.0243429 | + | 0.0760800i | ||||
\(611\) | − | 1272.30i | − | 0.0842416i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11694.1 | − | 11694.1i | 0.770504 | − | 0.770504i | −0.207691 | − | 0.978195i | \(-0.566595\pi\) |
0.978195 | + | 0.207691i | \(0.0665947\pi\) | |||||||
\(614\) | 3066.49 | 0.201553 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3843.43 | 0.251390 | ||||||||
\(617\) | −5586.69 | + | 5586.69i | −0.364525 | + | 0.364525i | −0.865476 | − | 0.500951i | \(-0.832984\pi\) |
0.500951 | + | 0.865476i | \(0.332984\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16137.1i | − | 1.04783i | −0.851771 | − | 0.523914i | \(-0.824471\pi\) | ||
0.851771 | − | 0.523914i | \(-0.175529\pi\) | |||||||
\(620\) | 1154.50 | + | 2240.91i | 0.0747835 | + | 0.145156i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −577.406 | − | 577.406i | −0.0372217 | − | 0.0372217i | ||||
\(623\) | −2105.69 | − | 2105.69i | −0.135414 | − | 0.135414i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5094.39 | − | 14771.2i | −0.326041 | − | 0.945356i | ||||
\(626\) | 2894.27i | 0.184790i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10228.0 | + | 10228.0i | −0.649906 | + | 0.649906i | ||||
\(629\) | 36816.1 | 2.33379 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25292.3 | 1.59567 | 0.797837 | − | 0.602874i | \(-0.205978\pi\) | ||||
0.797837 | + | 0.602874i | \(0.205978\pi\) | |||||||
\(632\) | 1853.45 | − | 1853.45i | 0.116656 | − | 0.116656i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1806.38i | 0.113156i | ||||||||
\(635\) | 13787.9 | + | 4411.64i | 0.861663 | + | 0.275702i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 275.717 | + | 275.717i | 0.0171496 | + | 0.0171496i | ||||
\(638\) | 798.729 | + | 798.729i | 0.0495643 | + | 0.0495643i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8425.03 | − | 2695.71i | −0.520357 | − | 0.166496i | ||||
\(641\) | − | 8057.35i | − | 0.496484i | −0.968698 | − | 0.248242i | \(-0.920147\pi\) | ||
0.968698 | − | 0.248242i | \(-0.0798528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15024.4 | − | 15024.4i | 0.921471 | − | 0.921471i | −0.0756629 | − | 0.997133i | \(-0.524107\pi\) |
0.997133 | + | 0.0756629i | \(0.0241073\pi\) | |||||||
\(644\) | −28778.2 | −1.76090 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3723.40 | 0.226773 | ||||||||
\(647\) | −2396.69 | + | 2396.69i | −0.145631 | + | 0.145631i | −0.776163 | − | 0.630532i | \(-0.782837\pi\) |
0.630532 | + | 0.776163i | \(0.282837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13531.0i | 0.818394i | ||||||||
\(650\) | 146.436 | + | 104.397i | 0.00883646 | + | 0.00629965i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −617.645 | − | 617.645i | −0.0370995 | − | 0.0370995i | ||||
\(653\) | −10852.1 | − | 10852.1i | −0.650343 | − | 0.650343i | 0.302732 | − | 0.953076i | \(-0.402101\pi\) |
−0.953076 | + | 0.302732i | \(0.902101\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3222.44 | + | 6254.82i | 0.192230 | + | 0.373124i | ||||
\(656\) | − | 27247.1i | − | 1.62168i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2207.16 | + | 2207.16i | −0.130766 | + | 0.130766i | ||||
\(659\) | 21164.7 | 1.25108 | 0.625538 | − | 0.780193i | \(-0.284879\pi\) | ||||
0.625538 | + | 0.780193i | \(0.284879\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6399.33 | −0.376558 | −0.188279 | − | 0.982116i | \(-0.560291\pi\) | ||||
−0.188279 | + | 0.982116i | \(0.560291\pi\) | |||||||
\(662\) | −857.380 | + | 857.380i | −0.0503369 | + | 0.0503369i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5947.09i | 0.347578i | ||||||||
\(665\) | −6907.74 | + | 21589.1i | −0.402813 | + | 1.25893i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12087.8 | − | 12087.8i | −0.701710 | − | 0.701710i | ||||
\(668\) | 3353.96 | + | 3353.96i | 0.194264 | + | 0.194264i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2854.65 | + | 1470.70i | −0.164604 | + | 0.0848028i | ||||
\(671\) | − | 7402.22i | − | 0.425871i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1618.29 | + | 1618.29i | −0.0926903 | + | 0.0926903i | −0.751932 | − | 0.659241i | \(-0.770878\pi\) |
0.659241 | + | 0.751932i | \(0.270878\pi\) | |||||||
\(674\) | 3446.61 | 0.196971 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17114.0 | −0.973713 | ||||||||
\(677\) | −16119.8 | + | 16119.8i | −0.915118 | + | 0.915118i | −0.996669 | − | 0.0815511i | \(-0.974013\pi\) |
0.0815511 | + | 0.996669i | \(0.474013\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16791.1i | 0.949017i | ||||||||
\(680\) | 6153.83 | − | 3170.40i | 0.347042 | − | 0.178793i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 231.997 | + | 231.997i | 0.0130258 | + | 0.0130258i | ||||
\(683\) | −23612.1 | − | 23612.1i | −1.32283 | − | 1.32283i | −0.911477 | − | 0.411351i | \(-0.865057\pi\) |
−0.411351 | − | 0.911477i | \(-0.634943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3184.66 | + | 9953.16i | −0.177634 | + | 0.555169i | ||||
\(686\) | 2016.89i | 0.112253i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1835.57 | + | 1835.57i | −0.101716 | + | 0.101716i | ||||
\(689\) | −1119.49 | −0.0619000 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12036.1 | 0.662624 | 0.331312 | − | 0.943521i | \(-0.392509\pi\) | ||||
0.331312 | + | 0.943521i | \(0.392509\pi\) | |||||||
\(692\) | −10894.0 | + | 10894.0i | −0.598451 | + | 0.598451i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 4712.02i | − | 0.257732i | ||||||
\(695\) | 7057.75 | + | 13699.3i | 0.385202 | + | 0.747687i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30814.2 | + | 30814.2i | 1.67457 | + | 1.67457i | ||||
\(698\) | 409.171 | + | 409.171i | 0.0221882 | + | 0.0221882i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3446.51 | + | 20563.9i | 0.186094 | + | 1.11035i | ||||
\(701\) | 33366.3i | 1.79776i | 0.438200 | + | 0.898878i | \(0.355616\pi\) | ||||
−0.438200 | + | 0.898878i | \(0.644384\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25810.7 | − | 25810.7i | 1.38473 | − | 1.38473i | ||||
\(704\) | 12583.9 | 0.673684 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −805.875 | −0.0429596 | ||||||||
\(707\) | 4514.19 | − | 4514.19i | 0.240132 | − | 0.240132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4987.22i | 0.264173i | 0.991238 | + | 0.132087i | \(0.0421677\pi\) | ||||
−0.991238 | + | 0.132087i | \(0.957832\pi\) | |||||||
\(710\) | −2644.30 | − | 846.084i | −0.139773 | − | 0.0447225i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 637.581 | + | 637.581i | 0.0335595 | + | 0.0335595i | ||||
\(713\) | −3510.98 | − | 3510.98i | −0.184414 | − | 0.184414i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1053.54 | − | 337.096i | −0.0551052 | − | 0.0176317i | ||||
\(716\) | 867.043i | 0.0452555i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1242.00 | + | 1242.00i | −0.0645560 | + | 0.0645560i | ||||
\(719\) | −33618.4 | −1.74375 | −0.871873 | − | 0.489732i | \(-0.837095\pi\) | ||||
−0.871873 | + | 0.489732i | \(0.837095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17403.6 | 0.898951 | ||||||||
\(722\) | 635.644 | − | 635.644i | 0.0327649 | − | 0.0327649i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5488.61i | 0.281744i | ||||||||
\(725\) | −7189.86 | + | 10085.1i | −0.368310 | + | 0.516625i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10057.9 | − | 10057.9i | −0.513106 | − | 0.513106i | 0.402371 | − | 0.915477i | \(-0.368186\pi\) |
−0.915477 | + | 0.402371i | \(0.868186\pi\) | |||||||
\(728\) | −342.983 | − | 342.983i | −0.0174613 | − | 0.0174613i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 220.197 | + | 427.407i | 0.0111642 | + | 0.0216699i | ||||
\(731\) | − | 4151.76i | − | 0.210066i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4209.55 | + | 4209.55i | −0.212119 | + | 0.212119i | −0.805167 | − | 0.593048i | \(-0.797924\pi\) |
0.593048 | + | 0.805167i | \(0.297924\pi\) | |||||||
\(734\) | −2610.32 | −0.131265 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13116.2 | 0.656890 | ||||||||
\(737\) | 13966.5 | − | 13966.5i | 0.698050 | − | 0.698050i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4750.38i | 0.236462i | 0.992986 | + | 0.118231i | \(0.0377223\pi\) | ||||
−0.992986 | + | 0.118231i | \(0.962278\pi\) | |||||||
\(740\) | 10232.3 | − | 31979.5i | 0.508308 | − | 1.58864i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1942.07 | + | 1942.07i | 0.0960857 | + | 0.0960857i | ||||
\(743\) | 16266.1 | + | 16266.1i | 0.803159 | + | 0.803159i | 0.983588 | − | 0.180429i | \(-0.0577487\pi\) |
−0.180429 | + | 0.983588i | \(0.557749\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9190.66 | − | 4734.96i | 0.451973 | − | 0.232853i | ||||
\(746\) | − | 1605.32i | − | 0.0787866i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14896.3 | + | 14896.3i | −0.728159 | + | 0.728159i | ||||
\(749\) | −6534.00 | −0.318754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32690.2 | −1.58839 | −0.794197 | − | 0.607660i | \(-0.792108\pi\) | ||||
−0.794197 | + | 0.607660i | \(0.792108\pi\) | |||||||
\(752\) | −15288.4 | + | 15288.4i | −0.741372 | + | 0.741372i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 142.555i | − | 0.00688536i | ||||||
\(755\) | 3993.12 | − | 2057.22i | 0.192483 | − | 0.0991656i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6722.97 | − | 6722.97i | −0.322788 | − | 0.322788i | 0.527048 | − | 0.849836i | \(-0.323299\pi\) |
−0.849836 | + | 0.527048i | \(0.823299\pi\) | |||||||
\(758\) | −2420.99 | − | 2420.99i | −0.116008 | − | 0.116008i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2091.59 | − | 6536.94i | 0.0998289 | − | 0.312000i | ||||
\(761\) | 7001.94i | 0.333535i | 0.985996 | + | 0.166767i | \(0.0533329\pi\) | ||||
−0.985996 | + | 0.166767i | \(0.946667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14098.4 | + | 14098.4i | −0.668932 | + | 0.668932i | ||||
\(764\) | −17347.5 | −0.821480 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4898.58 | −0.231061 | ||||||||
\(767\) | 1207.49 | − | 1207.49i | 0.0568448 | − | 0.0568448i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25176.4i | − | 1.18060i | −0.807183 | − | 0.590301i | \(-0.799009\pi\) | ||
0.807183 | − | 0.590301i | \(-0.200991\pi\) | |||||||
\(770\) | 1242.88 | + | 2412.45i | 0.0581690 | + | 0.112907i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15387.7 | − | 15387.7i | −0.717376 | − | 0.717376i | ||||
\(773\) | 7322.13 | + | 7322.13i | 0.340697 | + | 0.340697i | 0.856629 | − | 0.515932i | \(-0.172554\pi\) |
−0.515932 | + | 0.856629i | \(0.672554\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2088.35 | + | 2929.30i | −0.0967943 | + | 0.135772i | ||||
\(776\) | − | 5084.17i | − | 0.235195i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2487.83 | − | 2487.83i | 0.114644 | − | 0.114644i | ||||
\(779\) | 43205.9 | 1.98718 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17076.9 | 0.782405 | ||||||||
\(782\) | −4770.33 | + | 4770.33i | −0.218142 | + | 0.218142i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 6626.25i | − | 0.301852i | ||||||
\(785\) | −19660.7 | − | 6290.73i | −0.893911 | − | 0.286020i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16794.5 | + | 16794.5i | 0.760683 | + | 0.760683i | 0.976446 | − | 0.215763i | \(-0.0692237\pi\) |
−0.215763 | + | 0.976446i | \(0.569224\pi\) | |||||||
\(788\) | 21157.9 | + | 21157.9i | 0.956495 | + | 0.956495i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1762.74 | + | 564.016i | 0.0793868 | + | 0.0254010i | ||||
\(791\) | − | 32640.8i | − | 1.46722i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −660.565 | + | 660.565i | −0.0295805 | + | 0.0295805i | ||||
\(794\) | −1095.30 | −0.0489556 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6590.11 | 0.293443 | ||||||||
\(797\) | 18950.9 | − | 18950.9i | 0.842251 | − | 0.842251i | −0.146900 | − | 0.989151i | \(-0.546930\pi\) |
0.989151 | + | 0.146900i | \(0.0469296\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 34580.0i | − | 1.53110i | ||||||
\(800\) | −1570.81 | − | 9372.41i | −0.0694208 | − | 0.414206i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3927.01 | − | 3927.01i | −0.172902 | − | 0.172902i | ||||
\(803\) | −2091.10 | − | 2091.10i | −0.0918972 | − | 0.0918972i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18809.4 | − | 36509.5i | −0.823532 | − | 1.59850i | ||||
\(806\) | − | 41.4062i | − | 0.00180952i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1366.85 | + | 1366.85i | −0.0595118 | + | 0.0595118i | ||||
\(809\) | 3967.32 | 0.172415 | 0.0862074 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862074 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23204.4 | −1.00471 | −0.502353 | − | 0.864663i | \(-0.667532\pi\) | ||||
−0.502353 | + | 0.864663i | \(0.667532\pi\) | |||||||
\(812\) | 11687.1 | − | 11687.1i | 0.505093 | − | 0.505093i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 4370.11i | − | 0.188172i | ||||||
\(815\) | 379.883 | − | 1187.27i | 0.0163273 | − | 0.0510283i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2910.68 | − | 2910.68i | −0.124641 | − | 0.124641i | ||||
\(818\) | 1841.14 | + | 1841.14i | 0.0786968 | + | 0.0786968i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35330.4 | − | 18201.9i | 1.50462 | − | 0.775169i | ||||
\(821\) | 5783.29i | 0.245844i | 0.992416 | + | 0.122922i | \(0.0392265\pi\) | ||||
−0.992416 | + | 0.122922i | \(0.960773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2021.92 | − | 2021.92i | 0.0856375 | − | 0.0856375i | −0.662990 | − | 0.748628i | \(-0.730713\pi\) |
0.748628 | + | 0.662990i | \(0.230713\pi\) | |||||||
\(824\) | −5269.62 | −0.222786 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4189.47 | −0.176477 | ||||||||
\(827\) | 18025.3 | − | 18025.3i | 0.757922 | − | 0.757922i | −0.218022 | − | 0.975944i | \(-0.569961\pi\) |
0.975944 | + | 0.218022i | \(0.0699605\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42400.5i | 1.77640i | 0.459462 | + | 0.888198i | \(0.348042\pi\) | ||||
−0.459462 | + | 0.888198i | \(0.651958\pi\) | |||||||
\(830\) | −3732.89 | + | 1923.15i | −0.156109 | + | 0.0804261i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1122.97 | − | 1122.97i | −0.0467933 | − | 0.0467933i | ||||
\(833\) | 7493.75 | + | 7493.75i | 0.311696 | + | 0.311696i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2062.85 | + | 6447.13i | −0.0854947 | + | 0.267200i | ||||
\(836\) | 20886.7i | 0.864094i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2439.95 | − | 2439.95i | 0.100581 | − | 0.100581i | ||||
\(839\) | −38073.9 | −1.56670 | −0.783348 | − | 0.621584i | \(-0.786490\pi\) | ||||
−0.783348 | + | 0.621584i | \(0.786490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14571.1 | −0.597447 | ||||||||
\(842\) | 2611.04 | − | 2611.04i | 0.106868 | − | 0.106868i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 31102.3i | − | 1.26847i | ||||||
\(845\) | −11185.6 | − | 21711.6i | −0.455382 | − | 0.883908i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8236.11 | + | 8236.11i | 0.334116 | + | 0.334116i | ||||
\(848\) | 13452.2 | + | 13452.2i | 0.544754 | + | 0.544754i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3980.01 | + | 2837.42i | 0.160604 | + | 0.114497i | ||||
\(851\) | 66136.1i | 2.66406i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26447.7 | + | 26447.7i | −1.06161 | + | 1.06161i | −0.0636372 | + | 0.997973i | \(0.520270\pi\) |
−0.997973 | + | 0.0636372i | \(0.979730\pi\) | |||||||
\(854\) | 2291.88 | 0.0918342 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1978.43 | 0.0789967 | ||||||||
\(857\) | 18997.5 | − | 18997.5i | 0.757227 | − | 0.757227i | −0.218590 | − | 0.975817i | \(-0.570146\pi\) |
0.975817 | + | 0.218590i | \(0.0701457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29326.5i | 1.16485i | 0.812885 | + | 0.582425i | \(0.197896\pi\) | ||||
−0.812885 | + | 0.582425i | \(0.802104\pi\) | |||||||
\(860\) | −3606.34 | − | 1153.90i | −0.142995 | − | 0.0457532i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2414.95 | + | 2414.95i | 0.0954219 | + | 0.0954219i | ||||
\(863\) | −23070.8 | − | 23070.8i | −0.910011 | − | 0.910011i | 0.0862616 | − | 0.996273i | \(-0.472508\pi\) |
−0.996273 | + | 0.0862616i | \(0.972508\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20940.9 | − | 6700.36i | −0.823137 | − | 0.263375i | ||||
\(866\) | − | 2379.32i | − | 0.0933633i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3394.59 | − | 3394.59i | 0.132742 | − | 0.132742i | ||||
\(869\) | −11383.8 | −0.444381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2492.71 | −0.0969716 | ||||||||
\(872\) | 4268.84 | − | 4268.84i | 0.165781 | − | 0.165781i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6688.68i | 0.258865i | ||||||||
\(875\) | −23835.8 | + | 17812.9i | −0.920910 | + | 0.688214i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20252.6 | + | 20252.6i | 0.779795 | + | 0.779795i | 0.979796 | − | 0.200001i | \(-0.0640944\pi\) |
−0.200001 | + | 0.979796i | \(0.564094\pi\) | |||||||
\(878\) | 3022.67 | + | 3022.67i | 0.116185 | + | 0.116185i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8609.09 | + | 16710.5i | 0.329787 | + | 0.640124i | ||||
\(881\) | − | 15547.7i | − | 0.594569i | −0.954789 | − | 0.297284i | \(-0.903919\pi\) | ||
0.954789 | − | 0.297284i | \(-0.0960809\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17599.2 | − | 17599.2i | 0.670737 | − | 0.670737i | −0.287149 | − | 0.957886i | \(-0.592707\pi\) |
0.957886 | + | 0.287149i | \(0.0927075\pi\) | |||||||
\(884\) | 2658.66 | 0.101154 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −844.087 | −0.0320064 | ||||||||
\(887\) | −9099.97 | + | 9099.97i | −0.344472 | + | 0.344472i | −0.858046 | − | 0.513573i | \(-0.828321\pi\) |
0.513573 | + | 0.858046i | \(0.328321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 27569.2i | − | 1.04009i | ||||||
\(890\) | −194.020 | + | 606.378i | −0.00730736 | + | 0.0228380i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28205.9 | + | 28205.9i | 1.05875 | + | 1.05875i | ||||
\(893\) | −24243.0 | − | 24243.0i | −0.908467 | − | 0.908467i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1099.97 | + | 566.697i | −0.0410816 | + | 0.0211649i | ||||
\(896\) | 16846.0i | 0.628109i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1812.47 | − | 1812.47i | 0.0673528 | − | 0.0673528i | ||||
\(899\) | 2851.67 | 0.105794 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30426.8 | −1.12504 | ||||||||
\(902\) | 3657.68 | − | 3657.68i | 0.135019 | − | 0.135019i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9883.30i | 0.363621i | ||||||||
\(905\) | −6963.11 | + | 3587.34i | −0.255759 | + | 0.131765i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28827.2 | + | 28827.2i | 1.05534 | + | 1.05534i | 0.998376 | + | 0.0569624i | \(0.0181415\pi\) |
0.0569624 | + | 0.998376i | \(0.481858\pi\) | |||||||
\(908\) | 13590.9 | + | 13590.9i | 0.496728 | + | 0.496728i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 104.372 | − | 326.197i | 0.00380207 | − | 0.0118828i | ||||
\(911\) | 32922.1i | 1.19732i | 0.801003 | + | 0.598660i | \(0.204300\pi\) | ||||
−0.801003 | + | 0.598660i | \(0.795700\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18263.3 | − | 18263.3i | 0.662023 | − | 0.662023i | ||||
\(914\) | −5219.72 | −0.188898 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27167.0 | 0.979938 | ||||||||
\(917\) | 9474.99 | − | 9474.99i | 0.341212 | − | 0.341212i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28643.9i | 1.02815i | 0.857744 | + | 0.514077i | \(0.171865\pi\) | ||||
−0.857744 | + | 0.514077i | \(0.828135\pi\) | |||||||
\(920\) | 5695.28 | + | 11054.7i | 0.204096 | + | 0.396154i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3830.67 | − | 3830.67i | −0.136829 | − | 0.136829i | ||||
\(923\) | −1523.92 | − | 1523.92i | −0.0543450 | − | 0.0543450i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 47258.6 | − | 7920.53i | 1.67984 | − | 0.281541i | ||||
\(926\) | − | 1799.31i | − | 0.0638541i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5326.61 | + | 5326.61i | −0.188421 | + | 0.188421i | ||||
\(929\) | 12080.7 | 0.426648 | 0.213324 | − | 0.976981i | \(-0.431571\pi\) | ||||
0.213324 | + | 0.976981i | \(0.431571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10507.3 | 0.369885 | ||||||||
\(932\) | −8383.98 | + | 8383.98i | −0.294664 | + | 0.294664i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2450.08i | 0.0858343i | ||||||||
\(935\) | −28634.4 | − | 9161.98i | −1.00154 | − | 0.320459i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18170.0 | − | 18170.0i | −0.633500 | − | 0.633500i | 0.315444 | − | 0.948944i | \(-0.397846\pi\) |
−0.948944 | + | 0.315444i | \(0.897846\pi\) | |||||||
\(938\) | 4324.31 | + | 4324.31i | 0.150526 | + | 0.150526i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30037.2 | − | 9610.84i | −1.04224 | − | 0.333480i | ||||
\(941\) | − | 7693.26i | − | 0.266518i | −0.991081 | − | 0.133259i | \(-0.957456\pi\) | ||
0.991081 | − | 0.133259i | \(-0.0425442\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55354.4 | + | 55354.4i | −1.91155 | + | 1.91155i | ||||
\(944\) | −29019.4 | −1.00053 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −492.819 | −0.0169375 | ||||||||
\(947\) | −9792.71 | + | 9792.71i | −0.336030 | + | 0.336030i | −0.854871 | − | 0.518841i | \(-0.826364\pi\) |
0.518841 | + | 0.854871i | \(0.326364\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 373.216i | 0.0127662i | ||||||||
\(950\) | 4779.50 | − | 801.043i | 0.163229 | − | 0.0273571i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9321.99 | − | 9321.99i | −0.317361 | − | 0.317361i | ||||
\(953\) | 22620.8 | + | 22620.8i | 0.768899 | + | 0.768899i | 0.977913 | − | 0.209014i | \(-0.0670254\pi\) |
−0.209014 | + | 0.977913i | \(0.567025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11338.3 | − | 22007.9i | −0.384186 | − | 0.745715i | ||||
\(956\) | − | 30627.4i | − | 1.03615i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3059.01 | + | 3059.01i | −0.103165 | + | 0.103165i | ||||
\(959\) | 19901.5 | 0.670130 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28962.7 | −0.972197 | ||||||||
\(962\) | −389.984 | + | 389.984i | −0.0130702 | + | 0.0130702i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 37503.2i | − | 1.25300i | ||||||
\(965\) | 9464.20 | − | 29578.9i | 0.315713 | − | 0.986713i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4426.36 | − | 4426.36i | −0.147200 | − | 0.147200i | 0.629666 | − | 0.776866i | \(-0.283192\pi\) |
−0.776866 | + | 0.629666i | \(0.783192\pi\) | |||||||
\(968\) | −2493.81 | − | 2493.81i | −0.0828037 | − | 0.0828037i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3191.24 | − | 1644.10i | 0.105634 | − | 0.0544216i | ||||
\(971\) | − | 36943.3i | − | 1.22097i | −0.792026 | − | 0.610487i | \(-0.790974\pi\) | ||
0.792026 | − | 0.610487i | \(-0.209026\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20752.0 | − | 20752.0i | 0.683741 | − | 0.683741i | ||||
\(974\) | 1882.32 | 0.0619236 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15875.2 | 0.520650 | ||||||||
\(977\) | 14789.2 | − | 14789.2i | 0.484287 | − | 0.484287i | −0.422211 | − | 0.906498i | \(-0.638746\pi\) |
0.906498 | + | 0.422211i | \(0.138746\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3915.98i | − | 0.127840i | ||||||
\(980\) | 8592.04 | − | 4426.55i | 0.280064 | − | 0.144287i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5410.00 | + | 5410.00i | 0.175805 | + | 0.175805i | ||||
\(983\) | 12134.8 | + | 12134.8i | 0.393733 | + | 0.393733i | 0.876015 | − | 0.482283i | \(-0.160192\pi\) |
−0.482283 | + | 0.876015i | \(0.660192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13013.2 | + | 40670.6i | −0.420948 | + | 1.31561i | ||||
\(986\) | − | 3874.54i | − | 0.125142i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1863.91 | − | 1863.91i | 0.0600190 | − | 0.0600190i | ||||
\(989\) | 7458.19 | 0.239794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29327.6 | 0.940084 | 0.470042 | − | 0.882644i | \(-0.344239\pi\) | ||||
0.470042 | + | 0.882644i | \(0.344239\pi\) | |||||||
\(992\) | −1547.15 | + | 1547.15i | −0.0495182 | + | 0.0495182i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5287.34i | 0.168717i | ||||||||
\(995\) | 4307.28 | + | 8360.53i | 0.137236 | + | 0.266379i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44483.8 | − | 44483.8i | −1.41306 | − | 1.41306i | −0.735143 | − | 0.677912i | \(-0.762885\pi\) |
−0.677912 | − | 0.735143i | \(-0.737115\pi\) | |||||||
\(998\) | −2078.84 | − | 2078.84i | −0.0659365 | − | 0.0659365i | ||||
\(999\) | 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 | 45.4.f.a.17.3 | yes | 12 | |
3.2 | odd | 2 | inner | 45.4.f.a.17.4 | yes | 12 | |
4.3 | odd | 2 | 720.4.w.d.17.1 | 12 | |||
5.2 | odd | 4 | 225.4.f.c.143.3 | 12 | |||
5.3 | odd | 4 | inner | 45.4.f.a.8.4 | yes | 12 | |
5.4 | even | 2 | 225.4.f.c.107.4 | 12 | |||
12.11 | even | 2 | 720.4.w.d.17.6 | 12 | |||
15.2 | even | 4 | 225.4.f.c.143.4 | 12 | |||
15.8 | even | 4 | inner | 45.4.f.a.8.3 | ✓ | 12 | |
15.14 | odd | 2 | 225.4.f.c.107.3 | 12 | |||
20.3 | even | 4 | 720.4.w.d.593.6 | 12 | |||
60.23 | odd | 4 | 720.4.w.d.593.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.f.a.8.3 | ✓ | 12 | 15.8 | even | 4 | inner | |
45.4.f.a.8.4 | yes | 12 | 5.3 | odd | 4 | inner | |
45.4.f.a.17.3 | yes | 12 | 1.1 | even | 1 | trivial | |
45.4.f.a.17.4 | yes | 12 | 3.2 | odd | 2 | inner | |
225.4.f.c.107.3 | 12 | 15.14 | odd | 2 | |||
225.4.f.c.107.4 | 12 | 5.4 | even | 2 | |||
225.4.f.c.143.3 | 12 | 5.2 | odd | 4 | |||
225.4.f.c.143.4 | 12 | 15.2 | even | 4 | |||
720.4.w.d.17.1 | 12 | 4.3 | odd | 2 | |||
720.4.w.d.17.6 | 12 | 12.11 | even | 2 | |||
720.4.w.d.593.1 | 12 | 60.23 | odd | 4 | |||
720.4.w.d.593.6 | 12 | 20.3 | even | 4 |