Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.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: | \(13.2754297513\) |
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: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.4 | ||
Root | \(-2.02004 - 2.30794i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.143 |
Dual form | 225.4.f.c.107.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | \(-0.227070\pi\) |
−0.654378 | + | 0.756167i | \(0.727070\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 7.83422i | − | 0.979278i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.0557 | + | 15.0557i | −0.812931 | + | 0.812931i | −0.985072 | − | 0.172141i | \(-0.944931\pi\) |
0.172141 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(8\) | 4.55871 | − | 4.55871i | 0.201468 | − | 0.201468i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 27.9992i | − | 0.767462i | −0.923445 | − | 0.383731i | \(-0.874639\pi\) | ||
0.923445 | − | 0.383731i | \(-0.125361\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.49862 | − | 2.49862i | −0.0533071 | − | 0.0533071i | 0.679951 | − | 0.733258i | \(-0.262001\pi\) |
−0.733258 | + | 0.679951i | \(0.762001\pi\) | |||||||
\(14\) | −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 | \(-0.490237\pi\) |
−0.999530 | + | 0.0306653i | \(0.990237\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 95.2200i | 1.14974i | 0.818246 | + | 0.574868i | \(0.194946\pi\) | ||||
−0.818246 | + | 0.574868i | \(0.805054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.06104 | − | 8.06104i | 0.0781191 | − | 0.0781191i | ||||
\(23\) | −121.994 | + | 121.994i | −1.10598 | + | 1.10598i | −0.112302 | + | 0.993674i | \(0.535822\pi\) |
−0.993674 | + | 0.112302i | \(0.964178\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 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 | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −271.064 | + | 271.064i | −1.20439 | + | 1.20439i | −0.231578 | + | 0.972816i | \(0.574389\pi\) |
−0.972816 | + | 0.231578i | \(0.925611\pi\) | |||||||
\(38\) | −27.4140 | + | 27.4140i | −0.117030 | + | 0.117030i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 453.748i | − | 1.72838i | −0.503166 | − | 0.864190i | \(-0.667832\pi\) | ||
0.503166 | − | 0.864190i | \(-0.332168\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.5679 | − | 30.5679i | −0.108409 | − | 0.108409i | 0.650822 | − | 0.759230i | \(-0.274424\pi\) |
−0.759230 | + | 0.650822i | \(0.774424\pi\) | |||||||
\(44\) | −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 | \(-0.438708\pi\) |
−0.981519 | + | 0.191365i | \(0.938708\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 110.348i | − | 0.321713i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −19.5748 | + | 19.5748i | −0.0522025 | + | 0.0522025i | ||||
\(53\) | 224.021 | − | 224.021i | 0.580598 | − | 0.580598i | −0.354470 | − | 0.935068i | \(-0.615339\pi\) |
0.935068 | + | 0.354470i | \(0.115339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 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 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 498.817 | − | 498.817i | 0.909556 | − | 0.909556i | −0.0866805 | − | 0.996236i | \(-0.527626\pi\) |
0.996236 | + | 0.0866805i | \(0.0276259\pi\) | |||||||
\(68\) | −532.025 | + | 532.025i | −0.948788 | + | 0.948788i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 609.904i | 1.01947i | 0.860332 | + | 0.509735i | \(0.170256\pi\) | ||||
−0.860332 | + | 0.509735i | \(0.829744\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 74.6843 | + | 74.6843i | 0.119742 | + | 0.119742i | 0.764438 | − | 0.644697i | \(-0.223016\pi\) |
−0.644697 | + | 0.764438i | \(0.723016\pi\) | |||||||
\(74\) | −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 | \(-0.906507\pi\) | ||
0.957174 | − | 0.289513i | \(-0.0934935\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 130.635 | − | 130.635i | 0.175930 | − | 0.175930i | ||||
\(83\) | 652.278 | − | 652.278i | 0.862613 | − | 0.862613i | −0.129028 | − | 0.991641i | \(-0.541186\pi\) |
0.991641 | + | 0.129028i | \(0.0411858\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 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 | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −557.633 | + | 557.633i | −0.583701 | + | 0.583701i | −0.935918 | − | 0.352217i | \(-0.885428\pi\) |
0.352217 | + | 0.935918i | \(0.385428\pi\) | |||||||
\(98\) | 31.7693 | − | 31.7693i | 0.0327468 | − | 0.0327468i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 299.833i | 0.295391i | 0.989033 | + | 0.147695i | \(0.0471855\pi\) | ||||
−0.989033 | + | 0.147695i | \(0.952814\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −577.974 | − | 577.974i | −0.552907 | − | 0.552907i | 0.374372 | − | 0.927279i | \(-0.377858\pi\) |
−0.927279 | + | 0.374372i | \(0.877858\pi\) | |||||||
\(104\) | −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 | \(-0.205730\pi\) |
−0.602253 | + | 0.798305i | \(0.705730\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 936.415i | − | 0.822865i | −0.911440 | − | 0.411432i | \(-0.865029\pi\) | ||
0.911440 | − | 0.411432i | \(-0.134971\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 904.077 | − | 904.077i | 0.762743 | − | 0.762743i | ||||
\(113\) | 1084.00 | − | 1084.00i | 0.902428 | − | 0.902428i | −0.0932173 | − | 0.995646i | \(-0.529715\pi\) |
0.995646 | + | 0.0932173i | \(0.0297151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 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 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 915.574 | − | 915.574i | 0.639717 | − | 0.639717i | −0.310769 | − | 0.950486i | \(-0.600586\pi\) |
0.950486 | + | 0.310769i | \(0.100586\pi\) | |||||||
\(128\) | −559.457 | + | 559.457i | −0.386324 | + | 0.386324i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 629.329i | 0.419731i | 0.977730 | + | 0.209865i | \(0.0673026\pi\) | ||||
−0.977730 | + | 0.209865i | \(0.932697\pi\) | |||||||
\(132\) | 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 | \(-0.344137\pi\) |
−0.882494 | + | 0.470325i | \(0.844137\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1378.35i | 0.841081i | 0.907274 | + | 0.420540i | \(0.138160\pi\) | ||||
−0.907274 | + | 0.420540i | \(0.861840\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −175.593 | + | 175.593i | −0.103771 | + | 0.103771i | ||||
\(143\) | −69.9595 | + | 69.9595i | −0.0409112 | + | 0.0409112i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 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 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1305.55 | + | 1305.55i | −0.663659 | + | 0.663659i | −0.956240 | − | 0.292582i | \(-0.905486\pi\) |
0.292582 | + | 0.956240i | \(0.405486\pi\) | |||||||
\(158\) | 117.053 | − | 117.053i | 0.0589384 | − | 0.0589384i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3673.40i | − | 1.79816i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 78.8393 | + | 78.8393i | 0.0378845 | + | 0.0378845i | 0.725795 | − | 0.687911i | \(-0.241472\pi\) |
−0.687911 | + | 0.725795i | \(0.741472\pi\) | |||||||
\(164\) | −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 | \(-0.294798\pi\) |
−0.799303 | + | 0.600928i | \(0.794798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2184.51i | − | 0.994317i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −239.476 | + | 239.476i | −0.106162 | + | 0.106162i | ||||
\(173\) | −1390.57 | + | 1390.57i | −0.611114 | + | 0.611114i | −0.943236 | − | 0.332122i | \(-0.892235\pi\) |
0.332122 | + | 0.943236i | \(0.392235\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1901.44 | + | 1901.44i | −0.743567 | + | 0.743567i | ||||
\(188\) | −1994.59 | + | 1994.59i | −0.773780 | + | 0.773780i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2214.32i | − | 0.838862i | −0.907787 | − | 0.419431i | \(-0.862230\pi\) | ||
0.907787 | − | 0.419431i | \(-0.137770\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1964.16 | + | 1964.16i | 0.732556 | + | 0.732556i | 0.971125 | − | 0.238569i | \(-0.0766785\pi\) |
−0.238569 | + | 0.971125i | \(0.576678\pi\) | |||||||
\(194\) | −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 | \(-0.492678\pi\) |
−0.999735 | + | 0.0230004i | \(0.992678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 841.195i | 0.299652i | 0.988712 | + | 0.149826i | \(0.0478713\pi\) | ||||
−0.988712 | + | 0.149826i | \(0.952129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −86.3224 | + | 86.3224i | −0.0300674 | + | 0.0300674i | ||||
\(203\) | 1491.80 | − | 1491.80i | 0.515781 | − | 0.515781i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 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 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 433.303 | − | 433.303i | 0.135551 | − | 0.135551i | ||||
\(218\) | 269.596 | − | 269.596i | 0.0837584 | − | 0.0837584i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 339.365i | 0.103295i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3600.34 | − | 3600.34i | −1.08115 | − | 1.08115i | −0.996402 | − | 0.0847496i | \(-0.972991\pi\) |
−0.0847496 | − | 0.996402i | \(-0.527009\pi\) | |||||||
\(224\) | 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 | \(-0.366770\pi\) |
−0.913678 | + | 0.406439i | \(0.866770\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3467.74i | 1.00067i | 0.865831 | + | 0.500337i | \(0.166791\pi\) | ||||
−0.865831 | + | 0.500337i | \(0.833209\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −451.700 | + | 451.700i | −0.127826 | + | 0.127826i | ||||
\(233\) | −1070.17 | + | 1070.17i | −0.300899 | + | 0.300899i | −0.841365 | − | 0.540467i | \(-0.818248\pi\) |
0.540467 | + | 0.841365i | \(0.318248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 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 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 237.919 | − | 237.919i | 0.0612891 | − | 0.0612891i | ||||
\(248\) | −131.200 | + | 131.200i | −0.0335935 | + | 0.0335935i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2337.42i | 0.587794i | 0.955837 | + | 0.293897i | \(0.0949523\pi\) | ||||
−0.955837 | + | 0.293897i | \(0.905048\pi\) | |||||||
\(252\) | 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 | \(-0.196330\pi\) |
−0.578419 | + | 0.815740i | \(0.696330\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8162.10i | − | 1.95818i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −181.185 | + | 181.185i | −0.0427239 | + | 0.0427239i | ||||
\(263\) | 790.690 | − | 790.690i | 0.185384 | − | 0.185384i | −0.608313 | − | 0.793697i | \(-0.708153\pi\) |
0.793697 | + | 0.608313i | \(0.208153\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 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 | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −908.009 | + | 908.009i | −0.196957 | + | 0.196957i | −0.798694 | − | 0.601737i | \(-0.794475\pi\) |
0.601737 | + | 0.798694i | \(0.294475\pi\) | |||||||
\(278\) | −396.830 | + | 396.830i | −0.0856126 | + | 0.0856126i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7102.70i | 1.50787i | 0.656949 | + | 0.753935i | \(0.271847\pi\) | ||||
−0.656949 | + | 0.753935i | \(0.728153\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4721.93 | + | 4721.93i | 0.991837 | + | 0.991837i | 0.999967 | − | 0.00813014i | \(-0.00258793\pi\) |
−0.00813014 | + | 0.999967i | \(0.502588\pi\) | |||||||
\(284\) | 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 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 585.094 | − | 585.094i | 0.117260 | − | 0.117260i | ||||
\(293\) | −2078.57 | + | 2078.57i | −0.414442 | + | 0.414442i | −0.883283 | − | 0.468841i | \(-0.844672\pi\) |
0.468841 | + | 0.883283i | \(0.344672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 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 | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5325.58 | − | 5325.58i | 0.990056 | − | 0.990056i | −0.00989542 | − | 0.999951i | \(-0.503150\pi\) |
0.999951 | + | 0.00989542i | \(0.00314986\pi\) | |||||||
\(308\) | 3302.50 | − | 3302.50i | 0.610966 | − | 0.610966i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2005.56i | − | 0.365676i | −0.983143 | − | 0.182838i | \(-0.941472\pi\) | ||
0.983143 | − | 0.182838i | \(-0.0585283\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5026.49 | − | 5026.49i | −0.907713 | − | 0.907713i | 0.0883746 | − | 0.996087i | \(-0.471833\pi\) |
−0.996087 | + | 0.0883746i | \(0.971833\pi\) | |||||||
\(314\) | −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 | \(-0.378575\pi\) |
−0.928119 | + | 0.372283i | \(0.878575\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2774.31i | 0.486933i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1057.58 | − | 1057.58i | 0.183033 | − | 0.183033i | ||||
\(323\) | 6466.43 | − | 6466.43i | 1.11394 | − | 1.11394i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 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 | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5985.73 | − | 5985.73i | 0.967547 | − | 0.967547i | −0.0319428 | − | 0.999490i | \(-0.510169\pi\) |
0.999490 | + | 0.0319428i | \(0.0101694\pi\) | |||||||
\(338\) | 628.926 | − | 628.926i | 0.101210 | − | 0.101210i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 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 | 0.948130 | + | 0.317881i | \(0.102971\pi\) |
0.317881 | + | 0.948130i | \(0.397029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1421.22i | 0.217983i | 0.994043 | + | 0.108991i | \(0.0347621\pi\) | ||||
−0.994043 | + | 0.108991i | \(0.965238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1505.18 | + | 1505.18i | −0.227916 | + | 0.227916i | ||||
\(353\) | −1399.56 | + | 1399.56i | −0.211023 | + | 0.211023i | −0.804702 | − | 0.593679i | \(-0.797675\pi\) |
0.593679 | + | 0.804702i | \(0.297675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 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 | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4533.34 | + | 4533.34i | −0.644792 | + | 0.644792i | −0.951730 | − | 0.306938i | \(-0.900696\pi\) |
0.306938 | + | 0.951730i | \(0.400696\pi\) | |||||||
\(368\) | 7325.59 | − | 7325.59i | 1.03770 | − | 1.03770i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6745.59i | 0.943972i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2787.95 | + | 2787.95i | 0.387010 | + | 0.387010i | 0.873620 | − | 0.486609i | \(-0.161766\pi\) |
−0.486609 | + | 0.873620i | \(0.661766\pi\) | |||||||
\(374\) | −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 | \(-0.807002\pi\) | ||
0.821749 | − | 0.569849i | \(-0.192998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 637.508 | − | 637.508i | 0.0853868 | − | 0.0853868i | ||||
\(383\) | −8507.38 | + | 8507.38i | −1.13500 | + | 1.13500i | −0.145672 | + | 0.989333i | \(0.546534\pi\) |
−0.989333 | + | 0.145672i | \(0.953466\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 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 | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1902.21 | + | 1902.21i | −0.240476 | + | 0.240476i | −0.817047 | − | 0.576571i | \(-0.804390\pi\) |
0.576571 | + | 0.817047i | \(0.304390\pi\) | |||||||
\(398\) | −242.182 | + | 242.182i | −0.0305012 | + | 0.0305012i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 13640.1i | − | 1.69864i | −0.527882 | − | 0.849318i | \(-0.677014\pi\) | ||
0.527882 | − | 0.849318i | \(-0.322986\pi\) | |||||||
\(402\) | 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 | \(0.126340\pi\) | ||||
−0.922260 | + | 0.386569i | \(0.873660\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4527.98 | + | 4527.98i | −0.541450 | + | 0.541450i | ||||
\(413\) | −7275.86 | + | 7275.86i | −0.866880 | + | 0.866880i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 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 | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3980.30 | − | 3980.30i | 0.451102 | − | 0.451102i | ||||
\(428\) | 1699.98 | − | 1699.98i | 0.191990 | − | 0.191990i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8388.11i | 0.937450i | 0.883344 | + | 0.468725i | \(0.155287\pi\) | ||||
−0.883344 | + | 0.468725i | \(0.844713\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4132.17 | + | 4132.17i | 0.458613 | + | 0.458613i | 0.898200 | − | 0.439587i | \(-0.144875\pi\) |
−0.439587 | + | 0.898200i | \(0.644875\pi\) | |||||||
\(434\) | 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 | \(0.193333\pi\) | ||||
−0.821149 | + | 0.570714i | \(0.806667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −97.7038 | + | 97.7038i | −0.0105142 | + | 0.0105142i | ||||
\(443\) | −1465.93 | + | 1465.93i | −0.157220 | + | 0.157220i | −0.781333 | − | 0.624114i | \(-0.785460\pi\) |
0.624114 | + | 0.781333i | \(0.285460\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 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 | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9065.09 | + | 9065.09i | −0.927893 | + | 0.927893i | −0.997570 | − | 0.0696767i | \(-0.977803\pi\) |
0.0696767 | + | 0.997570i | \(0.477803\pi\) | |||||||
\(458\) | −998.368 | + | 998.368i | −0.101857 | + | 0.101857i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13305.5i | − | 1.34424i | −0.740440 | − | 0.672122i | \(-0.765383\pi\) | ||
0.740440 | − | 0.672122i | \(-0.234617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3124.86 | + | 3124.86i | 0.313660 | + | 0.313660i | 0.846326 | − | 0.532666i | \(-0.178810\pi\) |
−0.532666 | + | 0.846326i | \(0.678810\pi\) | |||||||
\(464\) | 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 | \(-0.346365\pi\) |
−0.885764 | + | 0.464135i | \(0.846365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15020.1i | 1.47881i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2203.05 | − | 2203.05i | 0.214838 | − | 0.214838i | ||||
\(473\) | −855.879 | + | 855.879i | −0.0831995 | + | 0.0831995i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 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 | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3269.03 | − | 3269.03i | 0.304177 | − | 0.304177i | −0.538469 | − | 0.842645i | \(-0.680997\pi\) |
0.842645 | + | 0.538469i | \(0.180997\pi\) | |||||||
\(488\) | −1205.19 | + | 1205.19i | −0.111796 | + | 0.111796i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18791.1i | 1.72715i | 0.504220 | + | 0.863575i | \(0.331780\pi\) | ||||
−0.504220 | + | 0.863575i | \(0.668220\pi\) | |||||||
\(492\) | 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 | \(-0.895010\pi\) | ||
0.946095 | − | 0.323889i | \(-0.104990\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −672.947 | + | 672.947i | −0.0598308 | + | 0.0598308i | ||||
\(503\) | −2081.38 | + | 2081.38i | −0.184501 | + | 0.184501i | −0.793314 | − | 0.608813i | \(-0.791646\pi\) |
0.608813 | + | 0.793314i | \(0.291646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 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 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7128.60 | + | 7128.60i | −0.606413 | + | 0.606413i | ||||
\(518\) | 2349.89 | − | 2349.89i | 0.199321 | − | 0.199321i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11837.5i | − | 0.995409i | −0.867347 | − | 0.497705i | \(-0.834176\pi\) | ||
0.867347 | − | 0.497705i | \(-0.165824\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5538.72 | + | 5538.72i | 0.463081 | + | 0.463081i | 0.899664 | − | 0.436583i | \(-0.143811\pi\) |
−0.436583 | + | 0.899664i | \(0.643811\pi\) | |||||||
\(524\) | 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 | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11231.2 | + | 11231.2i | −0.915287 | + | 0.915287i | ||||
\(533\) | −1133.74 | + | 1133.74i | −0.0921349 | + | 0.0921349i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 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 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3940.59 | − | 3940.59i | 0.308021 | − | 0.308021i | −0.536121 | − | 0.844141i | \(-0.680111\pi\) |
0.844141 | + | 0.536121i | \(0.180111\pi\) | |||||||
\(548\) | −5177.88 | + | 5177.88i | −0.403628 | + | 0.403628i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 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 | \(-0.200998\pi\) |
−0.590320 | + | 0.807170i | \(0.700998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 152.755i | 0.0115579i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2044.88 | + | 2044.88i | −0.153484 | + | 0.153484i | ||||
\(563\) | 12845.3 | − | 12845.3i | 0.961569 | − | 0.961569i | −0.0377198 | − | 0.999288i | \(-0.512009\pi\) |
0.999288 | + | 0.0377198i | \(0.0120094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 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 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −760.083 | + | 760.083i | −0.0548400 | + | 0.0548400i | −0.733995 | − | 0.679155i | \(-0.762346\pi\) |
0.679155 | + | 0.733995i | \(0.262346\pi\) | |||||||
\(578\) | −1241.04 | + | 1241.04i | −0.0893091 | + | 0.0893091i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 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 | \(-0.116929\pi\) |
−0.359139 | + | 0.933284i | \(0.616929\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2740.43i | − | 0.191711i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16277.1 | − | 16277.1i | 1.13004 | − | 1.13004i | ||||
\(593\) | −9861.32 | + | 9861.32i | −0.682893 | + | 0.682893i | −0.960651 | − | 0.277758i | \(-0.910409\pi\) |
0.277758 | + | 0.960651i | \(0.410409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17174.6 | − | 17174.6i | 1.14843 | − | 1.14843i | 0.161565 | − | 0.986862i | \(-0.448346\pi\) |
0.986862 | − | 0.161565i | \(-0.0516540\pi\) | |||||||
\(608\) | 5118.82 | − | 5118.82i | 0.341440 | − | 0.341440i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1272.30i | 0.0842416i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11694.1 | − | 11694.1i | −0.770504 | − | 0.770504i | 0.207691 | − | 0.978195i | \(-0.433405\pi\) |
−0.978195 | + | 0.207691i | \(0.933405\pi\) | |||||||
\(614\) | 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 | \(-0.167016\pi\) |
−0.500951 | + | 0.865476i | \(0.667016\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16137.1i | 1.04783i | 0.851771 | + | 0.523914i | \(0.175529\pi\) | ||||
−0.851771 | + | 0.523914i | \(0.824471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 577.406 | − | 577.406i | 0.0372217 | − | 0.0372217i | ||||
\(623\) | 2105.69 | − | 2105.69i | 0.135414 | − | 0.135414i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 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 | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −275.717 | + | 275.717i | −0.0171496 | + | 0.0171496i | ||||
\(638\) | −798.729 | + | 798.729i | −0.0495643 | + | 0.0495643i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8057.35i | 0.496484i | 0.968698 | + | 0.248242i | \(0.0798528\pi\) | ||||
−0.968698 | + | 0.248242i | \(0.920147\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15024.4 | − | 15024.4i | −0.921471 | − | 0.921471i | 0.0756629 | − | 0.997133i | \(-0.475893\pi\) |
−0.997133 | + | 0.0756629i | \(0.975893\pi\) | |||||||
\(644\) | −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 | \(-0.217163\pi\) |
−0.630532 | + | 0.776163i | \(0.717163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 13531.0i | − | 0.818394i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 617.645 | − | 617.645i | 0.0370995 | − | 0.0370995i | ||||
\(653\) | 10852.1 | − | 10852.1i | 0.650343 | − | 0.650343i | −0.302732 | − | 0.953076i | \(-0.597899\pi\) |
0.953076 | + | 0.302732i | \(0.0978988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 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 | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12087.8 | − | 12087.8i | 0.701710 | − | 0.701710i | ||||
\(668\) | −3353.96 | + | 3353.96i | −0.194264 | + | 0.194264i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7402.22i | 0.425871i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1618.29 | + | 1618.29i | 0.0926903 | + | 0.0926903i | 0.751932 | − | 0.659241i | \(-0.229122\pi\) |
−0.659241 | + | 0.751932i | \(0.729122\pi\) | |||||||
\(674\) | 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 | \(-0.0259874\pi\) |
−0.0815511 | + | 0.996669i | \(0.525987\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16791.1i | − | 0.949017i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −231.997 | + | 231.997i | −0.0130258 | + | 0.0130258i | ||||
\(683\) | 23612.1 | − | 23612.1i | 1.32283 | − | 1.32283i | 0.411351 | − | 0.911477i | \(-0.365057\pi\) |
0.911477 | − | 0.411351i | \(-0.134943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 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 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30814.2 | + | 30814.2i | −1.67457 | + | 1.67457i | ||||
\(698\) | −409.171 | + | 409.171i | −0.0221882 | + | 0.0221882i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33366.3i | − | 1.79776i | −0.438200 | − | 0.898878i | \(-0.644384\pi\) | ||
0.438200 | − | 0.898878i | \(-0.355616\pi\) | |||||||
\(702\) | 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 | \(-0.957832\pi\) | ||
0.991238 | − | 0.132087i | \(-0.0421677\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −637.581 | + | 637.581i | −0.0335595 | + | 0.0335595i | ||||
\(713\) | 3510.98 | − | 3510.98i | 0.184414 | − | 0.184414i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 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 | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10057.9 | − | 10057.9i | 0.513106 | − | 0.513106i | −0.402371 | − | 0.915477i | \(-0.631814\pi\) |
0.915477 | + | 0.402371i | \(0.131814\pi\) | |||||||
\(728\) | 342.983 | − | 342.983i | 0.0174613 | − | 0.0174613i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4151.76i | 0.210066i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4209.55 | + | 4209.55i | 0.212119 | + | 0.212119i | 0.805167 | − | 0.593048i | \(-0.202076\pi\) |
−0.593048 | + | 0.805167i | \(0.702076\pi\) | |||||||
\(734\) | −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 | \(-0.962278\pi\) | ||
0.992986 | − | 0.118231i | \(-0.0377223\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1942.07 | + | 1942.07i | −0.0960857 | + | 0.0960857i | ||||
\(743\) | −16266.1 | + | 16266.1i | −0.803159 | + | 0.803159i | −0.983588 | − | 0.180429i | \(-0.942251\pi\) |
0.180429 | + | 0.983588i | \(0.442251\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 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 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6722.97 | − | 6722.97i | 0.322788 | − | 0.322788i | −0.527048 | − | 0.849836i | \(-0.676701\pi\) |
0.849836 | + | 0.527048i | \(0.176701\pi\) | |||||||
\(758\) | 2420.99 | − | 2420.99i | 0.116008 | − | 0.116008i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 7001.94i | − | 0.333535i | −0.985996 | − | 0.166767i | \(-0.946667\pi\) | ||
0.985996 | − | 0.166767i | \(-0.0533329\pi\) | |||||||
\(762\) | 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 | \(0.200991\pi\) | ||||
−0.807183 | + | 0.590301i | \(0.799009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15387.7 | − | 15387.7i | 0.717376 | − | 0.717376i | ||||
\(773\) | −7322.13 | + | 7322.13i | −0.340697 | + | 0.340697i | −0.856629 | − | 0.515932i | \(-0.827446\pi\) |
0.515932 | + | 0.856629i | \(0.327446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 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 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16794.5 | + | 16794.5i | −0.760683 | + | 0.760683i | −0.976446 | − | 0.215763i | \(-0.930776\pi\) |
0.215763 | + | 0.976446i | \(0.430776\pi\) | |||||||
\(788\) | −21157.9 | + | 21157.9i | −0.956495 | + | 0.956495i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 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 | \(-0.453070\pi\) |
−0.989151 | + | 0.146900i | \(0.953070\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34580.0i | 1.53110i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3927.01 | − | 3927.01i | 0.172902 | − | 0.172902i | ||||
\(803\) | 2091.10 | − | 2091.10i | 0.0918972 | − | 0.0918972i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 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 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2910.68 | − | 2910.68i | 0.124641 | − | 0.124641i | ||||
\(818\) | −1841.14 | + | 1841.14i | −0.0786968 | + | 0.0786968i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5783.29i | − | 0.245844i | −0.992416 | − | 0.122922i | \(-0.960773\pi\) | ||
0.992416 | − | 0.122922i | \(-0.0392265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2021.92 | − | 2021.92i | −0.0856375 | − | 0.0856375i | 0.662990 | − | 0.748628i | \(-0.269287\pi\) |
−0.748628 | + | 0.662990i | \(0.769287\pi\) | |||||||
\(824\) | −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 | \(-0.430039\pi\) |
−0.975944 | + | 0.218022i | \(0.930039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 42400.5i | − | 1.77640i | −0.459462 | − | 0.888198i | \(-0.651958\pi\) | ||
0.459462 | − | 0.888198i | \(-0.348042\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1122.97 | − | 1122.97i | 0.0467933 | − | 0.0467933i | ||||
\(833\) | −7493.75 | + | 7493.75i | −0.311696 | + | 0.311696i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 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 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8236.11 | + | 8236.11i | −0.334116 | + | 0.334116i | ||||
\(848\) | −13452.2 | + | 13452.2i | −0.544754 | + | 0.544754i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 66136.1i | − | 2.66406i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26447.7 | + | 26447.7i | 1.06161 | + | 1.06161i | 0.997973 | + | 0.0636372i | \(0.0202701\pi\) |
0.0636372 | + | 0.997973i | \(0.479730\pi\) | |||||||
\(854\) | 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 | \(-0.429854\pi\) |
−0.975817 | + | 0.218590i | \(0.929854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 29326.5i | − | 1.16485i | −0.812885 | − | 0.582425i | \(-0.802104\pi\) | ||
0.812885 | − | 0.582425i | \(-0.197896\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2414.95 | + | 2414.95i | −0.0954219 | + | 0.0954219i | ||||
\(863\) | 23070.8 | − | 23070.8i | 0.910011 | − | 0.910011i | −0.0862616 | − | 0.996273i | \(-0.527492\pi\) |
0.996273 | + | 0.0862616i | \(0.0274921\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 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 | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20252.6 | + | 20252.6i | −0.779795 | + | 0.779795i | −0.979796 | − | 0.200001i | \(-0.935906\pi\) |
0.200001 | + | 0.979796i | \(0.435906\pi\) | |||||||
\(878\) | −3022.67 | + | 3022.67i | −0.116185 | + | 0.116185i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15547.7i | 0.594569i | 0.954789 | + | 0.297284i | \(0.0960809\pi\) | ||||
−0.954789 | + | 0.297284i | \(0.903919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17599.2 | − | 17599.2i | −0.670737 | − | 0.670737i | 0.287149 | − | 0.957886i | \(-0.407293\pi\) |
−0.957886 | + | 0.287149i | \(0.907293\pi\) | |||||||
\(884\) | 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 | \(-0.171679\pi\) |
−0.513573 | + | 0.858046i | \(0.671679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27569.2i | 1.04009i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28205.9 | + | 28205.9i | −1.05875 | + | 1.05875i | ||||
\(893\) | 24243.0 | − | 24243.0i | 0.908467 | − | 0.908467i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 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 | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28827.2 | + | 28827.2i | −1.05534 | + | 1.05534i | −0.0569624 | + | 0.998376i | \(0.518142\pi\) |
−0.998376 | + | 0.0569624i | \(0.981858\pi\) | |||||||
\(908\) | −13590.9 | + | 13590.9i | −0.496728 | + | 0.496728i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32922.1i | − | 1.19732i | −0.801003 | − | 0.598660i | \(-0.795700\pi\) | ||
0.801003 | − | 0.598660i | \(-0.204300\pi\) | |||||||
\(912\) | 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 | \(-0.828135\pi\) | ||
0.857744 | − | 0.514077i | \(-0.171865\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3830.67 | − | 3830.67i | 0.136829 | − | 0.136829i | ||||
\(923\) | 1523.92 | − | 1523.92i | 0.0543450 | − | 0.0543450i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 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 | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18170.0 | − | 18170.0i | 0.633500 | − | 0.633500i | −0.315444 | − | 0.948944i | \(-0.602154\pi\) |
0.948944 | + | 0.315444i | \(0.102154\pi\) | |||||||
\(938\) | −4324.31 | + | 4324.31i | −0.150526 | + | 0.150526i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7693.26i | 0.266518i | 0.991081 | + | 0.133259i | \(0.0425442\pi\) | ||||
−0.991081 | + | 0.133259i | \(0.957456\pi\) | |||||||
\(942\) | 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 | \(-0.173636\pi\) |
−0.518841 | + | 0.854871i | \(0.673636\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 373.216i | − | 0.0127662i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9321.99 | − | 9321.99i | 0.317361 | − | 0.317361i | ||||
\(953\) | −22620.8 | + | 22620.8i | −0.768899 | + | 0.768899i | −0.977913 | − | 0.209014i | \(-0.932975\pi\) |
0.209014 | + | 0.977913i | \(0.432975\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 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 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4426.36 | − | 4426.36i | 0.147200 | − | 0.147200i | −0.629666 | − | 0.776866i | \(-0.716808\pi\) |
0.776866 | + | 0.629666i | \(0.216808\pi\) | |||||||
\(968\) | 2493.81 | − | 2493.81i | 0.0828037 | − | 0.0828037i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36943.3i | 1.22097i | 0.792026 | + | 0.610487i | \(0.209026\pi\) | ||||
−0.792026 | + | 0.610487i | \(0.790974\pi\) | |||||||
\(972\) | 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 | \(-0.361254\pi\) |
−0.906498 | + | 0.422211i | \(0.861254\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3915.98i | 0.127840i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5410.00 | + | 5410.00i | −0.175805 | + | 0.175805i | ||||
\(983\) | −12134.8 | + | 12134.8i | −0.393733 | + | 0.393733i | −0.876015 | − | 0.482283i | \(-0.839808\pi\) |
0.482283 | + | 0.876015i | \(0.339808\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 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 | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44483.8 | − | 44483.8i | 1.41306 | − | 1.41306i | 0.677912 | − | 0.735143i | \(-0.262885\pi\) |
0.735143 | − | 0.677912i | \(-0.237115\pi\) | |||||||
\(998\) | 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 | 225.4.f.c.143.4 | 12 | ||
3.2 | odd | 2 | inner | 225.4.f.c.143.3 | 12 | ||
5.2 | odd | 4 | inner | 225.4.f.c.107.3 | 12 | ||
5.3 | odd | 4 | 45.4.f.a.17.4 | yes | 12 | ||
5.4 | even | 2 | 45.4.f.a.8.3 | ✓ | 12 | ||
15.2 | even | 4 | inner | 225.4.f.c.107.4 | 12 | ||
15.8 | even | 4 | 45.4.f.a.17.3 | yes | 12 | ||
15.14 | odd | 2 | 45.4.f.a.8.4 | yes | 12 | ||
20.3 | even | 4 | 720.4.w.d.17.6 | 12 | |||
20.19 | odd | 2 | 720.4.w.d.593.1 | 12 | |||
60.23 | odd | 4 | 720.4.w.d.17.1 | 12 | |||
60.59 | even | 2 | 720.4.w.d.593.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.f.a.8.3 | ✓ | 12 | 5.4 | even | 2 | ||
45.4.f.a.8.4 | yes | 12 | 15.14 | odd | 2 | ||
45.4.f.a.17.3 | yes | 12 | 15.8 | even | 4 | ||
45.4.f.a.17.4 | yes | 12 | 5.3 | odd | 4 | ||
225.4.f.c.107.3 | 12 | 5.2 | odd | 4 | inner | ||
225.4.f.c.107.4 | 12 | 15.2 | even | 4 | inner | ||
225.4.f.c.143.3 | 12 | 3.2 | odd | 2 | inner | ||
225.4.f.c.143.4 | 12 | 1.1 | even | 1 | trivial | ||
720.4.w.d.17.1 | 12 | 60.23 | odd | 4 | |||
720.4.w.d.17.6 | 12 | 20.3 | even | 4 | |||
720.4.w.d.593.1 | 12 | 20.19 | odd | 2 | |||
720.4.w.d.593.6 | 12 | 60.59 | even | 2 |