Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,3,Mod(161,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.n (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.1581053786\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.8 | ||
Character | \(\chi\) | \(=\) | 960.161 |
Dual form | 960.3.n.a.161.6 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.61015 | + | 2.53129i | −0.536717 | + | 0.843762i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.16215 | −1.16602 | −0.583010 | − | 0.812465i | \(-0.698125\pi\) | ||||
−0.583010 | + | 0.812465i | \(0.698125\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.81483 | − | 8.15151i | −0.423870 | − | 0.905723i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.16840 | −0.469855 | −0.234927 | − | 0.972013i | \(-0.575485\pi\) | ||||
−0.234927 | + | 0.972013i | \(0.575485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.76739i | − | 0.366723i | −0.983046 | − | 0.183361i | \(-0.941302\pi\) | ||
0.983046 | − | 0.183361i | \(-0.0586978\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.60041 | + | 5.66013i | −0.240027 | + | 0.377342i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.74659i | − | 0.102741i | −0.998680 | − | 0.0513703i | \(-0.983641\pi\) | ||
0.998680 | − | 0.0513703i | \(-0.0163589\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9.75481i | 0.513411i | 0.966490 | + | 0.256706i | \(0.0826371\pi\) | ||||
−0.966490 | + | 0.256706i | \(0.917363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.1423 | − | 20.6607i | 0.625823 | − | 0.983845i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.74019i | − | 0.249573i | −0.992184 | − | 0.124787i | \(-0.960175\pi\) | ||
0.992184 | − | 0.124787i | \(-0.0398246\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.7763 | + | 3.46871i | 0.991713 | + | 0.128471i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.7010 | 1.36900 | 0.684500 | − | 0.729013i | \(-0.260021\pi\) | ||||
0.684500 | + | 0.729013i | \(0.260021\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.67289 | 0.279771 | 0.139885 | − | 0.990168i | \(-0.455327\pi\) | ||||
0.139885 | + | 0.990168i | \(0.455327\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.32190 | − | 13.0827i | 0.252179 | − | 0.396446i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −18.2511 | −0.521460 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 71.0861i | − | 1.92124i | −0.277857 | − | 0.960622i | \(-0.589624\pi\) | ||
0.277857 | − | 0.960622i | \(-0.410376\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.0676 | + | 7.67622i | 0.309427 | + | 0.196826i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 62.7390i | 1.53022i | 0.643900 | + | 0.765110i | \(0.277315\pi\) | ||||
−0.643900 | + | 0.765110i | \(0.722685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 47.8315i | − | 1.11236i | −0.831061 | − | 0.556181i | \(-0.812266\pi\) | ||
0.831061 | − | 0.556181i | \(-0.187734\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.53022 | − | 18.2273i | −0.189561 | − | 0.405052i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 46.8289i | 0.996360i | 0.867074 | + | 0.498180i | \(0.165998\pi\) | ||||
−0.867074 | + | 0.498180i | \(0.834002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.6206 | 0.359605 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.42113 | + | 2.81228i | 0.0866887 | + | 0.0551427i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 81.3380 | 1.53468 | 0.767339 | − | 0.641241i | \(-0.221580\pi\) | ||||
0.767339 | + | 0.641241i | \(0.221580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.5569 | −0.210125 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24.6922 | − | 15.7067i | −0.433197 | − | 0.275556i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 34.8270 | 0.590288 | 0.295144 | − | 0.955453i | \(-0.404632\pi\) | ||||
0.295144 | + | 0.955453i | \(0.404632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4409i | 0.236736i | 0.992970 | + | 0.118368i | \(0.0377663\pi\) | ||||
−0.992970 | + | 0.118368i | \(0.962234\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 31.1372 | + | 66.5338i | 0.494242 | + | 1.05609i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.6602i | − | 0.164003i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.67810i | − | 0.114598i | −0.998357 | − | 0.0572992i | \(-0.981751\pi\) | ||
0.998357 | − | 0.0572992i | \(-0.0182489\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.5301 | + | 9.24256i | 0.210581 | + | 0.133950i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 41.0888i | 0.578715i | 0.957221 | + | 0.289357i | \(0.0934416\pi\) | ||||
−0.957221 | + | 0.289357i | \(0.906558\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.10709 | −0.0836588 | −0.0418294 | − | 0.999125i | \(-0.513319\pi\) | ||||
−0.0418294 | + | 0.999125i | \(0.513319\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.05075 | + | 12.6564i | −0.107343 | + | 0.168752i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 42.1853 | 0.547860 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 136.245 | 1.72461 | 0.862307 | − | 0.506386i | \(-0.169019\pi\) | ||||
0.862307 | + | 0.506386i | \(0.169019\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51.8941 | + | 62.1933i | −0.640668 | + | 0.767818i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −116.464 | −1.40318 | −0.701590 | − | 0.712581i | \(-0.747526\pi\) | ||||
−0.701590 | + | 0.712581i | \(0.747526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.90550i | − | 0.0459470i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −63.9245 | + | 100.495i | −0.734765 | + | 1.15511i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 73.1472i | − | 0.821879i | −0.911663 | − | 0.410939i | \(-0.865201\pi\) | ||
0.911663 | − | 0.410939i | \(-0.134799\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38.9122i | 0.427606i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.9647 | + | 21.9536i | −0.150158 | + | 0.236060i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.8124i | 0.229605i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.86582 | 0.0501631 | 0.0250815 | − | 0.999685i | \(-0.492015\pi\) | ||||
0.0250815 | + | 0.999685i | \(0.492015\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.7166 | + | 42.1303i | 0.199157 | + | 0.425558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 149.808 | 1.48325 | 0.741623 | − | 0.670817i | \(-0.234056\pi\) | ||||
0.741623 | + | 0.670817i | \(0.234056\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 98.6161 | 0.957438 | 0.478719 | − | 0.877968i | \(-0.341101\pi\) | ||||
0.478719 | + | 0.877968i | \(0.341101\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 29.3870 | − | 46.1988i | 0.279877 | − | 0.439989i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 53.6536 | 0.501435 | 0.250718 | − | 0.968060i | \(-0.419333\pi\) | ||||
0.250718 | + | 0.968060i | \(0.419333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.3967i | 0.0953824i | 0.998862 | + | 0.0476912i | \(0.0151863\pi\) | ||||
−0.998862 | + | 0.0476912i | \(0.984814\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 179.939 | + | 114.459i | 1.62107 | + | 1.03116i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 160.091i | − | 1.41673i | −0.705844 | − | 0.708367i | \(-0.749432\pi\) | ||
0.705844 | − | 0.708367i | \(-0.250568\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 12.8354i | − | 0.111613i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −38.8614 | + | 18.1868i | −0.332149 | + | 0.155443i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.2559i | 0.119798i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −94.2876 | −0.779237 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −158.811 | − | 101.019i | −1.29114 | − | 0.821295i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 175.172 | 1.37931 | 0.689653 | − | 0.724140i | \(-0.257763\pi\) | ||||
0.689653 | + | 0.724140i | \(0.257763\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 121.075 | + | 77.0160i | 0.938569 | + | 0.597023i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 189.821 | 1.44901 | 0.724507 | − | 0.689267i | \(-0.242067\pi\) | ||||
0.724507 | + | 0.689267i | \(0.242067\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 79.6202i | − | 0.598648i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 59.8735 | + | 7.75628i | 0.443508 | + | 0.0574539i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 180.907i | 1.32049i | 0.751050 | + | 0.660246i | \(0.229548\pi\) | ||||
−0.751050 | + | 0.660246i | \(0.770452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 169.479i | 1.21927i | 0.792682 | + | 0.609635i | \(0.208684\pi\) | ||||
−0.792682 | + | 0.609635i | \(0.791316\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −118.538 | − | 75.4016i | −0.840692 | − | 0.534763i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 24.6398i | 0.172306i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 88.7741 | 0.612235 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −28.3719 | + | 44.6029i | −0.193006 | + | 0.303421i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 177.189 | 1.18919 | 0.594594 | − | 0.804026i | \(-0.297313\pi\) | ||||
0.594594 | + | 0.804026i | \(0.297313\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −195.030 | −1.29159 | −0.645793 | − | 0.763512i | \(-0.723473\pi\) | ||||
−0.645793 | + | 0.763512i | \(0.723473\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.2374 | + | 6.66296i | −0.0930546 | + | 0.0435487i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.3932 | 0.125117 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.0487i | − | 0.121329i | −0.998158 | − | 0.0606647i | \(-0.980678\pi\) | ||
0.998158 | − | 0.0606647i | \(-0.0193220\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −130.966 | + | 205.890i | −0.823688 | + | 1.29490i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 46.8522i | 0.291008i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 178.468i | − | 1.09489i | −0.836841 | − | 0.547446i | \(-0.815600\pi\) | ||
0.836841 | − | 0.547446i | \(-0.184400\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.6083 | − | 29.2538i | 0.112778 | − | 0.177296i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 165.641i | − | 0.991860i | −0.868363 | − | 0.495930i | \(-0.834827\pi\) | ||
0.868363 | − | 0.495930i | \(-0.165173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 146.272 | 0.865515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 79.5164 | − | 37.2130i | 0.465008 | − | 0.217620i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.0955 | −0.0872570 | −0.0436285 | − | 0.999048i | \(-0.513892\pi\) | ||||
−0.0436285 | + | 0.999048i | \(0.513892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −40.8107 | −0.233204 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −56.0767 | + | 88.1572i | −0.316818 | + | 0.498063i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 241.590 | 1.34966 | 0.674831 | − | 0.737972i | \(-0.264216\pi\) | ||||
0.674831 | + | 0.737972i | \(0.264216\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 94.1790i | 0.520326i | 0.965565 | + | 0.260163i | \(0.0837763\pi\) | ||||
−0.965565 | + | 0.260163i | \(0.916224\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −36.5541 | − | 23.2520i | −0.199749 | − | 0.127060i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 158.953i | − | 0.859207i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.02709i | 0.0482732i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −218.552 | − | 28.3121i | −1.15636 | − | 0.149800i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 281.488i | − | 1.47376i | −0.676025 | − | 0.736879i | \(-0.736299\pi\) | ||
0.676025 | − | 0.736879i | \(-0.263701\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −165.831 | −0.859227 | −0.429614 | − | 0.903013i | \(-0.641350\pi\) | ||||
−0.429614 | + | 0.903013i | \(0.641350\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.9841 | + | 17.1646i | 0.138380 | + | 0.0880233i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 316.768 | 1.60796 | 0.803980 | − | 0.594656i | \(-0.202712\pi\) | ||||
0.803980 | + | 0.594656i | \(0.202712\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −176.704 | −0.887960 | −0.443980 | − | 0.896037i | \(-0.646434\pi\) | ||||
−0.443980 | + | 0.896037i | \(0.646434\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.4355 | + | 12.3629i | 0.0966939 | + | 0.0615069i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −324.045 | −1.59628 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 140.289i | 0.684335i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −46.7912 | + | 21.8979i | −0.226044 | + | 0.105787i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 50.4168i | − | 0.241229i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 102.122i | − | 0.483993i | −0.970277 | − | 0.241996i | \(-0.922198\pi\) | ||
0.970277 | − | 0.241996i | \(-0.0778022\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −104.007 | − | 66.1591i | −0.488298 | − | 0.310606i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 106.955i | − | 0.497463i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −70.7894 | −0.326219 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.83333 | − | 15.4588i | 0.0449011 | − | 0.0705881i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.32669 | −0.0376773 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −307.107 | −1.37716 | −0.688580 | − | 0.725160i | \(-0.741766\pi\) | ||||
−0.688580 | + | 0.725160i | \(0.741766\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.0742 | − | 40.7575i | −0.0847741 | − | 0.181145i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −243.151 | −1.07115 | −0.535575 | − | 0.844488i | \(-0.679905\pi\) | ||||
−0.535575 | + | 0.844488i | \(0.679905\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 357.133i | − | 1.55953i | −0.626070 | − | 0.779767i | \(-0.715338\pi\) | ||
0.626070 | − | 0.779767i | \(-0.284662\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −67.9246 | + | 106.783i | −0.294046 | + | 0.462264i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 183.981i | 0.789618i | 0.918763 | + | 0.394809i | \(0.129189\pi\) | ||||
−0.918763 | + | 0.394809i | \(0.870811\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 104.713i | 0.445586i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −219.374 | + | 344.874i | −0.925629 | + | 1.45516i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 347.730i | − | 1.45494i | −0.686141 | − | 0.727469i | \(-0.740697\pi\) | ||
0.686141 | − | 0.727469i | \(-0.259303\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −339.671 | −1.40942 | −0.704711 | − | 0.709495i | \(-0.748923\pi\) | ||||
−0.704711 | + | 0.709495i | \(0.748923\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −73.8717 | − | 231.499i | −0.303999 | − | 0.952672i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 39.4009 | 0.160820 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 46.5050 | 0.188280 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 187.524 | − | 294.804i | 0.753110 | − | 1.18395i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −75.7547 | −0.301812 | −0.150906 | − | 0.988548i | \(-0.548219\pi\) | ||||
−0.150906 | + | 0.988548i | \(0.548219\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.6676i | 0.117263i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.88594 | + | 6.28844i | 0.0387684 | + | 0.0246605i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 51.9361i | − | 0.202086i | −0.994882 | − | 0.101043i | \(-0.967782\pi\) | ||
0.994882 | − | 0.101043i | \(-0.0322179\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 580.215i | 2.24021i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −151.453 | − | 323.623i | −0.580278 | − | 1.23993i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 315.740i | − | 1.20053i | −0.799801 | − | 0.600266i | \(-0.795062\pi\) | ||
0.799801 | − | 0.600266i | \(-0.204938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 181.877 | 0.686329 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 185.157 | + | 117.778i | 0.693470 | + | 0.441116i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −335.479 | −1.24713 | −0.623567 | − | 0.781770i | \(-0.714317\pi\) | ||||
−0.623567 | + | 0.781770i | \(0.714317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −58.0706 | −0.214283 | −0.107141 | − | 0.994244i | \(-0.534170\pi\) | ||||
−0.107141 | + | 0.994244i | \(0.534170\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −98.4979 | − | 62.6544i | −0.360798 | − | 0.229503i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −25.8420 | −0.0939710 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.02211i | − | 0.00730004i | −0.999993 | − | 0.00365002i | \(-0.998838\pi\) | ||
0.999993 | − | 0.00365002i | \(-0.00116184\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −33.0856 | − | 70.6971i | −0.118586 | − | 0.253395i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 260.289i | 0.926296i | 0.886281 | + | 0.463148i | \(0.153280\pi\) | ||||
−0.886281 | + | 0.463148i | \(0.846720\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 270.345i | − | 0.955282i | −0.878555 | − | 0.477641i | \(-0.841492\pi\) | ||
0.878555 | − | 0.477641i | \(-0.158508\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −55.2135 | − | 35.1213i | −0.193732 | − | 0.123233i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 512.085i | − | 1.78427i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 285.949 | 0.989444 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.83470 | + | 12.3168i | −0.0269234 | + | 0.0423257i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 228.079 | 0.778426 | 0.389213 | − | 0.921148i | \(-0.372747\pi\) | ||||
0.389213 | + | 0.921148i | \(0.372747\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 77.8756 | 0.263985 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −138.390 | − | 17.9277i | −0.465961 | − | 0.0603626i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.3657 | −0.0915242 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 390.408i | 1.29704i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −241.213 | + | 379.207i | −0.796083 | + | 1.25151i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 32.2908i | 0.105872i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 450.897i | − | 1.46872i | −0.678760 | − | 0.734360i | \(-0.737482\pi\) | ||
0.678760 | − | 0.734360i | \(-0.262518\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −158.787 | + | 249.626i | −0.513873 | + | 0.807850i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 103.595i | − | 0.333103i | −0.986033 | − | 0.166551i | \(-0.946737\pi\) | ||
0.986033 | − | 0.166551i | \(-0.0532632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −356.467 | −1.13887 | −0.569436 | − | 0.822036i | \(-0.692838\pi\) | ||||
−0.569436 | + | 0.822036i | \(0.692838\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 69.6249 | + | 148.774i | 0.221032 | + | 0.472299i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −377.664 | −1.19137 | −0.595685 | − | 0.803218i | \(-0.703119\pi\) | ||||
−0.595685 | + | 0.803218i | \(0.703119\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −205.191 | −0.643231 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −86.3903 | + | 135.813i | −0.269129 | + | 0.423092i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.0377 | 0.0527482 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 23.8370i | − | 0.0733445i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −26.3170 | − | 16.7402i | −0.0804801 | − | 0.0511933i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 382.225i | − | 1.16178i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 185.939i | − | 0.561749i | −0.959744 | − | 0.280875i | \(-0.909376\pi\) | ||
0.959744 | − | 0.280875i | \(-0.0906245\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −579.458 | + | 271.181i | −1.74012 | + | 0.814359i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 17.1687i | − | 0.0512500i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 403.318 | 1.19679 | 0.598395 | − | 0.801201i | \(-0.295805\pi\) | ||||
0.598395 | + | 0.801201i | \(0.295805\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 405.236 | + | 257.770i | 1.19539 | + | 0.760385i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.8250 | −0.131452 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 256.123 | 0.746714 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 32.4902 | + | 20.6670i | 0.0941745 | + | 0.0599044i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 505.149 | 1.45576 | 0.727880 | − | 0.685704i | \(-0.240506\pi\) | ||||
0.727880 | + | 0.685704i | \(0.240506\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 524.781i | 1.50367i | 0.659351 | + | 0.751836i | \(0.270831\pi\) | ||||
−0.659351 | + | 0.751836i | \(0.729169\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.5367 | − | 127.653i | 0.0471132 | − | 0.363684i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 552.296i | 1.56458i | 0.622917 | + | 0.782288i | \(0.285948\pi\) | ||||
−0.622917 | + | 0.782288i | \(0.714052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 91.8772i | 0.258809i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −36.0859 | − | 22.9542i | −0.101081 | − | 0.0642975i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.42319i | − | 0.0262485i | −0.999914 | − | 0.0131242i | \(-0.995822\pi\) | ||
0.999914 | − | 0.0131242i | \(-0.00417769\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 265.844 | 0.736409 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 151.817 | − | 238.669i | 0.418229 | − | 0.657491i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.6559 | −0.0374133 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −83.5907 | −0.227768 | −0.113884 | − | 0.993494i | \(-0.536329\pi\) | ||||
−0.113884 | + | 0.993494i | \(0.536329\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 511.418 | − | 239.339i | 1.38596 | − | 0.648615i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −663.892 | −1.78947 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 354.792i | 0.951185i | 0.879666 | + | 0.475592i | \(0.157766\pi\) | ||||
−0.879666 | + | 0.475592i | \(0.842234\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −18.0020 | + | 28.3007i | −0.0480054 | + | 0.0754684i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 189.270i | − | 0.502043i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 375.899i | 0.991818i | 0.868374 | + | 0.495909i | \(0.165165\pi\) | ||||
−0.868374 | + | 0.495909i | \(0.834835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −282.053 | + | 443.410i | −0.740297 | + | 1.16381i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 596.645i | − | 1.55782i | −0.627136 | − | 0.778910i | \(-0.715773\pi\) | ||
0.627136 | − | 0.778910i | \(-0.284227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 94.3291 | 0.245011 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −389.899 | + | 182.469i | −1.00749 | + | 0.471497i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 353.985 | 0.909987 | 0.454993 | − | 0.890495i | \(-0.349642\pi\) | ||||
0.454993 | + | 0.890495i | \(0.349642\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.0258 | −0.0256413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −305.640 | + | 480.491i | −0.777710 | + | 1.22262i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 304.652 | 0.771271 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 184.801i | 0.465494i | 0.972537 | + | 0.232747i | \(0.0747714\pi\) | ||||
−0.972537 | + | 0.232747i | \(0.925229\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 201.542 | + | 128.201i | 0.505117 | + | 0.321305i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 106.165i | 0.264751i | 0.991200 | + | 0.132375i | \(0.0422604\pi\) | ||||
−0.991200 | + | 0.132375i | \(0.957740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 41.3471i | − | 0.102598i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −116.039 | + | 139.068i | −0.286515 | + | 0.343379i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 367.401i | 0.902706i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 192.636 | 0.470992 | 0.235496 | − | 0.971875i | \(-0.424329\pi\) | ||||
0.235496 | + | 0.971875i | \(0.424329\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −457.928 | − | 291.288i | −1.11418 | − | 0.708730i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −284.263 | −0.688289 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −260.421 | −0.627521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −428.999 | − | 272.886i | −1.02877 | − | 0.654403i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 616.975 | 1.47249 | 0.736247 | − | 0.676713i | \(-0.236596\pi\) | ||||
0.736247 | + | 0.676713i | \(0.236596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 173.681i | − | 0.412545i | −0.978495 | − | 0.206272i | \(-0.933867\pi\) | ||
0.978495 | − | 0.206272i | \(-0.0661333\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 381.726 | − | 178.645i | 0.902426 | − | 0.422328i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 8.73296i | − | 0.0205481i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 117.869i | − | 0.276039i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −62.3704 | − | 39.6738i | −0.145386 | − | 0.0924797i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 217.302i | − | 0.504182i | −0.967704 | − | 0.252091i | \(-0.918882\pi\) | ||
0.967704 | − | 0.252091i | \(-0.0811182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −683.809 | −1.57924 | −0.789618 | − | 0.613599i | \(-0.789721\pi\) | ||||
−0.789618 | + | 0.613599i | \(0.789721\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −142.940 | + | 224.713i | −0.328597 | + | 0.516581i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 55.9945 | 0.128134 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 515.364 | 1.17395 | 0.586975 | − | 0.809605i | \(-0.300319\pi\) | ||||
0.586975 | + | 0.809605i | \(0.300319\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −67.2198 | − | 143.635i | −0.152426 | − | 0.325702i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −56.6514 | −0.127881 | −0.0639407 | − | 0.997954i | \(-0.520367\pi\) | ||||
−0.0639407 | + | 0.997954i | \(0.520367\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 163.562i | − | 0.367555i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −285.301 | + | 448.516i | −0.638257 | + | 1.00339i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 526.462i | − | 1.17252i | −0.810122 | − | 0.586261i | \(-0.800599\pi\) | ||
0.810122 | − | 0.586261i | \(-0.199401\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 324.261i | − | 0.718981i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 314.027 | − | 493.676i | 0.693216 | − | 1.08979i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 87.0103i | 0.191231i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −62.7659 | −0.137343 | −0.0686717 | − | 0.997639i | \(-0.521876\pi\) | ||||
−0.0686717 | + | 0.997639i | \(0.521876\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.05843 | − | 46.7672i | 0.0131992 | − | 0.101889i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −171.672 | −0.372391 | −0.186195 | − | 0.982513i | \(-0.559616\pi\) | ||||
−0.186195 | + | 0.982513i | \(0.559616\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 174.511 | 0.376914 | 0.188457 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188457 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −31.2259 | + | 49.0897i | −0.0671525 | + | 0.105569i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −339.644 | −0.727289 | −0.363644 | − | 0.931538i | \(-0.618468\pi\) | ||||
−0.363644 | + | 0.931538i | \(0.618468\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 62.6697i | 0.133624i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 48.2177 | + | 30.6713i | 0.102373 | + | 0.0651195i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 247.213i | 0.522648i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 48.7741i | 0.102682i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −310.291 | − | 663.027i | −0.650505 | − | 1.38999i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 375.145i | − | 0.783185i | −0.920139 | − | 0.391592i | \(-0.871924\pi\) | ||
0.920139 | − | 0.391592i | \(-0.128076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −338.895 | −0.704564 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −118.597 | − | 75.4392i | −0.245541 | − | 0.156189i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.8803 | 0.0224336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −449.237 | −0.922458 | −0.461229 | − | 0.887281i | \(-0.652591\pi\) | ||||
−0.461229 | + | 0.887281i | \(0.652591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 451.753 | + | 287.360i | 0.923829 | + | 0.587647i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −296.423 | −0.603713 | −0.301857 | − | 0.953353i | \(-0.597606\pi\) | ||||
−0.301857 | + | 0.953353i | \(0.597606\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 69.3414i | − | 0.140652i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 44.0876 | + | 94.2061i | 0.0890659 | + | 0.190315i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 335.372i | − | 0.674794i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 847.011i | 1.69742i | 0.528861 | + | 0.848709i | \(0.322619\pi\) | ||||
−0.528861 | + | 0.848709i | \(0.677381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 419.284 | + | 266.706i | 0.836894 | + | 0.532348i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 600.517i | 1.19387i | 0.802289 | + | 0.596935i | \(0.203615\pi\) | ||||
−0.802289 | + | 0.596935i | \(0.796385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 334.980 | 0.663328 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −235.520 | + | 370.256i | −0.464536 | + | 0.730289i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 384.142 | 0.754699 | 0.377349 | − | 0.926071i | \(-0.376836\pi\) | ||||
0.377349 | + | 0.926071i | \(0.376836\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 49.8470 | 0.0975479 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −33.8366 | + | 261.197i | −0.0659584 | + | 0.509157i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 220.512 | 0.428179 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 242.031i | − | 0.468145i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.3060 | − | 38.2110i | 0.0468323 | − | 0.0736242i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 969.901i | − | 1.86161i | −0.365511 | − | 0.930807i | \(-0.619106\pi\) | ||
0.365511 | − | 0.930807i | \(-0.380894\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 403.371i | − | 0.771263i | −0.922653 | − | 0.385632i | \(-0.873984\pi\) | ||
0.922653 | − | 0.385632i | \(-0.126016\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 65.7114 | − | 103.304i | 0.125165 | − | 0.196769i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 15.1480i | − | 0.0287438i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 496.050 | 0.937713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −132.859 | − | 283.893i | −0.250206 | − | 0.534638i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 299.102 | 0.561166 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 119.973 | 0.224249 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −388.995 | + | 611.533i | −0.724386 | + | 1.13879i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −91.0705 | −0.168962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 834.729i | − | 1.54294i | −0.636267 | − | 0.771469i | \(-0.719522\pi\) | ||
0.636267 | − | 0.771469i | \(-0.280478\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −238.394 | − | 151.642i | −0.439031 | − | 0.279268i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23.2477i | 0.0426563i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 795.220i | − | 1.45378i | −0.686751 | − | 0.726892i | \(-0.740964\pi\) | ||
0.686751 | − | 0.726892i | \(-0.259036\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 117.715 | − | 55.0896i | 0.214417 | − | 0.100345i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 387.276i | 0.702860i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1112.05 | −2.01094 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 402.356 | + | 255.939i | 0.724966 | + | 0.461151i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 214.852 | 0.385731 | 0.192866 | − | 0.981225i | \(-0.438222\pi\) | ||||
0.192866 | + | 0.981225i | \(0.438222\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −228.032 | −0.407928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.8502 | − | 14.5350i | −0.0407311 | − | 0.0259090i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 526.184 | 0.934607 | 0.467304 | − | 0.884097i | \(-0.345225\pi\) | ||||
0.467304 | + | 0.884097i | \(0.345225\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 357.974i | − | 0.633583i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 423.567 | − | 507.630i | 0.747032 | − | 0.895292i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 255.284i | 0.448653i | 0.974514 | + | 0.224327i | \(0.0720183\pi\) | ||||
−0.974514 | + | 0.224327i | \(0.927982\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 190.752i | − | 0.334066i | −0.985951 | − | 0.167033i | \(-0.946581\pi\) | ||
0.985951 | − | 0.167033i | \(-0.0534187\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 712.526 | + | 453.237i | 1.24350 | + | 0.790990i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 28.7009i | − | 0.0499147i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1027.35 | 1.78050 | 0.890250 | − | 0.455471i | \(-0.150529\pi\) | ||||
0.890250 | + | 0.455471i | \(0.150529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 267.013 | − | 419.766i | 0.461162 | − | 0.724984i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 950.596 | 1.63614 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −420.387 | −0.721076 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −86.8968 | + | 40.6669i | −0.148542 | + | 0.0695161i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −236.995 | −0.403739 | −0.201869 | − | 0.979412i | \(-0.564702\pi\) | ||||
−0.201869 | + | 0.979412i | \(0.564702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 84.6025i | 0.143637i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −510.044 | + | 801.831i | −0.863019 | + | 1.35674i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1102.66i | 1.85946i | 0.368246 | + | 0.929728i | \(0.379958\pi\) | ||||
−0.368246 | + | 0.929728i | \(0.620042\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 31.8772i | 0.0535752i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 284.520 | − | 447.289i | 0.476583 | − | 0.749228i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 315.104i | 0.526050i | 0.964789 | + | 0.263025i | \(0.0847201\pi\) | ||||
−0.964789 | + | 0.263025i | \(0.915280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 163.211 | 0.271566 | 0.135783 | − | 0.990739i | \(-0.456645\pi\) | ||||
0.135783 | + | 0.990739i | \(0.456645\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −62.5880 | + | 29.2906i | −0.103794 | + | 0.0485749i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −210.834 | −0.348485 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −416.694 | −0.686482 | −0.343241 | − | 0.939247i | \(-0.611525\pi\) | ||||
−0.343241 | + | 0.939247i | \(0.611525\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 521.761 | − | 820.251i | 0.856751 | − | 1.34688i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 223.252 | 0.365388 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 376.371i | − | 0.613982i | −0.951712 | − | 0.306991i | \(-0.900678\pi\) | ||
0.951712 | − | 0.306991i | \(-0.0993222\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −355.111 | − | 225.886i | −0.577416 | − | 0.367294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 256.481i | 0.415691i | 0.978162 | + | 0.207846i | \(0.0666451\pi\) | ||||
−0.978162 | + | 0.207846i | \(0.933355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 943.976i | 1.52500i | 0.646987 | + | 0.762501i | \(0.276029\pi\) | ||||
−0.646987 | + | 0.762501i | \(0.723971\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 19.9111 | − | 153.701i | 0.0320629 | − | 0.247505i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 597.038i | 0.958328i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 127.619 | + | 81.1786i | 0.203540 | + | 0.129472i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −124.158 | −0.197390 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 979.595 | 1.55245 | 0.776224 | − | 0.630457i | \(-0.217132\pi\) | ||||
0.776224 | + | 0.630457i | \(0.217132\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 258.501 | + | 164.432i | 0.408375 | + | 0.259767i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 391.696 | 0.616844 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 84.0045i | − | 0.131875i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 334.935 | − | 156.747i | 0.524155 | − | 0.245300i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 194.583i | 0.303562i | 0.988414 | + | 0.151781i | \(0.0485008\pi\) | ||||
−0.988414 | + | 0.151781i | \(0.951499\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 364.353i | 0.566646i | 0.959025 | + | 0.283323i | \(0.0914368\pi\) | ||||
−0.959025 | + | 0.283323i | \(0.908563\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 270.733 | + | 172.213i | 0.419741 | + | 0.266997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 772.411i | 1.19384i | 0.802302 | + | 0.596918i | \(0.203608\pi\) | ||||
−0.802302 | + | 0.596918i | \(0.796392\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −180.000 | −0.277350 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 113.982 | − | 179.188i | 0.175087 | − | 0.275251i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 356.314 | 0.545657 | 0.272828 | − | 0.962063i | \(-0.412041\pi\) | ||||
0.272828 | + | 0.962063i | \(0.412041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 424.452 | 0.648019 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.2975 | + | 49.7820i | 0.0354605 | + | 0.0757717i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 498.693 | 0.756742 | 0.378371 | − | 0.925654i | \(-0.376484\pi\) | ||||
0.378371 | + | 0.925654i | \(0.376484\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 184.687i | − | 0.279405i | −0.990194 | − | 0.139703i | \(-0.955385\pi\) | ||
0.990194 | − | 0.139703i | \(-0.0446147\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.4072 | − | 21.0772i | 0.0202221 | − | 0.0317907i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 178.036i | − | 0.267724i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 227.891i | − | 0.341666i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 494.488 | − | 777.376i | 0.739145 | − | 1.16200i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 74.6364i | − | 0.111232i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −371.348 | −0.551781 | −0.275890 | − | 0.961189i | \(-0.588973\pi\) | ||||
−0.275890 | + | 0.961189i | \(0.588973\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 133.881 | + | 17.3436i | 0.198343 | + | 0.0256942i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 270.915 | 0.400170 | 0.200085 | − | 0.979779i | \(-0.435878\pi\) | ||||
0.200085 | + | 0.979779i | \(0.435878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.7155 | −0.0584912 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 391.510 | − | 615.485i | 0.574904 | − | 0.903796i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −581.504 | −0.851397 | −0.425698 | − | 0.904865i | \(-0.639972\pi\) | ||||
−0.425698 | + | 0.904865i | \(0.639972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 404.521i | 0.590542i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 904.007 | + | 575.038i | 1.31588 | + | 0.837028i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 387.770i | − | 0.562801i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 142.675i | 0.206476i | 0.994657 | + | 0.103238i | \(0.0329203\pi\) | ||||
−0.994657 | + | 0.103238i | \(0.967080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −160.930 | − | 343.873i | −0.232222 | − | 0.496210i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 378.966i | 0.545274i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 109.579 | 0.157216 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −465.709 | − | 296.237i | −0.666250 | − | 0.423801i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −268.963 | −0.383685 | −0.191843 | − | 0.981426i | \(-0.561446\pi\) | ||||
−0.191843 | + | 0.981426i | \(0.561446\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 693.431 | 0.986389 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −265.058 | − | 168.603i | −0.375969 | − | 0.239153i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1222.75 | −1.72950 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1204.06i | − | 1.69825i | −0.528190 | − | 0.849126i | \(-0.677129\pi\) | ||
0.528190 | − | 0.849126i | \(-0.322871\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −519.750 | − | 1110.60i | −0.731013 | − | 1.56202i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 49.7840i | − | 0.0698233i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 55.0963i | 0.0770577i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 880.205 | + | 559.898i | 1.22762 | + | 0.780889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1420.67i | 1.97589i | 0.154800 | + | 0.987946i | \(0.450527\pi\) | ||||
−0.154800 | + | 0.987946i | \(0.549473\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −804.919 | −1.11639 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 546.921 | − | 859.804i | 0.756460 | − | 1.18922i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 198.505 | 0.273800 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 532.985 | 0.733130 | 0.366565 | − | 0.930393i | \(-0.380534\pi\) | ||||
0.366565 | + | 0.930393i | \(0.380534\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 704.936 | + | 185.758i | 0.966990 | + | 0.254812i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −83.5422 | −0.114285 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 538.634i | − | 0.734835i | −0.930056 | − | 0.367418i | \(-0.880242\pi\) | ||
0.930056 | − | 0.367418i | \(-0.119758\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −63.4414 | + | 99.7351i | −0.0863149 | + | 0.135694i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.6835i | 0.0538446i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 792.423i | 1.07229i | 0.844126 | + | 0.536145i | \(0.180120\pi\) | ||||
−0.844126 | + | 0.536145i | \(0.819880\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −74.8801 | + | 117.718i | −0.101053 | + | 0.158863i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 657.405i | 0.884798i | 0.896818 | + | 0.442399i | \(0.145872\pi\) | ||||
−0.896818 | + | 0.442399i | \(0.854128\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 396.206 | 0.531821 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 444.291 | + | 949.357i | 0.594766 | + | 1.27089i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −437.928 | −0.584684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 735.089 | 0.978814 | 0.489407 | − | 0.872055i | \(-0.337213\pi\) | ||||
0.489407 | + | 0.872055i | \(0.337213\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 121.977 | − | 191.757i | 0.161987 | − | 0.254657i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −436.099 | −0.577615 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 613.660i | 0.810648i | 0.914173 | + | 0.405324i | \(0.132841\pi\) | ||||
−0.914173 | + | 0.405324i | \(0.867159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −75.0972 | − | 47.7693i | −0.0989423 | − | 0.0629371i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 76.5910i | − | 0.100645i | −0.998733 | − | 0.0503226i | \(-0.983975\pi\) | ||
0.998733 | − | 0.0503226i | \(-0.0160249\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 84.8593i | − | 0.111218i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −31.8357 | + | 14.8988i | −0.0416153 | + | 0.0194756i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 166.034i | − | 0.216472i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −577.971 | −0.751588 | −0.375794 | − | 0.926703i | \(-0.622630\pi\) | ||||
−0.375794 | + | 0.926703i | \(0.622630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 131.465 | + | 83.6249i | 0.170512 | + | 0.108463i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −696.300 | −0.900776 | −0.450388 | − | 0.892833i | \(-0.648714\pi\) | ||||
−0.450388 | + | 0.892833i | \(0.648714\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.3645 | 0.0559541 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1468.69 | − | 934.233i | −1.89021 | − | 1.20236i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −612.008 | −0.785632 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 212.363i | − | 0.271912i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1063.04 | + | 137.711i | 1.35765 | + | 0.175876i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 42.5942i | − | 0.0542601i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 712.691i | − | 0.905579i | −0.891617 | − | 0.452790i | \(-0.850429\pi\) | ||
0.891617 | − | 0.452790i | \(-0.149571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 799.228 | + | 508.388i | 1.01296 | + | 0.644345i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1306.69i | 1.65194i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68.8455 | 0.0868165 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −292.850 | + | 460.384i | −0.368364 | + | 0.579099i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 140.555 | 0.176355 | 0.0881774 | − | 0.996105i | \(-0.471896\pi\) | ||||
0.0881774 | + | 0.996105i | \(0.471896\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 81.7910 | 0.102367 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −596.260 | + | 279.044i | −0.744394 | + | 0.348370i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31.5639 | 0.0393075 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 104.765i | 0.130143i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 540.171 | − | 849.193i | 0.669357 | − | 1.05228i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 169.051i | 0.208963i | 0.994527 | + | 0.104482i | \(0.0333183\pi\) | ||||
−0.994527 | + | 0.104482i | \(0.966682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 237.265i | − | 0.292559i | −0.989243 | − | 0.146279i | \(-0.953270\pi\) | ||
0.989243 | − | 0.146279i | \(-0.0467298\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 93.5024 | − | 146.993i | 0.115009 | − | 0.180804i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 399.065i | − | 0.489651i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 466.588 | 0.571099 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 317.193 | − | 148.443i | 0.387293 | − | 0.181250i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1086.80 | −1.32375 | −0.661874 | − | 0.749615i | \(-0.730239\pi\) | ||||
−0.661874 | + | 0.749615i | \(0.730239\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −959.801 | −1.16622 | −0.583111 | − | 0.812392i | \(-0.698165\pi\) | ||||
−0.583111 | + | 0.812392i | \(0.698165\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 41.6095 | − | 65.4136i | 0.0504358 | − | 0.0792892i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1107.81 | 1.33955 | 0.669776 | − | 0.742563i | \(-0.266390\pi\) | ||||
0.669776 | + | 0.742563i | \(0.266390\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1451.55i | 1.75097i | 0.483249 | + | 0.875483i | \(0.339457\pi\) | ||||
−0.483249 | + | 0.875483i | \(0.660543\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.11854 | + | 3.25590i | 0.00615950 | + | 0.00391805i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 30.7761i | − | 0.0369460i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 370.384i | − | 0.443573i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 232.228 | + | 30.0838i | 0.277452 | + | 0.0359424i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 636.757i | 0.758948i | 0.925202 | + | 0.379474i | \(0.123895\pi\) | ||||
−0.925202 | + | 0.379474i | \(0.876105\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 735.167 | 0.874158 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −658.867 | − | 419.105i | −0.781574 | − | 0.497159i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 327.074 | 0.387070 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 769.589 | 0.908606 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 684.320 | + | 435.296i | 0.806031 | + | 0.512716i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −408.047 | −0.479492 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1114.31i | 1.30634i | 0.757212 | + | 0.653169i | \(0.226561\pi\) | ||||
−0.757212 | + | 0.653169i | \(0.773439\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 177.804 | − | 83.2108i | 0.207958 | − | 0.0973225i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 946.338i | 1.10425i | 0.833763 | + | 0.552123i | \(0.186182\pi\) | ||||
−0.833763 | + | 0.552123i | \(0.813818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 162.123i | − | 0.188735i | −0.995537 | − | 0.0943673i | \(-0.969917\pi\) | ||
0.995537 | − | 0.0943673i | \(-0.0300828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1296.23 | + | 824.534i | 1.50550 | + | 0.957647i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 463.268i | − | 0.536811i | −0.963306 | − | 0.268405i | \(-0.913503\pi\) | ||
0.963306 | − | 0.268405i | \(-0.0864967\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.7545 | −0.0390225 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −460.422 | + | 723.820i | −0.531051 | + | 0.834856i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −704.166 | −0.810318 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.6045 | −0.0420258 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.5623 | − | 39.6638i | −0.0212626 | − | 0.0454339i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −91.2556 | −0.104292 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 832.201i | 0.948918i | 0.880278 | + | 0.474459i | \(0.157356\pi\) | ||||
−0.880278 | + | 0.474459i | \(0.842644\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −367.241 | + | 577.333i | −0.417794 | + | 0.656807i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1415.53i | 1.60673i | 0.595484 | + | 0.803367i | \(0.296960\pi\) | ||||
−0.595484 | + | 0.803367i | \(0.703040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 762.559i | 0.863600i | 0.901969 | + | 0.431800i | \(0.142121\pi\) | ||||
−0.901969 | + | 0.431800i | \(0.857879\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −125.391 | + | 197.125i | −0.141685 | + | 0.222741i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 63.9277i | 0.0720718i | 0.999350 | + | 0.0360359i | \(0.0114731\pi\) | ||||
−0.999350 | + | 0.0360359i | \(0.988527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1429.78 | −1.60830 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 268.210 | − | 321.440i | 0.301021 | − | 0.360763i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −456.808 | −0.511543 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 540.211 | 0.603587 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 44.0629 | − | 69.2705i | 0.0491226 | − | 0.0772247i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 344.322 | 0.383006 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 142.064i | − | 0.157674i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −988.235 | − | 628.616i | −1.09439 | − | 0.696141i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 210.591i | 0.232697i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 839.954i | − | 0.926079i | −0.886338 | − | 0.463039i | \(-0.846759\pi\) | ||
0.886338 | − | 0.463039i | \(-0.153241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −571.492 | − | 1221.16i | −0.628704 | − | 1.34341i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1032.36i | 1.13322i | 0.823987 | + | 0.566609i | \(0.191745\pi\) | ||||
−0.823987 | + | 0.566609i | \(0.808255\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 601.933 | 0.659291 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −81.7374 | − | 51.9931i | −0.0893305 | − | 0.0568231i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1549.35 | −1.68958 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1199.54 | −1.30526 | −0.652632 | − | 0.757675i | \(-0.726335\pi\) | ||||
−0.652632 | + | 0.757675i | \(0.726335\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1141.35 | + | 726.012i | 1.23925 | + | 0.788287i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 195.886 | 0.212228 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 355.430i | − | 0.384249i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −376.204 | − | 803.870i | −0.405829 | − | 0.867173i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1098.06i | − | 1.18198i | −0.806678 | − | 0.590991i | \(-0.798737\pi\) | ||
0.806678 | − | 0.590991i | \(-0.201263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 171.886i | 0.184625i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 262.229 | + | 166.804i | 0.281060 | + | 0.178782i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.1852i | 0.0215884i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 672.270 | 0.717470 | 0.358735 | − | 0.933439i | \(-0.383208\pi\) | ||||
0.358735 | + | 0.933439i | \(0.383208\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 573.965 | − | 902.320i | 0.611252 | − | 0.960937i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 81.9534 | 0.0870919 | 0.0435459 | − | 0.999051i | \(-0.486135\pi\) | ||||
0.0435459 | + | 0.999051i | \(0.486135\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 360.134 | 0.381902 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −488.697 | − | 63.3079i | −0.517139 | − | 0.0669925i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1168.46 | 1.23386 | 0.616928 | − | 0.787020i | \(-0.288377\pi\) | ||||
0.616928 | + | 0.787020i | \(0.288377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.1149i | 0.0306796i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 608.096 | − | 955.976i | 0.639428 | − | 1.00523i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1422.35i | − | 1.49250i | −0.665669 | − | 0.746248i | \(-0.731854\pi\) | ||
0.665669 | − | 0.746248i | \(-0.268146\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 629.425i | − | 0.659084i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 330.388 | − | 519.396i | 0.345233 | − | 0.542734i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1476.59i | − | 1.53972i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −885.781 | −0.921728 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −204.679 | − | 437.357i | −0.212544 | − | 0.454161i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −370.809 | −0.384258 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −403.027 | −0.416781 | −0.208390 | − | 0.978046i | \(-0.566822\pi\) | ||||
−0.208390 | + | 0.978046i | \(0.566822\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.4332 | + | 43.1273i | −0.0283109 | + | 0.0445070i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 327.768 | 0.337558 | 0.168779 | − | 0.985654i | \(-0.446018\pi\) | ||||
0.168779 | + | 0.985654i | \(0.446018\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1383.31i | − | 1.42170i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 60.3382 | + | 38.3811i | 0.0618854 | + | 0.0393652i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 653.254i | − | 0.668633i | −0.942461 | − | 0.334316i | \(-0.891495\pi\) | ||
0.942461 | − | 0.334316i | \(-0.108505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 378.054i | 0.386164i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 84.7486 | − | 39.6616i | 0.0863900 | − | 0.0404298i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 870.902i | 0.885963i | 0.896531 | + | 0.442982i | \(0.146079\pi\) | ||||
−0.896531 | + | 0.442982i | \(0.853921\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 708.315 | 0.719102 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 967.521 | + | 615.439i | 0.980264 | + | 0.623545i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −274.562 | −0.277616 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1795.14 | −1.81145 | −0.905724 | − | 0.423869i | \(-0.860672\pi\) | ||||
−0.905724 | + | 0.423869i | \(0.860672\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 470.665 | + | 299.390i | 0.473983 | + | 0.301500i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −395.122 | −0.397108 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 877.803i | 0.880444i | 0.897889 | + | 0.440222i | \(0.145100\pi\) | ||||
−0.897889 | + | 0.440222i | \(0.854900\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 246.577 | − | 1903.42i | 0.246824 | − | 1.90532i |
(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 | 960.3.n.a.161.8 | yes | 24 | |
3.2 | odd | 2 | inner | 960.3.n.a.161.19 | yes | 24 | |
4.3 | odd | 2 | inner | 960.3.n.a.161.18 | yes | 24 | |
8.3 | odd | 2 | inner | 960.3.n.a.161.7 | yes | 24 | |
8.5 | even | 2 | inner | 960.3.n.a.161.17 | yes | 24 | |
12.11 | even | 2 | inner | 960.3.n.a.161.5 | ✓ | 24 | |
24.5 | odd | 2 | inner | 960.3.n.a.161.6 | yes | 24 | |
24.11 | even | 2 | inner | 960.3.n.a.161.20 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
960.3.n.a.161.5 | ✓ | 24 | 12.11 | even | 2 | inner | |
960.3.n.a.161.6 | yes | 24 | 24.5 | odd | 2 | inner | |
960.3.n.a.161.7 | yes | 24 | 8.3 | odd | 2 | inner | |
960.3.n.a.161.8 | yes | 24 | 1.1 | even | 1 | trivial | |
960.3.n.a.161.17 | yes | 24 | 8.5 | even | 2 | inner | |
960.3.n.a.161.18 | yes | 24 | 4.3 | odd | 2 | inner | |
960.3.n.a.161.19 | yes | 24 | 3.2 | odd | 2 | inner | |
960.3.n.a.161.20 | yes | 24 | 24.11 | even | 2 | inner |