Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(104,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11, 9, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.104");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.cs (of order \(18\), degree \(6\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{18}]$ |
Embedding invariants
Embedding label | 104.3 | ||
Character | \(\chi\) | \(=\) | 945.104 |
Dual form | 945.2.cs.a.209.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{11}{18}\right)\) | \(-1\) |
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 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(3\) | 0.306808 | − | 1.70466i | 0.177136 | − | 0.984186i | ||||
\(4\) | −1.53209 | − | 1.28558i | −0.766044 | − | 0.642788i | ||||
\(5\) | 2.20210 | + | 0.388289i | 0.984808 | + | 0.173648i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.02676 | − | 1.70066i | 0.766044 | − | 0.642788i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.81174 | − | 1.04601i | −0.937246 | − | 0.348669i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.48531 | + | 1.14354i | −1.95539 | + | 0.344789i | −0.956868 | + | 0.290522i | \(0.906171\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | −2.66153 | + | 2.21727i | −0.768317 | + | 0.640070i | ||||
\(13\) | −5.77616 | + | 2.10235i | −1.60202 | + | 0.583087i | −0.979839 | − | 0.199788i | \(-0.935975\pi\) |
−0.622179 | + | 0.782875i | \(0.713753\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.33752 | − | 3.63470i | 0.345347 | − | 0.938475i | ||||
\(16\) | 0.694593 | + | 3.93923i | 0.173648 | + | 0.984808i | ||||
\(17\) | −2.93500 | − | 1.69452i | −0.711841 | − | 0.410982i | 0.0999013 | − | 0.994997i | \(-0.468147\pi\) |
−0.811742 | + | 0.584016i | \(0.801481\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | −2.87463 | − | 3.42585i | −0.642788 | − | 0.766044i | ||||
\(21\) | −2.27721 | − | 3.97672i | −0.496929 | − | 0.867791i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.69846 | + | 1.71010i | 0.939693 | + | 0.342020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.64575 | + | 4.47214i | −0.509175 | + | 0.860663i | ||||
\(28\) | −5.29150 | −1.00000 | ||||||||
\(29\) | 3.67749 | − | 10.1038i | 0.682893 | − | 1.87623i | 0.287049 | − | 0.957916i | \(-0.407326\pi\) |
0.395844 | − | 0.918318i | \(-0.370452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.0404054 | + | 11.4061i | −0.00703368 | + | 1.98555i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.12348 | − | 2.95804i | 0.866025 | − | 0.500000i | ||||
\(36\) | 2.96311 | + | 5.21728i | 0.493852 | + | 0.869546i | ||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.81162 | + | 10.4914i | 0.290092 | + | 1.67997i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(44\) | 11.4062 | + | 6.58536i | 1.71955 | + | 0.992780i | ||||
\(45\) | −5.78557 | − | 3.39518i | −0.862461 | − | 0.506123i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.77652 | − | 4.50068i | −0.550862 | − | 0.656492i | 0.416724 | − | 0.909033i | \(-0.363178\pi\) |
−0.967586 | + | 0.252541i | \(0.918734\pi\) | |||||||
\(48\) | 6.92816 | + | 0.0245426i | 0.999994 | + | 0.00354242i | ||||
\(49\) | 1.21554 | − | 6.89365i | 0.173648 | − | 0.984808i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.78906 | + | 4.48328i | −0.530575 | + | 0.627785i | ||||
\(52\) | 11.5523 | + | 4.20470i | 1.60202 | + | 0.583087i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.7253 | −1.98556 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(60\) | −6.72188 | + | 3.84920i | −0.867791 | + | 0.496929i | ||||
\(61\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.47762 | + | 2.66179i | −0.942092 | + | 0.335354i | ||||
\(64\) | 4.00000 | − | 6.92820i | 0.500000 | − | 0.866025i | ||||
\(65\) | −13.5360 | + | 2.38676i | −1.67893 | + | 0.296041i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(68\) | 2.31824 | + | 6.36931i | 0.281128 | + | 0.772393i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.5297 | − | 8.38871i | −1.72435 | − | 0.995556i | −0.909262 | − | 0.416225i | \(-0.863353\pi\) |
−0.815092 | − | 0.579331i | \(-0.803314\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.258424 | − | 0.447604i | −0.0302463 | − | 0.0523881i | 0.850506 | − | 0.525965i | \(-0.176296\pi\) |
−0.880752 | + | 0.473577i | \(0.842962\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.35667 | − | 7.48461i | 0.503065 | − | 0.864249i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.1994 | + | 13.3470i | −1.27629 | + | 1.52103i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.82115 | + | 1.75476i | 0.542422 | + | 0.197425i | 0.598676 | − | 0.800991i | \(-0.295694\pi\) |
−0.0562544 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(80\) | 8.94427i | 1.00000i | ||||||||
\(81\) | 6.81174 | + | 5.88220i | 0.756860 | + | 0.653577i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.01767 | − | 2.79602i | 0.111704 | − | 0.306903i | −0.871227 | − | 0.490881i | \(-0.836675\pi\) |
0.982930 | + | 0.183977i | \(0.0588973\pi\) | |||||||
\(84\) | −1.62348 | + | 9.02022i | −0.177136 | + | 0.984186i | ||||
\(85\) | −5.80518 | − | 4.87113i | −0.629660 | − | 0.528348i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −16.0953 | − | 9.36881i | −1.72560 | − | 1.00444i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.13153 | + | 14.0842i | −0.852416 | + | 1.47643i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.21237 | − | 18.2182i | −0.326167 | − | 1.84978i | −0.501347 | − | 0.865246i | \(-0.667162\pi\) |
0.175180 | − | 0.984536i | \(-0.443949\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.4311 | + | 3.56836i | 1.95290 | + | 0.358634i | ||||
\(100\) | −5.00000 | − | 8.66025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.79670 | + | 15.8609i | −0.275567 | + | 1.56282i | 0.461588 | + | 0.887094i | \(0.347280\pi\) |
−0.737155 | + | 0.675724i | \(0.763831\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.47053 | − | 9.64134i | −0.338689 | − | 0.940898i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 9.80279 | − | 3.45040i | 0.943274 | − | 0.332015i | ||||
\(109\) | 19.3887 | 1.85710 | 0.928552 | − | 0.371203i | \(-0.121054\pi\) | ||||
0.928552 | + | 0.371203i | \(0.121054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.10705 | + | 6.80262i | 0.766044 | + | 0.642788i | ||||
\(113\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −18.6235 | + | 10.7523i | −1.72915 | + | 0.998323i | ||||
\(117\) | 18.4401 | + | 0.130648i | 1.70479 | + | 0.0120784i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.83034 | + | 1.55703i | −0.809476 | + | 0.142732i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.4150 | − | 11.0701i | 2.76500 | − | 1.00638i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.68246 | + | 5.59017i | 0.866025 | + | 0.500000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(132\) | 14.7253 | − | 17.4232i | 1.28167 | − | 1.51650i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.56268 | + | 8.82076i | −0.650892 | + | 0.759170i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(140\) | −11.6524 | − | 2.05463i | −0.984808 | − | 0.173648i | ||||
\(141\) | −8.83080 | + | 5.05684i | −0.743688 | + | 0.425863i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35.0561 | − | 20.2396i | 2.93154 | − | 1.69252i | ||||
\(144\) | 2.16745 | − | 11.8026i | 0.180621 | − | 0.983553i | ||||
\(145\) | 12.0214 | − | 20.8217i | 0.998323 | − | 1.72915i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.3784 | − | 4.18711i | −0.938475 | − | 0.345347i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.615493 | − | 1.69105i | −0.0504231 | − | 0.138536i | 0.911925 | − | 0.410358i | \(-0.134596\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.82808 | − | 21.7101i | −0.311525 | − | 1.76674i | −0.591078 | − | 0.806614i | \(-0.701298\pi\) |
0.279554 | − | 0.960130i | \(-0.409814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.47996 | + | 7.83457i | 0.523873 | + | 0.633388i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.7119 | − | 18.4028i | 0.857641 | − | 1.47340i | ||||
\(157\) | −2.65697 | + | 15.0684i | −0.212049 | + | 1.20259i | 0.673905 | + | 0.738818i | \(0.264616\pi\) |
−0.885954 | + | 0.463772i | \(0.846496\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.51784 | + | 25.1017i | −0.351714 | + | 1.95416i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.0888 | − | 3.54219i | −1.55452 | − | 0.274103i | −0.670625 | − | 0.741796i | \(-0.733974\pi\) |
−0.883891 | + | 0.467693i | \(0.845085\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.9856 | − | 15.9308i | 1.46043 | − | 1.22545i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.8031 | + | 2.61018i | −1.12546 | + | 0.198448i | −0.705235 | − | 0.708974i | \(-0.749158\pi\) |
−0.420221 | + | 0.907422i | \(0.638047\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.4310 | − | 4.52450i | 0.939693 | − | 0.342020i | ||||
\(176\) | −9.00930 | − | 24.7528i | −0.679101 | − | 1.86582i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.2482 | − | 12.8450i | −1.66291 | − | 0.960081i | −0.971316 | − | 0.237794i | \(-0.923576\pi\) |
−0.691594 | − | 0.722287i | \(-0.743091\pi\) | |||||||
\(180\) | 4.49925 | + | 12.6395i | 0.335354 | + | 0.942092i | ||||
\(181\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.9721 | + | 7.63322i | 1.53363 | + | 0.558196i | ||||
\(188\) | 11.7504i | 0.856989i | ||||||||
\(189\) | 2.24325 | + | 13.5635i | 0.163173 | + | 0.986598i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.02342 | + | 5.55930i | −0.146409 | + | 0.402257i | −0.991121 | − | 0.132966i | \(-0.957550\pi\) |
0.844711 | + | 0.535222i | \(0.179772\pi\) | |||||||
\(192\) | −10.5830 | − | 8.94427i | −0.763763 | − | 0.645497i | ||||
\(193\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0843332 | + | 23.8065i | −0.00603923 | + | 1.70482i | ||||
\(196\) | −10.7246 | + | 8.99903i | −0.766044 | + | 0.642788i | ||||
\(197\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.72973 | − | 26.7322i | −0.682893 | − | 1.87623i | ||||
\(204\) | 11.5688 | − | 1.99766i | 0.809976 | − | 0.139864i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.2937 | − | 21.2934i | −0.852416 | − | 1.47643i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.07847 | − | 6.11632i | 0.0742451 | − | 0.421065i | −0.924918 | − | 0.380166i | \(-0.875867\pi\) |
0.999163 | − | 0.0408987i | \(-0.0130221\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.7577 | + | 22.1944i | −1.28526 | + | 1.52074i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.842299 | + | 0.303197i | −0.0569173 | + | 0.0204882i | ||||
\(220\) | 22.5605 | + | 18.9305i | 1.52103 | + | 1.27629i | ||||
\(221\) | 20.5155 | + | 3.61743i | 1.38002 | + | 0.243335i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.7754 | − | 11.5589i | 0.922466 | − | 0.774041i | −0.0519836 | − | 0.998648i | \(-0.516554\pi\) |
0.974449 | + | 0.224607i | \(0.0721099\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4221 | − | 9.72298i | −0.761471 | − | 0.648199i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.6690 | − | 2.23388i | 0.840870 | − | 0.148268i | 0.263407 | − | 0.964685i | \(-0.415154\pi\) |
0.577463 | + | 0.816417i | \(0.304043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.3160 | + | 23.1862i | 1.27090 | + | 1.52554i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.56870 | − | 11.3773i | −0.428495 | − | 0.742175i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.47043 | − | 7.68006i | 0.290386 | − | 0.498873i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.49692 | − | 5.35922i | 0.290882 | − | 0.346659i | −0.600737 | − | 0.799447i | \(-0.705126\pi\) |
0.891618 | + | 0.452788i | \(0.149570\pi\) | |||||||
\(240\) | 15.2470 | + | 2.74417i | 0.984186 | + | 0.177136i | ||||
\(241\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 12.1170 | − | 9.80700i | 0.777309 | − | 0.629119i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.35346 | − | 14.7085i | 0.342020 | − | 0.939693i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.45404 | − | 2.59262i | −0.282263 | − | 0.164301i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | 14.8783 | + | 5.53495i | 0.937246 | + | 0.348669i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.0847 | + | 8.40137i | −0.631528 | + | 0.526114i | ||||
\(256\) | −15.0351 | + | 5.47232i | −0.939693 | + | 0.342020i | ||||
\(257\) | 10.4282 | + | 28.6513i | 0.650495 | + | 1.78722i | 0.615907 | + | 0.787819i | \(0.288790\pi\) |
0.0345877 | + | 0.999402i | \(0.488988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 23.8067 | + | 13.7448i | 1.47643 | + | 0.852416i | ||||
\(261\) | −20.9088 | + | 24.5626i | −1.29422 | + | 1.52039i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 4.63648 | − | 12.7386i | 0.281128 | − | 0.772393i | ||||
\(273\) | 21.5140 | + | 18.1827i | 1.30209 | + | 1.10046i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −32.4266 | − | 5.71768i | −1.95539 | − | 0.344789i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.3529 | − | 4.47039i | 1.51242 | − | 0.266681i | 0.644974 | − | 0.764204i | \(-0.276868\pi\) |
0.867451 | + | 0.497523i | \(0.165757\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.3550 | + | 6.68068i | −1.09109 | + | 0.397125i | −0.824025 | − | 0.566553i | \(-0.808277\pi\) |
−0.267067 | + | 0.963678i | \(0.586054\pi\) | |||||||
\(284\) | 11.4764 | + | 31.5312i | 0.681001 | + | 1.87103i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.75720 | − | 4.77561i | −0.162188 | − | 0.280918i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.0415 | − | 0.113505i | −1.87831 | − | 0.00665378i | ||||
\(292\) | −0.179500 | + | 1.01799i | −0.0105044 | + | 0.0595735i | ||||
\(293\) | −5.35006 | + | 6.37595i | −0.312554 | + | 0.372487i | −0.899336 | − | 0.437257i | \(-0.855950\pi\) |
0.586783 | + | 0.809745i | \(0.300394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.0445 | − | 32.0287i | 0.698891 | − | 1.85849i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −16.2968 | + | 5.86627i | −0.940898 | + | 0.338689i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0131 | + | 26.0034i | −0.856842 | + | 1.48409i | 0.0180837 | + | 0.999836i | \(0.494243\pi\) |
−0.874926 | + | 0.484257i | \(0.839090\pi\) | |||||||
\(308\) | 34.3170 | − | 6.05102i | 1.95539 | − | 0.344789i | ||||
\(309\) | 26.1794 | + | 9.63367i | 1.48929 | + | 0.548040i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.55328 | − | 31.4942i | −0.313890 | − | 1.78016i | −0.578378 | − | 0.815769i | \(-0.696314\pi\) |
0.264488 | − | 0.964389i | \(-0.414797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5000 | + | 2.95804i | −0.986013 | + | 0.166667i | ||||
\(316\) | −5.13056 | − | 8.88640i | −0.288617 | − | 0.499899i | ||||
\(317\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.2956 | + | 69.7318i | −0.688421 | + | 3.90423i | ||||
\(320\) | 11.4985 | − | 13.7034i | 0.642788 | − | 0.766044i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.87418 | − | 17.7690i | −0.159677 | − | 0.987169i | ||||
\(325\) | −30.7343 | −1.70483 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.94862 | − | 33.0512i | 0.328959 | − | 1.82774i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.3082 | − | 2.69925i | −0.843970 | − | 0.148815i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.1732 | − | 18.6055i | 1.21875 | − | 1.02265i | 0.219860 | − | 0.975531i | \(-0.429440\pi\) |
0.998889 | − | 0.0471205i | \(-0.0150045\pi\) | |||||||
\(332\) | −5.15366 | + | 2.97546i | −0.282844 | + | 0.163300i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 14.0835 | − | 11.7327i | 0.768317 | − | 0.640070i | ||||
\(337\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.63186 | + | 14.9260i | 0.142732 | + | 0.809476i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.26013 | − | 16.0390i | −0.500000 | − | 0.866025i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(348\) | 12.6151 | + | 35.0456i | 0.676243 | + | 1.87864i | ||||
\(349\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.88029 | − | 31.3941i | 0.313866 | − | 1.67569i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0241 | − | 33.0359i | 0.639977 | − | 1.75832i | −0.0118225 | − | 0.999930i | \(-0.503763\pi\) |
0.651799 | − | 0.758392i | \(-0.274014\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.7385 | − | 24.1145i | −1.52528 | − | 1.27986i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0550156 | + | 15.5304i | −0.00291174 | + | 0.821958i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.8765 | − | 12.6304i | 1.15460 | − | 0.666608i | 0.204595 | − | 0.978847i | \(-0.434412\pi\) |
0.950004 | + | 0.312239i | \(0.101079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.50000 | + | 16.4545i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.53928 | − | 55.2436i | −0.500682 | − | 2.89954i | ||||
\(364\) | 30.5646 | − | 11.1246i | 1.60202 | − | 0.583087i | ||||
\(365\) | −0.395275 | − | 1.08601i | −0.0206897 | − | 0.0568444i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.01410 | + | 28.4364i | 0.261734 | + | 1.48437i | 0.778177 | + | 0.628045i | \(0.216145\pi\) |
−0.516443 | + | 0.856322i | \(0.672744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.5000 | − | 14.7902i | 0.645497 | − | 0.763763i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 66.0927i | 3.40395i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.1756 | 1.39592 | 0.697958 | − | 0.716138i | \(-0.254092\pi\) | ||||
0.697958 | + | 0.716138i | \(0.254092\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −37.0394 | − | 6.53104i | −1.89262 | − | 0.333721i | −0.898236 | − | 0.439514i | \(-0.855151\pi\) |
−0.994388 | + | 0.105793i | \(0.966262\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.8447 | + | 25.0427i | −1.52103 | + | 1.27629i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.4993 | + | 32.0417i | −0.939159 | + | 1.62667i | ||||
\(389\) | 38.8357 | − | 6.84778i | 1.96905 | − | 0.347196i | 0.980360 | − | 0.197218i | \(-0.0631906\pi\) |
0.988689 | − | 0.149979i | \(-0.0479205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.93529 | + | 5.73614i | 0.499899 | + | 0.288617i | ||||
\(396\) | −25.1828 | − | 30.4472i | −1.26549 | − | 1.53003i | ||||
\(397\) | 0.115521 | + | 0.200088i | 0.00579782 | + | 0.0100421i | 0.868910 | − | 0.494971i | \(-0.164821\pi\) |
−0.863112 | + | 0.505013i | \(0.831488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.47296 | + | 19.6962i | −0.173648 | + | 0.984808i | ||||
\(401\) | −19.0139 | + | 22.6599i | −0.949510 | + | 1.13158i | 0.0416801 | + | 0.999131i | \(0.486729\pi\) |
−0.991190 | + | 0.132450i | \(0.957715\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.7161 | + | 15.5981i | 0.631869 | + | 0.775075i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 24.6751 | − | 20.7049i | 1.21566 | − | 1.02006i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.32667 | − | 5.76196i | 0.163300 | − | 0.282844i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(420\) | −7.07750 | + | 19.2330i | −0.345347 | + | 0.938475i | ||||
\(421\) | 4.98342 | + | 28.2624i | 0.242877 | + | 1.37742i | 0.825372 | + | 0.564590i | \(0.190966\pi\) |
−0.582495 | + | 0.812834i | \(0.697923\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.91084 | + | 16.6050i | 0.287395 | + | 0.807363i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.8922 | − | 12.9808i | −0.528348 | − | 0.629660i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.7462 | − | 65.9684i | −1.14648 | − | 3.18499i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 10.1456i | − | 0.488698i | −0.969687 | − | 0.244349i | \(-0.921426\pi\) | ||
0.969687 | − | 0.244349i | \(-0.0785743\pi\) | |||||||
\(432\) | −19.4545 | − | 7.31591i | −0.936005 | − | 0.351987i | ||||
\(433\) | 40.1484 | 1.92941 | 0.964703 | − | 0.263339i | \(-0.0848238\pi\) | ||||
0.964703 | + | 0.263339i | \(0.0848238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.8056 | − | 26.8807i | −1.52496 | − | 1.28883i | ||||
\(436\) | −29.7053 | − | 24.9257i | −1.42262 | − | 1.19372i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.6286 | + | 18.1117i | −0.506123 | + | 0.862461i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.07151 | + | 0.530378i | −0.145277 | + | 0.0250860i | ||||
\(448\) | −3.67544 | − | 20.8445i | −0.173648 | − | 0.984808i | ||||
\(449\) | −24.6822 | − | 14.2503i | −1.16482 | − | 0.672511i | −0.212368 | − | 0.977190i | \(-0.568118\pi\) |
−0.952455 | + | 0.304679i | \(0.901451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −38.1829 | − | 0.135260i | −1.79399 | − | 0.00635509i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −23.3752 | + | 27.8575i | −1.09585 | + | 1.30598i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.3434 | − | 8.64242i | 0.716168 | − | 0.403394i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.766044 | − | 0.642788i | \(-0.777778\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(464\) | 42.3557 | + | 7.46845i | 1.96631 | + | 0.346714i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.7669 | + | 13.7218i | −1.09980 | + | 0.634970i | −0.936169 | − | 0.351551i | \(-0.885654\pi\) |
−0.163632 | + | 0.986521i | \(0.552321\pi\) | |||||||
\(468\) | −28.0839 | − | 23.9063i | −1.29818 | − | 1.10507i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.8713 | + | 9.15234i | 1.14601 | + | 0.421717i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 15.5305 | + | 8.96656i | 0.711841 | + | 0.410982i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.642788 | − | 0.766044i | \(-0.722222\pi\) | ||||
0.642788 | + | 0.766044i | \(0.277778\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −60.8299 | − | 22.1403i | −2.76500 | − | 1.00638i | ||||
\(485\) | − | 41.3657i | − | 1.87832i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 37.0635 | + | 6.53529i | 1.67265 | + | 0.294934i | 0.928017 | − | 0.372539i | \(-0.121513\pi\) |
0.744635 | + | 0.667472i | \(0.232624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.9146 | + | 23.4231i | −1.25721 | + | 1.05492i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 41.4037 | + | 15.4028i | 1.86096 | + | 0.692303i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.7145 | + | 7.70804i | −1.96086 | + | 0.345753i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.7934 | + | 6.84022i | −0.841306 | + | 0.306210i | −0.726491 | − | 0.687176i | \(-0.758850\pi\) |
−0.114816 | + | 0.993387i | \(0.536628\pi\) | |||||||
\(500\) | −7.64780 | − | 21.0122i | −0.342020 | − | 0.939693i | ||||
\(501\) | −12.2016 | + | 33.1578i | −0.545129 | + | 1.48138i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.39864 | − | 0.807506i | −0.0623624 | − | 0.0360049i | 0.468495 | − | 0.883466i | \(-0.344797\pi\) |
−0.530857 | + | 0.847461i | \(0.678130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.3317 | − | 37.2517i | −0.947372 | − | 1.65440i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.28498 | − | 0.467696i | −0.0568444 | − | 0.0206897i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.3172 | + | 33.8412i | −0.542761 | + | 1.49122i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.6386 | + | 24.8697i | 1.30350 | + | 1.09377i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.0922274 | + | 26.0350i | −0.00404834 | + | 1.14281i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.4286 | + | 28.4552i | −0.718372 | + | 1.24426i | 0.243272 | + | 0.969958i | \(0.421779\pi\) |
−0.961644 | + | 0.274299i | \(0.911554\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.89882 | − | 22.5787i | −0.170158 | − | 0.985417i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −44.9593 | + | 7.76343i | −1.95660 | + | 0.337860i | ||||
\(529\) | −3.99391 | − | 22.6506i | −0.173648 | − | 0.984808i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.7223 | + | 33.9847i | −1.23946 | + | 1.46655i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 46.0975i | 1.98556i | ||||||||
\(540\) | 22.9265 | − | 3.79179i | 0.986598 | − | 0.163173i | ||||
\(541\) | 10.0117 | 0.430438 | 0.215219 | − | 0.976566i | \(-0.430953\pi\) | ||||
0.215219 | + | 0.976566i | \(0.430953\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.6959 | + | 7.52843i | 1.82889 | + | 0.322483i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7556 | − | 4.64265i | 0.542422 | − | 0.197425i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 15.2111 | + | 18.1279i | 0.642788 | + | 0.766044i | ||||
\(561\) | 19.4465 | − | 33.4084i | 0.821030 | − | 1.41050i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.4620 | + | 18.4269i | −0.651646 | + | 0.776601i | −0.986161 | − | 0.165789i | \(-0.946983\pi\) |
0.334515 | + | 0.942390i | \(0.391427\pi\) | |||||||
\(564\) | 20.0305 | + | 3.60513i | 0.843437 | + | 0.151803i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.8094 | + | 0.337394i | 0.999900 | + | 0.0141692i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0811 | − | 30.4452i | 0.464546 | − | 1.27633i | −0.457486 | − | 0.889217i | \(-0.651250\pi\) |
0.922032 | − | 0.387113i | \(-0.126528\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.5221 | − | 18.8983i | −0.942519 | − | 0.790867i | 0.0355029 | − | 0.999370i | \(-0.488697\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | −79.7286 | − | 14.0583i | −3.33362 | − | 0.587807i | ||||
\(573\) | 8.85591 | + | 5.15488i | 0.369961 | + | 0.215348i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −18.4939 | + | 15.2963i | −0.770579 | + | 0.637344i | ||||
\(577\) | 19.5020 | − | 33.7785i | 0.811880 | − | 1.40622i | −0.0996670 | − | 0.995021i | \(-0.531778\pi\) |
0.911547 | − | 0.411196i | \(-0.134889\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −45.1857 | + | 16.4462i | −1.87623 | + | 0.682893i | ||||
\(581\) | −2.69250 | − | 7.39758i | −0.111704 | − | 0.306903i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 40.5562 | + | 7.44780i | 1.67679 | + | 0.307929i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −23.6360 | − | 28.1683i | −0.975561 | − | 1.16263i | −0.986677 | − | 0.162690i | \(-0.947983\pi\) |
0.0111162 | − | 0.999938i | \(-0.496462\pi\) | |||||||
\(588\) | 12.0499 | + | 21.0428i | 0.496929 | + | 0.867791i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.8642i | 1.71916i | 0.511003 | + | 0.859579i | \(0.329274\pi\) | ||||
−0.511003 | + | 0.859579i | \(0.670726\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −20.0498 | −0.821963 | ||||||||
\(596\) | −1.23099 | + | 3.38211i | −0.0504231 | + | 0.138536i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.2381 | − | 2.51055i | −0.581751 | − | 0.102578i | −0.124975 | − | 0.992160i | \(-0.539885\pi\) |
−0.456776 | + | 0.889582i | \(0.650996\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
−0.766044 | + | 0.642788i | \(0.777778\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −22.0450 | + | 38.1831i | −0.897000 | + | 1.55365i | ||||
\(605\) | 71.2751 | − | 12.5677i | 2.89775 | − | 0.510951i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.5100 | − | 13.6525i | 1.52248 | − | 0.554139i | 0.560717 | − | 0.828008i | \(-0.310526\pi\) |
0.961767 | + | 0.273869i | \(0.0883034\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.5545 | + | 8.38423i | −1.96753 | + | 0.339746i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.2758 | + | 18.0571i | 1.26528 | + | 0.730512i | ||||
\(612\) | 0.144064 | − | 20.3337i | 0.00582343 | − | 0.821943i | ||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −40.0698 | + | 14.4237i | −1.60407 | + | 0.577408i | ||||
\(625\) | 19.1511 | + | 16.0697i | 0.766044 | + | 0.642788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.4423 | − | 19.6704i | 0.935449 | − | 0.784935i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.8200 | + | 22.2050i | −0.510357 | + | 0.883965i | 0.489570 | + | 0.871964i | \(0.337154\pi\) |
−0.999928 | + | 0.0120014i | \(0.996180\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.0954 | − | 3.71497i | −0.401255 | − | 0.147657i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.47174 | + | 42.3743i | 0.296041 | + | 1.67893i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.0790 | + | 38.7850i | 1.26902 | + | 1.53431i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.2312 | − | 30.0694i | −0.996572 | − | 1.18767i | −0.982213 | − | 0.187772i | \(-0.939873\pi\) |
−0.0143597 | − | 0.999897i | \(-0.504571\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.368634 | + | 2.09063i | −0.0145375 | + | 0.0824462i | −0.991213 | − | 0.132273i | \(-0.957772\pi\) |
0.976676 | + | 0.214719i | \(0.0688836\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 50.1875i | − | 1.97307i | −0.163543 | − | 0.986536i | \(-0.552292\pi\) | ||
0.163543 | − | 0.986536i | \(-0.447708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.258424 | + | 1.52886i | 0.0100821 | + | 0.0596464i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.7032 | − | 2.06359i | 0.455892 | − | 0.0803860i | 0.0590132 | − | 0.998257i | \(-0.481205\pi\) |
0.396878 | + | 0.917871i | \(0.370093\pi\) | |||||||
\(660\) | 39.1918 | − | 32.6499i | 1.52554 | − | 1.27090i | ||||
\(661\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.4608 | − | 33.8621i | 0.483938 | − | 1.31509i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 26.2240 | + | 31.2526i | 1.01464 | + | 1.20920i | ||||
\(669\) | −15.4776 | − | 27.0287i | −0.598399 | − | 1.04499i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
0.939693 | + | 0.342020i | \(0.111111\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.0788 | + | 16.4877i | −0.772832 | + | 0.634611i | ||||
\(676\) | −49.5678 | −1.90645 | ||||||||
\(677\) | 0.381004 | − | 1.04680i | 0.0146432 | − | 0.0402318i | −0.932156 | − | 0.362058i | \(-0.882074\pi\) |
0.946799 | + | 0.321826i | \(0.104297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37.4937 | − | 31.4609i | −1.43888 | − | 1.20736i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.0789315 | − | 22.2817i | 0.00302466 | − | 0.853837i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(692\) | 26.0352 | + | 15.0314i | 0.989709 | + | 0.571409i | ||||
\(693\) | 45.4509 | − | 25.8135i | 1.72654 | − | 0.980572i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −24.8619 | − | 9.04900i | −0.939693 | − | 0.342020i | ||||
\(701\) | 27.6284i | 1.04351i | 0.853095 | + | 0.521755i | \(0.174723\pi\) | ||||
−0.853095 | + | 0.521755i | \(0.825277\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −18.0186 | + | 49.5057i | −0.679101 | + | 1.86582i | ||||
\(705\) | −21.4098 | + | 7.70675i | −0.806340 | + | 0.290253i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.9403 | + | 29.3184i | −1.31221 | + | 1.10107i | −0.324314 | + | 0.945949i | \(0.605134\pi\) |
−0.987895 | + | 0.155125i | \(0.950422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.7203 | − | 9.97687i | −0.439547 | − | 0.374162i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 85.0557 | − | 30.9578i | 3.18090 | − | 1.15775i | ||||
\(716\) | 17.5730 | + | 48.2814i | 0.656734 | + | 1.80436i | ||||
\(717\) | −7.75597 | − | 9.30998i | −0.289652 | − | 0.347688i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 9.35577 | − | 25.1489i | 0.348669 | − | 0.937246i | ||||
\(721\) | 21.3056 | + | 36.9024i | 0.793463 | + | 1.37432i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.5571 | − | 41.1836i | 1.28342 | − | 1.52952i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −36.2243 | − | 13.1846i | −1.34349 | − | 0.488989i | −0.432577 | − | 0.901597i | \(-0.642396\pi\) |
−0.910909 | + | 0.412608i | \(0.864618\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | − | 23.6643i | −0.481481 | − | 0.876456i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.90330 | + | 4.95346i | 0.218043 | + | 0.182960i | 0.745266 | − | 0.666767i | \(-0.232322\pi\) |
−0.527223 | + | 0.849727i | \(0.676767\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −23.4305 | − | 13.6385i | −0.864249 | − | 0.503065i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8056 | − | 44.6967i | 0.949276 | − | 1.64419i | 0.202321 | − | 0.979319i | \(-0.435152\pi\) |
0.746955 | − | 0.664875i | \(-0.231515\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.342020 | − | 0.939693i | \(-0.611111\pi\) | ||||
0.342020 | + | 0.939693i | \(0.388889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.698758 | − | 3.96285i | −0.0256005 | − | 0.145188i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.78608 | + | 6.79719i | −0.211702 | + | 0.248696i | ||||
\(748\) | −22.3180 | − | 38.6560i | −0.816029 | − | 1.41340i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.87843 | + | 39.0095i | −0.250997 | + | 1.42348i | 0.555144 | + | 0.831754i | \(0.312663\pi\) |
−0.806142 | + | 0.591723i | \(0.798448\pi\) | |||||||
\(752\) | 15.1061 | − | 18.0027i | 0.550862 | − | 0.656492i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 49.2942i | − | 1.79400i | ||||||
\(756\) | 14.0000 | − | 23.6643i | 0.509175 | − | 0.860663i | ||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.2964 | − | 32.9736i | 1.42262 | − | 1.19372i | ||||
\(764\) | 10.2470 | − | 5.91608i | 0.370722 | − | 0.214036i | ||||
\(765\) | 11.2274 | + | 19.7686i | 0.405928 | + | 0.714735i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.71557 | + | 27.3087i | 0.170158 | + | 0.985417i | ||||
\(769\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 52.0403 | − | 8.98614i | 1.87418 | − | 0.323628i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 47.7223 | + | 27.5525i | 1.71645 | + | 0.990994i | 0.925179 | + | 0.379531i | \(0.123915\pi\) |
0.791273 | + | 0.611463i | \(0.209419\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 30.7343 | − | 36.3653i | 1.10046 | − | 1.30209i | ||||
\(781\) | 103.822 | + | 37.7882i | 3.71505 | + | 1.35217i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 35.4560 | + | 43.1785i | 1.26709 | + | 1.54307i | ||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | −11.7018 | + | 32.1504i | −0.417655 | + | 1.14750i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 42.9098 | + | 36.0056i | 1.52957 | + | 1.28346i | 0.801642 | + | 0.597804i | \(0.203960\pi\) |
0.727926 | + | 0.685656i | \(0.240484\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.8949 | − | 51.9134i | −0.669293 | − | 1.83887i | −0.528717 | − | 0.848798i | \(-0.677327\pi\) |
−0.140576 | − | 0.990070i | \(-0.544895\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.45757 | + | 19.6089i | 0.122320 | + | 0.693712i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.18781 | + | 2.60733i | 0.0772062 | + | 0.0920108i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.65514i | − | 0.233982i | −0.993133 | − | 0.116991i | \(-0.962675\pi\) | ||
0.993133 | − | 0.116991i | \(-0.0373249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | −19.4595 | + | 53.4644i | −0.682893 | + | 1.87623i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.2925 | − | 11.8119i | −0.710381 | − | 0.413501i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 37.5959 | − | 31.0955i | 1.31371 | − | 1.08657i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.6738 | + | 4.35066i | −0.861122 | + | 0.151839i | −0.586734 | − | 0.809780i | \(-0.699586\pi\) |
−0.274388 | + | 0.961619i | \(0.588475\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.6954 | + | 53.5220i | −0.685707 | + | 1.86340i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.53913 | + | 48.4278i | −0.296041 | + | 1.67893i | ||||
\(833\) | −15.2490 | + | 18.1731i | −0.528348 | + | 0.629660i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −42.8620 | − | 15.6005i | −1.48330 | − | 0.539878i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −66.3481 | − | 55.6727i | −2.28787 | − | 1.91975i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.157956 | − | 44.5896i | 0.00544029 | − | 1.53575i | ||||
\(844\) | −9.51530 | + | 7.98429i | −0.327530 | + | 0.274831i | ||||
\(845\) | 47.9938 | − | 27.7092i | 1.65104 | − | 0.953227i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 42.8174 | − | 74.1619i | 1.47122 | − | 2.54823i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.75682 | + | 33.3387i | 0.197574 | + | 1.14418i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 57.2711 | − | 9.88938i | 1.96208 | − | 0.338805i | ||||
\(853\) | 9.72827 | + | 55.1717i | 0.333090 | + | 1.88904i | 0.445335 | + | 0.895364i | \(0.353085\pi\) |
−0.112245 | + | 0.993681i | \(0.535804\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.1051 | − | 13.2346i | −0.379344 | − | 0.452085i | 0.542263 | − | 0.840209i | \(-0.317568\pi\) |
−0.921607 | + | 0.388124i | \(0.873123\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.6113 | −1.14282 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.98673 | + | 3.23490i | −0.305205 | + | 0.109863i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.2733 | − | 5.86698i | −1.12872 | − | 0.199024i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.0241 | + | 54.5851i | −0.339264 | + | 1.84743i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 29.1310 | − | 5.13658i | 0.984808 | − | 0.173648i | ||||
\(876\) | 1.68026 | + | 0.618314i | 0.0567707 | + | 0.0208909i | ||||
\(877\) | 0 | 0 | 0.939693 | − | 0.342020i | \(-0.111111\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.22740 | + | 11.0762i | 0.311232 | + | 0.373592i | ||||
\(880\) | −10.2281 | − | 58.0064i | −0.344789 | − | 1.95539i | ||||
\(881\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(884\) | −26.7811 | − | 31.9164i | −0.900744 | − | 1.07347i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.0121 | − | 17.8907i | 0.504056 | − | 0.600711i | −0.452678 | − | 0.891674i | \(-0.649531\pi\) |
0.956734 | + | 0.290963i | \(0.0939758\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −50.9027 | − | 30.3584i | −1.70531 | − | 1.01704i | ||||
\(892\) | −35.9649 | −1.20419 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −44.0051 | − | 36.9247i | −1.47093 | − | 1.23426i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 5.00000 | + | 29.5804i | 0.166667 | + | 0.986013i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.173648 | − | 0.984808i | \(-0.555556\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(908\) | −22.2818 | − | 12.8644i | −0.739449 | − | 0.426921i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.1997 | − | 16.9226i | −0.470458 | − | 0.560670i | 0.477678 | − | 0.878535i | \(-0.341479\pi\) |
−0.948136 | + | 0.317865i | \(0.897034\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.40255 | + | 19.2968i | −0.112608 | + | 0.638631i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −60.6113 | −1.99938 | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) | ||||
−0.999691 | + | 0.0248659i | \(0.992084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.7209 | + | 33.5703i | 1.30885 | + | 1.10618i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 101.562 | + | 17.9081i | 3.34294 | + | 0.589451i | ||||
\(924\) | 0.213805 | − | 60.3554i | 0.00703368 | − | 1.98555i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 24.4542 | − | 41.6712i | 0.803180 | − | 1.36866i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.984808 | − | 0.173648i | \(-0.0555556\pi\) | ||||
−0.984808 | + | 0.173648i | \(0.944444\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 43.2187 | + | 24.9523i | 1.41340 | + | 0.816029i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.7384 | + | 51.5084i | 0.971511 | + | 1.68271i | 0.690999 | + | 0.722856i | \(0.257171\pi\) |
0.280512 | + | 0.959851i | \(0.409496\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −55.3907 | − | 0.196218i | −1.80761 | − | 0.00640334i | ||||
\(940\) | −4.56257 | + | 25.8756i | −0.148815 | + | 0.843970i | ||||
\(941\) | 0 | 0 | 0.642788 | − | 0.766044i | \(-0.277778\pi\) | ||||
−0.642788 | + | 0.766044i | \(0.722222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.326685 | + | 30.7391i | −0.0106271 | + | 0.999944i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.342020 | − | 0.939693i | \(-0.388889\pi\) | ||||
−0.342020 | + | 0.939693i | \(0.611111\pi\) | |||||||
\(948\) | −16.7224 | + | 6.01945i | −0.543118 | + | 0.195503i | ||||
\(949\) | 2.43372 | + | 2.04213i | 0.0790019 | + | 0.0662905i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.61438 | + | 11.4564i | −0.214036 | + | 0.370722i | ||||
\(956\) | −13.7794 | + | 2.42968i | −0.445657 | + | 0.0785813i | ||||
\(957\) | 115.097 | + | 42.3541i | 3.72055 | + | 1.36911i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −19.8318 | − | 23.8054i | −0.640070 | − | 0.768317i | ||||
\(961\) | 5.38309 | + | 30.5290i | 0.173648 | + | 0.984808i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
−0.173648 | + | 0.984808i | \(0.555556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | −31.1720 | − | 0.552180i | −0.999843 | − | 0.0177112i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.42953 | + | 52.3916i | −0.301987 | + | 1.67787i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.984808 | − | 0.173648i | \(-0.944444\pi\) | ||||
0.984808 | + | 0.173648i | \(0.0555556\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −27.1109 | + | 15.6525i | −0.866025 | + | 0.500000i | ||||
\(981\) | −54.5160 | − | 20.2808i | −1.74056 | − | 0.647515i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.6150 | + | 8.04316i | −1.45489 | + | 0.256537i | −0.844498 | − | 0.535559i | \(-0.820101\pi\) |
−0.610396 | + | 0.792096i | \(0.708990\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.29800 | + | 25.2672i | −0.295959 | + | 0.804263i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.5023 | − | 52.8315i | −0.968936 | − | 1.67825i | −0.698645 | − | 0.715468i | \(-0.746213\pi\) |
−0.270291 | − | 0.962779i | \(-0.587120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.9132 | − | 43.5061i | −0.790596 | − | 1.38062i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.49098 | + | 9.69813i | 0.110616 | + | 0.307297i | ||||
\(997\) | 17.4034 | + | 6.33430i | 0.551170 | + | 0.200609i | 0.602566 | − | 0.798069i | \(-0.294145\pi\) |
−0.0513964 | + | 0.998678i | \(0.516367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 945.2.cs.a.104.3 | yes | 24 | |
5.4 | even | 2 | inner | 945.2.cs.a.104.2 | ✓ | 24 | |
7.6 | odd | 2 | inner | 945.2.cs.a.104.2 | ✓ | 24 | |
27.20 | odd | 18 | inner | 945.2.cs.a.209.3 | yes | 24 | |
35.34 | odd | 2 | CM | 945.2.cs.a.104.3 | yes | 24 | |
135.74 | odd | 18 | inner | 945.2.cs.a.209.2 | yes | 24 | |
189.20 | even | 18 | inner | 945.2.cs.a.209.2 | yes | 24 | |
945.209 | even | 18 | inner | 945.2.cs.a.209.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.cs.a.104.2 | ✓ | 24 | 5.4 | even | 2 | inner | |
945.2.cs.a.104.2 | ✓ | 24 | 7.6 | odd | 2 | inner | |
945.2.cs.a.104.3 | yes | 24 | 1.1 | even | 1 | trivial | |
945.2.cs.a.104.3 | yes | 24 | 35.34 | odd | 2 | CM | |
945.2.cs.a.209.2 | yes | 24 | 135.74 | odd | 18 | inner | |
945.2.cs.a.209.2 | yes | 24 | 189.20 | even | 18 | inner | |
945.2.cs.a.209.3 | yes | 24 | 27.20 | odd | 18 | inner | |
945.2.cs.a.209.3 | yes | 24 | 945.209 | even | 18 | inner |