Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.3 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.22 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.06455 | + | 0.858848i | −0.923296 | + | 0.384089i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.58783i | 1.35607i | 0.735028 | + | 0.678036i | \(0.237169\pi\) | ||||
−0.735028 | + | 0.678036i | \(0.762831\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.928323 | 0.279900 | 0.139950 | − | 0.990159i | \(-0.455306\pi\) | ||||
0.139950 | + | 0.990159i | \(0.455306\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.62224i | 1.55933i | 0.626198 | + | 0.779664i | \(0.284610\pi\) | ||||
−0.626198 | + | 0.779664i | \(0.715390\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.858848 | + | 2.06455i | 0.221754 | + | 0.533065i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.87254i | 1.66684i | 0.552643 | + | 0.833418i | \(0.313619\pi\) | ||||
−0.552643 | + | 0.833418i | \(0.686381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.74568 | −1.77698 | −0.888490 | − | 0.458896i | \(-0.848245\pi\) | ||||
−0.888490 | + | 0.458896i | \(0.848245\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.58783 | 0.782929 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.77684i | 1.41307i | 0.707678 | + | 0.706535i | \(0.249743\pi\) | ||||
−0.707678 | + | 0.706535i | \(0.750257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.52476 | − | 3.54628i | 0.704952 | − | 0.709255i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.69720 | −0.500858 | −0.250429 | − | 0.968135i | \(-0.580572\pi\) | ||||
−0.250429 | + | 0.968135i | \(0.580572\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.29620 | −0.412409 | −0.206204 | − | 0.978509i | \(-0.566111\pi\) | ||||
−0.206204 | + | 0.978509i | \(0.566111\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.928323i | − | 0.161600i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.08140 | − | 7.40727i | −0.520852 | − | 1.25206i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.1915i | − | 1.67548i | −0.546071 | − | 0.837739i | \(-0.683877\pi\) | ||
0.546071 | − | 0.837739i | \(-0.316123\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.62224 | 0.900278 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.54924 | −0.398125 | −0.199062 | − | 0.979987i | \(-0.563790\pi\) | ||||
−0.199062 | + | 0.979987i | \(0.563790\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.670329i | − | 0.102224i | −0.998693 | − | 0.0511121i | \(-0.983723\pi\) | ||
0.998693 | − | 0.0511121i | \(-0.0162766\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.06455 | − | 0.858848i | 0.307765 | − | 0.128030i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 10.2725i | − | 1.49840i | −0.662343 | − | 0.749201i | \(-0.730438\pi\) | ||
0.662343 | − | 0.749201i | \(-0.269562\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.87254 | −0.838934 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.87254 | 0.962348 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.41538i | − | 0.469139i | −0.972099 | − | 0.234570i | \(-0.924632\pi\) | ||
0.972099 | − | 0.234570i | \(-0.0753681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.91657 | + | 0.797289i | −0.258431 | + | 0.107506i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.74568i | 1.02594i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.49167 | 0.194199 | 0.0970995 | − | 0.995275i | \(-0.469044\pi\) | ||||
0.0970995 | + | 0.995275i | \(0.469044\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.8427 | 1.51630 | 0.758150 | − | 0.652080i | \(-0.226104\pi\) | ||||
0.758150 | + | 0.652080i | \(0.226104\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 3.58783i | − | 0.452024i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.82865 | − | 11.6074i | −0.598920 | − | 1.43972i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.00000i | − | 0.122169i | ||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.77684 | 0.815836 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.25041 | 0.385753 | 0.192876 | − | 0.981223i | \(-0.438218\pi\) | ||||
0.192876 | + | 0.981223i | \(0.438218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.6623i | − | 1.83313i | −0.399885 | − | 0.916565i | \(-0.630950\pi\) | ||
0.399885 | − | 0.916565i | \(-0.369050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.54628 | − | 3.52476i | −0.409489 | − | 0.407004i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.33067i | 0.379565i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.76733 | −0.536366 | −0.268183 | − | 0.963368i | \(-0.586423\pi\) | ||||
−0.268183 | + | 0.963368i | \(0.586423\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.48826i | 0.712179i | 0.934452 | + | 0.356090i | \(0.115890\pi\) | ||||
−0.934452 | + | 0.356090i | \(0.884110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.90247 | − | 14.1887i | −0.640213 | − | 1.53898i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.69720i | 0.289170i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.1791 | −1.29099 | −0.645493 | − | 0.763766i | \(-0.723348\pi\) | ||||
−0.645493 | + | 0.763766i | \(0.723348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.1716 | −2.11456 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.29620i | 0.238104i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.9914 | − | 6.65236i | 1.64068 | − | 0.682518i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.1180i | 1.12887i | 0.825479 | + | 0.564433i | \(0.190905\pi\) | ||||
−0.825479 | + | 0.564433i | \(0.809095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.928323 | −0.0933000 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0099 | 1.39403 | 0.697017 | − | 0.717054i | \(-0.254510\pi\) | ||||
0.697017 | + | 0.717054i | \(0.254510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.6012i | − | 1.14310i | −0.820567 | − | 0.571550i | \(-0.806342\pi\) | ||
0.820567 | − | 0.571550i | \(-0.193658\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.40727 | + | 3.08140i | −0.722875 | + | 0.300714i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.4097i | 1.97308i | 0.163509 | + | 0.986542i | \(0.447719\pi\) | ||||
−0.163509 | + | 0.986542i | \(0.552281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.36850 | −0.322644 | −0.161322 | − | 0.986902i | \(-0.551576\pi\) | ||||
−0.161322 | + | 0.986902i | \(0.551576\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1915 | −0.967338 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.8775i | 1.49363i | 0.665033 | + | 0.746814i | \(0.268417\pi\) | ||||
−0.665033 | + | 0.746814i | \(0.731583\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.82028 | − | 13.9912i | −0.542744 | − | 1.30468i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.62224i | − | 0.519776i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −24.6575 | −2.26035 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.1382 | −0.921656 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.54924i | 0.229857i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.23134 | + | 10.3487i | −0.378463 | + | 0.925617i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.35252i | 0.652431i | 0.945295 | + | 0.326215i | \(0.105773\pi\) | ||||
−0.945295 | + | 0.326215i | \(0.894227\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.670329 | −0.0590192 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2871 | 1.51038 | 0.755192 | − | 0.655504i | \(-0.227544\pi\) | ||||
0.755192 | + | 0.655504i | \(0.227544\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 27.7902i | − | 2.40972i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.858848 | − | 2.06455i | −0.0739179 | − | 0.177688i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.25580i | − | 0.534469i | −0.963632 | − | 0.267235i | \(-0.913890\pi\) | ||
0.963632 | − | 0.267235i | \(-0.0861098\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.7158 | 1.58745 | 0.793727 | − | 0.608274i | \(-0.208138\pi\) | ||||
0.793727 | + | 0.608274i | \(0.208138\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.2725 | −0.865102 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.21925i | 0.436456i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.56851 | − | 2.31649i | 0.462440 | − | 0.192374i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.87254i | 0.484359i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5604 | −0.865145 | −0.432572 | − | 0.901599i | \(-0.642394\pi\) | ||||
−0.432572 | + | 0.901599i | \(0.642394\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.707027 | −0.0575371 | −0.0287685 | − | 0.999586i | \(-0.509159\pi\) | ||||
−0.0287685 | + | 0.999586i | \(0.509159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 6.87254i | − | 0.555612i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.74062 | − | 1.97208i | 0.380776 | − | 0.158402i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 6.97439i | − | 0.556617i | −0.960492 | − | 0.278308i | \(-0.910226\pi\) | ||
0.960492 | − | 0.278308i | \(-0.0897737\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.41538 | −0.270858 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.3142 | −1.91623 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 18.3193i | − | 1.43488i | −0.696622 | − | 0.717438i | \(-0.745315\pi\) | ||
0.696622 | − | 0.717438i | \(-0.254685\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.797289 | + | 1.91657i | 0.0620689 | + | 0.149205i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.82349i | − | 0.450635i | −0.974285 | − | 0.225318i | \(-0.927658\pi\) | ||
0.974285 | − | 0.225318i | \(-0.0723419\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.6095 | −1.43150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.74568 | 0.592327 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 18.5918i | − | 1.41351i | −0.707459 | − | 0.706754i | \(-0.750159\pi\) | ||
0.707459 | − | 0.706754i | \(-0.249841\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.7234 | + | 12.6462i | 0.961802 | + | 0.955966i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 1.49167i | − | 0.112121i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.0429121 | −0.00320740 | −0.00160370 | − | 0.999999i | \(-0.500510\pi\) | ||||
−0.00160370 | + | 0.999999i | \(0.500510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.122684 | 0.00911900 | 0.00455950 | − | 0.999990i | \(-0.498549\pi\) | ||||
0.00455950 | + | 0.999990i | \(0.498549\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 11.8427i | − | 0.875436i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.75298 | + | 21.0410i | 0.643532 | + | 1.54696i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.37994i | 0.466547i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.58783 | −0.260976 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.4113 | −1.04276 | −0.521382 | − | 0.853323i | \(-0.674583\pi\) | ||||
−0.521382 | + | 0.853323i | \(0.674583\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.81325i | − | 0.202502i | −0.994861 | − | 0.101251i | \(-0.967715\pi\) | ||
0.994861 | − | 0.101251i | \(-0.0322846\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.6074 | + | 4.82865i | −0.831224 | + | 0.345787i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.4350i | − | 0.814707i | −0.913271 | − | 0.407353i | \(-0.866452\pi\) | ||
0.913271 | − | 0.407353i | \(-0.133548\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.3724 | −1.72772 | −0.863858 | − | 0.503736i | \(-0.831958\pi\) | ||||
−0.863858 | + | 0.503736i | \(0.831958\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 9.67710i | − | 0.679199i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.26305 | − | 2.18941i | 0.367587 | − | 0.152915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.77684i | − | 0.471023i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.19049 | −0.497377 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.29939 | 0.158296 | 0.0791482 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791482 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 3.25041i | − | 0.222715i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.575711 | + | 1.38393i | 0.0392631 | + | 0.0943832i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.23836i | − | 0.559257i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.6623 | −1.05836 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −38.6390 | −2.59914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.59585i | 0.575620i | 0.957687 | + | 0.287810i | \(0.0929272\pi\) | ||||
−0.957687 | + | 0.287810i | \(0.907073\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.52476 | + | 3.54628i | −0.234984 | + | 0.236418i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.8063i | 0.783611i | 0.920048 | + | 0.391806i | \(0.128149\pi\) | ||||
−0.920048 | + | 0.391806i | \(0.871851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.4280 | 1.54817 | 0.774083 | − | 0.633084i | \(-0.218211\pi\) | ||||
0.774083 | + | 0.633084i | \(0.218211\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.33067 | 0.219142 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.43414i | 0.552539i | 0.961080 | + | 0.276270i | \(0.0890982\pi\) | ||||
−0.961080 | + | 0.276270i | \(0.910902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.82254 | + | 21.2082i | 0.575519 | + | 1.38347i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.76733i | 0.309671i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.3248 | −1.05596 | −0.527982 | − | 0.849256i | \(-0.677051\pi\) | ||||
−0.527982 | + | 0.849256i | \(0.677051\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.9934 | 0.772565 | 0.386283 | − | 0.922380i | \(-0.373759\pi\) | ||||
0.386283 | + | 0.922380i | \(0.373759\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.1242 | − | 5.04362i | 0.774584 | − | 0.322225i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 43.5480i | − | 2.77090i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.48826 | 0.411177 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −26.3699 | −1.66445 | −0.832226 | − | 0.554436i | \(-0.812934\pi\) | ||||
−0.832226 | + | 0.554436i | \(0.812934\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.29110i | 0.395518i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.1887 | + | 5.90247i | −0.888532 | + | 0.369627i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.5740i | 1.28337i | 0.766968 | + | 0.641685i | \(0.221764\pi\) | ||||
−0.766968 | + | 0.641685i | \(0.778236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 36.5655 | 2.27207 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.69720 | 0.166953 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.88398i | − | 0.301159i | −0.988598 | − | 0.150580i | \(-0.951886\pi\) | ||
0.988598 | − | 0.150580i | \(-0.0481140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.93330 | + | 7.05124i | 0.180191 | + | 0.433154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1791i | 0.745351i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.13025 | 0.373768 | 0.186884 | − | 0.982382i | \(-0.440161\pi\) | ||||
0.186884 | + | 0.982382i | \(0.440161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.75729 | −0.288985 | −0.144492 | − | 0.989506i | \(-0.546155\pi\) | ||||
−0.144492 | + | 0.989506i | \(0.546155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.1716i | 1.22084i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.27212 | − | 3.29209i | 0.197316 | − | 0.198521i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 24.2685i | − | 1.45816i | −0.684431 | − | 0.729078i | \(-0.739949\pi\) | ||
0.684431 | − | 0.729078i | \(-0.260051\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.29620 | 0.137470 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.71136 | −0.579331 | −0.289666 | − | 0.957128i | \(-0.593544\pi\) | ||||
−0.289666 | + | 0.957128i | \(0.593544\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.4400i | − | 0.620593i | −0.950640 | − | 0.310296i | \(-0.899572\pi\) | ||
0.950640 | − | 0.310296i | \(-0.100428\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.65236 | − | 15.9914i | −0.394052 | − | 0.947247i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.14625i | − | 0.539886i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −30.2318 | −1.77834 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1180 | 0.651751 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.75711i | 0.277913i | 0.990298 | + | 0.138957i | \(0.0443749\pi\) | ||||
−0.990298 | + | 0.138957i | \(0.955625\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.07963 | + | 1.28112i | −0.179303 | + | 0.0745896i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.928323i | 0.0538668i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −38.1010 | −2.20344 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.40503 | 0.138623 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 14.0099i | − | 0.804846i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.4498 | + | 10.1711i | −1.39999 | + | 0.582393i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.6235i | 1.17704i | 0.808481 | + | 0.588522i | \(0.200290\pi\) | ||||
−0.808481 | + | 0.588522i | \(0.799710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.6012 | −0.659969 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4806 | 0.707709 | 0.353854 | − | 0.935301i | \(-0.384871\pi\) | ||||
0.353854 | + | 0.935301i | \(0.384871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.4911i | 1.27127i | 0.771989 | + | 0.635635i | \(0.219262\pi\) | ||||
−0.771989 | + | 0.635635i | \(0.780738\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.08140 | + | 7.40727i | 0.173617 | + | 0.417352i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.97888i | 0.448138i | 0.974573 | + | 0.224069i | \(0.0719341\pi\) | ||||
−0.974573 | + | 0.224069i | \(0.928066\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.50387 | −0.140190 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.4097 | 1.13916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 53.2325i | − | 2.96193i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19.9380 | + | 19.8170i | 1.10596 | + | 1.09925i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.36850i | 0.186278i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.8561 | 2.03194 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4582 | −1.28938 | −0.644689 | − | 0.764445i | \(-0.723013\pi\) | ||||
−0.644689 | + | 0.764445i | \(0.723013\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.1915i | 0.558493i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.858848 | + | 2.06455i | 0.0469239 | + | 0.112799i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9.71327i | − | 0.529116i | −0.964370 | − | 0.264558i | \(-0.914774\pi\) | ||
0.964370 | − | 0.264558i | \(-0.0852260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.8775 | 0.862347 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.13161 | −0.115433 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.04515i | 0.218418i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.9912 | + | 5.82028i | −0.753258 | + | 0.313353i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.90213i | 0.424208i | 0.977247 | + | 0.212104i | \(0.0680316\pi\) | ||||
−0.977247 | + | 0.212104i | \(0.931968\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.4309 | 1.36129 | 0.680644 | − | 0.732615i | \(-0.261700\pi\) | ||||
0.680644 | + | 0.732615i | \(0.261700\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.62224 | −0.300093 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.3652i | 1.03071i | 0.856978 | + | 0.515353i | \(0.172339\pi\) | ||||
−0.856978 | + | 0.515353i | \(0.827661\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.71065 | + | 2.79161i | −0.356164 | + | 0.148163i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.6575i | 1.30501i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.49695 | 0.131784 | 0.0658921 | − | 0.997827i | \(-0.479011\pi\) | ||||
0.0658921 | + | 0.997827i | \(0.479011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.9955 | 2.15766 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.1382i | 0.532118i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.4515 | + | 32.3356i | 0.704085 | + | 1.69252i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.3963i | 0.699283i | 0.936884 | + | 0.349641i | \(0.113697\pi\) | ||||
−0.936884 | + | 0.349641i | \(0.886303\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.54924 | 0.132708 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.2538 | 0.636187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.7845i | 1.23152i | 0.787935 | + | 0.615758i | \(0.211150\pi\) | ||||
−0.787935 | + | 0.615758i | \(0.788850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.3487 | + | 4.23134i | 0.534405 | + | 0.218505i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 15.1643i | − | 0.781001i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.45536 | −0.382956 | −0.191478 | − | 0.981497i | \(-0.561328\pi\) | ||||
−0.191478 | + | 0.981497i | \(0.561328\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.35252 | 0.376681 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0554i | 0.616002i | 0.951386 | + | 0.308001i | \(0.0996600\pi\) | ||||
−0.951386 | + | 0.308001i | \(0.900340\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.86054 | − | 6.87634i | −0.145787 | − | 0.350451i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.670329i | 0.0340747i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.27674 | 0.267542 | 0.133771 | − | 0.991012i | \(-0.457291\pi\) | ||||
0.133771 | + | 0.991012i | \(0.457291\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −46.5741 | −2.35535 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 17.2871i | − | 0.872021i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.84240 | − | 4.09441i | 0.495225 | − | 0.206012i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.4153i | 1.12499i | 0.826800 | + | 0.562496i | \(0.190159\pi\) | ||||
−0.826800 | + | 0.562496i | \(0.809841\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −27.7902 | −1.39125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.73635 | −0.236522 | −0.118261 | − | 0.992983i | \(-0.537732\pi\) | ||||
−0.118261 | + | 0.992983i | \(0.537732\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.9098i | − | 0.643081i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.06455 | + | 0.858848i | −0.102588 | + | 0.0426765i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.46104i | − | 0.468966i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.3376 | −1.15397 | −0.576986 | − | 0.816754i | \(-0.695771\pi\) | ||||
−0.576986 | + | 0.816754i | \(0.695771\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.25580 | −0.308576 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.35186i | 0.263348i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.57243 | − | 13.3954i | −0.273540 | − | 0.657553i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 18.7158i | − | 0.916517i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.9545 | −1.80534 | −0.902672 | − | 0.430329i | \(-0.858397\pi\) | ||||
−0.902672 | + | 0.430329i | \(0.858397\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3448 | 1.08902 | 0.544508 | − | 0.838755i | \(-0.316716\pi\) | ||||
0.544508 | + | 0.838755i | \(0.316716\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.2725i | 0.499467i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 24.3719 | + | 24.2240i | 1.18221 | + | 1.17504i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.4895i | 2.05621i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.21925 | 0.251988 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −24.8712 | −1.19800 | −0.599002 | − | 0.800747i | \(-0.704436\pi\) | ||||
−0.599002 | + | 0.800747i | \(0.704436\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.4150i | − | 1.55777i | −0.627168 | − | 0.778884i | \(-0.715786\pi\) | ||
0.627168 | − | 0.778884i | \(-0.284214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.31649 | − | 5.56851i | −0.111067 | − | 0.266990i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 52.4913i | − | 2.51100i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.50099 | 0.167093 | 0.0835467 | − | 0.996504i | \(-0.473375\pi\) | ||||
0.0835467 | + | 0.996504i | \(0.473375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.87254 | 0.279645 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.4807i | 0.497952i | 0.968510 | + | 0.248976i | \(0.0800940\pi\) | ||||
−0.968510 | + | 0.248976i | \(0.919906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.1445 | − | 10.4600i | 1.19196 | − | 0.495853i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5604i | 0.499492i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.7324 | 0.978422 | 0.489211 | − | 0.872165i | \(-0.337285\pi\) | ||||
0.489211 | + | 0.872165i | \(0.337285\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.36652 | −0.111435 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.707027i | 0.0332190i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 41.6454 | − | 17.3244i | 1.95237 | − | 0.812179i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.98131i | 0.233016i | 0.993190 | + | 0.116508i | \(0.0371700\pi\) | ||||
−0.993190 | + | 0.116508i | \(0.962830\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.87254 | −0.320783 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.26383 | 0.0588623 | 0.0294312 | − | 0.999567i | \(-0.490630\pi\) | ||||
0.0294312 | + | 0.999567i | \(0.490630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13.0429i | − | 0.606155i | −0.952966 | − | 0.303077i | \(-0.901986\pi\) | ||
0.952966 | − | 0.303077i | \(-0.0980141\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.97208 | − | 4.74062i | −0.0914532 | − | 0.219841i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.0737i | 1.76184i | 0.473265 | + | 0.880920i | \(0.343075\pi\) | ||||
−0.473265 | + | 0.880920i | \(0.656925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.58783 | 0.165671 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.97439 | −0.321363 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.622282i | − | 0.0286126i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −27.3017 | + | 27.4683i | −1.25269 | + | 1.26033i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.41538i | 0.156380i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.0184 | −1.41727 | −0.708634 | − | 0.705577i | \(-0.750688\pi\) | ||||
−0.708634 | + | 0.705577i | \(0.750688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 57.2992 | 2.61262 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.3142i | 1.10633i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.54871 | − | 22.9538i | −0.433584 | − | 1.04228i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.0052i | − | 0.770577i | −0.922796 | − | 0.385288i | \(-0.874102\pi\) | ||
0.922796 | − | 0.385288i | \(-0.125898\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.3193 | −0.828426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.53723 | −0.204762 | −0.102381 | − | 0.994745i | \(-0.532646\pi\) | ||||
−0.102381 | + | 0.994745i | \(0.532646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 18.5366i | − | 0.834847i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.91657 | − | 0.797289i | 0.0861435 | − | 0.0358355i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.6619i | 0.523109i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.7313 | −1.15189 | −0.575945 | − | 0.817489i | \(-0.695366\pi\) | ||||
−0.575945 | + | 0.817489i | \(0.695366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.82349 | −0.260174 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8694i | 0.885932i | 0.896538 | + | 0.442966i | \(0.146074\pi\) | ||||
−0.896538 | + | 0.442966i | \(0.853926\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28.9241 | + | 12.0324i | −1.28711 | + | 0.535433i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.6095i | 0.826479i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.0462 | −1.06583 | −0.532916 | − | 0.846168i | \(-0.678904\pi\) | ||||
−0.532916 | + | 0.846168i | \(0.678904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 56.1936 | 2.48586 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.74568i | − | 0.341980i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.96367 | + | 23.9513i | 0.439052 | + | 1.05542i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 9.53622i | − | 0.419403i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.5918 | −0.816090 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.2617 | 1.54484 | 0.772422 | − | 0.635109i | \(-0.219045\pi\) | ||||
0.772422 | + | 0.635109i | \(0.219045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 41.9031i | − | 1.83230i | −0.400839 | − | 0.916148i | \(-0.631281\pi\) | ||
0.400839 | − | 0.916148i | \(-0.368719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.6462 | − | 12.7234i | 0.551927 | − | 0.555296i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 15.7807i | − | 0.687418i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9256 | −0.996766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.49167 | −0.0647330 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 14.3324i | − | 0.620807i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.5289 | − | 42.1370i | −0.757839 | − | 1.82174i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0429121i | 0.00185179i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.45161 | −0.234818 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.7752 | 1.23714 | 0.618571 | − | 0.785729i | \(-0.287712\pi\) | ||||
0.618571 | + | 0.785729i | \(0.287712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 0.122684i | − | 0.00526485i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.95444 | − | 2.89303i | 0.297896 | − | 0.123924i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 32.5449i | − | 1.39152i | −0.718274 | − | 0.695761i | \(-0.755067\pi\) | ||
0.718274 | − | 0.695761i | \(-0.244933\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.8427 | −0.505433 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.8916 | 0.890014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 17.1044i | − | 0.727352i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.0410 | − | 8.75298i | 0.893139 | − | 0.371543i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 39.9011i | − | 1.69066i | −0.534242 | − | 0.845332i | \(-0.679403\pi\) | ||
0.534242 | − | 0.845332i | \(-0.320597\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.76875 | 0.159401 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.37994 | 0.269361 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.7320i | 1.33735i | 0.743557 | + | 0.668673i | \(0.233137\pi\) | ||||
−0.743557 | + | 0.668673i | \(0.766863\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.6363 | − | 32.7799i | −0.573686 | − | 1.37906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.58783i | 0.150675i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.70307 | 0.239085 | 0.119542 | − | 0.992829i | \(-0.461857\pi\) | ||||
0.119542 | + | 0.992829i | \(0.461857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.3786 | −1.35500 | −0.677500 | − | 0.735523i | \(-0.736937\pi\) | ||||
−0.677500 | + | 0.735523i | \(0.736937\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.4113i | 0.602040i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0326 | + | 23.8867i | 1.00223 | + | 0.996146i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.8739i | 0.535947i | 0.963426 | + | 0.267974i | \(0.0863540\pi\) | ||||
−0.963426 | + | 0.267974i | \(0.913646\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.81325 | −0.116915 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −23.2788 | −0.965767 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.17058i | − | 0.131312i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.82865 | + | 11.6074i | 0.199640 | + | 0.479907i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.341249i | 0.0140849i | 0.999975 | + | 0.00704243i | \(0.00224170\pi\) | ||||
−0.999975 | + | 0.00704243i | \(0.997758\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.7856 | 0.732843 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.4350 | −0.470371 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.9708i | 0.450518i | 0.974299 | + | 0.225259i | \(0.0723228\pi\) | ||||
−0.974299 | + | 0.225259i | \(0.927677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50.9067 | − | 21.1771i | 2.08697 | − | 0.868175i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.3724i | 0.997497i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.0535 | 1.02366 | 0.511829 | − | 0.859088i | \(-0.328968\pi\) | ||||
0.511829 | + | 0.859088i | \(0.328968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.3181 | 1.27749 | 0.638745 | − | 0.769418i | \(-0.279454\pi\) | ||||
0.638745 | + | 0.769418i | \(0.279454\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00000i | 0.0407231i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.9309 | − | 8.70719i | 0.850961 | − | 0.353998i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.72286i | 0.232284i | 0.993233 | + | 0.116142i | \(0.0370527\pi\) | ||||
−0.993233 | + | 0.116142i | \(0.962947\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.67710 | −0.392136 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.7546 | 2.33650 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.31428i | 0.0530831i | 0.999648 | + | 0.0265415i | \(0.00844943\pi\) | ||||
−0.999648 | + | 0.0265415i | \(0.991551\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.18941 | − | 5.26305i | −0.0882856 | − | 0.212226i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.05542i | − | 0.243782i | −0.992543 | − | 0.121891i | \(-0.961104\pi\) | ||
0.992543 | − | 0.121891i | \(-0.0388959\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.9572 | 1.24427 | 0.622137 | − | 0.782908i | \(-0.286265\pi\) | ||||
0.622137 | + | 0.782908i | \(0.286265\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.77684 | −0.271945 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 43.6967i | − | 1.75067i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.152143 | − | 24.9995i | −0.00608573 | − | 0.999981i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.19049i | 0.287161i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 70.0417 | 2.79275 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.6183 | −0.542138 | −0.271069 | − | 0.962560i | \(-0.587377\pi\) | ||||
−0.271069 | + | 0.962560i | \(0.587377\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.29939i | − | 0.0913924i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.31470 | − | 15.1797i | −0.250591 | − | 0.602387i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 33.0168i | − | 1.30817i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.25041 | −0.128584 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.2258 | 1.39134 | 0.695668 | − | 0.718363i | \(-0.255108\pi\) | ||||
0.695668 | + | 0.718363i | \(0.255108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.6823i | − | 0.736759i | −0.929675 | − | 0.368380i | \(-0.879913\pi\) | ||
0.929675 | − | 0.368380i | \(-0.120087\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38393 | − | 0.575711i | 0.0544922 | − | 0.0226686i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 25.4400i | − | 1.00015i | −0.865982 | − | 0.500075i | \(-0.833306\pi\) | ||
0.865982 | − | 0.500075i | \(-0.166694\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.38475 | 0.0543563 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.23836 | −0.322887 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.7060i | 0.771155i | 0.922676 | + | 0.385577i | \(0.125998\pi\) | ||||
−0.922676 | + | 0.385577i | \(0.874002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −35.6902 | + | 14.8470i | −1.39453 | + | 0.580121i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.6623i | 0.611044i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8827 | −0.891384 | −0.445692 | − | 0.895186i | \(-0.647042\pi\) | ||||
−0.445692 | + | 0.895186i | \(0.647042\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.1151 | 1.17134 | 0.585671 | − | 0.810549i | \(-0.300831\pi\) | ||||
0.585671 | + | 0.810549i | \(0.300831\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 38.6390i | 1.50062i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 23.8676 | + | 57.3743i | 0.925544 | + | 2.22488i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 18.2785i | − | 0.707747i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.59585 | 0.332335 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.9938 | 0.424412 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.96661i | − | 0.152902i | −0.997073 | − | 0.0764508i | \(-0.975641\pi\) | ||
0.997073 | − | 0.0764508i | \(-0.0243588\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.54628 | + | 3.52476i | 0.136496 | + | 0.135668i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 35.4909i | − | 1.36403i | −0.731339 | − | 0.682014i | \(-0.761104\pi\) | ||
0.731339 | − | 0.682014i | \(-0.238896\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.8896 | −1.53082 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8063 | 0.452418 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.2681i | 0.392899i | 0.980514 | + | 0.196450i | \(0.0629412\pi\) | ||||
−0.980514 | + | 0.196450i | \(0.937059\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.37278 | + | 12.9154i | 0.205283 | + | 0.493473i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 23.4280i | − | 0.893834i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.2021 | 0.731542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.9612 | 0.416983 | 0.208492 | − | 0.978024i | \(-0.433145\pi\) | ||||
0.208492 | + | 0.978024i | \(0.433145\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 3.33067i | − | 0.126522i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −38.6398 | + | 16.0740i | −1.46569 | + | 0.609723i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 17.5198i | − | 0.663608i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.43414 | 0.319009 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.9366 | −1.31954 | −0.659769 | − | 0.751469i | \(-0.729346\pi\) | ||||
−0.659769 | + | 0.751469i | \(0.729346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 78.9404i | 2.97729i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 21.2082 | − | 8.82254i | 0.798746 | − | 0.332276i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.2651i | 1.89041i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.3013 | −1.73888 | −0.869442 | − | 0.494036i | \(-0.835521\pi\) | ||||
−0.869442 | + | 0.494036i | \(0.835521\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.76733 | 0.178789 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 15.5610i | − | 0.582763i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.48255 | − | 10.7754i | −0.167638 | − | 0.402978i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.3248i | 0.609661i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.9488 | 1.15419 | 0.577097 | − | 0.816675i | \(-0.304185\pi\) | ||||
0.577097 | + | 0.816675i | \(0.304185\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.6232 | 1.55013 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 11.9934i | − | 0.446041i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.50698 | + | 9.56502i | −0.353080 | + | 0.355236i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.19242i | 0.118400i | 0.998246 | + | 0.0592001i | \(0.0188550\pi\) | ||||
−0.998246 | + | 0.0592001i | \(0.981145\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.60686 | 0.170391 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.42238i | − | 0.0525369i | −0.999655 | − | 0.0262684i | \(-0.991638\pi\) | ||
0.999655 | − | 0.0262684i | \(-0.00836247\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.04362 | − | 12.1242i | −0.186037 | − | 0.447206i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 0.928323i | − | 0.0341952i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.9270 | −0.806599 | −0.403299 | − | 0.915068i | \(-0.632137\pi\) | ||||
−0.403299 | + | 0.915068i | \(0.632137\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −43.5480 | −1.59978 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 37.8836i | − | 1.38981i | −0.719099 | − | 0.694907i | \(-0.755445\pi\) | ||
0.719099 | − | 0.694907i | \(-0.244555\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.8026 | − | 9.06982i | 0.798785 | − | 0.332292i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6.48826i | − | 0.237393i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −73.2267 | −2.67565 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.81778 | −0.102822 | −0.0514111 | − | 0.998678i | \(-0.516372\pi\) | ||||
−0.0514111 | + | 0.998678i | \(0.516372\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 26.3699i | 0.960972i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.45970 | − | 0.607229i | 0.0531237 | − | 0.0220993i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 3.57996i | − | 0.130116i | −0.997881 | − | 0.0650579i | \(-0.979277\pi\) | ||
0.997881 | − | 0.0650579i | \(-0.0207232\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.29110 | 0.228353 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.5794 | −0.782252 | −0.391126 | − | 0.920337i | \(-0.627914\pi\) | ||||
−0.391126 | + | 0.920337i | \(0.627914\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 12.0856i | − | 0.437528i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.90247 | + | 14.1887i | 0.213404 | + | 0.512994i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.38653i | 0.302820i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.8781 | 0.933187 | 0.466593 | − | 0.884472i | \(-0.345481\pi\) | ||||
0.466593 | + | 0.884472i | \(0.345481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.5740 | 0.740954 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.4485i | 1.59870i | 0.600866 | + | 0.799350i | \(0.294823\pi\) | ||||
−0.600866 | + | 0.799350i | \(0.705177\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.09354 | + | 8.14294i | −0.290728 | + | 0.292503i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 36.5655i | − | 1.31178i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.7456 | 0.707460 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.01743 | 0.107972 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.69720i | − | 0.0963901i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.98994 | + | 14.3990i | 0.213790 | + | 0.513922i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 21.6381i | − | 0.771316i | −0.922642 | − | 0.385658i | \(-0.873974\pi\) | ||
0.922642 | − | 0.385658i | \(-0.126026\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.88398 | −0.173874 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56.9657 | −2.02547 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 66.5823i | 2.36441i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.05124 | − | 2.93330i | 0.250082 | − | 0.104033i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 26.1468i | − | 0.926167i | −0.886315 | − | 0.463083i | \(-0.846743\pi\) | ||
0.886315 | − | 0.463083i | \(-0.153257\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.5983 | 2.49759 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.1791 | 0.430329 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14.5397i | − | 0.513093i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 50.1979 | − | 20.8822i | 1.76924 | − | 0.736000i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 6.13025i | − | 0.215795i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0292 | 0.387765 | 0.193882 | − | 0.981025i | \(-0.437892\pi\) | ||||
0.193882 | + | 0.981025i | \(0.437892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.8036 | −1.25723 | −0.628617 | − | 0.777715i | \(-0.716379\pi\) | ||||
−0.628617 | + | 0.777715i | \(0.716379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.75729i | 0.166845i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.7335 | + | 37.8211i | 0.551120 | + | 1.32482i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.19215i | 0.181650i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.1716 | 0.704854 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.7713 | −0.550423 | −0.275211 | − | 0.961384i | \(-0.588748\pi\) | ||||
−0.275211 | + | 0.961384i | \(0.588748\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.465569i | 0.0162287i | 0.999967 | + | 0.00811435i | \(0.00258291\pi\) | ||||
−0.999967 | + | 0.00811435i | \(0.997417\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.29209 | − | 3.27212i | −0.114616 | − | 0.113920i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 21.6674i | − | 0.753451i | −0.926325 | − | 0.376725i | \(-0.877050\pi\) | ||
0.926325 | − | 0.376725i | \(-0.122950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.1956 | −0.944541 | −0.472271 | − | 0.881454i | \(-0.656566\pi\) | ||||
−0.472271 | + | 0.881454i | \(0.656566\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.2685 | −0.841866 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 40.3592i | − | 1.39836i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.00149 | + | 12.0229i | 0.173084 | + | 0.416070i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2.29620i | − | 0.0793681i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −56.6311 | −1.95512 | −0.977562 | − | 0.210649i | \(-0.932442\pi\) | ||||
−0.977562 | + | 0.210649i | \(0.932442\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.7251 | −0.749142 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.71136i | 0.334477i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 38.4204 | − | 15.9828i | 1.32170 | − | 0.549824i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 36.3742i | − | 1.24983i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.4400 | −0.358300 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 69.0665 | 2.36757 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.7470i | − | 0.847320i | −0.905821 | − | 0.423660i | \(-0.860745\pi\) | ||
0.905821 | − | 0.423660i | \(-0.139255\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −15.9914 | + | 6.65236i | −0.546893 | + | 0.227506i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.4582i | 1.00627i | 0.864207 | + | 0.503137i | \(0.167821\pi\) | ||||
−0.864207 | + | 0.503137i | \(0.832179\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.74256 | −0.161814 | −0.0809069 | − | 0.996722i | \(-0.525782\pi\) | ||||
−0.0809069 | + | 0.996722i | \(0.525782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.14625 | −0.311703 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34.0453i | − | 1.15892i | −0.815002 | − | 0.579458i | \(-0.803264\pi\) | ||
0.815002 | − | 0.579458i | \(-0.196736\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.9675 | + | 38.3838i | 0.542913 | + | 1.30509i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 30.2318i | 1.02673i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.42562 | −0.150129 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.62224 | 0.190502 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 11.1180i | − | 0.376289i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.1294 | − | 15.1813i | −1.25520 | − | 0.513223i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.41962i | − | 0.0479371i | −0.999713 | − | 0.0239686i | \(-0.992370\pi\) | ||
0.999713 | − | 0.0239686i | \(-0.00763016\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.75711 | 0.160453 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.4417 | −1.05930 | −0.529648 | − | 0.848217i | \(-0.677676\pi\) | ||||
−0.529648 | + | 0.848217i | \(0.677676\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 24.9544i | − | 0.839783i | −0.907574 | − | 0.419892i | \(-0.862068\pi\) | ||
0.907574 | − | 0.419892i | \(-0.137932\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.28112 | + | 3.07963i | 0.0430643 | + | 0.103521i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 49.8369i | − | 1.67336i | −0.547694 | − | 0.836679i | \(-0.684494\pi\) | ||
0.547694 | − | 0.836679i | \(-0.315506\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.3796 | −0.884744 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.928323 | 0.0311000 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 79.5676i | 2.66263i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0885942 | − | 0.0368550i | 0.00296138 | − | 0.00123193i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 38.1010i | 1.27216i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.19330 | 0.206558 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.4724 | 0.781978 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.40503i | − | 0.0800343i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.253287 | + | 0.105367i | −0.00841953 | + | 0.00350250i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54.6325i | 1.81404i | 0.421085 | + | 0.907021i | \(0.361649\pi\) | ||||
−0.421085 | + | 0.907021i | \(0.638351\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.0099 | −0.464678 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.8502 | −0.757060 | −0.378530 | − | 0.925589i | \(-0.623570\pi\) | ||||
−0.378530 | + | 0.925589i | \(0.623570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.02321i | 0.199339i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10.1711 | + | 24.4498i | 0.336245 | + | 0.808287i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 62.0233i | 2.04819i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.5110 | −1.86413 | −0.932063 | − | 0.362296i | \(-0.881993\pi\) | ||||
−0.932063 | + | 0.362296i | \(0.881993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.6235 | 0.679567 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.2746i | 0.601515i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.1420 | − | 35.9227i | −1.18834 | − | 1.18113i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.6012i | 0.381034i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.67214 | 0.186097 | 0.0930485 | − | 0.995662i | \(-0.470339\pi\) | ||||
0.0930485 | + | 0.995662i | \(0.470339\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.4868 | 1.49077 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 12.4806i | − | 0.408596i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.47940 | − | 13.1717i | −0.179196 | − | 0.430761i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 37.0258i | − | 1.20958i | −0.796385 | − | 0.604790i | \(-0.793257\pi\) | ||
0.796385 | − | 0.604790i | \(-0.206743\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.4911 | 0.733969 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.1217 | 0.851545 | 0.425772 | − | 0.904830i | \(-0.360002\pi\) | ||||
0.425772 | + | 0.904830i | \(0.360002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 17.2758i | − | 0.562578i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.40727 | − | 3.08140i | 0.240958 | − | 0.100238i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 19.4693i | − | 0.632666i | −0.948648 | − | 0.316333i | \(-0.897548\pi\) | ||
0.948648 | − | 0.316333i | \(-0.102452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 88.0570 | 2.85845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.97888 | 0.258733 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.7179i | 1.80488i | 0.430815 | + | 0.902440i | \(0.358226\pi\) | ||||
−0.430815 | + | 0.902440i | \(0.641774\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.7529 | − | 12.3771i | 0.962780 | − | 0.400514i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.50387i | 0.0809388i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22.4448 | 0.724779 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.7275 | −0.829919 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 20.4097i | − | 0.657695i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.41616 | + | 5.80811i | 0.0777789 | + | 0.186970i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.6808i | 1.43684i | 0.695610 | + | 0.718419i | \(0.255134\pi\) | ||||
−0.695610 | + | 0.718419i | \(0.744866\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −53.2325 | −1.71007 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0457 | 0.675388 | 0.337694 | − | 0.941256i | \(-0.390353\pi\) | ||||
0.337694 | + | 0.941256i | \(0.390353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 67.1492i | 2.15270i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.8170 | − | 19.9380i | 0.634653 | − | 0.638527i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 23.1792i | − | 0.741568i | −0.928719 | − | 0.370784i | \(-0.879089\pi\) | ||
0.928719 | − | 0.370784i | \(-0.120911\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.3062 | −0.361347 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.36850 | 0.107548 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.5480i | 0.814855i | 0.913237 | + | 0.407428i | \(0.133574\pi\) | ||||
−0.913237 | + | 0.407428i | \(0.866426\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.82089 | + | 23.6081i | 0.312920 | + | 0.752216i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 36.8561i | − | 1.17314i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.54271 | 0.144450 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9306 | −0.601351 | −0.300675 | − | 0.953727i | \(-0.597212\pi\) | ||||
−0.300675 | + | 0.953727i | \(0.597212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.4582i | 0.744422i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50.3182 | − | 20.9322i | 1.59519 | − | 0.663596i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.0343i | 1.36291i | 0.731859 | + | 0.681456i | \(0.238653\pi\) | ||||
−0.731859 | + | 0.681456i | \(0.761347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.1915 | 0.322446 |
(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 | 4020.2.g.c.1609.3 | ✓ | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.22 | yes | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.3 | ✓ | 38 | 1.1 | even | 1 | trivial | |
4020.2.g.c.1609.22 | yes | 38 | 5.4 | even | 2 | inner |