Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(111,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.111");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.r (of order \(4\), degree \(2\), not 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: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 111.2 | ||
Character | \(\chi\) | \(=\) | 320.111 |
Dual form | 320.3.r.a.271.2 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.58499 | + | 3.58499i | −1.19500 | + | 1.19500i | −0.219350 | + | 0.975646i | \(0.570394\pi\) |
−0.975646 | + | 0.219350i | \(0.929606\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.58114 | + | 1.58114i | −0.316228 | + | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.0090 | −1.42986 | −0.714928 | − | 0.699198i | \(-0.753540\pi\) | ||||
−0.714928 | + | 0.699198i | \(0.753540\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 16.7043i | − | 1.85603i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.304644 | + | 0.304644i | 0.0276949 | + | 0.0276949i | 0.720819 | − | 0.693124i | \(-0.243766\pi\) |
−0.693124 | + | 0.720819i | \(0.743766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.87350 | + | 6.87350i | 0.528731 | + | 0.528731i | 0.920194 | − | 0.391463i | \(-0.128031\pi\) |
−0.391463 | + | 0.920194i | \(0.628031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 11.3367i | − | 0.755782i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −25.8031 | −1.51783 | −0.758916 | − | 0.651189i | \(-0.774270\pi\) | ||||
−0.758916 | + | 0.651189i | \(0.774270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.2562 | − | 10.2562i | 0.539802 | − | 0.539802i | −0.383669 | − | 0.923471i | \(-0.625340\pi\) |
0.923471 | + | 0.383669i | \(0.125340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 35.8821 | − | 35.8821i | 1.70867 | − | 1.70867i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.7343 | 1.46671 | 0.733355 | − | 0.679845i | \(-0.237953\pi\) | ||||
0.733355 | + | 0.679845i | \(0.237953\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 5.00000i | − | 0.200000i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.6197 | + | 27.6197i | 1.02295 | + | 1.02295i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 23.1650 | + | 23.1650i | 0.798794 | + | 0.798794i | 0.982905 | − | 0.184111i | \(-0.0589407\pi\) |
−0.184111 | + | 0.982905i | \(0.558941\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.31924i | − | 0.236104i | −0.993007 | − | 0.118052i | \(-0.962335\pi\) | ||
0.993007 | − | 0.118052i | \(-0.0376650\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.18429 | −0.0661907 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15.8256 | − | 15.8256i | 0.452160 | − | 0.452160i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.85014 | − | 6.85014i | 0.185139 | − | 0.185139i | −0.608452 | − | 0.793591i | \(-0.708209\pi\) |
0.793591 | + | 0.608452i | \(0.208209\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −49.2828 | −1.26366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 63.7855i | − | 1.55574i | −0.628423 | − | 0.777872i | \(-0.716299\pi\) | ||
0.628423 | − | 0.777872i | \(-0.283701\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −15.0257 | − | 15.0257i | −0.349434 | − | 0.349434i | 0.510465 | − | 0.859899i | \(-0.329473\pi\) |
−0.859899 | + | 0.510465i | \(0.829473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 26.4118 | + | 26.4118i | 0.586928 | + | 0.586928i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 41.8744i | − | 0.890944i | −0.895296 | − | 0.445472i | \(-0.853036\pi\) | ||
0.895296 | − | 0.445472i | \(-0.146964\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 51.1799 | 1.04449 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 92.5039 | − | 92.5039i | 1.81380 | − | 1.81380i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −36.5375 | + | 36.5375i | −0.689388 | + | 0.689388i | −0.962097 | − | 0.272709i | \(-0.912080\pi\) |
0.272709 | + | 0.962097i | \(0.412080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.963370 | −0.0175158 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 73.5369i | 1.29012i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −58.1638 | − | 58.1638i | −0.985828 | − | 0.985828i | 0.0140734 | − | 0.999901i | \(-0.495520\pi\) |
−0.999901 | + | 0.0140734i | \(0.995520\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −26.2928 | − | 26.2928i | −0.431030 | − | 0.431030i | 0.457949 | − | 0.888979i | \(-0.348584\pi\) |
−0.888979 | + | 0.457949i | \(0.848584\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 167.193i | 2.65386i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.7359 | −0.334399 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.48091 | − | 4.48091i | 0.0668793 | − | 0.0668793i | −0.672876 | − | 0.739755i | \(-0.734941\pi\) |
0.739755 | + | 0.672876i | \(0.234941\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −120.937 | + | 120.937i | −1.75271 | + | 1.75271i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5673 | −0.162919 | −0.0814595 | − | 0.996677i | \(-0.525958\pi\) | ||||
−0.0814595 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 101.723i | − | 1.39346i | −0.717332 | − | 0.696732i | \(-0.754637\pi\) | ||
0.717332 | − | 0.696732i | \(-0.245363\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.9249 | + | 17.9249i | 0.238999 | + | 0.238999i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.04918 | − | 3.04918i | −0.0395998 | − | 0.0395998i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 73.1288i | 0.925681i | 0.886442 | + | 0.462840i | \(0.153170\pi\) | ||||
−0.886442 | + | 0.462840i | \(0.846830\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −47.6943 | −0.588819 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −39.9292 | + | 39.9292i | −0.481075 | + | 0.481075i | −0.905475 | − | 0.424400i | \(-0.860485\pi\) |
0.424400 | + | 0.905475i | \(0.360485\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 40.7983 | − | 40.7983i | 0.479980 | − | 0.479980i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −166.093 | −1.90911 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 37.2154i | 0.418151i | 0.977899 | + | 0.209076i | \(0.0670455\pi\) | ||||
−0.977899 | + | 0.209076i | \(0.932955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −68.7968 | − | 68.7968i | −0.756008 | − | 0.756008i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26.2394 | + | 26.2394i | 0.282144 | + | 0.282144i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.4331i | 0.341401i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −114.749 | −1.18298 | −0.591490 | − | 0.806312i | \(-0.701460\pi\) | ||||
−0.591490 | + | 0.806312i | \(0.701460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.08886 | − | 5.08886i | 0.0514026 | − | 0.0514026i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.86189 | − | 3.86189i | 0.0382366 | − | 0.0382366i | −0.687730 | − | 0.725967i | \(-0.741393\pi\) |
0.725967 | + | 0.687730i | \(0.241393\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −82.3074 | −0.799101 | −0.399551 | − | 0.916711i | \(-0.630834\pi\) | ||||
−0.399551 | + | 0.916711i | \(0.630834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 113.469i | 1.08066i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 109.631 | + | 109.631i | 1.02459 | + | 1.02459i | 0.999690 | + | 0.0248967i | \(0.00792568\pi\) |
0.0248967 | + | 0.999690i | \(0.492074\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.99231 | − | 2.99231i | −0.0274524 | − | 0.0274524i | 0.693247 | − | 0.720700i | \(-0.256179\pi\) |
−0.720700 | + | 0.693247i | \(0.756179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 49.1153i | 0.442480i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 73.3488 | 0.649105 | 0.324552 | − | 0.945868i | \(-0.394786\pi\) | ||||
0.324552 | + | 0.945868i | \(0.394786\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −53.3387 | + | 53.3387i | −0.463815 | + | 0.463815i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 114.817 | − | 114.817i | 0.981340 | − | 0.981340i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 258.263 | 2.17028 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 120.814i | − | 0.998466i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 228.670 | + | 228.670i | 1.85911 | + | 1.85911i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.90569 | + | 7.90569i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 212.909i | − | 1.67645i | −0.545323 | − | 0.838226i | \(-0.683593\pi\) | ||
0.545323 | − | 0.838226i | \(-0.316407\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 107.734 | 0.835145 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −34.5741 | + | 34.5741i | −0.263924 | + | 0.263924i | −0.826646 | − | 0.562722i | \(-0.809754\pi\) |
0.562722 | + | 0.826646i | \(0.309754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −102.655 | + | 102.655i | −0.771838 | + | 0.771838i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −87.3413 | −0.646972 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 156.675i | − | 1.14362i | −0.820388 | − | 0.571808i | \(-0.806242\pi\) | ||
0.820388 | − | 0.571808i | \(-0.193758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −150.961 | − | 150.961i | −1.08605 | − | 1.08605i | −0.995931 | − | 0.0901190i | \(-0.971275\pi\) |
−0.0901190 | − | 0.995931i | \(-0.528725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 150.119 | + | 150.119i | 1.06467 | + | 1.06467i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.18794i | 0.0292863i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −73.2543 | −0.505202 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −183.479 | + | 183.479i | −1.24816 | + | 1.24816i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 96.4520 | − | 96.4520i | 0.647329 | − | 0.647329i | −0.305018 | − | 0.952347i | \(-0.598662\pi\) |
0.952347 | + | 0.305018i | \(0.0986624\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −29.4114 | −0.194777 | −0.0973886 | − | 0.995246i | \(-0.531049\pi\) | ||||
−0.0973886 | + | 0.995246i | \(0.531049\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 431.023i | 2.81714i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.5727 | + | 11.5727i | 0.0746628 | + | 0.0746628i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −117.658 | − | 117.658i | −0.749415 | − | 0.749415i | 0.224954 | − | 0.974369i | \(-0.427777\pi\) |
−0.974369 | + | 0.224954i | \(0.927777\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 261.973i | − | 1.64763i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −337.647 | −2.09718 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.81267 | − | 7.81267i | 0.0479305 | − | 0.0479305i | −0.682735 | − | 0.730666i | \(-0.739210\pi\) |
0.730666 | + | 0.682735i | \(0.239210\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.45367 | − | 3.45367i | 0.0209313 | − | 0.0209313i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 255.372 | 1.52918 | 0.764588 | − | 0.644520i | \(-0.222943\pi\) | ||||
0.764588 | + | 0.644520i | \(0.222943\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 74.5100i | − | 0.440888i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −171.323 | − | 171.323i | −1.00189 | − | 1.00189i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 27.0161 | + | 27.0161i | 0.156162 | + | 0.156162i | 0.780864 | − | 0.624701i | \(-0.214779\pi\) |
−0.624701 | + | 0.780864i | \(0.714779\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 50.0449i | 0.285971i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 417.033 | 2.35612 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −50.8893 | + | 50.8893i | −0.284298 | + | 0.284298i | −0.834820 | − | 0.550523i | \(-0.814428\pi\) |
0.550523 | + | 0.834820i | \(0.314428\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.6488 | + | 13.6488i | −0.0754079 | + | 0.0754079i | −0.743805 | − | 0.668397i | \(-0.766981\pi\) |
0.668397 | + | 0.743805i | \(0.266981\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 188.519 | 1.03016 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.6620i | 0.117092i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.86078 | − | 7.86078i | −0.0420362 | − | 0.0420362i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −276.446 | − | 276.446i | −1.46268 | − | 1.46268i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 263.019i | 1.37706i | 0.725206 | + | 0.688532i | \(0.241745\pi\) | ||||
−0.725206 | + | 0.688532i | \(0.758255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −58.9456 | −0.305418 | −0.152709 | − | 0.988271i | \(-0.548800\pi\) | ||||
−0.152709 | + | 0.988271i | \(0.548800\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 77.9230 | − | 77.9230i | 0.399605 | − | 0.399605i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.54461 | − | 9.54461i | 0.0484498 | − | 0.0484498i | −0.682467 | − | 0.730917i | \(-0.739093\pi\) |
0.730917 | + | 0.682467i | \(0.239093\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −103.151 | −0.518348 | −0.259174 | − | 0.965831i | \(-0.583450\pi\) | ||||
−0.259174 | + | 0.965831i | \(0.583450\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.1280i | 0.159841i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −231.859 | − | 231.859i | −1.14216 | − | 1.14216i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 100.854 | + | 100.854i | 0.491969 | + | 0.491969i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 563.508i | − | 2.72226i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.24900 | 0.0298995 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.93870 | + | 4.93870i | −0.0234062 | + | 0.0234062i | −0.718713 | − | 0.695307i | \(-0.755268\pi\) |
0.695307 | + | 0.718713i | \(0.255268\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 41.4685 | − | 41.4685i | 0.194688 | − | 0.194688i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 47.5153 | 0.221002 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 73.2582i | 0.337595i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 364.675 | + | 364.675i | 1.66518 | + | 1.66518i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −177.358 | − | 177.358i | −0.802524 | − | 0.802524i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 177.151i | − | 0.794401i | −0.917732 | − | 0.397200i | \(-0.869982\pi\) | ||
0.917732 | − | 0.397200i | \(-0.130018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −83.5214 | −0.371206 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 239.268 | − | 239.268i | 1.05404 | − | 1.05404i | 0.0555894 | − | 0.998454i | \(-0.482296\pi\) |
0.998454 | − | 0.0555894i | \(-0.0177038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −106.699 | + | 106.699i | −0.465933 | + | 0.465933i | −0.900594 | − | 0.434661i | \(-0.856868\pi\) |
0.434661 | + | 0.900594i | \(0.356868\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.8626 | 0.0946431 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 132.961i | 0.570649i | 0.958431 | + | 0.285324i | \(0.0921013\pi\) | ||||
−0.958431 | + | 0.285324i | \(0.907899\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 66.2092 | + | 66.2092i | 0.281741 | + | 0.281741i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −262.166 | − | 262.166i | −1.10618 | − | 1.10618i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 89.6649i | 0.375167i | 0.982249 | + | 0.187584i | \(0.0600655\pi\) | ||||
−0.982249 | + | 0.187584i | \(0.939934\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 259.019 | 1.07477 | 0.537383 | − | 0.843338i | \(-0.319413\pi\) | ||||
0.537383 | + | 0.843338i | \(0.319413\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −77.5940 | + | 77.5940i | −0.319317 | + | 0.319317i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −80.9225 | + | 80.9225i | −0.330296 | + | 0.330296i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 140.992 | 0.570819 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 286.292i | − | 1.14977i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −85.2338 | − | 85.2338i | −0.339577 | − | 0.339577i | 0.516631 | − | 0.856208i | \(-0.327186\pi\) |
−0.856208 | + | 0.516631i | \(0.827186\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.2770 | + | 10.2770i | 0.0406205 | + | 0.0406205i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 292.523i | 1.14715i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 451.683 | 1.75752 | 0.878760 | − | 0.477264i | \(-0.158372\pi\) | ||||
0.878760 | + | 0.477264i | \(0.158372\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −68.5629 | + | 68.5629i | −0.264722 | + | 0.264722i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 386.955 | − | 386.955i | 1.48259 | − | 1.48259i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.939393 | 0.00357184 | 0.00178592 | − | 0.999998i | \(-0.499432\pi\) | ||||
0.00178592 | + | 0.999998i | \(0.499432\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 115.542i | − | 0.436007i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −133.417 | − | 133.417i | −0.499689 | − | 0.499689i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 141.098 | + | 141.098i | 0.524527 | + | 0.524527i | 0.918935 | − | 0.394408i | \(-0.129050\pi\) |
−0.394408 | + | 0.918935i | \(0.629050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 237.677i | − | 0.877037i | −0.898722 | − | 0.438518i | \(-0.855503\pi\) | ||
0.898722 | − | 0.438518i | \(-0.144497\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 493.271 | 1.80685 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.52322 | − | 1.52322i | 0.00553899 | − | 0.00553899i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −301.681 | + | 301.681i | −1.08910 | + | 1.08910i | −0.0934800 | + | 0.995621i | \(0.529799\pi\) |
−0.995621 | + | 0.0934800i | \(0.970201\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −122.263 | −0.438217 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 209.865i | 0.746850i | 0.927660 | + | 0.373425i | \(0.121817\pi\) | ||||
−0.927660 | + | 0.373425i | \(0.878183\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −87.1403 | − | 87.1403i | −0.307916 | − | 0.307916i | 0.536184 | − | 0.844101i | \(-0.319865\pi\) |
−0.844101 | + | 0.536184i | \(0.819865\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −116.272 | − | 116.272i | −0.407972 | − | 0.407972i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 638.428i | 2.22449i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 376.801 | 1.30381 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 411.374 | − | 411.374i | 1.41366 | − | 1.41366i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 210.545 | − | 210.545i | 0.718583 | − | 0.718583i | −0.249732 | − | 0.968315i | \(-0.580343\pi\) |
0.968315 | + | 0.249732i | \(0.0803426\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 183.930 | 0.623492 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.8284i | 0.0566612i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 231.873 | + | 231.873i | 0.775495 | + | 0.775495i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 150.392 | + | 150.392i | 0.499640 | + | 0.499640i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 27.6897i | 0.0913851i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 83.1452 | 0.272607 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −345.339 | + | 345.339i | −1.12488 | + | 1.12488i | −0.133888 | + | 0.990996i | \(0.542746\pi\) |
−0.990996 | + | 0.133888i | \(0.957254\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 295.071 | − | 295.071i | 0.954923 | − | 0.954923i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 99.7096 | 0.320610 | 0.160305 | − | 0.987068i | \(-0.448752\pi\) | ||||
0.160305 | + | 0.987068i | \(0.448752\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 311.334i | − | 0.994678i | −0.867556 | − | 0.497339i | \(-0.834311\pi\) | ||
0.867556 | − | 0.497339i | \(-0.165689\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −264.355 | − | 264.355i | −0.839223 | − | 0.839223i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.2419 | + | 19.2419i | 0.0607000 | + | 0.0607000i | 0.736805 | − | 0.676105i | \(-0.236334\pi\) |
−0.676105 | + | 0.736805i | \(0.736334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.1142i | 0.0442451i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −786.050 | −2.44875 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −264.643 | + | 264.643i | −0.819328 | + | 0.819328i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.3675 | − | 34.3675i | 0.105746 | − | 0.105746i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.4548 | 0.0656110 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 419.120i | 1.27392i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −194.214 | − | 194.214i | −0.586750 | − | 0.586750i | 0.350000 | − | 0.936750i | \(-0.386182\pi\) |
−0.936750 | + | 0.350000i | \(0.886182\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −114.427 | − | 114.427i | −0.343623 | − | 0.343623i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.1699i | 0.0422982i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −552.303 | −1.63888 | −0.819441 | − | 0.573164i | \(-0.805716\pi\) | ||||
−0.819441 | + | 0.573164i | \(0.805716\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −262.955 | + | 262.955i | −0.775677 | + | 0.775677i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.22976 | − | 2.22976i | 0.00653890 | − | 0.00653890i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −21.8182 | −0.0636099 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 382.437i | − | 1.10851i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −119.162 | − | 119.162i | −0.343407 | − | 0.343407i | 0.514239 | − | 0.857647i | \(-0.328074\pi\) |
−0.857647 | + | 0.514239i | \(0.828074\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −170.249 | − | 170.249i | −0.487821 | − | 0.487821i | 0.419797 | − | 0.907618i | \(-0.362101\pi\) |
−0.907618 | + | 0.419797i | \(0.862101\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 379.688i | 1.08173i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −551.816 | −1.56322 | −0.781609 | − | 0.623769i | \(-0.785601\pi\) | ||||
−0.781609 | + | 0.623769i | \(0.785601\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.2894 | − | 18.2894i | 0.0515195 | − | 0.0515195i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −925.871 | + | 925.871i | −2.59347 | + | 2.59347i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −432.275 | −1.20411 | −0.602054 | − | 0.798456i | \(-0.705651\pi\) | ||||
−0.602054 | + | 0.798456i | \(0.705651\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 150.619i | 0.417228i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 433.118 | + | 433.118i | 1.19316 | + | 1.19316i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 160.838 | + | 160.838i | 0.440652 | + | 0.440652i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 223.982i | − | 0.610306i | −0.952303 | − | 0.305153i | \(-0.901292\pi\) | ||
0.952303 | − | 0.305153i | \(-0.0987076\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1065.49 | −2.88751 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 365.704 | − | 365.704i | 0.985725 | − | 0.985725i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −348.716 | + | 348.716i | −0.934897 | + | 0.934897i | −0.998007 | − | 0.0631100i | \(-0.979898\pi\) |
0.0631100 | + | 0.998007i | \(0.479898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −56.6836 | −0.151156 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 318.450i | 0.844694i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 374.578 | + | 374.578i | 0.988332 | + | 0.988332i | 0.999933 | − | 0.0116005i | \(-0.00369264\pi\) |
−0.0116005 | + | 0.999933i | \(0.503693\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 763.278 | + | 763.278i | 2.00335 | + | 2.00335i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 431.347i | − | 1.12623i | −0.826378 | − | 0.563116i | \(-0.809602\pi\) | ||
0.826378 | − | 0.563116i | \(-0.190398\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.64236 | 0.0250451 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −250.993 | + | 250.993i | −0.648560 | + | 0.648560i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 55.8528 | − | 55.8528i | 0.143580 | − | 0.143580i | −0.631663 | − | 0.775243i | \(-0.717627\pi\) |
0.775243 | + | 0.631663i | \(0.217627\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −870.452 | −2.22622 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 247.895i | − | 0.630777i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −115.627 | − | 115.627i | −0.292726 | − | 0.292726i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −104.083 | − | 104.083i | −0.262173 | − | 0.262173i | 0.563763 | − | 0.825936i | \(-0.309353\pi\) |
−0.825936 | + | 0.563763i | \(0.809353\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 736.030i | − | 1.84469i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.9517 | 0.0821738 | 0.0410869 | − | 0.999156i | \(-0.486918\pi\) | ||||
0.0410869 | + | 0.999156i | \(0.486918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 50.3088 | − | 50.3088i | 0.124836 | − | 0.124836i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 75.4114 | − | 75.4114i | 0.186201 | − | 0.186201i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.17371 | 0.0102548 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 559.822i | 1.36876i | 0.729126 | + | 0.684379i | \(0.239927\pi\) | ||||
−0.729126 | + | 0.684379i | \(0.760073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 561.679 | + | 561.679i | 1.36662 | + | 1.36662i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 582.161 | + | 582.161i | 1.40959 | + | 1.40959i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 126.267i | − | 0.304259i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1082.39 | 2.59565 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −168.614 | + | 168.614i | −0.402420 | + | 0.402420i | −0.879085 | − | 0.476665i | \(-0.841845\pi\) |
0.476665 | + | 0.879085i | \(0.341845\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 409.607 | − | 409.607i | 0.972937 | − | 0.972937i | −0.0267062 | − | 0.999643i | \(-0.508502\pi\) |
0.999643 | + | 0.0267062i | \(0.00850184\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −699.481 | −1.65362 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 129.016i | 0.303566i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 263.164 | + | 263.164i | 0.616310 | + | 0.616310i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −15.0137 | − | 15.0137i | −0.0349970 | − | 0.0349970i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 307.273i | 0.712930i | 0.934309 | + | 0.356465i | \(0.116018\pi\) | ||||
−0.934309 | + | 0.356465i | \(0.883982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −573.906 | −1.32542 | −0.662709 | − | 0.748877i | \(-0.730593\pi\) | ||||
−0.662709 | + | 0.748877i | \(0.730593\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 262.616 | − | 262.616i | 0.603714 | − | 0.603714i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 345.987 | − | 345.987i | 0.791733 | − | 0.791733i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 491.449 | 1.11947 | 0.559737 | − | 0.828670i | \(-0.310902\pi\) | ||||
0.559737 | + | 0.828670i | \(0.310902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 854.922i | − | 1.93860i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −343.974 | − | 343.974i | −0.776466 | − | 0.776466i | 0.202762 | − | 0.979228i | \(-0.435008\pi\) |
−0.979228 | + | 0.202762i | \(0.935008\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −58.8428 | − | 58.8428i | −0.132231 | − | 0.132231i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 691.558i | 1.54711i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −153.260 | −0.341337 | −0.170668 | − | 0.985329i | \(-0.554593\pi\) | ||||
−0.170668 | + | 0.985329i | \(0.554593\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.4319 | − | 19.4319i | 0.0430862 | − | 0.0430862i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 105.439 | − | 105.439i | 0.232758 | − | 0.232758i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 217.554 | 0.478142 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 708.281i | − | 1.54985i | −0.632054 | − | 0.774924i | \(-0.717788\pi\) | ||
0.632054 | − | 0.774924i | \(-0.282212\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −712.676 | − | 712.676i | −1.55267 | − | 1.55267i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.0249 | + | 20.0249i | 0.0434379 | + | 0.0434379i | 0.728492 | − | 0.685054i | \(-0.240221\pi\) |
−0.685054 | + | 0.728492i | \(0.740221\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.9338i | 0.0668117i | 0.999442 | + | 0.0334059i | \(0.0106354\pi\) | ||||
−0.999442 | + | 0.0334059i | \(0.989365\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −82.9762 | −0.178443 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −89.9400 | + | 89.9400i | −0.192591 | + | 0.192591i | −0.796815 | − | 0.604224i | \(-0.793483\pi\) |
0.604224 | + | 0.796815i | \(0.293483\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44.8494 | + | 44.8494i | −0.0956277 | + | 0.0956277i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 843.606 | 1.79110 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.15497i | − | 0.0193551i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −51.2812 | − | 51.2812i | −0.107960 | − | 0.107960i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 610.333 | + | 610.333i | 1.27952 | + | 1.27952i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 424.069i | 0.885322i | 0.896689 | + | 0.442661i | \(0.145965\pi\) | ||||
−0.896689 | + | 0.442661i | \(0.854035\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 94.1688 | 0.195777 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1210.46 | − | 1210.46i | 2.50613 | − | 2.50613i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 181.434 | − | 181.434i | 0.374091 | − | 0.374091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −509.544 | −1.04629 | −0.523146 | − | 0.852243i | \(-0.675242\pi\) | ||||
−0.523146 | + | 0.852243i | \(0.675242\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 56.0166i | 0.114553i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −232.469 | − | 232.469i | −0.473461 | − | 0.473461i | 0.429572 | − | 0.903033i | \(-0.358665\pi\) |
−0.903033 | + | 0.429572i | \(0.858665\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −597.730 | − | 597.730i | −1.21243 | − | 1.21243i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 16.0924i | 0.0325099i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 115.777 | 0.232951 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 609.443 | − | 609.443i | 1.22133 | − | 1.22133i | 0.254170 | − | 0.967160i | \(-0.418198\pi\) |
0.967160 | − | 0.254170i | \(-0.0818022\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −915.506 | + | 915.506i | −1.82736 | + | 1.82736i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 83.3154 | 0.165637 | 0.0828185 | − | 0.996565i | \(-0.473608\pi\) | ||||
0.0828185 | + | 0.996565i | \(0.473608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2124i | 0.0241829i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 267.118 | + | 267.118i | 0.526859 | + | 0.526859i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 534.566 | + | 534.566i | 1.05023 | + | 1.05023i | 0.998670 | + | 0.0515585i | \(0.0164189\pi\) |
0.0515585 | + | 0.998670i | \(0.483581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1018.14i | 1.99245i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 566.549 | 1.10438 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 130.139 | − | 130.139i | 0.252698 | − | 0.252698i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7568 | − | 12.7568i | 0.0246746 | − | 0.0246746i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −193.705 | −0.373227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 513.800i | 0.986181i | 0.869978 | + | 0.493091i | \(0.164133\pi\) | ||||
−0.869978 | + | 0.493091i | \(0.835867\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 146.299 | + | 146.299i | 0.279731 | + | 0.279731i | 0.833001 | − | 0.553271i | \(-0.186621\pi\) |
−0.553271 | + | 0.833001i | \(0.686621\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −179.411 | − | 179.411i | −0.341734 | − | 0.341734i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 188.859i | 0.358367i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 609.006 | 1.15124 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −971.585 | + | 971.585i | −1.82973 | + | 1.82973i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 438.429 | − | 438.429i | 0.822569 | − | 0.822569i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −346.683 | −0.648006 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 364.875i | − | 0.679469i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5917 | + | 15.5917i | 0.0289270 | + | 0.0289270i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −610.827 | − | 610.827i | −1.12907 | − | 1.12907i | −0.990328 | − | 0.138743i | \(-0.955694\pi\) |
−0.138743 | − | 0.990328i | \(-0.544306\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 97.8618i | − | 0.180224i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.46252 | 0.0173624 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 392.410 | − | 392.410i | 0.717386 | − | 0.717386i | −0.250683 | − | 0.968069i | \(-0.580655\pi\) |
0.968069 | + | 0.250683i | \(0.0806552\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −439.202 | + | 439.202i | −0.800004 | + | 0.800004i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 475.172 | 0.862381 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 731.945i | − | 1.32359i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −77.6581 | − | 77.6581i | −0.139925 | − | 0.139925i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −587.051 | − | 587.051i | −1.05395 | − | 1.05395i | −0.998459 | − | 0.0554921i | \(-0.982327\pi\) |
−0.0554921 | − | 0.998459i | \(-0.517673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 206.558i | − | 0.369513i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 56.3616 | 0.100466 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −168.514 | + | 168.514i | −0.299314 | + | 0.299314i | −0.840745 | − | 0.541431i | \(-0.817883\pi\) |
0.541431 | + | 0.840745i | \(0.317883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −115.975 | + | 115.975i | −0.205265 | + | 0.205265i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 477.372 | 0.841926 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 550.627i | − | 0.967711i | −0.875148 | − | 0.483855i | \(-0.839236\pi\) | ||
0.875148 | − | 0.483855i | \(-0.160764\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 163.518 | + | 163.518i | 0.286371 | + | 0.286371i | 0.835644 | − | 0.549272i | \(-0.185095\pi\) |
−0.549272 | + | 0.835644i | \(0.685095\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −942.921 | − | 942.921i | −1.64559 | − | 1.64559i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 168.672i | − | 0.293342i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.6965 | 0.0272037 | 0.0136018 | − | 0.999907i | \(-0.495670\pi\) | ||||
0.0136018 | + | 0.999907i | \(0.495670\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 211.319 | − | 211.319i | 0.364973 | − | 0.364973i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 399.651 | − | 399.651i | 0.687868 | − | 0.687868i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.2619 | −0.0381851 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 363.083i | 0.620654i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −715.538 | − | 715.538i | −1.21897 | − | 1.21897i | −0.967992 | − | 0.250983i | \(-0.919246\pi\) |
−0.250983 | − | 0.967992i | \(-0.580754\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −75.0678 | − | 75.0678i | −0.127450 | − | 0.127450i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 68.4346i | 0.115795i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −557.100 | −0.939460 | −0.469730 | − | 0.882810i | \(-0.655649\pi\) | ||||
−0.469730 | + | 0.882810i | \(0.655649\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −408.350 | + | 408.350i | −0.686303 | + | 0.686303i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 369.796 | − | 369.796i | 0.619424 | − | 0.619424i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −524.845 | −0.876202 | −0.438101 | − | 0.898926i | \(-0.644349\pi\) | ||||
−0.438101 | + | 0.898926i | \(0.644349\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 182.301i | − | 0.303330i | −0.988432 | − | 0.151665i | \(-0.951537\pi\) | ||
0.988432 | − | 0.151665i | \(-0.0484635\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −74.8504 | − | 74.8504i | −0.124130 | − | 0.124130i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 191.024 | + | 191.024i | 0.315743 | + | 0.315743i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 987.505i | − | 1.62686i | −0.581662 | − | 0.813431i | \(-0.697597\pi\) | ||
0.581662 | − | 0.813431i | \(-0.302403\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1662.42 | 2.72975 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 287.823 | − | 287.823i | 0.471069 | − | 0.471069i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 768.517 | − | 768.517i | 1.25370 | − | 1.25370i | 0.299648 | − | 0.954050i | \(-0.403131\pi\) |
0.954050 | − | 0.299648i | \(-0.0968692\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −723.119 | −1.17580 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 467.462i | 0.757636i | 0.925471 | + | 0.378818i | \(0.123669\pi\) | ||||
−0.925471 | + | 0.378818i | \(0.876331\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 272.667 | + | 272.667i | 0.440496 | + | 0.440496i | 0.892179 | − | 0.451682i | \(-0.149176\pi\) |
−0.451682 | + | 0.892179i | \(0.649176\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 931.734 | + | 931.734i | 1.50038 | + | 1.50038i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 372.489i | − | 0.597896i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −22.4026 | + | 22.4026i | −0.0357298 | + | 0.0357298i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −176.755 | + | 176.755i | −0.281009 | + | 0.281009i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1107.18 | −1.75465 | −0.877324 | − | 0.479898i | \(-0.840674\pi\) | ||||
−0.877324 | + | 0.479898i | \(0.840674\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 35.4104i | − | 0.0559405i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 336.639 | + | 336.639i | 0.530141 | + | 0.530141i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 351.785 | + | 351.785i | 0.552252 | + | 0.552252i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 193.223i | 0.302383i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −645.436 | −1.00692 | −0.503460 | − | 0.864018i | \(-0.667940\pi\) | ||||
−0.503460 | + | 0.864018i | \(0.667940\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −397.860 | + | 397.860i | −0.618756 | + | 0.618756i | −0.945212 | − | 0.326456i | \(-0.894145\pi\) |
0.326456 | + | 0.945212i | \(0.394145\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −170.342 | + | 170.342i | −0.264096 | + | 0.264096i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 386.850 | 0.597913 | 0.298956 | − | 0.954267i | \(-0.403361\pi\) | ||||
0.298956 | + | 0.954267i | \(0.403361\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 35.4386i | − | 0.0546049i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −262.630 | − | 262.630i | −0.403425 | − | 0.403425i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −557.600 | − | 557.600i | −0.853905 | − | 0.853905i | 0.136707 | − | 0.990612i | \(-0.456348\pi\) |
−0.990612 | + | 0.136707i | \(0.956348\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 109.333i | − | 0.166920i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1699.21 | −2.58631 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −85.5304 | + | 85.5304i | −0.129788 | + | 0.129788i | −0.769017 | − | 0.639229i | \(-0.779254\pi\) |
0.639229 | + | 0.769017i | \(0.279254\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −677.148 | + | 677.148i | −1.02443 | + | 1.02443i | −0.0247351 | + | 0.999694i | \(0.507874\pi\) |
−0.999694 | + | 0.0247351i | \(0.992126\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1271.65 | 1.91803 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 324.622i | − | 0.488153i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 781.457 | + | 781.457i | 1.17160 | + | 1.17160i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 635.086 | + | 635.086i | 0.949306 | + | 0.949306i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 16.0199i | − | 0.0238747i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1077.92 | 1.60167 | 0.800836 | − | 0.598884i | \(-0.204389\pi\) | ||||
0.800836 | + | 0.598884i | \(0.204389\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 138.099 | − | 138.099i | 0.204591 | − | 0.204591i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 926.183 | − | 926.183i | 1.36807 | − | 1.36807i | 0.504881 | − | 0.863189i | \(-0.331536\pi\) |
0.863189 | − | 0.504881i | \(-0.168464\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1148.52 | 1.69149 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1715.54i | 2.51915i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −548.522 | − | 548.522i | −0.803107 | − | 0.803107i | 0.180473 | − | 0.983580i | \(-0.442237\pi\) |
−0.983580 | + | 0.180473i | \(0.942237\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 247.725 | + | 247.725i | 0.361643 | + | 0.361643i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 765.027i | − | 1.11358i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −502.281 | −0.729001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.6062 | − | 21.6062i | 0.0312680 | − | 0.0312680i | −0.691300 | − | 0.722568i | \(-0.742962\pi\) |
0.722568 | + | 0.691300i | \(0.242962\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −50.9344 | + | 50.9344i | −0.0734984 | + | 0.0734984i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 477.380 | 0.686878 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1645.86i | 2.36136i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −476.664 | − | 476.664i | −0.681923 | − | 0.681923i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −462.868 | − | 462.868i | −0.660296 | − | 0.660296i | 0.295153 | − | 0.955450i | \(-0.404629\pi\) |
−0.955450 | + | 0.295153i | \(0.904629\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 140.513i | − | 0.199877i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −474.718 | −0.673359 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −38.6536 | + | 38.6536i | −0.0546728 | + | 0.0546728i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −91.9564 | + | 91.9564i | −0.129699 | + | 0.129699i | −0.768976 | − | 0.639277i | \(-0.779234\pi\) |
0.639277 | + | 0.768976i | \(0.279234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1221.56 | 1.71809 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 246.910i | − | 0.346297i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.62172 | − | 6.62172i | −0.00926115 | − | 0.00926115i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −321.448 | − | 321.448i | −0.448323 | − | 0.448323i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 463.016i | − | 0.643972i | −0.946744 | − | 0.321986i | \(-0.895650\pi\) | ||
0.946744 | − | 0.321986i | \(-0.104350\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 823.814 | 1.14260 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −928.579 | + | 928.579i | −1.28434 | + | 1.28434i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 115.825 | − | 115.825i | 0.159759 | − | 0.159759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 233.171 | 0.320730 | 0.160365 | − | 0.987058i | \(-0.448733\pi\) | ||||
0.160365 | + | 0.987058i | \(0.448733\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 985.596i | − | 1.35198i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 387.709 | + | 387.709i | 0.530382 | + | 0.530382i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 873.035 | + | 873.035i | 1.19104 | + | 1.19104i | 0.976775 | + | 0.214269i | \(0.0687368\pi\) |
0.214269 | + | 0.976775i | \(0.431263\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 580.212i | − | 0.789404i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.73017 | 0.00370443 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 127.699 | − | 127.699i | 0.172799 | − | 0.172799i | −0.615409 | − | 0.788208i | \(-0.711009\pi\) |
0.788208 | + | 0.615409i | \(0.211009\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −505.456 | + | 505.456i | −0.682127 | + | 0.682127i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −226.592 | −0.304968 | −0.152484 | − | 0.988306i | \(-0.548727\pi\) | ||||
−0.152484 | + | 0.988306i | \(0.548727\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 305.008i | 0.409407i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 666.989 | + | 666.989i | 0.892890 | + | 0.892890i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1097.29 | − | 1097.29i | −1.46501 | − | 1.46501i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 516.811i | − | 0.688164i | −0.938940 | − | 0.344082i | \(-0.888190\pi\) | ||
0.938940 | − | 0.344082i | \(-0.111810\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 611.124 | 0.811586 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46.5034 | − | 46.5034i | 0.0615940 | − | 0.0615940i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 135.597 | − | 135.597i | 0.179124 | − | 0.179124i | −0.611850 | − | 0.790974i | \(-0.709574\pi\) |
0.790974 | + | 0.611850i | \(0.209574\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −73.6857 | −0.0970826 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 268.435i | 0.352739i | 0.984324 | + | 0.176370i | \(0.0564354\pi\) | ||||
−0.984324 | + | 0.176370i | \(0.943565\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.9500 | + | 29.9500i | 0.0392530 | + | 0.0392530i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −681.507 | − | 681.507i | −0.890858 | − | 0.890858i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 799.578i | − | 1.04247i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −826.424 | −1.07467 | −0.537337 | − | 0.843368i | \(-0.680570\pi\) | ||||
−0.537337 | + | 0.843368i | \(0.680570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1619.28 | + | 1619.28i | −2.10023 | + | 2.10023i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1042.45 | + | 1042.45i | −1.34857 | + | 1.34857i | −0.461359 | + | 0.887213i | \(0.652638\pi\) |
−0.887213 | + | 0.461359i | \(0.847362\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −36.5962 | −0.0472209 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 491.595i | − | 0.632683i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −654.199 | − | 654.199i | −0.839793 | − | 0.839793i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.52390 | − | 3.52390i | −0.00451203 | − | 0.00451203i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1279.62i | 1.63426i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 372.068 | 0.473972 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 924.222 | − | 924.222i | 1.17436 | − | 1.17436i | 0.193201 | − | 0.981159i | \(-0.438113\pi\) |
0.981159 | − | 0.193201i | \(-0.0618870\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.36771 | + | 3.36771i | −0.00426833 | + | 0.00426833i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −734.148 | −0.928126 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 361.447i | − | 0.455797i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 414.216 | + | 414.216i | 0.521027 | + | 0.521027i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 761.055 | + | 761.055i | 0.954899 | + | 0.954899i | 0.999026 | − | 0.0441268i | \(-0.0140505\pi\) |
−0.0441268 | + | 0.999026i | \(0.514051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1080.49i | 1.35230i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 621.657 | 0.776101 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.9893 | − | 30.9893i | 0.0385919 | − | 0.0385919i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 533.866 | − | 533.866i | 0.663188 | − | 0.663188i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1011.67 | −1.25362 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 106.311i | − | 0.131410i | −0.997839 | − | 0.0657052i | \(-0.979070\pi\) | ||
0.997839 | − | 0.0657052i | \(-0.0209297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 602.747 | + | 602.747i | 0.743214 | + | 0.743214i | 0.973195 | − | 0.229981i | \(-0.0738664\pi\) |
−0.229981 | + | 0.973195i | \(0.573866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 852.069 | + | 852.069i | 1.04806 | + | 1.04806i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.7058i | 0.0303139i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −308.213 | −0.377250 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1149.20 | + | 1149.20i | −1.40317 | + | 1.40317i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 236.461 | − | 236.461i | 0.288016 | − | 0.288016i | −0.548280 | − | 0.836295i | \(-0.684717\pi\) |
0.836295 | + | 0.548280i | \(0.184717\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 412.888 | 0.501687 | 0.250843 | − | 0.968028i | \(-0.419292\pi\) | ||||
0.250843 | + | 0.968028i | \(0.419292\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.9215i | 0.0132381i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 772.140 | + | 772.140i | 0.933664 | + | 0.933664i | 0.997933 | − | 0.0642682i | \(-0.0204713\pi\) |
−0.0642682 | + | 0.997933i | \(0.520471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −163.360 | − | 163.360i | −0.197056 | − | 0.197056i | 0.601681 | − | 0.798737i | \(-0.294498\pi\) |
−0.798737 | + | 0.601681i | \(0.794498\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2163.05i | − | 2.60294i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1320.60 | −1.58535 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −403.779 | + | 403.779i | −0.483568 | + | 0.483568i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 202.155 | − | 202.155i | 0.241524 | − | 0.241524i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −156.751 | −0.186831 | −0.0934154 | − | 0.995627i | \(-0.529778\pi\) | ||||
−0.0934154 | + | 0.995627i | \(0.529778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 232.237i | 0.276144i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −752.363 | − | 752.363i | −0.892482 | − | 0.892482i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 117.811 | + | 117.811i | 0.139421 | + | 0.139421i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1209.23i | 1.42766i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 624.794 | 0.735917 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 231.085 | − | 231.085i | 0.271545 | − | 0.271545i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −933.500 | + | 933.500i | −1.09437 | + | 1.09437i | −0.0993169 | + | 0.995056i | \(0.531666\pi\) |
−0.995056 | + | 0.0993169i | \(0.968334\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 541.771 | 0.633650 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 988.694i | 1.15367i | 0.816861 | + | 0.576834i | \(0.195712\pi\) | ||||
−0.816861 | + | 0.576834i | \(0.804288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −868.729 | − | 868.729i | −1.01133 | − | 1.01133i | −0.999935 | − | 0.0113913i | \(-0.996374\pi\) |
−0.0113913 | − | 0.999935i | \(-0.503626\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2288.76 | − | 2288.76i | −2.65825 | − | 2.65825i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1065.18i | 1.23428i | 0.786854 | + | 0.617139i | \(0.211709\pi\) | ||||
−0.786854 | + | 0.617139i | \(0.788291\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −85.4324 | −0.0987658 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1350.83 | + | 1350.83i | −1.55805 | + | 1.55805i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.2783 | + | 22.2783i | −0.0256367 | + | 0.0256367i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 61.5991 | 0.0707222 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1916.80i | 2.19565i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −79.1280 | − | 79.1280i | −0.0904320 | − | 0.0904320i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −107.637 | − | 107.637i | −0.122733 | − | 0.122733i | 0.643072 | − | 0.765805i | \(-0.277659\pi\) |
−0.765805 | + | 0.643072i | \(0.777659\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1509.60i | 1.71741i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1289.21 | 1.46334 | 0.731672 | − | 0.681657i | \(-0.238740\pi\) | ||||
0.731672 | + | 0.681657i | \(0.238740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 89.1493 | − | 89.1493i | 0.100962 | − | 0.100962i | −0.654822 | − | 0.755783i | \(-0.727256\pi\) |
0.755783 | + | 0.654822i | \(0.227256\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −659.387 | + | 659.387i | −0.745071 | + | 0.745071i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1235.62 | −1.39303 | −0.696516 | − | 0.717541i | \(-0.745268\pi\) | ||||
−0.696516 | + | 0.717541i | \(0.745268\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2131.01i | 2.39708i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.5298 | − | 14.5298i | −0.0163073 | − | 0.0163073i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −429.473 | − | 429.473i | −0.480933 | − | 0.480933i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 160.926i | − | 0.179806i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1662.52 | −1.85343 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 169.550 | − | 169.550i | 0.188599 | − | 0.188599i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 942.783 | − | 942.783i | 1.04637 | − | 1.04637i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1078.30 | −1.19414 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 43.1614i | − | 0.0476921i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1170.07 | − | 1170.07i | −1.29004 | − | 1.29004i | −0.934757 | − | 0.355287i | \(-0.884383\pi\) |
−0.355287 | − | 0.934757i | \(-0.615617\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −64.5101 | − | 64.5101i | −0.0709682 | − | 0.0709682i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 174.325i | − | 0.191356i | −0.995412 | − | 0.0956781i | \(-0.969498\pi\) | ||
0.995412 | − | 0.0956781i | \(-0.0305019\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.3284 | −0.0266467 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −298.074 | + | 298.074i | −0.325764 | + | 0.325764i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 346.052 | − | 346.052i | 0.377374 | − | 0.377374i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1108.52 | 1.20622 | 0.603110 | − | 0.797658i | \(-0.293928\pi\) | ||||
0.603110 | + | 0.797658i | \(0.293928\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 2476.08i | − | 2.68846i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −79.5075 | − | 79.5075i | −0.0861403 | − | 0.0861403i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.2507 | − | 34.2507i | −0.0370278 | − | 0.0370278i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1374.89i | 1.48316i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −410.945 | −0.442352 | −0.221176 | − | 0.975234i | \(-0.570990\pi\) | ||||
−0.221176 | + | 0.975234i | \(0.570990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 524.912 | − | 524.912i | 0.563816 | − | 0.563816i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −357.458 | + | 357.458i | −0.383127 | + | 0.383127i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.8580 | 0.0265860 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 181.492i | − | 0.193694i | −0.995299 | − | 0.0968472i | \(-0.969124\pi\) | ||
0.995299 | − | 0.0968472i | \(-0.0308758\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1116.13 | + | 1116.13i | 1.18864 | + | 1.18864i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −363.737 | − | 363.737i | −0.386543 | − | 0.386543i | 0.486910 | − | 0.873452i | \(-0.338124\pi\) |
−0.873452 | + | 0.486910i | \(0.838124\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2151.76i | − | 2.28183i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 874.198 | 0.925077 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 616.971 | − | 616.971i | 0.651500 | − | 0.651500i | −0.301854 | − | 0.953354i | \(-0.597605\pi\) |
0.953354 | + | 0.301854i | \(0.0976055\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 699.192 | − | 699.192i | 0.736767 | − | 0.736767i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −137.964 | −0.145072 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 602.419i | − | 0.632129i | −0.948738 | − | 0.316064i | \(-0.897638\pi\) | ||
0.948738 | − | 0.316064i | \(-0.102362\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −415.870 | − | 415.870i | −0.435466 | − | 0.435466i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −50.5992 | − | 50.5992i | −0.0528727 | − | 0.0528727i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1568.16i | 1.63521i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 907.429 | 0.944255 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1831.30 | − | 1831.30i | 1.90166 | − | 1.90166i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 93.2012 | − | 93.2012i | 0.0965815 | − | 0.0965815i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1277.51 | −1.32111 | −0.660553 | − | 0.750779i | \(-0.729678\pi\) | ||||
−0.660553 | + | 0.750779i | \(0.729678\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1897.48i | − | 1.95819i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −122.966 | − | 122.966i | −0.126639 | − | 0.126639i | 0.640947 | − | 0.767585i | \(-0.278542\pi\) |
−0.767585 | + | 0.640947i | \(0.778542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1510.97 | + | 1510.97i | 1.55289 | + | 1.55289i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 246.414i | 0.252732i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 809.129 | 0.828177 | 0.414088 | − | 0.910237i | \(-0.364100\pi\) | ||||
0.414088 | + | 0.910237i | \(0.364100\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.3375 | + | 11.3375i | −0.0115807 | + | 0.0115807i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −49.9844 | + | 49.9844i | −0.0509525 | + | 0.0509525i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 986.542 | 1.00360 | 0.501802 | − | 0.864983i | \(-0.332671\pi\) | ||||
0.501802 | + | 0.864983i | \(0.332671\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.1827i | 0.0306423i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1502.54 | − | 1502.54i | −1.52233 | − | 1.52233i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −506.881 | − | 506.881i | −0.512519 | − | 0.512519i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 674.433i | 0.680558i | 0.940325 | + | 0.340279i | \(0.110521\pi\) | ||||
−0.940325 | + | 0.340279i | \(0.889479\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1392.51 | 1.40233 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 163.097 | − | 163.097i | 0.163916 | − | 0.163916i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1315.09 | + | 1315.09i | −1.31905 | + | 1.31905i | −0.404519 | + | 0.914530i | \(0.632561\pi\) |
−0.914530 | + | 0.404519i | \(0.867439\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 378.398 | 0.378777 |
(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 | 320.3.r.a.111.2 | 32 | ||
4.3 | odd | 2 | 80.3.r.a.51.7 | yes | 32 | ||
8.3 | odd | 2 | 640.3.r.a.351.2 | 32 | |||
8.5 | even | 2 | 640.3.r.b.351.15 | 32 | |||
16.3 | odd | 4 | 640.3.r.b.31.15 | 32 | |||
16.5 | even | 4 | 80.3.r.a.11.7 | ✓ | 32 | ||
16.11 | odd | 4 | inner | 320.3.r.a.271.2 | 32 | ||
16.13 | even | 4 | 640.3.r.a.31.2 | 32 | |||
20.3 | even | 4 | 400.3.k.h.99.16 | 32 | |||
20.7 | even | 4 | 400.3.k.g.99.1 | 32 | |||
20.19 | odd | 2 | 400.3.r.f.51.10 | 32 | |||
80.37 | odd | 4 | 400.3.k.h.299.16 | 32 | |||
80.53 | odd | 4 | 400.3.k.g.299.1 | 32 | |||
80.69 | even | 4 | 400.3.r.f.251.10 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.r.a.11.7 | ✓ | 32 | 16.5 | even | 4 | ||
80.3.r.a.51.7 | yes | 32 | 4.3 | odd | 2 | ||
320.3.r.a.111.2 | 32 | 1.1 | even | 1 | trivial | ||
320.3.r.a.271.2 | 32 | 16.11 | odd | 4 | inner | ||
400.3.k.g.99.1 | 32 | 20.7 | even | 4 | |||
400.3.k.g.299.1 | 32 | 80.53 | odd | 4 | |||
400.3.k.h.99.16 | 32 | 20.3 | even | 4 | |||
400.3.k.h.299.16 | 32 | 80.37 | odd | 4 | |||
400.3.r.f.51.10 | 32 | 20.19 | odd | 2 | |||
400.3.r.f.251.10 | 32 | 80.69 | even | 4 | |||
640.3.r.a.31.2 | 32 | 16.13 | even | 4 | |||
640.3.r.a.351.2 | 32 | 8.3 | odd | 2 | |||
640.3.r.b.31.15 | 32 | 16.3 | odd | 4 | |||
640.3.r.b.351.15 | 32 | 8.5 | even | 2 |