Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(809,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.b (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: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.15 | ||
Character | \(\chi\) | \(=\) | 810.809 |
Dual form | 810.3.b.c.809.16 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | −4.21457 | − | 2.69024i | −0.842914 | − | 0.538048i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.64672i | 1.09239i | 0.837659 | + | 0.546194i | \(0.183924\pi\) | ||||
−0.837659 | + | 0.546194i | \(0.816076\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.96030 | − | 3.80458i | −0.596030 | − | 0.380458i | ||||
\(11\) | − | 11.3743i | − | 1.03403i | −0.855977 | − | 0.517014i | \(-0.827043\pi\) | ||
0.855977 | − | 0.517014i | \(-0.172957\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.3829i | 1.10638i | 0.833055 | + | 0.553190i | \(0.186589\pi\) | ||||
−0.833055 | + | 0.553190i | \(0.813411\pi\) | |||||||
\(14\) | 10.8141i | 0.772435i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −17.3175 | −1.01868 | −0.509339 | − | 0.860566i | \(-0.670110\pi\) | ||||
−0.509339 | + | 0.860566i | \(0.670110\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31.8326 | −1.67540 | −0.837699 | − | 0.546132i | \(-0.816100\pi\) | ||||
−0.837699 | + | 0.546132i | \(0.816100\pi\) | |||||||
\(20\) | −8.42914 | − | 5.38048i | −0.421457 | − | 0.269024i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 16.0857i | − | 0.731169i | ||||||
\(23\) | 16.5149 | 0.718037 | 0.359019 | − | 0.933330i | \(-0.383111\pi\) | ||||
0.359019 | + | 0.933330i | \(0.383111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.5252 | + | 22.6764i | 0.421008 | + | 0.907057i | ||||
\(26\) | 20.3405i | 0.782328i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15.2934i | 0.546194i | ||||||||
\(29\) | 8.49209i | 0.292831i | 0.989223 | + | 0.146415i | \(0.0467736\pi\) | ||||
−0.989223 | + | 0.146415i | \(0.953226\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −45.8192 | −1.47804 | −0.739019 | − | 0.673684i | \(-0.764711\pi\) | ||||
−0.739019 | + | 0.673684i | \(0.764711\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −24.4907 | −0.720314 | ||||||||
\(35\) | 20.5715 | − | 32.2276i | 0.587758 | − | 0.920789i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 31.8348i | − | 0.860400i | −0.902734 | − | 0.430200i | \(-0.858443\pi\) | ||
0.902734 | − | 0.430200i | \(-0.141557\pi\) | |||||||
\(38\) | −45.0180 | −1.18469 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −11.9206 | − | 7.60915i | −0.298015 | − | 0.190229i | ||||
\(41\) | 68.3775i | 1.66774i | 0.551958 | + | 0.833872i | \(0.313881\pi\) | ||||
−0.551958 | + | 0.833872i | \(0.686119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 31.3825i | 0.729825i | 0.931042 | + | 0.364913i | \(0.118901\pi\) | ||||
−0.931042 | + | 0.364913i | \(0.881099\pi\) | |||||||
\(44\) | − | 22.7486i | − | 0.517014i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 23.3555 | 0.507729 | ||||||||
\(47\) | −46.0552 | −0.979897 | −0.489948 | − | 0.871751i | \(-0.662984\pi\) | ||||
−0.489948 | + | 0.871751i | \(0.662984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.47230 | −0.193312 | ||||||||
\(50\) | 14.8849 | + | 32.0693i | 0.297698 | + | 0.641386i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 28.7659i | 0.553190i | ||||||||
\(53\) | −53.6946 | −1.01311 | −0.506553 | − | 0.862209i | \(-0.669080\pi\) | ||||
−0.506553 | + | 0.862209i | \(0.669080\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −30.5996 | + | 47.9378i | −0.556357 | + | 0.871597i | ||||
\(56\) | 21.6282i | 0.386218i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.0096i | 0.207063i | ||||||||
\(59\) | 64.7702i | 1.09780i | 0.835888 | + | 0.548900i | \(0.184953\pi\) | ||||
−0.835888 | + | 0.548900i | \(0.815047\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −96.2754 | −1.57828 | −0.789142 | − | 0.614210i | \(-0.789475\pi\) | ||||
−0.789142 | + | 0.614210i | \(0.789475\pi\) | |||||||
\(62\) | −64.7981 | −1.04513 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 38.6935 | − | 60.6179i | 0.595285 | − | 0.932583i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.72446i | − | 0.0257382i | −0.999917 | − | 0.0128691i | \(-0.995904\pi\) | ||
0.999917 | − | 0.0128691i | \(-0.00409648\pi\) | |||||||
\(68\) | −34.6351 | −0.509339 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 29.0925 | − | 45.5768i | 0.415607 | − | 0.651096i | ||||
\(71\) | 26.5730i | 0.374268i | 0.982334 | + | 0.187134i | \(0.0599199\pi\) | ||||
−0.982334 | + | 0.187134i | \(0.940080\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 51.4318i | − | 0.704545i | −0.935898 | − | 0.352272i | \(-0.885409\pi\) | ||
0.935898 | − | 0.352272i | \(-0.114591\pi\) | |||||||
\(74\) | − | 45.0212i | − | 0.608395i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −63.6651 | −0.837699 | ||||||||
\(77\) | 86.9762 | 1.12956 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 59.2176 | 0.749590 | 0.374795 | − | 0.927108i | \(-0.377713\pi\) | ||||
0.374795 | + | 0.927108i | \(0.377713\pi\) | |||||||
\(80\) | −16.8583 | − | 10.7610i | −0.210729 | − | 0.134512i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 96.7004i | 1.17927i | ||||||||
\(83\) | 6.92825 | 0.0834729 | 0.0417365 | − | 0.999129i | \(-0.486711\pi\) | ||||
0.0417365 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 72.9859 | + | 46.5883i | 0.858658 | + | 0.548098i | ||||
\(86\) | 44.3815i | 0.516064i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 32.1714i | − | 0.365584i | ||||||
\(89\) | − | 115.787i | − | 1.30097i | −0.759518 | − | 0.650486i | \(-0.774565\pi\) | ||
0.759518 | − | 0.650486i | \(-0.225435\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −109.982 | −1.20860 | ||||||||
\(92\) | 33.0297 | 0.359019 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −65.1318 | −0.692892 | ||||||||
\(95\) | 134.161 | + | 85.6373i | 1.41222 | + | 0.901445i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 158.654i | 1.63561i | 0.575498 | + | 0.817803i | \(0.304808\pi\) | ||||
−0.575498 | + | 0.817803i | \(0.695192\pi\) | |||||||
\(98\) | −13.3959 | −0.136692 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 21.0504 | + | 45.3528i | 0.210504 | + | 0.453528i | ||||
\(101\) | − | 108.879i | − | 1.07801i | −0.842303 | − | 0.539004i | \(-0.818801\pi\) | ||
0.842303 | − | 0.539004i | \(-0.181199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 134.361i | 1.30447i | 0.758016 | + | 0.652236i | \(0.226169\pi\) | ||||
−0.758016 | + | 0.652236i | \(0.773831\pi\) | |||||||
\(104\) | 40.6811i | 0.391164i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −75.9356 | −0.716374 | ||||||||
\(107\) | 125.758 | 1.17531 | 0.587655 | − | 0.809111i | \(-0.300051\pi\) | ||||
0.587655 | + | 0.809111i | \(0.300051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −63.2406 | −0.580189 | −0.290094 | − | 0.956998i | \(-0.593687\pi\) | ||||
−0.290094 | + | 0.956998i | \(0.593687\pi\) | |||||||
\(110\) | −43.2744 | + | 67.7943i | −0.393404 | + | 0.616312i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 30.5869i | 0.273097i | ||||||||
\(113\) | 104.017 | 0.920509 | 0.460254 | − | 0.887787i | \(-0.347758\pi\) | ||||
0.460254 | + | 0.887787i | \(0.347758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −69.6030 | − | 44.4289i | −0.605244 | − | 0.386339i | ||||
\(116\) | 16.9842i | 0.146415i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 91.5989i | 0.776262i | ||||||||
\(119\) | − | 132.422i | − | 1.11279i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.37500 | −0.0692149 | ||||||||
\(122\) | −136.154 | −1.11602 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −91.6384 | −0.739019 | ||||||||
\(125\) | 16.6458 | − | 123.887i | 0.133167 | − | 0.991094i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 142.712i | − | 1.12371i | −0.827235 | − | 0.561857i | \(-0.810087\pi\) | ||
0.827235 | − | 0.561857i | \(-0.189913\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 54.7209 | − | 85.7266i | 0.420930 | − | 0.659435i | ||||
\(131\) | − | 206.387i | − | 1.57547i | −0.616014 | − | 0.787735i | \(-0.711253\pi\) | ||
0.616014 | − | 0.787735i | \(-0.288747\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 243.415i | − | 1.83019i | ||||||
\(134\) | − | 2.43876i | − | 0.0181997i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −48.9814 | −0.360157 | ||||||||
\(137\) | −164.121 | −1.19796 | −0.598981 | − | 0.800763i | \(-0.704428\pi\) | ||||
−0.598981 | + | 0.800763i | \(0.704428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 30.5580 | 0.219842 | 0.109921 | − | 0.993940i | \(-0.464940\pi\) | ||||
0.109921 | + | 0.993940i | \(0.464940\pi\) | |||||||
\(140\) | 41.1430 | − | 64.4553i | 0.293879 | − | 0.460395i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 37.5799i | 0.264647i | ||||||||
\(143\) | 163.596 | 1.14403 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.8458 | − | 35.7905i | 0.157557 | − | 0.246831i | ||||
\(146\) | − | 72.7355i | − | 0.498188i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 63.6696i | − | 0.430200i | ||||||
\(149\) | − | 77.9229i | − | 0.522973i | −0.965207 | − | 0.261486i | \(-0.915787\pi\) | ||
0.965207 | − | 0.261486i | \(-0.0842127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 43.0430 | 0.285053 | 0.142527 | − | 0.989791i | \(-0.454477\pi\) | ||||
0.142527 | + | 0.989791i | \(0.454477\pi\) | |||||||
\(152\) | −90.0361 | −0.592343 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 123.003 | 0.798720 | ||||||||
\(155\) | 193.108 | + | 123.265i | 1.24586 | + | 0.795256i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 59.3282i | − | 0.377887i | −0.981988 | − | 0.188943i | \(-0.939494\pi\) | ||
0.981988 | − | 0.188943i | \(-0.0605063\pi\) | |||||||
\(158\) | 83.7463 | 0.530040 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −23.8412 | − | 15.2183i | −0.149008 | − | 0.0951144i | ||||
\(161\) | 126.284i | 0.784375i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 79.1245i | 0.485426i | 0.970098 | + | 0.242713i | \(0.0780374\pi\) | ||||
−0.970098 | + | 0.242713i | \(0.921963\pi\) | |||||||
\(164\) | 136.755i | 0.833872i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.79803 | 0.0590243 | ||||||||
\(167\) | −101.516 | −0.607878 | −0.303939 | − | 0.952691i | \(-0.598302\pi\) | ||||
−0.303939 | + | 0.952691i | \(0.598302\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −37.8686 | −0.224075 | ||||||||
\(170\) | 103.218 | + | 65.8858i | 0.607163 | + | 0.387564i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 62.7650i | 0.364913i | ||||||||
\(173\) | 181.350 | 1.04826 | 0.524132 | − | 0.851637i | \(-0.324390\pi\) | ||||
0.524132 | + | 0.851637i | \(0.324390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −173.400 | + | 80.4833i | −0.990858 | + | 0.459904i | ||||
\(176\) | − | 45.4973i | − | 0.258507i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 163.747i | − | 0.919926i | ||||||
\(179\) | 90.4200i | 0.505140i | 0.967579 | + | 0.252570i | \(0.0812758\pi\) | ||||
−0.967579 | + | 0.252570i | \(0.918724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −160.779 | −0.888283 | −0.444141 | − | 0.895957i | \(-0.646491\pi\) | ||||
−0.444141 | + | 0.895957i | \(0.646491\pi\) | |||||||
\(182\) | −155.538 | −0.854606 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 46.7111 | 0.253865 | ||||||||
\(185\) | −85.6433 | + | 134.170i | −0.462937 | + | 0.725243i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 196.975i | 1.05334i | ||||||||
\(188\) | −92.1103 | −0.489948 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 189.732 | + | 121.109i | 0.998588 | + | 0.637418i | ||||
\(191\) | − | 170.467i | − | 0.892497i | −0.894909 | − | 0.446249i | \(-0.852760\pi\) | ||
0.894909 | − | 0.446249i | \(-0.147240\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 214.247i | 1.11009i | 0.831821 | + | 0.555044i | \(0.187299\pi\) | ||||
−0.831821 | + | 0.555044i | \(0.812701\pi\) | |||||||
\(194\) | 224.370i | 1.15655i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.9446 | −0.0966561 | ||||||||
\(197\) | −209.813 | −1.06504 | −0.532522 | − | 0.846416i | \(-0.678755\pi\) | ||||
−0.532522 | + | 0.846416i | \(0.678755\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 327.667 | 1.64657 | 0.823285 | − | 0.567628i | \(-0.192139\pi\) | ||||
0.823285 | + | 0.567628i | \(0.192139\pi\) | |||||||
\(200\) | 29.7698 | + | 64.1386i | 0.148849 | + | 0.320693i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 153.978i | − | 0.762267i | ||||||
\(203\) | −64.9366 | −0.319885 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 183.952 | − | 288.182i | 0.897327 | − | 1.40577i | ||||
\(206\) | 190.014i | 0.922400i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 57.5317i | 0.276595i | ||||||||
\(209\) | 362.074i | 1.73241i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 102.013 | 0.483473 | 0.241737 | − | 0.970342i | \(-0.422283\pi\) | ||||
0.241737 | + | 0.970342i | \(0.422283\pi\) | |||||||
\(212\) | −107.389 | −0.506553 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 177.849 | 0.831070 | ||||||||
\(215\) | 84.4265 | − | 132.264i | 0.392681 | − | 0.615180i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 350.366i | − | 1.61459i | ||||||
\(218\) | −89.4357 | −0.410255 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −61.1993 | + | 95.8757i | −0.278179 | + | 0.435799i | ||||
\(221\) | − | 249.077i | − | 1.12704i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 377.504i | 1.69284i | 0.532514 | + | 0.846421i | \(0.321247\pi\) | ||||
−0.532514 | + | 0.846421i | \(0.678753\pi\) | |||||||
\(224\) | 43.2564i | 0.193109i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 147.103 | 0.650898 | ||||||||
\(227\) | 269.454 | 1.18702 | 0.593512 | − | 0.804825i | \(-0.297741\pi\) | ||||
0.593512 | + | 0.804825i | \(0.297741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 423.862 | 1.85093 | 0.925463 | − | 0.378837i | \(-0.123676\pi\) | ||||
0.925463 | + | 0.378837i | \(0.123676\pi\) | |||||||
\(230\) | −98.4335 | − | 62.8320i | −0.427972 | − | 0.273183i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.0193i | 0.103531i | ||||||||
\(233\) | 70.8761 | 0.304189 | 0.152095 | − | 0.988366i | \(-0.451398\pi\) | ||||
0.152095 | + | 0.988366i | \(0.451398\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 194.103 | + | 123.899i | 0.825969 | + | 0.527232i | ||||
\(236\) | 129.540i | 0.548900i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 187.273i | − | 0.786863i | ||||||
\(239\) | − | 352.073i | − | 1.47311i | −0.676377 | − | 0.736555i | \(-0.736451\pi\) | ||
0.676377 | − | 0.736555i | \(-0.263549\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 87.5764 | 0.363388 | 0.181694 | − | 0.983355i | \(-0.441842\pi\) | ||||
0.181694 | + | 0.983355i | \(0.441842\pi\) | |||||||
\(242\) | −11.8440 | −0.0489423 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −192.551 | −0.789142 | ||||||||
\(245\) | 39.9217 | + | 25.4828i | 0.162946 | + | 0.104011i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 457.846i | − | 1.85363i | ||||||
\(248\) | −129.596 | −0.522565 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 23.5407 | − | 175.202i | 0.0941630 | − | 0.700809i | ||||
\(251\) | − | 2.67686i | − | 0.0106648i | −0.999986 | − | 0.00533238i | \(-0.998303\pi\) | ||
0.999986 | − | 0.00533238i | \(-0.00169736\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 187.845i | − | 0.742471i | ||||||
\(254\) | − | 201.825i | − | 0.794585i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −390.653 | −1.52005 | −0.760025 | − | 0.649894i | \(-0.774813\pi\) | ||||
−0.760025 | + | 0.649894i | \(0.774813\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 243.432 | 0.939891 | ||||||||
\(260\) | 77.3871 | − | 121.236i | 0.297643 | − | 0.466291i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 291.875i | − | 1.11403i | ||||||
\(263\) | −0.831141 | −0.00316023 | −0.00158012 | − | 0.999999i | \(-0.500503\pi\) | ||||
−0.00158012 | + | 0.999999i | \(0.500503\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 226.300 | + | 144.451i | 0.853961 | + | 0.545100i | ||||
\(266\) | − | 344.240i | − | 1.29414i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 3.44892i | − | 0.0128691i | ||||||
\(269\) | 126.427i | 0.469989i | 0.971997 | + | 0.234994i | \(0.0755072\pi\) | ||||
−0.971997 | + | 0.234994i | \(0.924493\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −359.481 | −1.32650 | −0.663249 | − | 0.748399i | \(-0.730823\pi\) | ||||
−0.663249 | + | 0.748399i | \(0.730823\pi\) | |||||||
\(272\) | −69.2701 | −0.254669 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −232.102 | −0.847087 | ||||||||
\(275\) | 257.929 | − | 119.717i | 0.937923 | − | 0.435335i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 424.766i | 1.53345i | 0.641975 | + | 0.766726i | \(0.278115\pi\) | ||||
−0.641975 | + | 0.766726i | \(0.721885\pi\) | |||||||
\(278\) | 43.2156 | 0.155452 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 58.1850 | − | 91.1535i | 0.207804 | − | 0.325548i | ||||
\(281\) | 372.569i | 1.32587i | 0.748677 | + | 0.662935i | \(0.230689\pi\) | ||||
−0.748677 | + | 0.662935i | \(0.769311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 453.237i | − | 1.60154i | −0.598970 | − | 0.800771i | \(-0.704423\pi\) | ||
0.598970 | − | 0.800771i | \(-0.295577\pi\) | |||||||
\(284\) | 53.1461i | 0.187134i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 231.360 | 0.808950 | ||||||||
\(287\) | −522.864 | −1.82182 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8967 | 0.0377048 | ||||||||
\(290\) | 32.3088 | − | 50.6154i | 0.111410 | − | 0.174536i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 102.864i | − | 0.352272i | ||||||
\(293\) | −105.139 | −0.358835 | −0.179418 | − | 0.983773i | \(-0.557421\pi\) | ||||
−0.179418 | + | 0.983773i | \(0.557421\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 174.247 | − | 272.978i | 0.590669 | − | 0.925351i | ||||
\(296\) | − | 90.0424i | − | 0.304197i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 110.200i | − | 0.369798i | ||||||
\(299\) | 237.532i | 0.794421i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −239.973 | −0.797253 | ||||||||
\(302\) | 60.8720 | 0.201563 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −127.330 | −0.418850 | ||||||||
\(305\) | 405.759 | + | 259.004i | 1.33036 | + | 0.849193i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 488.983i | − | 1.59278i | −0.604785 | − | 0.796389i | \(-0.706741\pi\) | ||
0.604785 | − | 0.796389i | \(-0.293259\pi\) | |||||||
\(308\) | 173.952 | 0.564780 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 273.096 | + | 174.323i | 0.880956 | + | 0.562331i | ||||
\(311\) | 57.9226i | 0.186246i | 0.995655 | + | 0.0931231i | \(0.0296850\pi\) | ||||
−0.995655 | + | 0.0931231i | \(0.970315\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 456.139i | − | 1.45731i | −0.684880 | − | 0.728656i | \(-0.740145\pi\) | ||
0.684880 | − | 0.728656i | \(-0.259855\pi\) | |||||||
\(314\) | − | 83.9028i | − | 0.267206i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 118.435 | 0.374795 | ||||||||
\(317\) | −483.080 | −1.52391 | −0.761955 | − | 0.647629i | \(-0.775761\pi\) | ||||
−0.761955 | + | 0.647629i | \(0.775761\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 96.5917 | 0.302795 | ||||||||
\(320\) | −33.7166 | − | 21.5219i | −0.105364 | − | 0.0672560i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 178.593i | 0.554637i | ||||||||
\(323\) | 551.261 | 1.70669 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −326.153 | + | 151.383i | −1.00355 | + | 0.465795i | ||||
\(326\) | 111.899i | 0.343248i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 193.401i | 0.589637i | ||||||||
\(329\) | − | 352.171i | − | 1.07043i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −85.4008 | −0.258008 | −0.129004 | − | 0.991644i | \(-0.541178\pi\) | ||||
−0.129004 | + | 0.991644i | \(0.541178\pi\) | |||||||
\(332\) | 13.8565 | 0.0417365 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −143.565 | −0.429835 | ||||||||
\(335\) | −4.63922 | + | 7.26786i | −0.0138484 | + | 0.0216951i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 498.720i | 1.47988i | 0.672672 | + | 0.739941i | \(0.265147\pi\) | ||||
−0.672672 | + | 0.739941i | \(0.734853\pi\) | |||||||
\(338\) | −53.5543 | −0.158445 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 145.972 | + | 93.1766i | 0.429329 | + | 0.274049i | ||||
\(341\) | 521.162i | 1.52833i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 302.257i | 0.881216i | ||||||||
\(344\) | 88.7631i | 0.258032i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 256.467 | 0.741235 | ||||||||
\(347\) | −494.070 | −1.42383 | −0.711917 | − | 0.702264i | \(-0.752173\pi\) | ||||
−0.711917 | + | 0.702264i | \(0.752173\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 371.772 | 1.06525 | 0.532624 | − | 0.846352i | \(-0.321206\pi\) | ||||
0.532624 | + | 0.846352i | \(0.321206\pi\) | |||||||
\(350\) | −245.225 | + | 113.821i | −0.700643 | + | 0.325202i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 64.3428i | − | 0.182792i | ||||||
\(353\) | 295.348 | 0.836679 | 0.418340 | − | 0.908291i | \(-0.362612\pi\) | ||||
0.418340 | + | 0.908291i | \(0.362612\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 71.4879 | − | 111.994i | 0.201374 | − | 0.315476i | ||||
\(356\) | − | 231.573i | − | 0.650486i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 127.873i | 0.357188i | ||||||||
\(359\) | − | 251.070i | − | 0.699359i | −0.936869 | − | 0.349679i | \(-0.886291\pi\) | ||
0.936869 | − | 0.349679i | \(-0.113709\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 652.312 | 1.80696 | ||||||||
\(362\) | −227.376 | −0.628111 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −219.964 | −0.604298 | ||||||||
\(365\) | −138.364 | + | 216.763i | −0.379079 | + | 0.593871i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 632.976i | 1.72473i | 0.506286 | + | 0.862366i | \(0.331018\pi\) | ||||
−0.506286 | + | 0.862366i | \(0.668982\pi\) | |||||||
\(368\) | 66.0594 | 0.179509 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −121.118 | + | 189.745i | −0.327346 | + | 0.512824i | ||||
\(371\) | − | 410.587i | − | 1.10670i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 183.030i | − | 0.490696i | −0.969435 | − | 0.245348i | \(-0.921098\pi\) | ||
0.969435 | − | 0.245348i | \(-0.0789022\pi\) | |||||||
\(374\) | 278.565i | 0.744825i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −130.264 | −0.346446 | ||||||||
\(377\) | −122.141 | −0.323982 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 274.778 | 0.725009 | 0.362504 | − | 0.931982i | \(-0.381922\pi\) | ||||
0.362504 | + | 0.931982i | \(0.381922\pi\) | |||||||
\(380\) | 268.321 | + | 171.275i | 0.706108 | + | 0.450723i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 241.077i | − | 0.631091i | ||||||
\(383\) | 374.185 | 0.976985 | 0.488492 | − | 0.872568i | \(-0.337547\pi\) | ||||
0.488492 | + | 0.872568i | \(0.337547\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −366.567 | − | 233.987i | −0.952123 | − | 0.607758i | ||||
\(386\) | 302.991i | 0.784951i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 317.308i | 0.817803i | ||||||||
\(389\) | − | 241.583i | − | 0.621037i | −0.950567 | − | 0.310518i | \(-0.899497\pi\) | ||
0.950567 | − | 0.310518i | \(-0.100503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −285.996 | −0.731449 | ||||||||
\(392\) | −26.7917 | −0.0683462 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −296.721 | −0.753099 | ||||||||
\(395\) | −249.577 | − | 159.310i | −0.631840 | − | 0.403315i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 267.415i | 0.673590i | 0.941578 | + | 0.336795i | \(0.109343\pi\) | ||||
−0.941578 | + | 0.336795i | \(0.890657\pi\) | |||||||
\(398\) | 463.392 | 1.16430 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 42.1008 | + | 90.7057i | 0.105252 | + | 0.226764i | ||||
\(401\) | 688.894i | 1.71794i | 0.512026 | + | 0.858970i | \(0.328895\pi\) | ||||
−0.512026 | + | 0.858970i | \(0.671105\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 659.014i | − | 1.63527i | ||||||
\(404\) | − | 217.758i | − | 0.539004i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −91.8343 | −0.226193 | ||||||||
\(407\) | −362.099 | −0.889678 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −253.327 | −0.619382 | −0.309691 | − | 0.950837i | \(-0.600226\pi\) | ||||
−0.309691 | + | 0.950837i | \(0.600226\pi\) | |||||||
\(410\) | 260.147 | − | 407.551i | 0.634506 | − | 0.994026i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 268.721i | 0.652236i | ||||||||
\(413\) | −495.279 | −1.19922 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.1996 | − | 18.6387i | −0.0703605 | − | 0.0449125i | ||||
\(416\) | 81.3621i | 0.195582i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 512.049i | 1.22500i | ||||||||
\(419\) | − | 515.612i | − | 1.23058i | −0.788302 | − | 0.615289i | \(-0.789039\pi\) | ||
0.788302 | − | 0.615289i | \(-0.210961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −517.082 | −1.22822 | −0.614112 | − | 0.789219i | \(-0.710486\pi\) | ||||
−0.614112 | + | 0.789219i | \(0.710486\pi\) | |||||||
\(422\) | 144.268 | 0.341867 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −151.871 | −0.358187 | ||||||||
\(425\) | −182.271 | − | 392.699i | −0.428872 | − | 0.923999i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 736.190i | − | 1.72410i | ||||||
\(428\) | 251.516 | 0.587655 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 119.397 | − | 187.049i | 0.277668 | − | 0.434998i | ||||
\(431\) | − | 290.795i | − | 0.674698i | −0.941380 | − | 0.337349i | \(-0.890470\pi\) | ||
0.941380 | − | 0.337349i | \(-0.109530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 358.909i | 0.828889i | 0.910075 | + | 0.414444i | \(0.136024\pi\) | ||||
−0.910075 | + | 0.414444i | \(0.863976\pi\) | |||||||
\(434\) | − | 495.493i | − | 1.14169i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −126.481 | −0.290094 | ||||||||
\(437\) | −525.710 | −1.20300 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −203.637 | −0.463866 | −0.231933 | − | 0.972732i | \(-0.574505\pi\) | ||||
−0.231933 | + | 0.972732i | \(0.574505\pi\) | |||||||
\(440\) | −86.5489 | + | 135.589i | −0.196702 | + | 0.308156i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 352.248i | − | 0.796940i | ||||||
\(443\) | 21.2268 | 0.0479160 | 0.0239580 | − | 0.999713i | \(-0.492373\pi\) | ||||
0.0239580 | + | 0.999713i | \(0.492373\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −311.494 | + | 487.990i | −0.699986 | + | 1.09661i | ||||
\(446\) | 533.871i | 1.19702i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 61.1737i | 0.136549i | ||||||||
\(449\) | 650.346i | 1.44843i | 0.689573 | + | 0.724216i | \(0.257798\pi\) | ||||
−0.689573 | + | 0.724216i | \(0.742202\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 777.747 | 1.72450 | ||||||||
\(452\) | 208.035 | 0.460254 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 381.066 | 0.839353 | ||||||||
\(455\) | 463.528 | + | 295.879i | 1.01874 | + | 0.650283i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 154.972i | 0.339107i | 0.985521 | + | 0.169553i | \(0.0542325\pi\) | ||||
−0.985521 | + | 0.169553i | \(0.945767\pi\) | |||||||
\(458\) | 599.432 | 1.30880 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −139.206 | − | 88.8579i | −0.302622 | − | 0.193169i | ||||
\(461\) | 351.985i | 0.763525i | 0.924261 | + | 0.381762i | \(0.124683\pi\) | ||||
−0.924261 | + | 0.381762i | \(0.875317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 100.306i | 0.216644i | 0.994116 | + | 0.108322i | \(0.0345477\pi\) | ||||
−0.994116 | + | 0.108322i | \(0.965452\pi\) | |||||||
\(464\) | 33.9684i | 0.0732077i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 100.234 | 0.215094 | ||||||||
\(467\) | 31.5687 | 0.0675989 | 0.0337994 | − | 0.999429i | \(-0.489239\pi\) | ||||
0.0337994 | + | 0.999429i | \(0.489239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.1865 | 0.0281161 | ||||||||
\(470\) | 274.503 | + | 175.220i | 0.584048 | + | 0.372809i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 183.198i | 0.388131i | ||||||||
\(473\) | 356.954 | 0.754660 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −335.044 | − | 721.849i | −0.705356 | − | 1.51968i | ||||
\(476\) | − | 264.844i | − | 0.556396i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 497.907i | − | 1.04165i | ||||||
\(479\) | 634.355i | 1.32433i | 0.749357 | + | 0.662166i | \(0.230362\pi\) | ||||
−0.749357 | + | 0.662166i | \(0.769638\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 457.878 | 0.951929 | ||||||||
\(482\) | 123.852 | 0.256954 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.7500 | −0.0346075 | ||||||||
\(485\) | 426.817 | − | 668.658i | 0.880035 | − | 1.37868i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 639.112i | 1.31235i | 0.754611 | + | 0.656173i | \(0.227826\pi\) | ||||
−0.754611 | + | 0.656173i | \(0.772174\pi\) | |||||||
\(488\) | −272.308 | −0.558008 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 56.4578 | + | 36.0381i | 0.115220 | + | 0.0735471i | ||||
\(491\) | 367.869i | 0.749224i | 0.927182 | + | 0.374612i | \(0.122224\pi\) | ||||
−0.927182 | + | 0.374612i | \(0.877776\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 147.062i | − | 0.298300i | ||||||
\(494\) | − | 647.491i | − | 1.31071i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −183.277 | −0.369510 | ||||||||
\(497\) | −203.196 | −0.408846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −494.543 | −0.991069 | −0.495534 | − | 0.868588i | \(-0.665028\pi\) | ||||
−0.495534 | + | 0.868588i | \(0.665028\pi\) | |||||||
\(500\) | 33.2916 | − | 247.773i | 0.0665833 | − | 0.495547i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 3.78565i | − | 0.00754113i | ||||||
\(503\) | −176.118 | −0.350135 | −0.175067 | − | 0.984556i | \(-0.556014\pi\) | ||||
−0.175067 | + | 0.984556i | \(0.556014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −292.910 | + | 458.878i | −0.580020 | + | 0.908668i | ||||
\(506\) | − | 265.653i | − | 0.525006i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 285.423i | − | 0.561857i | ||||||
\(509\) | 624.613i | 1.22714i | 0.789641 | + | 0.613569i | \(0.210267\pi\) | ||||
−0.789641 | + | 0.613569i | \(0.789733\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 393.284 | 0.769636 | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −552.467 | −1.07484 | ||||||||
\(515\) | 361.462 | − | 566.272i | 0.701868 | − | 1.09956i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 523.846i | 1.01324i | ||||||||
\(518\) | 344.265 | 0.664603 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 109.442 | − | 171.453i | 0.210465 | − | 0.329718i | ||||
\(521\) | − | 908.634i | − | 1.74402i | −0.489489 | − | 0.872009i | \(-0.662817\pi\) | ||
0.489489 | − | 0.872009i | \(-0.337183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 534.875i | 1.02271i | 0.859371 | + | 0.511353i | \(0.170855\pi\) | ||||
−0.859371 | + | 0.511353i | \(0.829145\pi\) | |||||||
\(524\) | − | 412.773i | − | 0.787735i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.17541 | −0.00223462 | ||||||||
\(527\) | 793.475 | 1.50565 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −256.260 | −0.484423 | ||||||||
\(530\) | 320.036 | + | 204.285i | 0.603841 | + | 0.385444i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 486.829i | − | 0.915093i | ||||||
\(533\) | −983.469 | −1.84516 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −530.017 | − | 338.320i | −0.990686 | − | 0.632374i | ||||
\(536\) | − | 4.87751i | − | 0.00909984i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 178.795i | 0.332332i | ||||||||
\(539\) | 107.741i | 0.199890i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −996.576 | −1.84210 | −0.921050 | − | 0.389444i | \(-0.872667\pi\) | ||||
−0.921050 | + | 0.389444i | \(0.872667\pi\) | |||||||
\(542\) | −508.383 | −0.937975 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −97.9627 | −0.180079 | ||||||||
\(545\) | 266.532 | + | 170.132i | 0.489049 | + | 0.312169i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 632.447i | 1.15621i | 0.815963 | + | 0.578105i | \(0.196208\pi\) | ||||
−0.815963 | + | 0.578105i | \(0.803792\pi\) | |||||||
\(548\) | −328.242 | −0.598981 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 364.766 | − | 169.305i | 0.663211 | − | 0.307828i | ||||
\(551\) | − | 270.325i | − | 0.490608i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 452.820i | 0.818843i | ||||||||
\(554\) | 600.710i | 1.08431i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 61.1161 | 0.109921 | ||||||||
\(557\) | −673.973 | −1.21001 | −0.605003 | − | 0.796223i | \(-0.706828\pi\) | ||||
−0.605003 | + | 0.796223i | \(0.706828\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −451.372 | −0.807463 | ||||||||
\(560\) | 82.2861 | − | 128.911i | 0.146939 | − | 0.230197i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 526.893i | 0.937531i | ||||||||
\(563\) | 336.483 | 0.597661 | 0.298831 | − | 0.954306i | \(-0.403403\pi\) | ||||
0.298831 | + | 0.954306i | \(0.403403\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −438.389 | − | 279.832i | −0.775910 | − | 0.495278i | ||||
\(566\) | − | 640.973i | − | 1.13246i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 75.1599i | 0.132324i | ||||||||
\(569\) | − | 410.792i | − | 0.721954i | −0.932575 | − | 0.360977i | \(-0.882443\pi\) | ||
0.932575 | − | 0.360977i | \(-0.117557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −444.795 | −0.778976 | −0.389488 | − | 0.921032i | \(-0.627348\pi\) | ||||
−0.389488 | + | 0.921032i | \(0.627348\pi\) | |||||||
\(572\) | 327.192 | 0.572014 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −739.441 | −1.28822 | ||||||||
\(575\) | 173.822 | + | 374.498i | 0.302300 | + | 0.651301i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 365.707i | − | 0.633808i | −0.948458 | − | 0.316904i | \(-0.897357\pi\) | ||
0.948458 | − | 0.316904i | \(-0.102643\pi\) | |||||||
\(578\) | 15.4102 | 0.0266613 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 45.6916 | − | 71.5811i | 0.0787786 | − | 0.123416i | ||||
\(581\) | 52.9784i | 0.0911848i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 610.739i | 1.04758i | ||||||||
\(584\) | − | 145.471i | − | 0.249094i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −148.689 | −0.253735 | ||||||||
\(587\) | 387.993 | 0.660976 | 0.330488 | − | 0.943810i | \(-0.392787\pi\) | ||||
0.330488 | + | 0.943810i | \(0.392787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1458.54 | 2.47630 | ||||||||
\(590\) | 246.423 | − | 386.050i | 0.417666 | − | 0.654322i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 127.339i | − | 0.215100i | ||||||
\(593\) | −657.706 | −1.10912 | −0.554558 | − | 0.832145i | \(-0.687113\pi\) | ||||
−0.554558 | + | 0.832145i | \(0.687113\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −356.248 | + | 558.103i | −0.598736 | + | 0.937988i | ||||
\(596\) | − | 155.846i | − | 0.261486i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 335.921i | 0.561741i | ||||||||
\(599\) | 534.335i | 0.892045i | 0.895022 | + | 0.446022i | \(0.147160\pi\) | ||||
−0.895022 | + | 0.446022i | \(0.852840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −900.532 | −1.49839 | −0.749195 | − | 0.662350i | \(-0.769559\pi\) | ||||
−0.749195 | + | 0.662350i | \(0.769559\pi\) | |||||||
\(602\) | −339.373 | −0.563743 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 86.0861 | 0.142527 | ||||||||
\(605\) | 35.2970 | + | 22.5308i | 0.0583422 | + | 0.0372410i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 870.321i | − | 1.43381i | −0.697172 | − | 0.716904i | \(-0.745559\pi\) | ||
0.697172 | − | 0.716904i | \(-0.254441\pi\) | |||||||
\(608\) | −180.072 | −0.296171 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 573.830 | + | 366.287i | 0.940705 | + | 0.600470i | ||||
\(611\) | − | 662.408i | − | 1.08414i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 252.101i | − | 0.411258i | −0.978630 | − | 0.205629i | \(-0.934076\pi\) | ||
0.978630 | − | 0.205629i | \(-0.0659240\pi\) | |||||||
\(614\) | − | 691.526i | − | 1.12626i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 246.006 | 0.399360 | ||||||||
\(617\) | −724.936 | −1.17494 | −0.587468 | − | 0.809247i | \(-0.699875\pi\) | ||||
−0.587468 | + | 0.809247i | \(0.699875\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 293.289 | 0.473811 | 0.236906 | − | 0.971533i | \(-0.423867\pi\) | ||||
0.236906 | + | 0.971533i | \(0.423867\pi\) | |||||||
\(620\) | 386.216 | + | 246.529i | 0.622930 | + | 0.397628i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 81.9149i | 0.131696i | ||||||||
\(623\) | 885.387 | 1.42117 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −403.440 | + | 477.348i | −0.645504 | + | 0.763757i | ||||
\(626\) | − | 645.078i | − | 1.03048i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 118.656i | − | 0.188943i | ||||||
\(629\) | 551.300i | 0.876471i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 397.922 | 0.630622 | 0.315311 | − | 0.948988i | \(-0.397891\pi\) | ||||
0.315311 | + | 0.948988i | \(0.397891\pi\) | |||||||
\(632\) | 167.493 | 0.265020 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −683.178 | −1.07757 | ||||||||
\(635\) | −383.929 | + | 601.468i | −0.604612 | + | 0.947194i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 136.239i | − | 0.213877i | ||||||
\(638\) | 136.601 | 0.214109 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −47.6824 | − | 30.4366i | −0.0745038 | − | 0.0475572i | ||||
\(641\) | 265.282i | 0.413857i | 0.978356 | + | 0.206928i | \(0.0663467\pi\) | ||||
−0.978356 | + | 0.206928i | \(0.933653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 251.091i | 0.390499i | 0.980754 | + | 0.195250i | \(0.0625517\pi\) | ||||
−0.980754 | + | 0.195250i | \(0.937448\pi\) | |||||||
\(644\) | 252.569i | 0.392188i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 779.601 | 1.20681 | ||||||||
\(647\) | −415.167 | −0.641680 | −0.320840 | − | 0.947133i | \(-0.603965\pi\) | ||||
−0.320840 | + | 0.947133i | \(0.603965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 736.716 | 1.13516 | ||||||||
\(650\) | −461.250 | + | 214.088i | −0.709616 | + | 0.329367i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 158.249i | 0.242713i | ||||||||
\(653\) | −847.279 | −1.29752 | −0.648758 | − | 0.760994i | \(-0.724711\pi\) | ||||
−0.648758 | + | 0.760994i | \(0.724711\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −555.230 | + | 869.831i | −0.847679 | + | 1.32799i | ||||
\(656\) | 273.510i | 0.416936i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 498.045i | − | 0.756907i | ||||||
\(659\) | 143.448i | 0.217676i | 0.994059 | + | 0.108838i | \(0.0347130\pi\) | ||||
−0.994059 | + | 0.108838i | \(0.965287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −303.035 | −0.458449 | −0.229224 | − | 0.973374i | \(-0.573619\pi\) | ||||
−0.229224 | + | 0.973374i | \(0.573619\pi\) | |||||||
\(662\) | −120.775 | −0.182439 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.5961 | 0.0295121 | ||||||||
\(665\) | −654.844 | + | 1025.89i | −0.984728 | + | 1.54269i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 140.246i | 0.210263i | ||||||||
\(668\) | −203.031 | −0.303939 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.56084 | + | 10.2783i | −0.00979230 | + | 0.0153408i | ||||
\(671\) | 1095.07i | 1.63199i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 278.524i | − | 0.413854i | −0.978356 | − | 0.206927i | \(-0.933654\pi\) | ||
0.978356 | − | 0.206927i | \(-0.0663462\pi\) | |||||||
\(674\) | 705.297i | 1.04643i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −75.7373 | −0.112037 | ||||||||
\(677\) | −813.121 | −1.20106 | −0.600532 | − | 0.799600i | \(-0.705045\pi\) | ||||
−0.600532 | + | 0.799600i | \(0.705045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1213.18 | −1.78672 | ||||||||
\(680\) | 206.435 | + | 131.772i | 0.303581 | + | 0.193782i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 737.034i | 1.08070i | ||||||||
\(683\) | 1081.42 | 1.58334 | 0.791668 | − | 0.610952i | \(-0.209213\pi\) | ||||
0.791668 | + | 0.610952i | \(0.209213\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 691.699 | + | 441.525i | 1.00978 | + | 0.644561i | ||||
\(686\) | 427.456i | 0.623114i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 125.530i | 0.182456i | ||||||||
\(689\) | − | 772.285i | − | 1.12088i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1059.73 | 1.53361 | 0.766807 | − | 0.641878i | \(-0.221844\pi\) | ||||
0.766807 | + | 0.641878i | \(0.221844\pi\) | |||||||
\(692\) | 362.700 | 0.524132 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −698.721 | −1.00680 | ||||||||
\(695\) | −128.789 | − | 82.2085i | −0.185308 | − | 0.118286i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1184.13i | − | 1.69889i | ||||||
\(698\) | 525.765 | 0.753245 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −346.800 | + | 160.967i | −0.495429 | + | 0.229952i | ||||
\(701\) | − | 716.640i | − | 1.02231i | −0.859488 | − | 0.511155i | \(-0.829218\pi\) | ||
0.859488 | − | 0.511155i | \(-0.170782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1013.38i | 1.44151i | ||||||||
\(704\) | − | 90.9945i | − | 0.129254i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 417.685 | 0.591622 | ||||||||
\(707\) | 832.566 | 1.17760 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −146.474 | −0.206592 | −0.103296 | − | 0.994651i | \(-0.532939\pi\) | ||||
−0.103296 | + | 0.994651i | \(0.532939\pi\) | |||||||
\(710\) | 101.099 | − | 158.383i | 0.142393 | − | 0.223075i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 327.494i | − | 0.459963i | ||||||
\(713\) | −756.697 | −1.06129 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −689.487 | − | 440.113i | −0.964317 | − | 0.615542i | ||||
\(716\) | 180.840i | 0.252570i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 355.066i | − | 0.494521i | ||||||
\(719\) | 329.272i | 0.457958i | 0.973431 | + | 0.228979i | \(0.0735388\pi\) | ||||
−0.973431 | + | 0.228979i | \(0.926461\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1027.42 | −1.42499 | ||||||||
\(722\) | 922.509 | 1.27771 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −321.558 | −0.444141 | ||||||||
\(725\) | −192.570 | + | 89.3810i | −0.265614 | + | 0.123284i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 332.250i | 0.457015i | 0.973542 | + | 0.228507i | \(0.0733845\pi\) | ||||
−0.973542 | + | 0.228507i | \(0.926615\pi\) | |||||||
\(728\) | −311.077 | −0.427303 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −195.676 | + | 306.549i | −0.268049 | + | 0.419930i | ||||
\(731\) | − | 543.467i | − | 0.743457i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 496.851i | 0.677833i | 0.940817 | + | 0.338916i | \(0.110060\pi\) | ||||
−0.940817 | + | 0.338916i | \(0.889940\pi\) | |||||||
\(734\) | 895.164i | 1.21957i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 93.4221 | 0.126932 | ||||||||
\(737\) | −19.6146 | −0.0266141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 493.117 | 0.667276 | 0.333638 | − | 0.942701i | \(-0.391724\pi\) | ||||
0.333638 | + | 0.942701i | \(0.391724\pi\) | |||||||
\(740\) | −171.287 | + | 268.340i | −0.231468 | + | 0.362622i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 580.658i | − | 0.782558i | ||||||
\(743\) | −816.847 | −1.09939 | −0.549695 | − | 0.835365i | \(-0.685256\pi\) | ||||
−0.549695 | + | 0.835365i | \(0.685256\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −209.632 | + | 328.412i | −0.281385 | + | 0.440821i | ||||
\(746\) | − | 258.843i | − | 0.346975i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 393.950i | 0.526671i | ||||||||
\(749\) | 961.638i | 1.28390i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 583.577 | 0.777067 | 0.388533 | − | 0.921435i | \(-0.372982\pi\) | ||||
0.388533 | + | 0.921435i | \(0.372982\pi\) | |||||||
\(752\) | −184.221 | −0.244974 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −172.734 | −0.229090 | ||||||||
\(755\) | −181.408 | − | 115.796i | −0.240275 | − | 0.153372i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 633.635i | − | 0.837034i | −0.908209 | − | 0.418517i | \(-0.862550\pi\) | ||
0.908209 | − | 0.418517i | \(-0.137450\pi\) | |||||||
\(758\) | 388.595 | 0.512658 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 379.463 | + | 242.219i | 0.499294 | + | 0.318709i | ||||
\(761\) | 745.689i | 0.979880i | 0.871756 | + | 0.489940i | \(0.162981\pi\) | ||||
−0.871756 | + | 0.489940i | \(0.837019\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 483.583i | − | 0.633791i | ||||||
\(764\) | − | 340.934i | − | 0.446249i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 529.178 | 0.690832 | ||||||||
\(767\) | −931.585 | −1.21458 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −431.418 | −0.561012 | −0.280506 | − | 0.959852i | \(-0.590502\pi\) | ||||
−0.280506 | + | 0.959852i | \(0.590502\pi\) | |||||||
\(770\) | −518.404 | − | 330.907i | −0.673252 | − | 0.429750i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 428.494i | 0.555044i | ||||||||
\(773\) | −248.851 | −0.321929 | −0.160964 | − | 0.986960i | \(-0.551460\pi\) | ||||
−0.160964 | + | 0.986960i | \(0.551460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −482.256 | − | 1039.02i | −0.622266 | − | 1.34066i | ||||
\(776\) | 448.741i | 0.578274i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 341.650i | − | 0.439139i | ||||||
\(779\) | − | 2176.63i | − | 2.79414i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 302.250 | 0.387004 | ||||||||
\(782\) | −404.460 | −0.517212 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −37.8892 | −0.0483280 | ||||||||
\(785\) | −159.607 | + | 250.043i | −0.203321 | + | 0.318526i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 929.437i | 1.18099i | 0.807042 | + | 0.590494i | \(0.201067\pi\) | ||||
−0.807042 | + | 0.590494i | \(0.798933\pi\) | |||||||
\(788\) | −419.627 | −0.532522 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −352.955 | − | 225.298i | −0.446778 | − | 0.285187i | ||||
\(791\) | 795.392i | 1.00555i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1384.72i | − | 1.74618i | ||||||
\(794\) | 378.182i | 0.476300i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 655.335 | 0.823285 | ||||||||
\(797\) | 584.059 | 0.732821 | 0.366411 | − | 0.930453i | \(-0.380587\pi\) | ||||
0.366411 | + | 0.930453i | \(0.380587\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 797.561 | 0.998199 | ||||||||
\(800\) | 59.5396 | + | 128.277i | 0.0744244 | + | 0.160347i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 974.243i | 1.21477i | ||||||||
\(803\) | −585.001 | −0.728519 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 339.736 | − | 532.235i | 0.422032 | − | 0.661161i | ||||
\(806\) | − | 931.987i | − | 1.15631i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 307.956i | − | 0.381134i | ||||||
\(809\) | 363.295i | 0.449067i | 0.974466 | + | 0.224533i | \(0.0720858\pi\) | ||||
−0.974466 | + | 0.224533i | \(0.927914\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 69.8507 | 0.0861290 | 0.0430645 | − | 0.999072i | \(-0.486288\pi\) | ||||
0.0430645 | + | 0.999072i | \(0.486288\pi\) | |||||||
\(812\) | −129.873 | −0.159942 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −512.085 | −0.629097 | ||||||||
\(815\) | 212.864 | − | 333.476i | 0.261183 | − | 0.409173i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 998.985i | − | 1.22275i | ||||||
\(818\) | −358.259 | −0.437969 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 367.904 | − | 576.364i | 0.448663 | − | 0.702883i | ||||
\(821\) | − | 183.472i | − | 0.223474i | −0.993738 | − | 0.111737i | \(-0.964359\pi\) | ||
0.993738 | − | 0.111737i | \(-0.0356414\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 534.931i | − | 0.649977i | −0.945718 | − | 0.324988i | \(-0.894640\pi\) | ||
0.945718 | − | 0.324988i | \(-0.105360\pi\) | |||||||
\(824\) | 380.029i | 0.461200i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −700.431 | −0.847979 | ||||||||
\(827\) | 640.632 | 0.774646 | 0.387323 | − | 0.921944i | \(-0.373400\pi\) | ||||
0.387323 | + | 0.921944i | \(0.373400\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 910.462 | 1.09827 | 0.549133 | − | 0.835735i | \(-0.314958\pi\) | ||||
0.549133 | + | 0.835735i | \(0.314958\pi\) | |||||||
\(830\) | −41.2945 | − | 26.3591i | −0.0497524 | − | 0.0317579i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 115.063i | 0.138297i | ||||||||
\(833\) | 164.037 | 0.196923 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 427.845 | + | 273.102i | 0.512389 | + | 0.327068i | ||||
\(836\) | 724.147i | 0.866205i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 729.186i | − | 0.870150i | ||||||
\(839\) | − | 41.5328i | − | 0.0495027i | −0.999694 | − | 0.0247513i | \(-0.992121\pi\) | ||
0.999694 | − | 0.0247513i | \(-0.00787940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 768.884 | 0.914250 | ||||||||
\(842\) | −731.265 | −0.868486 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 204.026 | 0.241737 | ||||||||
\(845\) | 159.600 | + | 101.876i | 0.188876 | + | 0.120563i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 64.0413i | − | 0.0756096i | ||||||
\(848\) | −214.778 | −0.253276 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −257.769 | − | 555.361i | −0.303258 | − | 0.653366i | ||||
\(851\) | − | 525.747i | − | 0.617799i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 426.015i | 0.499431i | 0.968319 | + | 0.249716i | \(0.0803371\pi\) | ||||
−0.968319 | + | 0.249716i | \(0.919663\pi\) | |||||||
\(854\) | − | 1041.13i | − | 1.21912i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 355.698 | 0.415535 | ||||||||
\(857\) | 662.580 | 0.773139 | 0.386570 | − | 0.922260i | \(-0.373660\pi\) | ||||
0.386570 | + | 0.922260i | \(0.373660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1402.18 | 1.63234 | 0.816168 | − | 0.577815i | \(-0.196094\pi\) | ||||
0.816168 | + | 0.577815i | \(0.196094\pi\) | |||||||
\(860\) | 168.853 | − | 264.527i | 0.196341 | − | 0.307590i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 411.246i | − | 0.477083i | ||||||
\(863\) | −54.6082 | −0.0632771 | −0.0316386 | − | 0.999499i | \(-0.510073\pi\) | ||||
−0.0316386 | + | 0.999499i | \(0.510073\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −764.312 | − | 487.875i | −0.883597 | − | 0.564017i | ||||
\(866\) | 507.574i | 0.586113i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 700.733i | − | 0.807296i | ||||||
\(869\) | − | 673.559i | − | 0.775097i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.8028 | 0.0284762 | ||||||||
\(872\) | −178.871 | −0.205128 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −743.467 | −0.850648 | ||||||||
\(875\) | 947.327 | + | 127.286i | 1.08266 | + | 0.145470i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 875.174i | 0.997918i | 0.866625 | + | 0.498959i | \(0.166284\pi\) | ||||
−0.866625 | + | 0.498959i | \(0.833716\pi\) | |||||||
\(878\) | −287.987 | −0.328003 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −122.399 | + | 191.751i | −0.139089 | + | 0.217899i | ||||
\(881\) | − | 1103.84i | − | 1.25294i | −0.779445 | − | 0.626471i | \(-0.784499\pi\) | ||
0.779445 | − | 0.626471i | \(-0.215501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 455.458i | − | 0.515808i | −0.966171 | − | 0.257904i | \(-0.916968\pi\) | ||
0.966171 | − | 0.257904i | \(-0.0830318\pi\) | |||||||
\(884\) | − | 498.153i | − | 0.563522i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.0192 | 0.0338817 | ||||||||
\(887\) | −951.037 | −1.07219 | −0.536097 | − | 0.844156i | \(-0.680102\pi\) | ||||
−0.536097 | + | 0.844156i | \(0.680102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1091.28 | 1.22753 | ||||||||
\(890\) | −440.518 | + | 690.123i | −0.494965 | + | 0.775419i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 755.008i | 0.846421i | ||||||||
\(893\) | 1466.05 | 1.64172 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 243.252 | − | 381.082i | 0.271790 | − | 0.425789i | ||||
\(896\) | 86.5127i | 0.0965544i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 919.728i | 1.02420i | ||||||||
\(899\) | − | 389.101i | − | 0.432815i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 929.857 | 1.03203 | ||||||||
\(902\) | 1099.90 | 1.21940 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 294.206 | 0.325449 | ||||||||
\(905\) | 677.615 | + | 432.535i | 0.748746 | + | 0.477939i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1349.31i | − | 1.48766i | −0.668370 | − | 0.743829i | \(-0.733008\pi\) | ||
0.668370 | − | 0.743829i | \(-0.266992\pi\) | |||||||
\(908\) | 538.909 | 0.593512 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 655.527 | + | 418.436i | 0.720360 | + | 0.459819i | ||||
\(911\) | 409.175i | 0.449149i | 0.974457 | + | 0.224575i | \(0.0720993\pi\) | ||||
−0.974457 | + | 0.224575i | \(0.927901\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 78.8041i | − | 0.0863134i | ||||||
\(914\) | 219.163i | 0.239785i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 847.725 | 0.925463 | ||||||||
\(917\) | 1578.18 | 1.72103 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −247.618 | −0.269443 | −0.134721 | − | 0.990884i | \(-0.543014\pi\) | ||||
−0.134721 | + | 0.990884i | \(0.543014\pi\) | |||||||
\(920\) | −196.867 | − | 125.664i | −0.213986 | − | 0.136591i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 497.782i | 0.539893i | ||||||||
\(923\) | −382.198 | −0.414082 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 721.899 | − | 335.068i | 0.780432 | − | 0.362236i | ||||
\(926\) | 141.854i | 0.153190i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 48.0385i | 0.0517657i | ||||||||
\(929\) | 274.384i | 0.295354i | 0.989036 | + | 0.147677i | \(0.0471796\pi\) | ||||
−0.989036 | + | 0.147677i | \(0.952820\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 301.528 | 0.323875 | ||||||||
\(932\) | 141.752 | 0.152095 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 44.6449 | 0.0477996 | ||||||||
\(935\) | 529.910 | − | 830.165i | 0.566749 | − | 0.887877i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 313.547i | − | 0.334629i | −0.985904 | − | 0.167315i | \(-0.946490\pi\) | ||
0.985904 | − | 0.167315i | \(-0.0535095\pi\) | |||||||
\(938\) | 18.6485 | 0.0198811 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 388.205 | + | 247.799i | 0.412984 | + | 0.263616i | ||||
\(941\) | − | 508.607i | − | 0.540496i | −0.962791 | − | 0.270248i | \(-0.912894\pi\) | ||
0.962791 | − | 0.270248i | \(-0.0871058\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1129.24i | 1.19750i | ||||||||
\(944\) | 259.081i | 0.274450i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 504.810 | 0.533625 | ||||||||
\(947\) | 1008.92 | 1.06539 | 0.532695 | − | 0.846307i | \(-0.321179\pi\) | ||||
0.532695 | + | 0.846307i | \(0.321179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 739.739 | 0.779494 | ||||||||
\(950\) | −473.824 | − | 1020.85i | −0.498762 | − | 1.07458i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 374.547i | − | 0.393431i | ||||||
\(953\) | −918.564 | −0.963865 | −0.481933 | − | 0.876208i | \(-0.660065\pi\) | ||||
−0.481933 | + | 0.876208i | \(0.660065\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −458.597 | + | 718.445i | −0.480206 | + | 0.752298i | ||||
\(956\) | − | 704.147i | − | 0.736555i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 897.113i | 0.936444i | ||||||||
\(959\) | − | 1254.99i | − | 1.30864i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1138.40 | 1.18460 | ||||||||
\(962\) | 647.537 | 0.673115 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 175.153 | 0.181694 | ||||||||
\(965\) | 576.376 | − | 902.959i | 0.597281 | − | 0.935709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 30.2629i | − | 0.0312957i | −0.999878 | − | 0.0156479i | \(-0.995019\pi\) | ||
0.999878 | − | 0.0156479i | \(-0.00498107\pi\) | |||||||
\(968\) | −23.6881 | −0.0244712 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 603.610 | − | 945.625i | 0.622279 | − | 0.974871i | ||||
\(971\) | 1003.74i | 1.03372i | 0.856071 | + | 0.516858i | \(0.172899\pi\) | ||||
−0.856071 | + | 0.516858i | \(0.827101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 233.669i | 0.240153i | ||||||||
\(974\) | 903.841i | 0.927968i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −385.101 | −0.394571 | ||||||||
\(977\) | −784.493 | −0.802961 | −0.401481 | − | 0.915868i | \(-0.631504\pi\) | ||||
−0.401481 | + | 0.915868i | \(0.631504\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1316.99 | −1.34524 | ||||||||
\(980\) | 79.8433 | + | 50.9655i | 0.0814728 | + | 0.0520056i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 520.245i | 0.529781i | ||||||||
\(983\) | −53.2332 | −0.0541539 | −0.0270769 | − | 0.999633i | \(-0.508620\pi\) | ||||
−0.0270769 | + | 0.999633i | \(0.508620\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 884.274 | + | 564.449i | 0.897740 | + | 0.573045i | ||||
\(986\) | − | 207.977i | − | 0.210930i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 915.691i | − | 0.926813i | ||||||
\(989\) | 518.277i | 0.524042i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1202.09 | 1.21300 | 0.606501 | − | 0.795082i | \(-0.292572\pi\) | ||||
0.606501 | + | 0.795082i | \(0.292572\pi\) | |||||||
\(992\) | −259.192 | −0.261283 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −287.363 | −0.289098 | ||||||||
\(995\) | −1380.98 | − | 881.505i | −1.38792 | − | 0.885934i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1336.97i | − | 1.34099i | −0.741914 | − | 0.670495i | \(-0.766082\pi\) | ||
0.741914 | − | 0.670495i | \(-0.233918\pi\) | |||||||
\(998\) | −699.390 | −0.700791 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 810.3.b.c.809.15 | yes | 24 | |
3.2 | odd | 2 | inner | 810.3.b.c.809.10 | yes | 24 | |
5.4 | even | 2 | inner | 810.3.b.c.809.9 | ✓ | 24 | |
9.2 | odd | 6 | 810.3.j.g.539.7 | 24 | |||
9.4 | even | 3 | 810.3.j.h.269.1 | 24 | |||
9.5 | odd | 6 | 810.3.j.h.269.7 | 24 | |||
9.7 | even | 3 | 810.3.j.g.539.1 | 24 | |||
15.14 | odd | 2 | inner | 810.3.b.c.809.16 | yes | 24 | |
45.4 | even | 6 | 810.3.j.g.269.7 | 24 | |||
45.14 | odd | 6 | 810.3.j.g.269.1 | 24 | |||
45.29 | odd | 6 | 810.3.j.h.539.1 | 24 | |||
45.34 | even | 6 | 810.3.j.h.539.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
810.3.b.c.809.9 | ✓ | 24 | 5.4 | even | 2 | inner | |
810.3.b.c.809.10 | yes | 24 | 3.2 | odd | 2 | inner | |
810.3.b.c.809.15 | yes | 24 | 1.1 | even | 1 | trivial | |
810.3.b.c.809.16 | yes | 24 | 15.14 | odd | 2 | inner | |
810.3.j.g.269.1 | 24 | 45.14 | odd | 6 | |||
810.3.j.g.269.7 | 24 | 45.4 | even | 6 | |||
810.3.j.g.539.1 | 24 | 9.7 | even | 3 | |||
810.3.j.g.539.7 | 24 | 9.2 | odd | 6 | |||
810.3.j.h.269.1 | 24 | 9.4 | even | 3 | |||
810.3.j.h.269.7 | 24 | 9.5 | odd | 6 | |||
810.3.j.h.539.1 | 24 | 45.29 | odd | 6 | |||
810.3.j.h.539.7 | 24 | 45.34 | even | 6 |