Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (of order \(3\), 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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{22})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 22x^{2} + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 98) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 667.2 | ||
Root | \(2.34521 - 4.06202i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.667 |
Dual form | 882.4.g.bi.361.2 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 4.69042 | − | 8.12404i | 0.419524 | − | 0.726636i | −0.576368 | − | 0.817190i | \(-0.695530\pi\) |
0.995892 | + | 0.0905542i | \(0.0288638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.38083 | − | 16.2481i | −0.296648 | − | 0.513809i | ||||
\(11\) | 10.0000 | + | 17.3205i | 0.274101 | + | 0.474757i | 0.969908 | − | 0.243472i | \(-0.0782863\pi\) |
−0.695807 | + | 0.718229i | \(0.744953\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 65.6658 | 1.40096 | 0.700478 | − | 0.713674i | \(-0.252970\pi\) | ||||
0.700478 | + | 0.713674i | \(0.252970\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 28.1425 | + | 48.7442i | 0.401503 | + | 0.695424i | 0.993908 | − | 0.110217i | \(-0.0351545\pi\) |
−0.592404 | + | 0.805641i | \(0.701821\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.69042 | + | 8.12404i | −0.0566345 | + | 0.0980938i | −0.892953 | − | 0.450151i | \(-0.851370\pi\) |
0.836318 | + | 0.548244i | \(0.184704\pi\) | |||||||
\(20\) | −37.5233 | −0.419524 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 40.0000 | 0.387638 | ||||||||
\(23\) | 24.0000 | − | 41.5692i | 0.217580 | − | 0.376860i | −0.736487 | − | 0.676451i | \(-0.763517\pi\) |
0.954068 | + | 0.299591i | \(0.0968503\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.5000 | + | 32.0429i | 0.148000 | + | 0.256344i | ||||
\(26\) | 65.6658 | − | 113.737i | 0.495313 | − | 0.857907i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 166.000 | 1.06295 | 0.531473 | − | 0.847075i | \(-0.321639\pi\) | ||||
0.531473 | + | 0.847075i | \(0.321639\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 103.189 | + | 178.729i | 0.597849 | + | 1.03550i | 0.993138 | + | 0.116948i | \(0.0373111\pi\) |
−0.395289 | + | 0.918557i | \(0.629356\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 112.570 | 0.567812 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 39.0000 | − | 67.5500i | 0.173285 | − | 0.300139i | −0.766281 | − | 0.642505i | \(-0.777895\pi\) |
0.939567 | + | 0.342366i | \(0.111228\pi\) | |||||||
\(38\) | 9.38083 | + | 16.2481i | 0.0400466 | + | 0.0693628i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −37.5233 | + | 64.9923i | −0.148324 | + | 0.256905i | ||||
\(41\) | −393.995 | −1.50077 | −0.750386 | − | 0.661000i | \(-0.770132\pi\) | ||||
−0.750386 | + | 0.661000i | \(0.770132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 436.000 | 1.54626 | 0.773132 | − | 0.634245i | \(-0.218689\pi\) | ||||
0.773132 | + | 0.634245i | \(0.218689\pi\) | |||||||
\(44\) | 40.0000 | − | 69.2820i | 0.137051 | − | 0.237379i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.0000 | − | 83.1384i | −0.153852 | − | 0.266480i | ||||
\(47\) | 103.189 | − | 178.729i | 0.320249 | − | 0.554687i | −0.660291 | − | 0.751010i | \(-0.729567\pi\) |
0.980539 | + | 0.196323i | \(0.0629002\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 74.0000 | 0.209304 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −131.332 | − | 227.473i | −0.350239 | − | 0.606632i | ||||
\(53\) | 31.0000 | + | 53.6936i | 0.0803430 | + | 0.139158i | 0.903397 | − | 0.428805i | \(-0.141065\pi\) |
−0.823054 | + | 0.567963i | \(0.807732\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 187.617 | 0.459968 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 166.000 | − | 287.520i | 0.375808 | − | 0.650919i | ||||
\(59\) | −333.020 | − | 576.807i | −0.734838 | − | 1.27278i | −0.954794 | − | 0.297267i | \(-0.903925\pi\) |
0.219956 | − | 0.975510i | \(-0.429409\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −136.022 | + | 235.597i | −0.285506 | + | 0.494510i | −0.972732 | − | 0.231933i | \(-0.925495\pi\) |
0.687226 | + | 0.726444i | \(0.258828\pi\) | |||||||
\(62\) | 412.757 | 0.845486 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 308.000 | − | 533.472i | 0.587734 | − | 1.01798i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −290.000 | − | 502.295i | −0.528793 | − | 0.915897i | −0.999436 | − | 0.0335729i | \(-0.989311\pi\) |
0.470643 | − | 0.882324i | \(-0.344022\pi\) | |||||||
\(68\) | 112.570 | − | 194.977i | 0.200752 | − | 0.347712i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 544.000 | 0.909309 | 0.454654 | − | 0.890668i | \(-0.349763\pi\) | ||||
0.454654 | + | 0.890668i | \(0.349763\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 300.187 | + | 519.938i | 0.481290 | + | 0.833619i | 0.999769 | − | 0.0214711i | \(-0.00683499\pi\) |
−0.518479 | + | 0.855090i | \(0.673502\pi\) | |||||||
\(74\) | −78.0000 | − | 135.100i | −0.122531 | − | 0.212230i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 37.5233 | 0.0566345 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 340.000 | − | 588.897i | 0.484215 | − | 0.838685i | −0.515621 | − | 0.856817i | \(-0.672439\pi\) |
0.999836 | + | 0.0181320i | \(0.00577190\pi\) | |||||||
\(80\) | 75.0467 | + | 129.985i | 0.104881 | + | 0.181659i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −393.995 | + | 682.419i | −0.530603 | + | 0.919032i | ||||
\(83\) | −196.997 | −0.260521 | −0.130261 | − | 0.991480i | \(-0.541581\pi\) | ||||
−0.130261 | + | 0.991480i | \(0.541581\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 528.000 | 0.673760 | ||||||||
\(86\) | 436.000 | − | 755.174i | 0.546687 | − | 0.946890i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −80.0000 | − | 138.564i | −0.0969094 | − | 0.167852i | ||||
\(89\) | −750.467 | + | 1299.85i | −0.893812 | + | 1.54813i | −0.0585446 | + | 0.998285i | \(0.518646\pi\) |
−0.835268 | + | 0.549843i | \(0.814687\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −192.000 | −0.217580 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −206.378 | − | 357.458i | −0.226450 | − | 0.392223i | ||||
\(95\) | 44.0000 | + | 76.2102i | 0.0475190 | + | 0.0823053i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −656.658 | −0.687356 | −0.343678 | − | 0.939088i | \(-0.611673\pi\) | ||||
−0.343678 | + | 0.939088i | \(0.611673\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 74.0000 | − | 128.172i | 0.0740000 | − | 0.128172i | ||||
\(101\) | 60.9754 | + | 105.612i | 0.0600721 | + | 0.104048i | 0.894497 | − | 0.447073i | \(-0.147534\pi\) |
−0.834425 | + | 0.551121i | \(0.814200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 684.801 | − | 1186.11i | 0.655101 | − | 1.13467i | −0.326767 | − | 0.945105i | \(-0.605959\pi\) |
0.981868 | − | 0.189564i | \(-0.0607073\pi\) | |||||||
\(104\) | −525.327 | −0.495313 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 124.000 | 0.113622 | ||||||||
\(107\) | −130.000 | + | 225.167i | −0.117454 | + | 0.203436i | −0.918758 | − | 0.394821i | \(-0.870807\pi\) |
0.801304 | + | 0.598257i | \(0.204140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −941.000 | − | 1629.86i | −0.826894 | − | 1.43222i | −0.900463 | − | 0.434932i | \(-0.856772\pi\) |
0.0735690 | − | 0.997290i | \(-0.476561\pi\) | |||||||
\(110\) | 187.617 | − | 324.962i | 0.162623 | − | 0.281672i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1286.00 | 1.07059 | 0.535295 | − | 0.844665i | \(-0.320200\pi\) | ||||
0.535295 | + | 0.844665i | \(0.320200\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −225.140 | − | 389.954i | −0.182560 | − | 0.316203i | ||||
\(116\) | −332.000 | − | 575.041i | −0.265736 | − | 0.460269i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1332.08 | −1.03922 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 465.500 | − | 806.270i | 0.349737 | − | 0.605762i | ||||
\(122\) | 272.044 | + | 471.194i | 0.201883 | + | 0.349671i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 412.757 | − | 714.915i | 0.298924 | − | 0.517752i | ||||
\(125\) | 1519.69 | 1.08741 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2312.00 | 1.61541 | 0.807704 | − | 0.589588i | \(-0.200710\pi\) | ||||
0.807704 | + | 0.589588i | \(0.200710\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −616.000 | − | 1066.94i | −0.415591 | − | 0.719824i | ||||
\(131\) | −126.641 | + | 219.349i | −0.0844633 | + | 0.146295i | −0.905162 | − | 0.425066i | \(-0.860251\pi\) |
0.820699 | + | 0.571361i | \(0.193584\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1160.00 | −0.747826 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −225.140 | − | 389.954i | −0.141953 | − | 0.245870i | ||||
\(137\) | −557.000 | − | 964.752i | −0.347356 | − | 0.601638i | 0.638423 | − | 0.769686i | \(-0.279587\pi\) |
−0.985779 | + | 0.168048i | \(0.946254\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1378.98 | 0.841466 | 0.420733 | − | 0.907185i | \(-0.361773\pi\) | ||||
0.420733 | + | 0.907185i | \(0.361773\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 544.000 | − | 942.236i | 0.321489 | − | 0.556836i | ||||
\(143\) | 656.658 | + | 1137.37i | 0.384004 | + | 0.665114i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 778.609 | − | 1348.59i | 0.445931 | − | 0.772375i | ||||
\(146\) | 1200.75 | 0.680647 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −312.000 | −0.173285 | ||||||||
\(149\) | −473.000 | + | 819.260i | −0.260065 | + | 0.450446i | −0.966259 | − | 0.257573i | \(-0.917077\pi\) |
0.706194 | + | 0.708018i | \(0.250411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −416.000 | − | 720.533i | −0.224196 | − | 0.388319i | 0.731882 | − | 0.681431i | \(-0.238642\pi\) |
−0.956078 | + | 0.293113i | \(0.905309\pi\) | |||||||
\(152\) | 37.5233 | − | 64.9923i | 0.0200233 | − | 0.0346814i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1936.00 | 1.00325 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1439.96 | − | 2494.08i | −0.731982 | − | 1.26783i | −0.956035 | − | 0.293253i | \(-0.905262\pi\) |
0.224053 | − | 0.974577i | \(-0.428071\pi\) | |||||||
\(158\) | −680.000 | − | 1177.79i | −0.342392 | − | 0.593040i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 300.187 | 0.148324 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −318.000 | + | 550.792i | −0.152808 | + | 0.264671i | −0.932259 | − | 0.361792i | \(-0.882165\pi\) |
0.779451 | + | 0.626463i | \(0.215498\pi\) | |||||||
\(164\) | 787.990 | + | 1364.84i | 0.375193 | + | 0.649854i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −196.997 | + | 341.210i | −0.0921082 | + | 0.159536i | ||||
\(167\) | 656.658 | 0.304274 | 0.152137 | − | 0.988359i | \(-0.451385\pi\) | ||||
0.152137 | + | 0.988359i | \(0.451385\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2115.00 | 0.962676 | ||||||||
\(170\) | 528.000 | − | 914.523i | 0.238210 | − | 0.412592i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −872.000 | − | 1510.35i | −0.386566 | − | 0.669552i | ||||
\(173\) | 333.020 | − | 576.807i | 0.146353 | − | 0.253490i | −0.783524 | − | 0.621361i | \(-0.786580\pi\) |
0.929877 | + | 0.367871i | \(0.119913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −320.000 | −0.137051 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1500.93 | + | 2599.69i | 0.632021 | + | 1.09469i | ||||
\(179\) | −1614.00 | − | 2795.53i | −0.673944 | − | 1.16731i | −0.976776 | − | 0.214262i | \(-0.931265\pi\) |
0.302832 | − | 0.953044i | \(-0.402068\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2823.63 | −1.15955 | −0.579776 | − | 0.814776i | \(-0.696860\pi\) | ||||
−0.579776 | + | 0.814776i | \(0.696860\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −192.000 | + | 332.554i | −0.0769262 | + | 0.133240i | ||||
\(185\) | −365.852 | − | 633.675i | −0.145395 | − | 0.251831i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −562.850 | + | 974.885i | −0.220105 | + | 0.381233i | ||||
\(188\) | −825.513 | −0.320249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 176.000 | 0.0672020 | ||||||||
\(191\) | −1068.00 | + | 1849.83i | −0.404596 | + | 0.700780i | −0.994274 | − | 0.106858i | \(-0.965921\pi\) |
0.589679 | + | 0.807638i | \(0.299254\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −829.000 | − | 1435.87i | −0.309185 | − | 0.535524i | 0.668999 | − | 0.743263i | \(-0.266723\pi\) |
−0.978184 | + | 0.207739i | \(0.933390\pi\) | |||||||
\(194\) | −656.658 | + | 1137.37i | −0.243017 | + | 0.420918i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 978.000 | 0.353704 | 0.176852 | − | 0.984237i | \(-0.443409\pi\) | ||||
0.176852 | + | 0.984237i | \(0.443409\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2467.16 | + | 4273.24i | 0.878855 | + | 1.52222i | 0.852598 | + | 0.522567i | \(0.175026\pi\) |
0.0262574 | + | 0.999655i | \(0.491641\pi\) | |||||||
\(200\) | −148.000 | − | 256.344i | −0.0523259 | − | 0.0906311i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 243.902 | 0.0849547 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1848.00 | + | 3200.83i | −0.629609 | + | 1.09052i | ||||
\(206\) | −1369.60 | − | 2372.22i | −0.463226 | − | 0.802332i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −525.327 | + | 909.892i | −0.175119 | + | 0.303316i | ||||
\(209\) | −187.617 | −0.0620943 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1556.00 | 0.507675 | 0.253838 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253838 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(212\) | 124.000 | − | 214.774i | 0.0401715 | − | 0.0695791i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 260.000 | + | 450.333i | 0.0830525 | + | 0.143851i | ||||
\(215\) | 2045.02 | − | 3542.08i | 0.648694 | − | 1.12357i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3764.00 | −1.16940 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −375.233 | − | 649.923i | −0.114992 | − | 0.199172i | ||||
\(221\) | 1848.00 | + | 3200.83i | 0.562488 | + | 0.974258i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2889.30 | 0.867630 | 0.433815 | − | 0.901002i | \(-0.357167\pi\) | ||||
0.433815 | + | 0.901002i | \(0.357167\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1286.00 | − | 2227.42i | 0.378511 | − | 0.655600i | ||||
\(227\) | −989.678 | − | 1714.17i | −0.289371 | − | 0.501205i | 0.684289 | − | 0.729211i | \(-0.260113\pi\) |
−0.973660 | + | 0.228006i | \(0.926779\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1383.67 | + | 2396.59i | −0.399282 | + | 0.691577i | −0.993638 | − | 0.112625i | \(-0.964074\pi\) |
0.594355 | + | 0.804203i | \(0.297407\pi\) | |||||||
\(230\) | −900.560 | −0.258179 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1328.00 | −0.375808 | ||||||||
\(233\) | −3245.00 | + | 5620.50i | −0.912391 | + | 1.58031i | −0.101713 | + | 0.994814i | \(0.532432\pi\) |
−0.810677 | + | 0.585493i | \(0.800901\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −968.000 | − | 1676.63i | −0.268704 | − | 0.465408i | ||||
\(236\) | −1332.08 | + | 2307.23i | −0.367419 | + | 0.636388i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4296.00 | 1.16270 | 0.581350 | − | 0.813654i | \(-0.302525\pi\) | ||||
0.581350 | + | 0.813654i | \(0.302525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2260.78 | − | 3915.79i | −0.604272 | − | 1.04663i | −0.992166 | − | 0.124926i | \(-0.960131\pi\) |
0.387894 | − | 0.921704i | \(-0.373203\pi\) | |||||||
\(242\) | −931.000 | − | 1612.54i | −0.247301 | − | 0.428339i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1088.18 | 0.285506 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −308.000 | + | 533.472i | −0.0793424 | + | 0.137425i | ||||
\(248\) | −825.513 | − | 1429.83i | −0.211372 | − | 0.366106i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1519.69 | − | 2632.19i | 0.384456 | − | 0.665897i | ||||
\(251\) | −5581.59 | −1.40361 | −0.701807 | − | 0.712367i | \(-0.747623\pi\) | ||||
−0.701807 | + | 0.712367i | \(0.747623\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 960.000 | 0.238556 | ||||||||
\(254\) | 2312.00 | − | 4004.50i | 0.571133 | − | 0.989231i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −750.467 | + | 1299.85i | −0.182151 | + | 0.315495i | −0.942613 | − | 0.333888i | \(-0.891639\pi\) |
0.760462 | + | 0.649383i | \(0.224973\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2464.00 | −0.587734 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 253.282 | + | 438.698i | 0.0597246 | + | 0.103446i | ||||
\(263\) | −200.000 | − | 346.410i | −0.0468917 | − | 0.0812189i | 0.841627 | − | 0.540059i | \(-0.181598\pi\) |
−0.888519 | + | 0.458841i | \(0.848265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 581.612 | 0.134823 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1160.00 | + | 2009.18i | −0.264397 | + | 0.457948i | ||||
\(269\) | −136.022 | − | 235.597i | −0.0308305 | − | 0.0534000i | 0.850198 | − | 0.526462i | \(-0.176482\pi\) |
−0.881029 | + | 0.473062i | \(0.843149\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3452.15 | + | 5979.29i | −0.773812 | + | 1.34028i | 0.161648 | + | 0.986848i | \(0.448319\pi\) |
−0.935460 | + | 0.353433i | \(0.885014\pi\) | |||||||
\(272\) | −900.560 | −0.200752 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2228.00 | −0.491235 | ||||||||
\(275\) | −370.000 | + | 640.859i | −0.0811340 | + | 0.140528i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3385.00 | + | 5862.99i | 0.734242 | + | 1.27174i | 0.955055 | + | 0.296428i | \(0.0957954\pi\) |
−0.220814 | + | 0.975316i | \(0.570871\pi\) | |||||||
\(278\) | 1378.98 | − | 2388.47i | 0.297503 | − | 0.515290i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1878.00 | −0.398691 | −0.199345 | − | 0.979929i | \(-0.563882\pi\) | ||||
−0.199345 | + | 0.979929i | \(0.563882\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −192.307 | − | 333.086i | −0.0403939 | − | 0.0699642i | 0.845122 | − | 0.534574i | \(-0.179528\pi\) |
−0.885516 | + | 0.464610i | \(0.846195\pi\) | |||||||
\(284\) | −1088.00 | − | 1884.47i | −0.227327 | − | 0.393742i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2626.63 | 0.543063 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 872.500 | − | 1511.21i | 0.177590 | − | 0.307595i | ||||
\(290\) | −1557.22 | − | 2697.18i | −0.315321 | − | 0.546151i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1200.75 | − | 2079.75i | 0.240645 | − | 0.416810i | ||||
\(293\) | 3742.95 | 0.746299 | 0.373149 | − | 0.927771i | \(-0.378278\pi\) | ||||
0.373149 | + | 0.927771i | \(0.378278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6248.00 | −1.23313 | ||||||||
\(296\) | −312.000 | + | 540.400i | −0.0612656 | + | 0.106115i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 946.000 | + | 1638.52i | 0.183894 | + | 0.318513i | ||||
\(299\) | 1575.98 | − | 2729.68i | 0.304820 | − | 0.527964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1664.00 | −0.317061 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −75.0467 | − | 129.985i | −0.0141586 | − | 0.0245235i | ||||
\(305\) | 1276.00 | + | 2210.10i | 0.239553 | + | 0.414917i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 722.324 | 0.134284 | 0.0671420 | − | 0.997743i | \(-0.478612\pi\) | ||||
0.0671420 | + | 0.997743i | \(0.478612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1936.00 | − | 3353.25i | 0.354701 | − | 0.614361i | ||||
\(311\) | 3639.76 | + | 6304.25i | 0.663640 | + | 1.14946i | 0.979652 | + | 0.200703i | \(0.0643226\pi\) |
−0.316012 | + | 0.948755i | \(0.602344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −759.847 | + | 1316.09i | −0.137218 | + | 0.237668i | −0.926442 | − | 0.376437i | \(-0.877149\pi\) |
0.789225 | + | 0.614104i | \(0.210483\pi\) | |||||||
\(314\) | −5759.83 | −1.03518 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2720.00 | −0.484215 | ||||||||
\(317\) | 1179.00 | − | 2042.09i | 0.208893 | − | 0.361814i | −0.742473 | − | 0.669876i | \(-0.766347\pi\) |
0.951366 | + | 0.308062i | \(0.0996805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1660.00 | + | 2875.20i | 0.291355 | + | 0.504641i | ||||
\(320\) | 300.187 | − | 519.938i | 0.0524404 | − | 0.0908295i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −528.000 | −0.0909557 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1214.82 | + | 2104.13i | 0.207341 | + | 0.359126i | ||||
\(326\) | 636.000 | + | 1101.58i | 0.108051 | + | 0.187151i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3151.96 | 0.530603 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1186.00 | + | 2054.21i | −0.196944 | + | 0.341117i | −0.947536 | − | 0.319649i | \(-0.896435\pi\) |
0.750592 | + | 0.660766i | \(0.229768\pi\) | |||||||
\(332\) | 393.995 | + | 682.419i | 0.0651304 | + | 0.112809i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 656.658 | − | 1137.37i | 0.107577 | − | 0.186329i | ||||
\(335\) | −5440.88 | −0.887365 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −250.000 | −0.0404106 | −0.0202053 | − | 0.999796i | \(-0.506432\pi\) | ||||
−0.0202053 | + | 0.999796i | \(0.506432\pi\) | |||||||
\(338\) | 2115.00 | − | 3663.29i | 0.340357 | − | 0.589516i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1056.00 | − | 1829.05i | −0.168440 | − | 0.291747i | ||||
\(341\) | −2063.78 | + | 3574.58i | −0.327742 | + | 0.567666i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −3488.00 | −0.546687 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −666.039 | − | 1153.61i | −0.103487 | − | 0.179245i | ||||
\(347\) | 4770.00 | + | 8261.88i | 0.737945 | + | 1.27816i | 0.953419 | + | 0.301649i | \(0.0975371\pi\) |
−0.215474 | + | 0.976510i | \(0.569130\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5712.93 | −0.876235 | −0.438117 | − | 0.898918i | \(-0.644355\pi\) | ||||
−0.438117 | + | 0.898918i | \(0.644355\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −320.000 | + | 554.256i | −0.0484547 | + | 0.0839260i | ||||
\(353\) | 2195.11 | + | 3802.05i | 0.330975 | + | 0.573265i | 0.982703 | − | 0.185187i | \(-0.0592891\pi\) |
−0.651728 | + | 0.758452i | \(0.725956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2551.59 | − | 4419.48i | 0.381476 | − | 0.660737i | ||||
\(356\) | 6003.73 | 0.893812 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6456.00 | −0.953101 | ||||||||
\(359\) | 920.000 | − | 1593.49i | 0.135253 | − | 0.234265i | −0.790441 | − | 0.612538i | \(-0.790149\pi\) |
0.925694 | + | 0.378273i | \(0.123482\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3385.50 | + | 5863.86i | 0.493585 | + | 0.854914i | ||||
\(362\) | −2823.63 | + | 4890.67i | −0.409963 | + | 0.710077i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5632.00 | 0.807650 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1482.17 | + | 2567.20i | 0.210814 | + | 0.365140i | 0.951969 | − | 0.306193i | \(-0.0990552\pi\) |
−0.741156 | + | 0.671333i | \(0.765722\pi\) | |||||||
\(368\) | 384.000 | + | 665.108i | 0.0543951 | + | 0.0942150i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1463.41 | −0.205619 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1991.00 | + | 3448.51i | −0.276381 | + | 0.478706i | −0.970483 | − | 0.241171i | \(-0.922468\pi\) |
0.694102 | + | 0.719877i | \(0.255802\pi\) | |||||||
\(374\) | 1125.70 | + | 1949.77i | 0.155638 | + | 0.269573i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −825.513 | + | 1429.83i | −0.113225 | + | 0.196111i | ||||
\(377\) | 10900.5 | 1.48914 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2676.00 | 0.362683 | 0.181342 | − | 0.983420i | \(-0.441956\pi\) | ||||
0.181342 | + | 0.983420i | \(0.441956\pi\) | |||||||
\(380\) | 176.000 | − | 304.841i | 0.0237595 | − | 0.0411527i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2136.00 | + | 3699.66i | 0.286092 | + | 0.495526i | ||||
\(383\) | 3517.81 | − | 6093.03i | 0.469326 | − | 0.812896i | −0.530059 | − | 0.847961i | \(-0.677830\pi\) |
0.999385 | + | 0.0350645i | \(0.0111637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3316.00 | −0.437254 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1313.32 | + | 2274.73i | 0.171839 | + | 0.297634i | ||||
\(389\) | 4329.00 | + | 7498.05i | 0.564239 | + | 0.977291i | 0.997120 | + | 0.0758397i | \(0.0241637\pi\) |
−0.432881 | + | 0.901451i | \(0.642503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2701.68 | 0.349437 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 978.000 | − | 1693.95i | 0.125053 | − | 0.216598i | ||||
\(395\) | −3189.48 | − | 5524.35i | −0.406279 | − | 0.703696i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4526.25 | − | 7839.70i | 0.572207 | − | 0.991091i | −0.424132 | − | 0.905600i | \(-0.639421\pi\) |
0.996339 | − | 0.0854907i | \(-0.0272458\pi\) | |||||||
\(398\) | 9868.63 | 1.24289 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −592.000 | −0.0740000 | ||||||||
\(401\) | −2853.00 | + | 4941.54i | −0.355292 | + | 0.615383i | −0.987168 | − | 0.159686i | \(-0.948952\pi\) |
0.631876 | + | 0.775069i | \(0.282285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6776.00 | + | 11736.4i | 0.837560 | + | 1.45070i | ||||
\(404\) | 243.902 | − | 422.450i | 0.0300360 | − | 0.0520239i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1560.00 | 0.189991 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1210.13 | − | 2096.00i | −0.146301 | − | 0.253400i | 0.783557 | − | 0.621320i | \(-0.213403\pi\) |
−0.929857 | + | 0.367920i | \(0.880070\pi\) | |||||||
\(410\) | 3696.00 | + | 6401.66i | 0.445201 | + | 0.771111i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5478.41 | −0.655101 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −924.000 | + | 1600.41i | −0.109295 | + | 0.189304i | ||||
\(416\) | 1050.65 | + | 1819.78i | 0.123828 | + | 0.214477i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −187.617 | + | 324.962i | −0.0219537 | + | 0.0380249i | ||||
\(419\) | 1510.31 | 0.176095 | 0.0880473 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880473 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16770.0 | −1.94138 | −0.970689 | − | 0.240341i | \(-0.922741\pi\) | ||||
−0.970689 | + | 0.240341i | \(0.922741\pi\) | |||||||
\(422\) | 1556.00 | − | 2695.07i | 0.179490 | − | 0.310886i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −248.000 | − | 429.549i | −0.0284055 | − | 0.0491998i | ||||
\(425\) | −1041.27 | + | 1803.54i | −0.118845 | + | 0.205846i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1040.00 | 0.117454 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4090.04 | − | 7084.16i | −0.458696 | − | 0.794485i | ||||
\(431\) | 668.000 | + | 1157.01i | 0.0746553 | + | 0.129307i | 0.900936 | − | 0.433951i | \(-0.142881\pi\) |
−0.826281 | + | 0.563258i | \(0.809548\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11163.2 | −1.23896 | −0.619479 | − | 0.785013i | \(-0.712656\pi\) | ||||
−0.619479 | + | 0.785013i | \(0.712656\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3764.00 | + | 6519.44i | −0.413447 | + | 0.716111i | ||||
\(437\) | 225.140 | + | 389.954i | 0.0246451 | + | 0.0426865i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1801.12 | − | 3119.63i | 0.195815 | − | 0.339161i | −0.751352 | − | 0.659901i | \(-0.770598\pi\) |
0.947167 | + | 0.320740i | \(0.103931\pi\) | |||||||
\(440\) | −1500.93 | −0.162623 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7392.00 | 0.795479 | ||||||||
\(443\) | 3174.00 | − | 5497.53i | 0.340409 | − | 0.589606i | −0.644099 | − | 0.764942i | \(-0.722768\pi\) |
0.984509 | + | 0.175336i | \(0.0561011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7040.00 | + | 12193.6i | 0.749951 | + | 1.29895i | ||||
\(446\) | 2889.30 | − | 5004.41i | 0.306754 | − | 0.531313i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7170.00 | −0.753615 | −0.376808 | − | 0.926292i | \(-0.622978\pi\) | ||||
−0.376808 | + | 0.926292i | \(0.622978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3939.95 | − | 6824.19i | −0.411364 | − | 0.712503i | ||||
\(452\) | −2572.00 | − | 4454.83i | −0.267648 | − | 0.463579i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3958.71 | −0.409232 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3433.00 | + | 5946.13i | −0.351398 | + | 0.608639i | −0.986495 | − | 0.163793i | \(-0.947627\pi\) |
0.635097 | + | 0.772433i | \(0.280960\pi\) | |||||||
\(458\) | 2767.35 | + | 4793.18i | 0.282335 | + | 0.489019i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −900.560 | + | 1559.82i | −0.0912800 | + | 0.158102i | ||||
\(461\) | −1378.98 | −0.139318 | −0.0696590 | − | 0.997571i | \(-0.522191\pi\) | ||||
−0.0696590 | + | 0.997571i | \(0.522191\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2648.00 | 0.265795 | 0.132897 | − | 0.991130i | \(-0.457572\pi\) | ||||
0.132897 | + | 0.991130i | \(0.457572\pi\) | |||||||
\(464\) | −1328.00 | + | 2300.16i | −0.132868 | + | 0.230135i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6490.00 | + | 11241.0i | 0.645158 | + | 1.11745i | ||||
\(467\) | −6167.90 | + | 10683.1i | −0.611170 | + | 1.05858i | 0.379874 | + | 0.925038i | \(0.375967\pi\) |
−0.991044 | + | 0.133539i | \(0.957366\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3872.00 | −0.380004 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2664.16 | + | 4614.45i | 0.259805 | + | 0.449995i | ||||
\(473\) | 4360.00 | + | 7551.74i | 0.423833 | + | 0.734100i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −347.091 | −0.0335276 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4296.00 | − | 7440.89i | 0.411076 | − | 0.712005i | ||||
\(479\) | −6669.77 | − | 11552.4i | −0.636221 | − | 1.10197i | −0.986255 | − | 0.165229i | \(-0.947164\pi\) |
0.350035 | − | 0.936737i | \(-0.386170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2560.97 | − | 4435.72i | 0.242765 | − | 0.420482i | ||||
\(482\) | −9043.12 | −0.854570 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3724.00 | −0.349737 | ||||||||
\(485\) | −3080.00 | + | 5334.72i | −0.288362 | + | 0.499458i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6968.00 | − | 12068.9i | −0.648358 | − | 1.12299i | −0.983515 | − | 0.180826i | \(-0.942123\pi\) |
0.335157 | − | 0.942162i | \(-0.391211\pi\) | |||||||
\(488\) | 1088.18 | − | 1884.78i | 0.100941 | − | 0.174836i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12276.0 | 1.12833 | 0.564163 | − | 0.825663i | \(-0.309199\pi\) | ||||
0.564163 | + | 0.825663i | \(0.309199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4671.65 | + | 8091.54i | 0.426776 | + | 0.739198i | ||||
\(494\) | 616.000 | + | 1066.94i | 0.0561035 | + | 0.0971742i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3302.05 | −0.298924 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1110.00 | − | 1922.58i | 0.0995800 | − | 0.172478i | −0.811931 | − | 0.583754i | \(-0.801583\pi\) |
0.911511 | + | 0.411276i | \(0.134917\pi\) | |||||||
\(500\) | −3039.39 | − | 5264.38i | −0.271851 | − | 0.470860i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5581.59 | + | 9667.61i | −0.496253 | + | 0.859535i | ||||
\(503\) | 11294.5 | 1.00119 | 0.500594 | − | 0.865682i | \(-0.333115\pi\) | ||||
0.500594 | + | 0.865682i | \(0.333115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1144.00 | 0.100807 | ||||||||
\(506\) | 960.000 | − | 1662.77i | 0.0843423 | − | 0.146085i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4624.00 | − | 8009.00i | −0.403852 | − | 0.699492i | ||||
\(509\) | −7940.87 | + | 13754.0i | −0.691499 | + | 1.19771i | 0.279848 | + | 0.960044i | \(0.409716\pi\) |
−0.971347 | + | 0.237667i | \(0.923617\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1500.93 | + | 2599.69i | 0.128800 | + | 0.223089i | ||||
\(515\) | −6424.00 | − | 11126.7i | −0.549661 | − | 0.952040i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4127.57 | 0.351122 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2464.00 | + | 4267.77i | −0.207795 | + | 0.359912i | ||||
\(521\) | 5806.73 | + | 10057.6i | 0.488287 | + | 0.845738i | 0.999909 | − | 0.0134723i | \(-0.00428850\pi\) |
−0.511622 | + | 0.859211i | \(0.670955\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6308.61 | + | 10926.8i | −0.527450 | + | 0.913570i | 0.472038 | + | 0.881578i | \(0.343518\pi\) |
−0.999488 | + | 0.0319918i | \(0.989815\pi\) | |||||||
\(524\) | 1013.13 | 0.0844633 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −800.000 | −0.0663149 | ||||||||
\(527\) | −5808.00 | + | 10059.8i | −0.480077 | + | 0.831517i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4931.50 | + | 8541.61i | 0.405318 | + | 0.702031i | ||||
\(530\) | 581.612 | − | 1007.38i | 0.0476672 | − | 0.0825619i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25872.0 | −2.10252 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1219.51 | + | 2112.25i | 0.0985494 | + | 0.170693i | ||||
\(536\) | 2320.00 | + | 4018.36i | 0.186957 | + | 0.323818i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −544.088 | −0.0436009 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −899.000 | + | 1557.11i | −0.0714437 | + | 0.123744i | −0.899534 | − | 0.436850i | \(-0.856094\pi\) |
0.828091 | + | 0.560594i | \(0.189427\pi\) | |||||||
\(542\) | 6904.29 | + | 11958.6i | 0.547167 | + | 0.947722i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −900.560 | + | 1559.82i | −0.0709764 | + | 0.122935i | ||||
\(545\) | −17654.7 | −1.38761 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1276.00 | 0.0997401 | 0.0498700 | − | 0.998756i | \(-0.484119\pi\) | ||||
0.0498700 | + | 0.998756i | \(0.484119\pi\) | |||||||
\(548\) | −2228.00 | + | 3859.01i | −0.173678 | + | 0.300819i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 740.000 | + | 1281.72i | 0.0573704 | + | 0.0993684i | ||||
\(551\) | −778.609 | + | 1348.59i | −0.0601994 | + | 0.104268i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13540.0 | 1.03837 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2757.96 | − | 4776.93i | −0.210366 | − | 0.364365i | ||||
\(557\) | 1347.00 | + | 2333.07i | 0.102467 | + | 0.177478i | 0.912701 | − | 0.408629i | \(-0.133993\pi\) |
−0.810233 | + | 0.586107i | \(0.800660\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28630.3 | 2.16625 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1878.00 | + | 3252.79i | −0.140958 | + | 0.244147i | ||||
\(563\) | −7884.59 | − | 13656.5i | −0.590223 | − | 1.02230i | −0.994202 | − | 0.107529i | \(-0.965706\pi\) |
0.403979 | − | 0.914768i | \(-0.367627\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6031.87 | − | 10447.5i | 0.449138 | − | 0.777930i | ||||
\(566\) | −769.228 | −0.0571256 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4352.00 | −0.321489 | ||||||||
\(569\) | 6303.00 | − | 10917.1i | 0.464386 | − | 0.804340i | −0.534788 | − | 0.844986i | \(-0.679608\pi\) |
0.999174 | + | 0.0406466i | \(0.0129418\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3426.00 | − | 5934.01i | −0.251092 | − | 0.434904i | 0.712735 | − | 0.701434i | \(-0.247456\pi\) |
−0.963827 | + | 0.266529i | \(0.914123\pi\) | |||||||
\(572\) | 2626.63 | − | 4549.46i | 0.192002 | − | 0.332557i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1776.00 | 0.128808 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7185.72 | − | 12446.0i | −0.518449 | − | 0.897981i | −0.999770 | − | 0.0214362i | \(-0.993176\pi\) |
0.481321 | − | 0.876545i | \(-0.340157\pi\) | |||||||
\(578\) | −1745.00 | − | 3022.43i | −0.125575 | − | 0.217503i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6228.87 | −0.445931 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −620.000 | + | 1073.87i | −0.0440442 | + | 0.0762868i | ||||
\(584\) | −2401.49 | − | 4159.51i | −0.170162 | − | 0.294729i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3742.95 | − | 6482.98i | 0.263857 | − | 0.457013i | ||||
\(587\) | −18977.4 | −1.33438 | −0.667191 | − | 0.744887i | \(-0.732503\pi\) | ||||
−0.667191 | + | 0.744887i | \(0.732503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1936.00 | −0.135435 | ||||||||
\(590\) | −6248.00 | + | 10821.9i | −0.435976 | + | 0.755133i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 624.000 | + | 1080.80i | 0.0433214 | + | 0.0750348i | ||||
\(593\) | 4108.80 | − | 7116.66i | 0.284534 | − | 0.492826i | −0.687962 | − | 0.725746i | \(-0.741495\pi\) |
0.972496 | + | 0.232920i | \(0.0748280\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3784.00 | 0.260065 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3151.96 | − | 5459.35i | −0.215540 | − | 0.373327i | ||||
\(599\) | −9552.00 | − | 16544.5i | −0.651559 | − | 1.12853i | −0.982744 | − | 0.184968i | \(-0.940782\pi\) |
0.331185 | − | 0.943566i | \(-0.392552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21538.4 | 1.46185 | 0.730923 | − | 0.682460i | \(-0.239090\pi\) | ||||
0.730923 | + | 0.682460i | \(0.239090\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1664.00 | + | 2882.13i | −0.112098 | + | 0.194159i | ||||
\(605\) | −4366.78 | − | 7563.48i | −0.293446 | − | 0.508263i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6866.77 | + | 11893.6i | −0.459166 | + | 0.795298i | −0.998917 | − | 0.0465262i | \(-0.985185\pi\) |
0.539751 | + | 0.841824i | \(0.318518\pi\) | |||||||
\(608\) | −300.187 | −0.0200233 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5104.00 | 0.338779 | ||||||||
\(611\) | 6776.00 | − | 11736.4i | 0.448654 | − | 0.777092i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14017.0 | − | 24278.2i | −0.923558 | − | 1.59965i | −0.793863 | − | 0.608096i | \(-0.791934\pi\) |
−0.129695 | − | 0.991554i | \(-0.541400\pi\) | |||||||
\(614\) | 722.324 | − | 1251.10i | 0.0474766 | − | 0.0822319i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8258.00 | 0.538824 | 0.269412 | − | 0.963025i | \(-0.413171\pi\) | ||||
0.269412 | + | 0.963025i | \(0.413171\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2565.66 | + | 4443.85i | 0.166595 | + | 0.288551i | 0.937221 | − | 0.348737i | \(-0.113389\pi\) |
−0.770625 | + | 0.637288i | \(0.780056\pi\) | |||||||
\(620\) | −3872.00 | − | 6706.50i | −0.250812 | − | 0.434419i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14559.1 | 0.938529 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4815.50 | − | 8340.69i | 0.308192 | − | 0.533804i | ||||
\(626\) | 1519.69 | + | 2632.19i | 0.0970275 | + | 0.168057i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5759.83 | + | 9976.32i | −0.365991 | + | 0.633915i | ||||
\(629\) | 4390.23 | 0.278299 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 912.000 | 0.0575375 | 0.0287687 | − | 0.999586i | \(-0.490841\pi\) | ||||
0.0287687 | + | 0.999586i | \(0.490841\pi\) | |||||||
\(632\) | −2720.00 | + | 4711.18i | −0.171196 | + | 0.296520i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2358.00 | − | 4084.18i | −0.147710 | − | 0.255841i | ||||
\(635\) | 10844.2 | − | 18782.8i | 0.677702 | − | 1.17381i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6640.00 | 0.412038 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −600.373 | − | 1039.88i | −0.0370810 | − | 0.0642262i | ||||
\(641\) | −445.000 | − | 770.763i | −0.0274203 | − | 0.0474934i | 0.851990 | − | 0.523559i | \(-0.175396\pi\) |
−0.879410 | + | 0.476065i | \(0.842063\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29352.6 | −1.80024 | −0.900120 | − | 0.435642i | \(-0.856521\pi\) | ||||
−0.900120 | + | 0.435642i | \(0.856521\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −528.000 | + | 914.523i | −0.0321577 | + | 0.0556988i | ||||
\(647\) | 5938.07 | + | 10285.0i | 0.360818 | + | 0.624956i | 0.988096 | − | 0.153840i | \(-0.0491641\pi\) |
−0.627277 | + | 0.778796i | \(0.715831\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6660.39 | − | 11536.1i | 0.402840 | − | 0.697739i | ||||
\(650\) | 4859.27 | 0.293225 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2544.00 | 0.152808 | ||||||||
\(653\) | −10763.0 | + | 18642.1i | −0.645006 | + | 1.11718i | 0.339294 | + | 0.940680i | \(0.389812\pi\) |
−0.984300 | + | 0.176502i | \(0.943522\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1188.00 | + | 2057.68i | 0.0708687 | + | 0.122748i | ||||
\(656\) | 3151.96 | − | 5459.35i | 0.187597 | − | 0.324927i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23452.0 | −1.38628 | −0.693141 | − | 0.720802i | \(-0.743774\pi\) | ||||
−0.693141 | + | 0.720802i | \(0.743774\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13334.9 | + | 23096.6i | 0.784668 | + | 1.35909i | 0.929197 | + | 0.369584i | \(0.120500\pi\) |
−0.144529 | + | 0.989501i | \(0.546167\pi\) | |||||||
\(662\) | 2372.00 | + | 4108.42i | 0.139260 | + | 0.241206i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1575.98 | 0.0921082 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3984.00 | − | 6900.49i | 0.231276 | − | 0.400582i | ||||
\(668\) | −1313.32 | − | 2274.73i | −0.0760685 | − | 0.131754i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5440.88 | + | 9423.88i | −0.313731 | + | 0.543398i | ||||
\(671\) | −5440.88 | −0.313030 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13858.0 | −0.793739 | −0.396870 | − | 0.917875i | \(-0.629904\pi\) | ||||
−0.396870 | + | 0.917875i | \(0.629904\pi\) | |||||||
\(674\) | −250.000 | + | 433.013i | −0.0142873 | + | 0.0247463i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4230.00 | − | 7326.57i | −0.240669 | − | 0.416851i | ||||
\(677\) | 16224.1 | − | 28101.0i | 0.921041 | − | 1.59529i | 0.123233 | − | 0.992378i | \(-0.460674\pi\) |
0.797808 | − | 0.602912i | \(-0.205993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4224.00 | −0.238210 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4127.57 | + | 7149.15i | 0.231749 | + | 0.401401i | ||||
\(683\) | −13906.0 | − | 24085.9i | −0.779060 | − | 1.34937i | −0.932484 | − | 0.361212i | \(-0.882363\pi\) |
0.153423 | − | 0.988161i | \(-0.450970\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10450.2 | −0.582895 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3488.00 | + | 6041.39i | −0.193283 | + | 0.334776i | ||||
\(689\) | 2035.64 | + | 3525.83i | 0.112557 | + | 0.194954i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 651.968 | − | 1129.24i | 0.0358929 | − | 0.0621684i | −0.847521 | − | 0.530762i | \(-0.821906\pi\) |
0.883414 | + | 0.468594i | \(0.155239\pi\) | |||||||
\(692\) | −2664.16 | −0.146353 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19080.0 | 1.04361 | ||||||||
\(695\) | 6468.00 | − | 11202.9i | 0.353015 | − | 0.611439i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11088.0 | − | 19205.0i | −0.602565 | − | 1.04367i | ||||
\(698\) | −5712.93 | + | 9895.08i | −0.309796 | + | 0.536582i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22906.0 | −1.23416 | −0.617081 | − | 0.786900i | \(-0.711685\pi\) | ||||
−0.617081 | + | 0.786900i | \(0.711685\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 365.852 | + | 633.675i | 0.0196279 | + | 0.0339965i | ||||
\(704\) | 640.000 | + | 1108.51i | 0.0342627 | + | 0.0593447i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8780.46 | 0.468069 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7543.00 | − | 13064.9i | 0.399553 | − | 0.692047i | −0.594117 | − | 0.804378i | \(-0.702499\pi\) |
0.993671 | + | 0.112332i | \(0.0358319\pi\) | |||||||
\(710\) | −5103.17 | − | 8838.95i | −0.269745 | − | 0.467211i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6003.73 | − | 10398.8i | 0.316010 | − | 0.547346i | ||||
\(713\) | 9906.16 | 0.520321 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12320.0 | 0.644394 | ||||||||
\(716\) | −6456.00 | + | 11182.1i | −0.336972 | + | 0.583653i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1840.00 | − | 3186.97i | −0.0956381 | − | 0.165650i | ||||
\(719\) | −10272.0 | + | 17791.6i | −0.532797 | + | 0.922832i | 0.466469 | + | 0.884538i | \(0.345526\pi\) |
−0.999266 | + | 0.0382947i | \(0.987807\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13542.0 | 0.698035 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5647.26 | + | 9781.34i | 0.289888 | + | 0.502100i | ||||
\(725\) | 3071.00 | + | 5319.13i | 0.157316 | + | 0.272479i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7223.24 | −0.368494 | −0.184247 | − | 0.982880i | \(-0.558985\pi\) | ||||
−0.184247 | + | 0.982880i | \(0.558985\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5632.00 | − | 9754.91i | 0.285547 | − | 0.494583i | ||||
\(731\) | 12270.1 | + | 21252.5i | 0.620830 | + | 1.07531i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14713.8 | + | 25485.1i | −0.741430 | + | 1.28419i | 0.210415 | + | 0.977612i | \(0.432519\pi\) |
−0.951844 | + | 0.306581i | \(0.900815\pi\) | |||||||
\(734\) | 5928.69 | 0.298136 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1536.00 | 0.0769262 | ||||||||
\(737\) | 5800.00 | − | 10045.9i | 0.289886 | − | 0.502097i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16334.0 | − | 28291.3i | −0.813066 | − | 1.40827i | −0.910708 | − | 0.413050i | \(-0.864463\pi\) |
0.0976420 | − | 0.995222i | \(-0.468870\pi\) | |||||||
\(740\) | −1463.41 | + | 2534.70i | −0.0726973 | + | 0.125915i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37056.0 | 1.82968 | 0.914840 | − | 0.403816i | \(-0.132316\pi\) | ||||
0.914840 | + | 0.403816i | \(0.132316\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4437.13 | + | 7685.34i | 0.218207 | + | 0.377945i | ||||
\(746\) | 3982.00 | + | 6897.03i | 0.195431 | + | 0.338496i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4502.80 | 0.220105 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9804.00 | − | 16981.0i | 0.476369 | − | 0.825095i | −0.523265 | − | 0.852170i | \(-0.675286\pi\) |
0.999633 | + | 0.0270752i | \(0.00861935\pi\) | |||||||
\(752\) | 1651.03 | + | 2859.66i | 0.0800621 | + | 0.138672i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10900.5 | − | 18880.3i | 0.526490 | − | 0.911908i | ||||
\(755\) | −7804.85 | −0.376222 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19378.0 | 0.930390 | 0.465195 | − | 0.885208i | \(-0.345984\pi\) | ||||
0.465195 | + | 0.885208i | \(0.345984\pi\) | |||||||
\(758\) | 2676.00 | − | 4634.97i | 0.128228 | − | 0.222097i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −352.000 | − | 609.682i | −0.0168005 | − | 0.0290993i | ||||
\(761\) | −6988.72 | + | 12104.8i | −0.332905 | + | 0.576609i | −0.983080 | − | 0.183176i | \(-0.941362\pi\) |
0.650175 | + | 0.759785i | \(0.274696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8544.00 | 0.404596 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7035.62 | − | 12186.1i | −0.331863 | − | 0.574804i | ||||
\(767\) | −21868.0 | − | 37876.5i | −1.02948 | − | 1.78310i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8536.56 | 0.400307 | 0.200154 | − | 0.979765i | \(-0.435856\pi\) | ||||
0.200154 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3316.00 | + | 5743.48i | −0.154593 | + | 0.267762i | ||||
\(773\) | −14648.2 | − | 25371.4i | −0.681576 | − | 1.18052i | −0.974500 | − | 0.224388i | \(-0.927962\pi\) |
0.292924 | − | 0.956136i | \(-0.405372\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3818.00 | + | 6612.97i | −0.176963 | + | 0.306509i | ||||
\(776\) | 5253.27 | 0.243017 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17316.0 | 0.797955 | ||||||||
\(779\) | 1848.00 | − | 3200.83i | 0.0849955 | − | 0.147216i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5440.00 | + | 9422.36i | 0.249243 | + | 0.431701i | ||||
\(782\) | 2701.68 | − | 4679.45i | 0.123545 | − | 0.213985i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −27016.0 | −1.22833 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6890.22 | − | 11934.2i | −0.312084 | − | 0.540545i | 0.666730 | − | 0.745300i | \(-0.267694\pi\) |
−0.978813 | + | 0.204755i | \(0.934360\pi\) | |||||||
\(788\) | −1956.00 | − | 3387.89i | −0.0884259 | − | 0.153158i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12757.9 | −0.574566 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8932.00 | + | 15470.7i | −0.399981 | + | 0.692787i | ||||
\(794\) | −9052.50 | − | 15679.4i | −0.404611 | − | 0.700807i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9868.63 | − | 17093.0i | 0.439428 | − | 0.761111i | ||||
\(797\) | 34868.6 | 1.54970 | 0.774848 | − | 0.632148i | \(-0.217826\pi\) | ||||
0.774848 | + | 0.632148i | \(0.217826\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11616.0 | 0.514324 | ||||||||
\(800\) | −592.000 | + | 1025.37i | −0.0261630 | + | 0.0453156i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5706.00 | + | 9883.08i | 0.251229 | + | 0.435142i | ||||
\(803\) | −6003.73 | + | 10398.8i | −0.263844 | + | 0.456992i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 27104.0 | 1.18449 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −487.803 | − | 844.900i | −0.0212387 | − | 0.0367865i | ||||
\(809\) | 7017.00 | + | 12153.8i | 0.304950 | + | 0.528189i | 0.977250 | − | 0.212090i | \(-0.0680269\pi\) |
−0.672300 | + | 0.740279i | \(0.734694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6632.25 | −0.287164 | −0.143582 | − | 0.989638i | \(-0.545862\pi\) | ||||
−0.143582 | + | 0.989638i | \(0.545862\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1560.00 | − | 2702.00i | 0.0671720 | − | 0.116345i | ||||
\(815\) | 2983.10 | + | 5166.89i | 0.128213 | + | 0.222071i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2045.02 | + | 3542.08i | −0.0875719 | + | 0.151679i | ||||
\(818\) | −4840.51 | −0.206900 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14784.0 | 0.629609 | ||||||||
\(821\) | 14311.0 | − | 24787.4i | 0.608352 | − | 1.05370i | −0.383160 | − | 0.923682i | \(-0.625164\pi\) |
0.991512 | − | 0.130015i | \(-0.0415026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12344.0 | − | 21380.4i | −0.522825 | − | 0.905559i | −0.999647 | − | 0.0265595i | \(-0.991545\pi\) |
0.476822 | − | 0.879000i | \(-0.341788\pi\) | |||||||
\(824\) | −5478.41 | + | 9488.88i | −0.231613 | + | 0.401166i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30756.0 | 1.29322 | 0.646609 | − | 0.762822i | \(-0.276187\pi\) | ||||
0.646609 | + | 0.762822i | \(0.276187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11618.2 | − | 20123.2i | −0.486750 | − | 0.843075i | 0.513134 | − | 0.858308i | \(-0.328484\pi\) |
−0.999884 | + | 0.0152333i | \(0.995151\pi\) | |||||||
\(830\) | 1848.00 | + | 3200.83i | 0.0772832 | + | 0.133858i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4202.61 | 0.175119 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3080.00 | − | 5334.72i | 0.127650 | − | 0.221096i | ||||
\(836\) | 375.233 | + | 649.923i | 0.0155236 | + | 0.0268876i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1510.31 | − | 2615.94i | 0.0622589 | − | 0.107836i | ||||
\(839\) | 24033.7 | 0.988957 | 0.494479 | − | 0.869190i | \(-0.335359\pi\) | ||||
0.494479 | + | 0.869190i | \(0.335359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3167.00 | 0.129854 | ||||||||
\(842\) | −16770.0 | + | 29046.5i | −0.686380 | + | 1.18885i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3112.00 | − | 5390.14i | −0.126919 | − | 0.219830i | ||||
\(845\) | 9920.23 | − | 17182.3i | 0.403865 | − | 0.699515i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −992.000 | −0.0401715 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2082.54 | + | 3607.07i | 0.0840361 | + | 0.145555i | ||||
\(851\) | −1872.00 | − | 3242.40i | −0.0754070 | − | 0.130609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23574.0 | −0.946260 | −0.473130 | − | 0.880993i | \(-0.656876\pi\) | ||||
−0.473130 | + | 0.880993i | \(0.656876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1040.00 | − | 1801.33i | 0.0415262 | − | 0.0719256i | ||||
\(857\) | 12242.0 | + | 21203.7i | 0.487956 | + | 0.845164i | 0.999904 | − | 0.0138519i | \(-0.00440933\pi\) |
−0.511948 | + | 0.859016i | \(0.671076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16477.4 | − | 28539.7i | 0.654485 | − | 1.13360i | −0.327538 | − | 0.944838i | \(-0.606219\pi\) |
0.982023 | − | 0.188763i | \(-0.0604479\pi\) | |||||||
\(860\) | −16360.2 | −0.648694 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2672.00 | 0.105579 | ||||||||
\(863\) | 20436.0 | − | 35396.2i | 0.806083 | − | 1.39618i | −0.109475 | − | 0.993990i | \(-0.534917\pi\) |
0.915558 | − | 0.402187i | \(-0.131750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3124.00 | − | 5410.93i | −0.122797 | − | 0.212690i | ||||
\(866\) | −11163.2 | + | 19335.2i | −0.438038 | + | 0.758703i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13600.0 | 0.530896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19043.1 | − | 32983.6i | −0.740816 | − | 1.28313i | ||||
\(872\) | 7528.00 | + | 13038.9i | 0.292351 | + | 0.506367i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 900.560 | 0.0348534 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6003.00 | − | 10397.5i | 0.231137 | − | 0.400341i | −0.727006 | − | 0.686631i | \(-0.759089\pi\) |
0.958143 | + | 0.286290i | \(0.0924222\pi\) | |||||||
\(878\) | −3602.24 | − | 6239.26i | −0.138462 | − | 0.239823i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1500.93 | + | 2599.69i | −0.0574960 | + | 0.0995859i | ||||
\(881\) | −35722.2 | −1.36607 | −0.683037 | − | 0.730383i | \(-0.739341\pi\) | ||||
−0.683037 | + | 0.730383i | \(0.739341\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19588.0 | 0.746533 | 0.373267 | − | 0.927724i | \(-0.378238\pi\) | ||||
0.373267 | + | 0.927724i | \(0.378238\pi\) | |||||||
\(884\) | 7392.00 | − | 12803.3i | 0.281244 | − | 0.487129i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6348.00 | − | 10995.1i | −0.240706 | − | 0.416914i | ||||
\(887\) | −20121.9 | + | 34852.1i | −0.761699 | + | 1.31930i | 0.180276 | + | 0.983616i | \(0.442301\pi\) |
−0.941974 | + | 0.335685i | \(0.891032\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 28160.0 | 1.06059 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5778.59 | − | 10008.8i | −0.216908 | − | 0.375695i | ||||
\(893\) | 968.000 | + | 1676.63i | 0.0362742 | + | 0.0628288i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30281.3 | −1.13094 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7170.00 | + | 12418.8i | −0.266443 | + | 0.461493i | ||||
\(899\) | 17129.4 | + | 29669.0i | 0.635481 | + | 1.10069i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1744.83 | + | 3022.14i | −0.0645159 | + | 0.111745i | ||||
\(902\) | −15759.8 | −0.581756 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10288.0 | −0.378511 | ||||||||
\(905\) | −13244.0 | + | 22939.3i | −0.486459 | + | 0.842572i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7934.00 | − | 13742.1i | −0.290457 | − | 0.503086i | 0.683461 | − | 0.729987i | \(-0.260474\pi\) |
−0.973918 | + | 0.226901i | \(0.927141\pi\) | |||||||
\(908\) | −3958.71 | + | 6856.69i | −0.144686 | + | 0.250603i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39832.0 | −1.44862 | −0.724310 | − | 0.689474i | \(-0.757842\pi\) | ||||
−0.724310 | + | 0.689474i | \(0.757842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1969.97 | − | 3412.10i | −0.0714092 | − | 0.123684i | ||||
\(914\) | 6866.00 | + | 11892.3i | 0.248476 | + | 0.430373i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 11069.4 | 0.399282 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15264.0 | − | 26438.0i | 0.547892 | − | 0.948977i | −0.450527 | − | 0.892763i | \(-0.648764\pi\) |
0.998419 | − | 0.0562141i | \(-0.0179029\pi\) | |||||||
\(920\) | 1801.12 | + | 3119.63i | 0.0645447 | + | 0.111795i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1378.98 | + | 2388.47i | −0.0492564 | + | 0.0853145i | ||||
\(923\) | 35722.2 | 1.27390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2886.00 | 0.102585 | ||||||||
\(926\) | 2648.00 | − | 4586.47i | 0.0939727 | − | 0.162765i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2656.00 | + | 4600.33i | 0.0939520 | + | 0.162730i | ||||
\(929\) | −8302.04 | + | 14379.5i | −0.293198 | + | 0.507834i | −0.974564 | − | 0.224109i | \(-0.928053\pi\) |
0.681366 | + | 0.731943i | \(0.261386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 25960.0 | 0.912391 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 12335.8 | + | 21366.2i | 0.432162 | + | 0.748527i | ||||
\(935\) | 5280.00 | + | 9145.23i | 0.184679 | + | 0.319873i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29943.6 | 1.04399 | 0.521993 | − | 0.852950i | \(-0.325189\pi\) | ||||
0.521993 | + | 0.852950i | \(0.325189\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3872.00 | + | 6706.50i | −0.134352 | + | 0.232704i | ||||
\(941\) | 2687.61 | + | 4655.07i | 0.0931068 | + | 0.161266i | 0.908817 | − | 0.417195i | \(-0.136987\pi\) |
−0.815710 | + | 0.578461i | \(0.803654\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9455.88 | + | 16378.1i | −0.326538 | + | 0.565581i | ||||
\(944\) | 10656.6 | 0.367419 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17440.0 | 0.599390 | ||||||||
\(947\) | 22606.0 | − | 39154.7i | 0.775709 | − | 1.34357i | −0.158686 | − | 0.987329i | \(-0.550726\pi\) |
0.934395 | − | 0.356238i | \(-0.115941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19712.0 | + | 34142.2i | 0.674266 | + | 1.16786i | ||||
\(950\) | −347.091 | + | 601.179i | −0.0118538 | + | 0.0205314i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34218.0 | −1.16310 | −0.581548 | − | 0.813512i | \(-0.697553\pi\) | ||||
−0.581548 | + | 0.813512i | \(0.697553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10018.7 | + | 17352.9i | 0.339475 | + | 0.587988i | ||||
\(956\) | −8592.00 | − | 14881.8i | −0.290675 | − | 0.503464i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26679.1 | −0.899752 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6400.50 | + | 11086.0i | −0.214847 | + | 0.372126i | ||||
\(962\) | −5121.93 | − | 8871.45i | −0.171661 | − | 0.297325i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9043.12 | + | 15663.1i | −0.302136 | + | 0.523315i | ||||
\(965\) | −15553.4 | −0.518842 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14464.0 | 0.481004 | 0.240502 | − | 0.970649i | \(-0.422688\pi\) | ||||
0.240502 | + | 0.970649i | \(0.422688\pi\) | |||||||
\(968\) | −3724.00 | + | 6450.16i | −0.123651 | + | 0.214169i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6160.00 | + | 10669.4i | 0.203903 | + | 0.353170i | ||||
\(971\) | 18916.4 | − | 32764.2i | 0.625188 | − | 1.08286i | −0.363316 | − | 0.931666i | \(-0.618356\pi\) |
0.988504 | − | 0.151192i | \(-0.0483111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −27872.0 | −0.916916 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2176.35 | − | 3769.55i | −0.0713764 | − | 0.123628i | ||||
\(977\) | 21031.0 | + | 36426.8i | 0.688681 | + | 1.19283i | 0.972265 | + | 0.233883i | \(0.0751433\pi\) |
−0.283584 | + | 0.958947i | \(0.591523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30018.7 | −0.979980 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12276.0 | − | 21262.7i | 0.398924 | − | 0.690956i | ||||
\(983\) | −21510.2 | − | 37256.8i | −0.697935 | − | 1.20886i | −0.969181 | − | 0.246349i | \(-0.920769\pi\) |
0.271246 | − | 0.962510i | \(-0.412564\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4587.23 | − | 7945.31i | 0.148387 | − | 0.257014i | ||||
\(986\) | 18686.6 | 0.603553 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2464.00 | 0.0793424 | ||||||||
\(989\) | 10464.0 | − | 18124.2i | 0.336437 | − | 0.582725i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10636.0 | − | 18422.1i | −0.340932 | − | 0.590512i | 0.643674 | − | 0.765300i | \(-0.277409\pi\) |
−0.984606 | + | 0.174788i | \(0.944076\pi\) | |||||||
\(992\) | −3302.05 | + | 5719.32i | −0.105686 | + | 0.183053i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46288.0 | 1.47480 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.9754 | − | 105.612i | −0.00193692 | − | 0.00335485i | 0.865055 | − | 0.501676i | \(-0.167283\pi\) |
−0.866992 | + | 0.498322i | \(0.833950\pi\) | |||||||
\(998\) | −2220.00 | − | 3845.15i | −0.0704137 | − | 0.121960i | ||||
\(999\) | 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 | 882.4.g.bi.667.2 | 4 | ||
3.2 | odd | 2 | 98.4.c.g.79.2 | 4 | |||
7.2 | even | 3 | 882.4.a.w.1.1 | 2 | |||
7.3 | odd | 6 | inner | 882.4.g.bi.361.1 | 4 | ||
7.4 | even | 3 | inner | 882.4.g.bi.361.2 | 4 | ||
7.5 | odd | 6 | 882.4.a.w.1.2 | 2 | |||
7.6 | odd | 2 | inner | 882.4.g.bi.667.1 | 4 | ||
21.2 | odd | 6 | 98.4.a.h.1.1 | ✓ | 2 | ||
21.5 | even | 6 | 98.4.a.h.1.2 | yes | 2 | ||
21.11 | odd | 6 | 98.4.c.g.67.2 | 4 | |||
21.17 | even | 6 | 98.4.c.g.67.1 | 4 | |||
21.20 | even | 2 | 98.4.c.g.79.1 | 4 | |||
84.23 | even | 6 | 784.4.a.z.1.2 | 2 | |||
84.47 | odd | 6 | 784.4.a.z.1.1 | 2 | |||
105.44 | odd | 6 | 2450.4.a.bs.1.2 | 2 | |||
105.89 | even | 6 | 2450.4.a.bs.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.4.a.h.1.1 | ✓ | 2 | 21.2 | odd | 6 | ||
98.4.a.h.1.2 | yes | 2 | 21.5 | even | 6 | ||
98.4.c.g.67.1 | 4 | 21.17 | even | 6 | |||
98.4.c.g.67.2 | 4 | 21.11 | odd | 6 | |||
98.4.c.g.79.1 | 4 | 21.20 | even | 2 | |||
98.4.c.g.79.2 | 4 | 3.2 | odd | 2 | |||
784.4.a.z.1.1 | 2 | 84.47 | odd | 6 | |||
784.4.a.z.1.2 | 2 | 84.23 | even | 6 | |||
882.4.a.w.1.1 | 2 | 7.2 | even | 3 | |||
882.4.a.w.1.2 | 2 | 7.5 | odd | 6 | |||
882.4.g.bi.361.1 | 4 | 7.3 | odd | 6 | inner | ||
882.4.g.bi.361.2 | 4 | 7.4 | even | 3 | inner | ||
882.4.g.bi.667.1 | 4 | 7.6 | odd | 2 | inner | ||
882.4.g.bi.667.2 | 4 | 1.1 | even | 1 | trivial | ||
2450.4.a.bs.1.1 | 2 | 105.89 | even | 6 | |||
2450.4.a.bs.1.2 | 2 | 105.44 | odd | 6 |