Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,6,Mod(143,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.143");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.n (of order \(4\), degree \(2\), 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: | \(64.1535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 271 x^{18} + 109637 x^{16} + 25993614 x^{14} + 5522961902 x^{12} + 881545050522 x^{10} + \cdots + 57\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{67}\cdot 3^{4}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 143.5 | ||
Root | \(-1.99079 + 10.4027i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.143 |
Dual form | 400.6.n.g.207.5 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.839817 | + | 0.839817i | −0.0538743 | + | 0.0538743i | −0.733531 | − | 0.679656i | \(-0.762129\pi\) |
0.679656 | + | 0.733531i | \(0.262129\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 99.3589 | + | 99.3589i | 0.766411 | + | 0.766411i | 0.977473 | − | 0.211062i | \(-0.0676921\pi\) |
−0.211062 | + | 0.977473i | \(0.567692\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 241.589i | 0.994195i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 637.781i | 1.58924i | 0.607107 | + | 0.794620i | \(0.292330\pi\) | ||||
−0.607107 | + | 0.794620i | \(0.707670\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 640.389 | + | 640.389i | 1.05096 | + | 1.05096i | 0.998630 | + | 0.0523281i | \(0.0166641\pi\) |
0.0523281 | + | 0.998630i | \(0.483336\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −648.760 | + | 648.760i | −0.544455 | + | 0.544455i | −0.924832 | − | 0.380377i | \(-0.875794\pi\) |
0.380377 | + | 0.924832i | \(0.375794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2506.12 | −1.59264 | −0.796321 | − | 0.604874i | \(-0.793224\pi\) | ||||
−0.796321 | + | 0.604874i | \(0.793224\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −166.887 | −0.0825797 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2801.60 | − | 2801.60i | 1.10430 | − | 1.10430i | 0.110413 | − | 0.993886i | \(-0.464783\pi\) |
0.993886 | − | 0.110413i | \(-0.0352174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −406.966 | − | 406.966i | −0.107436 | − | 0.107436i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4955.21i | − | 1.09413i | −0.837091 | − | 0.547063i | \(-0.815746\pi\) | ||
0.837091 | − | 0.547063i | \(-0.184254\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1961.18i | 0.366533i | 0.983063 | + | 0.183267i | \(0.0586672\pi\) | ||||
−0.983063 | + | 0.183267i | \(0.941333\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −535.619 | − | 535.619i | −0.0856192 | − | 0.0856192i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1897.88 | − | 1897.88i | 0.227911 | − | 0.227911i | −0.583909 | − | 0.811819i | \(-0.698477\pi\) |
0.811819 | + | 0.583909i | \(0.198477\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1075.62 | −0.113239 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5828.95 | −0.541540 | −0.270770 | − | 0.962644i | \(-0.587278\pi\) | ||||
−0.270770 | + | 0.962644i | \(0.587278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10692.1 | + | 10692.1i | −0.881844 | + | 0.881844i | −0.993722 | − | 0.111878i | \(-0.964314\pi\) |
0.111878 | + | 0.993722i | \(0.464314\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8309.52 | + | 8309.52i | 0.548695 | + | 0.548695i | 0.926063 | − | 0.377368i | \(-0.123171\pi\) |
−0.377368 | + | 0.926063i | \(0.623171\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2937.38i | 0.174771i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1089.68i | − | 0.0586642i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7437.17 | − | 7437.17i | −0.363679 | − | 0.363679i | 0.501487 | − | 0.865165i | \(-0.332787\pi\) |
−0.865165 | + | 0.501487i | \(0.832787\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2104.68 | − | 2104.68i | 0.0858025 | − | 0.0858025i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16738.4 | 0.626014 | 0.313007 | − | 0.949751i | \(-0.398664\pi\) | ||||
0.313007 | + | 0.949751i | \(0.398664\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23742.5 | 0.816961 | 0.408481 | − | 0.912767i | \(-0.366059\pi\) | ||||
0.408481 | + | 0.912767i | \(0.366059\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −24004.1 | + | 24004.1i | −0.761962 | + | 0.761962i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4154.05 | + | 4154.05i | 0.113054 | + | 0.113054i | 0.761371 | − | 0.648317i | \(-0.224527\pi\) |
−0.648317 | + | 0.761371i | \(0.724527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4705.66i | 0.118987i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12276.0i | − | 0.289008i | −0.989504 | − | 0.144504i | \(-0.953841\pi\) | ||
0.989504 | − | 0.144504i | \(-0.0461587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −36092.8 | − | 36092.8i | −0.792709 | − | 0.792709i | 0.189225 | − | 0.981934i | \(-0.439402\pi\) |
−0.981934 | + | 0.189225i | \(0.939402\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −63369.2 | + | 63369.2i | −1.21801 | + | 1.21801i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64330.4 | −1.15971 | −0.579854 | − | 0.814721i | \(-0.696890\pi\) | ||||
−0.579854 | + | 0.814721i | \(0.696890\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −58022.7 | −0.982619 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −62856.9 | + | 62856.9i | −1.00152 | + | 1.00152i | −0.00151672 | + | 0.999999i | \(0.500483\pi\) |
−0.999999 | + | 0.00151672i | \(0.999517\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4161.47 | + | 4161.47i | 0.0589453 | + | 0.0589453i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 24423.5i | − | 0.326838i | −0.986557 | − | 0.163419i | \(-0.947748\pi\) | ||
0.986557 | − | 0.163419i | \(-0.0522523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 127257.i | 1.61093i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1647.03 | − | 1647.03i | −0.0197467 | − | 0.0197467i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 89666.0 | − | 89666.0i | 0.967605 | − | 0.967605i | −0.0318862 | − | 0.999492i | \(-0.510151\pi\) |
0.999492 | + | 0.0318862i | \(0.0101514\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −154081. | −1.58002 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 31536.0 | 0.307612 | 0.153806 | − | 0.988101i | \(-0.450847\pi\) | ||||
0.153806 | + | 0.988101i | \(0.450847\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4384.20 | − | 4384.20i | 0.0407190 | − | 0.0407190i | −0.686454 | − | 0.727173i | \(-0.740834\pi\) |
0.727173 | + | 0.686454i | \(0.240834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 150691. | + | 150691.i | 1.27241 | + | 1.27241i | 0.944820 | + | 0.327589i | \(0.106236\pi\) |
0.327589 | + | 0.944820i | \(0.393764\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 201206.i | − | 1.62209i | −0.584984 | − | 0.811045i | \(-0.698899\pi\) | ||
0.584984 | − | 0.811045i | \(-0.301101\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3187.75i | 0.0245571i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 25930.0 | + | 25930.0i | 0.191032 | + | 0.191032i | 0.796142 | − | 0.605110i | \(-0.206871\pi\) |
−0.605110 | + | 0.796142i | \(0.706871\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −154711. | + | 154711.i | −1.04486 | + | 1.04486i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −128920. | −0.834552 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −245713. | −1.52569 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4895.25 | − | 4895.25i | 0.0291751 | − | 0.0291751i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 46278.8 | + | 46278.8i | 0.254609 | + | 0.254609i | 0.822857 | − | 0.568248i | \(-0.192379\pi\) |
−0.568248 | + | 0.822857i | \(0.692379\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 17958.8i | − | 0.0950175i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 83739.0i | 0.426333i | 0.977016 | + | 0.213167i | \(0.0683777\pi\) | ||||
−0.977016 | + | 0.213167i | \(0.931622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −249006. | − | 249006.i | −1.22062 | − | 1.22062i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −29275.6 | + | 29275.6i | −0.133261 | + | 0.133261i | −0.770591 | − | 0.637330i | \(-0.780039\pi\) |
0.637330 | + | 0.770591i | \(0.280039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 56681.4 | 0.248830 | 0.124415 | − | 0.992230i | \(-0.460295\pi\) | ||||
0.124415 | + | 0.992230i | \(0.460295\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13957.0 | −0.0591211 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −408428. | + | 408428.i | −1.67023 | + | 1.67023i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2466.86 | − | 2466.86i | −0.00941568 | − | 0.00941568i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 30050.0i | − | 0.110886i | −0.998462 | − | 0.0554432i | \(-0.982343\pi\) | ||
0.998462 | − | 0.0554432i | \(-0.0176572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 255984.i | 0.913631i | 0.889561 | + | 0.456816i | \(0.151010\pi\) | ||||
−0.889561 | + | 0.456816i | \(0.848990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −156734. | − | 156734.i | −0.541294 | − | 0.541294i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −30035.3 | + | 30035.3i | −0.0972486 | + | 0.0972486i | −0.754057 | − | 0.656809i | \(-0.771906\pi\) |
0.656809 | + | 0.754057i | \(0.271906\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12491.7 | 0.0391859 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 556728. | 1.69269 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −397588. | + | 397588.i | −1.17210 | + | 1.17210i | −0.190391 | + | 0.981708i | \(0.560976\pi\) |
−0.981708 | + | 0.190391i | \(0.939024\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 162249. | + | 162249.i | 0.450185 | + | 0.450185i | 0.895416 | − | 0.445231i | \(-0.146878\pi\) |
−0.445231 | + | 0.895416i | \(0.646878\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 448903.i | 1.20903i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 605453.i | − | 1.58340i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 158564. | + | 158564.i | 0.402800 | + | 0.402800i | 0.879219 | − | 0.476419i | \(-0.158065\pi\) |
−0.476419 | + | 0.879219i | \(0.658065\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14057.2 | + | 14057.2i | −0.0337261 | + | 0.0337261i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −509602. | −1.18877 | −0.594386 | − | 0.804180i | \(-0.702605\pi\) | ||||
−0.594386 | + | 0.804180i | \(0.702605\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −356971. | −0.809910 | −0.404955 | − | 0.914337i | \(-0.632713\pi\) | ||||
−0.404955 | + | 0.914337i | \(0.632713\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19939.3 | + | 19939.3i | −0.0440132 | + | 0.0440132i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −413767. | − | 413767.i | −0.865270 | − | 0.865270i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 80871.5i | − | 0.164680i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 296067.i | 0.587227i | 0.955924 | + | 0.293614i | \(0.0948579\pi\) | ||||
−0.955924 | + | 0.293614i | \(0.905142\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10953.8 | − | 10953.8i | −0.0211676 | − | 0.0211676i | 0.696444 | − | 0.717611i | \(-0.254765\pi\) |
−0.717611 | + | 0.696444i | \(0.754765\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 153834. | − | 153834.i | 0.282415 | − | 0.282415i | −0.551656 | − | 0.834071i | \(-0.686004\pi\) |
0.834071 | + | 0.551656i | \(0.186004\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 415211. | 0.743252 | 0.371626 | − | 0.928383i | \(-0.378800\pi\) | ||||
0.371626 | + | 0.928383i | \(0.378800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6977.28 | −0.0121814 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 492345. | − | 492345.i | 0.838550 | − | 0.838550i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 676837. | + | 676837.i | 1.09789 | + | 1.09789i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.59836e6i | − | 2.53109i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 673870.i | 1.04200i | 0.853555 | + | 0.521002i | \(0.174442\pi\) | ||||
−0.853555 | + | 0.521002i | \(0.825558\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10309.6 | + | 10309.6i | 0.0155701 | + | 0.0155701i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −194861. | + | 194861.i | −0.280915 | + | 0.280915i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 60622.7 | 0.0854132 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −830917. | −1.14440 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 916244. | − | 916244.i | 1.23381 | − | 1.23381i | 0.271323 | − | 0.962488i | \(-0.412539\pi\) |
0.962488 | − | 0.271323i | \(-0.0874611\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 317650. | + | 317650.i | 0.409152 | + | 0.409152i | 0.881443 | − | 0.472291i | \(-0.156573\pi\) |
−0.472291 | + | 0.881443i | \(0.656573\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.15003e6i | 1.44917i | 0.689183 | + | 0.724587i | \(0.257970\pi\) | ||||
−0.689183 | + | 0.724587i | \(0.742030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 106437.i | − | 0.131239i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −290928. | − | 290928.i | −0.351071 | − | 0.351071i | 0.509437 | − | 0.860508i | \(-0.329854\pi\) |
−0.860508 | + | 0.509437i | \(0.829854\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 54025.7 | − | 54025.7i | 0.0624784 | − | 0.0624784i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −152082. | −0.172220 | −0.0861101 | − | 0.996286i | \(-0.527444\pi\) | ||||
−0.0861101 | + | 0.996286i | \(0.527444\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 43181.5 | 0.0478912 | 0.0239456 | − | 0.999713i | \(-0.492377\pi\) | ||||
0.0239456 | + | 0.999713i | \(0.492377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 147621. | − | 147621.i | 0.160374 | − | 0.160374i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.60489e6 | − | 1.60489e6i | −1.67380 | − | 1.67380i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 105577.i | − | 0.107912i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 547660.i | − | 0.548689i | −0.961631 | − | 0.274345i | \(-0.911539\pi\) | ||
0.961631 | − | 0.274345i | \(-0.0884609\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.78681e6 | + | 1.78681e6i | 1.75500 | + | 1.75500i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 226438. | − | 226438.i | 0.213853 | − | 0.213853i | −0.592049 | − | 0.805902i | \(-0.701681\pi\) |
0.805902 | + | 0.592049i | \(0.201681\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 377143. | 0.349347 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.19713e6 | 1.08778 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21617.3 | + | 21617.3i | −0.0192714 | + | 0.0192714i | −0.716677 | − | 0.697405i | \(-0.754338\pi\) |
0.697405 | + | 0.716677i | \(0.254338\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20511.3 | + | 20511.3i | 0.0176082 | + | 0.0176082i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.78124e6i | 1.50087i | 0.660947 | + | 0.750433i | \(0.270155\pi\) | ||||
−0.660947 | + | 0.750433i | \(0.729845\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.45155e6i | − | 1.20063i | −0.799765 | − | 0.600314i | \(-0.795042\pi\) | ||
0.799765 | − | 0.600314i | \(-0.204958\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −106872. | − | 106872.i | −0.0867878 | − | 0.0867878i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 831788. | − | 831788.i | 0.651348 | − | 0.651348i | −0.301969 | − | 0.953318i | \(-0.597644\pi\) |
0.953318 | + | 0.301969i | \(0.0976441\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −473801. | −0.364406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.43146e6 | 1.83696 | 0.918482 | − | 0.395463i | \(-0.129416\pi\) | ||||
0.918482 | + | 0.395463i | \(0.129416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 141203. | − | 141203.i | 0.104804 | − | 0.104804i | −0.652760 | − | 0.757565i | \(-0.726389\pi\) |
0.757565 | + | 0.652760i | \(0.226389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −579158. | − | 579158.i | −0.415042 | − | 0.415042i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 578078.i | 0.407138i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 150606.i | 0.104258i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −540576. | − | 540576.i | −0.367864 | − | 0.367864i | 0.498834 | − | 0.866698i | \(-0.333762\pi\) |
−0.866698 | + | 0.498834i | \(0.833762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 259555. | − | 259555.i | 0.170741 | − | 0.170741i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.58823e6 | 2.32114 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.12471e6 | −1.35171 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26484.5 | + | 26484.5i | −0.0165724 | + | 0.0165724i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −779170. | − | 779170.i | −0.471831 | − | 0.471831i | 0.430676 | − | 0.902507i | \(-0.358275\pi\) |
−0.902507 | + | 0.430676i | \(0.858275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7363.86i | 0.00438742i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.56490e6i | − | 0.917459i | −0.888576 | − | 0.458730i | \(-0.848305\pi\) | ||
0.888576 | − | 0.458730i | \(-0.151695\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −684828. | − | 684828.i | −0.395112 | − | 0.395112i | 0.481393 | − | 0.876505i | \(-0.340131\pi\) |
−0.876505 | + | 0.481393i | \(0.840131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.90957e6 | + | 1.90957e6i | −1.06730 | + | 1.06730i | −0.0697372 | + | 0.997565i | \(0.522216\pi\) |
−0.997565 | + | 0.0697372i | \(0.977784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.16034e6 | 1.73883 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −253105. | −0.137100 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.62587e6 | − | 1.62587e6i | 0.867122 | − | 0.867122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 168976. | + | 168976.i | 0.0873890 | + | 0.0873890i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.65125e6i | 0.841052i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 740425.i | 0.371459i | 0.982601 | + | 0.185730i | \(0.0594649\pi\) | ||||
−0.982601 | + | 0.185730i | \(0.940535\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 458508. | + | 458508.i | 0.226588 | + | 0.226588i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.17170e6 | − | 2.17170e6i | 1.04166 | − | 1.04166i | 0.0425641 | − | 0.999094i | \(-0.486447\pi\) |
0.999094 | − | 0.0425641i | \(-0.0135527\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −43553.0 | −0.0205835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.25080e6 | −0.582510 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.37807e6 | − | 1.37807e6i | 0.632464 | − | 0.632464i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 706412. | + | 706412.i | 0.314945 | + | 0.314945i | 0.846822 | − | 0.531877i | \(-0.178513\pi\) |
−0.531877 | + | 0.846822i | \(0.678513\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.03307e6i | − | 1.33297i | −0.745520 | − | 0.666483i | \(-0.767799\pi\) | ||
0.745520 | − | 0.666483i | \(-0.232201\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 521234.i | − | 0.225821i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.72516e6 | + | 2.72516e6i | 1.16401 | + | 1.16401i | 0.983590 | + | 0.180418i | \(0.0577449\pi\) |
0.180418 | + | 0.983590i | \(0.442255\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 108269. | − | 108269.i | 0.0449609 | − | 0.0449609i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.47478e6 | −1.01345 | −0.506723 | − | 0.862109i | \(-0.669143\pi\) | ||||
−0.506723 | + | 0.862109i | \(0.669143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.80455e6 | 1.53651 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 206354. | − | 206354.i | 0.0821953 | − | 0.0821953i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −405936. | − | 405936.i | −0.157323 | − | 0.157323i | 0.624056 | − | 0.781379i | \(-0.285484\pi\) |
−0.781379 | + | 0.624056i | \(0.785484\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1.40821e6i | − | 0.538397i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1.47790e6i | − | 0.557455i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 378559. | + | 378559.i | 0.140884 | + | 0.140884i | 0.774031 | − | 0.633147i | \(-0.218237\pi\) |
−0.633147 | + | 0.774031i | \(0.718237\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.17326e6 | − | 3.17326e6i | 1.14988 | − | 1.14988i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.91279e6 | −1.39923 | −0.699614 | − | 0.714521i | \(-0.746645\pi\) | ||||
−0.699614 | + | 0.714521i | \(0.746645\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −77731.5 | −0.0274337 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.53247e6 | − | 2.53247e6i | 0.882161 | − | 0.882161i | −0.111593 | − | 0.993754i | \(-0.535595\pi\) |
0.993754 | + | 0.111593i | \(0.0355952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.58310e6 | − | 2.58310e6i | −0.876725 | − | 0.876725i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.01392e6i | 1.00985i | 0.863163 | + | 0.504925i | \(0.168480\pi\) | ||||
−0.863163 | + | 0.504925i | \(0.831520\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.63513e6i | 1.20248i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −70325.4 | − | 70325.4i | −0.0229684 | − | 0.0229684i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.43650e6 | + | 3.43650e6i | −1.09431 | + | 1.09431i | −0.0992459 | + | 0.995063i | \(0.531643\pi\) |
−0.995063 | + | 0.0992459i | \(0.968357\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 418238. | 0.131520 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.30306e6 | −1.33634 | −0.668169 | − | 0.744009i | \(-0.732922\pi\) | ||||
−0.668169 | + | 0.744009i | \(0.732922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.25592e6 | + | 1.25592e6i | −0.385211 | + | 0.385211i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.21043e6 | + | 1.21043e6i | 0.362205 | + | 0.362205i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 452926.i | 0.133881i | 0.997757 | + | 0.0669405i | \(0.0213238\pi\) | ||||
−0.997757 | + | 0.0669405i | \(0.978676\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 49172.2i | − | 0.0143587i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.66311e6 | + | 1.66311e6i | 0.479784 | + | 0.479784i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −47602.0 | + | 47602.0i | −0.0134056 | + | 0.0134056i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 448753. | 0.124874 | 0.0624370 | − | 0.998049i | \(-0.480113\pi\) | ||||
0.0624370 | + | 0.998049i | \(0.480113\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.61031e6 | 0.992748 | 0.496374 | − | 0.868109i | \(-0.334664\pi\) | ||||
0.496374 | + | 0.868109i | \(0.334664\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.00749e6 | + | 2.00749e6i | −0.545510 | + | 0.545510i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.35903e6 | + | 2.35903e6i | 0.626128 | + | 0.626128i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 686009.i | − | 0.179964i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.33480e6i | 0.864722i | 0.901701 | + | 0.432361i | \(0.142319\pi\) | ||||
−0.901701 | + | 0.432361i | \(0.857681\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.26797e6 | − | 4.26797e6i | −1.09396 | − | 1.09396i | −0.995101 | − | 0.0988602i | \(-0.968480\pi\) |
−0.0988602 | − | 0.995101i | \(-0.531520\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.02115e6 | + | 7.02115e6i | −1.75875 | + | 1.75875i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 985119. | 0.243965 | 0.121982 | − | 0.992532i | \(-0.461075\pi\) | ||||
0.121982 | + | 0.992532i | \(0.461075\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −709641. | −0.173757 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −941343. | + | 941343.i | −0.227897 | + | 0.227897i | −0.811814 | − | 0.583917i | \(-0.801519\pi\) |
0.583917 | + | 0.811814i | \(0.301519\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25236.5 | + | 25236.5i | 0.00597393 | + | 0.00597393i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 2.05024e6i | − | 0.479941i | −0.970780 | − | 0.239971i | \(-0.922862\pi\) | ||
0.970780 | − | 0.239971i | \(-0.0771378\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.71759e6i | − | 0.860638i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −214980. | − | 214980.i | −0.0492213 | − | 0.0492213i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.54554e6 | − | 5.54554e6i | 1.24209 | − | 1.24209i | 0.282958 | − | 0.959132i | \(-0.408684\pi\) |
0.959132 | − | 0.282958i | \(-0.0913157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 528047. | 0.116988 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.71258e6 | −0.813624 | −0.406812 | − | 0.913512i | \(-0.633360\pi\) | ||||
−0.406812 | + | 0.913512i | \(0.633360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.14889e6 | + | 4.14889e6i | −0.899455 | + | 0.899455i | −0.995388 | − | 0.0959328i | \(-0.969417\pi\) |
0.0959328 | + | 0.995388i | \(0.469417\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −599788. | − | 599788.i | −0.127264 | − | 0.127264i | 0.640606 | − | 0.767870i | \(-0.278683\pi\) |
−0.767870 | + | 0.640606i | \(0.778683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 825483.i | 0.173291i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 50448.4i | − | 0.0104784i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.81922e6 | − | 6.81922e6i | −1.40146 | − | 1.40146i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.79674e6 | − | 1.79674e6i | 0.361568 | − | 0.361568i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −130460. | −0.0259799 | −0.0129900 | − | 0.999916i | \(-0.504135\pi\) | ||||
−0.0129900 | + | 0.999916i | \(0.504135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.43077e6 | 0.479049 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −467550. | + | 467550.i | −0.0911927 | + | 0.0911927i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.53566e6 | + | 5.53566e6i | 1.05766 | + | 1.05766i | 0.998232 | + | 0.0594298i | \(0.0189283\pi\) |
0.0594298 | + | 0.998232i | \(0.481072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 667803.i | − | 0.126292i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.06198e6i | 0.385993i | 0.981199 | + | 0.192997i | \(0.0618206\pi\) | ||||
−0.981199 | + | 0.192997i | \(0.938179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.21474e6 | + | 3.21474e6i | 0.595702 | + | 0.595702i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.21973e6 | − | 1.21973e6i | 0.221499 | − | 0.221499i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.96927e6 | −0.713608 | −0.356804 | − | 0.934179i | \(-0.616134\pi\) | ||||
−0.356804 | + | 0.934179i | \(0.616134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −272519. | −0.0485068 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.68593e6 | + | 7.68593e6i | −1.35449 | + | 1.35449i | −0.473928 | + | 0.880564i | \(0.657164\pi\) |
−0.880564 | + | 0.473928i | \(0.842836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −376996. | − | 376996.i | −0.0651354 | − | 0.0651354i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 149834.i | 0.0256340i | 0.999918 | + | 0.0128170i | \(0.00407988\pi\) | ||||
−0.999918 | + | 0.0128170i | \(0.995920\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.17229e6i | − | 1.21508i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.01991e6 | + | 1.01991e6i | 0.171107 | + | 0.171107i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.29965e6 | + | 5.29965e6i | −0.872009 | + | 0.872009i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −266330. | −0.0434011 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.13714e6 | 0.183536 | 0.0917678 | − | 0.995780i | \(-0.470748\pi\) | ||||
0.0917678 | + | 0.995780i | \(0.470748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.86949e6 | + | 4.86949e6i | −0.778447 | + | 0.778447i | −0.979567 | − | 0.201119i | \(-0.935542\pi\) |
0.201119 | + | 0.979567i | \(0.435542\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.27234e6 | − | 1.27234e6i | −0.199561 | − | 0.199561i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9.26159e6i | − | 1.43895i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.04382e6i | 0.622380i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.73280e6 | − | 3.73280e6i | −0.569136 | − | 0.569136i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 427972. | − | 427972.i | 0.0640442 | − | 0.0640442i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.87341e6 | −0.277754 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.42771e6 | −0.944198 | −0.472099 | − | 0.881546i | \(-0.656503\pi\) | ||||
−0.472099 | + | 0.881546i | \(0.656503\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 299790. | − | 299790.i | 0.0436333 | − | 0.0436333i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.88980e6 | + | 6.88980e6i | 0.984551 | + | 0.984551i | 0.999882 | − | 0.0153314i | \(-0.00488033\pi\) |
−0.0153314 | + | 0.999882i | \(0.504880\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.73593e6i | 0.812219i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.24184e7i | 1.74255i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.39179e6 | − | 6.39179e6i | −0.888812 | − | 0.888812i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 626234. | − | 626234.i | 0.0855261 | − | 0.0855261i | −0.663049 | − | 0.748576i | \(-0.730738\pi\) |
0.748576 | + | 0.663049i | \(0.230738\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.36942e7 | −1.85356 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 694977. | 0.0932316 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.78102e6 | − | 3.78102e6i | 0.502733 | − | 0.502733i | −0.409553 | − | 0.912286i | \(-0.634315\pi\) |
0.912286 | + | 0.409553i | \(0.134315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.76507e6 | − | 5.76507e6i | −0.753090 | − | 0.753090i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.86991e6i | − | 0.760065i | −0.924973 | − | 0.380032i | \(-0.875913\pi\) | ||
0.924973 | − | 0.380032i | \(-0.124087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.63228e6i | 0.466218i | 0.972451 | + | 0.233109i | \(0.0748899\pi\) | ||||
−0.972451 | + | 0.233109i | \(0.925110\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −248642. | − | 248642.i | −0.0316365 | − | 0.0316365i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.85335e6 | + | 7.85335e6i | −0.982009 | + | 0.982009i | −0.999841 | − | 0.0178322i | \(-0.994324\pi\) |
0.0178322 | + | 0.999841i | \(0.494324\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 18398.4 | 0.00228078 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.24908e7 | −1.53514 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.74328e6 | − | 4.74328e6i | 0.577973 | − | 0.577973i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.62105e6 | + | 4.62105e6i | 0.553535 | + | 0.553535i | 0.927459 | − | 0.373924i | \(-0.121988\pi\) |
−0.373924 | + | 0.927459i | \(0.621988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.91496e6i | − | 0.583757i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 258386.i | 0.0304298i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.65088e6 | + | 6.65088e6i | 0.776681 | + | 0.776681i | 0.979265 | − | 0.202584i | \(-0.0649340\pi\) |
−0.202584 | + | 0.979265i | \(0.564934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −348701. | + | 348701.i | −0.0400422 | + | 0.0400422i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.31406e6 | −0.491269 | −0.245634 | − | 0.969363i | \(-0.578996\pi\) | ||||
−0.245634 | + | 0.969363i | \(0.578996\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43695e7 | 1.62277 | 0.811384 | − | 0.584513i | \(-0.198714\pi\) | ||||
0.811384 | + | 0.584513i | \(0.198714\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00357e6 | + | 1.00357e6i | −0.112397 | + | 0.112397i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 997962. | + | 997962.i | 0.109937 | + | 0.109937i | 0.759935 | − | 0.649999i | \(-0.225231\pi\) |
−0.649999 | + | 0.759935i | \(0.725231\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 826959.i | 0.0903526i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.06426e7i | 1.15331i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.18198e6 | + | 6.18198e6i | 0.664472 | + | 0.664472i | 0.956431 | − | 0.291959i | \(-0.0943071\pi\) |
−0.291959 | + | 0.956431i | \(0.594307\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 274155. | − | 274155.i | 0.0289924 | − | 0.0289924i | −0.692462 | − | 0.721454i | \(-0.743474\pi\) |
0.721454 | + | 0.692462i | \(0.243474\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.04395e7 | −1.09510 | −0.547549 | − | 0.836774i | \(-0.684439\pi\) | ||||
−0.547549 | + | 0.836774i | \(0.684439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.28031e6 | −0.237283 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.42669e6 | − | 2.42669e6i | 0.250492 | − | 0.250492i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.34233e6 | + | 1.34233e6i | 0.136361 | + | 0.136361i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.46254e6i | 0.248174i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.95332e7i | − | 1.95299i | −0.215544 | − | 0.976494i | \(-0.569152\pi\) | ||
0.215544 | − | 0.976494i | \(-0.430848\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −565927. | − | 565927.i | −0.0561373 | − | 0.0561373i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.88107e6 | + | 1.88107e6i | −0.183677 | + | 0.183677i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.96574e6 | 0.287330 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.16310e7 | 1.11808 | 0.559038 | − | 0.829142i | \(-0.311171\pi\) | ||||
0.559038 | + | 0.829142i | \(0.311171\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.86995e6 | + | 8.86995e6i | −0.846045 | + | 0.846045i | −0.989637 | − | 0.143592i | \(-0.954135\pi\) |
0.143592 | + | 0.989637i | \(0.454135\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.82351e6 | + | 7.82351e6i | 0.734752 | + | 0.734752i | 0.971557 | − | 0.236805i | \(-0.0761003\pi\) |
−0.236805 | + | 0.971557i | \(0.576100\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.06754e7i | 0.994887i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 327295.i | − | 0.0302682i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.80259e6 | + | 5.80259e6i | 0.532524 | + | 0.532524i | 0.921323 | − | 0.388799i | \(-0.127110\pi\) |
−0.388799 | + | 0.921323i | \(0.627110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.71964e6 | − | 8.71964e6i | 0.788107 | − | 0.788107i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.87531e7 | 1.68213 | 0.841065 | − | 0.540934i | \(-0.181929\pi\) | ||||
0.841065 | + | 0.540934i | \(0.181929\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.79645e7 | −1.59923 | −0.799615 | − | 0.600513i | \(-0.794963\pi\) | ||||
−0.799615 | + | 0.600513i | \(0.794963\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 697819. | − | 697819.i | 0.0616536 | − | 0.0616536i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.38825e7 | − | 1.38825e7i | −1.20824 | − | 1.20824i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.53895e6i | 0.132941i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.51425e7i | 1.29835i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.23479e7 | − | 1.23479e7i | −1.05089 | − | 1.05089i | −0.998634 | − | 0.0522545i | \(-0.983359\pi\) |
−0.0522545 | − | 0.998634i | \(-0.516641\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.66444e6 | − | 5.66444e6i | 0.474991 | − | 0.474991i | −0.428535 | − | 0.903525i | \(-0.640970\pi\) |
0.903525 | + | 0.428535i | \(0.140970\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.78182e7 | 1.48317 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −533536. | −0.0440855 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.21820e6 | + | 2.21820e6i | −0.181948 | + | 0.181948i | −0.792204 | − | 0.610256i | \(-0.791067\pi\) |
0.610256 | + | 0.792204i | \(0.291067\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −965815. | − | 965815.i | −0.0780732 | − | 0.0780732i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.52536e6i | − | 0.764422i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.63246e7i | − | 1.30061i | −0.759674 | − | 0.650304i | \(-0.774642\pi\) | ||
0.759674 | − | 0.650304i | \(-0.225358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.53093e7 | − | 1.53093e7i | −1.21094 | − | 1.21094i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.78159e6 | − | 3.78159e6i | 0.294844 | − | 0.294844i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 488652. | 0.0378274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.64161e7 | 1.26175 | 0.630876 | − | 0.775884i | \(-0.282696\pi\) | ||||
0.630876 | + | 0.775884i | \(0.282696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.75633e6 | + | 4.75633e6i | −0.362981 | + | 0.362981i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.13338e6 | + | 3.13338e6i | 0.235757 | + | 0.235757i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.37201e6i | 0.177215i | 0.996067 | + | 0.0886077i | \(0.0282417\pi\) | ||||
−0.996067 | + | 0.0886077i | \(0.971758\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.55415e7i | − | 1.15298i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.49445e6 | + | 5.49445e6i | 0.404762 | + | 0.404762i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 127721. | − | 127721.i | 0.00927824 | − | 0.00927824i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.62894e6 | 0.622494 | 0.311247 | − | 0.950329i | \(-0.399253\pi\) | ||||
0.311247 | + | 0.950329i | \(0.399253\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 871219. | 0.0624150 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −36264.6 | + | 36264.6i | −0.00258010 | + | 0.00258010i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.16170e7 | − | 1.16170e7i | −0.815187 | − | 0.815187i | 0.170219 | − | 0.985406i | \(-0.445552\pi\) |
−0.985406 | + | 0.170219i | \(0.945552\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.38516e7i | − | 0.965339i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.38732e7i | − | 0.960249i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.58933e6 | + | 7.58933e6i | 0.521727 | + | 0.521727i | 0.918093 | − | 0.396366i | \(-0.129729\pi\) |
−0.396366 | + | 0.918093i | \(0.629729\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.64937e6 | + | 2.64937e6i | −0.179669 | + | 0.179669i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.89099e6 | 0.127373 | 0.0636867 | − | 0.997970i | \(-0.479714\pi\) | ||||
0.0636867 | + | 0.997970i | \(0.479714\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.69563e6 | 0.180350 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.86435e7 | − | 1.86435e7i | 1.23895 | − | 1.23895i | 0.278523 | − | 0.960430i | \(-0.410155\pi\) |
0.960430 | − | 0.278523i | \(-0.0898447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.51856e7 | − | 1.51856e7i | −0.995702 | − | 0.995702i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.99449e7i | 1.95038i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.60302e6i | 0.297813i | 0.988851 | + | 0.148906i | \(0.0475753\pi\) | ||||
−0.988851 | + | 0.148906i | \(0.952425\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 459934. | + | 459934.i | 0.0295602 | + | 0.0295602i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.60445e6 | + | 6.60445e6i | −0.418887 | + | 0.418887i | −0.884820 | − | 0.465933i | \(-0.845719\pi\) |
0.465933 | + | 0.884820i | \(0.345719\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.00118e6 | −0.189098 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.76470e6 | −0.486030 | −0.243015 | − | 0.970023i | \(-0.578136\pi\) | ||||
−0.243015 | + | 0.970023i | \(0.578136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.99916e7 | − | 1.99916e7i | 1.24319 | − | 1.24319i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.07191e7 | + | 1.07191e7i | 0.657915 | + | 0.657915i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.03998e7i | 0.634172i | 0.948397 | + | 0.317086i | \(0.102704\pi\) | ||||
−0.948397 | + | 0.317086i | \(0.897296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 380332.i | 0.0230424i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.28295e7 | + | 2.28295e7i | 1.37419 | + | 1.37419i | 0.854125 | + | 0.520068i | \(0.174093\pi\) |
0.520068 | + | 0.854125i | \(0.325907\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −316731. | + | 316731.i | −0.0188208 | + | 0.0188208i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.46081e7 | 0.862480 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.82938e6 | 0.459303 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.01661e6 | + | 2.01661e6i | −0.117548 | + | 0.117548i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.72096e6 | − | 5.72096e6i | −0.329255 | − | 0.329255i | 0.523048 | − | 0.852303i | \(-0.324795\pi\) |
−0.852303 | + | 0.523048i | \(0.824795\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 36309.2i | − | 0.00207646i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.15276e6i | 0.292818i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.52044e7 | + | 1.52044e7i | 0.858592 | + | 0.858592i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.79102e6 | + | 4.79102e6i | −0.267167 | + | 0.267167i | −0.827957 | − | 0.560791i | \(-0.810497\pi\) |
0.560791 | + | 0.827957i | \(0.310497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.07818e7 | −0.597479 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.90046e6 | 0.324941 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.30193e7 | − | 2.30193e7i | 1.25980 | − | 1.25980i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.49592e6 | − | 1.49592e6i | −0.0808580 | − | 0.0808580i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.42552e7i | 0.765778i | 0.923794 | + | 0.382889i | \(0.125071\pi\) | ||||
−0.923794 | + | 0.382889i | \(0.874929\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.56090e7i | 1.36723i | 0.729843 | + | 0.683614i | \(0.239593\pi\) | ||||
−0.729843 | + | 0.683614i | \(0.760407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.21904e6 | + | 1.21904e6i | 0.0646830 | + | 0.0646830i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.67957e7 | − | 2.67957e7i | 1.40446 | − | 1.40446i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.07439e7 | −1.60158 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.31917e6 | 0.120081 | 0.0600406 | − | 0.998196i | \(-0.480877\pi\) | ||||
0.0600406 | + | 0.998196i | \(0.480877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.90869e6 | − | 4.90869e6i | 0.252619 | − | 0.252619i | −0.569425 | − | 0.822044i | \(-0.692834\pi\) |
0.822044 | + | 0.569425i | \(0.192834\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.02142e7 | + | 2.02142e7i | 1.02776 | + | 1.02776i | 0.999604 | + | 0.0281570i | \(0.00896383\pi\) |
0.0281570 | + | 0.999604i | \(0.491036\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 4.54977e6i | − | 0.229934i | −0.993369 | − | 0.114967i | \(-0.963324\pi\) | ||
0.993369 | − | 0.114967i | \(-0.0366762\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.39710e6i | 0.0701818i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.90566e6 | − | 1.90566e6i | −0.0951551 | − | 0.0951551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 798135. | − | 798135.i | 0.0393788 | − | 0.0393788i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.98332e7 | 0.972719 | 0.486360 | − | 0.873759i | \(-0.338325\pi\) | ||||
0.486360 | + | 0.873759i | \(0.338325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.04300e6 | −0.197112 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.04198e6 | + | 2.04198e6i | −0.0989651 | + | 0.0989651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.44138e7 | − | 2.44138e7i | −1.16930 | − | 1.16930i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 237170.i | 0.0112925i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.06342e7i | − | 0.503363i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 693392. | + | 693392.i | 0.0326292 | + | 0.0326292i | 0.723233 | − | 0.690604i | \(-0.242655\pi\) |
−0.690604 | + | 0.723233i | \(0.742655\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.01743e7 | + | 2.01743e7i | −0.938308 | + | 0.938308i | −0.998205 | − | 0.0598966i | \(-0.980923\pi\) |
0.0598966 | + | 0.998205i | \(0.480923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.16047e7 | 0.999001 | 0.499501 | − | 0.866314i | \(-0.333517\pi\) | ||||
0.499501 | + | 0.866314i | \(0.333517\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 972774. | 0.0447202 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.05264e6 | − | 7.05264e6i | 0.322348 | − | 0.322348i | −0.527319 | − | 0.849667i | \(-0.676803\pi\) |
0.849667 | + | 0.527319i | \(0.176803\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −485480. | − | 485480.i | −0.0219343 | − | 0.0219343i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.10287e7i | − | 1.84305i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.32041e6i | 0.237629i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.16623e7 | + | 2.16623e7i | 0.961988 | + | 0.961988i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.77065e7 | − | 1.77065e7i | 0.777381 | − | 0.777381i | −0.202004 | − | 0.979385i | \(-0.564745\pi\) |
0.979385 | + | 0.202004i | \(0.0647453\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 907969. | 0.0396368 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.88929e7 | −1.25416 | −0.627078 | − | 0.778957i | \(-0.715749\pi\) | ||||
−0.627078 | + | 0.778957i | \(0.715749\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.58238e6 | − | 4.58238e6i | 0.197783 | − | 0.197783i | −0.601266 | − | 0.799049i | \(-0.705337\pi\) |
0.799049 | + | 0.601266i | \(0.205337\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.54412e6 | − | 9.54412e6i | −0.407312 | − | 0.407312i | 0.473488 | − | 0.880800i | \(-0.342995\pi\) |
−0.880800 | + | 0.473488i | \(0.842995\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.19643e6i | 0.390270i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 3.70057e7i | − | 1.56162i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.08247e7 | − | 2.08247e7i | −0.873875 | − | 0.873875i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.01345e6 | + | 3.01345e6i | −0.125050 | + | 0.125050i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.71808e6 | 0.401034 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.64987e6 | 0.396013 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.78437e6 | − | 1.78437e6i | 0.0728224 | − | 0.0728224i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.57152e7 | − | 1.57152e7i | −0.634312 | − | 0.634312i | 0.314835 | − | 0.949147i | \(-0.398051\pi\) |
−0.949147 | + | 0.314835i | \(0.898051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.61877e6i | 0.305826i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.37011e7i | − | 1.34539i | −0.739920 | − | 0.672694i | \(-0.765137\pi\) | ||
0.739920 | − | 0.672694i | \(-0.234863\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.00889e7 | − | 4.00889e7i | −1.59165 | − | 1.59165i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.32021e6 | + | 8.32021e6i | −0.326747 | + | 0.326747i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.69860e7 | 0.663440 | 0.331720 | − | 0.943378i | \(-0.392371\pi\) | ||||
0.331720 | + | 0.943378i | \(0.392371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.30872e6 | 0.0508391 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.86139e6 | − | 7.86139e6i | 0.303735 | − | 0.303735i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.05918e6 | + | 1.05918e6i | 0.0404827 | + | 0.0404827i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.74089e7i | 1.04196i | 0.853568 | + | 0.520982i | \(0.174434\pi\) | ||||
−0.853568 | + | 0.520982i | \(0.825566\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.36144e6i | − | 0.278348i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.31423e6 | + | 1.31423e6i | 0.0494275 | + | 0.0494275i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.46447e7 | − | 3.46447e7i | 1.28910 | − | 1.28910i | 0.353769 | − | 0.935333i | \(-0.384900\pi\) |
0.935333 | − | 0.353769i | \(-0.115100\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.15026e6 | 0.0425728 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.97677e7 | 0.727750 | 0.363875 | − | 0.931448i | \(-0.381454\pi\) | ||||
0.363875 | + | 0.931448i | \(0.381454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.63304e7 | + | 1.63304e7i | −0.598022 | + | 0.598022i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.45673e7 | + | 1.45673e7i | 0.527842 | + | 0.527842i | 0.919928 | − | 0.392086i | \(-0.128247\pi\) |
−0.392086 | + | 0.919928i | \(0.628247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 4.62269e7i | − | 1.66621i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 3.20738e6i | − | 0.115000i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.23751e7 | + | 2.23751e7i | 0.798055 | + | 0.798055i | 0.982789 | − | 0.184734i | \(-0.0591422\pi\) |
−0.184734 | + | 0.982789i | \(0.559142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.65411e6 | + | 2.65411e6i | −0.0936782 | + | 0.0936782i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.81757e6 | −0.204266 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.47829e7 | 0.865653 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.64053e7 | + | 3.64053e7i | −1.26502 | + | 1.26502i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.87842e7 | + | 2.87842e7i | 0.989894 | + | 0.989894i | 0.999949 | − | 0.0100555i | \(-0.00320081\pi\) |
−0.0100555 | + | 0.999949i | \(0.503201\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.73087e6i | 0.0934311i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.09828e7i | 1.73530i | 0.497173 | + | 0.867651i | \(0.334371\pi\) | ||||
−0.497173 | + | 0.867651i | \(0.665629\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.63180e6 | + | 5.63180e6i | 0.190706 | + | 0.190706i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.93752e7 | + | 3.93752e7i | −1.31973 | + | 1.31973i | −0.405749 | + | 0.913984i | \(0.632989\pi\) |
−0.913984 | + | 0.405749i | \(0.867011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.55768e7 | 0.519424 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.86093e7 | 1.61267 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.47236e7 | + | 2.47236e7i | −0.816070 | + | 0.816070i | −0.985536 | − | 0.169466i | \(-0.945796\pi\) |
0.169466 | + | 0.985536i | \(0.445796\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.38675e6 | − | 1.38675e6i | −0.0453111 | − | 0.0453111i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.99100e7i | 1.94764i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.85549e7i | 0.923627i | 0.886977 | + | 0.461814i | \(0.152801\pi\) | ||||
−0.886977 | + | 0.461814i | \(0.847199\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −621822. | − | 621822.i | −0.0200121 | − | 0.0200121i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.29416e7 | − | 1.29416e7i | 0.412335 | − | 0.412335i | −0.470216 | − | 0.882551i | \(-0.655824\pi\) |
0.882551 | + | 0.470216i | \(0.155824\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.54475e6 | −0.0489716 |
(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 | 400.6.n.g.143.5 | 20 | ||
4.3 | odd | 2 | inner | 400.6.n.g.143.6 | 20 | ||
5.2 | odd | 4 | inner | 400.6.n.g.207.6 | 20 | ||
5.3 | odd | 4 | 80.6.n.d.47.5 | ✓ | 20 | ||
5.4 | even | 2 | 80.6.n.d.63.6 | yes | 20 | ||
20.3 | even | 4 | 80.6.n.d.47.6 | yes | 20 | ||
20.7 | even | 4 | inner | 400.6.n.g.207.5 | 20 | ||
20.19 | odd | 2 | 80.6.n.d.63.5 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.6.n.d.47.5 | ✓ | 20 | 5.3 | odd | 4 | ||
80.6.n.d.47.6 | yes | 20 | 20.3 | even | 4 | ||
80.6.n.d.63.5 | yes | 20 | 20.19 | odd | 2 | ||
80.6.n.d.63.6 | yes | 20 | 5.4 | even | 2 | ||
400.6.n.g.143.5 | 20 | 1.1 | even | 1 | trivial | ||
400.6.n.g.143.6 | 20 | 4.3 | odd | 2 | inner | ||
400.6.n.g.207.5 | 20 | 20.7 | even | 4 | inner | ||
400.6.n.g.207.6 | 20 | 5.2 | odd | 4 | inner |