Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,8,Mod(9,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.9");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.24770050968\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1348x^{2} + 93051 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 9.1 | ||
Root | \(-35.7074i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.9 |
Dual form | 20.8.c.a.9.4 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 71.4148i | − | 1.52709i | −0.645756 | − | 0.763544i | \(-0.723458\pi\) | ||
0.645756 | − | 0.763544i | \(-0.276542\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −279.408 | − | 7.49513i | −0.999640 | − | 0.0268154i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 860.515i | 0.948233i | 0.880462 | + | 0.474117i | \(0.157232\pi\) | ||||
−0.880462 | + | 0.474117i | \(0.842768\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2913.08 | −1.33200 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5468.16 | −1.23870 | −0.619351 | − | 0.785114i | \(-0.712604\pi\) | ||||
−0.619351 | + | 0.785114i | \(0.712604\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 14343.8i | − | 1.81076i | −0.424599 | − | 0.905382i | \(-0.639585\pi\) | ||
0.424599 | − | 0.905382i | \(-0.360415\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −535.264 | + | 19953.9i | −0.0409495 | + | 1.52654i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 8677.25i | 0.428362i | 0.976794 | + | 0.214181i | \(0.0687082\pi\) | ||||
−0.976794 | + | 0.214181i | \(0.931292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5340.48 | 0.178625 | 0.0893126 | − | 0.996004i | \(-0.471533\pi\) | ||||
0.0893126 | + | 0.996004i | \(0.471533\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 61453.5 | 1.44804 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 74802.5i | − | 1.28194i | −0.767565 | − | 0.640971i | \(-0.778532\pi\) | ||
0.767565 | − | 0.640971i | \(-0.221468\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 78012.6 | + | 4188.40i | 0.998562 | + | 0.0536115i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 51852.9i | 0.506990i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −91625.0 | −0.697624 | −0.348812 | − | 0.937193i | \(-0.613415\pi\) | ||||
−0.348812 | + | 0.937193i | \(0.613415\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −103909. | −0.626450 | −0.313225 | − | 0.949679i | \(-0.601409\pi\) | ||||
−0.313225 | + | 0.949679i | \(0.601409\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 390508.i | 1.89161i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6449.67 | − | 240435.i | 0.0254273 | − | 0.947892i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 467238.i | − | 1.51647i | −0.651984 | − | 0.758233i | \(-0.726063\pi\) | ||
0.651984 | − | 0.758233i | \(-0.273937\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.02436e6 | −2.76520 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 385741. | 0.874083 | 0.437042 | − | 0.899441i | \(-0.356026\pi\) | ||||
0.437042 | + | 0.899441i | \(0.356026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 257098.i | 0.493128i | 0.969126 | + | 0.246564i | \(0.0793016\pi\) | ||||
−0.969126 | + | 0.246564i | \(0.920698\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 813938. | + | 21833.9i | 1.33152 | + | 0.0357181i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 762177.i | 1.07081i | 0.844595 | + | 0.535406i | \(0.179841\pi\) | ||||
−0.844595 | + | 0.535406i | \(0.820159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 83057.6 | 0.100854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 619684. | 0.654146 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.14032e6i | − | 1.05211i | −0.850450 | − | 0.526055i | \(-0.823670\pi\) | ||
0.850450 | − | 0.526055i | \(-0.176330\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.52785e6 | + | 40984.6i | 1.23826 | + | 0.0332163i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 381389.i | − | 0.272776i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.31663e6 | −1.46850 | −0.734252 | − | 0.678877i | \(-0.762467\pi\) | ||||
−0.734252 | + | 0.678877i | \(0.762467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.89127e6 | 1.06684 | 0.533418 | − | 0.845852i | \(-0.320907\pi\) | ||||
0.533418 | + | 0.845852i | \(0.320907\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.50675e6i | − | 1.26304i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −107509. | + | 4.00777e6i | −0.0485564 | + | 1.81011i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.89718e6i | 0.770630i | 0.922785 | + | 0.385315i | \(0.125907\pi\) | ||||
−0.922785 | + | 0.385315i | \(0.874093\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.34201e6 | −1.95764 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.84022e6 | −0.941776 | −0.470888 | − | 0.882193i | \(-0.656066\pi\) | ||||
−0.470888 | + | 0.882193i | \(0.656066\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.59537e6i | 0.780854i | 0.920634 | + | 0.390427i | \(0.127673\pi\) | ||||
−0.920634 | + | 0.390427i | \(0.872327\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 299114. | − | 5.57126e6i | 0.0818695 | − | 1.52489i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 4.70543e6i | − | 1.17458i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.49695e6 | 1.25437 | 0.627187 | − | 0.778869i | \(-0.284206\pi\) | ||||
0.627187 | + | 0.778869i | \(0.284206\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.66784e6 | −0.557779 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.79174e6i | 0.727889i | 0.931421 | + | 0.363945i | \(0.118570\pi\) | ||||
−0.931421 | + | 0.363945i | \(0.881430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 65037.1 | − | 2.42449e6i | 0.0114867 | − | 0.428208i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.54339e6i | 1.06533i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.95833e6 | 0.294456 | 0.147228 | − | 0.989103i | \(-0.452965\pi\) | ||||
0.147228 | + | 0.989103i | \(0.452965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23430e7 | 1.71703 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.42063e6i | 0.956644i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.49217e6 | − | 40027.6i | −0.178561 | − | 0.00478991i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.19937e7i | − | 1.33429i | −0.744927 | − | 0.667146i | \(-0.767516\pi\) | ||
0.744927 | − | 0.667146i | \(-0.232484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.59292e7 | 1.64995 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.86841e6 | −0.663333 | −0.331666 | − | 0.943397i | \(-0.607611\pi\) | ||||
−0.331666 | + | 0.943397i | \(0.607611\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.12684e6i | − | 0.372124i | −0.982538 | − | 0.186062i | \(-0.940427\pi\) | ||
0.982538 | − | 0.186062i | \(-0.0595725\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.71706e7 | − | 460602.i | −1.44751 | − | 0.0388297i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.40370e6i | − | 0.268601i | −0.990941 | − | 0.134301i | \(-0.957121\pi\) | ||
0.990941 | − | 0.134301i | \(-0.0428788\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.28461e7 | 0.950123 | 0.475062 | − | 0.879953i | \(-0.342426\pi\) | ||||
0.475062 | + | 0.879953i | \(0.342426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.33678e7 | −2.31578 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.61131e7i | − | 1.05052i | −0.850942 | − | 0.525260i | \(-0.823968\pi\) | ||
0.850942 | − | 0.525260i | \(-0.176032\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −560655. | + | 2.09004e7i | −0.0343758 | + | 1.28148i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.17846e7i | 2.41193i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.46690e6 | −0.406187 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.04136e7 | 0.534382 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 2.75477e7i | − | 1.33480i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.17660e7 | − | 1.75499e6i | −0.996765 | − | 0.0803691i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.17289e7i | − | 0.941295i | −0.882321 | − | 0.470647i | \(-0.844020\pi\) | ||
0.882321 | − | 0.470647i | \(-0.155980\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.83606e7 | 0.753050 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.22973e6 | −0.164385 | −0.0821927 | − | 0.996616i | \(-0.526192\pi\) | ||||
−0.0821927 | + | 0.996616i | \(0.526192\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.59556e6i | 0.169378i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 388644. | − | 1.44881e7i | 0.0135952 | − | 0.506808i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.51787e7i | − | 0.504327i | −0.967685 | − | 0.252163i | \(-0.918858\pi\) | ||
0.967685 | − | 0.252163i | \(-0.0811421\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.87908e7 | 1.22512 | 0.612558 | − | 0.790426i | \(-0.290141\pi\) | ||||
0.612558 | + | 0.790426i | \(0.290141\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.44307e7 | 1.63522 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.84340e7i | 2.24300i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.56008e7 | + | 686742.i | 0.697373 | + | 0.0187071i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 5.93154e6i | − | 0.154013i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.06288e6 | −0.0263228 | −0.0131614 | − | 0.999913i | \(-0.504190\pi\) | ||||
−0.0131614 | + | 0.999913i | \(0.504190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.03412e7 | −1.66261 | −0.831305 | − | 0.555816i | \(-0.812406\pi\) | ||||
−0.831305 | + | 0.555816i | \(0.812406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.52775e7i | − | 0.570577i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.90329e7 | + | 778810.i | 0.626225 | + | 0.0167985i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 886457.i | 0.0182814i | 0.999958 | + | 0.00914068i | \(0.00290961\pi\) | ||||
−0.999958 | + | 0.00914068i | \(0.997090\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.14358e7 | −1.60667 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.43686e7 | 1.21558 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.82444e7i | 0.872549i | 0.899814 | + | 0.436275i | \(0.143702\pi\) | ||||
−0.899814 | + | 0.436275i | \(0.856298\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.92691e6 | − | 1.09111e8i | 0.0507242 | − | 1.89093i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.45878e7i | − | 1.07311i | −0.843867 | − | 0.536553i | \(-0.819726\pi\) | ||
0.843867 | − | 0.536553i | \(-0.180274\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.42995e8 | −2.27886 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.55572e7 | −0.237928 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.46835e7i | 0.215610i | 0.994172 | + | 0.107805i | \(0.0343823\pi\) | ||||
−0.994172 | + | 0.107805i | \(0.965618\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.60418e6 | + | 6.71310e7i | −0.0508362 | + | 0.946869i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.65442e8i | 2.24253i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.60914e6 | 0.0600667 | 0.0300334 | − | 0.999549i | \(-0.490439\pi\) | ||||
0.0300334 | + | 0.999549i | \(0.490439\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.97056e6 | −0.0247011 | −0.0123505 | − | 0.999924i | \(-0.503931\pi\) | ||||
−0.0123505 | + | 0.999924i | \(0.503931\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 1.35064e8i | − | 1.62915i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.50202e6 | + | 1.30550e8i | −0.0406646 | + | 1.51592i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.74486e7i | − | 0.530612i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.46202e7 | −0.480745 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.09793e7 | 0.425547 | 0.212774 | − | 0.977102i | \(-0.431750\pi\) | ||||
0.212774 | + | 0.977102i | \(0.431750\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 8.19388e7i | − | 0.820425i | −0.911990 | − | 0.410213i | \(-0.865454\pi\) | ||
0.911990 | − | 0.410213i | \(-0.134546\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.86214e8 | + | 7.67770e6i | 2.76420 | + | 0.0741498i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.46698e8i | − | 1.36708i | −0.729914 | − | 0.683539i | \(-0.760440\pi\) | ||
0.729914 | − | 0.683539i | \(-0.239560\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.53885e7 | −0.138423 | −0.0692116 | − | 0.997602i | \(-0.522048\pi\) | ||||
−0.0692116 | + | 0.997602i | \(0.522048\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.35486e8 | 1.17682 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 7.88447e7i | − | 0.661510i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.07779e8 | − | 2.89118e6i | −0.873769 | − | 0.0234389i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.17906e8i | 1.70755i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.92026e7 | −0.221263 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.37621e7 | −0.320708 | −0.160354 | − | 0.987060i | \(-0.551264\pi\) | ||||
−0.160354 | + | 0.987060i | \(0.551264\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.02834e8i | 1.43818i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.92699e6 | − | 7.18354e7i | 0.0132234 | − | 0.492951i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.94150e7i | − | 0.594021i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.85348e8 | 1.19243 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.24464e8 | 0.775662 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.33168e7i | 0.261571i | 0.991411 | + | 0.130785i | \(0.0417499\pi\) | ||||
−0.991411 | + | 0.130785i | \(0.958250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.27257e8 | − | 1.22011e7i | −1.33008 | − | 0.0714105i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.64636e8i | 0.934186i | 0.884208 | + | 0.467093i | \(0.154699\pi\) | ||||
−0.884208 | + | 0.467093i | \(0.845301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.98853e8 | −1.09423 | −0.547114 | − | 0.837058i | \(-0.684273\pi\) | ||||
−0.547114 | + | 0.837058i | \(0.684273\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.36038e8 | −1.79368 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.39144e7i | − | 0.331019i | −0.986208 | − | 0.165510i | \(-0.947073\pi\) | ||
0.986208 | − | 0.165510i | \(-0.0529269\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.71262e6 | − | 2.12958e8i | 0.0287143 | − | 1.07043i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3.92564e8i | − | 1.91554i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.82882e7 | 0.323559 | 0.161779 | − | 0.986827i | \(-0.448277\pi\) | ||||
0.161779 | + | 0.986827i | \(0.448277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.19558e8 | −1.01039 | −0.505195 | − | 0.863005i | \(-0.668579\pi\) | ||||
−0.505195 | + | 0.863005i | \(0.668579\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.03926e8i | 1.35877i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.32069e7 | − | 622528.i | −0.100818 | − | 0.00270444i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 7.66026e7i | − | 0.323448i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.70786e8 | 1.11155 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.20435e7 | −0.167819 | −0.0839094 | − | 0.996473i | \(-0.526741\pi\) | ||||
−0.0839094 | + | 0.996473i | \(0.526741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.09032e8i | 1.58794i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.73145e8 | − | 4.64462e6i | −0.653911 | − | 0.0175412i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.47945e8i | 0.911151i | 0.890197 | + | 0.455575i | \(0.150566\pi\) | ||||
−0.890197 | + | 0.455575i | \(0.849434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.02066e8 | 1.43796 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.66911e8 | 0.929233 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.95042e8i | − | 1.00009i | −0.866000 | − | 0.500044i | \(-0.833317\pi\) | ||
0.866000 | − | 0.500044i | \(-0.166683\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.54686e6 | + | 3.18615e8i | −0.0282128 | + | 1.05173i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.39854e8i | − | 0.449661i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.39709e8 | 1.06408 | 0.532040 | − | 0.846719i | \(-0.321426\pi\) | ||||
0.532040 | + | 0.846719i | \(0.321426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.43577e7 | −0.257473 | −0.128737 | − | 0.991679i | \(-0.541092\pi\) | ||||
−0.128737 | + | 0.991679i | \(0.541092\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 8.81475e8i | − | 2.62205i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.26586e8 | − | 2.29028e7i | −1.23692 | − | 0.0664087i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.20428e8i | 0.905840i | 0.891551 | + | 0.452920i | \(0.149618\pi\) | ||||
−0.891551 | + | 0.452920i | \(0.850382\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.02695e8 | 0.834430 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.84239e8 | 1.57079 | 0.785395 | − | 0.618994i | \(-0.212460\pi\) | ||||
0.785395 | + | 0.618994i | \(0.212460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.39110e8i | − | 1.15165i | −0.817573 | − | 0.575826i | \(-0.804681\pi\) | ||
0.817573 | − | 0.575826i | \(-0.195319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.85857e6 | + | 1.06563e8i | −0.00731461 | + | 0.272678i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.31936e8i | 0.828835i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.35044e8 | 0.816506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.56526e8 | −2.03758 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.26225e8i | 1.22218i | 0.791561 | + | 0.611090i | \(0.209269\pi\) | ||||
−0.791561 | + | 0.611090i | \(0.790731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.47286e8 | + | 1.73635e7i | 1.46798 | + | 0.0393785i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 2.83540e8i | − | 0.628010i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.07295e9 | −2.32129 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.21237e8 | −0.467601 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.90507e8i | 1.01297i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.28435e8 | − | 1.41753e7i | −1.06645 | − | 0.0286077i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.65685e8i | 0.524062i | 0.965059 | + | 0.262031i | \(0.0843922\pi\) | ||||
−0.965059 | + | 0.262031i | \(0.915608\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.94718e8 | −0.568266 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.87733e7 | −0.0542410 | −0.0271205 | − | 0.999632i | \(-0.508634\pi\) | ||||
−0.0271205 | + | 0.999632i | \(0.508634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.64576e8i | − | 1.22501i | −0.790467 | − | 0.612505i | \(-0.790162\pi\) | ||
0.790467 | − | 0.612505i | \(-0.209838\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.87884e7 | + | 7.00405e8i | −0.0338691 | + | 1.26259i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6.01423e8i | − | 1.06041i | −0.847871 | − | 0.530203i | \(-0.822116\pi\) | ||
0.847871 | − | 0.530203i | \(-0.177884\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.01020e8 | 0.864148 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.43075e8 | −0.410178 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.63407e7i | 0.0765162i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.00775e7 | − | 1.11900e9i | 0.0970778 | − | 1.80816i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.17405e8i | − | 1.45092i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.55864e8 | −1.01538 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.07797e9 | 1.63383 | 0.816916 | − | 0.576757i | \(-0.195682\pi\) | ||||
0.816916 | + | 0.576757i | \(0.195682\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.36110e9i | 2.01993i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.42196e7 | − | 5.30086e8i | 0.0206647 | − | 0.770352i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.17944e9i | 1.67869i | 0.543602 | + | 0.839343i | \(0.317060\pi\) | ||||
−0.543602 | + | 0.839343i | \(0.682940\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.15071e9 | −1.60424 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.68190e8 | 0.775985 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.80143e8i | 1.04387i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.49260e9 | + | 4.00391e7i | 1.95694 | + | 0.0524949i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 3.42964e8i | − | 0.440651i | −0.975426 | − | 0.220326i | \(-0.929288\pi\) | ||
0.975426 | − | 0.220326i | \(-0.0707120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.51245e7 | 0.107193 | 0.0535964 | − | 0.998563i | \(-0.482932\pi\) | ||||
0.0535964 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.43766e8 | 0.918040 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.46737e7i | 0.0903558i | 0.998979 | + | 0.0451779i | \(0.0143855\pi\) | ||||
−0.998979 | + | 0.0451779i | \(0.985615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.93580e8 | + | 2.12878e7i | 0.941438 | + | 0.0252541i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.33247e8i | 0.620283i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.59926e8 | 0.752774 | 0.376387 | − | 0.926463i | \(-0.377166\pi\) | ||||
0.376387 | + | 0.926463i | \(0.377166\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.65351e8 | −0.968093 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.43686e8i | − | 0.816049i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.94527e7 | − | 7.25168e8i | 0.0209389 | − | 0.780573i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.14445e9i | − | 1.20855i | −0.796774 | − | 0.604277i | \(-0.793462\pi\) | ||
0.796774 | − | 0.604277i | \(-0.206538\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.12370e9 | −1.16428 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.81263e8 | 0.997646 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 1.92846e9i | − | 1.92411i | −0.272861 | − | 0.962053i | \(-0.587970\pi\) | ||
0.272861 | − | 0.962053i | \(-0.412030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.25332e8 | + | 1.55441e9i | −0.122731 | + | 1.52215i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.31425e9i | 1.26323i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.70589e8 | −0.444022 | −0.222011 | − | 0.975044i | \(-0.571262\pi\) | ||||
−0.222011 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.55177e9 | −1.43744 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.05122e8i | − | 0.368460i | −0.982883 | − | 0.184230i | \(-0.941021\pi\) | ||
0.982883 | − | 0.184230i | \(-0.0589791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.52678e7 | + | 1.31474e9i | −0.0314968 | + | 1.17416i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.48948e8i | − | 0.656846i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.58753e9 | −1.36741 | −0.683706 | − | 0.729758i | \(-0.739633\pi\) | ||||
−0.683706 | + | 0.729758i | \(0.739633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.49080e8 | 0.549135 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.02065e8i | 0.251031i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.53589e9 | − | 4.12004e7i | −1.25392 | − | 0.0336366i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.89890e7i | − | 0.0312734i | −0.999878 | − | 0.0156367i | \(-0.995022\pi\) | ||
0.999878 | − | 0.0156367i | \(-0.00497752\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.28191e8 | 0.258656 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.43635e8 | 0.575910 | 0.287955 | − | 0.957644i | \(-0.407025\pi\) | ||||
0.287955 | + | 0.957644i | \(0.407025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.49044e9i | 1.13435i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.45416e8 | + | 1.99958e7i | 0.557579 | + | 0.0149571i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.55493e9i | 1.87845i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.04931e7 | −0.0364922 | −0.0182461 | − | 0.999834i | \(-0.505808\pi\) | ||||
−0.0182461 | + | 0.999834i | \(0.505808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.08398e9 | −0.770152 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.99350e9i | − | 1.39248i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.84196e7 | − | 1.05944e9i | 0.0195186 | − | 0.727627i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.77024e9i | − | 1.87086i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.65771e8 | −0.641394 | −0.320697 | − | 0.947182i | \(-0.603917\pi\) | ||||
−0.320697 | + | 0.947182i | \(0.603917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.22814e9 | −1.45531 | −0.727655 | − | 0.685943i | \(-0.759390\pi\) | ||||
−0.727655 | + | 0.685943i | \(0.759390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 2.22028e9i | − | 1.42632i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.63438e7 | + | 6.76935e8i | −0.0229651 | + | 0.427746i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.62746e9i | 1.01161i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.60136e9 | 3.42525 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.66758e9 | 1.60490 | 0.802449 | − | 0.596721i | \(-0.203530\pi\) | ||||
0.802449 | + | 0.596721i | \(0.203530\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.53592e9i | 0.909201i | 0.890695 | + | 0.454601i | \(0.150218\pi\) | ||||
−0.890695 | + | 0.454601i | \(0.849782\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.90436e7 | − | 1.82827e9i | 0.0285673 | − | 1.06495i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.99481e8i | − | 0.228987i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.31907e9 | 0.744119 | 0.372060 | − | 0.928209i | \(-0.378652\pi\) | ||||
0.372060 | + | 0.928209i | \(0.378652\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.41953e8 | −0.134337 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.85200e9i | 1.55860i | 0.626649 | + | 0.779302i | \(0.284426\pi\) | ||||
−0.626649 | + | 0.779302i | \(0.715574\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.47173e8 | − | 1.46779e7i | −0.294350 | − | 0.00789597i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.59054e7i | 0.0401973i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.27931e9 | 1.70970 | 0.854851 | − | 0.518874i | \(-0.173649\pi\) | ||||
0.854851 | + | 0.518874i | \(0.173649\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.10930e9 | −1.08273 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.02341e9i | 2.53895i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.44874e9 | − | 9.25127e7i | −1.71641 | − | 0.0460428i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 1.70952e9i | − | 0.837852i | −0.908020 | − | 0.418926i | \(-0.862407\pi\) | ||
0.908020 | − | 0.418926i | \(-0.137593\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.49940e8 | −0.217175 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.36612e9 | 1.60021 | 0.800105 | − | 0.599861i | \(-0.204777\pi\) | ||||
0.800105 | + | 0.599861i | \(0.204777\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.88893e7i | 0.0182095i | 0.999959 | + | 0.00910473i | \(0.00289817\pi\) | ||||
−0.999959 | + | 0.00910473i | \(0.997102\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.56186e7 | − | 2.07338e9i | 0.0256528 | − | 0.956300i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 4.12767e9i | − | 1.87541i | −0.347436 | − | 0.937704i | \(-0.612948\pi\) | ||
0.347436 | − | 0.937704i | \(-0.387052\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.63255e9 | −0.730736 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.33062e7 | 0.0279173 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1.40586e9i | − | 0.610839i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.16625e8 | + | 2.23681e7i | 0.178368 | + | 0.00957637i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.32185e9i | 1.40141i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.52474e9 | −0.633900 | −0.316950 | − | 0.948442i | \(-0.602659\pi\) | ||||
−0.316950 | + | 0.948442i | \(0.602659\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.70196e9 | −2.74596 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.59688e9i | − | 1.85630i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.98942e7 | + | 3.35113e9i | −0.0357796 | + | 1.33381i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.13272e9i | 0.444399i | 0.975001 | + | 0.222199i | \(0.0713236\pi\) | ||||
−0.975001 | + | 0.222199i | \(0.928676\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.44536e9 | 1.33246 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.26065e9 | 0.861884 | 0.430942 | − | 0.902380i | \(-0.358181\pi\) | ||||
0.430942 | + | 0.902380i | \(0.358181\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7.95053e8i | − | 0.298835i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.45074e9 | − | 1.19391e8i | −1.64936 | − | 0.0442440i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 2.44405e9i | − | 0.893024i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.60721e8 | 0.165992 | 0.0829958 | − | 0.996550i | \(-0.473551\pi\) | ||||
0.0829958 | + | 0.996550i | \(0.473551\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.61252e9 | −1.63873 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.49112e8i | 0.297493i | 0.988875 | + | 0.148747i | \(0.0475239\pi\) | ||||
−0.988875 | + | 0.148747i | \(0.952476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.91909e9 | + | 5.14797e7i | 0.663094 | + | 0.0177875i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.02120e10i | 3.48003i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.54063e8 | −0.287063 | −0.143532 | − | 0.989646i | \(-0.545846\pi\) | ||||
−0.143532 | + | 0.989646i | \(0.545846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.23336e9 | −0.740432 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.76919e8i | 0.0905612i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.09312e7 | + | 1.15307e9i | −0.00997866 | + | 0.371990i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.16771e9i | − | 1.32642i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.04862e9 | 0.329256 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.64909e9 | 1.75003 | 0.875016 | − | 0.484093i | \(-0.160851\pi\) | ||||
0.875016 | + | 0.484093i | \(0.160851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.30599e9i | − | 1.01052i | −0.862967 | − | 0.505260i | \(-0.831396\pi\) | ||
0.862967 | − | 0.505260i | \(-0.168604\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.79415e9 | + | 2.57392e8i | 1.44595 | + | 0.0776314i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 9.01642e8i | − | 0.268347i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.19059e9 | −0.643377 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.74854e9 | 1.95604 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.53299e9i | − | 1.58276i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.55112e7 | + | 9.51021e8i | −0.00720266 | + | 0.268505i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 3.29161e8i | − | 0.0917272i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.54172e8 | −0.124928 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.97074e9 | 0.806629 | 0.403314 | − | 0.915061i | \(-0.367858\pi\) | ||||
0.403314 | + | 0.915061i | \(0.367858\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.40727e8i | 0.0377207i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.58931e9 | − | 9.62835e7i | −0.949781 | − | 0.0254779i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.68111e9i | − | 1.22291i | −0.791281 | − | 0.611453i | \(-0.790585\pi\) | ||
0.791281 | − | 0.611453i | \(-0.209415\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.50941e9 | −1.42102 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.89322e8 | −0.124613 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.73021e9i | 1.18944i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9.32322e9 | + | 2.50096e8i | 2.31494 | + | 0.0620985i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.64883e9i | 0.894666i | 0.894367 | + | 0.447333i | \(0.147626\pi\) | ||||
−0.894367 | + | 0.447333i | \(0.852374\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.68776e9 | 0.892939 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.38853e9 | −0.810292 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.10106e9i | 1.67704i | 0.544869 | + | 0.838521i | \(0.316579\pi\) | ||||
−0.544869 | + | 0.838521i | \(0.683421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.20770e8 | + | 4.50213e9i | −0.0281701 | + | 1.05014i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.29572e9i | − | 0.528905i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.60359e9 | −1.04762 | −0.523810 | − | 0.851835i | \(-0.675490\pi\) | ||||
−0.523810 | + | 0.851835i | \(0.675490\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.37732e9 | 0.983971 | 0.491985 | − | 0.870603i | \(-0.336271\pi\) | ||||
0.491985 | + | 0.870603i | \(0.336271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.92653e9i | − | 0.649848i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.13303e8 | − | 5.83554e9i | 0.0687269 | − | 1.28010i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.10061e9i | 1.10537i | 0.833391 | + | 0.552684i | \(0.186396\pi\) | ||||
−0.833391 | + | 0.552684i | \(0.813604\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.85165e9 | −1.25286 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.26285e9 | −0.690208 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.23546e9i | 1.30325i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.13181e8 | − | 1.16749e10i | 0.0646770 | − | 2.41107i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 7.99745e9i | − | 1.63199i | −0.578057 | − | 0.815996i | \(-0.696189\pi\) | ||
0.578057 | − | 0.815996i | \(-0.303811\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.54923e8 | −0.111900 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.04764e10 | −2.08765 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.40837e9i | 1.65585i | 0.560841 | + | 0.827924i | \(0.310478\pi\) | ||||
−0.560841 | + | 0.827924i | \(0.689522\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.08631e9 | + | 5.59654e7i | 0.406041 | + | 0.0108921i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.09896e9i | 0.211385i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.34084e9 | −1.39557 | −0.697785 | − | 0.716307i | \(-0.745831\pi\) | ||||
−0.697785 | + | 0.716307i | \(0.745831\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.46145e9 | 0.462520 | 0.231260 | − | 0.972892i | \(-0.425715\pi\) | ||||
0.231260 | + | 0.972892i | \(0.425715\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5.52662e9i | − | 1.02648i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.90964e9 | − | 7.80513e7i | −0.534190 | − | 0.0143297i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.52629e9i | − | 0.639967i | −0.947423 | − | 0.319984i | \(-0.896323\pi\) | ||
0.947423 | − | 0.319984i | \(-0.103677\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.63068e9 | −1.01018 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.09325e10 | 1.93899 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 9.77585e9i | − | 1.71413i | −0.515211 | − | 0.857064i | \(-0.672286\pi\) | ||
0.515211 | − | 0.857064i | \(-0.327714\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.06473e8 | + | 7.69704e9i | −0.0357933 | + | 1.33432i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.58671e9i | 1.47173i | 0.677127 | + | 0.735866i | \(0.263225\pi\) | ||||
−0.677127 | + | 0.735866i | \(0.736775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.59570e9 | −0.609349 | −0.304674 | − | 0.952457i | \(-0.598548\pi\) | ||||
−0.304674 | + | 0.952457i | \(0.598548\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.87872e9 | 0.649933 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.68517e9i | 0.279213i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.06843e9 | + | 6.53497e8i | 0.994252 | + | 0.107069i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.08550e9i | 0.337889i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.05434e9 | 0.649596 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.07303e9 | −0.170024 | −0.0850121 | − | 0.996380i | \(-0.527093\pi\) | ||||
−0.0850121 | + | 0.996380i | \(0.527093\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.12526e9i | 0.489749i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.62861e8 | + | 6.07124e9i | −0.0252412 | + | 0.940956i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.19136e9i | − | 0.182623i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.27379e9 | 1.25444 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.55897e8 | 0.0983632 | 0.0491816 | − | 0.998790i | \(-0.484339\pi\) | ||||
0.0491816 | + | 0.998790i | \(0.484339\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.80837e9i | 0.416596i | 0.978065 | + | 0.208298i | \(0.0667925\pi\) | ||||
−0.978065 | + | 0.208298i | \(0.933208\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.13011e9 | − | 1.37616e8i | −0.752779 | − | 0.0201934i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 3.26212e9i | − | 0.473516i | −0.971569 | − | 0.236758i | \(-0.923915\pi\) | ||
0.971569 | − | 0.236758i | \(-0.0760848\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.26677e10 | 1.81904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.38556e9 | −0.907122 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.08084e10i | − | 1.51902i | −0.650494 | − | 0.759511i | \(-0.725438\pi\) | ||
0.650494 | − | 0.759511i | \(-0.274562\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.18182e9 | + | 3.17024e7i | 0.164326 | + | 0.00440806i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 7.56053e9i | − | 1.04010i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.98310e9 | 0.542153 | 0.271077 | − | 0.962558i | \(-0.412620\pi\) | ||||
0.271077 | + | 0.962558i | \(0.412620\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.29255e9 | 0.578109 | 0.289055 | − | 0.957313i | \(-0.406659\pi\) | ||||
0.289055 | + | 0.957313i | \(0.406659\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 8.88861e9i | − | 1.18450i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.44443e7 | − | 1.28404e9i | 0.00454195 | − | 0.169317i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.85378e9i | 0.894314i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.09346e9 | 0.399442 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.03417e10 | −1.32149 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.87778e9i | − | 0.490377i | −0.969475 | − | 0.245189i | \(-0.921150\pi\) | ||
0.969475 | − | 0.245189i | \(-0.0788499\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.17181e8 | + | 4.04518e9i | −0.0271805 | + | 0.506261i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.11448e8i | 0.0881217i | 0.999029 | + | 0.0440609i | \(0.0140295\pi\) | ||||
−0.999029 | + | 0.0440609i | \(0.985970\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.03207e10 | 1.26522 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.17574e10 | 1.42658 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5.88562e9i | − | 0.706838i | −0.935465 | − | 0.353419i | \(-0.885019\pi\) | ||
0.935465 | − | 0.353419i | \(-0.114981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.13766e8 | + | 4.24105e9i | −0.0135237 | + | 0.504146i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.42010e10i | 1.67098i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.63565e10 | −1.90512 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.37685e10 | −1.58750 | −0.793750 | − | 0.608244i | \(-0.791874\pi\) | ||||
−0.793750 | + | 0.608244i | \(0.791874\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.37073e10i | 1.56454i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.08385e10 | − | 2.90742e8i | −1.22467 | − | 0.0328520i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.34717e9i | 0.374424i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.56444e9 | −0.505495 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.72222e9 | 0.517766 | 0.258883 | − | 0.965909i | \(-0.416646\pi\) | ||||
0.258883 | + | 0.965909i | \(0.416646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.49528e9i | − | 0.270879i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.52084e10 | − | 4.07966e8i | −1.63464 | − | 0.0438492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 5.91037e9i | − | 0.628994i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.89205e9 | 0.831626 | 0.415813 | − | 0.909450i | \(-0.363497\pi\) | ||||
0.415813 | + | 0.909450i | \(0.363497\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.60131e10 | −1.67082 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.77264e9i | 0.803073i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.87874e8 | − | 2.19151e10i | 0.0601469 | − | 2.24219i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 4.87679e9i | − | 0.494102i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.46373e10 | 1.46862 | 0.734311 | − | 0.678813i | \(-0.237505\pi\) | ||||
0.734311 | + | 0.678813i | \(0.237505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.55121e9 | 0.352860 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.56797e10i | 1.54295i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.14791e9 | − | 3.83762e8i | −0.696620 | − | 0.0374007i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.36906e10i | − | 1.32146i | −0.750624 | − | 0.660729i | \(-0.770247\pi\) | ||
0.750624 | − | 0.660729i | \(-0.229753\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.58702e10 | 1.51718 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.23091e9 | −0.211237 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.39509e9i | 0.693553i | 0.937948 | + | 0.346776i | \(0.112724\pi\) | ||||
−0.937948 | + | 0.346776i | \(0.887276\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.44577e7 | + | 1.65732e9i | −0.00412992 | + | 0.153958i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.03741e10i | − | 0.954580i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.61194e10 | −1.46924 | −0.734620 | − | 0.678479i | \(-0.762639\pi\) | ||||
−0.734620 | + | 0.678479i | \(0.762639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.47056e9 | −0.493933 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.86465e9i | − | 0.435101i | −0.976049 | − | 0.217551i | \(-0.930193\pi\) | ||
0.976049 | − | 0.217551i | \(-0.0698067\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.96977e8 | + | 7.96643e6i | 0.0263134 | + | 0.000705857i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.10456e10i | − | 0.969547i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.92893e9 | 0.254697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.68210e9 | −0.231065 | −0.115533 | − | 0.993304i | \(-0.536858\pi\) | ||||
−0.115533 | + | 0.993304i | \(0.536858\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.00253e9i | 0.256274i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.96539e10 | + | 5.27217e8i | 1.66201 | + | 0.0445836i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.25746e10i | 1.05356i | 0.850002 | + | 0.526779i | \(0.176600\pi\) | ||||
−0.850002 | + | 0.526779i | \(0.823400\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.92110e10 | 2.42493 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.02931e8 | −0.0660438 | −0.0330219 | − | 0.999455i | \(-0.510513\pi\) | ||||
−0.0330219 | + | 0.999455i | \(0.510513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.10543e10i | 0.900938i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.89458e8 | + | 7.06274e9i | −0.0153003 | + | 0.570372i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.32293e10i | 2.65911i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.44845e9 | −0.749236 | −0.374618 | − | 0.927179i | \(-0.622226\pi\) | ||||
−0.374618 | + | 0.927179i | \(0.622226\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.77070e10 | 1.39141 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 8.28701e9i | − | 0.645312i | −0.946516 | − | 0.322656i | \(-0.895424\pi\) | ||
0.946516 | − | 0.322656i | \(-0.104576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.10620e9 | − | 4.35212e8i | −0.625549 | − | 0.0335849i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 2.87134e10i | − | 2.19590i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.06004e9 | 0.156133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.55308e10 | 1.16658 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 4.75102e9i | − | 0.353688i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.64411e6 | − | 2.47683e8i | 0.000490222 | − | 0.0182748i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.78703e10i | 1.30684i | 0.756997 | + | 0.653418i | \(0.226666\pi\) | ||||
−0.756997 | + | 0.653418i | \(0.773334\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.10703e10 | −1.52722 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.38656e10 | 0.996138 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.71279e10i | − | 1.93179i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.27538e10 | + | 6.10372e8i | 1.60609 | + | 0.0430834i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.71398e9i | 0.679662i | 0.940486 | + | 0.339831i | \(0.110370\pi\) | ||||
−0.940486 | + | 0.339831i | \(0.889630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.61360e9 | −0.458695 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.70477e9 | −0.392215 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.41919e10i | − | 0.967246i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.79851e10 | − | 4.82452e8i | −1.21514 | − | 0.0325963i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 2.42603e10i | − | 1.62494i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.81490e9 | 0.518924 | 0.259462 | − | 0.965753i | \(-0.416455\pi\) | ||||
0.259462 | + | 0.965753i | \(0.416455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.86034e10 | −1.22467 | −0.612334 | − | 0.790599i | \(-0.709769\pi\) | ||||
−0.612334 | + | 0.790599i | \(0.709769\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.02439e9i | 0.393185i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.61598e8 | − | 1.34799e10i | 0.0233978 | − | 0.872235i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.37303e9i | 0.0880851i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.59562e10 | −2.28708 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.49536e10 | −0.943072 | −0.471536 | − | 0.881847i | \(-0.656300\pi\) | ||||
−0.471536 | + | 0.881847i | \(0.656300\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.91042e9i | 0.557184i | 0.960409 | + | 0.278592i | \(0.0898678\pi\) | ||||
−0.960409 | + | 0.278592i | \(0.910132\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.63560e9 | + | 3.04645e10i | −0.101412 | + | 1.88889i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.03382e10i | 1.86518i | 0.360935 | + | 0.932591i | \(0.382457\pi\) | ||||
−0.360935 | + | 0.932591i | \(0.617543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.12896e10 | −0.688239 | −0.344120 | − | 0.938926i | \(-0.611823\pi\) | ||||
−0.344120 | + | 0.938926i | \(0.611823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.28833e10 | 1.38330 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.20711e8i | 0.0432020i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.84094e8 | + | 1.80463e10i | −0.0287758 | + | 1.07272i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.38797e9i | − | 0.317604i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.92069e10 | 1.12277 | 0.561384 | − | 0.827556i | \(-0.310269\pi\) | ||||
0.561384 | + | 0.827556i | \(0.310269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.85473e9 | −0.513321 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 4.17233e10i | − | 2.39874i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.99540e10 | + | 1.07177e9i | 2.27804 | + | 0.0611087i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.96105e9i | 0.506719i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.13590e10 | −1.75867 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.49506e10 | −1.94402 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.06518e9i | 0.444931i | 0.974941 | + | 0.222465i | \(0.0714104\pi\) | ||||
−0.974941 | + | 0.222465i | \(0.928590\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.34682e9 | + | 1.16604e8i | 0.237843 | + | 0.00638015i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 8.33806e9i | − | 0.452514i | −0.974068 | − | 0.226257i | \(-0.927351\pi\) | ||
0.974068 | − | 0.226257i | \(-0.0726489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.50871e10 | −1.88873 | −0.944367 | − | 0.328892i | \(-0.893325\pi\) | ||||
−0.944367 | + | 0.328892i | \(0.893325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.37052e10 | 1.26570 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.03137e10i | 1.07585i | 0.842993 | + | 0.537925i | \(0.180792\pi\) | ||||
−0.842993 | + | 0.537925i | \(0.819208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.10055e8 | − | 4.10270e9i | 0.00578168 | − | 0.215533i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 2.39271e10i | − | 1.24688i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00582e10 | −1.55380 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.72127e10 | 1.39543 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.49385e10i | 1.77727i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.51019e9 | − | 1.87299e10i | 0.0762086 | − | 0.945166i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.85549e10i | − | 0.928879i | −0.885605 | − | 0.464440i | \(-0.846256\pi\) | ||
0.885605 | − | 0.464440i | \(-0.153744\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.75803e10 | 1.86638 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.77206e10 | 0.873097 | 0.436549 | − | 0.899681i | \(-0.356201\pi\) | ||||
0.436549 | + | 0.899681i | \(0.356201\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.69416e9i | 0.229454i | 0.993397 | + | 0.114727i | \(0.0365993\pi\) | ||||
−0.993397 | + | 0.114727i | \(0.963401\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.24001e9 | − | 4.62258e10i | 0.0601345 | − | 2.24173i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.71147e10i | − | 1.78572i | −0.450336 | − | 0.892859i | \(-0.648696\pi\) | ||
0.450336 | − | 0.892859i | \(-0.351304\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.86981e10 | 0.892567 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.45882e10 | 0.690922 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.07039e9i | 0.191274i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.28783e9 | − | 3.45461e7i | −0.0600451 | − | 0.00161071i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.66246e10i | 3.54482i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.52065e9 | 0.437026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.89484e9 | 0.450684 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.57996e10i | 0.714067i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.50591e8 | + | 1.47696e7i | 0.0246922 | + | 0.000662369i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 9.96301e9i | − | 0.443369i | −0.975118 | − | 0.221684i | \(-0.928845\pi\) | ||
0.975118 | − | 0.221684i | \(-0.0711555\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.00082e10 | 0.883558 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.95417e10 | −0.856343 | −0.428171 | − | 0.903698i | \(-0.640842\pi\) | ||||
−0.428171 | + | 0.903698i | \(0.640842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.07338e10i | − | 0.901637i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.01233e9 | + | 3.77381e10i | −0.0436864 | + | 1.62857i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 3.63974e9i | − | 0.155876i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.22276e10 | −0.944687 | −0.472343 | − | 0.881415i | \(-0.656592\pi\) | ||||
−0.472343 | + | 0.881415i | \(0.656592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.89738e10 | 0.800289 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.07395e10i | 1.70533i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.95698e9 | − | 3.64505e10i | 0.0813000 | − | 1.51428i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.20218e10i | 0.495668i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.77199e10 | 0.725115 | 0.362557 | − | 0.931961i | \(-0.381904\pi\) | ||||
0.362557 | + | 0.931961i | \(0.381904\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.43567e8 | 0.0180151 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.05484e9i | 0.0828308i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.55633e8 | + | 1.32575e10i | −0.0142286 | + | 0.530422i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.62760e9i | 0.302900i | 0.988465 | + | 0.151450i | \(0.0483942\pi\) | ||||
−0.988465 | + | 0.151450i | \(0.951606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.74606e10 | −1.87070 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.75184e10 | −1.46784 | −0.733922 | − | 0.679233i | \(-0.762312\pi\) | ||||
−0.733922 | + | 0.679233i | \(0.762312\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.88544e10i | − | 1.12052i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.24672e10 | + | 3.34434e8i | 0.480572 | + | 0.0128914i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 3.60633e10i | − | 1.37988i | −0.723868 | − | 0.689939i | \(-0.757637\pi\) | ||
0.723868 | − | 0.689939i | \(-0.242363\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.72275e10 | 1.41394 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.29505e10 | −1.61933 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.82515e10i | − | 1.80587i | −0.429782 | − | 0.902933i | \(-0.641410\pi\) | ||
0.429782 | − | 0.902933i | \(-0.358590\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.14499e10 | − | 3.07146e8i | −0.425394 | − | 0.0114112i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 3.57803e10i | − | 1.31963i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.30615e10 | 0.478219 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.67156e10 | −0.607560 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.91525e9i | 0.357777i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.14142e8 | + | 2.28944e10i | −0.0220000 | + | 0.820130i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.37995e10i | 0.490763i | 0.969427 | + | 0.245381i | \(0.0789132\pi\) | ||||
−0.969427 | + | 0.245381i | \(0.921087\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.30941e9 | 0.116847 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.97135e10 | 1.39210 | 0.696051 | − | 0.717992i | \(-0.254939\pi\) | ||||
0.696051 | + | 0.717992i | \(0.254939\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.33801e10i | 1.16169i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.99129e10 | − | 4.29042e9i | −2.76122 | − | 0.148246i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.50857e9i | − | 0.0860589i | −0.999074 | − | 0.0430294i | \(-0.986299\pi\) | ||
0.999074 | − | 0.0430294i | \(-0.0137009\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.07085e10 | −0.364744 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.74218e10 | −1.26556 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.09376e9i | 0.137463i | 0.997635 | + | 0.0687313i | \(0.0218951\pi\) | ||||
−0.997635 | + | 0.0687313i | \(0.978105\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.09952e9 | + | 4.09887e10i | −0.0366588 | + | 1.36659i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.68385e10i | 1.55057i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.92316e10 | 0.632162 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.58598e10 | 0.517653 | 0.258827 | − | 0.965924i | \(-0.416664\pi\) | ||||
0.258827 | + | 0.965924i | \(0.416664\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 7.69828e10i | − | 2.49501i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.29966e9 | + | 1.15339e8i | 0.138374 | + | 0.00371188i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.86132e10i | 1.23396i | 0.786977 | + | 0.616982i | \(0.211645\pi\) | ||||
−0.786977 | + | 0.616982i | \(0.788355\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.42277e10 | 0.768833 |
(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 | 20.8.c.a.9.1 | ✓ | 4 | |
3.2 | odd | 2 | 180.8.d.b.109.4 | 4 | |||
4.3 | odd | 2 | 80.8.c.c.49.4 | 4 | |||
5.2 | odd | 4 | 100.8.a.e.1.1 | 4 | |||
5.3 | odd | 4 | 100.8.a.e.1.4 | 4 | |||
5.4 | even | 2 | inner | 20.8.c.a.9.4 | yes | 4 | |
8.3 | odd | 2 | 320.8.c.i.129.1 | 4 | |||
8.5 | even | 2 | 320.8.c.j.129.4 | 4 | |||
15.14 | odd | 2 | 180.8.d.b.109.3 | 4 | |||
20.3 | even | 4 | 400.8.a.bk.1.1 | 4 | |||
20.7 | even | 4 | 400.8.a.bk.1.4 | 4 | |||
20.19 | odd | 2 | 80.8.c.c.49.1 | 4 | |||
40.19 | odd | 2 | 320.8.c.i.129.4 | 4 | |||
40.29 | even | 2 | 320.8.c.j.129.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.8.c.a.9.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
20.8.c.a.9.4 | yes | 4 | 5.4 | even | 2 | inner | |
80.8.c.c.49.1 | 4 | 20.19 | odd | 2 | |||
80.8.c.c.49.4 | 4 | 4.3 | odd | 2 | |||
100.8.a.e.1.1 | 4 | 5.2 | odd | 4 | |||
100.8.a.e.1.4 | 4 | 5.3 | odd | 4 | |||
180.8.d.b.109.3 | 4 | 15.14 | odd | 2 | |||
180.8.d.b.109.4 | 4 | 3.2 | odd | 2 | |||
320.8.c.i.129.1 | 4 | 8.3 | odd | 2 | |||
320.8.c.i.129.4 | 4 | 40.19 | odd | 2 | |||
320.8.c.j.129.1 | 4 | 40.29 | even | 2 | |||
320.8.c.j.129.4 | 4 | 8.5 | even | 2 | |||
400.8.a.bk.1.1 | 4 | 20.3 | even | 4 | |||
400.8.a.bk.1.4 | 4 | 20.7 | even | 4 |