Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,5,Mod(193,400)]
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([0, 0, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.193");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.p (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(41.3479852335\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.257 |
Dual form | 400.5.p.c.193.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 9.00000 | − | 9.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.0000 | + | 29.0000i | 0.591837 | + | 0.591837i | 0.938127 | − | 0.346291i | \(-0.112559\pi\) |
−0.346291 | + | 0.938127i | \(0.612559\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 81.0000i | − | 1.00000i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 118.000 | 0.975207 | 0.487603 | − | 0.873065i | \(-0.337871\pi\) | ||||
0.487603 | + | 0.873065i | \(0.337871\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −69.0000 | + | 69.0000i | −0.408284 | + | 0.408284i | −0.881140 | − | 0.472856i | \(-0.843223\pi\) |
0.472856 | + | 0.881140i | \(0.343223\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 271.000 | + | 271.000i | 0.937716 | + | 0.937716i | 0.998171 | − | 0.0604547i | \(-0.0192551\pi\) |
−0.0604547 | + | 0.998171i | \(0.519255\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 280.000i | − | 0.775623i | −0.921739 | − | 0.387812i | \(-0.873231\pi\) | ||
0.921739 | − | 0.387812i | \(-0.126769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 522.000 | 1.18367 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 269.000 | − | 269.000i | 0.508507 | − | 0.508507i | −0.405561 | − | 0.914068i | \(-0.632924\pi\) |
0.914068 | + | 0.405561i | \(0.132924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 680.000i | 0.808561i | 0.914635 | + | 0.404281i | \(0.132478\pi\) | ||||
−0.914635 | + | 0.404281i | \(0.867522\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −202.000 | −0.210198 | −0.105099 | − | 0.994462i | \(-0.533516\pi\) | ||||
−0.105099 | + | 0.994462i | \(0.533516\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1062.00 | − | 1062.00i | 0.975207 | − | 0.975207i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 651.000 | + | 651.000i | 0.475530 | + | 0.475530i | 0.903699 | − | 0.428169i | \(-0.140841\pi\) |
−0.428169 | + | 0.903699i | \(0.640841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1242.00i | 0.816568i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1682.00 | 1.00059 | 0.500297 | − | 0.865854i | \(-0.333224\pi\) | ||||
0.500297 | + | 0.865854i | \(0.333224\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1089.00 | − | 1089.00i | 0.588967 | − | 0.588967i | −0.348385 | − | 0.937352i | \(-0.613270\pi\) |
0.937352 | + | 0.348385i | \(0.113270\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1269.00 | + | 1269.00i | 0.574468 | + | 0.574468i | 0.933374 | − | 0.358906i | \(-0.116850\pi\) |
−0.358906 | + | 0.933374i | \(0.616850\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 719.000i | − | 0.299459i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4878.00 | 1.87543 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 611.000 | − | 611.000i | 0.217515 | − | 0.217515i | −0.589935 | − | 0.807450i | \(-0.700847\pi\) |
0.807450 | + | 0.589935i | \(0.200847\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2520.00 | − | 2520.00i | −0.775623 | − | 0.775623i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1160.00i | − | 0.333238i | −0.986021 | − | 0.166619i | \(-0.946715\pi\) | ||
0.986021 | − | 0.166619i | \(-0.0532849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5598.00 | −1.50443 | −0.752217 | − | 0.658915i | \(-0.771016\pi\) | ||||
−0.752217 | + | 0.658915i | \(0.771016\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2349.00 | − | 2349.00i | 0.591837 | − | 0.591837i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −751.000 | − | 751.000i | −0.167298 | − | 0.167298i | 0.618493 | − | 0.785791i | \(-0.287744\pi\) |
−0.785791 | + | 0.618493i | \(0.787744\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4842.00i | − | 1.01701i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6442.00 | −1.27792 | −0.638961 | − | 0.769240i | \(-0.720635\pi\) | ||||
−0.638961 | + | 0.769240i | \(0.720635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2951.00 | − | 2951.00i | 0.553762 | − | 0.553762i | −0.373762 | − | 0.927525i | \(-0.621932\pi\) |
0.927525 | + | 0.373762i | \(0.121932\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3422.00 | + | 3422.00i | 0.577163 | + | 0.577163i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10560.0i | − | 1.69204i | −0.533154 | − | 0.846018i | \(-0.678993\pi\) | ||
0.533154 | − | 0.846018i | \(-0.321007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6231.00 | + | 6231.00i | −0.904485 | + | 0.904485i | −0.995820 | − | 0.0913348i | \(-0.970887\pi\) |
0.0913348 | + | 0.995820i | \(0.470887\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6120.00 | + | 6120.00i | 0.808561 | + | 0.808561i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 14480.0i | − | 1.82805i | −0.405656 | − | 0.914026i | \(-0.632957\pi\) | ||
0.405656 | − | 0.914026i | \(-0.367043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4002.00 | −0.483275 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1818.00 | + | 1818.00i | −0.210198 | + | 0.210198i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7311.00 | + | 7311.00i | 0.777022 | + | 0.777022i | 0.979323 | − | 0.202301i | \(-0.0648420\pi\) |
−0.202301 | + | 0.979323i | \(0.564842\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 9558.00i | − | 0.975207i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −878.000 | −0.0860700 | −0.0430350 | − | 0.999074i | \(-0.513703\pi\) | ||||
−0.0430350 | + | 0.999074i | \(0.513703\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10429.0 | − | 10429.0i | 0.983033 | − | 0.983033i | −0.0168252 | − | 0.999858i | \(-0.505356\pi\) |
0.999858 | + | 0.0168252i | \(0.00535587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4711.00 | − | 4711.00i | −0.411477 | − | 0.411477i | 0.470776 | − | 0.882253i | \(-0.343974\pi\) |
−0.882253 | + | 0.470776i | \(0.843974\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22040.0i | 1.85506i | 0.373745 | + | 0.927531i | \(0.378073\pi\) | ||||
−0.373745 | + | 0.927531i | \(0.621927\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11718.0 | 0.951059 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2111.00 | − | 2111.00i | 0.165322 | − | 0.165322i | −0.619597 | − | 0.784920i | \(-0.712704\pi\) |
0.784920 | + | 0.619597i | \(0.212704\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5589.00 | + | 5589.00i | 0.408284 | + | 0.408284i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15718.0i | 1.10995i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −717.000 | −0.0489721 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15138.0 | − | 15138.0i | 1.00059 | − | 1.00059i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5909.00 | + | 5909.00i | 0.366359 | + | 0.366359i | 0.866147 | − | 0.499789i | \(-0.166589\pi\) |
−0.499789 | + | 0.866147i | \(0.666589\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 19602.0i | − | 1.17793i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6358.00 | 0.370491 | 0.185246 | − | 0.982692i | \(-0.440692\pi\) | ||||
0.185246 | + | 0.982692i | \(0.440692\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8120.00 | − | 8120.00i | 0.459042 | − | 0.459042i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −20409.0 | − | 20409.0i | −1.08738 | − | 1.08738i | −0.995798 | − | 0.0915804i | \(-0.970808\pi\) |
−0.0915804 | − | 0.995798i | \(-0.529192\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9400.00i | 0.486517i | 0.969961 | + | 0.243259i | \(0.0782164\pi\) | ||||
−0.969961 | + | 0.243259i | \(0.921784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22842.0 | 1.14894 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8142.00 | + | 8142.00i | −0.398161 | + | 0.398161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6471.00 | − | 6471.00i | −0.299459 | − | 0.299459i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13800.0i | 0.621594i | 0.950476 | + | 0.310797i | \(0.100596\pi\) | ||||
−0.950476 | + | 0.310797i | \(0.899404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18998.0 | 0.833209 | 0.416605 | − | 0.909088i | \(-0.363220\pi\) | ||||
0.416605 | + | 0.909088i | \(0.363220\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21951.0 | − | 21951.0i | 0.937716 | − | 0.937716i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16371.0 | + | 16371.0i | 0.664165 | + | 0.664165i | 0.956359 | − | 0.292194i | \(-0.0943853\pi\) |
−0.292194 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 10998.0i | − | 0.435030i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15602.0 | 0.601906 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20009.0 | − | 20009.0i | 0.753096 | − | 0.753096i | −0.221960 | − | 0.975056i | \(-0.571245\pi\) |
0.975056 | + | 0.221960i | \(0.0712455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1549.00 | + | 1549.00i | 0.0555416 | + | 0.0555416i | 0.734332 | − | 0.678790i | \(-0.237496\pi\) |
−0.678790 | + | 0.734332i | \(0.737496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19039.0i | 0.666608i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −22680.0 | −0.775623 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2789.00 | + | 2789.00i | −0.0931872 | + | 0.0931872i | −0.752164 | − | 0.658976i | \(-0.770990\pi\) |
0.658976 | + | 0.752164i | \(0.270990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10440.0 | − | 10440.0i | −0.333238 | − | 0.333238i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2600.00i | 0.0811460i | 0.999177 | + | 0.0405730i | \(0.0129183\pi\) | ||||
−0.999177 | + | 0.0405730i | \(0.987082\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −44398.0 | −1.35521 | −0.677604 | − | 0.735427i | \(-0.736982\pi\) | ||||
−0.677604 | + | 0.735427i | \(0.736982\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −50382.0 | + | 50382.0i | −1.50443 | + | 1.50443i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31978.0 | + | 31978.0i | 0.914467 | + | 0.914467i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14678.0 | 0.402346 | 0.201173 | − | 0.979556i | \(-0.435525\pi\) | ||||
0.201173 | + | 0.979556i | \(0.435525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −42849.0 | + | 42849.0i | −1.15034 | + | 1.15034i | −0.163855 | + | 0.986484i | \(0.552393\pi\) |
−0.986484 | + | 0.163855i | \(0.947607\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10971.0 | + | 10971.0i | 0.282692 | + | 0.282692i | 0.834182 | − | 0.551490i | \(-0.185940\pi\) |
−0.551490 | + | 0.834182i | \(0.685940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 38160.0i | 0.963612i | 0.876278 | + | 0.481806i | \(0.160019\pi\) | ||||
−0.876278 | + | 0.481806i | \(0.839981\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13518.0 | −0.334596 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19720.0 | + | 19720.0i | −0.478536 | + | 0.478536i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21789.0 | − | 21789.0i | −0.508507 | − | 0.508507i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 33040.0i | − | 0.756393i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −72842.0 | −1.63613 | −0.818063 | − | 0.575128i | \(-0.804952\pi\) | ||||
−0.818063 | + | 0.575128i | \(0.804952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −57978.0 | + | 57978.0i | −1.27792 | + | 1.27792i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5858.00 | − | 5858.00i | −0.124403 | − | 0.124403i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 53118.0i | − | 1.10752i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37398.0 | −0.765709 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −30891.0 | + | 30891.0i | −0.621187 | + | 0.621187i | −0.945835 | − | 0.324648i | \(-0.894754\pi\) |
0.324648 | + | 0.945835i | \(0.394754\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −54911.0 | − | 54911.0i | −1.06563 | − | 1.06563i | −0.997689 | − | 0.0679438i | \(-0.978356\pi\) |
−0.0679438 | − | 0.997689i | \(-0.521644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 50280.0i | − | 0.958792i | −0.877599 | − | 0.479396i | \(-0.840856\pi\) | ||
0.877599 | − | 0.479396i | \(-0.159144\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 61596.0 | 1.15433 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2391.00 | − | 2391.00i | 0.0440421 | − | 0.0440421i | −0.684743 | − | 0.728785i | \(-0.740085\pi\) |
0.728785 | + | 0.684743i | \(0.240085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −95040.0 | − | 95040.0i | −1.69204 | − | 1.69204i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17760.0i | 0.310919i | 0.987842 | + | 0.155459i | \(0.0496858\pi\) | ||||
−0.987842 | + | 0.155459i | \(0.950314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28238.0 | −0.486183 | −0.243092 | − | 0.970003i | \(-0.578162\pi\) | ||||
−0.243092 | + | 0.970003i | \(0.578162\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | − | 59049.0i | 1.00000 | − | 1.00000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19320.0 | + | 19320.0i | 0.316675 | + | 0.316675i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 112158.i | 1.80897i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −121002. | −1.92064 | −0.960318 | − | 0.278907i | \(-0.910028\pi\) | ||||
−0.960318 | + | 0.278907i | \(0.910028\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31742.0 | − | 31742.0i | 0.495899 | − | 0.495899i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 72431.0 | + | 72431.0i | 1.09663 | + | 1.09663i | 0.994803 | + | 0.101823i | \(0.0324674\pi\) |
0.101823 | + | 0.994803i | \(0.467533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 37758.0i | 0.562872i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 55080.0 | 0.808561 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14771.0 | + | 14771.0i | −0.213549 | + | 0.213549i | −0.805773 | − | 0.592224i | \(-0.798250\pi\) |
0.592224 | + | 0.805773i | \(0.298250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −130320. | − | 130320.i | −1.82805 | − | 1.82805i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 89720.0i | 1.23989i | 0.784644 | + | 0.619947i | \(0.212846\pi\) | ||||
−0.784644 | + | 0.619947i | \(0.787154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −68202.0 | −0.928664 | −0.464332 | − | 0.885661i | \(-0.653706\pi\) | ||||
−0.464332 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −36018.0 | + | 36018.0i | −0.483275 | + | 0.483275i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18549.0 | − | 18549.0i | −0.241747 | − | 0.241747i | 0.575826 | − | 0.817573i | \(-0.304681\pi\) |
−0.817573 | + | 0.575826i | \(0.804681\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16362.0i | 0.210198i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2322.00 | 0.0294069 | 0.0147035 | − | 0.999892i | \(-0.495320\pi\) | ||||
0.0147035 | + | 0.999892i | \(0.495320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −91711.0 | + | 91711.0i | −1.14511 | + | 1.14511i | −0.157613 | + | 0.987501i | \(0.550380\pi\) |
−0.987501 | + | 0.157613i | \(0.949620\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48778.0 | + | 48778.0i | 0.592189 | + | 0.592189i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 63361.0i | 0.758624i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 131598. | 1.55404 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4851.00 | − | 4851.00i | 0.0565062 | − | 0.0565062i | −0.678289 | − | 0.734795i | \(-0.737278\pi\) |
0.734795 | + | 0.678289i | \(0.237278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37122.0i | 0.415230i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 63162.0 | 0.697145 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7902.00 | + | 7902.00i | −0.0860700 | + | 0.0860700i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 42849.0 | + | 42849.0i | 0.454636 | + | 0.454636i | 0.896890 | − | 0.442254i | \(-0.145821\pi\) |
−0.442254 | + | 0.896890i | \(0.645821\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 187722.i | − | 1.96607i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 72278.0 | 0.747283 | 0.373642 | − | 0.927573i | \(-0.378109\pi\) | ||||
0.373642 | + | 0.927573i | \(0.378109\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18249.0 | + | 18249.0i | −0.186273 | + | 0.186273i | −0.794083 | − | 0.607810i | \(-0.792048\pi\) |
0.607810 | + | 0.794083i | \(0.292048\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25149.0 | − | 25149.0i | −0.250266 | − | 0.250266i | 0.570814 | − | 0.821080i | \(-0.306628\pi\) |
−0.821080 | + | 0.570814i | \(0.806628\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 80240.0i | 0.788514i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −84798.0 | −0.822954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 75880.0 | − | 75880.0i | 0.727315 | − | 0.727315i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 198360. | + | 198360.i | 1.85506 | + | 1.85506i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 73602.0i | 0.679983i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 54038.0 | 0.493223 | 0.246611 | − | 0.969114i | \(-0.420683\pi\) | ||||
0.246611 | + | 0.969114i | \(0.420683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 52731.0 | − | 52731.0i | 0.475530 | − | 0.475530i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8529.00 | − | 8529.00i | −0.0750997 | − | 0.0750997i | 0.668559 | − | 0.743659i | \(-0.266911\pi\) |
−0.743659 | + | 0.668559i | \(0.766911\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 37998.0i | − | 0.330645i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23836.0 | −0.204986 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 90480.0 | − | 90480.0i | 0.769067 | − | 0.769067i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −56551.0 | − | 56551.0i | −0.469658 | − | 0.469658i | 0.432146 | − | 0.901804i | \(-0.357756\pi\) |
−0.901804 | + | 0.432146i | \(0.857756\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22520.0i | − | 0.184892i | −0.995718 | − | 0.0924459i | \(-0.970531\pi\) | ||
0.995718 | − | 0.0924459i | \(-0.0294685\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 44511.0 | − | 44511.0i | 0.357205 | − | 0.357205i | −0.505576 | − | 0.862782i | \(-0.668720\pi\) |
0.862782 | + | 0.505576i | \(0.168720\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 141462. | + | 141462.i | 1.10995 | + | 1.10995i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9680.00i | 0.0751080i | 0.999295 | + | 0.0375540i | \(0.0119566\pi\) | ||||
−0.999295 | + | 0.0375540i | \(0.988043\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51921.0 | 0.398409 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6453.00 | + | 6453.00i | −0.0489721 | + | 0.0489721i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14971.0 | − | 14971.0i | −0.111152 | − | 0.111152i | 0.649343 | − | 0.760496i | \(-0.275044\pi\) |
−0.760496 | + | 0.649343i | \(0.775044\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 136242.i | − | 1.00059i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35438.0 | 0.257467 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13811.0 | − | 13811.0i | 0.0992676 | − | 0.0992676i | −0.655729 | − | 0.754996i | \(-0.727639\pi\) |
0.754996 | + | 0.655729i | \(0.227639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −46920.0 | − | 46920.0i | −0.330123 | − | 0.330123i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 251080.i | − | 1.74797i | −0.485954 | − | 0.873984i | \(-0.661528\pi\) | ||
0.485954 | − | 0.873984i | \(-0.338472\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 106362. | 0.732717 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −86091.0 | + | 86091.0i | −0.586895 | + | 0.586895i | −0.936789 | − | 0.349894i | \(-0.886217\pi\) |
0.349894 | + | 0.936789i | \(0.386217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −88209.0 | − | 88209.0i | −0.588967 | − | 0.588967i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 75000.0i | − | 0.495635i | −0.968807 | − | 0.247818i | \(-0.920287\pi\) | ||
0.968807 | − | 0.247818i | \(-0.0797134\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 145798. | 0.953670 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 57222.0 | − | 57222.0i | 0.370491 | − | 0.370491i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29149.0 | − | 29149.0i | −0.184945 | − | 0.184945i | 0.608562 | − | 0.793507i | \(-0.291747\pi\) |
−0.793507 | + | 0.608562i | \(0.791747\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 146160.i | − | 0.918085i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −45918.0 | −0.285558 | −0.142779 | − | 0.989755i | \(-0.545604\pi\) | ||||
−0.142779 | + | 0.989755i | \(0.545604\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13938.0 | − | 13938.0i | 0.0858204 | − | 0.0858204i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 76818.0 | + | 76818.0i | 0.463740 | + | 0.463740i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 78720.0i | 0.470585i | 0.971925 | + | 0.235293i | \(0.0756049\pi\) | ||||
−0.971925 | + | 0.235293i | \(0.924395\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −367362. | −2.17476 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33640.0 | − | 33640.0i | 0.197222 | − | 0.197222i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 84600.0 | + | 84600.0i | 0.486517 | + | 0.486517i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14760.0i | 0.0840733i | 0.999116 | + | 0.0420367i | \(0.0133846\pi\) | ||||
−0.999116 | + | 0.0420367i | \(0.986615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 221282. | 1.24848 | 0.624240 | − | 0.781232i | \(-0.285409\pi\) | ||||
0.624240 | + | 0.781232i | \(0.285409\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 102789. | − | 102789.i | 0.574468 | − | 0.574468i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −162342. | − | 162342.i | −0.890379 | − | 0.890379i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 146556.i | 0.796323i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −212522. | −1.14406 | −0.572031 | − | 0.820232i | \(-0.693844\pi\) | ||||
−0.572031 | + | 0.820232i | \(0.693844\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −145409. | + | 145409.i | −0.775560 | + | 0.775560i | −0.979072 | − | 0.203512i | \(-0.934764\pi\) |
0.203512 | + | 0.979072i | \(0.434764\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −75320.0 | − | 75320.0i | −0.394410 | − | 0.394410i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 299440.i | 1.55375i | 0.629656 | + | 0.776874i | \(0.283196\pi\) | ||||
−0.629656 | + | 0.776874i | \(0.716804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −58239.0 | −0.299459 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 240609. | − | 240609.i | 1.22604 | − | 1.22604i | 0.260590 | − | 0.965450i | \(-0.416083\pi\) |
0.965450 | − | 0.260590i | \(-0.0839170\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 124200. | + | 124200.i | 0.621594 | + | 0.621594i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 82480.0i | − | 0.409125i | −0.978854 | − | 0.204562i | \(-0.934423\pi\) | ||
0.978854 | − | 0.204562i | \(-0.0655772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 198476. | 0.975787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 170982. | − | 170982.i | 0.833209 | − | 0.833209i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 188151. | + | 188151.i | 0.900895 | + | 0.900895i | 0.995514 | − | 0.0946187i | \(-0.0301632\pi\) |
−0.0946187 | + | 0.995514i | \(0.530163\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −326158. | −1.53471 | −0.767355 | − | 0.641223i | \(-0.778427\pi\) | ||||
−0.767355 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −218731. | + | 218731.i | −1.02035 | + | 1.02035i | −0.0205595 | + | 0.999789i | \(0.506545\pi\) |
−0.999789 | + | 0.0205595i | \(0.993455\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 59249.0 | + | 59249.0i | 0.271673 | + | 0.271673i | 0.829774 | − | 0.558100i | \(-0.188470\pi\) |
−0.558100 | + | 0.829774i | \(0.688470\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 43558.0i | − | 0.198026i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 294678. | 1.32833 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 128502. | − | 128502.i | 0.574365 | − | 0.574365i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −49491.0 | − | 49491.0i | −0.217515 | − | 0.217515i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 273440.i | − | 1.19177i | −0.803071 | − | 0.595883i | \(-0.796802\pi\) | ||
0.803071 | − | 0.595883i | \(-0.203198\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −89838.0 | −0.388302 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 140418. | − | 140418.i | 0.601906 | − | 0.601906i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −123651. | − | 123651.i | −0.521362 | − | 0.521362i | 0.396620 | − | 0.917983i | \(-0.370183\pi\) |
−0.917983 | + | 0.396620i | \(0.870183\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 360162.i | − | 1.50619i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −198442. | −0.823134 | −0.411567 | − | 0.911379i | \(-0.635018\pi\) | ||||
−0.411567 | + | 0.911379i | \(0.635018\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −184280. | + | 184280.i | −0.758201 | + | 0.758201i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −186818. | − | 186818.i | −0.756321 | − | 0.756321i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 269240.i | − | 1.08128i | −0.841254 | − | 0.540640i | \(-0.818182\pi\) | ||
0.841254 | − | 0.540640i | \(-0.181818\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27882.0 | 0.111083 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 109869. | − | 109869.i | 0.434249 | − | 0.434249i | −0.455822 | − | 0.890071i | \(-0.650655\pi\) |
0.890071 | + | 0.455822i | \(0.150655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 171351. | + | 171351.i | 0.666608 | + | 0.666608i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 211000.i | − | 0.814417i | −0.913335 | − | 0.407209i | \(-0.866502\pi\) | ||
0.913335 | − | 0.407209i | \(-0.133498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 171158. | 0.655474 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 149742. | + | 149742.i | 0.560225 | + | 0.560225i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 50202.0i | 0.186374i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 297282. | 1.09520 | 0.547600 | − | 0.836740i | \(-0.315542\pi\) | ||||
0.547600 | + | 0.836740i | \(0.315542\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25071.0 | + | 25071.0i | −0.0916576 | + | 0.0916576i | −0.751449 | − | 0.659791i | \(-0.770645\pi\) |
0.659791 | + | 0.751449i | \(0.270645\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −54742.0 | − | 54742.0i | −0.197106 | − | 0.197106i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 135119.i | 0.482842i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −93960.0 | −0.333238 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −116058. | + | 116058.i | −0.408527 | + | 0.408527i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 23400.0 | + | 23400.0i | 0.0811460 | + | 0.0811460i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 84842.0i | − | 0.292034i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −142478. | −0.486803 | −0.243402 | − | 0.969926i | \(-0.578263\pi\) | ||||
−0.243402 | + | 0.969926i | \(0.578263\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −399582. | + | 399582.i | −1.35521 | + | 1.35521i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 291009. | + | 291009.i | 0.972594 | + | 0.972594i | 0.999634 | − | 0.0270399i | \(-0.00860813\pi\) |
−0.0270399 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 453438.i | 1.50443i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 190400. | 0.627139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 306240. | − | 306240.i | 1.00141 | − | 1.00141i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 83091.0 | + | 83091.0i | 0.267820 | + | 0.267820i | 0.828221 | − | 0.560401i | \(-0.189353\pi\) |
−0.560401 | + | 0.828221i | \(0.689353\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 150282.i | 0.480932i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 575604. | 1.82893 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43449.0 | − | 43449.0i | 0.137076 | − | 0.137076i | −0.635239 | − | 0.772316i | \(-0.719098\pi\) |
0.772316 | + | 0.635239i | \(0.219098\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 190269. | + | 190269.i | 0.591837 | + | 0.591837i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 270560.i | − | 0.835678i | −0.908521 | − | 0.417839i | \(-0.862788\pi\) | ||
0.908521 | − | 0.417839i | \(-0.137212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −57482.0 | −0.176303 | −0.0881515 | − | 0.996107i | \(-0.528096\pi\) | ||||
−0.0881515 | + | 0.996107i | \(0.528096\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 132102. | − | 132102.i | 0.402346 | − | 0.402346i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −195889. | − | 195889.i | −0.588381 | − | 0.588381i | 0.348812 | − | 0.937193i | \(-0.386585\pi\) |
−0.937193 | + | 0.348812i | \(0.886585\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 771282.i | 2.30068i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −361398. | −1.07062 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 72098.0 | − | 72098.0i | 0.212122 | − | 0.212122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −404631. | − | 404631.i | −1.17431 | − | 1.17431i | −0.981171 | − | 0.193139i | \(-0.938133\pi\) |
−0.193139 | − | 0.981171i | \(-0.561867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56560.0i | 0.163034i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 197478. | 0.565384 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 210991. | − | 210991.i | 0.600005 | − | 0.600005i | −0.340309 | − | 0.940314i | \(-0.610532\pi\) |
0.940314 | + | 0.340309i | \(0.110532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 343440. | + | 343440.i | 0.963612 | + | 0.963612i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 300560.i | − | 0.837679i | −0.908060 | − | 0.418839i | \(-0.862437\pi\) | ||
0.908060 | − | 0.418839i | \(-0.137563\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 367442. | 1.01728 | 0.508639 | − | 0.860980i | \(-0.330149\pi\) | ||||
0.508639 | + | 0.860980i | \(0.330149\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −60831.0 | + | 60831.0i | −0.167298 | + | 0.167298i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 146469. | + | 146469.i | 0.397529 | + | 0.397529i | 0.877360 | − | 0.479832i | \(-0.159302\pi\) |
−0.479832 | + | 0.877360i | \(0.659302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 354960.i | 0.957072i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −175122. | −0.469092 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −160989. | + | 160989.i | −0.428425 | + | 0.428425i | −0.888092 | − | 0.459666i | \(-0.847969\pi\) |
0.459666 | + | 0.888092i | \(0.347969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −320409. | − | 320409.i | −0.841656 | − | 0.841656i | 0.147419 | − | 0.989074i | \(-0.452904\pi\) |
−0.989074 | + | 0.147419i | \(0.952904\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 341160.i | − | 0.890383i | −0.895435 | − | 0.445191i | \(-0.853136\pi\) | ||
0.895435 | − | 0.445191i | \(-0.146864\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 419920. | − | 419920.i | 1.08191 | − | 1.08191i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −297360. | − | 297360.i | −0.756393 | − | 0.756393i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 352842.i | 0.891824i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 390998. | 0.982010 | 0.491005 | − | 0.871157i | \(-0.336630\pi\) | ||||
0.491005 | + | 0.871157i | \(0.336630\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −655578. | + | 655578.i | −1.63613 | + | 1.63613i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 49611.0 | + | 49611.0i | 0.122264 | + | 0.122264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 521802.i | 1.27792i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −585038. | −1.42386 | −0.711931 | − | 0.702249i | \(-0.752179\pi\) | ||||
−0.711931 | + | 0.702249i | \(0.752179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31911.0 | + | 31911.0i | −0.0771824 | + | 0.0771824i | −0.744644 | − | 0.667462i | \(-0.767381\pi\) |
0.667462 | + | 0.744644i | \(0.267381\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −280931. | − | 280931.i | −0.671106 | − | 0.671106i | 0.286865 | − | 0.957971i | \(-0.407387\pi\) |
−0.957971 | + | 0.286865i | \(0.907387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 136880.i | − | 0.324975i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −105444. | −0.248805 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −523989. | + | 523989.i | −1.22884 | + | 1.22884i | −0.264439 | + | 0.964402i | \(0.585187\pi\) |
−0.964402 | + | 0.264439i | \(0.914813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −239031. | − | 239031.i | −0.553762 | − | 0.553762i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 404360.i | 0.931102i | 0.885021 | + | 0.465551i | \(0.154144\pi\) | ||||
−0.885021 | + | 0.465551i | \(0.845856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5278.00 | −0.0120800 | −0.00603999 | − | 0.999982i | \(-0.501923\pi\) | ||||
−0.00603999 | + | 0.999982i | \(0.501923\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −336582. | + | 336582.i | −0.765709 | + | 0.765709i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 182920. | + | 182920.i | 0.411159 | + | 0.411159i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 556038.i | 1.24237i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −660564. | −1.46713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 332111. | − | 332111.i | 0.733252 | − | 0.733252i | −0.238011 | − | 0.971263i | \(-0.576495\pi\) |
0.971263 | + | 0.238011i | \(0.0764953\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −578309. | − | 578309.i | −1.26178 | − | 1.26178i | −0.950231 | − | 0.311546i | \(-0.899153\pi\) |
−0.311546 | − | 0.950231i | \(-0.600847\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 424038.i | 0.919740i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −988398. | −2.13127 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −349311. | + | 349311.i | −0.748809 | + | 0.748809i | −0.974255 | − | 0.225447i | \(-0.927616\pi\) |
0.225447 | + | 0.974255i | \(0.427616\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −452520. | − | 452520.i | −0.958792 | − | 0.958792i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 84318.0i | 0.177616i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −282762. | −0.592195 | −0.296098 | − | 0.955158i | \(-0.595685\pi\) | ||||
−0.296098 | + | 0.955158i | \(0.595685\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 277182. | − | 277182.i | 0.577163 | − | 0.577163i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 455822. | + | 455822.i | 0.938274 | + | 0.938274i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 43038.0i | − | 0.0880841i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 270242. | 0.549942 | 0.274971 | − | 0.961453i | \(-0.411332\pi\) | ||||
0.274971 | + | 0.961453i | \(0.411332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 182280. | − | 182280.i | 0.368832 | − | 0.368832i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −25462.0 | − | 25462.0i | −0.0509394 | − | 0.0509394i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 297800.i | − | 0.592423i | −0.955122 | − | 0.296212i | \(-0.904277\pi\) | ||
0.955122 | − | 0.296212i | \(-0.0957234\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −855360. | −1.69204 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −54338.0 | + | 54338.0i | −0.106887 | + | 0.106887i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 159840. | + | 159840.i | 0.310919 | + | 0.310919i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 913760.i | − | 1.76756i | −0.467902 | − | 0.883780i | \(-0.654990\pi\) | ||
0.467902 | − | 0.883780i | \(-0.345010\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 604882. | 1.16359 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −254142. | + | 254142.i | −0.486183 | + | 0.486183i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −417651. | − | 417651.i | −0.790214 | − | 0.790214i | 0.191315 | − | 0.981529i | \(-0.438725\pi\) |
−0.981529 | + | 0.191315i | \(0.938725\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 531441.i | − | 1.00000i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 590238. | 1.10457 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −394549. | + | 394549.i | −0.734333 | + | 0.734333i | −0.971475 | − | 0.237142i | \(-0.923789\pi\) |
0.237142 | + | 0.971475i | \(0.423789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −88618.0 | − | 88618.0i | −0.163150 | − | 0.163150i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 109880.i | − | 0.201201i | −0.994927 | − | 0.100600i | \(-0.967924\pi\) | ||
0.994927 | − | 0.100600i | \(-0.0320764\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 347760. | 0.633349 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −466451. | + | 466451.i | −0.844945 | + | 0.844945i | −0.989497 | − | 0.144552i | \(-0.953826\pi\) |
0.144552 | + | 0.989497i | \(0.453826\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 504711. | + | 504711.i | 0.904485 | + | 0.904485i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 273238.i | − | 0.487054i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.01092e6 | −1.79241 | −0.896206 | − | 0.443638i | \(-0.853687\pi\) | ||||
−0.896206 | + | 0.443638i | \(0.853687\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.08902e6 | + | 1.08902e6i | −1.92064 | + | 1.92064i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −313269. | − | 313269.i | −0.546671 | − | 0.546671i | 0.378806 | − | 0.925476i | \(-0.376335\pi\) |
−0.925476 | + | 0.378806i | \(0.876335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 571356.i | − | 0.991798i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 142082. | 0.245341 | 0.122670 | − | 0.992447i | \(-0.460854\pi\) | ||||
0.122670 | + | 0.992447i | \(0.460854\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −639160. | + | 639160.i | −1.09789 | + | 1.09789i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 80040.0 | + | 80040.0i | 0.136056 | + | 0.136056i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13280.0i | 0.0224567i | 0.999937 | + | 0.0112283i | \(0.00357417\pi\) | ||||
−0.999937 | + | 0.0112283i | \(0.996426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.30376e6 | 2.19325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 782211. | − | 782211.i | 1.30908 | − | 1.30908i | 0.386994 | − | 0.922082i | \(-0.373513\pi\) |
0.922082 | − | 0.386994i | \(-0.126487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 339822. | + | 339822.i | 0.562872 | + | 0.562872i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 470960.i | − | 0.776085i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −760156. | −1.24624 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 201409. | + | 201409.i | 0.325184 | + | 0.325184i | 0.850752 | − | 0.525568i | \(-0.176147\pi\) |
−0.525568 | + | 0.850752i | \(0.676147\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 265878.i | 0.427099i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 122438. | 0.195688 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 386262. | − | 386262.i | 0.614236 | − | 0.614236i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36291.0 | + | 36291.0i | 0.0571324 | + | 0.0571324i | 0.735096 | − | 0.677963i | \(-0.237137\pi\) |
−0.677963 | + | 0.735096i | \(0.737137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 687798.i | 1.07738i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.17288e6 | −1.82805 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 348218. | − | 348218.i | 0.540033 | − | 0.540033i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 807480. | + | 807480.i | 1.23989 | + | 1.23989i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 71600.0i | − | 0.109400i | −0.998503 | − | 0.0546998i | \(-0.982580\pi\) | ||
0.998503 | − | 0.0546998i | \(-0.0174202\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 103318. | 0.157085 | 0.0785424 | − | 0.996911i | \(-0.474973\pi\) | ||||
0.0785424 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −613818. | + | 613818.i | −0.928664 | + | 0.928664i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −304920. | − | 304920.i | −0.456817 | − | 0.456817i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 324162.i | 0.483275i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −157438. | −0.233573 | −0.116787 | − | 0.993157i | \(-0.537259\pi\) | ||||
−0.116787 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 791309. | − | 791309.i | 1.16828 | − | 1.16828i | 0.185666 | − | 0.982613i | \(-0.440556\pi\) |
0.982613 | − | 0.185666i | \(-0.0594441\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −889671. | − | 889671.i | −1.30082 | − | 1.30082i | −0.927837 | − | 0.372987i | \(-0.878334\pi\) |
−0.372987 | − | 0.927837i | \(-0.621666\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 618280.i | − | 0.899655i | −0.893115 | − | 0.449828i | \(-0.851485\pi\) | ||
0.893115 | − | 0.449828i | \(-0.148515\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −333882. | −0.483494 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 194849. | − | 194849.i | 0.280807 | − | 0.280807i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 821360.i | 1.16684i | 0.812172 | + | 0.583418i | \(0.198285\pi\) | ||||
−0.812172 | + | 0.583418i | \(0.801715\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 244881. | 0.346229 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20898.0 | − | 20898.0i | 0.0294069 | − | 0.0294069i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20793.0 | − | 20793.0i | −0.0289835 | − | 0.0289835i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.65080e6i | 2.29023i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 350238. | 0.483620 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 698291. | − | 698291.i | 0.959706 | − | 0.959706i | −0.0395127 | − | 0.999219i | \(-0.512581\pi\) |
0.999219 | + | 0.0395127i | \(0.0125806\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −144489. | − | 144489.i | −0.196731 | − | 0.196731i | 0.601866 | − | 0.798597i | \(-0.294424\pi\) |
−0.798597 | + | 0.601866i | \(0.794424\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 943480.i | 1.27863i | 0.768943 | + | 0.639317i | \(0.220783\pi\) | ||||
−0.768943 | + | 0.639317i | \(0.779217\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 878004. | 1.18438 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 438149. | − | 438149.i | 0.588302 | − | 0.588302i | −0.348869 | − | 0.937171i | \(-0.613434\pi\) |
0.937171 | + | 0.348869i | \(0.113434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 570249. | + | 570249.i | 0.758624 | + | 0.758624i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.24608e6i | − | 1.65009i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 103638. | 0.136610 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 592191. | − | 592191.i | 0.777022 | − | 0.777022i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −281469. | − | 281469.i | −0.365958 | − | 0.365958i | 0.500043 | − | 0.866001i | \(-0.333318\pi\) |
−0.866001 | + | 0.500043i | \(0.833318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 87318.0i | − | 0.113012i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 876722. | 1.12956 | 0.564781 | − | 0.825241i | \(-0.308961\pi\) | ||||
0.564781 | + | 0.825241i | \(0.308961\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −327431. | + | 327431.i | −0.419951 | + | 0.419951i | −0.885187 | − | 0.465236i | \(-0.845969\pi\) |
0.465236 | + | 0.885187i | \(0.345969\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −477171. | − | 477171.i | −0.606494 | − | 0.606494i | 0.335534 | − | 0.942028i | \(-0.391083\pi\) |
−0.942028 | + | 0.335534i | \(0.891083\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 342722.i | 0.433649i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 774198. | 0.975207 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 355320. | − | 355320.i | 0.445571 | − | 0.445571i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 334098. | + | 334098.i | 0.415230 | + | 0.415230i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 137360.i | − | 0.169958i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 331162. | 0.407935 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 568458. | − | 568458.i | 0.697145 | − | 0.697145i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.11209e6 | + | 1.11209e6i | 1.35184 | + | 1.35184i | 0.883604 | + | 0.468235i | \(0.155110\pi\) |
0.468235 | + | 0.883604i | \(0.344890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 71118.0i | 0.0860700i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 883958. | 1.06511 | 0.532556 | − | 0.846395i | \(-0.321232\pi\) | ||||
0.532556 | + | 0.846395i | \(0.321232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −735258. | + | 735258.i | −0.882060 | + | 0.882060i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 184382. | + | 184382.i | 0.219270 | + | 0.219270i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.24040e6i | − | 1.46869i | −0.678775 | − | 0.734346i | \(-0.737489\pi\) | ||
0.678775 | − | 0.734346i | \(-0.262511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 771282. | 0.909272 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 444498. | − | 444498.i | 0.521755 | − | 0.521755i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −844749. | − | 844749.i | −0.983033 | − | 0.983033i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.22744e6i | 1.42223i | 0.703077 | + | 0.711113i | \(0.251809\pi\) | ||||
−0.703077 | + | 0.711113i | \(0.748191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −201320. | −0.232267 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 650502. | − | 650502.i | 0.747283 | − | 0.747283i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.07047e6 | + | 1.07047e6i | 1.21926 | + | 1.21926i | 0.967892 | + | 0.251366i | \(0.0808799\pi\) |
0.251366 | + | 0.967892i | \(0.419120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 328482.i | 0.372546i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 558642. | 0.630891 | 0.315446 | − | 0.948944i | \(-0.397846\pi\) | ||||
0.315446 | + | 0.948944i | \(0.397846\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 452458. | − | 452458.i | 0.508809 | − | 0.508809i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −191711. | − | 191711.i | −0.213770 | − | 0.213770i | 0.592097 | − | 0.805867i | \(-0.298300\pi\) |
−0.805867 | + | 0.592097i | \(0.798300\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 407238.i | 0.452185i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −452682. | −0.500532 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 630231. | − | 630231.i | 0.693927 | − | 0.693927i | −0.269166 | − | 0.963094i | \(-0.586748\pi\) |
0.963094 | + | 0.269166i | \(0.0867482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 722160. | + | 722160.i | 0.788514 | + | 0.788514i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1.18372e6i | − | 1.28710i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −882717. | −0.955817 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −381591. | + | 381591.i | −0.411477 | + | 0.411477i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −345491. | − | 345491.i | −0.369474 | − | 0.369474i | 0.497811 | − | 0.867285i | \(-0.334137\pi\) |
−0.867285 | + | 0.497811i | \(0.834137\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.36584e6i | − | 1.45463i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.08308e6 | −1.14874 | −0.574372 | − | 0.818595i | \(-0.694753\pi\) | ||||
−0.574372 | + | 0.818595i | \(0.694753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −272600. | + | 272600.i | −0.287939 | + | 0.287939i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 146751. | + | 146751.i | 0.153742 | + | 0.153742i | 0.779787 | − | 0.626045i | \(-0.215327\pi\) |
−0.626045 | + | 0.779787i | \(0.715327\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.70864e6i | − | 1.78273i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.78524e6 | 1.85506 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 466909. | − | 466909.i | 0.483198 | − | 0.483198i | −0.422953 | − | 0.906151i | \(-0.639007\pi\) |
0.906151 | + | 0.422953i | \(0.139007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 662418. | + | 662418.i | 0.679983 | + | 0.679983i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 585882.i | − | 0.598987i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 901238. | 0.917682 | 0.458841 | − | 0.888518i | \(-0.348265\pi\) | ||||
0.458841 | + | 0.888518i | \(0.348265\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 486342. | − | 486342.i | 0.493223 | − | 0.493223i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −152149. | − | 152149.i | −0.153066 | − | 0.153066i | 0.626420 | − | 0.779486i | \(-0.284520\pi\) |
−0.779486 | + | 0.626420i | \(0.784520\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 400.5.p.c.257.1 | 2 | ||
4.3 | odd | 2 | 50.5.c.b.7.1 | 2 | |||
5.2 | odd | 4 | 80.5.p.b.33.1 | 2 | |||
5.3 | odd | 4 | inner | 400.5.p.c.193.1 | 2 | ||
5.4 | even | 2 | 80.5.p.b.17.1 | 2 | |||
12.11 | even | 2 | 450.5.g.a.307.1 | 2 | |||
20.3 | even | 4 | 50.5.c.b.43.1 | 2 | |||
20.7 | even | 4 | 10.5.c.a.3.1 | ✓ | 2 | ||
20.19 | odd | 2 | 10.5.c.a.7.1 | yes | 2 | ||
40.19 | odd | 2 | 320.5.p.b.257.1 | 2 | |||
40.27 | even | 4 | 320.5.p.b.193.1 | 2 | |||
40.29 | even | 2 | 320.5.p.i.257.1 | 2 | |||
40.37 | odd | 4 | 320.5.p.i.193.1 | 2 | |||
60.23 | odd | 4 | 450.5.g.a.343.1 | 2 | |||
60.47 | odd | 4 | 90.5.g.b.73.1 | 2 | |||
60.59 | even | 2 | 90.5.g.b.37.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.5.c.a.3.1 | ✓ | 2 | 20.7 | even | 4 | ||
10.5.c.a.7.1 | yes | 2 | 20.19 | odd | 2 | ||
50.5.c.b.7.1 | 2 | 4.3 | odd | 2 | |||
50.5.c.b.43.1 | 2 | 20.3 | even | 4 | |||
80.5.p.b.17.1 | 2 | 5.4 | even | 2 | |||
80.5.p.b.33.1 | 2 | 5.2 | odd | 4 | |||
90.5.g.b.37.1 | 2 | 60.59 | even | 2 | |||
90.5.g.b.73.1 | 2 | 60.47 | odd | 4 | |||
320.5.p.b.193.1 | 2 | 40.27 | even | 4 | |||
320.5.p.b.257.1 | 2 | 40.19 | odd | 2 | |||
320.5.p.i.193.1 | 2 | 40.37 | odd | 4 | |||
320.5.p.i.257.1 | 2 | 40.29 | even | 2 | |||
400.5.p.c.193.1 | 2 | 5.3 | odd | 4 | inner | ||
400.5.p.c.257.1 | 2 | 1.1 | even | 1 | trivial | ||
450.5.g.a.307.1 | 2 | 12.11 | even | 2 | |||
450.5.g.a.343.1 | 2 | 60.23 | odd | 4 |