Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,5,Mod(193,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.193");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(33.0783881868\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.193 |
Dual form | 320.5.p.b.257.1 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −9.00000 | − | 9.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.0000 | + | 20.0000i | 0.600000 | + | 0.800000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.0000 | − | 29.0000i | 0.591837 | − | 0.591837i | −0.346291 | − | 0.938127i | \(-0.612559\pi\) |
0.938127 | + | 0.346291i | \(0.112559\pi\) | |||||||
\(8\) | 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 | 0.472856 | − | 0.881140i | \(-0.343223\pi\) |
−0.881140 | + | 0.472856i | \(0.843223\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 45.0000 | − | 315.000i | 0.200000 | − | 1.40000i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −271.000 | + | 271.000i | −0.937716 | + | 0.937716i | −0.998171 | − | 0.0604547i | \(-0.980745\pi\) |
0.0604547 | + | 0.998171i | \(0.480745\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 280.000i | 0.775623i | 0.921739 | + | 0.387812i | \(0.126769\pi\) | ||||
−0.921739 | + | 0.387812i | \(0.873231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −522.000 | −1.18367 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 269.000 | + | 269.000i | 0.508507 | + | 0.508507i | 0.914068 | − | 0.405561i | \(-0.132924\pi\) |
−0.405561 | + | 0.914068i | \(0.632924\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −175.000 | + | 600.000i | −0.280000 | + | 0.960000i | ||||
\(26\) | 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 | \(-0.466484\pi\) | ||||
0.105099 | + | 0.994462i | \(0.466484\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1062.00 | − | 1062.00i | −0.975207 | − | 0.975207i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1015.00 | + | 145.000i | 0.828571 | + | 0.118367i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 651.000 | − | 651.000i | 0.475530 | − | 0.475530i | −0.428169 | − | 0.903699i | \(-0.640841\pi\) |
0.903699 | + | 0.428169i | \(0.140841\pi\) | |||||||
\(38\) | 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 | \(-0.386730\pi\) |
−0.937352 | + | 0.348385i | \(0.886730\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1620.00 | + | 1215.00i | −0.800000 | + | 0.600000i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1269.00 | − | 1269.00i | 0.574468 | − | 0.574468i | −0.358906 | − | 0.933374i | \(-0.616850\pi\) |
0.933374 | + | 0.358906i | \(0.116850\pi\) | |||||||
\(48\) | 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 | 0.807450 | − | 0.589935i | \(-0.200847\pi\) |
−0.589935 | + | 0.807450i | \(0.700847\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1770.00 | + | 2360.00i | 0.585124 | + | 0.780165i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2520.00 | − | 2520.00i | 0.775623 | − | 0.775623i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1160.00i | 0.333238i | 0.986021 | + | 0.166619i | \(0.0532849\pi\) | ||||
−0.986021 | + | 0.166619i | \(0.946715\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5598.00 | 1.50443 | 0.752217 | − | 0.658915i | \(-0.228984\pi\) | ||||
0.752217 | + | 0.658915i | \(0.228984\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2349.00 | + | 2349.00i | 0.591837 | + | 0.591837i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 345.000 | − | 2415.00i | 0.0816568 | − | 0.571598i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 751.000 | − | 751.000i | 0.167298 | − | 0.167298i | −0.618493 | − | 0.785791i | \(-0.712256\pi\) |
0.785791 | + | 0.618493i | \(0.212256\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4842.00i | − | 1.01701i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6442.00 | 1.27792 | 0.638961 | − | 0.769240i | \(-0.279365\pi\) | ||||
0.638961 | + | 0.769240i | \(0.279365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2951.00 | − | 2951.00i | −0.553762 | − | 0.553762i | 0.373762 | − | 0.927525i | \(-0.378068\pi\) |
−0.927525 | + | 0.373762i | \(0.878068\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6975.00 | − | 3825.00i | 1.24000 | − | 0.680000i | ||||
\(76\) | 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 | \(-0.0291134\pi\) |
−0.0913348 | + | 0.995820i | \(0.529113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9485.00 | − | 1355.00i | −1.31280 | − | 0.187543i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6120.00 | − | 6120.00i | 0.808561 | − | 0.808561i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14480.0i | 1.82805i | 0.405656 | + | 0.914026i | \(0.367043\pi\) | ||||
−0.405656 | + | 0.914026i | \(0.632957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4002.00 | −0.483275 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1818.00 | − | 1818.00i | −0.210198 | − | 0.210198i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5600.00 | + | 4200.00i | −0.620499 | + | 0.465374i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7311.00 | + | 7311.00i | −0.777022 | + | 0.777022i | −0.979323 | − | 0.202301i | \(-0.935158\pi\) |
0.202301 | + | 0.979323i | \(0.435158\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9558.00i | 0.975207i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 878.000 | 0.0860700 | 0.0430350 | − | 0.999074i | \(-0.486297\pi\) | ||||
0.0430350 | + | 0.999074i | \(0.486297\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10429.0 | + | 10429.0i | 0.983033 | + | 0.983033i | 0.999858 | − | 0.0168252i | \(-0.00535587\pi\) |
−0.0168252 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7830.00 | − | 10440.0i | −0.710204 | − | 0.946939i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4711.00 | − | 4711.00i | 0.411477 | − | 0.411477i | −0.470776 | − | 0.882253i | \(-0.656026\pi\) |
0.882253 | + | 0.470776i | \(0.156026\pi\) | |||||||
\(108\) | 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 | \(-0.287296\pi\) |
−0.784920 | + | 0.619597i | \(0.787296\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1345.00 | + | 9415.00i | −0.101701 | + | 0.711909i | ||||
\(116\) | 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 | ||||||||
\(125\) | −14625.0 | + | 5500.00i | −0.936000 | + | 0.352000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5909.00 | − | 5909.00i | 0.366359 | − | 0.366359i | −0.499789 | − | 0.866147i | \(-0.666589\pi\) |
0.866147 | + | 0.499789i | \(0.166589\pi\) | |||||||
\(128\) | 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 | 0.0915804 | − | 0.995798i | \(-0.470808\pi\) |
0.995798 | − | 0.0915804i | \(-0.0291919\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 9400.00i | − | 0.486517i | −0.969961 | − | 0.243259i | \(-0.921784\pi\) | ||
0.969961 | − | 0.243259i | \(-0.0782164\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22842.0 | −1.14894 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8142.00 | − | 8142.00i | −0.398161 | − | 0.398161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13600.0 | + | 10200.0i | −0.646849 | + | 0.485137i | ||||
\(146\) | 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 | \(-0.636780\pi\) | ||||
−0.416605 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21951.0 | − | 21951.0i | −0.937716 | − | 0.937716i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3030.00 | + | 4040.00i | 0.126119 | + | 0.168158i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16371.0 | − | 16371.0i | 0.664165 | − | 0.664165i | −0.292194 | − | 0.956359i | \(-0.594385\pi\) |
0.956359 | + | 0.292194i | \(0.0943853\pi\) | |||||||
\(158\) | 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 | \(-0.428755\pi\) |
−0.975056 | + | 0.221960i | \(0.928755\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5310.00 | − | 37170.0i | 0.195041 | − | 1.36529i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1549.00 | − | 1549.00i | 0.0555416 | − | 0.0555416i | −0.678790 | − | 0.734332i | \(-0.737496\pi\) |
0.734332 | + | 0.678790i | \(0.237496\pi\) | |||||||
\(168\) | 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 | 0.658976 | − | 0.752164i | \(-0.270990\pi\) |
−0.752164 | + | 0.658976i | \(0.770990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12325.0 | + | 22475.0i | 0.402449 | + | 0.733878i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10440.0 | − | 10440.0i | 0.333238 | − | 0.333238i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 2600.00i | − | 0.0811460i | −0.999177 | − | 0.0405730i | \(-0.987082\pi\) | ||
0.999177 | − | 0.0405730i | \(-0.0129183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 44398.0 | 1.35521 | 0.677604 | − | 0.735427i | \(-0.263018\pi\) | ||||
0.677604 | + | 0.735427i | \(0.263018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −50382.0 | − | 50382.0i | −1.50443 | − | 1.50443i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22785.0 | + | 3255.00i | 0.665741 | + | 0.0951059i | ||||
\(186\) | 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 | \(-0.564475\pi\) | ||||
−0.201173 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 42849.0 | + | 42849.0i | 1.15034 | + | 1.15034i | 0.986484 | + | 0.163855i | \(0.0523930\pi\) |
0.163855 | + | 0.986484i | \(0.447607\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24840.0 | + | 18630.0i | −0.653254 | + | 0.489941i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10971.0 | − | 10971.0i | 0.282692 | − | 0.282692i | −0.551490 | − | 0.834182i | \(-0.685940\pi\) |
0.834182 | + | 0.551490i | \(0.185940\pi\) | |||||||
\(198\) | 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 | ||||||||
\(205\) | 25230.0 | + | 33640.0i | 0.600357 | + | 0.800476i | ||||
\(206\) | 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 | ||||||||
\(215\) | 5445.00 | − | 38115.0i | 0.117793 | − | 0.824554i | ||||
\(216\) | 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 | 0.324648 | − | 0.945835i | \(-0.394754\pi\) |
−0.945835 | + | 0.324648i | \(0.894754\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −48600.0 | − | 14175.0i | −0.960000 | − | 0.280000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 54911.0 | − | 54911.0i | 1.06563 | − | 1.06563i | 0.0679438 | − | 0.997689i | \(-0.478356\pi\) |
0.997689 | − | 0.0679438i | \(-0.0216439\pi\) | |||||||
\(228\) | 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 | \(-0.259915\pi\) |
−0.728785 | + | 0.684743i | \(0.759915\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 44415.0 | + | 6345.00i | 0.804255 | + | 0.114894i | ||||
\(236\) | 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 | ||||||||
\(245\) | −14380.0 | + | 10785.0i | −0.239567 | + | 0.179675i | ||||
\(246\) | 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 | ||||||||
\(255\) | 73170.0 | + | 97560.0i | 1.12526 | + | 1.50035i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −72431.0 | + | 72431.0i | −1.09663 | + | 1.09663i | −0.101823 | + | 0.994803i | \(0.532467\pi\) |
−0.994803 | + | 0.101823i | \(0.967533\pi\) | |||||||
\(258\) | 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 | 0.592224 | − | 0.805773i | \(-0.298250\pi\) |
−0.805773 | + | 0.592224i | \(0.798250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3055.00 | + | 21385.0i | −0.0435030 | + | 0.304521i | ||||
\(266\) | 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 | \(-0.346294\pi\) | ||||
0.464332 | + | 0.885661i | \(0.346294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 36018.0 | + | 36018.0i | 0.483275 | + | 0.483275i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20650.0 | + | 70800.0i | −0.273058 | + | 0.936198i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18549.0 | + | 18549.0i | −0.241747 | + | 0.241747i | −0.817573 | − | 0.575826i | \(-0.804681\pi\) |
0.575826 | + | 0.817573i | \(0.304681\pi\) | |||||||
\(278\) | 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 | 0.987501 | + | 0.157613i | \(0.0503797\pi\) |
0.157613 | + | 0.987501i | \(0.449620\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 88200.0 | + | 12600.0i | 1.08587 | + | 0.155125i | ||||
\(286\) | 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 | 0.734795 | − | 0.678289i | \(-0.237278\pi\) |
−0.678289 | + | 0.734795i | \(0.737278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23200.0 | + | 17400.0i | −0.266590 | + | 0.199943i | ||||
\(296\) | 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 | ||||||||
\(305\) | 83970.0 | + | 111960.i | 0.902661 | + | 1.20355i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −42849.0 | + | 42849.0i | −0.454636 | + | 0.454636i | −0.896890 | − | 0.442254i | \(-0.854179\pi\) |
0.442254 | + | 0.896890i | \(0.354179\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 187722.i | − | 1.96607i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −72278.0 | −0.747283 | −0.373642 | − | 0.927573i | \(-0.621891\pi\) | ||||
−0.373642 | + | 0.927573i | \(0.621891\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18249.0 | + | 18249.0i | 0.186273 | + | 0.186273i | 0.794083 | − | 0.607810i | \(-0.207952\pi\) |
−0.607810 | + | 0.794083i | \(0.707952\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11745.0 | + | 82215.0i | −0.118367 | + | 0.828571i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25149.0 | + | 25149.0i | −0.250266 | + | 0.250266i | −0.821080 | − | 0.570814i | \(-0.806628\pi\) |
0.570814 | + | 0.821080i | \(0.306628\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | 53475.0 | − | 29325.0i | 0.506272 | − | 0.277633i | ||||
\(326\) | 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 | ||||||||
\(335\) | 26285.0 | + | 3755.00i | 0.234217 | + | 0.0334596i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8529.00 | − | 8529.00i | 0.0750997 | − | 0.0750997i | −0.668559 | − | 0.743659i | \(-0.733089\pi\) |
0.743659 | + | 0.668559i | \(0.233089\pi\) | |||||||
\(338\) | 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 | ||||||||
\(345\) | 96840.0 | − | 72630.0i | 0.813611 | − | 0.610208i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 56551.0 | − | 56551.0i | 0.469658 | − | 0.469658i | −0.432146 | − | 0.901804i | \(-0.642244\pi\) |
0.901804 | + | 0.432146i | \(0.142244\pi\) | |||||||
\(348\) | 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 | \(-0.331280\pi\) |
−0.862782 | + | 0.505576i | \(0.831280\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 96630.0 | + | 128840.i | 0.766753 | + | 1.02234i | ||||
\(356\) | 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 | ||||||||
\(365\) | 14755.0 | − | 103285.i | 0.110752 | − | 0.775267i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14971.0 | + | 14971.0i | −0.111152 | + | 0.111152i | −0.760496 | − | 0.649343i | \(-0.775044\pi\) |
0.649343 | + | 0.760496i | \(0.275044\pi\) | |||||||
\(368\) | 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 | 0.754996 | − | 0.655729i | \(-0.227639\pi\) |
−0.655729 | + | 0.754996i | \(0.727639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 181125. | + | 82125.0i | 1.28800 | + | 0.584000i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 46920.0 | − | 46920.0i | 0.330123 | − | 0.330123i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 251080.i | 1.74797i | 0.485954 | + | 0.873984i | \(0.338472\pi\) | ||||
−0.485954 | + | 0.873984i | \(0.661528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −106362. | −0.732717 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −86091.0 | − | 86091.0i | −0.586895 | − | 0.586895i | 0.349894 | − | 0.936789i | \(-0.386217\pi\) |
−0.936789 | + | 0.349894i | \(0.886217\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 119770. | + | 17110.0i | 0.808028 | + | 0.115433i | ||||
\(386\) | 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 | ||||||||
\(395\) | 211200. | − | 158400.i | 1.35363 | − | 1.01522i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29149.0 | + | 29149.0i | −0.184945 | + | 0.184945i | −0.793507 | − | 0.608562i | \(-0.791747\pi\) |
0.608562 | + | 0.793507i | \(0.291747\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 98415.0 | + | 131220.i | 0.600000 | + | 0.800000i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 76818.0 | − | 76818.0i | 0.463740 | − | 0.463740i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 78720.0i | − | 0.470585i | −0.971925 | − | 0.235293i | \(-0.924395\pi\) | ||
0.971925 | − | 0.235293i | \(-0.0756049\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −367362. | −2.17476 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33640.0 | + | 33640.0i | 0.197222 | + | 0.197222i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31155.0 | + | 218085.i | −0.180897 | + | 1.26628i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −84600.0 | + | 84600.0i | −0.486517 | + | 0.486517i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 14760.0i | − | 0.0840733i | −0.999116 | − | 0.0420367i | \(-0.986615\pi\) | ||
0.999116 | − | 0.0420367i | \(-0.0133846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −221282. | −1.24848 | −0.624240 | − | 0.781232i | \(-0.714591\pi\) | ||||
−0.624240 | + | 0.781232i | \(0.714591\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 102789. | + | 102789.i | 0.574468 | + | 0.574468i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −115175. | − | 210025.i | −0.637647 | − | 1.16277i | ||||
\(426\) | 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 | \(-0.306156\pi\) | ||||
0.572031 | + | 0.820232i | \(0.306156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 145409. | + | 145409.i | 0.775560 | + | 0.775560i | 0.979072 | − | 0.203512i | \(-0.0652357\pi\) |
−0.203512 | + | 0.979072i | \(0.565236\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 214200. | + | 30600.0i | 1.13199 | + | 0.161712i | ||||
\(436\) | 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 | −0.965450 | − | 0.260590i | \(-0.916083\pi\) |
−0.260590 | − | 0.965450i | \(-0.583917\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −289600. | + | 217200.i | −1.46244 | + | 1.09683i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 124200. | − | 124200.i | 0.621594 | − | 0.621594i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 82480.0i | 0.409125i | 0.978854 | + | 0.204562i | \(0.0655772\pi\) | ||||
−0.978854 | + | 0.204562i | \(0.934423\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 198476. | 0.975787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 170982. | + | 170982.i | 0.833209 | + | 0.833209i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −60030.0 | − | 80040.0i | −0.289965 | − | 0.386620i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −188151. | + | 188151.i | −0.900895 | + | 0.900895i | −0.995514 | − | 0.0946187i | \(-0.969837\pi\) |
0.0946187 | + | 0.995514i | \(0.469837\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 326158. | 1.53471 | 0.767355 | − | 0.641223i | \(-0.221573\pi\) | ||||
0.767355 | + | 0.641223i | \(0.221573\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −218731. | − | 218731.i | −1.02035 | − | 1.02035i | −0.999789 | − | 0.0205595i | \(-0.993455\pi\) |
−0.0205595 | − | 0.999789i | \(-0.506545\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9090.00 | − | 63630.0i | 0.0420395 | − | 0.294277i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −59249.0 | + | 59249.0i | −0.271673 | + | 0.271673i | −0.829774 | − | 0.558100i | \(-0.811530\pi\) |
0.558100 | + | 0.829774i | \(0.311530\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | −168000. | − | 49000.0i | −0.744598 | − | 0.217175i | ||||
\(476\) | 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 | ||||||||
\(485\) | −255885. | − | 36555.0i | −1.08783 | − | 0.155404i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −123651. | + | 123651.i | −0.521362 | + | 0.521362i | −0.917983 | − | 0.396620i | \(-0.870183\pi\) |
0.396620 | + | 0.917983i | \(0.370183\pi\) | |||||||
\(488\) | 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 | ||||||||
\(495\) | −191160. | + | 143370.i | −0.780165 | + | 0.585124i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 186818. | − | 186818.i | 0.756321 | − | 0.756321i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 269240.i | 1.08128i | 0.841254 | + | 0.540640i | \(0.181818\pi\) | ||||
−0.841254 | + | 0.540640i | \(0.818182\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27882.0 | −0.111083 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 109869. | + | 109869.i | 0.434249 | + | 0.434249i | 0.890071 | − | 0.455822i | \(-0.150655\pi\) |
−0.455822 | + | 0.890071i | \(0.650655\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13170.0 | + | 17560.0i | 0.0516420 | + | 0.0688560i | ||||
\(506\) | 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 | ||||||||
\(515\) | −52145.0 | + | 365015.i | −0.196607 | + | 1.37625i | ||||
\(516\) | 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 | \(-0.229355\pi\) |
−0.659791 | + | 0.751449i | \(0.729355\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 91350.0 | − | 313200.i | 0.331429 | − | 1.13633i | ||||
\(526\) | 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 | ||||||||
\(535\) | 164885. | + | 23555.0i | 0.576068 | + | 0.0822954i | ||||
\(536\) | 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 | \(-0.421737\pi\) | ||||
0.243402 | + | 0.969926i | \(0.421737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −399582. | − | 399582.i | −1.35521 | − | 1.35521i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −440800. | + | 330600.i | −1.48405 | + | 1.11304i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −291009. | + | 291009.i | −0.972594 | + | 0.972594i | −0.999634 | − | 0.0270399i | \(-0.991392\pi\) |
0.0270399 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(548\) | 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 | ||||||||
\(555\) | −175770. | − | 234360.i | −0.570636 | − | 0.760847i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 83091.0 | − | 83091.0i | 0.267820 | − | 0.267820i | −0.560401 | − | 0.828221i | \(-0.689353\pi\) |
0.828221 | + | 0.560401i | \(0.189353\pi\) | |||||||
\(558\) | 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 | \(-0.280902\pi\) |
−0.772316 | + | 0.635239i | \(0.780902\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10555.0 | − | 73885.0i | 0.0330645 | − | 0.231451i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 190269. | − | 190269.i | 0.591837 | − | 0.591837i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 270560.i | 0.835678i | 0.908521 | + | 0.417839i | \(0.137212\pi\) | ||||
−0.908521 | + | 0.417839i | \(0.862788\pi\) | |||||||
\(570\) | 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 | ||||||||
\(575\) | −208475. | + | 114325.i | −0.630548 | + | 0.345784i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 195889. | − | 195889.i | 0.588381 | − | 0.588381i | −0.348812 | − | 0.937193i | \(-0.613415\pi\) |
0.937193 | + | 0.348812i | \(0.113415\pi\) | |||||||
\(578\) | 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 | ||||||||
\(585\) | 195615. | + | 27945.0i | 0.571598 | + | 0.0816568i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 404631. | − | 404631.i | 1.17431 | − | 1.17431i | 0.193139 | − | 0.981171i | \(-0.438133\pi\) |
0.981171 | − | 0.193139i | \(-0.0618669\pi\) | |||||||
\(588\) | 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 | \(-0.389468\pi\) |
−0.940314 | + | 0.340309i | \(0.889468\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −314360. | + | 235770.i | −0.887960 | + | 0.665970i | ||||
\(596\) | 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 | ||||||||
\(605\) | −10755.0 | − | 14340.0i | −0.0293832 | − | 0.0391777i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 146469. | − | 146469.i | 0.397529 | − | 0.397529i | −0.479832 | − | 0.877360i | \(-0.659302\pi\) |
0.877360 | + | 0.479832i | \(0.159302\pi\) | |||||||
\(608\) | 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 | 0.459666 | − | 0.888092i | \(-0.347969\pi\) |
−0.888092 | + | 0.459666i | \(0.847969\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 75690.0 | − | 529830.i | 0.200119 | − | 1.40083i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 320409. | − | 320409.i | 0.841656 | − | 0.841656i | −0.147419 | − | 0.989074i | \(-0.547096\pi\) |
0.989074 | + | 0.147419i | \(0.0470965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 341160.i | 0.890383i | 0.895435 | + | 0.445191i | \(0.146864\pi\) | ||||
−0.895435 | + | 0.445191i | \(0.853136\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 419920. | + | 419920.i | 1.08191 | + | 1.08191i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −329375. | − | 210000.i | −0.843200 | − | 0.537600i | ||||
\(626\) | 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 | \(-0.663370\pi\) | ||||
−0.491005 | + | 0.871157i | \(0.663370\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 655578. | + | 655578.i | 1.63613 | + | 1.63613i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 206815. | + | 29545.0i | 0.512902 | + | 0.0732717i | ||||
\(636\) | 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 | \(-0.232619\pi\) |
−0.667462 | + | 0.744644i | \(0.732619\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −392040. | + | 294030.i | −0.942347 | + | 0.706760i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −280931. | + | 280931.i | −0.671106 | + | 0.671106i | −0.957971 | − | 0.286865i | \(-0.907387\pi\) |
0.286865 | + | 0.957971i | \(0.407387\pi\) | |||||||
\(648\) | 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 | −0.964402 | − | 0.264439i | \(-0.914813\pi\) |
−0.264439 | − | 0.964402i | \(-0.585187\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 95370.0 | + | 127160.i | 0.222295 | + | 0.296393i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 239031. | − | 239031.i | 0.553762 | − | 0.553762i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 404360.i | − | 0.931102i | −0.885021 | − | 0.465551i | \(-0.845856\pi\) | ||
0.885021 | − | 0.465551i | \(-0.154144\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5278.00 | 0.0120800 | 0.00603999 | − | 0.999982i | \(-0.498077\pi\) | ||||
0.00603999 | + | 0.999982i | \(0.498077\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −336582. | − | 336582.i | −0.765709 | − | 0.765709i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −40600.0 | + | 284200.i | −0.0918085 | + | 0.642659i | ||||
\(666\) | 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 | \(-0.423505\pi\) |
−0.971263 | + | 0.238011i | \(0.923505\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −578309. | + | 578309.i | −1.26178 | + | 1.26178i | −0.311546 | + | 0.950231i | \(0.600847\pi\) |
−0.950231 | + | 0.311546i | \(0.899153\pi\) | |||||||
\(678\) | 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 | \(-0.0723842\pi\) |
−0.225447 | + | 0.974255i | \(0.572384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 714315. | + | 102045.i | 1.52233 | + | 0.217476i | ||||
\(686\) | 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 | ||||||||
\(695\) | 188000. | − | 141000.i | 0.389214 | − | 0.291910i | ||||
\(696\) | 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 | \(-0.588668\pi\) | ||||
−0.274971 | + | 0.961453i | \(0.588668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 182280. | + | 182280.i | 0.368832 | + | 0.368832i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −342630. | − | 456840.i | −0.689362 | − | 0.919149i | ||||
\(706\) | 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 | ||||||||
\(715\) | 40710.0 | − | 284970.i | 0.0796323 | − | 0.557426i | ||||
\(716\) | 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 | ||||||||
\(725\) | −408000. | − | 119000.i | −0.776219 | − | 0.226397i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −417651. | + | 417651.i | −0.790214 | + | 0.790214i | −0.981529 | − | 0.191315i | \(-0.938725\pi\) |
0.191315 | + | 0.981529i | \(0.438725\pi\) | |||||||
\(728\) | 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 | 0.237142 | − | 0.971475i | \(-0.423789\pi\) |
−0.971475 | + | 0.237142i | \(0.923789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 226485. | + | 32355.0i | 0.419242 | + | 0.0598917i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 88618.0 | − | 88618.0i | 0.163150 | − | 0.163150i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 109880.i | 0.201201i | 0.994927 | + | 0.100600i | \(0.0320764\pi\) | ||||
−0.994927 | + | 0.100600i | \(0.967924\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −347760. | −0.633349 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −466451. | − | 466451.i | −0.844945 | − | 0.844945i | 0.144552 | − | 0.989497i | \(-0.453826\pi\) |
−0.989497 | + | 0.144552i | \(0.953826\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −276000. | + | 207000.i | −0.497275 | + | 0.372956i | ||||
\(746\) | 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 | \(-0.146313\pi\) | ||||
0.896206 | + | 0.443638i | \(0.146313\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.08902e6 | + | 1.08902e6i | 1.92064 | + | 1.92064i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −284970. | − | 379960.i | −0.499925 | − | 0.666567i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −313269. | + | 313269.i | −0.546671 | + | 0.546671i | −0.925476 | − | 0.378806i | \(-0.876335\pi\) |
0.378806 | + | 0.925476i | \(0.376335\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | 109755. | − | 768285.i | 0.187543 | − | 1.31280i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 80040.0 | − | 80040.0i | 0.136056 | − | 0.136056i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13280.0i | − | 0.0224567i | −0.999937 | − | 0.0112283i | \(-0.996426\pi\) | ||
0.999937 | − | 0.0112283i | \(-0.00357417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.30376e6 | 2.19325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 782211. | + | 782211.i | 1.30908 | + | 1.30908i | 0.922082 | + | 0.386994i | \(0.126487\pi\) |
0.386994 | + | 0.922082i | \(0.373513\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35350.0 | + | 121200.i | −0.0588554 | + | 0.201790i | ||||
\(776\) | 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 | ||||||||
\(785\) | 572985. | + | 81855.0i | 0.929831 | + | 0.132833i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −201409. | + | 201409.i | −0.325184 | + | 0.325184i | −0.850752 | − | 0.525568i | \(-0.823853\pi\) |
0.525568 | + | 0.850752i | \(0.323853\pi\) | |||||||
\(788\) | 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 | ||||||||
\(795\) | 219960. | − | 164970.i | 0.348024 | − | 0.261018i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36291.0 | − | 36291.0i | 0.0571324 | − | 0.0571324i | −0.677963 | − | 0.735096i | \(-0.737137\pi\) |
0.735096 | + | 0.677963i | \(0.237137\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 234030. | + | 312040.i | 0.361143 | + | 0.481525i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 807480. | − | 807480.i | 1.23989 | − | 1.23989i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 71600.0i | 0.109400i | 0.998503 | + | 0.0546998i | \(0.0174202\pi\) | ||||
−0.998503 | + | 0.0546998i | \(0.982580\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | 100045. | − | 700315.i | 0.150619 | − | 1.05433i | ||||
\(816\) | 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 | \(-0.462741\pi\) | ||||
0.116787 | + | 0.993157i | \(0.462741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 791309. | + | 791309.i | 1.16828 | + | 1.16828i | 0.982613 | + | 0.185666i | \(0.0594441\pi\) |
0.185666 | + | 0.982613i | \(0.440556\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 823050. | − | 451350.i | 1.20926 | − | 0.663140i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 889671. | − | 889671.i | 1.30082 | − | 1.30082i | 0.372987 | − | 0.927837i | \(-0.378334\pi\) |
0.927837 | − | 0.372987i | \(-0.121666\pi\) | |||||||
\(828\) | 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 | ||||||||
\(835\) | 54215.0 | + | 7745.00i | 0.0777583 | + | 0.0111083i | ||||
\(836\) | 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 | ||||||||
\(845\) | 380780. | − | 285585.i | 0.533287 | − | 0.399965i | ||||
\(846\) | 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 | 0.999219 | − | 0.0395127i | \(-0.0125806\pi\) |
−0.0395127 | + | 0.999219i | \(0.512581\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −340200. | − | 453600.i | −0.465374 | − | 0.620499i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 144489. | − | 144489.i | 0.196731 | − | 0.196731i | −0.601866 | − | 0.798597i | \(-0.705576\pi\) |
0.798597 | + | 0.601866i | \(0.205576\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 943480.i | − | 1.27863i | −0.768943 | − | 0.639317i | \(-0.779217\pi\) | ||
0.768943 | − | 0.639317i | \(-0.220783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −878004. | −1.18438 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 438149. | + | 438149.i | 0.588302 | + | 0.588302i | 0.937171 | − | 0.348869i | \(-0.113434\pi\) |
−0.348869 | + | 0.937171i | \(0.613434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13945.0 | − | 97615.0i | 0.0186374 | − | 0.130462i | ||||
\(866\) | 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 | ||||||||
\(875\) | −264625. | + | 583625.i | −0.345633 | + | 0.762286i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −281469. | + | 281469.i | −0.365958 | + | 0.365958i | −0.866001 | − | 0.500043i | \(-0.833318\pi\) |
0.500043 | + | 0.866001i | \(0.333318\pi\) | |||||||
\(878\) | 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 | \(-0.154031\pi\) |
−0.465236 | + | 0.885187i | \(0.654031\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 365400. | + | 52200.0i | 0.466533 | + | 0.0666475i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −477171. | + | 477171.i | −0.606494 | + | 0.606494i | −0.942028 | − | 0.335534i | \(-0.891083\pi\) |
0.335534 | + | 0.942028i | \(0.391083\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | 52000.0 | − | 39000.0i | 0.0649168 | − | 0.0486876i | ||||
\(896\) | 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 | ||||||||
\(905\) | 665970. | + | 887960.i | 0.813125 | + | 1.08417i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.11209e6 | + | 1.11209e6i | −1.35184 | + | 1.35184i | −0.468235 | + | 0.883604i | \(0.655110\pi\) |
−0.883604 | + | 0.468235i | \(0.844890\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 71118.0i | 0.0860700i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −883958. | −1.06511 | −0.532556 | − | 0.846395i | \(-0.678768\pi\) | ||||
−0.532556 | + | 0.846395i | \(0.678768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 735258. | + | 735258.i | 0.882060 | + | 0.882060i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 251910. | − | 1.76337e6i | 0.300887 | − | 2.10621i | ||||
\(916\) | 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 | ||||||||
\(925\) | 276675. | + | 504525.i | 0.323360 | + | 0.589657i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −844749. | + | 844749.i | −0.983033 | + | 0.983033i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.22744e6i | − | 1.42223i | −0.703077 | − | 0.711113i | \(-0.748191\pi\) | ||
0.703077 | − | 0.711113i | \(-0.251809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −201320. | −0.232267 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 650502. | + | 650502.i | 0.747283 | + | 0.747283i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.11923e6 | − | 159890.i | −1.28025 | − | 0.182893i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.07047e6 | + | 1.07047e6i | −1.21926 | + | 1.21926i | −0.251366 | + | 0.967892i | \(0.580880\pi\) |
−0.967892 | + | 0.251366i | \(0.919120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 328482.i | − | 0.372546i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −558642. | −0.630891 | −0.315446 | − | 0.948944i | \(-0.602154\pi\) | ||||
−0.315446 | + | 0.948944i | \(0.602154\pi\) | |||||||
\(942\) | 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 | \(-0.701700\pi\) |
0.805867 | + | 0.592097i | \(0.201700\pi\) | |||||||
\(948\) | 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 | \(-0.413252\pi\) |
−0.963094 | + | 0.269166i | \(0.913252\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −220170. | − | 293560.i | −0.241408 | − | 0.321877i | ||||
\(956\) | 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 | ||||||||
\(965\) | −214245. | + | 1.49972e6i | −0.230068 | + | 1.61048i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −345491. | + | 345491.i | −0.369474 | + | 0.369474i | −0.867285 | − | 0.497811i | \(-0.834137\pi\) |
0.497811 | + | 0.867285i | \(0.334137\pi\) | |||||||
\(968\) | 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 | ||||||||
\(975\) | −745200. | − | 217350.i | −0.783905 | − | 0.228639i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −146751. | + | 146751.i | −0.153742 | + | 0.153742i | −0.779787 | − | 0.626045i | \(-0.784673\pi\) |
0.626045 | + | 0.779787i | \(0.284673\pi\) | |||||||
\(978\) | 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 | 0.906151 | − | 0.422953i | \(-0.139007\pi\) |
−0.422953 | + | 0.906151i | \(0.639007\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 383985. | + | 54855.0i | 0.395769 | + | 0.0565384i | ||||
\(986\) | 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 | \(-0.651735\pi\) | ||||
−0.458841 | + | 0.888518i | \(0.651735\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −486342. | − | 486342.i | −0.493223 | − | 0.493223i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −763200. | + | 572400.i | −0.770890 | + | 0.578167i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −152149. | + | 152149.i | −0.153066 | + | 0.153066i | −0.779486 | − | 0.626420i | \(-0.784520\pi\) |
0.626420 | + | 0.779486i | \(0.284520\pi\) | |||||||
\(998\) | 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 | 320.5.p.b.193.1 | 2 | ||
4.3 | odd | 2 | 320.5.p.i.193.1 | 2 | |||
5.2 | odd | 4 | inner | 320.5.p.b.257.1 | 2 | ||
8.3 | odd | 2 | 80.5.p.b.33.1 | 2 | |||
8.5 | even | 2 | 10.5.c.a.3.1 | ✓ | 2 | ||
20.7 | even | 4 | 320.5.p.i.257.1 | 2 | |||
24.5 | odd | 2 | 90.5.g.b.73.1 | 2 | |||
40.3 | even | 4 | 400.5.p.c.257.1 | 2 | |||
40.13 | odd | 4 | 50.5.c.b.7.1 | 2 | |||
40.19 | odd | 2 | 400.5.p.c.193.1 | 2 | |||
40.27 | even | 4 | 80.5.p.b.17.1 | 2 | |||
40.29 | even | 2 | 50.5.c.b.43.1 | 2 | |||
40.37 | odd | 4 | 10.5.c.a.7.1 | yes | 2 | ||
120.29 | odd | 2 | 450.5.g.a.343.1 | 2 | |||
120.53 | even | 4 | 450.5.g.a.307.1 | 2 | |||
120.77 | even | 4 | 90.5.g.b.37.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.5.c.a.3.1 | ✓ | 2 | 8.5 | even | 2 | ||
10.5.c.a.7.1 | yes | 2 | 40.37 | odd | 4 | ||
50.5.c.b.7.1 | 2 | 40.13 | odd | 4 | |||
50.5.c.b.43.1 | 2 | 40.29 | even | 2 | |||
80.5.p.b.17.1 | 2 | 40.27 | even | 4 | |||
80.5.p.b.33.1 | 2 | 8.3 | odd | 2 | |||
90.5.g.b.37.1 | 2 | 120.77 | even | 4 | |||
90.5.g.b.73.1 | 2 | 24.5 | odd | 2 | |||
320.5.p.b.193.1 | 2 | 1.1 | even | 1 | trivial | ||
320.5.p.b.257.1 | 2 | 5.2 | odd | 4 | inner | ||
320.5.p.i.193.1 | 2 | 4.3 | odd | 2 | |||
320.5.p.i.257.1 | 2 | 20.7 | even | 4 | |||
400.5.p.c.193.1 | 2 | 40.19 | odd | 2 | |||
400.5.p.c.257.1 | 2 | 40.3 | even | 4 | |||
450.5.g.a.307.1 | 2 | 120.53 | even | 4 | |||
450.5.g.a.343.1 | 2 | 120.29 | odd | 2 |