Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [90,5,Mod(37,90)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(90, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("90.37");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 90 = 2 \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 90.g (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.30329667755\) |
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 | 37.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 90.37 |
Dual form | 90.5.g.b.73.1 |
$q$-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 \(\left(\mathbb{Z}/90\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 2.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.00000i | 0.500000i | ||||||||
\(5\) | 15.0000 | − | 20.0000i | 0.600000 | − | 0.800000i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29.0000 | + | 29.0000i | 0.591837 | + | 0.591837i | 0.938127 | − | 0.346291i | \(-0.112559\pi\) |
−0.346291 | + | 0.938127i | \(0.612559\pi\) | |||||||
\(8\) | −16.0000 | + | 16.0000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 70.0000 | − | 10.0000i | 0.700000 | − | 0.100000i | ||||
\(11\) | 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 | \(-0.656777\pi\) |
0.881140 | + | 0.472856i | \(0.156777\pi\) | |||||||
\(14\) | 116.000i | 0.591837i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | 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 | \(0.126769\pi\) | ||||
−0.921739 | + | 0.387812i | \(0.873231\pi\) | |||||||
\(20\) | 160.000 | + | 120.000i | 0.400000 | + | 0.300000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 236.000 | + | 236.000i | 0.487603 | + | 0.487603i | ||||
\(23\) | −269.000 | + | 269.000i | −0.508507 | + | 0.508507i | −0.914068 | − | 0.405561i | \(-0.867076\pi\) |
0.405561 | + | 0.914068i | \(0.367076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −175.000 | − | 600.000i | −0.280000 | − | 0.960000i | ||||
\(26\) | 276.000 | 0.408284 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −232.000 | + | 232.000i | −0.295918 | + | 0.295918i | ||||
\(29\) | − | 680.000i | − | 0.808561i | −0.914635 | − | 0.404281i | \(-0.867522\pi\) | ||
0.914635 | − | 0.404281i | \(-0.132478\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 202.000 | 0.210198 | 0.105099 | − | 0.994462i | \(-0.466484\pi\) | ||||
0.105099 | + | 0.994462i | \(0.466484\pi\) | |||||||
\(32\) | −128.000 | − | 128.000i | −0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1084.00i | 0.937716i | ||||||||
\(35\) | 1015.00 | − | 145.000i | 0.828571 | − | 0.118367i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −651.000 | − | 651.000i | −0.475530 | − | 0.475530i | 0.428169 | − | 0.903699i | \(-0.359159\pi\) |
−0.903699 | + | 0.428169i | \(0.859159\pi\) | |||||||
\(38\) | −560.000 | + | 560.000i | −0.387812 | + | 0.387812i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 80.0000 | + | 560.000i | 0.0500000 | + | 0.350000i | ||||
\(41\) | −1682.00 | −1.00059 | −0.500297 | − | 0.865854i | \(-0.666776\pi\) | ||||
−0.500297 | + | 0.865854i | \(0.666776\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1089.00 | − | 1089.00i | 0.588967 | − | 0.588967i | −0.348385 | − | 0.937352i | \(-0.613270\pi\) |
0.937352 | + | 0.348385i | \(0.113270\pi\) | |||||||
\(44\) | 944.000i | 0.487603i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1076.00 | −0.508507 | ||||||||
\(47\) | −1269.00 | − | 1269.00i | −0.574468 | − | 0.574468i | 0.358906 | − | 0.933374i | \(-0.383150\pi\) |
−0.933374 | + | 0.358906i | \(0.883150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 719.000i | − | 0.299459i | ||||||
\(50\) | 850.000 | − | 1550.00i | 0.340000 | − | 0.620000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 552.000 | + | 552.000i | 0.204142 | + | 0.204142i | ||||
\(53\) | 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 | ||||||||
\(55\) | 1770.00 | − | 2360.00i | 0.585124 | − | 0.780165i | ||||
\(56\) | −928.000 | −0.295918 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1360.00 | − | 1360.00i | 0.404281 | − | 0.404281i | ||||
\(59\) | − | 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 | \(0.771016\pi\) | |||||||
\(62\) | 404.000 | + | 404.000i | 0.105099 | + | 0.105099i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 512.000i | − | 0.125000i | ||||||
\(65\) | −345.000 | − | 2415.00i | −0.0816568 | − | 0.571598i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −751.000 | − | 751.000i | −0.167298 | − | 0.167298i | 0.618493 | − | 0.785791i | \(-0.287744\pi\) |
−0.785791 | + | 0.618493i | \(0.787744\pi\) | |||||||
\(68\) | −2168.00 | + | 2168.00i | −0.468858 | + | 0.468858i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2320.00 | + | 1740.00i | 0.473469 | + | 0.355102i | ||||
\(71\) | −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 | −0.927525 | − | 0.373762i | \(-0.878068\pi\) |
0.373762 | + | 0.927525i | \(0.378068\pi\) | |||||||
\(74\) | − | 2604.00i | − | 0.475530i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2240.00 | −0.387812 | ||||||||
\(77\) | 3422.00 | + | 3422.00i | 0.577163 | + | 0.577163i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10560.0i | 1.69204i | 0.533154 | + | 0.846018i | \(0.321007\pi\) | ||||
−0.533154 | + | 0.846018i | \(0.678993\pi\) | |||||||
\(80\) | −960.000 | + | 1280.00i | −0.150000 | + | 0.200000i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3364.00 | − | 3364.00i | −0.500297 | − | 0.500297i | ||||
\(83\) | 6231.00 | − | 6231.00i | 0.904485 | − | 0.904485i | −0.0913348 | − | 0.995820i | \(-0.529113\pi\) |
0.995820 | + | 0.0913348i | \(0.0291134\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9485.00 | − | 1355.00i | 1.31280 | − | 0.187543i | ||||
\(86\) | 4356.00 | 0.588967 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1888.00 | + | 1888.00i | −0.243802 | + | 0.243802i | ||||
\(89\) | 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 | ||||||||
\(92\) | −2152.00 | − | 2152.00i | −0.254253 | − | 0.254253i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 5076.00i | − | 0.574468i | ||||||
\(95\) | 5600.00 | + | 4200.00i | 0.620499 | + | 0.465374i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7311.00 | − | 7311.00i | −0.777022 | − | 0.777022i | 0.202301 | − | 0.979323i | \(-0.435158\pi\) |
−0.979323 | + | 0.202301i | \(0.935158\pi\) | |||||||
\(98\) | 1438.00 | − | 1438.00i | 0.149729 | − | 0.149729i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4800.00 | − | 1400.00i | 0.480000 | − | 0.140000i | ||||
\(101\) | 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 | −0.0168252 | − | 0.999858i | \(-0.505356\pi\) |
0.999858 | + | 0.0168252i | \(0.00535587\pi\) | |||||||
\(104\) | 2208.00i | 0.204142i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2444.00 | 0.217515 | ||||||||
\(107\) | 4711.00 | + | 4711.00i | 0.411477 | + | 0.411477i | 0.882253 | − | 0.470776i | \(-0.156026\pi\) |
−0.470776 | + | 0.882253i | \(0.656026\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 22040.0i | 1.85506i | 0.373745 | + | 0.927531i | \(0.378073\pi\) | ||||
−0.373745 | + | 0.927531i | \(0.621927\pi\) | |||||||
\(110\) | 8260.00 | − | 1180.00i | 0.682645 | − | 0.0975207i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1856.00 | − | 1856.00i | −0.147959 | − | 0.147959i | ||||
\(113\) | 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 | ||||||||
\(115\) | 1345.00 | + | 9415.00i | 0.101701 | + | 0.711909i | ||||
\(116\) | 5440.00 | 0.404281 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2320.00 | − | 2320.00i | 0.166619 | − | 0.166619i | ||||
\(119\) | 15718.0i | 1.10995i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −717.000 | −0.0489721 | ||||||||
\(122\) | −11196.0 | − | 11196.0i | −0.752217 | − | 0.752217i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1616.00i | 0.105099i | ||||||||
\(125\) | −14625.0 | − | 5500.00i | −0.936000 | − | 0.352000i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5909.00 | + | 5909.00i | 0.366359 | + | 0.366359i | 0.866147 | − | 0.499789i | \(-0.166589\pi\) |
−0.499789 | + | 0.866147i | \(0.666589\pi\) | |||||||
\(128\) | 1024.00 | − | 1024.00i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4140.00 | − | 5520.00i | 0.244970 | − | 0.326627i | ||||
\(131\) | 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 | ||||
\(134\) | − | 3004.00i | − | 0.167298i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8672.00 | −0.468858 | ||||||||
\(137\) | −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 | \(-0.921784\pi\) | ||
0.969961 | − | 0.243259i | \(-0.0782164\pi\) | |||||||
\(140\) | 1160.00 | + | 8120.00i | 0.0591837 | + | 0.414286i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12884.0 | − | 12884.0i | −0.638961 | − | 0.638961i | ||||
\(143\) | 8142.00 | − | 8142.00i | 0.398161 | − | 0.398161i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13600.0 | − | 10200.0i | −0.646849 | − | 0.485137i | ||||
\(146\) | −11804.0 | −0.553762 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5208.00 | − | 5208.00i | 0.237765 | − | 0.237765i | ||||
\(149\) | − | 13800.0i | − | 0.621594i | −0.950476 | − | 0.310797i | \(-0.899404\pi\) | ||
0.950476 | − | 0.310797i | \(-0.100596\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18998.0 | −0.833209 | −0.416605 | − | 0.909088i | \(-0.636780\pi\) | ||||
−0.416605 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(152\) | −4480.00 | − | 4480.00i | −0.193906 | − | 0.193906i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13688.0i | 0.577163i | ||||||||
\(155\) | 3030.00 | − | 4040.00i | 0.126119 | − | 0.168158i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16371.0 | − | 16371.0i | −0.664165 | − | 0.664165i | 0.292194 | − | 0.956359i | \(-0.405615\pi\) |
−0.956359 | + | 0.292194i | \(0.905615\pi\) | |||||||
\(158\) | −21120.0 | + | 21120.0i | −0.846018 | + | 0.846018i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4480.00 | + | 640.000i | −0.175000 | + | 0.0250000i | ||||
\(161\) | −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 | \(0.0712455\pi\) | |||||||
\(164\) | − | 13456.0i | − | 0.500297i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24924.0 | 0.904485 | ||||||||
\(167\) | −1549.00 | − | 1549.00i | −0.0555416 | − | 0.0555416i | 0.678790 | − | 0.734332i | \(-0.262504\pi\) |
−0.734332 | + | 0.678790i | \(0.762504\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19039.0i | 0.666608i | ||||||||
\(170\) | 21680.0 | + | 16260.0i | 0.750173 | + | 0.562630i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8712.00 | + | 8712.00i | 0.294484 | + | 0.294484i | ||||
\(173\) | −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 | ||||||||
\(175\) | 12325.0 | − | 22475.0i | 0.402449 | − | 0.733878i | ||||
\(176\) | −7552.00 | −0.243802 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −28960.0 | + | 28960.0i | −0.914026 | + | 0.914026i | ||||
\(179\) | 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 | \(0.736982\pi\) | |||||||
\(182\) | 8004.00 | + | 8004.00i | 0.241637 | + | 0.241637i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 8608.00i | − | 0.254253i | ||||||
\(185\) | −22785.0 | + | 3255.00i | −0.665741 | + | 0.0951059i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31978.0 | + | 31978.0i | 0.914467 | + | 0.914467i | ||||
\(188\) | 10152.0 | − | 10152.0i | 0.287234 | − | 0.287234i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2800.00 | + | 19600.0i | 0.0775623 | + | 0.542936i | ||||
\(191\) | 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 | \(-0.447607\pi\) |
0.986484 | − | 0.163855i | \(-0.0523930\pi\) | |||||||
\(194\) | − | 29244.0i | − | 0.777022i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5752.00 | 0.149729 | ||||||||
\(197\) | 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 | \(-0.839981\pi\) | ||
0.876278 | − | 0.481806i | \(-0.160019\pi\) | |||||||
\(200\) | 12400.0 | + | 6800.00i | 0.310000 | + | 0.170000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1756.00 | + | 1756.00i | 0.0430350 | + | 0.0430350i | ||||
\(203\) | 19720.0 | − | 19720.0i | 0.478536 | − | 0.478536i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25230.0 | + | 33640.0i | −0.600357 | + | 0.800476i | ||||
\(206\) | 41716.0 | 0.983033 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4416.00 | + | 4416.00i | −0.102071 | + | 0.102071i | ||||
\(209\) | 33040.0i | 0.756393i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 72842.0 | 1.63613 | 0.818063 | − | 0.575128i | \(-0.195048\pi\) | ||||
0.818063 | + | 0.575128i | \(0.195048\pi\) | |||||||
\(212\) | 4888.00 | + | 4888.00i | 0.108758 | + | 0.108758i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18844.0i | 0.411477i | ||||||||
\(215\) | −5445.00 | − | 38115.0i | −0.117793 | − | 0.824554i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5858.00 | + | 5858.00i | 0.124403 | + | 0.124403i | ||||
\(218\) | −44080.0 | + | 44080.0i | −0.927531 | + | 0.927531i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 18880.0 | + | 14160.0i | 0.390083 | + | 0.292562i | ||||
\(221\) | 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 | \(0.394754\pi\) | |||||||
\(224\) | − | 7424.00i | − | 0.147959i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8444.00 | 0.165322 | ||||||||
\(227\) | 54911.0 | + | 54911.0i | 1.06563 | + | 1.06563i | 0.997689 | + | 0.0679438i | \(0.0216439\pi\) |
0.0679438 | + | 0.997689i | \(0.478356\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 50280.0i | − | 0.958792i | −0.877599 | − | 0.479396i | \(-0.840856\pi\) | ||
0.877599 | − | 0.479396i | \(-0.159144\pi\) | |||||||
\(230\) | −16140.0 | + | 21520.0i | −0.305104 | + | 0.406805i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10880.0 | + | 10880.0i | 0.202140 | + | 0.202140i | ||||
\(233\) | 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 | ||||||||
\(235\) | −44415.0 | + | 6345.00i | −0.804255 | + | 0.114894i | ||||
\(236\) | 9280.00 | 0.166619 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −31436.0 | + | 31436.0i | −0.554975 | + | 0.554975i | ||||
\(239\) | 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 | \(0.578162\pi\) | |||||||
\(242\) | −1434.00 | − | 1434.00i | −0.0244860 | − | 0.0244860i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 44784.0i | − | 0.752217i | ||||||
\(245\) | −14380.0 | − | 10785.0i | −0.239567 | − | 0.179675i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19320.0 | + | 19320.0i | 0.316675 | + | 0.316675i | ||||
\(248\) | −3232.00 | + | 3232.00i | −0.0525494 | + | 0.0525494i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −18250.0 | − | 40250.0i | −0.292000 | − | 0.644000i | ||||
\(251\) | −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 | ||||
\(254\) | 23636.0i | 0.366359i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 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 | ||||||
\(260\) | 19320.0 | − | 2760.00i | 0.285799 | − | 0.0408284i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12716.0 | + | 12716.0i | 0.185246 | + | 0.185246i | ||||
\(263\) | 14771.0 | − | 14771.0i | 0.213549 | − | 0.213549i | −0.592224 | − | 0.805773i | \(-0.701750\pi\) |
0.805773 | + | 0.592224i | \(0.201750\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3055.00 | − | 21385.0i | −0.0435030 | − | 0.304521i | ||||
\(266\) | −32480.0 | −0.459042 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6008.00 | − | 6008.00i | 0.0836489 | − | 0.0836489i | ||||
\(269\) | − | 89720.0i | − | 1.23989i | −0.784644 | − | 0.619947i | \(-0.787154\pi\) | ||
0.784644 | − | 0.619947i | \(-0.212846\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 68202.0 | 0.928664 | 0.464332 | − | 0.885661i | \(-0.346294\pi\) | ||||
0.464332 | + | 0.885661i | \(0.346294\pi\) | |||||||
\(272\) | −17344.0 | − | 17344.0i | −0.234429 | − | 0.234429i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 81636.0i | − | 1.08738i | ||||||
\(275\) | −20650.0 | − | 70800.0i | −0.273058 | − | 0.936198i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18549.0 | + | 18549.0i | 0.241747 | + | 0.241747i | 0.817573 | − | 0.575826i | \(-0.195319\pi\) |
−0.575826 | + | 0.817573i | \(0.695319\pi\) | |||||||
\(278\) | 18800.0 | − | 18800.0i | 0.243259 | − | 0.243259i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13920.0 | + | 18560.0i | −0.177551 | + | 0.236735i | ||||
\(281\) | −2322.00 | −0.0294069 | −0.0147035 | − | 0.999892i | \(-0.504680\pi\) | ||||
−0.0147035 | + | 0.999892i | \(0.504680\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −91711.0 | + | 91711.0i | −1.14511 | + | 1.14511i | −0.157613 | + | 0.987501i | \(0.550380\pi\) |
−0.987501 | + | 0.157613i | \(0.949620\pi\) | |||||||
\(284\) | − | 51536.0i | − | 0.638961i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 32568.0 | 0.398161 | ||||||||
\(287\) | −48778.0 | − | 48778.0i | −0.592189 | − | 0.592189i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 63361.0i | 0.758624i | ||||||||
\(290\) | −6800.00 | − | 47600.0i | −0.0808561 | − | 0.565993i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −23608.0 | − | 23608.0i | −0.276881 | − | 0.276881i | ||||
\(293\) | 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 | ||||||||
\(295\) | −23200.0 | − | 17400.0i | −0.266590 | − | 0.199943i | ||||
\(296\) | 20832.0 | 0.237765 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27600.0 | − | 27600.0i | 0.310797 | − | 0.310797i | ||||
\(299\) | 37122.0i | 0.415230i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 63162.0 | 0.697145 | ||||||||
\(302\) | −37996.0 | − | 37996.0i | −0.416605 | − | 0.416605i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 17920.0i | − | 0.193906i | ||||||
\(305\) | −83970.0 | + | 111960.i | −0.902661 | + | 1.20355i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 42849.0 | + | 42849.0i | 0.454636 | + | 0.454636i | 0.896890 | − | 0.442254i | \(-0.145821\pi\) |
−0.442254 | + | 0.896890i | \(0.645821\pi\) | |||||||
\(308\) | −27376.0 | + | 27376.0i | −0.288582 | + | 0.288582i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14140.0 | − | 2020.00i | 0.147138 | − | 0.0210198i | ||||
\(311\) | 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 | −0.607810 | − | 0.794083i | \(-0.707952\pi\) |
0.794083 | + | 0.607810i | \(0.207952\pi\) | |||||||
\(314\) | − | 65484.0i | − | 0.664165i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84480.0 | −0.846018 | ||||||||
\(317\) | −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 | ||||||
\(320\) | −10240.0 | − | 7680.00i | −0.100000 | − | 0.0750000i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −31204.0 | − | 31204.0i | −0.300953 | − | 0.300953i | ||||
\(323\) | −75880.0 | + | 75880.0i | −0.727315 | + | 0.727315i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −53475.0 | − | 29325.0i | −0.506272 | − | 0.277633i | ||||
\(326\) | 80036.0 | 0.753096 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 26912.0 | − | 26912.0i | 0.250149 | − | 0.250149i | ||||
\(329\) | − | 73602.0i | − | 0.679983i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −54038.0 | −0.493223 | −0.246611 | − | 0.969114i | \(-0.579317\pi\) | ||||
−0.246611 | + | 0.969114i | \(0.579317\pi\) | |||||||
\(332\) | 49848.0 | + | 49848.0i | 0.452243 | + | 0.452243i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6196.00i | − | 0.0555416i | ||||||
\(335\) | −26285.0 | + | 3755.00i | −0.234217 | + | 0.0334596i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8529.00 | + | 8529.00i | 0.0750997 | + | 0.0750997i | 0.743659 | − | 0.668559i | \(-0.233089\pi\) |
−0.668559 | + | 0.743659i | \(0.733089\pi\) | |||||||
\(338\) | −38078.0 | + | 38078.0i | −0.333304 | + | 0.333304i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10840.0 | + | 75880.0i | 0.0937716 | + | 0.656401i | ||||
\(341\) | 23836.0 | 0.204986 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 90480.0 | − | 90480.0i | 0.769067 | − | 0.769067i | ||||
\(344\) | 34848.0i | 0.294484i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11156.0 | −0.0931872 | ||||||||
\(347\) | 56551.0 | + | 56551.0i | 0.469658 | + | 0.469658i | 0.901804 | − | 0.432146i | \(-0.142244\pi\) |
−0.432146 | + | 0.901804i | \(0.642244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 22520.0i | − | 0.184892i | −0.995718 | − | 0.0924459i | \(-0.970531\pi\) | ||
0.995718 | − | 0.0924459i | \(-0.0294685\pi\) | |||||||
\(350\) | 69600.0 | − | 20300.0i | 0.568163 | − | 0.165714i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15104.0 | − | 15104.0i | −0.121901 | − | 0.121901i | ||||
\(353\) | 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 | ||||||||
\(355\) | −96630.0 | + | 128840.i | −0.766753 | + | 1.02234i | ||||
\(356\) | −115840. | −0.914026 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5200.00 | + | 5200.00i | −0.0405730 | + | 0.0405730i | ||||
\(359\) | 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 | ||||||||
\(362\) | −88796.0 | − | 88796.0i | −0.677604 | − | 0.677604i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 32016.0i | 0.241637i | ||||||||
\(365\) | 14755.0 | + | 103285.i | 0.110752 | + | 0.775267i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14971.0 | − | 14971.0i | −0.111152 | − | 0.111152i | 0.649343 | − | 0.760496i | \(-0.275044\pi\) |
−0.760496 | + | 0.649343i | \(0.775044\pi\) | |||||||
\(368\) | 17216.0 | − | 17216.0i | 0.127127 | − | 0.127127i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −52080.0 | − | 39060.0i | −0.380424 | − | 0.285318i | ||||
\(371\) | 35438.0 | 0.257467 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13811.0 | + | 13811.0i | −0.0992676 | + | 0.0992676i | −0.754996 | − | 0.655729i | \(-0.772361\pi\) |
0.655729 | + | 0.754996i | \(0.272361\pi\) | |||||||
\(374\) | 127912.i | 0.914467i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 40608.0 | 0.287234 | ||||||||
\(377\) | −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 | \(0.661528\pi\) | |||||||
\(380\) | −33600.0 | + | 44800.0i | −0.232687 | + | 0.310249i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 29356.0 | + | 29356.0i | 0.201173 | + | 0.201173i | ||||
\(383\) | 86091.0 | − | 86091.0i | 0.586895 | − | 0.586895i | −0.349894 | − | 0.936789i | \(-0.613783\pi\) |
0.936789 | + | 0.349894i | \(0.113783\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 119770. | − | 17110.0i | 0.808028 | − | 0.115433i | ||||
\(386\) | 171396. | 1.15034 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 58488.0 | − | 58488.0i | 0.388511 | − | 0.388511i | ||||
\(389\) | 75000.0i | 0.495635i | 0.968807 | + | 0.247818i | \(0.0797134\pi\) | ||||
−0.968807 | + | 0.247818i | \(0.920287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −145798. | −0.953670 | ||||||||
\(392\) | 11504.0 | + | 11504.0i | 0.0748646 | + | 0.0748646i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 43884.0i | 0.282692i | ||||||||
\(395\) | 211200. | + | 158400.i | 1.35363 | + | 1.01522i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29149.0 | + | 29149.0i | 0.184945 | + | 0.184945i | 0.793507 | − | 0.608562i | \(-0.208253\pi\) |
−0.608562 | + | 0.793507i | \(0.708253\pi\) | |||||||
\(398\) | 76320.0 | − | 76320.0i | 0.481806 | − | 0.481806i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11200.0 | + | 38400.0i | 0.0700000 | + | 0.240000i | ||||
\(401\) | 45918.0 | 0.285558 | 0.142779 | − | 0.989755i | \(-0.454396\pi\) | ||||
0.142779 | + | 0.989755i | \(0.454396\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13938.0 | − | 13938.0i | 0.0858204 | − | 0.0858204i | ||||
\(404\) | 7024.00i | 0.0430350i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 78880.0 | 0.478536 | ||||||||
\(407\) | −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 | \(0.924395\pi\) | |||||||
\(410\) | −117740. | + | 16820.0i | −0.700416 | + | 0.100059i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 83432.0 | + | 83432.0i | 0.491517 | + | 0.491517i | ||||
\(413\) | 33640.0 | − | 33640.0i | 0.197222 | − | 0.197222i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31155.0 | − | 218085.i | −0.180897 | − | 1.26628i | ||||
\(416\) | −17664.0 | −0.102071 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −66080.0 | + | 66080.0i | −0.378196 | + | 0.378196i | ||||
\(419\) | 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 | \(0.285409\pi\) | |||||||
\(422\) | 145684. | + | 145684.i | 0.818063 | + | 0.818063i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19552.0i | 0.108758i | ||||||||
\(425\) | 115175. | − | 210025.i | 0.637647 | − | 1.16277i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −162342. | − | 162342.i | −0.890379 | − | 0.890379i | ||||
\(428\) | −37688.0 | + | 37688.0i | −0.205738 | + | 0.205738i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 65340.0 | − | 87120.0i | 0.353380 | − | 0.471174i | ||||
\(431\) | −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 | −0.203512 | − | 0.979072i | \(-0.565236\pi\) |
0.979072 | + | 0.203512i | \(0.0652357\pi\) | |||||||
\(434\) | 23432.0i | 0.124403i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −176320. | −0.927531 | ||||||||
\(437\) | −75320.0 | − | 75320.0i | −0.394410 | − | 0.394410i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 299440.i | − | 1.55375i | −0.629656 | − | 0.776874i | \(-0.716804\pi\) | ||
0.629656 | − | 0.776874i | \(-0.283196\pi\) | |||||||
\(440\) | 9440.00 | + | 66080.0i | 0.0487603 | + | 0.341322i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 74796.0 | + | 74796.0i | 0.382855 | + | 0.382855i | ||||
\(443\) | −240609. | + | 240609.i | −1.22604 | + | 1.22604i | −0.260590 | + | 0.965450i | \(0.583917\pi\) |
−0.965450 | + | 0.260590i | \(0.916083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 289600. | + | 217200.i | 1.46244 | + | 1.09683i | ||||
\(446\) | −123564. | −0.621187 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14848.0 | − | 14848.0i | 0.0739796 | − | 0.0739796i | ||||
\(449\) | 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 | ||||||||
\(452\) | 16888.0 | + | 16888.0i | 0.0826611 | + | 0.0826611i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 219644.i | 1.06563i | ||||||||
\(455\) | 60030.0 | − | 80040.0i | 0.289965 | − | 0.386620i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −188151. | − | 188151.i | −0.900895 | − | 0.900895i | 0.0946187 | − | 0.995514i | \(-0.469837\pi\) |
−0.995514 | + | 0.0946187i | \(0.969837\pi\) | |||||||
\(458\) | 100560. | − | 100560.i | 0.479396 | − | 0.479396i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −75320.0 | + | 10760.0i | −0.355955 | + | 0.0508507i | ||||
\(461\) | 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 | −0.0205595 | + | 0.999789i | \(0.506545\pi\) |
−0.999789 | + | 0.0205595i | \(0.993455\pi\) | |||||||
\(464\) | 43520.0i | 0.202140i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9564.00 | 0.0440421 | ||||||||
\(467\) | −59249.0 | − | 59249.0i | −0.271673 | − | 0.271673i | 0.558100 | − | 0.829774i | \(-0.311530\pi\) |
−0.829774 | + | 0.558100i | \(0.811530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 43558.0i | − | 0.198026i | ||||||
\(470\) | −101520. | − | 76140.0i | −0.459574 | − | 0.344681i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18560.0 | + | 18560.0i | 0.0833094 | + | 0.0833094i | ||||
\(473\) | 128502. | − | 128502.i | 0.574365 | − | 0.574365i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 168000. | − | 49000.0i | 0.744598 | − | 0.217175i | ||||
\(476\) | −125744. | −0.554975 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −35520.0 | + | 35520.0i | −0.155459 | + | 0.155459i | ||||
\(479\) | − | 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 | ||||||||
\(482\) | −56476.0 | − | 56476.0i | −0.243092 | − | 0.243092i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 5736.00i | − | 0.0244860i | ||||||
\(485\) | −255885. | + | 36555.0i | −1.08783 | + | 0.155404i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −123651. | − | 123651.i | −0.521362 | − | 0.521362i | 0.396620 | − | 0.917983i | \(-0.370183\pi\) |
−0.917983 | + | 0.396620i | \(0.870183\pi\) | |||||||
\(488\) | 89568.0 | − | 89568.0i | 0.376109 | − | 0.376109i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7190.00 | − | 50330.0i | −0.0299459 | − | 0.209621i | ||||
\(491\) | −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 | ||||
\(494\) | 77280.0i | 0.316675i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12928.0 | −0.0525494 | ||||||||
\(497\) | −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 | \(0.818182\pi\) | |||||||
\(500\) | 44000.0 | − | 117000.i | 0.176000 | − | 0.468000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −242004. | − | 242004.i | −0.960318 | − | 0.960318i | ||||
\(503\) | −109869. | + | 109869.i | −0.434249 | + | 0.434249i | −0.890071 | − | 0.455822i | \(-0.849345\pi\) |
0.455822 | + | 0.890071i | \(0.349345\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13170.0 | − | 17560.0i | 0.0516420 | − | 0.0688560i | ||||
\(506\) | −126968. | −0.495899 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −47272.0 | + | 47272.0i | −0.183179 | + | 0.183179i | ||||
\(509\) | 211000.i | 0.814417i | 0.913335 | + | 0.407209i | \(0.133498\pi\) | ||||
−0.913335 | + | 0.407209i | \(0.866502\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −171158. | −0.655474 | ||||||||
\(512\) | 8192.00 | + | 8192.00i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 289724.i | 1.09663i | ||||||||
\(515\) | −52145.0 | − | 365015.i | −0.196607 | − | 1.37625i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −149742. | − | 149742.i | −0.560225 | − | 0.560225i | ||||
\(518\) | 75516.0 | − | 75516.0i | 0.281436 | − | 0.281436i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 44160.0 | + | 33120.0i | 0.163314 | + | 0.122485i | ||||
\(521\) | −297282. | −1.09520 | −0.547600 | − | 0.836740i | \(-0.684458\pi\) | ||||
−0.547600 | + | 0.836740i | \(0.684458\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25071.0 | + | 25071.0i | −0.0916576 | + | 0.0916576i | −0.751449 | − | 0.659791i | \(-0.770645\pi\) |
0.659791 | + | 0.751449i | \(0.270645\pi\) | |||||||
\(524\) | 50864.0i | 0.185246i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 59084.0 | 0.213549 | ||||||||
\(527\) | 54742.0 | + | 54742.0i | 0.197106 | + | 0.197106i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 135119.i | 0.482842i | ||||||||
\(530\) | 36660.0 | − | 48880.0i | 0.130509 | − | 0.174012i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −64960.0 | − | 64960.0i | −0.229521 | − | 0.229521i | ||||
\(533\) | −116058. | + | 116058.i | −0.408527 | + | 0.408527i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 164885. | − | 23555.0i | 0.576068 | − | 0.0822954i | ||||
\(536\) | 24032.0 | 0.0836489 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 179440. | − | 179440.i | 0.619947 | − | 0.619947i | ||||
\(539\) | − | 84842.0i | − | 0.292034i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −142478. | −0.486803 | −0.243402 | − | 0.969926i | \(-0.578263\pi\) | ||||
−0.243402 | + | 0.969926i | \(0.578263\pi\) | |||||||
\(542\) | 136404. | + | 136404.i | 0.464332 | + | 0.464332i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 69376.0i | − | 0.234429i | ||||||
\(545\) | 440800. | + | 330600.i | 1.48405 | + | 1.11304i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 291009. | + | 291009.i | 0.972594 | + | 0.972594i | 0.999634 | − | 0.0270399i | \(-0.00860813\pi\) |
−0.0270399 | + | 0.999634i | \(0.508608\pi\) | |||||||
\(548\) | 163272. | − | 163272.i | 0.543689 | − | 0.543689i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 100300. | − | 182900.i | 0.331570 | − | 0.604628i | ||||
\(551\) | 190400. | 0.627139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −306240. | + | 306240.i | −1.00141 | + | 1.00141i | ||||
\(554\) | 74196.0i | 0.241747i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 75200.0 | 0.243259 | ||||||||
\(557\) | 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 | ||||||
\(560\) | −64960.0 | + | 9280.00i | −0.207143 | + | 0.0295918i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4644.00 | − | 4644.00i | −0.0147035 | − | 0.0147035i | ||||
\(563\) | −43449.0 | + | 43449.0i | −0.137076 | + | 0.137076i | −0.772316 | − | 0.635239i | \(-0.780902\pi\) |
0.635239 | + | 0.772316i | \(0.280902\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10555.0 | − | 73885.0i | −0.0330645 | − | 0.231451i | ||||
\(566\) | −366844. | −1.14511 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 103072. | − | 103072.i | 0.319480 | − | 0.319480i | ||||
\(569\) | 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 | \(-0.471904\pi\) | ||||
0.0881515 | + | 0.996107i | \(0.471904\pi\) | |||||||
\(572\) | 65136.0 | + | 65136.0i | 0.199081 | + | 0.199081i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 195112.i | − | 0.592189i | ||||||
\(575\) | 208475. | + | 114325.i | 0.630548 | + | 0.345784i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 195889. | + | 195889.i | 0.588381 | + | 0.588381i | 0.937193 | − | 0.348812i | \(-0.113415\pi\) |
−0.348812 | + | 0.937193i | \(0.613415\pi\) | |||||||
\(578\) | −126722. | + | 126722.i | −0.379312 | + | 0.379312i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 81600.0 | − | 108800.i | 0.242568 | − | 0.323424i | ||||
\(581\) | 361398. | 1.07062 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 72098.0 | − | 72098.0i | 0.212122 | − | 0.212122i | ||||
\(584\) | − | 94432.0i | − | 0.276881i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19404.0 | 0.0565062 | ||||||||
\(587\) | 404631. | + | 404631.i | 1.17431 | + | 1.17431i | 0.981171 | + | 0.193139i | \(0.0618669\pi\) |
0.193139 | + | 0.981171i | \(0.438133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56560.0i | 0.163034i | ||||||||
\(590\) | −11600.0 | − | 81200.0i | −0.0333238 | − | 0.233266i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 41664.0 | + | 41664.0i | 0.118882 | + | 0.118882i | ||||
\(593\) | 210991. | − | 210991.i | 0.600005 | − | 0.600005i | −0.340309 | − | 0.940314i | \(-0.610532\pi\) |
0.940314 | + | 0.340309i | \(0.110532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 314360. | + | 235770.i | 0.887960 | + | 0.665970i | ||||
\(596\) | 110400. | 0.310797 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −74244.0 | + | 74244.0i | −0.207615 | + | 0.207615i | ||||
\(599\) | − | 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 | \(0.330149\pi\) | |||||||
\(602\) | 126324. | + | 126324.i | 0.348572 | + | 0.348572i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 151984.i | − | 0.416605i | ||||||
\(605\) | −10755.0 | + | 14340.0i | −0.0293832 | + | 0.0391777i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 146469. | + | 146469.i | 0.397529 | + | 0.397529i | 0.877360 | − | 0.479832i | \(-0.159302\pi\) |
−0.479832 | + | 0.877360i | \(0.659302\pi\) | |||||||
\(608\) | 35840.0 | − | 35840.0i | 0.0969529 | − | 0.0969529i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −391860. | + | 55980.0i | −1.05310 | + | 0.150443i | ||||
\(611\) | −175122. | −0.469092 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 160989. | − | 160989.i | 0.428425 | − | 0.428425i | −0.459666 | − | 0.888092i | \(-0.652031\pi\) |
0.888092 | + | 0.459666i | \(0.152031\pi\) | |||||||
\(614\) | 171396.i | 0.454636i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −109504. | −0.288582 | ||||||||
\(617\) | −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 | \(0.146864\pi\) | ||||
−0.895435 | + | 0.445191i | \(0.853136\pi\) | |||||||
\(620\) | 32320.0 | + | 24240.0i | 0.0840791 | + | 0.0630593i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 144556. | + | 144556.i | 0.373642 | + | 0.373642i | ||||
\(623\) | −419920. | + | 419920.i | −1.08191 | + | 1.08191i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −329375. | + | 210000.i | −0.843200 | + | 0.537600i | ||||
\(626\) | 72996.0 | 0.186273 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 130968. | − | 130968.i | 0.332082 | − | 0.332082i | ||||
\(629\) | − | 352842.i | − | 0.891824i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −390998. | −0.982010 | −0.491005 | − | 0.871157i | \(-0.663370\pi\) | ||||
−0.491005 | + | 0.871157i | \(0.663370\pi\) | |||||||
\(632\) | −168960. | − | 168960.i | −0.423009 | − | 0.423009i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 100596.i | − | 0.250266i | ||||||
\(635\) | 206815. | − | 29545.0i | 0.512902 | − | 0.0732717i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −49611.0 | − | 49611.0i | −0.122264 | − | 0.122264i | ||||
\(638\) | 160480. | − | 160480.i | 0.394257 | − | 0.394257i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −5120.00 | − | 35840.0i | −0.0125000 | − | 0.0875000i | ||||
\(641\) | 585038. | 1.42386 | 0.711931 | − | 0.702249i | \(-0.247821\pi\) | ||||
0.711931 | + | 0.702249i | \(0.247821\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31911.0 | + | 31911.0i | −0.0771824 | + | 0.0771824i | −0.744644 | − | 0.667462i | \(-0.767381\pi\) |
0.667462 | + | 0.744644i | \(0.267381\pi\) | |||||||
\(644\) | − | 124816.i | − | 0.300953i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −303520. | −0.727315 | ||||||||
\(647\) | 280931. | + | 280931.i | 0.671106 | + | 0.671106i | 0.957971 | − | 0.286865i | \(-0.0926131\pi\) |
−0.286865 | + | 0.957971i | \(0.592613\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 136880.i | − | 0.324975i | ||||||
\(650\) | −48300.0 | − | 165600.i | −0.114320 | − | 0.391953i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 160072. | + | 160072.i | 0.376548 | + | 0.376548i | ||||
\(653\) | −523989. | + | 523989.i | −1.22884 | + | 1.22884i | −0.264439 | + | 0.964402i | \(0.585187\pi\) |
−0.964402 | + | 0.264439i | \(0.914813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 95370.0 | − | 127160.i | 0.222295 | − | 0.296393i | ||||
\(656\) | 107648. | 0.250149 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 147204. | − | 147204.i | 0.339991 | − | 0.339991i | ||||
\(659\) | 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 | \(0.501923\pi\) | |||||||
\(662\) | −108076. | − | 108076.i | −0.246611 | − | 0.246611i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 199392.i | 0.452243i | ||||||||
\(665\) | 40600.0 | + | 284200.i | 0.0918085 | + | 0.642659i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 182920. | + | 182920.i | 0.411159 | + | 0.411159i | ||||
\(668\) | 12392.0 | − | 12392.0i | 0.0277708 | − | 0.0277708i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −60080.0 | − | 45060.0i | −0.133838 | − | 0.100379i | ||||
\(671\) | −660564. | −1.46713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −332111. | + | 332111.i | −0.733252 | + | 0.733252i | −0.971263 | − | 0.238011i | \(-0.923505\pi\) |
0.238011 | + | 0.971263i | \(0.423505\pi\) | |||||||
\(674\) | 34116.0i | 0.0750997i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −152312. | −0.333304 | ||||||||
\(677\) | −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 | ||||||
\(680\) | −130080. | + | 173440.i | −0.281315 | + | 0.375087i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 47672.0 | + | 47672.0i | 0.102493 | + | 0.102493i | ||||
\(683\) | 349311. | − | 349311.i | 0.748809 | − | 0.748809i | −0.225447 | − | 0.974255i | \(-0.572384\pi\) |
0.974255 | + | 0.225447i | \(0.0723842\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −714315. | + | 102045.i | −1.52233 | + | 0.217476i | ||||
\(686\) | 361920. | 0.769067 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −69696.0 | + | 69696.0i | −0.147242 | + | 0.147242i | ||||
\(689\) | − | 84318.0i | − | 0.177616i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 282762. | 0.592195 | 0.296098 | − | 0.955158i | \(-0.404315\pi\) | ||||
0.296098 | + | 0.955158i | \(0.404315\pi\) | |||||||
\(692\) | −22312.0 | − | 22312.0i | −0.0465936 | − | 0.0465936i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 226204.i | 0.469658i | ||||||||
\(695\) | −188000. | − | 141000.i | −0.389214 | − | 0.291910i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −455822. | − | 455822.i | −0.938274 | − | 0.938274i | ||||
\(698\) | 45040.0 | − | 45040.0i | 0.0924459 | − | 0.0924459i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 179800. | + | 98600.0i | 0.366939 | + | 0.201224i | ||||
\(701\) | −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 | ||||
\(704\) | − | 60416.0i | − | 0.121901i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 178044. | 0.357205 | ||||||||
\(707\) | 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 | \(-0.0957234\pi\) | |||||||
\(710\) | −450940. | + | 64420.0i | −0.894545 | + | 0.127792i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −231680. | − | 231680.i | −0.457013 | − | 0.457013i | ||||
\(713\) | −54338.0 | + | 54338.0i | −0.106887 | + | 0.106887i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40710.0 | − | 284970.i | −0.0796323 | − | 0.557426i | ||||
\(716\) | −20800.0 | −0.0405730 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19360.0 | + | 19360.0i | −0.0375540 | + | 0.0375540i | ||||
\(719\) | − | 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 | ||||||||
\(722\) | 103842. | + | 103842.i | 0.199204 | + | 0.199204i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 355184.i | − | 0.677604i | ||||||
\(725\) | −408000. | + | 119000.i | −0.776219 | + | 0.226397i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −417651. | − | 417651.i | −0.790214 | − | 0.790214i | 0.191315 | − | 0.981529i | \(-0.438725\pi\) |
−0.981529 | + | 0.191315i | \(0.938725\pi\) | |||||||
\(728\) | −64032.0 | + | 64032.0i | −0.120819 | + | 0.120819i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −177060. | + | 236080.i | −0.332257 | + | 0.443010i | ||||
\(731\) | 590238. | 1.10457 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 394549. | − | 394549.i | 0.734333 | − | 0.734333i | −0.237142 | − | 0.971475i | \(-0.576211\pi\) |
0.971475 | + | 0.237142i | \(0.0762107\pi\) | |||||||
\(734\) | − | 59884.0i | − | 0.111152i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 68864.0 | 0.127127 | ||||||||
\(737\) | −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 | \(0.967924\pi\) | |||||||
\(740\) | −26040.0 | − | 182280.i | −0.0475530 | − | 0.332871i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 70876.0 | + | 70876.0i | 0.128733 | + | 0.128733i | ||||
\(743\) | 466451. | − | 466451.i | 0.844945 | − | 0.844945i | −0.144552 | − | 0.989497i | \(-0.546174\pi\) |
0.989497 | + | 0.144552i | \(0.0461742\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −276000. | − | 207000.i | −0.497275 | − | 0.372956i | ||||
\(746\) | −55244.0 | −0.0992676 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −255824. | + | 255824.i | −0.457234 | + | 0.457234i | ||||
\(749\) | 273238.i | 0.487054i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.01092e6 | 1.79241 | 0.896206 | − | 0.443638i | \(-0.146313\pi\) | ||||
0.896206 | + | 0.443638i | \(0.146313\pi\) | |||||||
\(752\) | 81216.0 | + | 81216.0i | 0.143617 | + | 0.143617i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 187680.i | − | 0.330123i | ||||||
\(755\) | −284970. | + | 379960.i | −0.499925 | + | 0.666567i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 313269. | + | 313269.i | 0.546671 | + | 0.546671i | 0.925476 | − | 0.378806i | \(-0.123665\pi\) |
−0.378806 | + | 0.925476i | \(0.623665\pi\) | |||||||
\(758\) | −502160. | + | 502160.i | −0.873984 | + | 0.873984i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −156800. | + | 22400.0i | −0.271468 | + | 0.0387812i | ||||
\(761\) | −142082. | −0.245341 | −0.122670 | − | 0.992447i | \(-0.539146\pi\) | ||||
−0.122670 | + | 0.992447i | \(0.539146\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −639160. | + | 639160.i | −1.09789 | + | 1.09789i | ||||
\(764\) | 117424.i | 0.201173i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 344364. | 0.586895 | ||||||||
\(767\) | −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 | \(0.996426\pi\) | |||||||
\(770\) | 273760. | + | 205320.i | 0.461730 | + | 0.346298i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 342792. | + | 342792.i | 0.575170 | + | 0.575170i | ||||
\(773\) | 782211. | − | 782211.i | 1.30908 | − | 1.30908i | 0.386994 | − | 0.922082i | \(-0.373513\pi\) |
0.922082 | − | 0.386994i | \(-0.126487\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35350.0 | − | 121200.i | −0.0588554 | − | 0.201790i | ||||
\(776\) | 233952. | 0.388511 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −150000. | + | 150000.i | −0.247818 | + | 0.247818i | ||||
\(779\) | − | 470960.i | − | 0.776085i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −760156. | −1.24624 | ||||||||
\(782\) | −291596. | − | 291596.i | −0.476835 | − | 0.476835i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 46016.0i | 0.0748646i | ||||||||
\(785\) | −572985. | + | 81855.0i | −0.929831 | + | 0.132833i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 201409. | + | 201409.i | 0.325184 | + | 0.325184i | 0.850752 | − | 0.525568i | \(-0.176147\pi\) |
−0.525568 | + | 0.850752i | \(0.676147\pi\) | |||||||
\(788\) | −87768.0 | + | 87768.0i | −0.141346 | + | 0.141346i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 105600. | + | 739200.i | 0.169204 | + | 1.18443i | ||||
\(791\) | 122438. | 0.195688 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −386262. | + | 386262.i | −0.614236 | + | 0.614236i | ||||
\(794\) | 116596.i | 0.184945i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 305280. | 0.481806 | ||||||||
\(797\) | 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 | ||||||
\(800\) | −54400.0 | + | 99200.0i | −0.0850000 | + | 0.155000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 91836.0 | + | 91836.0i | 0.142779 | + | 0.142779i | ||||
\(803\) | −348218. | + | 348218.i | −0.540033 | + | 0.540033i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −234030. | + | 312040.i | −0.361143 | + | 0.481525i | ||||
\(806\) | 55752.0 | 0.0858204 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14048.0 | + | 14048.0i | −0.0215175 | + | 0.0215175i | ||||
\(809\) | 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 | \(-0.525027\pi\) | ||||
−0.0785424 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(812\) | 157760. | + | 157760.i | 0.239268 | + | 0.239268i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 307272.i | − | 0.463740i | ||||||
\(815\) | −100045. | − | 700315.i | −0.150619 | − | 1.05433i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 304920. | + | 304920.i | 0.456817 | + | 0.456817i | ||||
\(818\) | −157440. | + | 157440.i | −0.235293 | + | 0.235293i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −269120. | − | 201840.i | −0.400238 | − | 0.300178i | ||||
\(821\) | 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 | 0.185666 | − | 0.982613i | \(-0.440556\pi\) |
0.982613 | − | 0.185666i | \(-0.0594441\pi\) | |||||||
\(824\) | 333728.i | 0.491517i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 134560. | 0.197222 | ||||||||
\(827\) | 889671. | + | 889671.i | 1.30082 | + | 1.30082i | 0.927837 | + | 0.372987i | \(0.121666\pi\) |
0.372987 | + | 0.927837i | \(0.378334\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 618280.i | − | 0.899655i | −0.893115 | − | 0.449828i | \(-0.851485\pi\) | ||
0.893115 | − | 0.449828i | \(-0.148515\pi\) | |||||||
\(830\) | 373860. | − | 498480.i | 0.542691 | − | 0.723588i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −35328.0 | − | 35328.0i | −0.0510355 | − | 0.0510355i | ||||
\(833\) | 194849. | − | 194849.i | 0.280807 | − | 0.280807i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −54215.0 | + | 7745.00i | −0.0777583 | + | 0.0111083i | ||||
\(836\) | −264320. | −0.378196 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −29520.0 | + | 29520.0i | −0.0420367 | + | 0.0420367i | ||||
\(839\) | 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 | ||||||||
\(842\) | 442564. | + | 442564.i | 0.624240 | + | 0.624240i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 582736.i | 0.818063i | ||||||||
\(845\) | 380780. | + | 285585.i | 0.533287 | + | 0.399965i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20793.0 | − | 20793.0i | −0.0289835 | − | 0.0289835i | ||||
\(848\) | −39104.0 | + | 39104.0i | −0.0543788 | + | 0.0543788i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 650400. | − | 189700.i | 0.900208 | − | 0.262561i | ||||
\(851\) | 350238. | 0.483620 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −698291. | + | 698291.i | −0.959706 | + | 0.959706i | −0.999219 | − | 0.0395127i | \(-0.987419\pi\) |
0.0395127 | + | 0.999219i | \(0.487419\pi\) | |||||||
\(854\) | − | 649368.i | − | 0.890379i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −150752. | −0.205738 | ||||||||
\(857\) | −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 | \(-0.779217\pi\) | ||
0.768943 | − | 0.639317i | \(-0.220783\pi\) | |||||||
\(860\) | 304920. | − | 43560.0i | 0.412277 | − | 0.0588967i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −425044. | − | 425044.i | −0.572031 | − | 0.572031i | ||||
\(863\) | −438149. | + | 438149.i | −0.588302 | + | 0.588302i | −0.937171 | − | 0.348869i | \(-0.886566\pi\) |
0.348869 | + | 0.937171i | \(0.386566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13945.0 | + | 97615.0i | 0.0186374 | + | 0.130462i | ||||
\(866\) | 581636. | 0.775560 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −46864.0 | + | 46864.0i | −0.0622014 | + | 0.0622014i | ||||
\(869\) | 1.24608e6i | 1.65009i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −103638. | −0.136610 | ||||||||
\(872\) | −352640. | − | 352640.i | −0.463766 | − | 0.463766i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 301280.i | − | 0.394410i | ||||||
\(875\) | −264625. | − | 583625.i | −0.345633 | − | 0.762286i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 281469. | + | 281469.i | 0.365958 | + | 0.365958i | 0.866001 | − | 0.500043i | \(-0.166682\pi\) |
−0.500043 | + | 0.866001i | \(0.666682\pi\) | |||||||
\(878\) | 598880. | − | 598880.i | 0.776874 | − | 0.776874i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −113280. | + | 151040.i | −0.146281 | + | 0.195041i | ||||
\(881\) | −876722. | −1.12956 | −0.564781 | − | 0.825241i | \(-0.691039\pi\) | ||||
−0.564781 | + | 0.825241i | \(0.691039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −327431. | + | 327431.i | −0.419951 | + | 0.419951i | −0.885187 | − | 0.465236i | \(-0.845969\pi\) |
0.465236 | + | 0.885187i | \(0.345969\pi\) | |||||||
\(884\) | 299184.i | 0.382855i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −962436. | −1.22604 | ||||||||
\(887\) | 477171. | + | 477171.i | 0.606494 | + | 0.606494i | 0.942028 | − | 0.335534i | \(-0.108917\pi\) |
−0.335534 | + | 0.942028i | \(0.608917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 342722.i | 0.433649i | ||||||||
\(890\) | 144800. | + | 1.01360e6i | 0.182805 | + | 1.27964i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −247128. | − | 247128.i | −0.310593 | − | 0.310593i | ||||
\(893\) | 355320. | − | 355320.i | 0.445571 | − | 0.445571i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52000.0 | + | 39000.0i | 0.0649168 | + | 0.0486876i | ||||
\(896\) | 59392.0 | 0.0739796 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −164960. | + | 164960.i | −0.204562 | + | 0.204562i | ||||
\(899\) | − | 137360.i | − | 0.169958i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 331162. | 0.407935 | ||||||||
\(902\) | −396952. | − | 396952.i | −0.487893 | − | 0.487893i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 67552.0i | 0.0826611i | ||||||||
\(905\) | −665970. | + | 887960.i | −0.813125 | + | 1.08417i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.11209e6 | + | 1.11209e6i | 1.35184 | + | 1.35184i | 0.883604 | + | 0.468235i | \(0.155110\pi\) |
0.468235 | + | 0.883604i | \(0.344890\pi\) | |||||||
\(908\) | −439288. | + | 439288.i | −0.532816 | + | 0.532816i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 280140. | − | 40020.0i | 0.338292 | − | 0.0483275i | ||||
\(911\) | 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 | ||||
\(914\) | − | 752604.i | − | 0.900895i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 402240. | 0.479396 | ||||||||
\(917\) | 184382. | + | 184382.i | 0.219270 | + | 0.219270i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.24040e6i | 1.46869i | 0.678775 | + | 0.734346i | \(0.262511\pi\) | ||||
−0.678775 | + | 0.734346i | \(0.737489\pi\) | |||||||
\(920\) | −172160. | − | 129120.i | −0.203403 | − | 0.152552i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 652316. | + | 652316.i | 0.767355 | + | 0.767355i | ||||
\(923\) | −444498. | + | 444498.i | −0.521755 | + | 0.521755i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −276675. | + | 504525.i | −0.323360 | + | 0.589657i | ||||
\(926\) | −874924. | −1.02035 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −87040.0 | + | 87040.0i | −0.101070 | + | 0.101070i | ||||
\(929\) | − | 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 | ||||||||
\(932\) | 19128.0 | + | 19128.0i | 0.0220210 | + | 0.0220210i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 236996.i | − | 0.271673i | ||||||
\(935\) | 1.11923e6 | − | 159890.i | 1.28025 | − | 0.182893i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.07047e6 | − | 1.07047e6i | −1.21926 | − | 1.21926i | −0.967892 | − | 0.251366i | \(-0.919120\pi\) |
−0.251366 | − | 0.967892i | \(-0.580880\pi\) | |||||||
\(938\) | 87116.0 | − | 87116.0i | 0.0990130 | − | 0.0990130i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −50760.0 | − | 355320.i | −0.0574468 | − | 0.402128i | ||||
\(941\) | −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 | ||||
\(944\) | 74240.0i | 0.0833094i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 514008. | 0.574365 | ||||||||
\(947\) | 191711. | + | 191711.i | 0.213770 | + | 0.213770i | 0.805867 | − | 0.592097i | \(-0.201700\pi\) |
−0.592097 | + | 0.805867i | \(0.701700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 407238.i | 0.452185i | ||||||||
\(950\) | 434000. | + | 238000.i | 0.480886 | + | 0.263712i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −251488. | − | 251488.i | −0.277487 | − | 0.277487i | ||||
\(953\) | 630231. | − | 630231.i | 0.693927 | − | 0.693927i | −0.269166 | − | 0.963094i | \(-0.586748\pi\) |
0.963094 | + | 0.269166i | \(0.0867482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 220170. | − | 293560.i | 0.241408 | − | 0.321877i | ||||
\(956\) | −142080. | −0.155459 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 546880. | − | 546880.i | 0.595883 | − | 0.595883i | ||||
\(959\) | − | 1.18372e6i | − | 1.28710i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −882717. | −0.955817 | ||||||||
\(962\) | −179676. | − | 179676.i | −0.194151 | − | 0.194151i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 225904.i | − | 0.243092i | ||||||
\(965\) | −214245. | − | 1.49972e6i | −0.230068 | − | 1.61048i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −345491. | − | 345491.i | −0.369474 | − | 0.369474i | 0.497811 | − | 0.867285i | \(-0.334137\pi\) |
−0.867285 | + | 0.497811i | \(0.834137\pi\) | |||||||
\(968\) | 11472.0 | − | 11472.0i | 0.0122430 | − | 0.0122430i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −584880. | − | 438660.i | −0.621618 | − | 0.466213i | ||||
\(971\) | −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 | ||||
\(974\) | − | 494604.i | − | 0.521362i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 358272. | 0.376109 | ||||||||
\(977\) | 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 | ||||||||
\(980\) | 86280.0 | − | 115040.i | 0.0898376 | − | 0.119783i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −396884. | − | 396884.i | −0.411567 | − | 0.411567i | ||||
\(983\) | −466909. | + | 466909.i | −0.483198 | + | 0.483198i | −0.906151 | − | 0.422953i | \(-0.860993\pi\) |
0.422953 | + | 0.906151i | \(0.360993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 383985. | − | 54855.0i | 0.395769 | − | 0.0565384i | ||||
\(986\) | 737120. | 0.758201 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −154560. | + | 154560.i | −0.158337 | + | 0.158337i | ||||
\(989\) | 585882.i | 0.598987i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −901238. | −0.917682 | −0.458841 | − | 0.888518i | \(-0.651735\pi\) | ||||
−0.458841 | + | 0.888518i | \(0.651735\pi\) | |||||||
\(992\) | −25856.0 | − | 25856.0i | −0.0262747 | − | 0.0262747i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 747272.i | − | 0.756321i | ||||||
\(995\) | −763200. | − | 572400.i | −0.770890 | − | 0.578167i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 152149. | + | 152149.i | 0.153066 | + | 0.153066i | 0.779486 | − | 0.626420i | \(-0.215480\pi\) |
−0.626420 | + | 0.779486i | \(0.715480\pi\) | |||||||
\(998\) | −538480. | + | 538480.i | −0.540640 | + | 0.540640i | ||||
\(999\) | 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 | 90.5.g.b.37.1 | 2 | ||
3.2 | odd | 2 | 10.5.c.a.7.1 | yes | 2 | ||
5.2 | odd | 4 | 450.5.g.a.343.1 | 2 | |||
5.3 | odd | 4 | inner | 90.5.g.b.73.1 | 2 | ||
5.4 | even | 2 | 450.5.g.a.307.1 | 2 | |||
12.11 | even | 2 | 80.5.p.b.17.1 | 2 | |||
15.2 | even | 4 | 50.5.c.b.43.1 | 2 | |||
15.8 | even | 4 | 10.5.c.a.3.1 | ✓ | 2 | ||
15.14 | odd | 2 | 50.5.c.b.7.1 | 2 | |||
24.5 | odd | 2 | 320.5.p.b.257.1 | 2 | |||
24.11 | even | 2 | 320.5.p.i.257.1 | 2 | |||
60.23 | odd | 4 | 80.5.p.b.33.1 | 2 | |||
60.47 | odd | 4 | 400.5.p.c.193.1 | 2 | |||
60.59 | even | 2 | 400.5.p.c.257.1 | 2 | |||
120.53 | even | 4 | 320.5.p.b.193.1 | 2 | |||
120.83 | odd | 4 | 320.5.p.i.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.5.c.a.3.1 | ✓ | 2 | 15.8 | even | 4 | ||
10.5.c.a.7.1 | yes | 2 | 3.2 | odd | 2 | ||
50.5.c.b.7.1 | 2 | 15.14 | odd | 2 | |||
50.5.c.b.43.1 | 2 | 15.2 | even | 4 | |||
80.5.p.b.17.1 | 2 | 12.11 | even | 2 | |||
80.5.p.b.33.1 | 2 | 60.23 | odd | 4 | |||
90.5.g.b.37.1 | 2 | 1.1 | even | 1 | trivial | ||
90.5.g.b.73.1 | 2 | 5.3 | odd | 4 | inner | ||
320.5.p.b.193.1 | 2 | 120.53 | even | 4 | |||
320.5.p.b.257.1 | 2 | 24.5 | odd | 2 | |||
320.5.p.i.193.1 | 2 | 120.83 | odd | 4 | |||
320.5.p.i.257.1 | 2 | 24.11 | even | 2 | |||
400.5.p.c.193.1 | 2 | 60.47 | odd | 4 | |||
400.5.p.c.257.1 | 2 | 60.59 | even | 2 | |||
450.5.g.a.307.1 | 2 | 5.4 | even | 2 | |||
450.5.g.a.343.1 | 2 | 5.2 | odd | 4 |