Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,5,Mod(7,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.7");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.c (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: | \(5.16849815419\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.43 |
Dual form | 50.5.c.b.7.1 |
$q$-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 \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||
\(3\) | −9.00000 | − | 9.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(4\) | − | 8.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −36.0000 | −1.00000 | ||||||||
\(7\) | −29.0000 | + | 29.0000i | −0.591837 | + | 0.591837i | −0.938127 | − | 0.346291i | \(-0.887441\pi\) |
0.346291 | + | 0.938127i | \(0.387441\pi\) | |||||||
\(8\) | −16.0000 | − | 16.0000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 81.0000i | 1.00000i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −118.000 | −0.975207 | −0.487603 | − | 0.873065i | \(-0.662129\pi\) | ||||
−0.487603 | + | 0.873065i | \(0.662129\pi\) | |||||||
\(12\) | −72.0000 | + | 72.0000i | −0.500000 | + | 0.500000i | ||||
\(13\) | −69.0000 | − | 69.0000i | −0.408284 | − | 0.408284i | 0.472856 | − | 0.881140i | \(-0.343223\pi\) |
−0.881140 | + | 0.472856i | \(0.843223\pi\) | |||||||
\(14\) | 116.000i | 0.591837i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | 271.000 | − | 271.000i | 0.937716 | − | 0.937716i | −0.0604547 | − | 0.998171i | \(-0.519255\pi\) |
0.998171 | + | 0.0604547i | \(0.0192551\pi\) | |||||||
\(18\) | 162.000 | + | 162.000i | 0.500000 | + | 0.500000i | ||||
\(19\) | − | 280.000i | − | 0.775623i | −0.921739 | − | 0.387812i | \(-0.873231\pi\) | ||
0.921739 | − | 0.387812i | \(-0.126769\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 522.000 | 1.18367 | ||||||||
\(22\) | −236.000 | + | 236.000i | −0.487603 | + | 0.487603i | ||||
\(23\) | −269.000 | − | 269.000i | −0.508507 | − | 0.508507i | 0.405561 | − | 0.914068i | \(-0.367076\pi\) |
−0.914068 | + | 0.405561i | \(0.867076\pi\) | |||||||
\(24\) | 288.000i | 0.500000i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −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 | ||||
\(33\) | 1062.00 | + | 1062.00i | 0.975207 | + | 0.975207i | ||||
\(34\) | − | 1084.00i | − | 0.937716i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 648.000 | 0.500000 | ||||||||
\(37\) | 651.000 | − | 651.000i | 0.475530 | − | 0.475530i | −0.428169 | − | 0.903699i | \(-0.640841\pi\) |
0.903699 | + | 0.428169i | \(0.140841\pi\) | |||||||
\(38\) | −560.000 | − | 560.000i | −0.387812 | − | 0.387812i | ||||
\(39\) | 1242.00i | 0.816568i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1682.00 | 1.00059 | 0.500297 | − | 0.865854i | \(-0.333224\pi\) | ||||
0.500297 | + | 0.865854i | \(0.333224\pi\) | |||||||
\(42\) | 1044.00 | − | 1044.00i | 0.591837 | − | 0.591837i | ||||
\(43\) | −1089.00 | − | 1089.00i | −0.588967 | − | 0.588967i | 0.348385 | − | 0.937352i | \(-0.386730\pi\) |
−0.937352 | + | 0.348385i | \(0.886730\pi\) | |||||||
\(44\) | 944.000i | 0.487603i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1076.00 | −0.508507 | ||||||||
\(47\) | −1269.00 | + | 1269.00i | −0.574468 | + | 0.574468i | −0.933374 | − | 0.358906i | \(-0.883150\pi\) |
0.358906 | + | 0.933374i | \(0.383150\pi\) | |||||||
\(48\) | 576.000 | + | 576.000i | 0.250000 | + | 0.250000i | ||||
\(49\) | 719.000i | 0.299459i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4878.00 | −1.87543 | ||||||||
\(52\) | −552.000 | + | 552.000i | −0.204142 | + | 0.204142i | ||||
\(53\) | 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 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 928.000 | 0.295918 | ||||||||
\(57\) | −2520.00 | + | 2520.00i | −0.775623 | + | 0.775623i | ||||
\(58\) | −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 | ||||
\(63\) | −2349.00 | − | 2349.00i | −0.591837 | − | 0.591837i | ||||
\(64\) | 512.000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4248.00 | 0.975207 | ||||||||
\(67\) | 751.000 | − | 751.000i | 0.167298 | − | 0.167298i | −0.618493 | − | 0.785791i | \(-0.712256\pi\) |
0.785791 | + | 0.618493i | \(0.212256\pi\) | |||||||
\(68\) | −2168.00 | − | 2168.00i | −0.468858 | − | 0.468858i | ||||
\(69\) | 4842.00i | 1.01701i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6442.00 | 1.27792 | 0.638961 | − | 0.769240i | \(-0.279365\pi\) | ||||
0.638961 | + | 0.769240i | \(0.279365\pi\) | |||||||
\(72\) | 1296.00 | − | 1296.00i | 0.250000 | − | 0.250000i | ||||
\(73\) | 2951.00 | + | 2951.00i | 0.553762 | + | 0.553762i | 0.927525 | − | 0.373762i | \(-0.121932\pi\) |
−0.373762 | + | 0.927525i | \(0.621932\pi\) | |||||||
\(74\) | − | 2604.00i | − | 0.475530i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2240.00 | −0.387812 | ||||||||
\(77\) | 3422.00 | − | 3422.00i | 0.577163 | − | 0.577163i | ||||
\(78\) | 2484.00 | + | 2484.00i | 0.408284 | + | 0.408284i | ||||
\(79\) | − | 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 | ||||||||
\(82\) | 3364.00 | − | 3364.00i | 0.500297 | − | 0.500297i | ||||
\(83\) | 6231.00 | + | 6231.00i | 0.904485 | + | 0.904485i | 0.995820 | − | 0.0913348i | \(-0.0291134\pi\) |
−0.0913348 | + | 0.995820i | \(0.529113\pi\) | |||||||
\(84\) | − | 4176.00i | − | 0.591837i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4356.00 | −0.588967 | ||||||||
\(87\) | −6120.00 | + | 6120.00i | −0.808561 | + | 0.808561i | ||||
\(88\) | 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 | ||||
\(93\) | −1818.00 | − | 1818.00i | −0.210198 | − | 0.210198i | ||||
\(94\) | 5076.00i | 0.574468i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2304.00 | 0.250000 | ||||||||
\(97\) | 7311.00 | − | 7311.00i | 0.777022 | − | 0.777022i | −0.202301 | − | 0.979323i | \(-0.564842\pi\) |
0.979323 | + | 0.202301i | \(0.0648420\pi\) | |||||||
\(98\) | 1438.00 | + | 1438.00i | 0.149729 | + | 0.149729i | ||||
\(99\) | − | 9558.00i | − | 0.975207i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −878.000 | −0.0860700 | −0.0430350 | − | 0.999074i | \(-0.513703\pi\) | ||||
−0.0430350 | + | 0.999074i | \(0.513703\pi\) | |||||||
\(102\) | −9756.00 | + | 9756.00i | −0.937716 | + | 0.937716i | ||||
\(103\) | −10429.0 | − | 10429.0i | −0.983033 | − | 0.983033i | 0.0168252 | − | 0.999858i | \(-0.494644\pi\) |
−0.999858 | + | 0.0168252i | \(0.994644\pi\) | |||||||
\(104\) | 2208.00i | 0.204142i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2444.00 | 0.217515 | ||||||||
\(107\) | 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 | \(-0.621927\pi\) | ||
0.373745 | − | 0.927531i | \(-0.378073\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11718.0 | −0.951059 | ||||||||
\(112\) | 1856.00 | − | 1856.00i | 0.147959 | − | 0.147959i | ||||
\(113\) | 2111.00 | + | 2111.00i | 0.165322 | + | 0.165322i | 0.784920 | − | 0.619597i | \(-0.212704\pi\) |
−0.619597 | + | 0.784920i | \(0.712704\pi\) | |||||||
\(114\) | 10080.0i | 0.775623i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5440.00 | −0.404281 | ||||||||
\(117\) | 5589.00 | − | 5589.00i | 0.408284 | − | 0.408284i | ||||
\(118\) | −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 | ||||
\(123\) | −15138.0 | − | 15138.0i | −1.00059 | − | 1.00059i | ||||
\(124\) | − | 1616.00i | − | 0.105099i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9396.00 | −0.591837 | ||||||||
\(127\) | −5909.00 | + | 5909.00i | −0.366359 | + | 0.366359i | −0.866147 | − | 0.499789i | \(-0.833411\pi\) |
0.499789 | + | 0.866147i | \(0.333411\pi\) | |||||||
\(128\) | 1024.00 | + | 1024.00i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 19602.0i | 1.17793i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6358.00 | −0.370491 | −0.185246 | − | 0.982692i | \(-0.559308\pi\) | ||||
−0.185246 | + | 0.982692i | \(0.559308\pi\) | |||||||
\(132\) | 8496.00 | − | 8496.00i | 0.487603 | − | 0.487603i | ||||
\(133\) | 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 | −0.0915804 | + | 0.995798i | \(0.529192\pi\) |
−0.995798 | + | 0.0915804i | \(0.970808\pi\) | |||||||
\(138\) | 9684.00 | + | 9684.00i | 0.508507 | + | 0.508507i | ||||
\(139\) | 9400.00i | 0.486517i | 0.969961 | + | 0.243259i | \(0.0782164\pi\) | ||||
−0.969961 | + | 0.243259i | \(0.921784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22842.0 | 1.14894 | ||||||||
\(142\) | 12884.0 | − | 12884.0i | 0.638961 | − | 0.638961i | ||||
\(143\) | 8142.00 | + | 8142.00i | 0.398161 | + | 0.398161i | ||||
\(144\) | − | 5184.00i | − | 0.250000i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11804.0 | 0.553762 | ||||||||
\(147\) | 6471.00 | − | 6471.00i | 0.299459 | − | 0.299459i | ||||
\(148\) | −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 | ||||
\(153\) | 21951.0 | + | 21951.0i | 0.937716 | + | 0.937716i | ||||
\(154\) | − | 13688.0i | − | 0.577163i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9936.00 | 0.408284 | ||||||||
\(157\) | 16371.0 | − | 16371.0i | 0.664165 | − | 0.664165i | −0.292194 | − | 0.956359i | \(-0.594385\pi\) |
0.956359 | + | 0.292194i | \(0.0943853\pi\) | |||||||
\(158\) | −21120.0 | − | 21120.0i | −0.846018 | − | 0.846018i | ||||
\(159\) | − | 10998.0i | − | 0.435030i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15602.0 | 0.601906 | ||||||||
\(162\) | 13122.0 | − | 13122.0i | 0.500000 | − | 0.500000i | ||||
\(163\) | −20009.0 | − | 20009.0i | −0.753096 | − | 0.753096i | 0.221960 | − | 0.975056i | \(-0.428755\pi\) |
−0.975056 | + | 0.221960i | \(0.928755\pi\) | |||||||
\(164\) | − | 13456.0i | − | 0.500297i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 24924.0 | 0.904485 | ||||||||
\(167\) | −1549.00 | + | 1549.00i | −0.0555416 | + | 0.0555416i | −0.734332 | − | 0.678790i | \(-0.762504\pi\) |
0.678790 | + | 0.734332i | \(0.262504\pi\) | |||||||
\(168\) | −8352.00 | − | 8352.00i | −0.295918 | − | 0.295918i | ||||
\(169\) | − | 19039.0i | − | 0.666608i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22680.0 | 0.775623 | ||||||||
\(172\) | −8712.00 | + | 8712.00i | −0.294484 | + | 0.294484i | ||||
\(173\) | −2789.00 | − | 2789.00i | −0.0931872 | − | 0.0931872i | 0.658976 | − | 0.752164i | \(-0.270990\pi\) |
−0.752164 | + | 0.658976i | \(0.770990\pi\) | |||||||
\(174\) | 24480.0i | 0.808561i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7552.00 | 0.243802 | ||||||||
\(177\) | −10440.0 | + | 10440.0i | −0.333238 | + | 0.333238i | ||||
\(178\) | 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 | ||||
\(183\) | 50382.0 | + | 50382.0i | 1.50443 | + | 1.50443i | ||||
\(184\) | 8608.00i | 0.254253i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7272.00 | −0.210198 | ||||||||
\(187\) | −31978.0 | + | 31978.0i | −0.914467 | + | 0.914467i | ||||
\(188\) | 10152.0 | + | 10152.0i | 0.287234 | + | 0.287234i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14678.0 | −0.402346 | −0.201173 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201173 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(192\) | 4608.00 | − | 4608.00i | 0.125000 | − | 0.125000i | ||||
\(193\) | −42849.0 | − | 42849.0i | −1.15034 | − | 1.15034i | −0.986484 | − | 0.163855i | \(-0.947607\pi\) |
−0.163855 | − | 0.986484i | \(-0.552393\pi\) | |||||||
\(194\) | − | 29244.0i | − | 0.777022i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5752.00 | 0.149729 | ||||||||
\(197\) | 10971.0 | − | 10971.0i | 0.282692 | − | 0.282692i | −0.551490 | − | 0.834182i | \(-0.685940\pi\) |
0.834182 | + | 0.551490i | \(0.185940\pi\) | |||||||
\(198\) | −19116.0 | − | 19116.0i | −0.487603 | − | 0.487603i | ||||
\(199\) | 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 | ||||||||
\(202\) | −1756.00 | + | 1756.00i | −0.0430350 | + | 0.0430350i | ||||
\(203\) | 19720.0 | + | 19720.0i | 0.478536 | + | 0.478536i | ||||
\(204\) | 39024.0i | 0.937716i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −41716.0 | −0.983033 | ||||||||
\(207\) | 21789.0 | − | 21789.0i | 0.508507 | − | 0.508507i | ||||
\(208\) | 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 | ||||
\(213\) | −57978.0 | − | 57978.0i | −1.27792 | − | 1.27792i | ||||
\(214\) | − | 18844.0i | − | 0.411477i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5858.00 | + | 5858.00i | −0.124403 | + | 0.124403i | ||||
\(218\) | −44080.0 | − | 44080.0i | −0.927531 | − | 0.927531i | ||||
\(219\) | − | 53118.0i | − | 1.10752i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −37398.0 | −0.765709 | ||||||||
\(222\) | −23436.0 | + | 23436.0i | −0.475530 | + | 0.475530i | ||||
\(223\) | 30891.0 | + | 30891.0i | 0.621187 | + | 0.621187i | 0.945835 | − | 0.324648i | \(-0.105246\pi\) |
−0.324648 | + | 0.945835i | \(0.605246\pi\) | |||||||
\(224\) | − | 7424.00i | − | 0.147959i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8444.00 | 0.165322 | ||||||||
\(227\) | 54911.0 | − | 54911.0i | 1.06563 | − | 1.06563i | 0.0679438 | − | 0.997689i | \(-0.478356\pi\) |
0.997689 | − | 0.0679438i | \(-0.0216439\pi\) | |||||||
\(228\) | 20160.0 | + | 20160.0i | 0.387812 | + | 0.387812i | ||||
\(229\) | 50280.0i | 0.958792i | 0.877599 | + | 0.479396i | \(0.159144\pi\) | ||||
−0.877599 | + | 0.479396i | \(0.840856\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −61596.0 | −1.15433 | ||||||||
\(232\) | −10880.0 | + | 10880.0i | −0.202140 | + | 0.202140i | ||||
\(233\) | 2391.00 | + | 2391.00i | 0.0440421 | + | 0.0440421i | 0.728785 | − | 0.684743i | \(-0.240085\pi\) |
−0.684743 | + | 0.728785i | \(0.740085\pi\) | |||||||
\(234\) | − | 22356.0i | − | 0.408284i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9280.00 | −0.166619 | ||||||||
\(237\) | −95040.0 | + | 95040.0i | −1.69204 | + | 1.69204i | ||||
\(238\) | 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 | ||||
\(243\) | −59049.0 | − | 59049.0i | −1.00000 | − | 1.00000i | ||||
\(244\) | 44784.0i | 0.752217i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −60552.0 | −1.00059 | ||||||||
\(247\) | −19320.0 | + | 19320.0i | −0.316675 | + | 0.316675i | ||||
\(248\) | −3232.00 | − | 3232.00i | −0.0525494 | − | 0.0525494i | ||||
\(249\) | − | 112158.i | − | 1.80897i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 121002. | 1.92064 | 0.960318 | − | 0.278907i | \(-0.0899722\pi\) | ||||
0.960318 | + | 0.278907i | \(0.0899722\pi\) | |||||||
\(252\) | −18792.0 | + | 18792.0i | −0.295918 | + | 0.295918i | ||||
\(253\) | 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 | 0.101823 | − | 0.994803i | \(-0.467533\pi\) |
0.994803 | − | 0.101823i | \(-0.0324674\pi\) | |||||||
\(258\) | 39204.0 | + | 39204.0i | 0.588967 | + | 0.588967i | ||||
\(259\) | 37758.0i | 0.562872i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 55080.0 | 0.808561 | ||||||||
\(262\) | −12716.0 | + | 12716.0i | −0.185246 | + | 0.185246i | ||||
\(263\) | 14771.0 | + | 14771.0i | 0.213549 | + | 0.213549i | 0.805773 | − | 0.592224i | \(-0.201750\pi\) |
−0.592224 | + | 0.805773i | \(0.701750\pi\) | |||||||
\(264\) | − | 33984.0i | − | 0.487603i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 32480.0 | 0.459042 | ||||||||
\(267\) | 130320. | − | 130320.i | 1.82805 | − | 1.82805i | ||||
\(268\) | −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 | ||||
\(273\) | −36018.0 | − | 36018.0i | −0.483275 | − | 0.483275i | ||||
\(274\) | 81636.0i | 1.08738i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 38736.0 | 0.508507 | ||||||||
\(277\) | −18549.0 | + | 18549.0i | −0.241747 | + | 0.241747i | −0.817573 | − | 0.575826i | \(-0.804681\pi\) |
0.575826 | + | 0.817573i | \(0.304681\pi\) | |||||||
\(278\) | 18800.0 | + | 18800.0i | 0.243259 | + | 0.243259i | ||||
\(279\) | 16362.0i | 0.210198i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2322.00 | 0.0294069 | 0.0147035 | − | 0.999892i | \(-0.495320\pi\) | ||||
0.0147035 | + | 0.999892i | \(0.495320\pi\) | |||||||
\(282\) | 45684.0 | − | 45684.0i | 0.574468 | − | 0.574468i | ||||
\(283\) | 91711.0 | + | 91711.0i | 1.14511 | + | 1.14511i | 0.987501 | + | 0.157613i | \(0.0503797\pi\) |
0.157613 | + | 0.987501i | \(0.449620\pi\) | |||||||
\(284\) | − | 51536.0i | − | 0.638961i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 32568.0 | 0.398161 | ||||||||
\(287\) | −48778.0 | + | 48778.0i | −0.592189 | + | 0.592189i | ||||
\(288\) | −10368.0 | − | 10368.0i | −0.125000 | − | 0.125000i | ||||
\(289\) | − | 63361.0i | − | 0.758624i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −131598. | −1.55404 | ||||||||
\(292\) | 23608.0 | − | 23608.0i | 0.276881 | − | 0.276881i | ||||
\(293\) | 4851.00 | + | 4851.00i | 0.0565062 | + | 0.0565062i | 0.734795 | − | 0.678289i | \(-0.237278\pi\) |
−0.678289 | + | 0.734795i | \(0.737278\pi\) | |||||||
\(294\) | − | 25884.0i | − | 0.299459i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −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 | ||||
\(303\) | 7902.00 | + | 7902.00i | 0.0860700 | + | 0.0860700i | ||||
\(304\) | 17920.0i | 0.193906i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 87804.0 | 0.937716 | ||||||||
\(307\) | −42849.0 | + | 42849.0i | −0.454636 | + | 0.454636i | −0.896890 | − | 0.442254i | \(-0.854179\pi\) |
0.442254 | + | 0.896890i | \(0.354179\pi\) | |||||||
\(308\) | −27376.0 | − | 27376.0i | −0.288582 | − | 0.288582i | ||||
\(309\) | 187722.i | 1.96607i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −72278.0 | −0.747283 | −0.373642 | − | 0.927573i | \(-0.621891\pi\) | ||||
−0.373642 | + | 0.927573i | \(0.621891\pi\) | |||||||
\(312\) | 19872.0 | − | 19872.0i | 0.204142 | − | 0.204142i | ||||
\(313\) | −18249.0 | − | 18249.0i | −0.186273 | − | 0.186273i | 0.607810 | − | 0.794083i | \(-0.292048\pi\) |
−0.794083 | + | 0.607810i | \(0.792048\pi\) | |||||||
\(314\) | − | 65484.0i | − | 0.664165i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −84480.0 | −0.846018 | ||||||||
\(317\) | −25149.0 | + | 25149.0i | −0.250266 | + | 0.250266i | −0.821080 | − | 0.570814i | \(-0.806628\pi\) |
0.570814 | + | 0.821080i | \(0.306628\pi\) | |||||||
\(318\) | −21996.0 | − | 21996.0i | −0.217515 | − | 0.217515i | ||||
\(319\) | 80240.0i | 0.788514i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −84798.0 | −0.822954 | ||||||||
\(322\) | 31204.0 | − | 31204.0i | 0.300953 | − | 0.300953i | ||||
\(323\) | −75880.0 | − | 75880.0i | −0.727315 | − | 0.727315i | ||||
\(324\) | − | 52488.0i | − | 0.500000i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −80036.0 | −0.753096 | ||||||||
\(327\) | −198360. | + | 198360.i | −1.85506 | + | 1.85506i | ||||
\(328\) | −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 | ||||
\(333\) | 52731.0 | + | 52731.0i | 0.475530 | + | 0.475530i | ||||
\(334\) | 6196.00i | 0.0555416i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −33408.0 | −0.295918 | ||||||||
\(337\) | −8529.00 | + | 8529.00i | −0.0750997 | + | 0.0750997i | −0.743659 | − | 0.668559i | \(-0.766911\pi\) |
0.668559 | + | 0.743659i | \(0.266911\pi\) | |||||||
\(338\) | −38078.0 | − | 38078.0i | −0.333304 | − | 0.333304i | ||||
\(339\) | − | 37998.0i | − | 0.330645i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23836.0 | −0.204986 | ||||||||
\(342\) | 45360.0 | − | 45360.0i | 0.387812 | − | 0.387812i | ||||
\(343\) | −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 | −0.432146 | − | 0.901804i | \(-0.642244\pi\) |
0.901804 | + | 0.432146i | \(0.142244\pi\) | |||||||
\(348\) | 48960.0 | + | 48960.0i | 0.404281 | + | 0.404281i | ||||
\(349\) | 22520.0i | 0.184892i | 0.995718 | + | 0.0924459i | \(0.0294685\pi\) | ||||
−0.995718 | + | 0.0924459i | \(0.970531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15104.0 | − | 15104.0i | 0.121901 | − | 0.121901i | ||||
\(353\) | 44511.0 | + | 44511.0i | 0.357205 | + | 0.357205i | 0.862782 | − | 0.505576i | \(-0.168720\pi\) |
−0.505576 | + | 0.862782i | \(0.668720\pi\) | |||||||
\(354\) | 41760.0i | 0.333238i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 115840. | 0.914026 | ||||||||
\(357\) | 141462. | − | 141462.i | 1.10995 | − | 1.10995i | ||||
\(358\) | 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 | ||||
\(363\) | 6453.00 | + | 6453.00i | 0.0489721 | + | 0.0489721i | ||||
\(364\) | − | 32016.0i | − | 0.241637i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 201528. | 1.50443 | ||||||||
\(367\) | 14971.0 | − | 14971.0i | 0.111152 | − | 0.111152i | −0.649343 | − | 0.760496i | \(-0.724956\pi\) |
0.760496 | + | 0.649343i | \(0.224956\pi\) | |||||||
\(368\) | 17216.0 | + | 17216.0i | 0.127127 | + | 0.127127i | ||||
\(369\) | 136242.i | 1.00059i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −35438.0 | −0.257467 | ||||||||
\(372\) | −14544.0 | + | 14544.0i | −0.105099 | + | 0.105099i | ||||
\(373\) | 13811.0 | + | 13811.0i | 0.0992676 | + | 0.0992676i | 0.754996 | − | 0.655729i | \(-0.227639\pi\) |
−0.655729 | + | 0.754996i | \(0.727639\pi\) | |||||||
\(374\) | 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 | \(-0.661528\pi\) | ||
0.485954 | − | 0.873984i | \(-0.338472\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 106362. | 0.732717 | ||||||||
\(382\) | −29356.0 | + | 29356.0i | −0.201173 | + | 0.201173i | ||||
\(383\) | 86091.0 | + | 86091.0i | 0.586895 | + | 0.586895i | 0.936789 | − | 0.349894i | \(-0.113783\pi\) |
−0.349894 | + | 0.936789i | \(0.613783\pi\) | |||||||
\(384\) | − | 18432.0i | − | 0.125000i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −171396. | −1.15034 | ||||||||
\(387\) | 88209.0 | − | 88209.0i | 0.588967 | − | 0.588967i | ||||
\(388\) | −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 | ||||
\(393\) | 57222.0 | + | 57222.0i | 0.370491 | + | 0.370491i | ||||
\(394\) | − | 43884.0i | − | 0.282692i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −76464.0 | −0.487603 | ||||||||
\(397\) | −29149.0 | + | 29149.0i | −0.184945 | + | 0.184945i | −0.793507 | − | 0.608562i | \(-0.791747\pi\) |
0.608562 | + | 0.793507i | \(0.291747\pi\) | |||||||
\(398\) | 76320.0 | + | 76320.0i | 0.481806 | + | 0.481806i | ||||
\(399\) | − | 146160.i | − | 0.918085i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −45918.0 | −0.285558 | −0.142779 | − | 0.989755i | \(-0.545604\pi\) | ||||
−0.142779 | + | 0.989755i | \(0.545604\pi\) | |||||||
\(402\) | −27036.0 | + | 27036.0i | −0.167298 | + | 0.167298i | ||||
\(403\) | −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 | ||||
\(408\) | 78048.0 | + | 78048.0i | 0.468858 | + | 0.468858i | ||||
\(409\) | − | 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 | ||||||||
\(412\) | −83432.0 | + | 83432.0i | −0.491517 | + | 0.491517i | ||||
\(413\) | 33640.0 | + | 33640.0i | 0.197222 | + | 0.197222i | ||||
\(414\) | − | 87156.0i | − | 0.508507i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 17664.0 | 0.102071 | ||||||||
\(417\) | 84600.0 | − | 84600.0i | 0.486517 | − | 0.486517i | ||||
\(418\) | 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 | ||||
\(423\) | −102789. | − | 102789.i | −0.574468 | − | 0.574468i | ||||
\(424\) | − | 19552.0i | − | 0.108758i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −231912. | −1.27792 | ||||||||
\(427\) | 162342. | − | 162342.i | 0.890379 | − | 0.890379i | ||||
\(428\) | −37688.0 | − | 37688.0i | −0.205738 | − | 0.205738i | ||||
\(429\) | − | 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 | 0.203512 | − | 0.979072i | \(-0.434764\pi\) |
−0.979072 | + | 0.203512i | \(0.934764\pi\) | |||||||
\(434\) | 23432.0i | 0.124403i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −176320. | −0.927531 | ||||||||
\(437\) | −75320.0 | + | 75320.0i | −0.394410 | + | 0.394410i | ||||
\(438\) | −106236. | − | 106236.i | −0.553762 | − | 0.553762i | ||||
\(439\) | 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 | ||||||||
\(442\) | −74796.0 | + | 74796.0i | −0.382855 | + | 0.382855i | ||||
\(443\) | −240609. | − | 240609.i | −1.22604 | − | 1.22604i | −0.965450 | − | 0.260590i | \(-0.916083\pi\) |
−0.260590 | − | 0.965450i | \(-0.583917\pi\) | |||||||
\(444\) | 93744.0i | 0.475530i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 123564. | 0.621187 | ||||||||
\(447\) | −124200. | + | 124200.i | −0.621594 | + | 0.621594i | ||||
\(448\) | −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 | ||||
\(453\) | 170982. | + | 170982.i | 0.833209 | + | 0.833209i | ||||
\(454\) | − | 219644.i | − | 1.06563i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 80640.0 | 0.387812 | ||||||||
\(457\) | 188151. | − | 188151.i | 0.900895 | − | 0.900895i | −0.0946187 | − | 0.995514i | \(-0.530163\pi\) |
0.995514 | + | 0.0946187i | \(0.0301632\pi\) | |||||||
\(458\) | 100560. | + | 100560.i | 0.479396 | + | 0.479396i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −326158. | −1.53471 | −0.767355 | − | 0.641223i | \(-0.778427\pi\) | ||||
−0.767355 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(462\) | −123192. | + | 123192.i | −0.577163 | + | 0.577163i | ||||
\(463\) | 218731. | + | 218731.i | 1.02035 | + | 1.02035i | 0.999789 | + | 0.0205595i | \(0.00654474\pi\) |
0.0205595 | + | 0.999789i | \(0.493455\pi\) | |||||||
\(464\) | 43520.0i | 0.202140i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9564.00 | 0.0440421 | ||||||||
\(467\) | −59249.0 | + | 59249.0i | −0.271673 | + | 0.271673i | −0.829774 | − | 0.558100i | \(-0.811530\pi\) |
0.558100 | + | 0.829774i | \(0.311530\pi\) | |||||||
\(468\) | −44712.0 | − | 44712.0i | −0.204142 | − | 0.204142i | ||||
\(469\) | 43558.0i | 0.198026i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −294678. | −1.32833 | ||||||||
\(472\) | −18560.0 | + | 18560.0i | −0.0833094 | + | 0.0833094i | ||||
\(473\) | 128502. | + | 128502.i | 0.574365 | + | 0.574365i | ||||
\(474\) | 380160.i | 1.69204i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 125744. | 0.554975 | ||||||||
\(477\) | −49491.0 | + | 49491.0i | −0.217515 | + | 0.217515i | ||||
\(478\) | 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 | ||||
\(483\) | −140418. | − | 140418.i | −0.601906 | − | 0.601906i | ||||
\(484\) | 5736.00i | 0.0244860i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −236196. | −1.00000 | ||||||||
\(487\) | 123651. | − | 123651.i | 0.521362 | − | 0.521362i | −0.396620 | − | 0.917983i | \(-0.629817\pi\) |
0.917983 | + | 0.396620i | \(0.129817\pi\) | |||||||
\(488\) | 89568.0 | + | 89568.0i | 0.376109 | + | 0.376109i | ||||
\(489\) | 360162.i | 1.50619i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 198442. | 0.823134 | 0.411567 | − | 0.911379i | \(-0.364982\pi\) | ||||
0.411567 | + | 0.911379i | \(0.364982\pi\) | |||||||
\(492\) | −121104. | + | 121104.i | −0.500297 | + | 0.500297i | ||||
\(493\) | −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 | ||||
\(498\) | −224316. | − | 224316.i | −0.904485 | − | 0.904485i | ||||
\(499\) | − | 269240.i | − | 1.08128i | −0.841254 | − | 0.540640i | \(-0.818182\pi\) | ||
0.841254 | − | 0.540640i | \(-0.181818\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27882.0 | 0.111083 | ||||||||
\(502\) | 242004. | − | 242004.i | 0.960318 | − | 0.960318i | ||||
\(503\) | −109869. | − | 109869.i | −0.434249 | − | 0.434249i | 0.455822 | − | 0.890071i | \(-0.349345\pi\) |
−0.890071 | + | 0.455822i | \(0.849345\pi\) | |||||||
\(504\) | 75168.0i | 0.295918i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 126968. | 0.495899 | ||||||||
\(507\) | −171351. | + | 171351.i | −0.666608 | + | 0.666608i | ||||
\(508\) | 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 | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 156816. | 0.588967 | ||||||||
\(517\) | 149742. | − | 149742.i | 0.560225 | − | 0.560225i | ||||
\(518\) | 75516.0 | + | 75516.0i | 0.281436 | + | 0.281436i | ||||
\(519\) | 50202.0i | 0.186374i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 297282. | 1.09520 | 0.547600 | − | 0.836740i | \(-0.315542\pi\) | ||||
0.547600 | + | 0.836740i | \(0.315542\pi\) | |||||||
\(522\) | 110160. | − | 110160.i | 0.404281 | − | 0.404281i | ||||
\(523\) | 25071.0 | + | 25071.0i | 0.0916576 | + | 0.0916576i | 0.751449 | − | 0.659791i | \(-0.229355\pi\) |
−0.659791 | + | 0.751449i | \(0.729355\pi\) | |||||||
\(524\) | 50864.0i | 0.185246i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 59084.0 | 0.213549 | ||||||||
\(527\) | 54742.0 | − | 54742.0i | 0.197106 | − | 0.197106i | ||||
\(528\) | −67968.0 | − | 67968.0i | −0.243802 | − | 0.243802i | ||||
\(529\) | − | 135119.i | − | 0.482842i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 93960.0 | 0.333238 | ||||||||
\(532\) | 64960.0 | − | 64960.0i | 0.229521 | − | 0.229521i | ||||
\(533\) | −116058. | − | 116058.i | −0.408527 | − | 0.408527i | ||||
\(534\) | − | 521280.i | − | 1.82805i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24032.0 | −0.0836489 | ||||||||
\(537\) | 23400.0 | − | 23400.0i | 0.0811460 | − | 0.0811460i | ||||
\(538\) | −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 | ||||
\(543\) | 399582. | + | 399582.i | 1.35521 | + | 1.35521i | ||||
\(544\) | 69376.0i | 0.234429i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −144072. | −0.483275 | ||||||||
\(547\) | −291009. | + | 291009.i | −0.972594 | + | 0.972594i | −0.999634 | − | 0.0270399i | \(-0.991392\pi\) |
0.0270399 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(548\) | 163272. | + | 163272.i | 0.543689 | + | 0.543689i | ||||
\(549\) | − | 453438.i | − | 1.50443i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −190400. | −0.627139 | ||||||||
\(552\) | 77472.0 | − | 77472.0i | 0.254253 | − | 0.254253i | ||||
\(553\) | 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 | −0.560401 | − | 0.828221i | \(-0.689353\pi\) |
0.828221 | + | 0.560401i | \(0.189353\pi\) | |||||||
\(558\) | 32724.0 | + | 32724.0i | 0.105099 | + | 0.105099i | ||||
\(559\) | 150282.i | 0.480932i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 575604. | 1.82893 | ||||||||
\(562\) | 4644.00 | − | 4644.00i | 0.0147035 | − | 0.0147035i | ||||
\(563\) | −43449.0 | − | 43449.0i | −0.137076 | − | 0.137076i | 0.635239 | − | 0.772316i | \(-0.280902\pi\) |
−0.772316 | + | 0.635239i | \(0.780902\pi\) | |||||||
\(564\) | − | 182736.i | − | 0.574468i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 366844. | 1.14511 | ||||||||
\(567\) | −190269. | + | 190269.i | −0.591837 | + | 0.591837i | ||||
\(568\) | −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 | ||||
\(573\) | 132102. | + | 132102.i | 0.402346 | + | 0.402346i | ||||
\(574\) | 195112.i | 0.592189i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −41472.0 | −0.125000 | ||||||||
\(577\) | −195889. | + | 195889.i | −0.588381 | + | 0.588381i | −0.937193 | − | 0.348812i | \(-0.886585\pi\) |
0.348812 | + | 0.937193i | \(0.386585\pi\) | |||||||
\(578\) | −126722. | − | 126722.i | −0.379312 | − | 0.379312i | ||||
\(579\) | 771282.i | 2.30068i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −361398. | −1.07062 | ||||||||
\(582\) | −263196. | + | 263196.i | −0.777022 | + | 0.777022i | ||||
\(583\) | −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 | 0.193139 | − | 0.981171i | \(-0.438133\pi\) |
0.981171 | − | 0.193139i | \(-0.0618669\pi\) | |||||||
\(588\) | −51768.0 | − | 51768.0i | −0.149729 | − | 0.149729i | ||||
\(589\) | − | 56560.0i | − | 0.163034i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −197478. | −0.565384 | ||||||||
\(592\) | −41664.0 | + | 41664.0i | −0.118882 | + | 0.118882i | ||||
\(593\) | 210991. | + | 210991.i | 0.600005 | + | 0.600005i | 0.940314 | − | 0.340309i | \(-0.110532\pi\) |
−0.340309 | + | 0.940314i | \(0.610532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −110400. | −0.310797 | ||||||||
\(597\) | 343440. | − | 343440.i | 0.963612 | − | 0.963612i | ||||
\(598\) | 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 | ||||
\(603\) | 60831.0 | + | 60831.0i | 0.167298 | + | 0.167298i | ||||
\(604\) | 151984.i | 0.416605i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 31608.0 | 0.0860700 | ||||||||
\(607\) | −146469. | + | 146469.i | −0.397529 | + | 0.397529i | −0.877360 | − | 0.479832i | \(-0.840698\pi\) |
0.479832 | + | 0.877360i | \(0.340698\pi\) | |||||||
\(608\) | 35840.0 | + | 35840.0i | 0.0969529 | + | 0.0969529i | ||||
\(609\) | − | 354960.i | − | 0.957072i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 175122. | 0.469092 | ||||||||
\(612\) | 175608. | − | 175608.i | 0.468858 | − | 0.468858i | ||||
\(613\) | −160989. | − | 160989.i | −0.428425 | − | 0.428425i | 0.459666 | − | 0.888092i | \(-0.347969\pi\) |
−0.888092 | + | 0.459666i | \(0.847969\pi\) | |||||||
\(614\) | 171396.i | 0.454636i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −109504. | −0.288582 | ||||||||
\(617\) | −320409. | + | 320409.i | −0.841656 | + | 0.841656i | −0.989074 | − | 0.147419i | \(-0.952904\pi\) |
0.147419 | + | 0.989074i | \(0.452904\pi\) | |||||||
\(618\) | 375444. | + | 375444.i | 0.983033 | + | 0.983033i | ||||
\(619\) | − | 341160.i | − | 0.890383i | −0.895435 | − | 0.445191i | \(-0.853136\pi\) | ||
0.895435 | − | 0.445191i | \(-0.146864\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −144556. | + | 144556.i | −0.373642 | + | 0.373642i | ||||
\(623\) | −419920. | − | 419920.i | −1.08191 | − | 1.08191i | ||||
\(624\) | − | 79488.0i | − | 0.204142i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −72996.0 | −0.186273 | ||||||||
\(627\) | 297360. | − | 297360.i | 0.756393 | − | 0.756393i | ||||
\(628\) | −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 | ||||
\(633\) | −655578. | − | 655578.i | −1.63613 | − | 1.63613i | ||||
\(634\) | 100596.i | 0.250266i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −87984.0 | −0.217515 | ||||||||
\(637\) | 49611.0 | − | 49611.0i | 0.122264 | − | 0.122264i | ||||
\(638\) | 160480. | + | 160480.i | 0.394257 | + | 0.394257i | ||||
\(639\) | 521802.i | 1.27792i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −585038. | −1.42386 | −0.711931 | − | 0.702249i | \(-0.752179\pi\) | ||||
−0.711931 | + | 0.702249i | \(0.752179\pi\) | |||||||
\(642\) | −169596. | + | 169596.i | −0.411477 | + | 0.411477i | ||||
\(643\) | 31911.0 | + | 31911.0i | 0.0771824 | + | 0.0771824i | 0.744644 | − | 0.667462i | \(-0.232619\pi\) |
−0.667462 | + | 0.744644i | \(0.732619\pi\) | |||||||
\(644\) | − | 124816.i | − | 0.300953i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −303520. | −0.727315 | ||||||||
\(647\) | 280931. | − | 280931.i | 0.671106 | − | 0.671106i | −0.286865 | − | 0.957971i | \(-0.592613\pi\) |
0.957971 | + | 0.286865i | \(0.0926131\pi\) | |||||||
\(648\) | −104976. | − | 104976.i | −0.250000 | − | 0.250000i | ||||
\(649\) | 136880.i | 0.324975i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 105444. | 0.248805 | ||||||||
\(652\) | −160072. | + | 160072.i | −0.376548 | + | 0.376548i | ||||
\(653\) | −523989. | − | 523989.i | −1.22884 | − | 1.22884i | −0.964402 | − | 0.264439i | \(-0.914813\pi\) |
−0.264439 | − | 0.964402i | \(-0.585187\pi\) | |||||||
\(654\) | 793440.i | 1.85506i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −107648. | −0.250149 | ||||||||
\(657\) | −239031. | + | 239031.i | −0.553762 | + | 0.553762i | ||||
\(658\) | −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 | ||||
\(663\) | 336582. | + | 336582.i | 0.765709 | + | 0.765709i | ||||
\(664\) | − | 199392.i | − | 0.452243i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 210924. | 0.475530 | ||||||||
\(667\) | −182920. | + | 182920.i | −0.411159 | + | 0.411159i | ||||
\(668\) | 12392.0 | + | 12392.0i | 0.0277708 | + | 0.0277708i | ||||
\(669\) | − | 556038.i | − | 1.24237i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 660564. | 1.46713 | ||||||||
\(672\) | −66816.0 | + | 66816.0i | −0.147959 | + | 0.147959i | ||||
\(673\) | 332111. | + | 332111.i | 0.733252 | + | 0.733252i | 0.971263 | − | 0.238011i | \(-0.0764953\pi\) |
−0.238011 | + | 0.971263i | \(0.576495\pi\) | |||||||
\(674\) | 34116.0i | 0.0750997i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −152312. | −0.333304 | ||||||||
\(677\) | −578309. | + | 578309.i | −1.26178 | + | 1.26178i | −0.311546 | + | 0.950231i | \(0.600847\pi\) |
−0.950231 | + | 0.311546i | \(0.899153\pi\) | |||||||
\(678\) | −75996.0 | − | 75996.0i | −0.165322 | − | 0.165322i | ||||
\(679\) | 424038.i | 0.919740i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −988398. | −2.13127 | ||||||||
\(682\) | −47672.0 | + | 47672.0i | −0.102493 | + | 0.102493i | ||||
\(683\) | 349311. | + | 349311.i | 0.748809 | + | 0.748809i | 0.974255 | − | 0.225447i | \(-0.0723842\pi\) |
−0.225447 | + | 0.974255i | \(0.572384\pi\) | |||||||
\(684\) | − | 181440.i | − | 0.387812i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −361920. | −0.769067 | ||||||||
\(687\) | 452520. | − | 452520.i | 0.958792 | − | 0.958792i | ||||
\(688\) | 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 | ||||
\(693\) | 277182. | + | 277182.i | 0.577163 | + | 0.577163i | ||||
\(694\) | − | 226204.i | − | 0.469658i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 195840. | 0.404281 | ||||||||
\(697\) | 455822. | − | 455822.i | 0.938274 | − | 0.938274i | ||||
\(698\) | 45040.0 | + | 45040.0i | 0.0924459 | + | 0.0924459i | ||||
\(699\) | − | 43038.0i | − | 0.0880841i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 270242. | 0.549942 | 0.274971 | − | 0.961453i | \(-0.411332\pi\) | ||||
0.274971 | + | 0.961453i | \(0.411332\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −182280. | − | 182280.i | −0.368832 | − | 0.368832i | ||||
\(704\) | − | 60416.0i | − | 0.121901i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 178044. | 0.357205 | ||||||||
\(707\) | 25462.0 | − | 25462.0i | 0.0509394 | − | 0.0509394i | ||||
\(708\) | 83520.0 | + | 83520.0i | 0.166619 | + | 0.166619i | ||||
\(709\) | 297800.i | 0.592423i | 0.955122 | + | 0.296212i | \(0.0957234\pi\) | ||||
−0.955122 | + | 0.296212i | \(0.904277\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 855360. | 1.69204 | ||||||||
\(712\) | 231680. | − | 231680.i | 0.457013 | − | 0.457013i | ||||
\(713\) | −54338.0 | − | 54338.0i | −0.106887 | − | 0.106887i | ||||
\(714\) | − | 565848.i | − | 1.10995i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20800.0 | 0.0405730 | ||||||||
\(717\) | 159840. | − | 159840.i | 0.310919 | − | 0.310919i | ||||
\(718\) | 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 | ||||
\(723\) | 254142. | + | 254142.i | 0.486183 | + | 0.486183i | ||||
\(724\) | 355184.i | 0.677604i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25812.0 | 0.0489721 | ||||||||
\(727\) | 417651. | − | 417651.i | 0.790214 | − | 0.790214i | −0.191315 | − | 0.981529i | \(-0.561275\pi\) |
0.981529 | + | 0.191315i | \(0.0612751\pi\) | |||||||
\(728\) | −64032.0 | − | 64032.0i | −0.120819 | − | 0.120819i | ||||
\(729\) | 531441.i | 1.00000i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −590238. | −1.10457 | ||||||||
\(732\) | 403056. | − | 403056.i | 0.752217 | − | 0.752217i | ||||
\(733\) | −394549. | − | 394549.i | −0.734333 | − | 0.734333i | 0.237142 | − | 0.971475i | \(-0.423789\pi\) |
−0.971475 | + | 0.237142i | \(0.923789\pi\) | |||||||
\(734\) | − | 59884.0i | − | 0.111152i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 68864.0 | 0.127127 | ||||||||
\(737\) | −88618.0 | + | 88618.0i | −0.163150 | + | 0.163150i | ||||
\(738\) | 272484. | + | 272484.i | 0.500297 | + | 0.500297i | ||||
\(739\) | − | 109880.i | − | 0.201201i | −0.994927 | − | 0.100600i | \(-0.967924\pi\) | ||
0.994927 | − | 0.100600i | \(-0.0320764\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 347760. | 0.633349 | ||||||||
\(742\) | −70876.0 | + | 70876.0i | −0.128733 | + | 0.128733i | ||||
\(743\) | 466451. | + | 466451.i | 0.844945 | + | 0.844945i | 0.989497 | − | 0.144552i | \(-0.0461742\pi\) |
−0.144552 | + | 0.989497i | \(0.546174\pi\) | |||||||
\(744\) | 58176.0i | 0.105099i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 55244.0 | 0.0992676 | ||||||||
\(747\) | −504711. | + | 504711.i | −0.904485 | + | 0.904485i | ||||
\(748\) | 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 | ||||
\(753\) | −1.08902e6 | − | 1.08902e6i | −1.92064 | − | 1.92064i | ||||
\(754\) | 187680.i | 0.330123i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −313269. | + | 313269.i | −0.546671 | + | 0.546671i | −0.925476 | − | 0.378806i | \(-0.876335\pi\) |
0.378806 | + | 0.925476i | \(0.376335\pi\) | |||||||
\(758\) | −502160. | − | 502160.i | −0.873984 | − | 0.873984i | ||||
\(759\) | − | 571356.i | − | 0.991798i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 142082. | 0.245341 | 0.122670 | − | 0.992447i | \(-0.460854\pi\) | ||||
0.122670 | + | 0.992447i | \(0.460854\pi\) | |||||||
\(762\) | 212724. | − | 212724.i | 0.366359 | − | 0.366359i | ||||
\(763\) | 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 | ||||
\(768\) | −36864.0 | − | 36864.0i | −0.0625000 | − | 0.0625000i | ||||
\(769\) | − | 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 | ||||||||
\(772\) | −342792. | + | 342792.i | −0.575170 | + | 0.575170i | ||||
\(773\) | 782211. | + | 782211.i | 1.30908 | + | 1.30908i | 0.922082 | + | 0.386994i | \(0.126487\pi\) |
0.386994 | + | 0.922082i | \(0.373513\pi\) | |||||||
\(774\) | − | 352836.i | − | 0.588967i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −233952. | −0.388511 | ||||||||
\(777\) | 339822. | − | 339822.i | 0.562872 | − | 0.562872i | ||||
\(778\) | 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 | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 228888. | 0.370491 | ||||||||
\(787\) | −201409. | + | 201409.i | −0.325184 | + | 0.325184i | −0.850752 | − | 0.525568i | \(-0.823853\pi\) |
0.525568 | + | 0.850752i | \(0.323853\pi\) | |||||||
\(788\) | −87768.0 | − | 87768.0i | −0.141346 | − | 0.141346i | ||||
\(789\) | − | 265878.i | − | 0.427099i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −122438. | −0.195688 | ||||||||
\(792\) | −152928. | + | 152928.i | −0.243802 | + | 0.243802i | ||||
\(793\) | 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 | −0.677963 | − | 0.735096i | \(-0.737137\pi\) |
0.735096 | + | 0.677963i | \(0.237137\pi\) | |||||||
\(798\) | −292320. | − | 292320.i | −0.459042 | − | 0.459042i | ||||
\(799\) | 687798.i | 1.07738i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.17288e6 | −1.82805 | ||||||||
\(802\) | −91836.0 | + | 91836.0i | −0.142779 | + | 0.142779i | ||||
\(803\) | −348218. | − | 348218.i | −0.540033 | − | 0.540033i | ||||
\(804\) | 108144.i | 0.167298i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −55752.0 | −0.0858204 | ||||||||
\(807\) | −807480. | + | 807480.i | −1.23989 | + | 1.23989i | ||||
\(808\) | 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 | ||||
\(813\) | −613818. | − | 613818.i | −0.928664 | − | 0.928664i | ||||
\(814\) | 307272.i | 0.463740i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 312192. | 0.468858 | ||||||||
\(817\) | −304920. | + | 304920.i | −0.456817 | + | 0.456817i | ||||
\(818\) | −157440. | − | 157440.i | −0.235293 | − | 0.235293i | ||||
\(819\) | 324162.i | 0.483275i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −157438. | −0.233573 | −0.116787 | − | 0.993157i | \(-0.537259\pi\) | ||||
−0.116787 | + | 0.993157i | \(0.537259\pi\) | |||||||
\(822\) | 734724. | − | 734724.i | 1.08738 | − | 1.08738i | ||||
\(823\) | −791309. | − | 791309.i | −1.16828 | − | 1.16828i | −0.982613 | − | 0.185666i | \(-0.940556\pi\) |
−0.185666 | − | 0.982613i | \(-0.559444\pi\) | |||||||
\(824\) | 333728.i | 0.491517i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 134560. | 0.197222 | ||||||||
\(827\) | 889671. | − | 889671.i | 1.30082 | − | 1.30082i | 0.372987 | − | 0.927837i | \(-0.378334\pi\) |
0.927837 | − | 0.372987i | \(-0.121666\pi\) | |||||||
\(828\) | −174312. | − | 174312.i | −0.254253 | − | 0.254253i | ||||
\(829\) | 618280.i | 0.899655i | 0.893115 | + | 0.449828i | \(0.148515\pi\) | ||||
−0.893115 | + | 0.449828i | \(0.851485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 333882. | 0.483494 | ||||||||
\(832\) | 35328.0 | − | 35328.0i | 0.0510355 | − | 0.0510355i | ||||
\(833\) | 194849. | + | 194849.i | 0.280807 | + | 0.280807i | ||||
\(834\) | − | 338400.i | − | 0.486517i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 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 | ||||
\(843\) | −20898.0 | − | 20898.0i | −0.0294069 | − | 0.0294069i | ||||
\(844\) | − | 582736.i | − | 0.818063i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −411156. | −0.574468 | ||||||||
\(847\) | 20793.0 | − | 20793.0i | 0.0289835 | − | 0.0289835i | ||||
\(848\) | −39104.0 | − | 39104.0i | −0.0543788 | − | 0.0543788i | ||||
\(849\) | − | 1.65080e6i | − | 2.29023i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −350238. | −0.483620 | ||||||||
\(852\) | −463824. | + | 463824.i | −0.638961 | + | 0.638961i | ||||
\(853\) | 698291. | + | 698291.i | 0.959706 | + | 0.959706i | 0.999219 | − | 0.0395127i | \(-0.0125806\pi\) |
−0.0395127 | + | 0.999219i | \(0.512581\pi\) | |||||||
\(854\) | − | 649368.i | − | 0.890379i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −150752. | −0.205738 | ||||||||
\(857\) | −144489. | + | 144489.i | −0.196731 | + | 0.196731i | −0.798597 | − | 0.601866i | \(-0.794424\pi\) |
0.601866 | + | 0.798597i | \(0.294424\pi\) | |||||||
\(858\) | −293112. | − | 293112.i | −0.398161 | − | 0.398161i | ||||
\(859\) | 943480.i | 1.27863i | 0.768943 | + | 0.639317i | \(0.220783\pi\) | ||||
−0.768943 | + | 0.639317i | \(0.779217\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 878004. | 1.18438 | ||||||||
\(862\) | 425044. | − | 425044.i | 0.572031 | − | 0.572031i | ||||
\(863\) | −438149. | − | 438149.i | −0.588302 | − | 0.588302i | 0.348869 | − | 0.937171i | \(-0.386566\pi\) |
−0.937171 | + | 0.348869i | \(0.886566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −581636. | −0.775560 | ||||||||
\(867\) | −570249. | + | 570249.i | −0.758624 | + | 0.758624i | ||||
\(868\) | 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 | ||||
\(873\) | 592191. | + | 592191.i | 0.777022 | + | 0.777022i | ||||
\(874\) | 301280.i | 0.394410i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −424944. | −0.553762 | ||||||||
\(877\) | −281469. | + | 281469.i | −0.365958 | + | 0.365958i | −0.866001 | − | 0.500043i | \(-0.833318\pi\) |
0.500043 | + | 0.866001i | \(0.333318\pi\) | |||||||
\(878\) | 598880. | + | 598880.i | 0.776874 | + | 0.776874i | ||||
\(879\) | − | 87318.0i | − | 0.113012i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 876722. | 1.12956 | 0.564781 | − | 0.825241i | \(-0.308961\pi\) | ||||
0.564781 | + | 0.825241i | \(0.308961\pi\) | |||||||
\(882\) | −116478. | + | 116478.i | −0.149729 | + | 0.149729i | ||||
\(883\) | 327431. | + | 327431.i | 0.419951 | + | 0.419951i | 0.885187 | − | 0.465236i | \(-0.154031\pi\) |
−0.465236 | + | 0.885187i | \(0.654031\pi\) | |||||||
\(884\) | 299184.i | 0.382855i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −962436. | −1.22604 | ||||||||
\(887\) | 477171. | − | 477171.i | 0.606494 | − | 0.606494i | −0.335534 | − | 0.942028i | \(-0.608917\pi\) |
0.942028 | + | 0.335534i | \(0.108917\pi\) | |||||||
\(888\) | 187488. | + | 187488.i | 0.237765 | + | 0.237765i | ||||
\(889\) | − | 342722.i | − | 0.433649i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −774198. | −0.975207 | ||||||||
\(892\) | 247128. | − | 247128.i | 0.310593 | − | 0.310593i | ||||
\(893\) | 355320. | + | 355320.i | 0.445571 | + | 0.445571i | ||||
\(894\) | 496800.i | 0.621594i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −59392.0 | −0.0739796 | ||||||||
\(897\) | 334098. | − | 334098.i | 0.415230 | − | 0.415230i | ||||
\(898\) | 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 | ||||
\(903\) | −568458. | − | 568458.i | −0.697145 | − | 0.697145i | ||||
\(904\) | − | 67552.0i | − | 0.0826611i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 683928. | 0.833209 | ||||||||
\(907\) | −1.11209e6 | + | 1.11209e6i | −1.35184 | + | 1.35184i | −0.468235 | + | 0.883604i | \(0.655110\pi\) |
−0.883604 | + | 0.468235i | \(0.844890\pi\) | |||||||
\(908\) | −439288. | − | 439288.i | −0.532816 | − | 0.532816i | ||||
\(909\) | − | 71118.0i | − | 0.0860700i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −883958. | −1.06511 | −0.532556 | − | 0.846395i | \(-0.678768\pi\) | ||||
−0.532556 | + | 0.846395i | \(0.678768\pi\) | |||||||
\(912\) | 161280. | − | 161280.i | 0.193906 | − | 0.193906i | ||||
\(913\) | −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 | \(-0.737489\pi\) | ||
0.678775 | − | 0.734346i | \(-0.262511\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 771282. | 0.909272 | ||||||||
\(922\) | −652316. | + | 652316.i | −0.767355 | + | 0.767355i | ||||
\(923\) | −444498. | − | 444498.i | −0.521755 | − | 0.521755i | ||||
\(924\) | 492768.i | 0.577163i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 874924. | 1.02035 | ||||||||
\(927\) | 844749. | − | 844749.i | 0.983033 | − | 0.983033i | ||||
\(928\) | 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 | ||||
\(933\) | 650502. | + | 650502.i | 0.747283 | + | 0.747283i | ||||
\(934\) | 236996.i | 0.271673i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −178848. | −0.204142 | ||||||||
\(937\) | 1.07047e6 | − | 1.07047e6i | 1.21926 | − | 1.21926i | 0.251366 | − | 0.967892i | \(-0.419120\pi\) |
0.967892 | − | 0.251366i | \(-0.0808799\pi\) | |||||||
\(938\) | 87116.0 | + | 87116.0i | 0.0990130 | + | 0.0990130i | ||||
\(939\) | 328482.i | 0.372546i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 558642. | 0.630891 | 0.315446 | − | 0.948944i | \(-0.397846\pi\) | ||||
0.315446 | + | 0.948944i | \(0.397846\pi\) | |||||||
\(942\) | −589356. | + | 589356.i | −0.664165 | + | 0.664165i | ||||
\(943\) | −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 | −0.592097 | − | 0.805867i | \(-0.701700\pi\) |
0.805867 | + | 0.592097i | \(0.201700\pi\) | |||||||
\(948\) | 760320. | + | 760320.i | 0.846018 | + | 0.846018i | ||||
\(949\) | − | 407238.i | − | 0.452185i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 452682. | 0.500532 | ||||||||
\(952\) | 251488. | − | 251488.i | 0.277487 | − | 0.277487i | ||||
\(953\) | 630231. | + | 630231.i | 0.693927 | + | 0.693927i | 0.963094 | − | 0.269166i | \(-0.0867482\pi\) |
−0.269166 | + | 0.963094i | \(0.586748\pi\) | |||||||
\(954\) | 197964.i | 0.217515i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 142080. | 0.155459 | ||||||||
\(957\) | 722160. | − | 722160.i | 0.788514 | − | 0.788514i | ||||
\(958\) | −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 | ||||
\(963\) | 381591. | + | 381591.i | 0.411477 | + | 0.411477i | ||||
\(964\) | 225904.i | 0.243092i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −561672. | −0.601906 | ||||||||
\(967\) | 345491. | − | 345491.i | 0.369474 | − | 0.369474i | −0.497811 | − | 0.867285i | \(-0.665863\pi\) |
0.867285 | + | 0.497811i | \(0.165863\pi\) | |||||||
\(968\) | 11472.0 | + | 11472.0i | 0.0122430 | + | 0.0122430i | ||||
\(969\) | 1.36584e6i | 1.45463i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.08308e6 | 1.14874 | 0.574372 | − | 0.818595i | \(-0.305247\pi\) | ||||
0.574372 | + | 0.818595i | \(0.305247\pi\) | |||||||
\(972\) | −472392. | + | 472392.i | −0.500000 | + | 0.500000i | ||||
\(973\) | −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 | −0.626045 | − | 0.779787i | \(-0.715327\pi\) |
0.779787 | + | 0.626045i | \(0.215327\pi\) | |||||||
\(978\) | 720324. | + | 720324.i | 0.753096 | + | 0.753096i | ||||
\(979\) | − | 1.70864e6i | − | 1.78273i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.78524e6 | 1.85506 | ||||||||
\(982\) | 396884. | − | 396884.i | 0.411567 | − | 0.411567i | ||||
\(983\) | −466909. | − | 466909.i | −0.483198 | − | 0.483198i | 0.422953 | − | 0.906151i | \(-0.360993\pi\) |
−0.906151 | + | 0.422953i | \(0.860993\pi\) | |||||||
\(984\) | 484416.i | 0.500297i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −737120. | −0.758201 | ||||||||
\(987\) | −662418. | + | 662418.i | −0.679983 | + | 0.679983i | ||||
\(988\) | 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 | ||||
\(993\) | 486342. | + | 486342.i | 0.493223 | + | 0.493223i | ||||
\(994\) | 747272.i | 0.756321i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −897264. | −0.904485 | ||||||||
\(997\) | −152149. | + | 152149.i | −0.153066 | + | 0.153066i | −0.779486 | − | 0.626420i | \(-0.784520\pi\) |
0.626420 | + | 0.779486i | \(0.284520\pi\) | |||||||
\(998\) | −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 | 50.5.c.b.43.1 | 2 | ||
3.2 | odd | 2 | 450.5.g.a.343.1 | 2 | |||
4.3 | odd | 2 | 400.5.p.c.193.1 | 2 | |||
5.2 | odd | 4 | inner | 50.5.c.b.7.1 | 2 | ||
5.3 | odd | 4 | 10.5.c.a.7.1 | yes | 2 | ||
5.4 | even | 2 | 10.5.c.a.3.1 | ✓ | 2 | ||
15.2 | even | 4 | 450.5.g.a.307.1 | 2 | |||
15.8 | even | 4 | 90.5.g.b.37.1 | 2 | |||
15.14 | odd | 2 | 90.5.g.b.73.1 | 2 | |||
20.3 | even | 4 | 80.5.p.b.17.1 | 2 | |||
20.7 | even | 4 | 400.5.p.c.257.1 | 2 | |||
20.19 | odd | 2 | 80.5.p.b.33.1 | 2 | |||
40.3 | even | 4 | 320.5.p.i.257.1 | 2 | |||
40.13 | odd | 4 | 320.5.p.b.257.1 | 2 | |||
40.19 | odd | 2 | 320.5.p.i.193.1 | 2 | |||
40.29 | even | 2 | 320.5.p.b.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.5.c.a.3.1 | ✓ | 2 | 5.4 | even | 2 | ||
10.5.c.a.7.1 | yes | 2 | 5.3 | odd | 4 | ||
50.5.c.b.7.1 | 2 | 5.2 | odd | 4 | inner | ||
50.5.c.b.43.1 | 2 | 1.1 | even | 1 | trivial | ||
80.5.p.b.17.1 | 2 | 20.3 | even | 4 | |||
80.5.p.b.33.1 | 2 | 20.19 | odd | 2 | |||
90.5.g.b.37.1 | 2 | 15.8 | even | 4 | |||
90.5.g.b.73.1 | 2 | 15.14 | odd | 2 | |||
320.5.p.b.193.1 | 2 | 40.29 | even | 2 | |||
320.5.p.b.257.1 | 2 | 40.13 | odd | 4 | |||
320.5.p.i.193.1 | 2 | 40.19 | odd | 2 | |||
320.5.p.i.257.1 | 2 | 40.3 | even | 4 | |||
400.5.p.c.193.1 | 2 | 4.3 | odd | 2 | |||
400.5.p.c.257.1 | 2 | 20.7 | even | 4 | |||
450.5.g.a.307.1 | 2 | 15.2 | even | 4 | |||
450.5.g.a.343.1 | 2 | 3.2 | odd | 2 |