Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1280,4,Mod(641,1280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1280.641");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1280 = 2^{8} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1280.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(75.5224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.2 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1280.641 |
Dual form | 1280.4.d.v.641.3 |
$q$-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 \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 4.47214i | − 0.860663i | −0.902671 | − | 0.430331i | \(-0.858397\pi\) | ||||
0.902671 | − | 0.430331i | \(-0.141603\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −31.3050 | −1.69031 | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820491\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.00000 | 0.259259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 8.94427i | − 0.245164i | −0.992458 | − | 0.122582i | \(-0.960883\pi\) | ||||
0.992458 | − | 0.122582i | \(-0.0391174\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 62.0000i | − 1.32275i | −0.750057 | − | 0.661373i | \(-0.769974\pi\) | ||||
0.750057 | − | 0.661373i | \(-0.230026\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 22.3607 | 0.384900 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −46.0000 | −0.656273 | −0.328136 | − | 0.944630i | \(-0.606421\pi\) | ||||
−0.328136 | + | 0.944630i | \(0.606421\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 107.331i | − 1.29597i | −0.761652 | − | 0.647986i | \(-0.775611\pi\) | ||||
0.761652 | − | 0.647986i | \(-0.224389\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 140.000i | 1.45479i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 192.302 | 1.74338 | 0.871689 | − | 0.490059i | \(-0.163025\pi\) | ||||
0.871689 | + | 0.490059i | \(0.163025\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 152.053i | − 1.08380i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 90.0000i | − 0.576296i | −0.957586 | − | 0.288148i | \(-0.906961\pi\) | ||||
0.957586 | − | 0.288148i | \(-0.0930395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 152.053 | 0.880950 | 0.440475 | − | 0.897765i | \(-0.354810\pi\) | ||||
0.440475 | + | 0.897765i | \(0.354810\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −40.0000 | −0.211003 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 156.525i | − 0.755929i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 214.000i | 0.950848i | 0.879757 | + | 0.475424i | \(0.157705\pi\) | ||||
−0.879757 | + | 0.475424i | \(0.842295\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −277.272 | −1.13844 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000 | 0.0380912 | 0.0190456 | − | 0.999819i | \(-0.493937\pi\) | ||||
0.0190456 | + | 0.999819i | \(0.493937\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 67.0820i | − 0.237905i | −0.992900 | − | 0.118953i | \(-0.962046\pi\) | ||||
0.992900 | − | 0.118953i | \(-0.0379536\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 35.0000i | 0.115944i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −398.020 | −1.23526 | −0.617630 | − | 0.786469i | \(-0.711907\pi\) | ||||
−0.617630 | + | 0.786469i | \(0.711907\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 637.000 | 1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 205.718i | 0.564830i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 678.000i | 1.75718i | 0.477578 | + | 0.878589i | \(0.341515\pi\) | ||||
−0.477578 | + | 0.878589i | \(0.658485\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 44.7214 | 0.109640 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −480.000 | −1.11540 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 411.437i | − 0.907872i | −0.891034 | − | 0.453936i | \(-0.850019\pi\) | ||||
0.891034 | − | 0.453936i | \(-0.149981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 250.000i | 0.524741i | 0.964967 | + | 0.262371i | \(0.0845043\pi\) | ||||
−0.964967 | + | 0.262371i | \(0.915496\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −219.135 | −0.438228 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 310.000 | 0.591550 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 49.1935i | − 0.0897006i | −0.998994 | − | 0.0448503i | \(-0.985719\pi\) | ||||
0.998994 | − | 0.0448503i | \(-0.0142811\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 860.000i | − 1.50046i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −366.715 | −0.612973 | −0.306486 | − | 0.951875i | \(-0.599153\pi\) | ||||
−0.306486 | + | 0.951875i | \(0.599153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −522.000 | −0.836924 | −0.418462 | − | 0.908234i | \(-0.637431\pi\) | ||||
−0.418462 | + | 0.908234i | \(0.637431\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 111.803i | 0.172133i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 280.000i | 0.414402i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −876.539 | −1.24833 | −0.624166 | − | 0.781291i | \(-0.714561\pi\) | ||||
−0.624166 | + | 0.781291i | \(0.714561\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −491.000 | −0.673525 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 380.132i | − 0.502709i | −0.967895 | − | 0.251355i | \(-0.919124\pi\) | ||||
0.967895 | − | 0.251355i | \(-0.0808760\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 230.000i | − 0.293494i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −402.492 | −0.495997 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −970.000 | −1.15528 | −0.577639 | − | 0.816292i | \(-0.696026\pi\) | ||||
−0.577639 | + | 0.816292i | \(0.696026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1940.91i | 2.23585i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 680.000i | − 0.758201i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 536.656 | 0.579577 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −934.000 | −0.977663 | −0.488832 | − | 0.872378i | \(-0.662577\pi\) | ||||
−0.488832 | + | 0.872378i | \(0.662577\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 62.6099i | − 0.0635609i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 602.000i | 0.593082i | 0.955020 | + | 0.296541i | \(0.0958331\pi\) | ||||
−0.955020 | + | 0.296541i | \(0.904167\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1829.10 | −1.74978 | −0.874888 | − | 0.484325i | \(-0.839065\pi\) | ||||
−0.874888 | + | 0.484325i | \(0.839065\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −700.000 | −0.650600 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1525.00i | − 1.37782i | −0.724845 | − | 0.688912i | \(-0.758089\pi\) | ||||
0.724845 | − | 0.688912i | \(-0.241911\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2154.00i | 1.89281i | 0.322989 | + | 0.946403i | \(0.395312\pi\) | ||||
−0.322989 | + | 0.946403i | \(0.604688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 957.037 | 0.818360 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2182.00 | −1.81651 | −0.908254 | − | 0.418420i | \(-0.862584\pi\) | ||||
−0.908254 | + | 0.418420i | \(0.862584\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 961.509i | 0.779663i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 434.000i | − 0.342934i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1440.03 | 1.10930 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1251.00 | 0.939895 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 44.7214i | − 0.0327837i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 125.000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1310.34 | −0.915539 | −0.457770 | − | 0.889071i | \(-0.651352\pi\) | ||||
−0.457770 | + | 0.889071i | \(0.651352\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −300.000 | −0.204756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 205.718i | 0.137204i | 0.997644 | + | 0.0686019i | \(0.0218538\pi\) | ||||
−0.997644 | + | 0.0686019i | \(0.978146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3360.00i | 2.19059i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 760.263 | 0.484689 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2094.00 | 1.30586 | 0.652929 | − | 0.757419i | \(-0.273540\pi\) | ||||
0.652929 | + | 0.757419i | \(0.273540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 1377.42i | − 0.840511i | −0.907406 | − | 0.420256i | \(-0.861940\pi\) | ||||
0.907406 | − | 0.420256i | \(-0.138060\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1780.00i | 1.06314i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −554.545 | −0.324289 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 450.000 | 0.257727 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2848.75i | − 1.59837i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 334.000i | 0.183640i | 0.995776 | + | 0.0918200i | \(0.0292684\pi\) | ||||
−0.995776 | + | 0.0918200i | \(0.970732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3139.44 | 1.69195 | 0.845973 | − | 0.533225i | \(-0.179020\pi\) | ||||
0.845973 | + | 0.533225i | \(0.179020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −322.000 | −0.170145 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 760.263i | 0.393973i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 834.000i | 0.423952i | 0.977275 | + | 0.211976i | \(0.0679898\pi\) | ||||
−0.977275 | + | 0.211976i | \(0.932010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3032.11 | 1.51234 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6020.00 | −2.94685 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3090.25i | 1.48495i | 0.669874 | + | 0.742475i | \(0.266348\pi\) | ||||
−0.669874 | + | 0.742475i | \(0.733652\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 200.000i | − 0.0943635i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.47214 | 0.00207224 | 0.00103612 | − | 0.999999i | \(-0.499670\pi\) | ||||
0.00103612 | + | 0.999999i | \(0.499670\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1647.00 | −0.749659 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 751.319i | − 0.335993i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 1838.00i | − 0.807749i | −0.914814 | − | 0.403874i | \(-0.867663\pi\) | ||||
0.914814 | − | 0.403874i | \(-0.132337\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 782.624 | 0.338062 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1840.00 | −0.781372 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1842.52i | − 0.769365i | −0.923049 | − | 0.384683i | \(-0.874311\pi\) | ||||
0.923049 | − | 0.384683i | \(-0.125689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 1862.00i | − 0.764648i | −0.924028 | − | 0.382324i | \(-0.875124\pi\) | ||||
0.924028 | − | 0.382324i | \(-0.124876\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1118.03 | 0.451625 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1070.00 | −0.425232 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 411.437i | 0.160894i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4760.00i | 1.83195i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2066.13 | 0.782721 | 0.391360 | − | 0.920237i | \(-0.372005\pi\) | ||||
0.391360 | + | 0.920237i | \(0.372005\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3378.00 | 1.25986 | 0.629932 | − | 0.776650i | \(-0.283083\pi\) | ||||
0.629932 | + | 0.776650i | \(0.283083\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1386.36i | − 0.509125i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 66.0000i | − 0.0238696i | −0.999929 | − | 0.0119348i | \(-0.996201\pi\) | ||||
0.999929 | − | 0.0119348i | \(-0.00379905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1216.42 | −0.433316 | −0.216658 | − | 0.976248i | \(-0.569516\pi\) | ||||
−0.216658 | + | 0.976248i | \(0.569516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −220.000 | −0.0772020 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2817.45i | 0.974118i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 50.0000i | 0.0170349i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1346.11 | 0.451987 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −960.000 | −0.317725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5286.06i | 1.72468i | 0.506329 | + | 0.862341i | \(0.331002\pi\) | ||||
−0.506329 | + | 0.862341i | \(0.668998\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1640.00i | 0.527563i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 335.410 | 0.106394 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4760.00 | −1.48908 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2334.45i | 0.720310i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2852.00i | 0.868083i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2965.03 | −0.890371 | −0.445186 | − | 0.895438i | \(-0.646862\pi\) | ||||
−0.445186 | + | 0.895438i | \(0.646862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −175.000 | −0.0518519 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4369.28i | 1.27753i | 0.769402 | + | 0.638765i | \(0.220554\pi\) | ||||
−0.769402 | + | 0.638765i | \(0.779446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3250.00i | 0.937843i | 0.883240 | + | 0.468921i | \(0.155357\pi\) | ||||
−0.883240 | + | 0.468921i | \(0.844643\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1252.20 | 0.356661 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3298.00 | −0.927293 | −0.463646 | − | 0.886020i | \(-0.653459\pi\) | ||||
−0.463646 | + | 0.886020i | \(0.653459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 1990.10i | − 0.552425i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3920.00i | 1.07439i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 554.545 | 0.150086 | 0.0750429 | − | 0.997180i | \(-0.476091\pi\) | ||||
0.0750429 | + | 0.997180i | \(0.476091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5150.00 | 1.37652 | 0.688259 | − | 0.725465i | \(-0.258375\pi\) | ||||
0.688259 | + | 0.725465i | \(0.258375\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 1909.60i | − 0.504119i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3185.00i | 0.830540i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6654.54 | −1.71424 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1700.00 | −0.432663 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1386.36i | 0.348631i | 0.984690 | + | 0.174316i | \(0.0557713\pi\) | ||||
−0.984690 | + | 0.174316i | \(0.944229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1720.00i | − 0.427413i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1028.59 | −0.252600 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4166.00 | −1.01116 | −0.505580 | − | 0.862780i | \(-0.668721\pi\) | ||||
−0.505580 | + | 0.862780i | \(0.668721\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 6699.26i | − 1.60723i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 630.000i | − 0.149410i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 961.509 | 0.225434 | 0.112717 | − | 0.993627i | \(-0.464045\pi\) | ||||
0.112717 | + | 0.993627i | \(0.464045\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3390.00 | −0.785834 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4337.97i | 0.994305i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 1494.00i | − 0.338627i | −0.985562 | − | 0.169314i | \(-0.945845\pi\) | ||||
0.985562 | − | 0.169314i | \(-0.0541551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5017.74 | −1.12474 | −0.562372 | − | 0.826884i | \(-0.690111\pi\) | ||||
−0.562372 | + | 0.826884i | \(0.690111\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8680.00 | 1.92431 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 223.607i | 0.0490327i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1006.00i | 0.218212i | 0.994030 | + | 0.109106i | \(0.0347988\pi\) | ||||
−0.994030 | + | 0.109106i | \(0.965201\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1064.37 | 0.228395 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3210.00 | 0.681468 | 0.340734 | − | 0.940160i | \(-0.389324\pi\) | ||||
0.340734 | + | 0.940160i | \(0.389324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3635.85i | 0.763705i | 0.924223 | + | 0.381853i | \(0.124714\pi\) | ||||
−0.924223 | + | 0.381853i | \(0.875286\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2400.00i | − 0.498820i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −313.050 | −0.0643858 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2797.00 | −0.569306 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4176.97i | 0.841439i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3622.00i | 0.722183i | 0.932530 | + | 0.361091i | \(0.117596\pi\) | ||||
−0.932530 | + | 0.361091i | \(0.882404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2057.18 | 0.406013 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1360.00 | −0.265708 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 11922.7i | − 2.30605i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2100.00i | 0.402133i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2692.23 | 0.510443 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1250.00 | −0.234671 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2088.49i | − 0.388261i | −0.980976 | − | 0.194131i | \(-0.937811\pi\) | ||||
0.980976 | − | 0.194131i | \(-0.0621886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8180.00i | 1.50597i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8899.55 | −1.62266 | −0.811330 | − | 0.584589i | \(-0.801256\pi\) | ||||
−0.811330 | + | 0.584589i | \(0.801256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8778.00 | −1.58518 | −0.792591 | − | 0.609754i | \(-0.791268\pi\) | ||||
−0.792591 | + | 0.609754i | \(0.791268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 1095.67i | − 0.195982i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 5046.00i | − 0.894043i | −0.894523 | − | 0.447021i | \(-0.852485\pi\) | ||||
0.894523 | − | 0.447021i | \(-0.147515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −804.984 | −0.141287 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6820.00 | −1.18584 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4937.24i | 0.850512i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1550.00i | 0.264549i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9632.98 | 1.62907 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12460.0 | 2.08797 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 313.050i | − 0.0519842i | −0.999662 | − | 0.0259921i | \(-0.991726\pi\) | ||||
0.999662 | − | 0.0259921i | \(-0.00827447\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1498.00i | 0.246516i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 245.967 | 0.0401153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2574.00 | −0.416067 | −0.208034 | − | 0.978122i | \(-0.566706\pi\) | ||||
−0.208034 | + | 0.978122i | \(0.566706\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9758.20i | 1.56340i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1360.00i | − 0.215977i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9203.66 | −1.44884 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4300.00 | 0.671027 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2643.03i | 0.408892i | 0.978878 | + | 0.204446i | \(0.0655392\pi\) | ||||
−0.978878 | + | 0.204446i | \(0.934461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 10170.0i | − 1.55985i | −0.625873 | − | 0.779925i | \(-0.715257\pi\) | ||||
0.625873 | − | 0.779925i | \(-0.284743\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9427.26 | −1.43359 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −318.000 | −0.0479474 | −0.0239737 | − | 0.999713i | \(-0.507632\pi\) | ||||
−0.0239737 | + | 0.999713i | \(0.507632\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1833.58i | − 0.274130i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 6440.00i | − 0.954737i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12378.9 | 1.81987 | 0.909933 | − | 0.414755i | \(-0.136133\pi\) | ||||
0.909933 | + | 0.414755i | \(0.136133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4661.00 | −0.679545 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 5594.64i | − 0.808933i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2610.00i | − 0.374284i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3072.36 | 0.436991 | 0.218496 | − | 0.975838i | \(-0.429885\pi\) | ||||
0.218496 | + | 0.975838i | \(0.429885\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 70.0000 | 0.00987549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 21224.8i | − 2.97017i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3278.00i | 0.455036i | 0.973774 | + | 0.227518i | \(0.0730610\pi\) | ||||
−0.973774 | + | 0.227518i | \(0.926939\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −559.017 | −0.0769800 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5580.00 | −0.762293 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5116.12i | 0.693397i | 0.937977 | + | 0.346699i | \(0.112697\pi\) | ||||
−0.937977 | + | 0.346699i | \(0.887303\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5860.00i | 0.787971i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1149.34 | 0.153338 | 0.0766690 | − | 0.997057i | \(-0.475572\pi\) | ||||
0.0766690 | + | 0.997057i | \(0.475572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1400.00 | −0.185326 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 469.574i | − 0.0616791i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 834.000i | − 0.108703i | −0.998522 | − | 0.0543515i | \(-0.982691\pi\) | ||||
0.998522 | − | 0.0543515i | \(-0.0173092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8845.88 | −1.14413 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 920.000 | 0.118086 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4382.69i | − 0.558271i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 8734.00i | − 1.10415i | −0.833795 | − | 0.552074i | \(-0.813837\pi\) | ||||
0.833795 | − | 0.552074i | \(-0.186163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15026.4 | 1.88536 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 242.000 | 0.0301369 | 0.0150685 | − | 0.999886i | \(-0.495203\pi\) | ||||
0.0150685 | + | 0.999886i | \(0.495203\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 9427.26i | − 1.16527i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 2455.00i | − 0.301210i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1914.07 | 0.233113 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6514.00 | 0.787522 | 0.393761 | − | 0.919213i | \(-0.371174\pi\) | ||||
0.393761 | + | 0.919213i | \(0.371174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 9364.65i | − 1.12390i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12880.0i | 1.53458i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1900.66 | 0.224818 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6160.00 | −0.723397 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 16081.8i | − 1.87505i | −0.347913 | − | 0.937527i | \(-0.613110\pi\) | ||||
0.347913 | − | 0.937527i | \(-0.386890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 7250.00i | − 0.839295i | −0.907687 | − | 0.419648i | \(-0.862154\pi\) | ||||
0.907687 | − | 0.419648i | \(-0.137846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2786.14 | −0.320252 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1150.00 | 0.131255 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 7826.24i | − 0.886975i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2480.00i | 0.279104i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4981.96 | −0.556781 | −0.278390 | − | 0.960468i | \(-0.589801\pi\) | ||||
−0.278390 | + | 0.960468i | \(0.589801\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11482.0 | 1.27434 | 0.637171 | − | 0.770723i | \(-0.280105\pi\) | ||||
0.637171 | + | 0.770723i | \(0.280105\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 2012.46i | − 0.221816i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 20640.0i | − 2.25937i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3792.37 | 0.412301 | 0.206150 | − | 0.978520i | \(-0.433906\pi\) | ||||
0.206150 | + | 0.978520i | \(0.433906\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4459.00 | 0.481481 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 746.847i | − 0.0800988i | −0.999198 | − | 0.0400494i | \(-0.987248\pi\) | ||||
0.999198 | − | 0.0400494i | \(-0.0127515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 4850.00i | − 0.516656i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1493.69 | 0.158052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1306.00 | −0.137269 | −0.0686347 | − | 0.997642i | \(-0.521864\pi\) | ||||
−0.0686347 | + | 0.997642i | \(0.521864\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 89.4427i | − 0.00933857i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 14040.0i | − 1.45620i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9704.54 | −0.999902 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9526.00 | 0.975071 | 0.487536 | − | 0.873103i | \(-0.337896\pi\) | ||||
0.487536 | + | 0.873103i | \(0.337896\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6994.42i | 0.711267i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1518.00i | 0.153363i | 0.997056 | + | 0.0766815i | \(0.0244325\pi\) | ||||
−0.997056 | + | 0.0766815i | \(0.975568\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17293.7 | −1.73587 | −0.867936 | − | 0.496676i | \(-0.834554\pi\) | ||||
−0.867936 | + | 0.496676i | \(0.834554\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3400.00 | 0.339078 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16980.7i | 1.68260i | 0.540570 | + | 0.841299i | \(0.318208\pi\) | ||||
−0.540570 | + | 0.841299i | \(0.681792\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1540.00i | 0.151622i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3729.76 | 0.364880 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −600.000 | −0.0583256 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2683.28i | 0.259195i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4746.00i | 0.455565i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3810.26 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13268.0 | 1.25773 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26922.3i | 2.53624i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 4670.00i | − 0.437224i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1310.34 | 0.121924 | 0.0609620 | − | 0.998140i | \(-0.480583\pi\) | ||||
0.0609620 | + | 0.998140i | \(0.480583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13820.0 | 1.27804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2960.55i | 0.272114i | 0.990701 | + | 0.136057i | \(0.0434430\pi\) | ||||
−0.990701 | + | 0.136057i | \(0.956557\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4140.00i | 0.378207i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 313.050 | 0.0284253 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11480.0 | 1.03611 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19319.6i | 1.73320i | 0.499006 | + | 0.866598i | \(0.333699\pi\) | ||||
−0.499006 | + | 0.866598i | \(0.666301\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 20.0000i | − 0.00178350i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3072.36 | 0.272345 | 0.136173 | − | 0.990685i | \(-0.456520\pi\) | ||||
0.136173 | + | 0.990685i | \(0.456520\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3010.00 | −0.265234 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7365.61i | 0.645203i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18550.0i | 1.61535i | 0.589626 | + | 0.807676i | \(0.299275\pi\) | ||||
−0.589626 | + | 0.807676i | \(0.700725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16341.2 | 1.41466 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −16320.0 | −1.40457 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 9145.52i | − 0.782524i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3560.00i | 0.302841i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8219.79 | −0.695200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2102.00 | 0.176757 | 0.0883784 | − | 0.996087i | \(-0.471832\pi\) | ||||
0.0883784 | + | 0.996087i | \(0.471832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17696.2i | 1.47955i | 0.672856 | + | 0.739773i | \(0.265067\pi\) | ||||
−0.672856 | + | 0.739773i | \(0.734933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3500.00i | − 0.290957i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6994.42 | −0.578144 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24813.0 | 2.03937 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2880.06i | − 0.235374i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 620.000i | − 0.0503850i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7624.99 | 0.616182 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8240.00 | −0.662164 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5697.50i | − 0.455304i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 9922.00i | − 0.788503i | −0.919003 | − | 0.394251i | \(-0.871004\pi\) | ||||
0.919003 | − | 0.394251i | \(-0.128996\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8327.12 | −0.658105 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10770.0 | −0.846488 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3716.34i | − 0.290493i | −0.989396 | − | 0.145246i | \(-0.953603\pi\) | ||||
0.989396 | − | 0.145246i | \(-0.0463975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1750.00i | 0.136044i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9659.81 | −0.746864 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27440.0 | 2.11007 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4785.19i | 0.365982i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 15094.0i | − 1.14821i | −0.818781 | − | 0.574105i | \(-0.805350\pi\) | ||||
0.818781 | − | 0.574105i | \(-0.194650\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4159.09 | −0.314688 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1840.00 | 0.138476 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 5657.25i | − 0.423490i | −0.977325 | − | 0.211745i | \(-0.932085\pi\) | ||||
0.977325 | − | 0.211745i | \(-0.0679146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 10910.0i | − 0.812367i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15370.7 | 1.13847 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5906.00 | 0.435136 | 0.217568 | − | 0.976045i | \(-0.430188\pi\) | ||||
0.217568 | + | 0.976045i | \(0.430188\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 4892.52i | − 0.358573i | −0.983797 | − | 0.179287i | \(-0.942621\pi\) | ||||
0.983797 | − | 0.179287i | \(-0.0573790\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 9240.00i | − 0.673659i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4807.55 | −0.348676 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13286.0 | −0.958585 | −0.479292 | − | 0.877655i | \(-0.659107\pi\) | ||||
−0.479292 | + | 0.877655i | \(0.659107\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 15106.9i | − 1.08432i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11900.0i | 0.849734i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6064.22 | 0.430796 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2170.00 | 0.153365 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9029.24i | 0.634884i | 0.948278 | + | 0.317442i | \(0.102824\pi\) | ||||
−0.948278 | + | 0.317442i | \(0.897176\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 16320.0i | − 1.14169i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −295.161 | −0.0205437 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11442.0 | 0.792355 | 0.396178 | − | 0.918174i | \(-0.370336\pi\) | ||||
0.396178 | + | 0.918174i | \(0.370336\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7200.14i | 0.496096i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5440.00i | 0.372939i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14149.8 | −0.965187 | −0.482593 | − | 0.875845i | \(-0.660305\pi\) | ||||
−0.482593 | + | 0.875845i | \(0.660305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3110.00 | −0.211081 | −0.105540 | − | 0.994415i | \(-0.533657\pi\) | ||||
−0.105540 | + | 0.994415i | \(0.533657\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 344.354i | − 0.0232557i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6255.00i | 0.420334i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11193.8 | 0.748502 | 0.374251 | − | 0.927327i | \(-0.377900\pi\) | ||||
0.374251 | + | 0.927327i | \(0.377900\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12600.0 | 0.838387 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 24677.2i | 1.63394i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5342.00i | 0.351976i | 0.984392 | + | 0.175988i | \(0.0563120\pi\) | ||||
−0.984392 | + | 0.175988i | \(0.943688\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 223.607 | 0.0146613 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19714.0 | −1.28631 | −0.643157 | − | 0.765734i | \(-0.722376\pi\) | ||||
−0.643157 | + | 0.765734i | \(0.722376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 13166.0i | − 0.854903i | −0.904038 | − | 0.427451i | \(-0.859411\pi\) | ||||
0.904038 | − | 0.427451i | \(-0.140589\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 29240.0i | − 1.88947i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30365.8 | 1.95278 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4293.25i | 0.273454i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 9844.00i | − 0.624016i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12262.6 | 0.773639 | 0.386820 | − | 0.922155i | \(-0.373574\pi\) | ||||
0.386820 | + | 0.922155i | \(0.373574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23640.0 | 1.48437 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 6551.68i | − 0.409442i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 39494.0i | − 2.45653i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2567.01 | −0.158919 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2690.00 | −0.165754 | −0.0828772 | − | 0.996560i | \(-0.526411\pi\) | ||||
−0.0828772 | + | 0.996560i | \(0.526411\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 12240.2i | − 0.750712i | −0.926881 | − | 0.375356i | \(-0.877520\pi\) | ||||
0.926881 | − | 0.375356i | \(-0.122480\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1500.00i | − 0.0915697i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17973.5 | −1.09214 | −0.546068 | − | 0.837741i | \(-0.683876\pi\) | ||||
−0.546068 | + | 0.837741i | \(0.683876\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3680.00 | −0.222577 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21287.4i | 1.28159i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 3478.00i | − 0.208430i | −0.994555 | − | 0.104215i | \(-0.966767\pi\) | ||||
0.994555 | − | 0.104215i | \(-0.0332330\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1028.59 | −0.0613594 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3654.00 | −0.216980 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10572.1i | 0.624934i | 0.949929 | + | 0.312467i | \(0.101155\pi\) | ||||
−0.949929 | + | 0.312467i | \(0.898845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 110.000i | 0.00647277i | 0.999995 | + | 0.00323639i | \(0.00103018\pi\) | ||||
−0.999995 | + | 0.00323639i | \(0.998970\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12754.5 | 0.747127 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16800.0 | −0.979663 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 17307.2i | − 1.00470i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13260.0i | 0.766310i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2236.07 | 0.128647 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14278.0 | −0.817796 | −0.408898 | − | 0.912580i | \(-0.634087\pi\) | ||||
−0.408898 | + | 0.912580i | \(0.634087\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3801.32i | 0.216760i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 18386.0i | − 1.04377i | −0.853016 | − | 0.521884i | \(-0.825229\pi\) | ||||
0.853016 | − | 0.521884i | \(-0.174771\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29238.8 | 1.65255 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19540.0 | 1.09952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15317.1i | 0.858113i | 0.903278 | + | 0.429057i | \(0.141154\pi\) | ||||
−0.903278 | + | 0.429057i | \(0.858846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10470.0i | 0.583997i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14534.4 | 0.807167 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42036.0 | 2.32430 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 9507.76i | − 0.523433i | −0.965145 | − | 0.261717i | \(-0.915711\pi\) | ||||
0.965145 | − | 0.261717i | \(-0.0842886\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1960.00i | 0.107438i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6887.09 | 0.375888 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −460.000 | −0.0249982 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14749.1i | 0.798086i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 15830.0i | − 0.852911i | −0.904508 | − | 0.426456i | \(-0.859762\pi\) | ||||
0.904508 | − | 0.426456i | \(-0.140238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22968.9 | 1.23227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8900.00 | −0.475452 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 18845.6i | − 1.00249i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20050.0i | 1.06205i | 0.847356 | + | 0.531025i | \(0.178193\pi\) | ||||
−0.847356 | + | 0.531025i | \(0.821807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6135.77 | −0.323642 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29240.0 | 1.53583 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2772.72i | − 0.145027i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2480.00i | − 0.129173i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −21126.4 | −1.09580 | −0.547900 | − | 0.836544i | \(-0.684573\pi\) | ||||
−0.547900 | + | 0.836544i | \(0.684573\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 57260.0 | 2.95766 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 23031.5i | − 1.18472i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2250.00i | 0.115259i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11336.9 | −0.578351 | −0.289175 | − | 0.957276i | \(-0.593381\pi\) | ||||
−0.289175 | + | 0.957276i | \(0.593381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21797.0 | −1.10740 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3085.77i | 0.156131i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 17198.0i | − 0.866607i | −0.901248 | − | 0.433303i | \(-0.857348\pi\) | ||||
0.901248 | − | 0.433303i | \(-0.142652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 14243.8 | 0.714815 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −440.000 | −0.0219913 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 4597.36i | − 0.228845i | −0.993432 | − | 0.114423i | \(-0.963498\pi\) | ||||
0.993432 | − | 0.114423i | \(-0.0365018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29760.0i | 1.47539i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2419.43 | −0.119462 | −0.0597309 | − | 0.998215i | \(-0.519024\pi\) | ||||
−0.0597309 | + | 0.998215i | \(0.519024\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1670.00 | −0.0821263 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 2660.92i | − 0.130332i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 47740.0i | 2.32895i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7432.69 | −0.361149 | −0.180574 | − | 0.983561i | \(-0.557796\pi\) | ||||
−0.180574 | + | 0.983561i | \(0.557796\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6200.00 | 0.300054 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15697.2i | 0.756662i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 11474.0i | − 0.550898i | −0.961316 | − | 0.275449i | \(-0.911174\pi\) | ||||
0.961316 | − | 0.275449i | \(-0.0888265\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7692.07 | −0.367858 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31802.0 | −1.51488 | −0.757439 | − | 0.652906i | \(-0.773550\pi\) | ||||
−0.757439 | + | 0.652906i | \(0.773550\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 67430.9i | − 3.19942i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 1610.00i | − 0.0760911i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25509.1 | −1.20089 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5310.00 | −0.249003 | −0.124502 | − | 0.992219i | \(-0.539733\pi\) | ||||
−0.124502 | + | 0.992219i | \(0.539733\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18630.9i | 0.870267i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 37938.0i | − 1.76525i | −0.470082 | − | 0.882623i | \(-0.655776\pi\) | ||||
0.470082 | − | 0.882623i | \(-0.344224\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3801.32 | −0.176190 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −29960.0 | −1.38328 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 1073.31i | − 0.0493651i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3280.00i | 0.150279i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13684.7 | −0.624588 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4170.00 | −0.189597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 37633.0i | − 1.70454i | −0.523103 | − | 0.852270i | \(-0.675226\pi\) | ||||
0.523103 | − | 0.852270i | \(-0.324774\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 4300.00i | − 0.194023i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 68307.4 | 3.07046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15500.0 | 0.694100 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15160.5i | 0.676338i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 17526.0i | − 0.778924i | −0.921042 | − | 0.389462i | \(-0.872661\pi\) | ||||
0.921042 | − | 0.389462i | \(-0.127339\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18308.9 | 0.810667 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6790.00 | −0.299517 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4668.91i | 0.205183i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 30100.0i | − 1.31787i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6681.37 | −0.291444 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8970.00 | −0.389825 | −0.194912 | − | 0.980821i | \(-0.562442\pi\) | ||||
−0.194912 | + | 0.980821i | \(0.562442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 3550.88i | − 0.153746i | −0.997041 | − | 0.0768731i | \(-0.975506\pi\) | ||||
0.997041 | − | 0.0768731i | \(-0.0244936\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22440.0i | 0.968026i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15451.2 | −0.664090 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7200.00 | −0.308318 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 13586.3i | 0.579665i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15550.0i | 0.661022i | 0.943802 | + | 0.330511i | \(0.107221\pi\) | ||||
−0.943802 | + | 0.330511i | \(0.892779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26712.1 | −1.13138 | −0.565689 | − | 0.824619i | \(-0.691390\pi\) | ||||
−0.565689 | + | 0.824619i | \(0.691390\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1000.00 | 0.0422006 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 863.122i | − 0.0362923i | −0.999835 | − | 0.0181461i | \(-0.994224\pi\) | ||||
0.999835 | − | 0.0181461i | \(-0.00577641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19066.0i | 0.798781i | 0.916781 | + | 0.399391i | \(0.130778\pi\) | ||||
−0.916781 | + | 0.399391i | \(0.869222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4498.97 | 0.187807 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29302.0 | −1.21879 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.3607i | 0 0.000926734i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 23120.0i | − 0.954772i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47744.5 | −1.96463 | −0.982315 | − | 0.187238i | \(-0.940047\pi\) | ||||
−0.982315 | + | 0.187238i | \(0.940047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16289.0 | 0.667883 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 14355.6i | − 0.586514i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 8235.00i | − 0.335258i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39162.5 | −1.58871 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16260.0 | 0.657293 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41152.6i | 1.65769i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14462.0i | 0.580503i | 0.956950 | + | 0.290252i | \(0.0937390\pi\) | ||||
−0.956950 | + | 0.290252i | \(0.906261\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3756.59 | 0.150261 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29346.0 | −1.16971 | −0.584854 | − | 0.811138i | \(-0.698848\pi\) | ||||
−0.584854 | + | 0.811138i | \(0.698848\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22807.9i | 0.905932i | 0.891528 | + | 0.452966i | \(0.149634\pi\) | ||||
−0.891528 | + | 0.452966i | \(0.850366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1400.00i | 0.0554145i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24753.3 | −0.976375 | −0.488187 | − | 0.872739i | \(-0.662342\pi\) | ||||
−0.488187 | + | 0.872739i | \(0.662342\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9190.00 | 0.361236 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12508.6i | 0.489981i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7840.00i | 0.306046i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3050.00 | −0.118651 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6538.00 | −0.253468 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3913.12i | 0.151186i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 32126.0i | − 1.23696i | −0.785799 | − | 0.618482i | \(-0.787748\pi\) | ||||
0.785799 | − | 0.618482i | \(-0.212252\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16198.1 | 0.621556 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33570.0 | −1.28377 | −0.641885 | − | 0.766801i | \(-0.721848\pi\) | ||||
−0.641885 | + | 0.766801i | \(0.721848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6435.40i | 0.245265i | 0.992452 | + | 0.122632i | \(0.0391336\pi\) | ||||
−0.992452 | + | 0.122632i | \(0.960866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 9200.00i | − 0.349440i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46827.7 | −1.77263 | −0.886314 | − | 0.463084i | \(-0.846743\pi\) | ||||
−0.886314 | + | 0.463084i | \(0.846743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 41020.0 | 1.54754 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4391.64i | 0.165124i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 42720.0i | 1.60086i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9212.60 | 0.344071 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −53320.0 | −1.98473 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 13684.7i | − 0.507688i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 31188.0i | − 1.15319i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9391.49 | 0.346101 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9310.00 | 0.341961 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11980.9i | 0.438608i | 0.975657 | + | 0.219304i | \(0.0703787\pi\) | ||||
−0.975657 | + | 0.219304i | \(0.929621\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4214.00i | 0.153762i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24194.3 | 0.879903 | 0.439951 | − | 0.898022i | \(-0.354996\pi\) | ||||
0.439951 | + | 0.898022i | \(0.354996\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3400.00 | −0.123246 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5590.17i | 0.201973i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6440.00i | − 0.231917i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37512.3 | −1.34648 | −0.673240 | − | 0.739424i | \(-0.735098\pi\) | ||||
−0.673240 | + | 0.739424i | \(0.735098\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9340.00 | −0.334162 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22736.3i | 0.810808i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 5350.00i | − 0.190170i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12803.7 | −0.453646 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21994.0 | −0.776749 | −0.388374 | − | 0.921502i | \(-0.626963\pi\) | ||||
−0.388374 | + | 0.921502i | \(0.626963\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 68370.0i | − 2.40681i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39800.0i | 1.39656i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2057.18 | −0.0719541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16286.0 | 0.567813 | 0.283906 | − | 0.958852i | \(-0.408370\pi\) | ||||
0.283906 | + | 0.958852i | \(0.408370\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39256.4i | 1.36431i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24302.0i | 0.841894i | 0.907085 | + | 0.420947i | \(0.138302\pi\) | ||||
−0.907085 | + | 0.420947i | \(0.861698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1923.02 | 0.0664073 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −23800.0 | −0.819274 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 19869.7i | − 0.681815i | −0.940097 | − | 0.340907i | \(-0.889266\pi\) | ||||
0.940097 | − | 0.340907i | \(-0.110734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32364.0i | 1.10704i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22566.4 | −0.769470 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22422.0 | 0.762140 | 0.381070 | − | 0.924546i | \(-0.375556\pi\) | ||||
0.381070 | + | 0.924546i | \(0.375556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10330.6i | 0.350043i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3600.00i | 0.121600i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −65552.6 | −2.20730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6671.00 | −0.223927 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 10675.0i | − 0.357214i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16890.0i | 0.563428i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43777.7 | 1.45584 | 0.727920 | − | 0.685662i | \(-0.240487\pi\) | ||||
0.727920 | + | 0.685662i | \(0.240487\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22080.0 | 0.732004 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 25714.8i | − 0.849873i | −0.905223 | − | 0.424936i | \(-0.860296\pi\) | ||||
0.905223 | − | 0.424936i | \(-0.139704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 43120.0i | 1.42072i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6931.81 | 0.227688 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28986.0 | 0.949175 | 0.474588 | − | 0.880208i | \(-0.342597\pi\) | ||||
0.474588 | + | 0.880208i | \(0.342597\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8675.94i | 0.283232i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15078.0i | 0.490727i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32123.4 | 1.04229 | 0.521147 | − | 0.853467i | \(-0.325504\pi\) | ||||
0.521147 | + | 0.853467i | \(0.325504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 330.000 | 0.0106748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 55722.8i | − 1.79704i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 12900.0i | − 0.414758i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11994.3 | 0.384471 | 0.192235 | − | 0.981349i | \(-0.438426\pi\) | ||||
0.192235 | + | 0.981349i | \(0.438426\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1400.00 | −0.0447408 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 6082.10i | − 0.193785i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 406.000i | 0.0128968i | 0.999979 | + | 0.00644842i | \(0.00205261\pi\) | ||||
−0.999979 | + | 0.00644842i | \(0.997947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32539.3 | 1.03053 |
(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 | 1280.4.d.v.641.2 | 4 | ||
4.3 | odd | 2 | inner | 1280.4.d.v.641.4 | 4 | ||
8.3 | odd | 2 | inner | 1280.4.d.v.641.1 | 4 | ||
8.5 | even | 2 | inner | 1280.4.d.v.641.3 | 4 | ||
16.3 | odd | 4 | 320.4.a.q.1.1 | 2 | |||
16.5 | even | 4 | 160.4.a.d.1.1 | ✓ | 2 | ||
16.11 | odd | 4 | 160.4.a.d.1.2 | yes | 2 | ||
16.13 | even | 4 | 320.4.a.q.1.2 | 2 | |||
48.5 | odd | 4 | 1440.4.a.bb.1.2 | 2 | |||
48.11 | even | 4 | 1440.4.a.bb.1.1 | 2 | |||
80.19 | odd | 4 | 1600.4.a.cg.1.2 | 2 | |||
80.27 | even | 4 | 800.4.c.l.449.1 | 4 | |||
80.29 | even | 4 | 1600.4.a.cg.1.1 | 2 | |||
80.37 | odd | 4 | 800.4.c.l.449.4 | 4 | |||
80.43 | even | 4 | 800.4.c.l.449.3 | 4 | |||
80.53 | odd | 4 | 800.4.c.l.449.2 | 4 | |||
80.59 | odd | 4 | 800.4.a.o.1.1 | 2 | |||
80.69 | even | 4 | 800.4.a.o.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.4.a.d.1.1 | ✓ | 2 | 16.5 | even | 4 | ||
160.4.a.d.1.2 | yes | 2 | 16.11 | odd | 4 | ||
320.4.a.q.1.1 | 2 | 16.3 | odd | 4 | |||
320.4.a.q.1.2 | 2 | 16.13 | even | 4 | |||
800.4.a.o.1.1 | 2 | 80.59 | odd | 4 | |||
800.4.a.o.1.2 | 2 | 80.69 | even | 4 | |||
800.4.c.l.449.1 | 4 | 80.27 | even | 4 | |||
800.4.c.l.449.2 | 4 | 80.53 | odd | 4 | |||
800.4.c.l.449.3 | 4 | 80.43 | even | 4 | |||
800.4.c.l.449.4 | 4 | 80.37 | odd | 4 | |||
1280.4.d.v.641.1 | 4 | 8.3 | odd | 2 | inner | ||
1280.4.d.v.641.2 | 4 | 1.1 | even | 1 | trivial | ||
1280.4.d.v.641.3 | 4 | 8.5 | even | 2 | inner | ||
1280.4.d.v.641.4 | 4 | 4.3 | odd | 2 | inner | ||
1440.4.a.bb.1.1 | 2 | 48.11 | even | 4 | |||
1440.4.a.bb.1.2 | 2 | 48.5 | odd | 4 | |||
1600.4.a.cg.1.1 | 2 | 80.29 | even | 4 | |||
1600.4.a.cg.1.2 | 2 | 80.19 | odd | 4 |