Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,3,Mod(97,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.c (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: | \(21.3624527258\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 30x^{6} + 84x^{5} + 597x^{4} - 384x^{3} - 4236x^{2} + 688x + 13378 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 392) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Root | \(5.16940 - 1.84776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.97 |
Dual form | 784.3.c.g.97.4 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.34336i | 0.447787i | 0.974614 | + | 0.223893i | \(0.0718767\pi\) | ||||
−0.974614 | + | 0.223893i | \(0.928123\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.62165i | 1.32433i | 0.749358 | + | 0.662165i | \(0.230362\pi\) | ||||
−0.749358 | + | 0.662165i | \(0.769638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.19538 | 0.799487 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.5385 | 1.13987 | 0.569933 | − | 0.821691i | \(-0.306969\pi\) | ||||
0.569933 | + | 0.821691i | \(0.306969\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 2.63066i | − 0.202359i | −0.994868 | − | 0.101179i | \(-0.967738\pi\) | ||||
0.994868 | − | 0.101179i | \(-0.0322616\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.89526 | −0.593017 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 26.4811i | 1.55771i | 0.627202 | + | 0.778857i | \(0.284200\pi\) | ||||
−0.627202 | + | 0.778857i | \(0.715800\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 10.2708i | − 0.540569i | −0.962780 | − | 0.270285i | \(-0.912882\pi\) | ||||
0.962780 | − | 0.270285i | \(-0.0871178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 43.4955 | 1.89111 | 0.945555 | − | 0.325463i | \(-0.105520\pi\) | ||||
0.945555 | + | 0.325463i | \(0.105520\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −18.8462 | −0.753850 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 21.7562i | 0.805786i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.1226 | 0.349054 | 0.174527 | − | 0.984652i | \(-0.444160\pi\) | ||||
0.174527 | + | 0.984652i | \(0.444160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 47.1721i | − 1.52168i | −0.648939 | − | 0.760840i | \(-0.724787\pi\) | ||||
0.648939 | − | 0.760840i | \(-0.275213\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.8438i | 0.510417i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.26470 | 0.223370 | 0.111685 | − | 0.993744i | \(-0.464375\pi\) | ||||
0.111685 | + | 0.993744i | \(0.464375\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.53392 | 0.0906134 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 66.9187i | 1.63216i | 0.577937 | + | 0.816081i | \(0.303858\pi\) | ||||
−0.577937 | + | 0.816081i | \(0.696142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −80.9734 | −1.88310 | −0.941551 | − | 0.336870i | \(-0.890632\pi\) | ||||
−0.941551 | + | 0.336870i | \(0.890632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 47.6453i | 1.05878i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 27.9374i | − 0.594412i | −0.954813 | − | 0.297206i | \(-0.903945\pi\) | ||||
0.954813 | − | 0.297206i | \(-0.0960548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −35.5737 | −0.697523 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −74.8533 | −1.41233 | −0.706164 | − | 0.708049i | \(-0.749576\pi\) | ||||
−0.706164 | + | 0.708049i | \(0.749576\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 83.0258i | 1.50956i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.7974 | 0.242060 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 70.6398i | 1.19728i | 0.801017 | + | 0.598642i | \(0.204293\pi\) | ||||
−0.801017 | + | 0.598642i | \(0.795707\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22.2629i | 0.364965i | 0.983209 | + | 0.182482i | \(0.0584133\pi\) | ||||
−0.983209 | + | 0.182482i | \(0.941587\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17.4193 | 0.267990 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62.3319 | −0.930327 | −0.465163 | − | 0.885225i | \(-0.654004\pi\) | ||||
−0.465163 | + | 0.885225i | \(0.654004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 58.4301i | 0.846813i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −17.1596 | −0.241684 | −0.120842 | − | 0.992672i | \(-0.538559\pi\) | ||||
−0.120842 | + | 0.992672i | \(0.538559\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 34.8985i | 0.478062i | 0.971012 | + | 0.239031i | \(0.0768297\pi\) | ||||
−0.971012 | + | 0.239031i | \(0.923170\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 25.3173i | − 0.337564i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 109.450 | 1.38544 | 0.692719 | − | 0.721208i | \(-0.256413\pi\) | ||||
0.692719 | + | 0.721208i | \(0.256413\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 35.5320 | 0.438667 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.8247i | 0.130418i | 0.997872 | + | 0.0652088i | \(0.0207713\pi\) | ||||
−0.997872 | + | 0.0652088i | \(0.979229\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −175.349 | −2.06293 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.5982i | 0.156302i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 116.218i | − 1.30582i | −0.757435 | − | 0.652910i | \(-0.773548\pi\) | ||||
0.757435 | − | 0.652910i | \(-0.226452\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 63.3691 | 0.681388 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 68.0097 | 0.715892 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 55.5922i | − 0.573116i | −0.958063 | − | 0.286558i | \(-0.907489\pi\) | ||||
0.958063 | − | 0.286558i | \(-0.0925110\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 90.2196 | 0.911309 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0374i | 0.0993798i | 0.998765 | + | 0.0496899i | \(0.0158233\pi\) | ||||
−0.998765 | + | 0.0496899i | \(0.984177\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 69.9520i | 0.679145i | 0.940580 | + | 0.339573i | \(0.110282\pi\) | ||||
−0.940580 | + | 0.339573i | \(0.889718\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.0152 | 0.140329 | 0.0701645 | − | 0.997535i | \(-0.477648\pi\) | ||||
0.0701645 | + | 0.997535i | \(0.477648\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 123.641 | 1.13432 | 0.567160 | − | 0.823608i | \(-0.308042\pi\) | ||||
0.567160 | + | 0.823608i | \(0.308042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.1025i | 0.100022i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −87.6080 | −0.775292 | −0.387646 | − | 0.921808i | \(-0.626712\pi\) | ||||
−0.387646 | + | 0.921808i | \(0.626712\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 288.012i | 2.50445i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 18.9286i | − 0.161783i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 36.2148 | 0.299295 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −89.8958 | −0.730860 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 40.7480i | 0.325984i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −151.557 | −1.19336 | −0.596679 | − | 0.802480i | \(-0.703514\pi\) | ||||
−0.596679 | + | 0.802480i | \(0.703514\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 108.776i | − 0.843228i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 124.133i | 0.947580i | 0.880638 | + | 0.473790i | \(0.157114\pi\) | ||||
−0.880638 | + | 0.473790i | \(0.842886\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −144.062 | −1.06713 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 109.282 | 0.797679 | 0.398840 | − | 0.917021i | \(-0.369413\pi\) | ||||
0.398840 | + | 0.917021i | \(0.369413\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 17.7902i | − 0.127987i | −0.997950 | − | 0.0639935i | \(-0.979616\pi\) | ||||
0.997950 | − | 0.0639935i | \(-0.0203837\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37.5299 | 0.266170 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 32.9846i | − 0.230662i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 67.0281i | 0.462262i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 108.377 | 0.727359 | 0.363680 | − | 0.931524i | \(-0.381520\pi\) | ||||
0.363680 | + | 0.931524i | \(0.381520\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −55.2634 | −0.365983 | −0.182991 | − | 0.983115i | \(-0.558578\pi\) | ||||
−0.182991 | + | 0.983115i | \(0.558578\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 190.542i | 1.24537i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 312.357 | 2.01521 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 220.451i | − 1.40415i | −0.712104 | − | 0.702074i | \(-0.752257\pi\) | ||||
0.712104 | − | 0.702074i | \(-0.247743\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 100.555i | − 0.632421i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 58.6895 | 0.360058 | 0.180029 | − | 0.983661i | \(-0.442381\pi\) | ||||
0.180029 | + | 0.983661i | \(0.442381\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −111.533 | −0.675960 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 99.5134i | − 0.595888i | −0.954583 | − | 0.297944i | \(-0.903699\pi\) | ||||
0.954583 | − | 0.297944i | \(-0.0963009\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 162.080 | 0.959051 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 73.9025i | − 0.432178i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 142.523i | − 0.823830i | −0.911222 | − | 0.411915i | \(-0.864860\pi\) | ||||
0.911222 | − | 0.411915i | \(-0.135140\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −94.8946 | −0.536128 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −273.297 | −1.52680 | −0.763401 | − | 0.645925i | \(-0.776472\pi\) | ||||
−0.763401 | + | 0.645925i | \(0.776472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 289.628i | − 1.60015i | −0.599898 | − | 0.800077i | \(-0.704792\pi\) | ||||
0.599898 | − | 0.800077i | \(-0.295208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −29.9070 | −0.163426 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 54.7259i | 0.295816i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 332.034i | 1.77558i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −69.5686 | −0.364234 | −0.182117 | − | 0.983277i | \(-0.558295\pi\) | ||||
−0.182117 | + | 0.983277i | \(0.558295\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −131.805 | −0.682929 | −0.341464 | − | 0.939895i | \(-0.610923\pi\) | ||||
−0.341464 | + | 0.939895i | \(0.610923\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23.4004i | 0.120002i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 39.1914 | 0.198941 | 0.0994706 | − | 0.995041i | \(-0.468285\pi\) | ||||
0.0994706 | + | 0.995041i | \(0.468285\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 290.424i | − 1.45942i | −0.683758 | − | 0.729709i | \(-0.739656\pi\) | ||||
0.683758 | − | 0.729709i | \(-0.260344\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − 83.7342i | − 0.416588i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −443.112 | −2.16152 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 312.967 | 1.51192 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 128.781i | − 0.616177i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 114.121 | 0.540860 | 0.270430 | − | 0.962740i | \(-0.412834\pi\) | ||||
0.270430 | + | 0.962740i | \(0.412834\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 23.0515i | − 0.108223i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 536.178i | − 2.49385i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −46.8813 | −0.214070 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 69.6629 | 0.315217 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.6810i | 0.128615i | 0.997930 | + | 0.0643073i | \(0.0204838\pi\) | ||||
−0.997930 | + | 0.0643073i | \(0.979516\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −135.606 | −0.602693 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 266.857i | − 1.17558i | −0.809013 | − | 0.587791i | \(-0.799998\pi\) | ||||
0.809013 | − | 0.587791i | \(-0.200002\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 333.709i | 1.45724i | 0.684917 | + | 0.728621i | \(0.259839\pi\) | ||||
−0.684917 | + | 0.728621i | \(0.740161\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 171.449 | 0.735834 | 0.367917 | − | 0.929859i | \(-0.380071\pi\) | ||||
0.367917 | + | 0.929859i | \(0.380071\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 184.992 | 0.787198 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 147.030i | 0.620380i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −143.422 | −0.600092 | −0.300046 | − | 0.953925i | \(-0.597002\pi\) | ||||
−0.300046 | + | 0.953925i | \(0.597002\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 133.666i | − 0.554631i | −0.960779 | − | 0.277315i | \(-0.910555\pi\) | ||||
0.960779 | − | 0.277315i | \(-0.0894447\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.538i | 1.00222i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.0190 | −0.109389 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.5414 | −0.0583993 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 330.489i | − 1.31669i | −0.752716 | − | 0.658345i | \(-0.771257\pi\) | ||||
0.752716 | − | 0.658345i | \(-0.228743\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 545.370 | 2.15561 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 235.556i | − 0.923751i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 314.754i | 1.22473i | 0.790577 | + | 0.612363i | \(0.209781\pi\) | ||||
−0.790577 | + | 0.612363i | \(0.790219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 72.8357 | 0.279064 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 367.843 | 1.39864 | 0.699320 | − | 0.714808i | \(-0.253486\pi\) | ||||
0.699320 | + | 0.714808i | \(0.253486\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 495.653i | − 1.87039i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 156.123 | 0.584729 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 345.780i | 1.28543i | 0.766107 | + | 0.642713i | \(0.222191\pi\) | ||||
−0.766107 | + | 0.642713i | \(0.777809\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 285.011i | − 1.05170i | −0.850577 | − | 0.525851i | \(-0.823747\pi\) | ||||
0.850577 | − | 0.525851i | \(-0.176253\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −236.304 | −0.859288 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 44.2716 | 0.159825 | 0.0799126 | − | 0.996802i | \(-0.474536\pi\) | ||||
0.0799126 | + | 0.996802i | \(0.474536\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 339.421i | − 1.21656i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 328.085 | 1.16756 | 0.583781 | − | 0.811911i | \(-0.301573\pi\) | ||||
0.583781 | + | 0.811911i | \(0.301573\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 492.334i | 1.73970i | 0.493319 | + | 0.869849i | \(0.335784\pi\) | ||||
−0.493319 | + | 0.869849i | \(0.664216\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 91.3615i | 0.320567i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −412.250 | −1.42647 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 74.6803 | 0.256633 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 381.762i | − 1.30294i | −0.758674 | − | 0.651470i | \(-0.774152\pi\) | ||||
0.758674 | − | 0.651470i | \(-0.225848\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −467.752 | −1.58560 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 272.791i | 0.918489i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 114.422i | − 0.382682i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.4838 | −0.0445009 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −147.417 | −0.483334 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 121.613i | 0.396134i | 0.980188 | + | 0.198067i | \(0.0634664\pi\) | ||||
−0.980188 | + | 0.198067i | \(0.936534\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −93.9706 | −0.304112 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 534.326i | − 1.71809i | −0.511901 | − | 0.859044i | \(-0.671059\pi\) | ||||
0.511901 | − | 0.859044i | \(-0.328941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 171.823i | − 0.548956i | −0.961593 | − | 0.274478i | \(-0.911495\pi\) | ||||
0.961593 | − | 0.274478i | \(-0.0885051\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 114.739 | 0.361954 | 0.180977 | − | 0.983487i | \(-0.442074\pi\) | ||||
0.180977 | + | 0.983487i | \(0.442074\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 126.922 | 0.397875 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.1708i | 0.0628374i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 271.983 | 0.842052 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 49.5781i | 0.152548i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 166.094i | 0.507933i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 84.0141 | 0.253819 | 0.126910 | − | 0.991914i | \(-0.459494\pi\) | ||||
0.126910 | + | 0.991914i | \(0.459494\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 59.4677 | 0.178582 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 412.740i | − 1.23206i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.76645 | 0.00820906 | 0.00410453 | − | 0.999992i | \(-0.498693\pi\) | ||||
0.00410453 | + | 0.999992i | \(0.498693\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 117.689i | − 0.347166i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 591.469i | − 1.73451i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −386.904 | −1.12146 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −440.603 | −1.26975 | −0.634875 | − | 0.772615i | \(-0.718948\pi\) | ||||
−0.634875 | + | 0.772615i | \(0.718948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 400.441i | 1.14740i | 0.819067 | + | 0.573698i | \(0.194492\pi\) | ||||
−0.819067 | + | 0.573698i | \(0.805508\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 57.2333 | 0.163058 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 94.2209i | − 0.266915i | −0.991055 | − | 0.133457i | \(-0.957392\pi\) | ||||
0.991055 | − | 0.133457i | \(-0.0426079\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 113.625i | − 0.320070i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 369.162 | 1.02831 | 0.514153 | − | 0.857699i | \(-0.328106\pi\) | ||||
0.514153 | + | 0.857699i | \(0.328106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 255.510 | 0.707785 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 48.6494i | 0.134020i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −231.086 | −0.633112 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 267.748i | − 0.729557i | −0.931094 | − | 0.364779i | \(-0.881145\pi\) | ||||
0.931094 | − | 0.364779i | \(-0.118855\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 481.506i | 1.30489i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −105.916 | −0.283957 | −0.141979 | − | 0.989870i | \(-0.545346\pi\) | ||||
−0.141979 | + | 0.989870i | \(0.545346\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −54.7392 | −0.145971 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 26.6290i | − 0.0706340i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.04037 | −0.0212147 | −0.0106074 | − | 0.999944i | \(-0.503376\pi\) | ||||
−0.0106074 | + | 0.999944i | \(0.503376\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 203.595i | − 0.534370i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 317.869i | 0.829946i | 0.909834 | + | 0.414973i | \(0.136209\pi\) | ||||
−0.909834 | + | 0.414973i | \(0.863791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −582.635 | −1.50552 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −393.345 | −1.01117 | −0.505584 | − | 0.862777i | \(-0.668723\pi\) | ||||
−0.505584 | + | 0.862777i | \(0.668723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1151.81i | 2.94581i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −166.755 | −0.424313 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 724.737i | 1.83478i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 72.2070i | 0.181882i | 0.995856 | + | 0.0909408i | \(0.0289874\pi\) | ||||
−0.995856 | + | 0.0909408i | \(0.971013\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 480.257 | 1.19765 | 0.598824 | − | 0.800881i | \(-0.295635\pi\) | ||||
0.598824 | + | 0.800881i | \(0.295635\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −124.094 | −0.307925 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 235.281i | 0.580940i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 103.627 | 0.254612 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 719.727i | − 1.75972i | −0.475230 | − | 0.879862i | \(-0.657635\pi\) | ||||
0.475230 | − | 0.879862i | \(-0.342365\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 146.805i | 0.357190i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −71.6771 | −0.172716 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.8986 | 0.0573108 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 473.040i | − 1.12897i | −0.825442 | − | 0.564487i | \(-0.809074\pi\) | ||||
0.825442 | − | 0.564487i | \(-0.190926\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 179.357 | 0.426027 | 0.213014 | − | 0.977049i | \(-0.431672\pi\) | ||||
0.213014 | + | 0.977049i | \(0.431672\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 201.020i | − 0.475225i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 499.070i | − 1.17428i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 44.3102 | 0.103287 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −58.2137 | −0.135067 | −0.0675333 | − | 0.997717i | \(-0.521513\pi\) | ||||
−0.0675333 | + | 0.997717i | \(0.521513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 241.364i | 0.557422i | 0.960375 | + | 0.278711i | \(0.0899071\pi\) | ||||
−0.960375 | + | 0.278711i | \(0.910093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −90.0428 | −0.206995 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 446.734i | − 1.02228i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 215.956i | − 0.491927i | −0.969279 | − | 0.245964i | \(-0.920896\pi\) | ||||
0.969279 | − | 0.245964i | \(-0.0791044\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −213.818 | −0.482658 | −0.241329 | − | 0.970443i | \(-0.577583\pi\) | ||||
−0.241329 | + | 0.970443i | \(0.577583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 769.555 | 1.72934 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 145.589i | 0.325702i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −625.904 | −1.39400 | −0.696998 | − | 0.717073i | \(-0.745481\pi\) | ||||
−0.696998 | + | 0.717073i | \(0.745481\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 839.062i | 1.86045i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 74.2386i | − 0.163882i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 606.081 | 1.32622 | 0.663108 | − | 0.748523i | \(-0.269237\pi\) | ||||
0.663108 | + | 0.748523i | \(0.269237\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −576.129 | −1.25518 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 268.244i | 0.581874i | 0.956742 | + | 0.290937i | \(0.0939670\pi\) | ||||
−0.956742 | + | 0.290937i | \(0.906033\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 417.587 | 0.901916 | 0.450958 | − | 0.892545i | \(-0.351082\pi\) | ||||
0.450958 | + | 0.892545i | \(0.351082\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 419.608i | 0.902382i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 236.015i | − 0.505386i | −0.967547 | − | 0.252693i | \(-0.918684\pi\) | ||||
0.967547 | − | 0.252693i | \(-0.0813162\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 296.145 | 0.628759 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1015.29 | −2.14649 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 193.566i | 0.407508i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −538.599 | −1.12914 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 570.507i | 1.19104i | 0.803342 | + | 0.595519i | \(0.203053\pi\) | ||||
−0.803342 | + | 0.595519i | \(0.796947\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 21.7416i | − 0.0452009i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 368.112 | 0.758994 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −56.0345 | −0.115061 | −0.0575303 | − | 0.998344i | \(-0.518323\pi\) | ||||
−0.0575303 | + | 0.998344i | \(0.518323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 78.8411i | 0.161229i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 70.3733 | 0.143326 | 0.0716632 | − | 0.997429i | \(-0.477169\pi\) | ||||
0.0716632 | + | 0.997429i | \(0.477169\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 268.057i | 0.543726i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 597.402i | 1.20687i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 716.646 | 1.43617 | 0.718083 | − | 0.695958i | \(-0.245020\pi\) | ||||
0.718083 | + | 0.695958i | \(0.245020\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 133.682 | 0.266831 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 46.1333i | − 0.0917164i | −0.998948 | − | 0.0458582i | \(-0.985398\pi\) | ||||
0.998948 | − | 0.0458582i | \(-0.0146022\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −66.4639 | −0.131612 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 217.731i | 0.429450i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 336.883i | 0.661852i | 0.943657 | + | 0.330926i | \(0.107361\pi\) | ||||
−0.943657 | + | 0.330926i | \(0.892639\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 223.454 | 0.435583 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −463.197 | −0.899412 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 350.294i | − 0.677551i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 191.459 | 0.368900 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 237.877i | 0.456578i | 0.973593 | + | 0.228289i | \(0.0733131\pi\) | ||||
−0.973593 | + | 0.228289i | \(0.926687\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 847.694i | 1.62083i | 0.585856 | + | 0.810415i | \(0.300758\pi\) | ||||
−0.585856 | + | 0.810415i | \(0.699242\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1249.17 | 2.37034 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1362.86 | 2.57629 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 508.280i | 0.957213i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 176.040 | 0.330282 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 99.4254i | 0.185842i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 367.137i | − 0.683681i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.8830 | −0.0829630 | −0.0414815 | − | 0.999139i | \(-0.513208\pi\) | ||||
−0.0414815 | + | 0.999139i | \(0.513208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 389.074 | 0.716527 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 818.706i | 1.50221i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −400.295 | −0.731800 | −0.365900 | − | 0.930654i | \(-0.619239\pi\) | ||||
−0.365900 | + | 0.930654i | \(0.619239\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 160.190i | 0.291785i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 103.967i | − 0.188688i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −73.5166 | −0.132462 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −185.832 | −0.333631 | −0.166815 | − | 0.985988i | \(-0.553348\pi\) | ||||
−0.166815 | + | 0.985988i | \(0.553348\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 213.014i | 0.381062i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −446.042 | −0.795083 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 73.7683i | − 0.131027i | −0.997852 | − | 0.0655136i | \(-0.979131\pi\) | ||||
0.997852 | − | 0.0655136i | \(-0.0208686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 580.110i | − 1.02674i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 128.128 | 0.225180 | 0.112590 | − | 0.993642i | \(-0.464085\pi\) | ||||
0.112590 | + | 0.993642i | \(0.464085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1139.98 | 1.99646 | 0.998232 | − | 0.0594309i | \(-0.0189286\pi\) | ||||
0.998232 | + | 0.0594309i | \(0.0189286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 93.4557i | − 0.163099i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −819.727 | −1.42561 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 287.859i | 0.498890i | 0.968389 | + | 0.249445i | \(0.0802482\pi\) | ||||
−0.968389 | + | 0.249445i | \(0.919752\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 177.062i | − 0.305806i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −938.551 | −1.60986 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 125.339 | 0.214254 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.5536i | 0.0196825i | 0.999952 | + | 0.00984123i | \(0.00313261\pi\) | ||||
−0.999952 | + | 0.00984123i | \(0.996867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −484.496 | −0.822573 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 52.6482i | 0.0890832i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 128.281i | − 0.216325i | −0.994133 | − | 0.108163i | \(-0.965503\pi\) | ||||
0.994133 | − | 0.108163i | \(-0.0344967\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 390.144 | 0.653507 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −633.531 | −1.05765 | −0.528824 | − | 0.848731i | \(-0.677367\pi\) | ||||
−0.528824 | + | 0.848731i | \(0.677367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 323.899i | 0.538933i | 0.963010 | + | 0.269467i | \(0.0868474\pi\) | ||||
−0.963010 | + | 0.269467i | \(0.913153\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −448.502 | −0.743784 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 239.801i | 0.396366i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 638.673i | − 1.05218i | −0.850429 | − | 0.526090i | \(-0.823658\pi\) | ||||
0.850429 | − | 0.526090i | \(-0.176342\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −73.4938 | −0.120284 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −981.273 | −1.60077 | −0.800386 | − | 0.599485i | \(-0.795372\pi\) | ||||
−0.800386 | + | 0.599485i | \(0.795372\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 595.259i | − 0.967900i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 208.446 | 0.337837 | 0.168919 | − | 0.985630i | \(-0.445972\pi\) | ||||
0.168919 | + | 0.985630i | \(0.445972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 425.590i | − 0.687545i | −0.939053 | − | 0.343772i | \(-0.888295\pi\) | ||||
0.939053 | − | 0.343772i | \(-0.111705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 946.298i | 1.52383i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −740.975 | −1.18556 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 172.999 | 0.275916 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 218.858i | 0.347947i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −575.230 | −0.911616 | −0.455808 | − | 0.890078i | \(-0.650650\pi\) | ||||
−0.455808 | + | 0.890078i | \(0.650650\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 153.306i | 0.242190i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1003.55i | − 1.58040i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −123.470 | −0.193224 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −199.166 | −0.310711 | −0.155356 | − | 0.987859i | \(-0.549652\pi\) | ||||
−0.155356 | + | 0.987859i | \(0.549652\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 898.859i | 1.39791i | 0.715164 | + | 0.698957i | \(0.246352\pi\) | ||||
−0.715164 | + | 0.698957i | \(0.753648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 720.279 | 1.11671 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 386.160i | 0.596848i | 0.954433 | + | 0.298424i | \(0.0964609\pi\) | ||||
−0.954433 | + | 0.298424i | \(0.903539\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 885.719i | 1.36474i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 143.549 | 0.219830 | 0.109915 | − | 0.993941i | \(-0.464942\pi\) | ||||
0.109915 | + | 0.993941i | \(0.464942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −821.965 | −1.25491 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 251.108i | 0.382204i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 251.484 | 0.381614 | 0.190807 | − | 0.981628i | \(-0.438890\pi\) | ||||
0.190807 | + | 0.981628i | \(0.438890\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 366.721i | 0.554797i | 0.960755 | + | 0.277399i | \(0.0894723\pi\) | ||||
−0.960755 | + | 0.277399i | \(0.910528\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 93.5823i | 0.141150i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 440.286 | 0.660099 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.5290 | −0.0575919 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 279.144i | 0.416011i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1082.98 | 1.60919 | 0.804593 | − | 0.593827i | \(-0.202383\pi\) | ||||
0.804593 | + | 0.593827i | \(0.202383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 410.023i | − 0.607442i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 953.601i | − 1.40857i | −0.709918 | − | 0.704284i | \(-0.751268\pi\) | ||||
0.709918 | − | 0.704284i | \(-0.248732\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 358.485 | 0.526410 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 173.809 | 0.254479 | 0.127240 | − | 0.991872i | \(-0.459388\pi\) | ||||
0.127240 | + | 0.991872i | \(0.459388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 723.627i | 1.05639i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −448.291 | −0.652534 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 196.914i | 0.285796i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 211.539i | 0.306135i | 0.988216 | + | 0.153067i | \(0.0489151\pi\) | ||||
−0.988216 | + | 0.153067i | \(0.951085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 117.800 | 0.169497 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1772.08 | −2.54244 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 230.318i | 0.329496i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −757.766 | −1.08098 | −0.540489 | − | 0.841351i | \(-0.681761\pi\) | ||||
−0.540489 | + | 0.841351i | \(0.681761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 84.8852i | − 0.120747i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 248.510i | 0.352497i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −462.742 | −0.652669 | −0.326334 | − | 0.945254i | \(-0.605814\pi\) | ||||
−0.326334 | + | 0.945254i | \(0.605814\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 787.532 | 1.10764 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2051.77i | − 2.87766i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 218.413 | 0.305472 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 192.667i | − 0.268713i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 1255.46i | − 1.74611i | −0.487618 | − | 0.873057i | \(-0.662134\pi\) | ||||
0.487618 | − | 0.873057i | \(-0.337866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 179.562 | 0.248356 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −190.772 | −0.263134 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 190.560i | − 0.262118i | −0.991375 | − | 0.131059i | \(-0.958162\pi\) | ||||
0.991375 | − | 0.131059i | \(-0.0418377\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.37128 | −0.0101115 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2144.27i | − 2.93333i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 892.327i | 1.21736i | 0.793415 | + | 0.608681i | \(0.208301\pi\) | ||||
−0.793415 | + | 0.608681i | \(0.791699\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −781.550 | −1.06045 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.4208 | −0.0343989 | −0.0171995 | − | 0.999852i | \(-0.505475\pi\) | ||||
−0.0171995 | + | 0.999852i | \(0.505475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 36.2963i | − 0.0489828i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 662.948 | 0.892258 | 0.446129 | − | 0.894969i | \(-0.352802\pi\) | ||||
0.446129 | + | 0.894969i | \(0.352802\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 717.631i | 0.963264i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 77.8876i | 0.104267i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1163.23 | −1.54891 | −0.774457 | − | 0.632627i | \(-0.781977\pi\) | ||||
−0.774457 | + | 0.632627i | \(0.781977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 443.966 | 0.589596 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 365.935i | − 0.484682i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −670.569 | −0.885825 | −0.442912 | − | 0.896565i | \(-0.646055\pi\) | ||||
−0.442912 | + | 0.896565i | \(0.646055\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 732.628i | 0.965254i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1358.97i | − 1.78577i | −0.450288 | − | 0.892883i | \(-0.648679\pi\) | ||||
0.450288 | − | 0.892883i | \(-0.351321\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1261.70 | −1.64928 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 185.829 | 0.242281 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1174.06i | 1.52674i | 0.645961 | + | 0.763370i | \(0.276457\pi\) | ||||
−0.645961 | + | 0.763370i | \(0.723543\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −422.828 | −0.548416 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1147.55i | 1.48455i | 0.670098 | + | 0.742273i | \(0.266252\pi\) | ||||
−0.670098 | + | 0.742273i | \(0.733748\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 889.017i | 1.14712i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 687.309 | 0.882297 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −215.156 | −0.275488 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 220.229i | 0.281263i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1459.75 | 1.85956 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 910.396i | − 1.15679i | −0.815756 | − | 0.578397i | \(-0.803679\pi\) | ||||
0.815756 | − | 0.578397i | \(-0.196321\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 494.145i | 0.626292i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 58.5660 | 0.0738538 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 665.840 | 0.837534 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1079.02i | − 1.35386i | −0.736050 | − | 0.676928i | \(-0.763311\pi\) | ||||
0.736050 | − | 0.676928i | \(-0.236689\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 739.813 | 0.925924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 836.233i | − 1.04399i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 437.576i | 0.544927i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −464.507 | −0.575597 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1027.32 | 1.26986 | 0.634930 | − | 0.772569i | \(-0.281029\pi\) | ||||
0.634930 | + | 0.772569i | \(0.281029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 984.329i | − 1.21372i | −0.794808 | − | 0.606861i | \(-0.792428\pi\) | ||||
0.794808 | − | 0.606861i | \(-0.207572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 382.872 | 0.470938 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 388.621i | 0.476836i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 831.663i | 1.01795i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1118.94 | 1.36290 | 0.681449 | − | 0.731866i | \(-0.261350\pi\) | ||||
0.681449 | + | 0.731866i | \(0.261350\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −110.690 | −0.134496 | −0.0672481 | − | 0.997736i | \(-0.521422\pi\) | ||||
−0.0672481 | + | 0.997736i | \(0.521422\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 317.442i | − 0.384778i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −600.694 | −0.726353 | −0.363177 | − | 0.931720i | \(-0.618308\pi\) | ||||
−0.363177 | + | 0.931720i | \(0.618308\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1051.77i | − 1.26872i | −0.773037 | − | 0.634361i | \(-0.781263\pi\) | ||||
0.773037 | − | 0.634361i | \(-0.218737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 59.4727i | 0.0715676i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 658.943 | 0.789153 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1026.29 | 1.22615 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 147.774i | − 0.176131i | −0.996115 | − | 0.0880656i | \(-0.971931\pi\) | ||||
0.996115 | − | 0.0880656i | \(-0.0280685\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −738.534 | −0.878161 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 440.736i | 0.522818i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1073.23i | 1.27010i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −661.382 | −0.779013 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 359.477 | 0.422417 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 773.138i | − 0.906376i | −0.891415 | − | 0.453188i | \(-0.850287\pi\) | ||||
0.891415 | − | 0.453188i | \(-0.149713\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 489.356 | 0.572346 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 941.605i | − 1.09872i | −0.835585 | − | 0.549361i | \(-0.814871\pi\) | ||||
0.835585 | − | 0.549361i | \(-0.185129\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 733.892i | − 0.854356i | −0.904167 | − | 0.427178i | \(-0.859508\pi\) | ||||
0.904167 | − | 0.427178i | \(-0.140492\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −739.946 | −0.857412 | −0.428706 | − | 0.903444i | \(-0.641030\pi\) | ||||
−0.428706 | + | 0.903444i | \(0.641030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 943.734 | 1.09102 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 553.800i | − 0.638754i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1372.34 | 1.57921 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 163.974i | 0.188260i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 400.007i | − 0.458199i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 506.992 | 0.578098 | 0.289049 | − | 0.957314i | \(-0.406661\pi\) | ||||
0.289049 | + | 0.957314i | \(0.406661\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 512.843 | 0.583439 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 112.813i | − 0.128052i | −0.997948 | − | 0.0640258i | \(-0.979606\pi\) | ||||
0.997948 | − | 0.0640258i | \(-0.0203940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −133.113 | −0.150751 | −0.0753754 | − | 0.997155i | \(-0.524016\pi\) | ||||
−0.0753754 | + | 0.997155i | \(0.524016\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 628.359i | − 0.710010i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 489.556i | 0.551923i | 0.961169 | + | 0.275962i | \(0.0889963\pi\) | ||||
−0.961169 | + | 0.275962i | \(0.911004\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 445.519 | 0.500022 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −286.940 | −0.321321 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1809.68i | − 2.02199i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 153.710 | 0.171360 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 477.502i | − 0.531148i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 1982.20i | − 2.20000i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1917.81 | 2.11913 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 259.207 | 0.285785 | 0.142892 | − | 0.989738i | \(-0.454360\pi\) | ||||
0.142892 | + | 0.989738i | \(0.454360\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 72.2227i | 0.0794529i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 752.359 | 0.825860 | 0.412930 | − | 0.910763i | \(-0.364505\pi\) | ||||
0.412930 | + | 0.910763i | \(0.364505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 135.725i | 0.148659i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 198.034i | − 0.216430i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −330.959 | −0.360130 | −0.180065 | − | 0.983655i | \(-0.557631\pi\) | ||||
−0.180065 | + | 0.983655i | \(0.557631\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −163.370 | −0.177384 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.1411i | 0.0489069i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −155.759 | −0.168388 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 503.331i | 0.542968i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 229.551i | 0.247094i | 0.992339 | + | 0.123547i | \(0.0394270\pi\) | ||||
−0.992339 | + | 0.123547i | \(0.960573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 717.792 | 0.769337 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2198.62 | −2.35146 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 503.860i | − 0.537738i | −0.963177 | − | 0.268869i | \(-0.913350\pi\) | ||||
0.963177 | − | 0.268869i | \(-0.0866499\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 230.820 | 0.245815 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1272.07i | − 1.35183i | −0.736979 | − | 0.675916i | \(-0.763748\pi\) | ||||
0.736979 | − | 0.675916i | \(-0.236252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2910.66i | 3.08660i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −972.545 | −1.02698 | −0.513488 | − | 0.858097i | \(-0.671647\pi\) | ||||
−0.513488 | + | 0.858097i | \(0.671647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 91.8062 | 0.0967399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 154.136i | 0.162078i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −345.615 | −0.362660 | −0.181330 | − | 0.983422i | \(-0.558040\pi\) | ||||
−0.181330 | + | 0.983422i | \(0.558040\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 460.659i | − 0.482366i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 170.502i | 0.178163i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1264.21 | −1.31551 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 108.040 | 0.112191 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 872.768i | − 0.904423i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1385.34 | 1.43261 | 0.716306 | − | 0.697786i | \(-0.245831\pi\) | ||||
0.716306 | + | 0.697786i | \(0.245831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 365.371i | 0.377059i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1121.88i | − 1.15538i | −0.816256 | − | 0.577691i | \(-0.803954\pi\) | ||||
0.816256 | − | 0.577691i | \(-0.196046\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −66.6012 | −0.0683089 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 648.848 | 0.664123 | 0.332061 | − | 0.943258i | \(-0.392256\pi\) | ||||
0.332061 | + | 0.943258i | \(0.392256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1457.20i | − 1.48846i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 889.643 | 0.906874 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1913.46i | 1.94655i | 0.229637 | + | 0.973276i | \(0.426246\pi\) | ||||
−0.229637 | + | 0.973276i | \(0.573754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 259.512i | 0.263464i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3521.98 | −3.56115 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −243.968 | −0.246184 | −0.123092 | − | 0.992395i | \(-0.539281\pi\) | ||||
−0.123092 | + | 0.992395i | \(0.539281\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 112.861i | 0.113657i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1923.09 | 1.93275 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 384.602i | − 0.385759i | −0.981222 | − | 0.192880i | \(-0.938217\pi\) | ||||
0.981222 | − | 0.192880i | \(-0.0617827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 179.809i | 0.179989i |
(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 | 784.3.c.g.97.5 | 8 | ||
4.3 | odd | 2 | 392.3.c.b.97.4 | ✓ | 8 | ||
7.2 | even | 3 | 784.3.s.k.129.4 | 16 | |||
7.3 | odd | 6 | 784.3.s.k.705.4 | 16 | |||
7.4 | even | 3 | 784.3.s.k.705.5 | 16 | |||
7.5 | odd | 6 | 784.3.s.k.129.5 | 16 | |||
7.6 | odd | 2 | inner | 784.3.c.g.97.4 | 8 | ||
12.11 | even | 2 | 3528.3.f.e.2449.2 | 8 | |||
28.3 | even | 6 | 392.3.o.d.313.5 | 16 | |||
28.11 | odd | 6 | 392.3.o.d.313.4 | 16 | |||
28.19 | even | 6 | 392.3.o.d.129.4 | 16 | |||
28.23 | odd | 6 | 392.3.o.d.129.5 | 16 | |||
28.27 | even | 2 | 392.3.c.b.97.5 | yes | 8 | ||
84.83 | odd | 2 | 3528.3.f.e.2449.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
392.3.c.b.97.4 | ✓ | 8 | 4.3 | odd | 2 | ||
392.3.c.b.97.5 | yes | 8 | 28.27 | even | 2 | ||
392.3.o.d.129.4 | 16 | 28.19 | even | 6 | |||
392.3.o.d.129.5 | 16 | 28.23 | odd | 6 | |||
392.3.o.d.313.4 | 16 | 28.11 | odd | 6 | |||
392.3.o.d.313.5 | 16 | 28.3 | even | 6 | |||
784.3.c.g.97.4 | 8 | 7.6 | odd | 2 | inner | ||
784.3.c.g.97.5 | 8 | 1.1 | even | 1 | trivial | ||
784.3.s.k.129.4 | 16 | 7.2 | even | 3 | |||
784.3.s.k.129.5 | 16 | 7.5 | odd | 6 | |||
784.3.s.k.705.4 | 16 | 7.3 | odd | 6 | |||
784.3.s.k.705.5 | 16 | 7.4 | even | 3 | |||
3528.3.f.e.2449.2 | 8 | 12.11 | even | 2 | |||
3528.3.f.e.2449.7 | 8 | 84.83 | odd | 2 |