Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,4,Mod(863,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.863");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.f (of order \(2\), degree \(1\), 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: | \(101.955300490\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.58594980096.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 21x^{6} + 341x^{4} - 2100x^{2} + 10000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 863.8 | ||
Root | \(-2.33962 + 1.35078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.863 |
Dual form | 1728.4.f.c.863.7 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 12.8226 | 1.14689 | 0.573444 | − | 0.819245i | \(-0.305607\pi\) | ||||
0.573444 | + | 0.819245i | \(0.305607\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.2094i | 0.929219i | 0.885516 | + | 0.464609i | \(0.153805\pi\) | ||||
−0.885516 | + | 0.464609i | \(0.846195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 28.7466i | − 0.787949i | −0.919121 | − | 0.393974i | \(-0.871100\pi\) | ||||
0.919121 | − | 0.393974i | \(-0.128900\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 33.2716i | 0.709837i | 0.934897 | + | 0.354919i | \(0.115491\pi\) | ||||
−0.934897 | + | 0.354919i | \(0.884509\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 5.37188i | − 0.0766396i | −0.999266 | − | 0.0383198i | \(-0.987799\pi\) | ||||
0.999266 | − | 0.0383198i | \(-0.0122006\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 50.9548 | 0.615254 | 0.307627 | − | 0.951507i | \(-0.400465\pi\) | ||||
0.307627 | + | 0.951507i | \(0.400465\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −210.628 | −1.90952 | −0.954761 | − | 0.297375i | \(-0.903889\pi\) | ||||
−0.954761 | + | 0.297375i | \(0.903889\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 39.4187 | 0.315350 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −83.1384 | −0.532359 | −0.266180 | − | 0.963923i | \(-0.585761\pi\) | ||||
−0.266180 | + | 0.963923i | \(0.585761\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 40.4187i | 0.234175i | 0.993122 | + | 0.117087i | \(0.0373558\pi\) | ||||
−0.993122 | + | 0.117087i | \(0.962644\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 220.669i | 1.06571i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 264.078i | 1.17336i | 0.809820 | + | 0.586678i | \(0.199565\pi\) | ||||
−0.809820 | + | 0.586678i | \(0.800435\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 399.769i | 1.52277i | 0.648303 | + | 0.761383i | \(0.275479\pi\) | ||||
−0.648303 | + | 0.761383i | \(0.724521\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 208.008 | 0.737697 | 0.368849 | − | 0.929489i | \(-0.379752\pi\) | ||||
0.368849 | + | 0.929489i | \(0.379752\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −178.397 | −0.553656 | −0.276828 | − | 0.960919i | \(-0.589283\pi\) | ||||
−0.276828 | + | 0.960919i | \(0.589283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 46.8375 | 0.136552 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 82.3049 | 0.213310 | 0.106655 | − | 0.994296i | \(-0.465986\pi\) | ||||
0.106655 | + | 0.994296i | \(0.465986\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 368.606i | − 0.903688i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 554.056i | − 1.22258i | −0.791409 | − | 0.611288i | \(-0.790652\pi\) | ||||
0.791409 | − | 0.611288i | \(-0.209348\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 349.230i | 0.733022i | 0.930414 | + | 0.366511i | \(0.119448\pi\) | ||||
−0.930414 | + | 0.366511i | \(0.880552\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 426.628i | 0.814103i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −664.263 | −1.21123 | −0.605617 | − | 0.795756i | \(-0.707074\pi\) | ||||
−0.605617 | + | 0.795756i | \(0.707074\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −399.769 | −0.668223 | −0.334111 | − | 0.942534i | \(-0.608436\pi\) | ||||
−0.334111 | + | 0.942534i | \(0.608436\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −802.212 | −1.28619 | −0.643095 | − | 0.765786i | \(-0.722350\pi\) | ||||
−0.643095 | + | 0.765786i | \(0.722350\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 494.712 | 0.732177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 322.653i | 0.459510i | 0.973248 | + | 0.229755i | \(0.0737925\pi\) | ||||
−0.973248 | + | 0.229755i | \(0.926207\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 148.502i | 0.196388i | 0.995167 | + | 0.0981938i | \(0.0313065\pi\) | ||||
−0.995167 | + | 0.0981938i | \(0.968693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 68.8814i | − 0.0878969i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 826.397i | 0.984246i | 0.870526 | + | 0.492123i | \(0.163779\pi\) | ||||
−0.870526 | + | 0.492123i | \(0.836221\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −572.584 | −0.659594 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 653.372 | 0.705627 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1115.47 | 1.16762 | 0.583808 | − | 0.811892i | \(-0.301562\pi\) | ||||
0.583808 | + | 0.811892i | \(0.301562\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −998.495 | −0.983702 | −0.491851 | − | 0.870679i | \(-0.663680\pi\) | ||||
−0.491851 | + | 0.870679i | \(0.663680\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 664.653i | 0.635827i | 0.948120 | + | 0.317914i | \(0.102982\pi\) | ||||
−0.948120 | + | 0.317914i | \(0.897018\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1533.94i | 1.38590i | 0.720984 | + | 0.692952i | \(0.243690\pi\) | ||||
−0.720984 | + | 0.692952i | \(0.756310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 350.838i | 0.308295i | 0.988048 | + | 0.154148i | \(0.0492631\pi\) | ||||
−0.988048 | + | 0.154148i | \(0.950737\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2036.45i | − 1.69533i | −0.530528 | − | 0.847667i | \(-0.678006\pi\) | ||||
0.530528 | − | 0.847667i | \(-0.321994\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2700.80 | −2.19001 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 92.4467 | 0.0712149 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 504.631 | 0.379137 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1097.37 | −0.785216 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 930.237i | − 0.649962i | −0.945720 | − | 0.324981i | \(-0.894642\pi\) | ||||
0.945720 | − | 0.324981i | \(-0.105358\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 2161.23i | − 1.44143i | −0.693230 | − | 0.720716i | \(-0.743813\pi\) | ||||
0.693230 | − | 0.720716i | \(-0.256187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 876.899i | 0.571705i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 1333.60i | − 0.831660i | −0.909442 | − | 0.415830i | \(-0.863491\pi\) | ||||
0.909442 | − | 0.415830i | \(-0.136509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −896.434 | −0.547011 | −0.273505 | − | 0.961870i | \(-0.588183\pi\) | ||||
−0.273505 | + | 0.961870i | \(0.588183\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 956.447 | 0.559315 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1066.05 | −0.610556 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3510.05 | 1.92990 | 0.964949 | − | 0.262436i | \(-0.0845260\pi\) | ||||
0.964949 | + | 0.262436i | \(0.0845260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 57.2593i | 0.0308589i | 0.999881 | + | 0.0154294i | \(0.00491154\pi\) | ||||
−0.999881 | + | 0.0154294i | \(0.995088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 518.273i | 0.268572i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3194.95i | 1.62411i | 0.583583 | + | 0.812054i | \(0.301650\pi\) | ||||
−0.583583 | + | 0.812054i | \(0.698350\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 3624.78i | − 1.77436i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3329.21 | −1.59978 | −0.799888 | − | 0.600149i | \(-0.795108\pi\) | ||||
−0.799888 | + | 0.600149i | \(0.795108\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 545.934 | 0.252968 | 0.126484 | − | 0.991969i | \(-0.459631\pi\) | ||||
0.126484 | + | 0.991969i | \(0.459631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1090.00 | 0.496131 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 565.396 | 0.248475 | 0.124238 | − | 0.992252i | \(-0.460351\pi\) | ||||
0.124238 | + | 0.992252i | \(0.460351\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 678.372i | 0.293029i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 101.379i | 0.0423319i | 0.999776 | + | 0.0211660i | \(0.00673784\pi\) | ||||
−0.999776 | + | 0.0211660i | \(0.993262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2627.48i | 1.07900i | 0.841985 | + | 0.539501i | \(0.181387\pi\) | ||||
−0.841985 | + | 0.539501i | \(0.818613\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3386.17i | 1.34571i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −154.424 | −0.0603881 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2306.17 | 0.873656 | 0.436828 | − | 0.899545i | \(-0.356102\pi\) | ||||
0.436828 | + | 0.899545i | \(0.356102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2712.68 | −1.01173 | −0.505863 | − | 0.862614i | \(-0.668826\pi\) | ||||
−0.505863 | + | 0.862614i | \(0.668826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4816.24 | −1.74184 | −0.870922 | − | 0.491422i | \(-0.836477\pi\) | ||||
−0.870922 | + | 0.491422i | \(0.836477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 82.2343i | − 0.0292936i | −0.999893 | − | 0.0146468i | \(-0.995338\pi\) | ||||
0.999893 | − | 0.0146468i | \(-0.00466240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1430.76i | − 0.494678i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5126.07i | 1.74644i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 1464.78i | − 0.484789i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1687.94 | −0.550722 | −0.275361 | − | 0.961341i | \(-0.588797\pi\) | ||||
−0.275361 | + | 0.961341i | \(0.588797\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2667.21 | 0.846056 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −695.581 | −0.217600 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 178.731 | 0.0544016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3379.31i | − 1.01478i | −0.861718 | − | 0.507388i | \(-0.830611\pi\) | ||||
0.861718 | − | 0.507388i | \(-0.169389\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4987.10i | 1.45818i | 0.684420 | + | 0.729088i | \(0.260055\pi\) | ||||
−0.684420 | + | 0.729088i | \(0.739945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5767.34i | 1.66426i | 0.554577 | + | 0.832132i | \(0.312880\pi\) | ||||
−0.554577 | + | 0.832132i | \(0.687120\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3144.43i | 0.884114i | 0.896987 | + | 0.442057i | \(0.145751\pi\) | ||||
−0.896987 | + | 0.442057i | \(0.854249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2287.51 | −0.634981 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3305.59 | −0.894647 | −0.447324 | − | 0.894372i | \(-0.647623\pi\) | ||||
−0.447324 | + | 0.894372i | \(0.647623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1831.69 | 0.489584 | 0.244792 | − | 0.969576i | \(-0.421280\pi\) | ||||
0.244792 | + | 0.969576i | \(0.421280\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 600.578 | 0.156610 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1695.35i | 0.436730i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 1414.56i | − 0.355721i | −0.984056 | − | 0.177860i | \(-0.943082\pi\) | ||||
0.984056 | − | 0.177860i | \(-0.0569176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6054.85i | 1.50461i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 1328.23i | − 0.322384i | −0.986923 | − | 0.161192i | \(-0.948466\pi\) | ||||
0.986923 | − | 0.161192i | \(-0.0515339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4544.62 | −1.09030 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2183.74 | −0.511996 | −0.255998 | − | 0.966677i | \(-0.582404\pi\) | ||||
−0.255998 | + | 0.966677i | \(0.582404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1055.36 | 0.244643 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3062.47 | 0.694133 | 0.347067 | − | 0.937840i | \(-0.387178\pi\) | ||||
0.347067 | + | 0.937840i | \(0.387178\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6305.23i | 1.41334i | 0.707543 | + | 0.706670i | \(0.249804\pi\) | ||||
−0.707543 | + | 0.706670i | \(0.750196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 1133.16i | − 0.248480i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 445.733i | 0.0966841i | 0.998831 | + | 0.0483420i | \(0.0153937\pi\) | ||||
−0.998831 | + | 0.0483420i | \(0.984606\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7864.20i | 1.66953i | 0.550604 | + | 0.834767i | \(0.314397\pi\) | ||||
−0.550604 | + | 0.834767i | \(0.685603\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7392.73 | −1.55283 | −0.776417 | − | 0.630219i | \(-0.782965\pi\) | ||||
−0.776417 | + | 0.630219i | \(0.782965\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6879.77 | −1.41498 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4884.14 | 0.994126 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2427.07 | 0.483929 | 0.241965 | − | 0.970285i | \(-0.422208\pi\) | ||||
0.241965 | + | 0.970285i | \(0.422208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 7104.43i | − 1.40216i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 7007.94i | − 1.35545i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3579.69i | 0.685482i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4478.03i | 0.840693i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3728.66 | −0.693179 | −0.346590 | − | 0.938017i | \(-0.612660\pi\) | ||||
−0.346590 | + | 0.938017i | \(0.612660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1560.35 | 0.284499 | 0.142249 | − | 0.989831i | \(-0.454566\pi\) | ||||
0.142249 | + | 0.989831i | \(0.454566\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2962.43 | 0.534973 | 0.267486 | − | 0.963562i | \(-0.413807\pi\) | ||||
0.267486 | + | 0.963562i | \(0.413807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2345.65 | −0.415599 | −0.207800 | − | 0.978171i | \(-0.566630\pi\) | ||||
−0.207800 | + | 0.978171i | \(0.566630\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2389.95i | 0.419472i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 273.723i | − 0.0471528i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1311.53i | 0.223847i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3070.10i | − 0.514468i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6705.67 | −1.11353 | −0.556763 | − | 0.830672i | \(-0.687957\pi\) | ||||
−0.556763 | + | 0.830672i | \(0.687957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8517.57 | −1.38915 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12348.8 | −1.99608 | −0.998041 | − | 0.0625651i | \(-0.980072\pi\) | ||||
−0.998041 | + | 0.0625651i | \(0.980072\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1161.90 | 0.184518 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6708.86i | 1.05611i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10627.8i | 1.64419i | 0.569354 | + | 0.822093i | \(0.307194\pi\) | ||||
−0.569354 | + | 0.822093i | \(0.692806\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5775.38i | 0.885813i | 0.896568 | + | 0.442907i | \(0.146053\pi\) | ||||
−0.896568 | + | 0.442907i | \(0.853947\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 4470.41i | − 0.674040i | −0.941498 | − | 0.337020i | \(-0.890581\pi\) | ||||
0.941498 | − | 0.337020i | \(-0.109419\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5126.07 | −0.766376 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6357.57 | −0.934651 | −0.467326 | − | 0.884085i | \(-0.654782\pi\) | ||||
−0.467326 | + | 0.884085i | \(0.654782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4262.61 | −0.621463 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10286.4 | −1.47511 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 10116.1i | − 1.43884i | −0.694576 | − | 0.719419i | \(-0.744408\pi\) | ||||
0.694576 | − | 0.719419i | \(-0.255592\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1416.42i | 0.198212i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 11393.6i | − 1.58160i | −0.612076 | − | 0.790799i | \(-0.709665\pi\) | ||||
0.612076 | − | 0.790799i | \(-0.290335\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2766.15i | − 0.377888i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7733.63 | −1.04815 | −0.524076 | − | 0.851671i | \(-0.675589\pi\) | ||||
−0.524076 | + | 0.851671i | \(0.675589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4461.92 | 0.595283 | 0.297641 | − | 0.954678i | \(-0.403800\pi\) | ||||
0.297641 | + | 0.954678i | \(0.403800\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6343.48 | 0.839724 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1915.57 | 0.249674 | 0.124837 | − | 0.992177i | \(-0.460159\pi\) | ||||
0.124837 | + | 0.992177i | \(0.460159\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1131.47i | 0.146345i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4137.25i | 0.527006i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6336.81i | 0.801096i | 0.916276 | + | 0.400548i | \(0.131180\pi\) | ||||
−0.916276 | + | 0.400548i | \(0.868820\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7255.80i | 0.903584i | 0.892123 | + | 0.451792i | \(0.149215\pi\) | ||||
−0.892123 | + | 0.451792i | \(0.850785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1344.80 | −0.166226 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7591.36 | 0.924545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1825.12 | −0.220651 | −0.110326 | − | 0.993895i | \(-0.535189\pi\) | ||||
−0.110326 | + | 0.993895i | \(0.535189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9534.96 | 1.13604 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1904.18i | 0.225234i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 6707.50i | − 0.782059i | −0.920378 | − | 0.391030i | \(-0.872119\pi\) | ||||
0.920378 | − | 0.391030i | \(-0.127881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5228.42i | 0.605267i | 0.953107 | + | 0.302633i | \(0.0978658\pi\) | ||||
−0.953107 | + | 0.302633i | \(0.902134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 211.753i | − 0.0241683i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6010.03 | −0.681138 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14973.8 | 1.67347 | 0.836733 | − | 0.547610i | \(-0.184462\pi\) | ||||
0.836733 | + | 0.547610i | \(0.184462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5512.13 | 0.611769 | 0.305885 | − | 0.952069i | \(-0.401048\pi\) | ||||
0.305885 | + | 0.952069i | \(0.401048\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −10732.5 | −1.17484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 10803.7i | − 1.17456i | −0.809384 | − | 0.587280i | \(-0.800199\pi\) | ||||
0.809384 | − | 0.587280i | \(-0.199801\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 10661.8i | − 1.14347i | −0.820437 | − | 0.571736i | \(-0.806270\pi\) | ||||
0.820437 | − | 0.571736i | \(-0.193730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10596.5i | 1.12882i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 1971.98i | − 0.207269i | −0.994615 | − | 0.103634i | \(-0.966953\pi\) | ||||
0.994615 | − | 0.103634i | \(-0.0330472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11492.0 | 1.19986 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7342.00 | −0.756480 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5583.23 | 0.571494 | 0.285747 | − | 0.958305i | \(-0.407758\pi\) | ||||
0.285747 | + | 0.958305i | \(0.407758\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8969.56 | 0.906191 | 0.453095 | − | 0.891462i | \(-0.350320\pi\) | ||||
0.453095 | + | 0.891462i | \(0.350320\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11521.2i | 1.15645i | 0.815879 | + | 0.578223i | \(0.196254\pi\) | ||||
−0.815879 | + | 0.578223i | \(0.803746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 12869.1i | − 1.27518i | −0.770374 | − | 0.637592i | \(-0.779930\pi\) | ||||
0.770374 | − | 0.637592i | \(-0.220070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 11431.6i | − 1.12550i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 5979.54i | − 0.581268i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2008.57 | 0.194020 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13860.7 | 1.32216 | 0.661078 | − | 0.750317i | \(-0.270099\pi\) | ||||
0.661078 | + | 0.750317i | \(0.270099\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8786.31 | −0.832892 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14303.2 | 1.33912 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2514.65i | 0.233983i | 0.993133 | + | 0.116992i | \(0.0373251\pi\) | ||||
−0.993133 | + | 0.116992i | \(0.962675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18593.4i | 1.70897i | 0.519473 | + | 0.854487i | \(0.326128\pi\) | ||||
−0.519473 | + | 0.854487i | \(0.673872\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 446.610i | 0.0407998i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 6879.77i | − 0.620925i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16174.6 | 1.45105 | 0.725525 | − | 0.688196i | \(-0.241597\pi\) | ||||
0.725525 | + | 0.688196i | \(0.241597\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12844.3 | 1.13857 | 0.569284 | − | 0.822141i | \(-0.307220\pi\) | ||||
0.569284 | + | 0.822141i | \(0.307220\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12803.3 | −1.12820 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6251.37 | −0.544375 | −0.272188 | − | 0.962244i | \(-0.587747\pi\) | ||||
−0.272188 | + | 0.962244i | \(0.587747\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 13805.6i | − 1.19515i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8522.57i | 0.729222i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5128.31i | 0.436253i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 16125.0i | − 1.35595i | −0.735084 | − | 0.677976i | \(-0.762857\pi\) | ||||
0.735084 | − | 0.677976i | \(-0.237143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1658.32 | −0.138649 | −0.0693243 | − | 0.997594i | \(-0.522084\pi\) | ||||
−0.0693243 | + | 0.997594i | \(0.522084\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 217.125 | 0.0179471 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32197.2 | 2.64627 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13300.9 | −1.08092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19669.1i | 1.58948i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1346.42i | − 0.107596i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13148.3i | 1.04490i | 0.852670 | + | 0.522450i | \(0.174982\pi\) | ||||
−0.852670 | + | 0.522450i | \(0.825018\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4498.65i | 0.353580i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11717.8 | 0.915939 | 0.457970 | − | 0.888968i | \(-0.348577\pi\) | ||||
0.457970 | + | 0.888968i | \(0.348577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4236.30 | −0.327536 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5552.66 | −0.426986 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9502.18 | −0.722837 | −0.361418 | − | 0.932404i | \(-0.617707\pi\) | ||||
−0.361418 | + | 0.932404i | \(0.617707\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6920.78i | 0.523645i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14447.8i | 1.08153i | 0.841172 | + | 0.540767i | \(0.181866\pi\) | ||||
−0.841172 | + | 0.540767i | \(0.818134\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 26112.5i | − 1.94436i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 9621.31i | − 0.708869i | −0.935081 | − | 0.354434i | \(-0.884673\pi\) | ||||
0.935081 | − | 0.354434i | \(-0.115327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19427.4 | 1.42384 | 0.711919 | − | 0.702261i | \(-0.247826\pi\) | ||||
0.711919 | + | 0.702261i | \(0.247826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8302.70 | −0.602168 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18385.3 | −1.32650 | −0.663249 | − | 0.748399i | \(-0.730823\pi\) | ||||
−0.663249 | + | 0.748399i | \(0.730823\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2555.62 | −0.182487 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2365.99i | − 0.168078i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 17584.3i | − 1.23642i | −0.786011 | − | 0.618212i | \(-0.787857\pi\) | ||||
0.786011 | − | 0.618212i | \(-0.212143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2059.53i | 0.144077i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10005.0i | 0.692841i | 0.938079 | + | 0.346420i | \(0.112603\pi\) | ||||
−0.938079 | + | 0.346420i | \(0.887397\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1185.41 | 0.0816755 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11002.4 | 0.750493 | 0.375246 | − | 0.926925i | \(-0.377558\pi\) | ||||
0.375246 | + | 0.926925i | \(0.377558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17683.9 | 1.20024 | 0.600118 | − | 0.799912i | \(-0.295120\pi\) | ||||
0.600118 | + | 0.799912i | \(0.295120\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6470.68 | 0.434827 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 237.714i | − 0.0158954i | −0.999968 | − | 0.00794772i | \(-0.997470\pi\) | ||||
0.999968 | − | 0.00794772i | \(-0.00252986\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 5935.55i | − 0.393006i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 22429.5i | − 1.47784i | −0.673790 | − | 0.738922i | \(-0.735335\pi\) | ||||
0.673790 | − | 0.738922i | \(-0.264665\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 16485.8i | − 1.07568i | −0.843047 | − | 0.537840i | \(-0.819240\pi\) | ||||
0.843047 | − | 0.537840i | \(-0.180760\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5726.03 | 0.371807 | 0.185904 | − | 0.982568i | \(-0.440479\pi\) | ||||
0.185904 | + | 0.982568i | \(0.440479\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14221.8 | −0.914580 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18998.5 | −1.21590 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1418.60 | 0.0899255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 18543.9i | − 1.16992i | −0.811060 | − | 0.584962i | \(-0.801109\pi\) | ||||
0.811060 | − | 0.584962i | \(-0.198891\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 11928.0i | − 0.745433i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1558.36i | 0.0969300i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24637.0i | 1.51810i | 0.651032 | + | 0.759050i | \(0.274336\pi\) | ||||
−0.651032 | + | 0.759050i | \(0.725664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8950.99 | −0.548977 | −0.274489 | − | 0.961590i | \(-0.588509\pi\) | ||||
−0.274489 | + | 0.961590i | \(0.588509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30126.3 | −1.83058 | −0.915292 | − | 0.402791i | \(-0.868040\pi\) | ||||
−0.915292 | + | 0.402791i | \(0.868040\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15927.2 | −0.963327 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10405.4 | 0.623578 | 0.311789 | − | 0.950151i | \(-0.399072\pi\) | ||||
0.311789 | + | 0.950151i | \(0.399072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 27712.6i | − 1.65316i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23235.2i | 1.37347i | 0.726910 | + | 0.686733i | \(0.240956\pi\) | ||||
−0.726910 | + | 0.686733i | \(0.759044\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 29301.5i | − 1.72420i | −0.506739 | − | 0.862099i | \(-0.669149\pi\) | ||||
0.506739 | − | 0.862099i | \(-0.330851\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 11244.1i | 0.655682i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17511.3 | 1.01655 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10039.2 | 0.577584 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19148.5 | 1.09676 | 0.548380 | − | 0.836229i | \(-0.315245\pi\) | ||||
0.548380 | + | 0.836229i | \(0.315245\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29994.5 | 1.70278 | 0.851391 | − | 0.524532i | \(-0.175760\pi\) | ||||
0.851391 | + | 0.524532i | \(0.175760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19196.5i | 1.08497i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 5269.84i | − 0.295234i | −0.989045 | − | 0.147617i | \(-0.952840\pi\) | ||||
0.989045 | − | 0.147617i | \(-0.0471603\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 17100.2i | − 0.953820i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2738.42i | 0.151416i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20435.8 | 1.12506 | 0.562528 | − | 0.826778i | \(-0.309829\pi\) | ||||
0.562528 | + | 0.826778i | \(0.309829\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11494.6 | −0.627360 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2147.51 | 0.116704 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12475.4 | −0.672165 | −0.336082 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336082 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13456.0i | 0.721912i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 17183.5i | − 0.914075i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 25405.1i | − 1.34571i | −0.739773 | − | 0.672856i | \(-0.765067\pi\) | ||||
0.739773 | − | 0.672856i | \(-0.234933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8513.32i | − 0.447162i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12264.1 | 0.641472 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4498.65 | −0.233340 | −0.116670 | − | 0.993171i | \(-0.537222\pi\) | ||||
−0.116670 | + | 0.993171i | \(0.537222\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11438.3 | −0.590823 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3277.21 | −0.167879 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 25698.4i | − 1.31101i | −0.755193 | − | 0.655503i | \(-0.772457\pi\) | ||||
0.755193 | − | 0.655503i | \(-0.227543\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1117.40i | − 0.0565368i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16107.3i | − 0.811644i | −0.913952 | − | 0.405822i | \(-0.866985\pi\) | ||||
0.913952 | − | 0.405822i | \(-0.133015\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19095.3i | 0.954390i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −799.199 | −0.0397822 | −0.0198911 | − | 0.999802i | \(-0.506332\pi\) | ||||
−0.0198911 | + | 0.999802i | \(0.506332\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17026.9 | −0.840722 | −0.420361 | − | 0.907357i | \(-0.638097\pi\) | ||||
−0.420361 | + | 0.907357i | \(0.638097\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45008.0 | 2.21338 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −26398.2 | −1.28781 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32026.8i | 1.55616i | 0.628167 | + | 0.778078i | \(0.283805\pi\) | ||||
−0.628167 | + | 0.778078i | \(0.716195\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 734.212i | 0.0353917i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 39862.3i | − 1.91390i | −0.290261 | − | 0.956948i | \(-0.593742\pi\) | ||||
0.290261 | − | 0.956948i | \(-0.406258\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22217.8i | 1.05834i | 0.848517 | + | 0.529168i | \(0.177496\pi\) | ||||
−0.848517 | + | 0.529168i | \(0.822504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6037.70 | −0.286474 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18434.3 | 0.867829 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26842.6 | −1.25874 | −0.629369 | − | 0.777106i | \(-0.716687\pi\) | ||||
−0.629369 | + | 0.777106i | \(0.716687\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −36697.0 | −1.70750 | −0.853752 | − | 0.520680i | \(-0.825679\pi\) | ||||
−0.853752 | + | 0.520680i | \(0.825679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1593.26i | 0.0738470i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20370.1i | 0.936887i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11492.0i | 0.526525i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40967.5i | 1.86267i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8335.44 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35046.0 | 1.57534 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11619.4 | −0.520326 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35046.2 | 1.55759 | 0.778796 | − | 0.627277i | \(-0.215831\pi\) | ||||
0.778796 | + | 0.627277i | \(0.215831\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 958.327i | 0.0424320i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23060.9i | 1.01345i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 46479.0i | − 2.03499i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6462.51i | 0.280853i | 0.990091 | + | 0.140426i | \(0.0448473\pi\) | ||||
−0.990091 | + | 0.140426i | \(0.955153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42136.5 | 1.82443 | 0.912214 | − | 0.409713i | \(-0.134371\pi\) | ||||
0.912214 | + | 0.409713i | \(0.134371\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42689.0 | −1.83476 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10599.0 | 0.453871 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5323.70 | −0.226307 | −0.113154 | − | 0.993577i | \(-0.536095\pi\) | ||||
−0.113154 | + | 0.993577i | \(0.536095\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12239.0i | 0.518379i | 0.965826 | + | 0.259190i | \(0.0834555\pi\) | ||||
−0.965826 | + | 0.259190i | \(0.916545\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33925.6i | 1.42649i | 0.700915 | + | 0.713245i | \(0.252775\pi\) | ||||
−0.700915 | + | 0.713245i | \(0.747225\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28954.3i | 1.21306i | 0.795061 | + | 0.606529i | \(0.207439\pi\) | ||||
−0.795061 | + | 0.606529i | \(0.792561\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 251.605i | − 0.0104653i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7000.29 | 0.290126 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7786.74 | −0.320415 | −0.160208 | − | 0.987083i | \(-0.551216\pi\) | ||||
−0.160208 | + | 0.987083i | \(0.551216\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17477.0 | −0.716594 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13976.6 | 0.569006 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8684.39i | 0.352301i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 55622.3i | − 2.24055i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 39947.8i | − 1.60350i | −0.597658 | − | 0.801751i | \(-0.703902\pi\) | ||||
0.597658 | − | 0.801751i | \(-0.296098\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 38134.2i | − 1.52000i | −0.649924 | − | 0.759999i | \(-0.725199\pi\) | ||||
0.649924 | − | 0.759999i | \(-0.274801\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29831.8 | 1.18492 | 0.592461 | − | 0.805599i | \(-0.298156\pi\) | ||||
0.592461 | + | 0.805599i | \(0.298156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4059.65 | −0.160130 | −0.0800649 | − | 0.996790i | \(-0.525513\pi\) | ||||
−0.0800649 | + | 0.996790i | \(0.525513\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7249.84 | 0.284973 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9275.19 | 0.362070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 22101.1i | − 0.859779i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 18885.1i | − 0.729638i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21003.1i | 0.808692i | 0.914606 | + | 0.404346i | \(0.132501\pi\) | ||||
−0.914606 | + | 0.404346i | \(0.867499\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 49825.5i | − 1.90541i | −0.303898 | − | 0.952704i | \(-0.598288\pi\) | ||||
0.303898 | − | 0.952704i | \(-0.401712\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9171.08 | 0.349526 | 0.174763 | − | 0.984611i | \(-0.444084\pi\) | ||||
0.174763 | + | 0.984611i | \(0.444084\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26060.2 | 0.986488 | 0.493244 | − | 0.869891i | \(-0.335811\pi\) | ||||
0.493244 | + | 0.869891i | \(0.335811\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16008.8 | 0.603957 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9090.17 | −0.340639 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1299.94i | 0.0485499i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 3360.35i | − 0.124665i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 442.132i | − 0.0163480i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 33691.1i | 1.23749i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35645.0 | 1.30493 | 0.652467 | − | 0.757817i | \(-0.273734\pi\) | ||||
0.652467 | + | 0.757817i | \(0.273734\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10782.5 | −0.392141 | −0.196070 | − | 0.980590i | \(-0.562818\pi\) | ||||
−0.196070 | + | 0.980590i | \(0.562818\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4268.92 | 0.154743 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 37193.4 | 1.33941 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20191.1i | 0.724748i | 0.932033 | + | 0.362374i | \(0.118034\pi\) | ||||
−0.932033 | + | 0.362374i | \(0.881966\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 13300.9i | − 0.474329i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10409.6i | 0.370018i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 37161.0i | − 1.31239i | −0.754590 | − | 0.656196i | \(-0.772164\pi\) | ||||
0.754590 | − | 0.656196i | \(-0.227836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2386.59 | 0.0840144 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1980.11 | −0.0692583 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6784.39 | 0.236538 | 0.118269 | − | 0.992982i | \(-0.462265\pi\) | ||||
0.118269 | + | 0.992982i | \(0.462265\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10527.9 | 0.364718 | 0.182359 | − | 0.983232i | \(-0.441627\pi\) | ||||
0.182359 | + | 0.983232i | \(0.441627\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 84202.5i | − 2.90775i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 20262.1i | − 0.695281i | −0.937628 | − | 0.347640i | \(-0.886983\pi\) | ||||
0.937628 | − | 0.347640i | \(-0.113017\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 26690.9i | − 0.912985i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 21691.3i | − 0.737304i | −0.929567 | − | 0.368652i | \(-0.879819\pi\) | ||||
0.929567 | − | 0.368652i | \(-0.120181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29571.0 | 1.00198 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 22950.5 | 0.772794 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28157.3 | 0.945162 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34783.6 | −1.16034 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22236.5i | 0.739481i | 0.929135 | + | 0.369741i | \(0.120553\pi\) | ||||
−0.929135 | + | 0.369741i | \(0.879447\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27549.5i | 0.910511i | 0.890361 | + | 0.455255i | \(0.150452\pi\) | ||||
−0.890361 | + | 0.455255i | \(0.849548\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 15427.1i | − 0.508293i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 34859.6i | − 1.14151i | −0.821120 | − | 0.570756i | \(-0.806650\pi\) | ||||
0.821120 | − | 0.570756i | \(-0.193350\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23756.1 | 0.775535 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52096.9 | 1.69037 | 0.845184 | − | 0.534475i | \(-0.179491\pi\) | ||||
0.845184 | + | 0.534475i | \(0.179491\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −61756.7 | −1.99770 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43812.4 | −1.40865 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53076.9i | 1.70135i | 0.525688 | + | 0.850677i | \(0.323808\pi\) | ||||
−0.525688 | + | 0.850677i | \(0.676192\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 1054.46i | − 0.0335965i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 2814.79i | − 0.0894136i | −0.999000 | − | 0.0447068i | \(-0.985765\pi\) | ||||
0.999000 | − | 0.0447068i | \(-0.0142354\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.4.f.c.863.8 | yes | 8 | |
3.2 | odd | 2 | 1728.4.f.g.863.2 | yes | 8 | ||
4.3 | odd | 2 | 1728.4.f.g.863.7 | yes | 8 | ||
8.3 | odd | 2 | 1728.4.f.g.863.1 | yes | 8 | ||
8.5 | even | 2 | inner | 1728.4.f.c.863.2 | yes | 8 | |
12.11 | even | 2 | inner | 1728.4.f.c.863.1 | ✓ | 8 | |
24.5 | odd | 2 | 1728.4.f.g.863.8 | yes | 8 | ||
24.11 | even | 2 | inner | 1728.4.f.c.863.7 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1728.4.f.c.863.1 | ✓ | 8 | 12.11 | even | 2 | inner | |
1728.4.f.c.863.2 | yes | 8 | 8.5 | even | 2 | inner | |
1728.4.f.c.863.7 | yes | 8 | 24.11 | even | 2 | inner | |
1728.4.f.c.863.8 | yes | 8 | 1.1 | even | 1 | trivial | |
1728.4.f.g.863.1 | yes | 8 | 8.3 | odd | 2 | ||
1728.4.f.g.863.2 | yes | 8 | 3.2 | odd | 2 | ||
1728.4.f.g.863.7 | yes | 8 | 4.3 | odd | 2 | ||
1728.4.f.g.863.8 | yes | 8 | 24.5 | odd | 2 |