Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2432,2,Mod(1217,2432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2432, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2432.1217");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2432 = 2^{7} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2432.c (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: | \(19.4196177716\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 170x^{16} + 6593x^{12} + 64168x^{8} + 95760x^{4} + 4096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{19} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1217.9 | ||
Root | \(-0.323980 + 0.323980i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2432.1217 |
Dual form | 2432.2.c.j.1217.12 |
$q$-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 \(\left(\mathbb{Z}/2432\mathbb{Z}\right)^\times\).
\(n\) | \(1407\) | \(1921\) | \(2053\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 0.458177i | − 0.264529i | −0.991214 | − | 0.132264i | \(-0.957775\pi\) | ||||
0.991214 | − | 0.132264i | \(-0.0422248\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 3.00397i | − 1.34341i | −0.740817 | − | 0.671707i | \(-0.765561\pi\) | ||||
0.740817 | − | 0.671707i | \(-0.234439\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.21624 | −0.837660 | −0.418830 | − | 0.908065i | \(-0.637560\pi\) | ||||
−0.418830 | + | 0.908065i | \(0.637560\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.79007 | 0.930025 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.02382i | 1.51474i | 0.652987 | + | 0.757369i | \(0.273516\pi\) | ||||
−0.652987 | + | 0.757369i | \(0.726484\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.22021i | − 1.44783i | −0.689892 | − | 0.723913i | \(-0.742342\pi\) | ||||
0.689892 | − | 0.723913i | \(-0.257658\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.37635 | −0.355372 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.73025 | 1.87486 | 0.937430 | − | 0.348174i | \(-0.113198\pi\) | ||||
0.937430 | + | 0.348174i | \(0.113198\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 1.00000i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.01543i | 0.221585i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.51613 | 1.35871 | 0.679353 | − | 0.733811i | \(-0.262260\pi\) | ||||
0.679353 | + | 0.733811i | \(0.262260\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.02382 | −0.804764 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 2.65288i | − 0.510547i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.23562i | 0.415145i | 0.978220 | + | 0.207572i | \(0.0665563\pi\) | ||||
−0.978220 | + | 0.207572i | \(0.933444\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.33566 | −0.599103 | −0.299551 | − | 0.954080i | \(-0.596837\pi\) | ||||
−0.299551 | + | 0.954080i | \(0.596837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.30180 | 0.400692 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.65751i | 1.12533i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.45208i | − 0.238720i | −0.992851 | − | 0.119360i | \(-0.961916\pi\) | ||||
0.992851 | − | 0.119360i | \(-0.0380843\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.39178 | −0.382991 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.16461 | −0.494228 | −0.247114 | − | 0.968986i | \(-0.579482\pi\) | ||||
−0.247114 | + | 0.968986i | \(0.579482\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 2.16101i | − 0.329551i | −0.986331 | − | 0.164776i | \(-0.947310\pi\) | ||||
0.986331 | − | 0.164776i | \(-0.0526900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 8.38129i | − 1.24941i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.95256 | 1.45173 | 0.725865 | − | 0.687837i | \(-0.241440\pi\) | ||||
0.725865 | + | 0.687837i | \(0.241440\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.08828 | −0.298325 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 3.54182i | − 0.495954i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.66810i | 0.915935i | 0.888969 | + | 0.457967i | \(0.151422\pi\) | ||||
−0.888969 | + | 0.457967i | \(0.848578\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.0914 | 2.03492 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.458177 | −0.0606871 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 3.89126i | − 0.506599i | −0.967388 | − | 0.253299i | \(-0.918484\pi\) | ||||
0.967388 | − | 0.253299i | \(-0.0815157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 7.05259i | − 0.902991i | −0.892273 | − | 0.451496i | \(-0.850891\pi\) | ||||
0.892273 | − | 0.451496i | \(-0.149109\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.18347 | −0.779044 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.6813 | −1.94503 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 13.2767i | − 1.62201i | −0.585041 | − | 0.811004i | \(-0.698922\pi\) | ||||
0.585041 | − | 0.811004i | \(-0.301078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 2.98554i | − 0.359417i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.72840 | 0.679836 | 0.339918 | − | 0.940455i | \(-0.389601\pi\) | ||||
0.339918 | + | 0.940455i | \(0.389601\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.89754 | 0.690254 | 0.345127 | − | 0.938556i | \(-0.387836\pi\) | ||||
0.345127 | + | 0.938556i | \(0.387836\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.84362i | 0.212883i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 11.1340i | − 1.26884i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9369 | −1.79304 | −0.896522 | − | 0.442998i | \(-0.853915\pi\) | ||||
−0.896522 | + | 0.442998i | \(0.853915\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.15473 | 0.794970 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.71734i | − 0.956852i | −0.878128 | − | 0.478426i | \(-0.841207\pi\) | ||||
0.878128 | − | 0.478426i | \(-0.158793\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 23.2214i | − 2.51871i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.02431 | 0.109818 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.79938 | 0.402734 | 0.201367 | − | 0.979516i | \(-0.435462\pi\) | ||||
0.201367 | + | 0.979516i | \(0.435462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.5692i | 1.21279i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.52833i | 0.158480i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00397 | −0.308201 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.94645 | −0.400701 | −0.200351 | − | 0.979724i | \(-0.564208\pi\) | ||||
−0.200351 | + | 0.979724i | \(0.564208\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.0168i | 1.40874i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 6.32025i | − 0.628888i | −0.949276 | − | 0.314444i | \(-0.898182\pi\) | ||||
0.949276 | − | 0.314444i | \(-0.101818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.71201 | −0.464288 | −0.232144 | − | 0.972681i | \(-0.574574\pi\) | ||||
−0.232144 | + | 0.972681i | \(0.574574\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.05032 | 0.297681 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 18.5550i | 1.79378i | 0.442249 | + | 0.896892i | \(0.354181\pi\) | ||||
−0.442249 | + | 0.896892i | \(0.645819\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.25995i | 0.886942i | 0.896289 | + | 0.443471i | \(0.146253\pi\) | ||||
−0.896289 | + | 0.443471i | \(0.853747\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.665309 | −0.0631483 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.97386 | −0.750118 | −0.375059 | − | 0.927001i | \(-0.622378\pi\) | ||||
−0.375059 | + | 0.927001i | \(0.622378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 19.5742i | − 1.82531i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 14.5648i | − 1.34651i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.1321 | −1.57050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.2387 | −1.29443 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.44995i | 0.130738i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.93242i | − 0.262284i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.32912 | −0.739090 | −0.369545 | − | 0.929213i | \(-0.620486\pi\) | ||||
−0.369545 | + | 0.929213i | \(0.620486\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.990126 | −0.0871758 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 16.3831i | − 1.43140i | −0.698408 | − | 0.715700i | \(-0.746108\pi\) | ||||
0.698408 | − | 0.715700i | \(-0.253892\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.21624i | 0.192172i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.96916 | −0.685876 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2267 | −1.38634 | −0.693172 | − | 0.720772i | \(-0.743788\pi\) | ||||
−0.693172 | + | 0.720772i | \(0.743788\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.38904i | 0.372273i | 0.982524 | + | 0.186137i | \(0.0595967\pi\) | ||||
−0.982524 | + | 0.186137i | \(0.940403\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 4.56004i | − 0.384024i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 26.2254 | 2.19308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.71574 | 0.557712 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.956802i | 0.0789157i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 1.28542i | − 0.105306i | −0.998613 | − | 0.0526528i | \(-0.983232\pi\) | ||||
0.998613 | − | 0.0526528i | \(-0.0167677\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.07295 | 0.738346 | 0.369173 | − | 0.929361i | \(-0.379641\pi\) | ||||
0.369173 | + | 0.929361i | \(0.379641\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.5680 | 1.74367 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.0202i | 0.804844i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.13656i | 0.250325i | 0.992136 | + | 0.125162i | \(0.0399452\pi\) | ||||
−0.992136 | + | 0.125162i | \(0.960055\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.05517 | 0.242291 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.4413 | −1.13813 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.9640i | − 1.17207i | −0.810286 | − | 0.586035i | \(-0.800688\pi\) | ||||
0.810286 | − | 0.586035i | \(-0.199312\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 6.91453i | − 0.538295i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.0799 | −1.63121 | −0.815607 | − | 0.578606i | \(-0.803597\pi\) | ||||
−0.815607 | + | 0.578606i | \(0.803597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.2506 | −1.09620 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.79007i | − 0.213362i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 23.7808i | − 1.80802i | −0.427510 | − | 0.904011i | \(-0.640609\pi\) | ||||
0.427510 | − | 0.904011i | \(-0.359391\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.91775 | 0.674118 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.78289 | −0.134010 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 14.3018i | − 1.06897i | −0.845179 | − | 0.534483i | \(-0.820506\pi\) | ||||
0.845179 | − | 0.534483i | \(-0.179494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.9014i | 1.03328i | 0.856203 | + | 0.516640i | \(0.172818\pi\) | ||||
−0.856203 | + | 0.516640i | \(0.827182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.23133 | −0.238867 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.36199 | −0.320700 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 38.8353i | 2.83992i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.87942i | 0.427665i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.17747 | 0.157557 | 0.0787783 | − | 0.996892i | \(-0.474898\pi\) | ||||
0.0787783 | + | 0.996892i | \(0.474898\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.6410 | 1.91766 | 0.958831 | − | 0.283978i | \(-0.0916541\pi\) | ||||
0.958831 | + | 0.283978i | \(0.0916541\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.18483i | 0.514516i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.8500i | − 1.48550i | −0.669570 | − | 0.742749i | \(-0.733521\pi\) | ||||
0.669570 | − | 0.742749i | \(-0.266479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.24710 | 0.301069 | 0.150535 | − | 0.988605i | \(-0.451901\pi\) | ||||
0.150535 | + | 0.988605i | \(0.451901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.08308 | −0.429068 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.95468i | − 0.347750i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.50637i | 0.663954i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.1805 | 1.26363 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.02382 | 0.347505 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1134i | 1.24698i | 0.781833 | + | 0.623488i | \(0.214285\pi\) | ||||
−0.781833 | + | 0.623488i | \(0.785715\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 2.62462i | − 0.179836i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.49161 | −0.442724 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.39263 | 0.501845 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 2.70212i | − 0.182592i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 40.3535i | − 2.71447i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.71952 | −0.249078 | −0.124539 | − | 0.992215i | \(-0.539745\pi\) | ||||
−0.124539 | + | 0.992215i | \(0.539745\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.2267 | −0.748450 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.8318i | 1.18354i | 0.806108 | + | 0.591769i | \(0.201570\pi\) | ||||
−0.806108 | + | 0.591769i | \(0.798430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 13.5159i | − 0.893158i | −0.894744 | − | 0.446579i | \(-0.852642\pi\) | ||||
0.894744 | − | 0.446579i | \(-0.147358\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.10134 | −0.335644 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.5061 | 1.21238 | 0.606189 | − | 0.795321i | \(-0.292698\pi\) | ||||
0.606189 | + | 0.795321i | \(0.292698\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 29.8972i | − 1.95028i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.30194i | 0.474312i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.6874 | 0.755995 | 0.377997 | − | 0.925807i | \(-0.376613\pi\) | ||||
0.377997 | + | 0.925807i | \(0.376613\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2701 | 0.661554 | 0.330777 | − | 0.943709i | \(-0.392689\pi\) | ||||
0.330777 | + | 0.943709i | \(0.392689\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 11.2368i | − 0.720839i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.27312i | 0.400775i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.22021 | −0.332154 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.99409 | −0.253115 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.1064i | 1.58470i | 0.610066 | + | 0.792350i | \(0.291143\pi\) | ||||
−0.610066 | + | 0.792350i | \(0.708857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.7358i | 2.05808i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.6395 | −0.666273 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.5905 | 0.785374 | 0.392687 | − | 0.919672i | \(-0.371546\pi\) | ||||
0.392687 | + | 0.919672i | \(0.371546\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.21815i | 0.199966i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.23755i | 0.386095i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.7749 | 1.40436 | 0.702181 | − | 0.711999i | \(-0.252210\pi\) | ||||
0.702181 | + | 0.711999i | \(0.252210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.0308 | 1.23048 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1.74079i | − 0.106535i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.0271i | 1.03816i | 0.854725 | + | 0.519081i | \(0.173726\pi\) | ||||
−0.854725 | + | 0.519081i | \(0.826274\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.19591 | 0.497866 | 0.248933 | − | 0.968521i | \(-0.419920\pi\) | ||||
0.248933 | + | 0.968521i | \(0.419920\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.30076 | 0.320817 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 20.2149i | − 1.21901i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.7174i | 1.12462i | 0.826927 | + | 0.562309i | \(0.190087\pi\) | ||||
−0.826927 | + | 0.562309i | \(0.809913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.30675 | −0.557180 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.189116 | −0.0112817 | −0.00564087 | − | 0.999984i | \(-0.501796\pi\) | ||||
−0.00564087 | + | 0.999984i | \(0.501796\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6357i | 0.632226i | 0.948722 | + | 0.316113i | \(0.102378\pi\) | ||||
−0.948722 | + | 0.316113i | \(0.897622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.37635i | 0.0815279i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.01353 | 0.413995 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.7567 | 2.51510 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.80817i | 0.105997i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.6765i | 1.61688i | 0.588580 | + | 0.808439i | \(0.299687\pi\) | ||||
−0.588580 | + | 0.808439i | \(0.700313\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.6892 | −0.680572 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.3276 | 0.773345 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 34.0155i | − 1.96717i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.78932i | 0.276052i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.89579 | −0.166359 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.1857 | −1.21309 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 8.14707i | − 0.464978i | −0.972599 | − | 0.232489i | \(-0.925313\pi\) | ||||
0.972599 | − | 0.232489i | \(-0.0746869\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.15894i | 0.122818i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.1283 | −0.631030 | −0.315515 | − | 0.948921i | \(-0.602177\pi\) | ||||
−0.315515 | + | 0.948921i | \(0.602177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.2647 | 0.580198 | 0.290099 | − | 0.956997i | \(-0.406312\pi\) | ||||
0.290099 | + | 0.956997i | \(0.406312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.5750i | 1.04658i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.14866i | 0.401509i | 0.979642 | + | 0.200754i | \(0.0643393\pi\) | ||||
−0.979642 | + | 0.200754i | \(0.935661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.2314 | −0.628836 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.50150 | 0.474508 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 7.73025i | − 0.430122i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.0052i | 1.16516i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.24270 | 0.234622 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.0573 | −1.21606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 28.4370i | − 1.56304i | −0.623881 | − | 0.781519i | \(-0.714445\pi\) | ||||
0.623881 | − | 0.781519i | \(-0.285555\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 4.05140i | − 0.222016i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.8828 | −2.17903 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.9197 | −1.03062 | −0.515311 | − | 0.857003i | \(-0.672324\pi\) | ||||
−0.515311 | + | 0.857003i | \(0.672324\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.65344i | 0.198428i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 16.7578i | − 0.907484i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1418 | 1.08756 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.96847 | −0.482846 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.34140i | 0.125693i | 0.998023 | + | 0.0628466i | \(0.0200179\pi\) | ||||
−0.998023 | + | 0.0628466i | \(0.979982\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 14.8506i | − 0.794935i | −0.917616 | − | 0.397468i | \(-0.869889\pi\) | ||||
0.917616 | − | 0.397468i | \(-0.130111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.8486 | −0.739183 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.9690 | −0.903168 | −0.451584 | − | 0.892229i | \(-0.649141\pi\) | ||||
−0.451584 | + | 0.892229i | \(0.649141\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 17.2079i | − 0.913302i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.84953i | 0.415441i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.2107 | −1.70002 | −0.850008 | − | 0.526770i | \(-0.823403\pi\) | ||||
−0.850008 | + | 0.526770i | \(0.823403\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.52387i | 0.342414i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 17.7160i | − 0.927298i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2366 | 0.534347 | 0.267173 | − | 0.963648i | \(-0.413910\pi\) | ||||
0.267173 | + | 0.963648i | \(0.413910\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.82948 | −0.459644 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 14.7781i | − 0.767242i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.1908i | 1.56322i | 0.623767 | + | 0.781610i | \(0.285601\pi\) | ||||
−0.623767 | + | 0.781610i | \(0.714399\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.34357 | −0.0693815 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.6704 | 0.601057 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 15.9865i | − 0.821173i | −0.911822 | − | 0.410586i | \(-0.865324\pi\) | ||||
0.911822 | − | 0.410586i | \(-0.134676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.81622i | 0.195511i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.6961 | 1.15971 | 0.579857 | − | 0.814718i | \(-0.303108\pi\) | ||||
0.579857 | + | 0.814718i | \(0.303108\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −33.4461 | −1.70457 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 6.02938i | − 0.306491i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 12.1956i | − 0.618341i | −0.951007 | − | 0.309170i | \(-0.899949\pi\) | ||||
0.951007 | − | 0.309170i | \(-0.100051\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.3713 | 2.54738 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.50638 | −0.378647 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 47.8740i | 2.40880i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7422i | 0.539137i | 0.962981 | + | 0.269568i | \(0.0868810\pi\) | ||||
−0.962981 | + | 0.269568i | \(0.913119\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.01543 | 0.0508351 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.65983 | −0.282639 | −0.141319 | − | 0.989964i | \(-0.545134\pi\) | ||||
−0.141319 | + | 0.989964i | \(0.545134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.4129i | 0.867396i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 21.4926i | − 1.06797i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.29497 | 0.361598 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.6645 | 1.36792 | 0.683960 | − | 0.729520i | \(-0.260256\pi\) | ||||
0.683960 | + | 0.729520i | \(0.260256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.43473i | 0.366728i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.62396i | 0.424357i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −26.1866 | −1.28545 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.01096 | 0.0984770 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.91763i | 0.337948i | 0.985620 | + | 0.168974i | \(0.0540454\pi\) | ||||
−0.985620 | + | 0.168974i | \(0.945955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.07015i | 0.149630i | 0.997197 | + | 0.0748150i | \(0.0238366\pi\) | ||||
−0.997197 | + | 0.0748150i | \(0.976163\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 27.7684 | 1.35014 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.1051 | −1.50882 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.6302i | 0.756400i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 12.0159i | − 0.580132i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2015 | −0.635893 | −0.317946 | − | 0.948109i | \(-0.602993\pi\) | ||||
−0.317946 | + | 0.948109i | \(0.602993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1544 | −0.968559 | −0.484279 | − | 0.874913i | \(-0.660918\pi\) | ||||
−0.484279 | + | 0.874913i | \(0.660918\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 3.07700i | − 0.147531i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 6.51613i | − 0.311709i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.72144 | −0.0821601 | −0.0410800 | − | 0.999156i | \(-0.513080\pi\) | ||||
−0.0410800 | + | 0.999156i | \(0.513080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.82645 | −0.277450 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.0168i | 1.80623i | 0.429395 | + | 0.903117i | \(0.358727\pi\) | ||||
−0.429395 | + | 0.903117i | \(0.641273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 11.4132i | − 0.541039i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.588950 | −0.0278564 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.1861 | −1.28299 | −0.641496 | − | 0.767127i | \(-0.721686\pi\) | ||||
−0.641496 | + | 0.767127i | \(0.721686\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 15.8984i | − 0.748626i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 4.15702i | − 0.195314i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34.7536 | 1.62927 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.8069 | −0.739415 | −0.369708 | − | 0.929148i | \(-0.620542\pi\) | ||||
−0.369708 | + | 0.929148i | \(0.620542\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 20.5074i | − 0.957204i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.7741i | 1.38672i | 0.720593 | + | 0.693358i | \(0.243870\pi\) | ||||
−0.720593 | + | 0.693358i | \(0.756130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8339 | 0.549967 | 0.274984 | − | 0.961449i | \(-0.411328\pi\) | ||||
0.274984 | + | 0.961449i | \(0.411328\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.59104 | 0.212904 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 30.6052i | − 1.41624i | −0.706091 | − | 0.708121i | \(-0.749543\pi\) | ||||
0.706091 | − | 0.708121i | \(-0.250457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.4244i | 1.35869i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.43710 | 0.0662181 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.8565 | 0.499184 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.02382i | 0.184625i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.6045i | 0.851842i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.3908 | 0.566150 | 0.283075 | − | 0.959098i | \(-0.408645\pi\) | ||||
0.283075 | + | 0.959098i | \(0.408645\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.58015 | −0.345625 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.61668i | 0.301069i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.8550i | 0.538308i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.61617 | −0.345122 | −0.172561 | − | 0.984999i | \(-0.555204\pi\) | ||||
−0.172561 | + | 0.984999i | \(0.555204\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.85616 | −0.310046 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 3.09291i | − 0.139581i | −0.997562 | − | 0.0697906i | \(-0.977767\pi\) | ||||
0.997562 | − | 0.0697906i | \(-0.0222331\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.2819i | 0.778338i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 42.1061 | 1.89253 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.6955 | −0.569472 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.55042i | 0.293237i | 0.989193 | + | 0.146618i | \(0.0468390\pi\) | ||||
−0.989193 | + | 0.146618i | \(0.953161\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.65835i | 0.431503i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −34.9332 | −1.55760 | −0.778798 | − | 0.627275i | \(-0.784170\pi\) | ||||
−0.778798 | + | 0.627275i | \(0.784170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.9858 | −0.844858 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.52928i | 0.289976i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 10.6461i | − 0.471882i | −0.971767 | − | 0.235941i | \(-0.924183\pi\) | ||||
0.971767 | − | 0.235941i | \(-0.0758171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0704 | −0.578199 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.65288 | −0.117128 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.1547i | 0.623732i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 49.9999i | 2.19899i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.8958 | −0.478274 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.7087 | 1.47681 | 0.738403 | − | 0.674359i | \(-0.235580\pi\) | ||||
0.738403 | + | 0.674359i | \(0.235580\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 3.61224i | − 0.157952i | −0.996877 | − | 0.0789761i | \(-0.974835\pi\) | ||||
0.996877 | − | 0.0789761i | \(-0.0251651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 4.08591i | − 0.178324i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.7855 | −1.12323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4599 | 0.846084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 10.8569i | − 0.471149i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.5199i | 0.715556i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 55.7388 | 2.40980 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.55276 | −0.282772 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 10.4911i | − 0.451885i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.1835i | 1.94259i | 0.237876 | + | 0.971295i | \(0.423549\pi\) | ||||
−0.237876 | + | 0.971295i | \(0.576451\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.36929 | 0.273332 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.8166 | 1.19153 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.9716i | 1.11047i | 0.831695 | + | 0.555233i | \(0.187371\pi\) | ||||
−0.831695 | + | 0.555233i | \(0.812629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 19.6772i | − 0.839804i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.23562 | 0.0952408 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 35.3201 | 1.50196 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.99857i | 0.0848344i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.5515i | 1.16739i | 0.811972 | + | 0.583697i | \(0.198394\pi\) | ||||
−0.811972 | + | 0.583697i | \(0.801606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.2809 | −0.477132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.7935 | 0.751241 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.8531i | 0.625985i | 0.949756 | + | 0.312992i | \(0.101331\pi\) | ||||
−0.949756 | + | 0.312992i | \(0.898669\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.9532i | 1.00772i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15.8566 | −0.665915 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.86281 | 0.203859 | 0.101930 | − | 0.994792i | \(-0.467498\pi\) | ||||
0.101930 | + | 0.994792i | \(0.467498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.6960i | 0.907948i | 0.891015 | + | 0.453974i | \(0.149994\pi\) | ||||
−0.891015 | + | 0.453974i | \(0.850006\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 0.997669i | − 0.0416782i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.2197 | −1.09344 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.5083 | 1.18682 | 0.593409 | − | 0.804901i | \(-0.297782\pi\) | ||||
0.593409 | + | 0.804901i | \(0.297782\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 12.2063i | − 0.507277i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.3197i | 0.801517i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −33.4993 | −1.38740 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −43.7521 | −1.80893 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 22.5133i | − 0.929224i | −0.885514 | − | 0.464612i | \(-0.846194\pi\) | ||||
0.885514 | − | 0.464612i | \(-0.153806\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.33566i | 0.137444i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.55298 | −0.392957 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0209 | −0.452574 | −0.226287 | − | 0.974061i | \(-0.572659\pi\) | ||||
−0.226287 | + | 0.974061i | \(0.572659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 51.4642i | 2.10983i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.94593i | − 0.0796414i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7308 | 0.765319 | 0.382659 | − | 0.923890i | \(-0.375008\pi\) | ||||
0.382659 | + | 0.923890i | \(0.375008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.8859 | −0.607209 | −0.303604 | − | 0.952798i | \(-0.598190\pi\) | ||||
−0.303604 | + | 0.952798i | \(0.598190\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 37.0430i | − 1.50851i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 42.7727i | 1.73896i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.9701 | 1.54116 | 0.770579 | − | 0.637345i | \(-0.219967\pi\) | ||||
0.770579 | + | 0.637345i | \(0.219967\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.27012 | −0.0919900 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 51.9544i | − 2.10185i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 28.5379i | − 1.15264i | −0.817226 | − | 0.576318i | \(-0.804489\pi\) | ||||
0.817226 | − | 0.576318i | \(-0.195511\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.35560 | 0.175635 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.91835 | −0.157747 | −0.0788733 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788733 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5.37059i | − 0.215862i | −0.994158 | − | 0.107931i | \(-0.965577\pi\) | ||||
0.994158 | − | 0.107931i | \(-0.0344226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 17.2865i | − 0.693684i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.42035 | −0.337354 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.9280 | −1.15712 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.30180i | − 0.0919250i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 11.2249i | − 0.447567i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6483 | −0.742377 | −0.371189 | − | 0.928557i | \(-0.621050\pi\) | ||||
−0.371189 | + | 0.928557i | \(0.621050\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.29913 | 0.329861 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 25.0204i | 0.992905i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.9012i | 0.431923i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.9827 | 0.632264 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 42.2857 | 1.67018 | 0.835092 | − | 0.550111i | \(-0.185415\pi\) | ||||
0.835092 | + | 0.550111i | \(0.185415\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.4426i | 0.727305i | 0.931535 | + | 0.363652i | \(0.118470\pi\) | ||||
−0.931535 | + | 0.363652i | \(0.881530\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.97431i | 0.117113i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.19012 | −0.0861024 | −0.0430512 | − | 0.999073i | \(-0.513708\pi\) | ||||
−0.0430512 | + | 0.999073i | \(0.513708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.5490 | 0.767364 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 3.38714i | − 0.132752i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.8208i | 1.71484i | 0.514617 | + | 0.857420i | \(0.327934\pi\) | ||||
−0.514617 | + | 0.857420i | \(0.672066\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −49.2144 | −1.92296 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.4546 | 0.641954 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.0297i | 0.429657i | 0.976652 | + | 0.214829i | \(0.0689193\pi\) | ||||
−0.976652 | + | 0.214829i | \(0.931081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 7.49137i | − 0.291381i | −0.989330 | − | 0.145690i | \(-0.953460\pi\) | ||||
0.989330 | − | 0.145690i | \(-0.0465403\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.4890 | −0.718055 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.65751 | 0.258167 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.5676i | 0.564060i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.70420i | 0.0658882i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.4309 | 1.36780 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.6195 | −1.33448 | −0.667242 | − | 0.744841i | \(-0.732525\pi\) | ||||
−0.667242 | + | 0.744841i | \(0.732525\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.6747i | 0.410870i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.0201i | 1.11533i | 0.830066 | + | 0.557666i | \(0.188303\pi\) | ||||
−0.830066 | + | 0.557666i | \(0.811697\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.74629 | 0.335652 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.17012 | 0.313080 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 13.3799i | − 0.511966i | −0.966681 | − | 0.255983i | \(-0.917601\pi\) | ||||
0.966681 | − | 0.255983i | \(-0.0823991\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.7446i | 1.86244i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.19269 | −0.236266 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.8089 | 1.32611 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.7415i | 1.54988i | 0.632035 | + | 0.774940i | \(0.282220\pi\) | ||||
−0.632035 | + | 0.774940i | \(0.717780\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 31.0646i | − 1.18005i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.1845 | 0.500118 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.4632 | −0.926609 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 8.47909i | − 0.320709i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 43.7760i | − 1.65340i | −0.562645 | − | 0.826698i | \(-0.690216\pi\) | ||||
0.562645 | − | 0.826698i | \(-0.309784\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.45208 | −0.0547662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.6982 | −0.515904 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.0072i | 0.526795i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 26.0155i | − 0.977031i | −0.872555 | − | 0.488516i | \(-0.837538\pi\) | ||||
0.872555 | − | 0.488516i | \(-0.162462\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −44.4652 | −1.66758 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.7356 | −0.814005 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 78.7801i | − 2.94621i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 5.35490i | − 0.199982i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.3051 | −1.16748 | −0.583741 | − | 0.811940i | \(-0.698412\pi\) | ||||
−0.583741 | + | 0.811940i | \(0.698412\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4430 | 0.388916 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 4.70552i | − 0.175000i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 8.99574i | − 0.334093i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.31403 | −0.271262 | −0.135631 | − | 0.990759i | \(-0.543306\pi\) | ||||
−0.135631 | + | 0.990759i | \(0.543306\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 16.3158 | 0.604287 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 16.7051i | − 0.617862i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 13.0935i | − 0.483620i | −0.970324 | − | 0.241810i | \(-0.922259\pi\) | ||||
0.970324 | − | 0.241810i | \(-0.0777411\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.87420 | 0.106016 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 66.6997 | 2.45692 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.5782i | 0.389124i | 0.980890 | + | 0.194562i | \(0.0623285\pi\) | ||||
−0.980890 | + | 0.194562i | \(0.937672\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.39178i | 0.0878642i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.6180 | −0.866460 | −0.433230 | − | 0.901283i | \(-0.642626\pi\) | ||||
−0.433230 | + | 0.901283i | \(0.642626\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.86136 | −0.141469 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 24.3220i | − 0.889896i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 41.1225i | − 1.50258i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.5994 | −0.897644 | −0.448822 | − | 0.893621i | \(-0.648156\pi\) | ||||
−0.448822 | + | 0.893621i | \(0.648156\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.5032 | 0.419199 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 27.2548i | − 0.991905i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 3.03483i | − 0.110303i | −0.998478 | − | 0.0551514i | \(-0.982436\pi\) | ||||
0.998478 | − | 0.0551514i | \(-0.0175642\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.9988 | 0.544423 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.15330 | 0.295557 | 0.147778 | − | 0.989020i | \(-0.452788\pi\) | ||||
0.147778 | + | 0.989020i | \(0.452788\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 20.5223i | − 0.742956i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 64.7894i | − 2.34247i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −20.3132 | −0.733466 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.2744 | −0.514747 | −0.257374 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257374 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 5.76868i | − 0.207754i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.2404i | 1.62718i | 0.581437 | + | 0.813591i | \(0.302491\pi\) | ||||
−0.581437 | + | 0.813591i | \(0.697509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.4221 | 0.482136 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.47448 | 0.0528968 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.16461i | 0.113384i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.7784i | 1.02977i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.93084 | 0.211951 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.42212 | 0.336290 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 50.1656i | − 1.78821i | −0.447856 | − | 0.894106i | \(-0.647812\pi\) | ||||
0.447856 | − | 0.894106i | \(-0.352188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 10.4349i | − 0.371494i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.6720 | 0.628344 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −36.8160 | −1.30737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 9.17764i | − 0.325497i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 21.7396i | − 0.770056i | −0.922905 | − | 0.385028i | \(-0.874192\pi\) | ||||
0.922905 | − | 0.385028i | \(-0.125808\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 76.9357 | 2.72179 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.6006 | 0.374552 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.6281i | 1.04555i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 43.3812i | 1.52899i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.80144 | 0.274624 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.48695 | 0.333543 | 0.166772 | − | 0.985996i | \(-0.446666\pi\) | ||||
0.166772 | + | 0.985996i | \(0.446666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 22.6529i | − 0.795450i | −0.917505 | − | 0.397725i | \(-0.869800\pi\) | ||||
0.917505 | − | 0.397725i | \(-0.130200\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 3.75518i | − 0.131700i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −44.9513 | −1.57458 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.16101 | −0.0756042 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 32.2790i | 1.12792i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 26.4552i | − 0.923292i | −0.887064 | − | 0.461646i | \(-0.847259\pi\) | ||||
0.887064 | − | 0.461646i | \(-0.152741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.1129 | 1.22396 | 0.611980 | − | 0.790873i | \(-0.290373\pi\) | ||||
0.611980 | + | 0.790873i | \(0.290373\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.26202 | −0.322462 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.4003i | 0.952803i | 0.879228 | + | 0.476402i | \(0.158059\pi\) | ||||
−0.879228 | + | 0.476402i | \(0.841941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.2213i | 0.875972i | 0.898982 | + | 0.437986i | \(0.144308\pi\) | ||||
−0.898982 | + | 0.437986i | \(0.855692\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.57588 | 0.297494 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.1429 | −0.559319 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 63.3234i | 2.19140i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.84912i | 0.305870i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.8869 | 1.27348 | 0.636738 | − | 0.771080i | \(-0.280283\pi\) | ||||
0.636738 | + | 0.771080i | \(0.280283\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.0020 | 0.827655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.0866488i | 0.00298434i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.8082i | 1.47265i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.5565 | 1.08429 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.87303 | 0.167242 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 9.46193i | − 0.324351i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.36746i | − 0.115300i | −0.998337 | − | 0.0576499i | \(-0.981639\pi\) | ||||
0.998337 | − | 0.0576499i | \(-0.0183607\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.38129 | −0.286634 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16.0416 | 0.547970 | 0.273985 | − | 0.961734i | \(-0.411658\pi\) | ||||
0.273985 | + | 0.961734i | \(0.411658\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7310i | 0.502614i | 0.967907 | + | 0.251307i | \(0.0808603\pi\) | ||||
−0.967907 | + | 0.251307i | \(0.919140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 3.21344i | − 0.109514i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41.3034 | 1.40598 | 0.702991 | − | 0.711198i | \(-0.251847\pi\) | ||||
0.702991 | + | 0.711198i | \(0.251847\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −71.4368 | −2.42892 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 19.5901i | − 0.665316i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 80.0642i | − 2.71599i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −69.3071 | −2.34838 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11.0109 | −0.372662 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.49895i | 0.219704i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 3.84438i | − 0.129815i | −0.997891 | − | 0.0649077i | \(-0.979325\pi\) | ||||
0.997891 | − | 0.0649077i | \(-0.0206753\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.6807 | 0.427711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.57677 | −0.154195 | −0.0770976 | − | 0.997024i | \(-0.524565\pi\) | ||||
−0.0770976 | + | 0.997024i | \(0.524565\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.34140i | 0.0787945i | 0.999224 | + | 0.0393972i | \(0.0125438\pi\) | ||||
−0.999224 | + | 0.0393972i | \(0.987456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.35573i | 0.180031i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.1958 | −1.61826 | −0.809129 | − | 0.587631i | \(-0.800061\pi\) | ||||
−0.809129 | + | 0.587631i | \(0.800061\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.4593 | 0.619106 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 35.9441i | 1.20417i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 9.95256i | − 0.333050i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.9621 | −1.43607 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.5851 | −0.520373 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 7.45729i | − 0.248714i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 51.5461i | 1.71725i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.19436 | 0.0730237 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.7593 | 1.38812 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 4.08133i | − 0.135518i | −0.997702 | − | 0.0677592i | \(-0.978415\pi\) | ||||
0.997702 | − | 0.0677592i | \(-0.0215850\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 17.6340i | − 0.584881i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 54.1174 | 1.79299 | 0.896495 | − | 0.443054i | \(-0.146105\pi\) | ||||
0.896495 | + | 0.443054i | \(0.146105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.7943 | 1.44938 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.70682i | 0.320898i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.3089i | 1.19903i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.1252 | −1.05971 | −0.529857 | − | 0.848087i | \(-0.677754\pi\) | ||||
−0.529857 | + | 0.848087i | \(0.677754\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.73280 | −0.123000 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 29.9034i | − 0.984284i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.84290i | 0.192113i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.1469 | −0.431800 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.9339 | −0.358730 | −0.179365 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179365 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.08828i | 0.0684406i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.09875i | 0.166926i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 116.660 | 3.81519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.5172 | 1.51965 | 0.759825 | − | 0.650127i | \(-0.225284\pi\) | ||||
0.759825 | + | 0.650127i | \(0.225284\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 4.70307i | − 0.153479i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 39.9678i | − 1.30291i | −0.758686 | − | 0.651457i | \(-0.774158\pi\) | ||||
0.758686 | − | 0.651457i | \(-0.225842\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −20.6210 | −0.671511 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.6616 | 0.574531 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 33.7011i | − 1.09514i | −0.836761 | − | 0.547569i | \(-0.815553\pi\) | ||||
0.836761 | − | 0.547569i | \(-0.184447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 30.7864i | − 0.999368i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.27535 | 0.106211 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.1472 | 0.976564 | 0.488282 | − | 0.872686i | \(-0.337624\pi\) | ||||
0.488282 | + | 0.872686i | \(0.337624\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 6.54106i | − 0.211664i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.14596i | 0.166345i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.9624 | 1.16129 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8733 | −0.641076 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 51.7700i | 1.66826i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 80.0287i | − 2.57622i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.1010 | −1.12877 | −0.564385 | − | 0.825511i | \(-0.690887\pi\) | ||||
−0.564385 | + | 0.825511i | \(0.690887\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.54182 | −0.113780 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 38.1884i | − 1.22552i | −0.790268 | − | 0.612762i | \(-0.790059\pi\) | ||||
0.790268 | − | 0.612762i | \(-0.209941\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 9.72716i | − 0.311839i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.62409 | 0.308217 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.6596 | 0.724946 | 0.362473 | − | 0.931994i | \(-0.381933\pi\) | ||||
0.362473 | + | 0.931994i | \(0.381933\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.0874i | 0.610036i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.8359i | 0.824878i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.47180 | −0.0469430 | −0.0234715 | − | 0.999725i | \(-0.507472\pi\) | ||||
−0.0234715 | + | 0.999725i | \(0.507472\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −62.6326 | −1.99564 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1061i | 0.321682i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 14.0814i | − 0.447763i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.6228 | −0.972767 | −0.486383 | − | 0.873746i | \(-0.661684\pi\) | ||||
−0.486383 | + | 0.873746i | \(0.661684\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.0292 | −0.413469 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 12.7582i | − 0.404461i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.61232i | 0.241085i | 0.992708 | + | 0.120542i | \(0.0384634\pi\) | ||||
−0.992708 | + | 0.120542i | \(0.961537\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.85219 | −0.121878 |
(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 | 2432.2.c.j.1217.9 | ✓ | 20 | |
4.3 | odd | 2 | inner | 2432.2.c.j.1217.11 | yes | 20 | |
8.3 | odd | 2 | inner | 2432.2.c.j.1217.10 | yes | 20 | |
8.5 | even | 2 | inner | 2432.2.c.j.1217.12 | yes | 20 | |
16.3 | odd | 4 | 4864.2.a.bs.1.5 | 10 | |||
16.5 | even | 4 | 4864.2.a.bs.1.6 | 10 | |||
16.11 | odd | 4 | 4864.2.a.bt.1.6 | 10 | |||
16.13 | even | 4 | 4864.2.a.bt.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2432.2.c.j.1217.9 | ✓ | 20 | 1.1 | even | 1 | trivial | |
2432.2.c.j.1217.10 | yes | 20 | 8.3 | odd | 2 | inner | |
2432.2.c.j.1217.11 | yes | 20 | 4.3 | odd | 2 | inner | |
2432.2.c.j.1217.12 | yes | 20 | 8.5 | even | 2 | inner | |
4864.2.a.bs.1.5 | 10 | 16.3 | odd | 4 | |||
4864.2.a.bs.1.6 | 10 | 16.5 | even | 4 | |||
4864.2.a.bt.1.5 | 10 | 16.13 | even | 4 | |||
4864.2.a.bt.1.6 | 10 | 16.11 | odd | 4 |