Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(673,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.673");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - x^{10} - 861 x^{8} - 2158 x^{7} + 8654 x^{6} + 118244 x^{5} + 707300 x^{4} + \cdots + 43264 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 673.11 | ||
Root | \(-1.74348 - 0.467165i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.673 |
Dual form | 1344.4.c.g.673.2 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.9871i | 1.25105i | 0.780206 | + | 0.625523i | \(0.215114\pi\) | ||||
−0.780206 | + | 0.625523i | \(0.784886\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 51.5791i | − 1.41379i | −0.707319 | − | 0.706895i | \(-0.750095\pi\) | ||||
0.707319 | − | 0.706895i | \(-0.249905\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 30.7945i | − 0.656988i | −0.944506 | − | 0.328494i | \(-0.893459\pi\) | ||||
0.944506 | − | 0.328494i | \(-0.106541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −41.9613 | −0.722292 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.246192 | 0.00351238 | 0.00175619 | − | 0.999998i | \(-0.499441\pi\) | ||||
0.00175619 | + | 0.999998i | \(0.499441\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.72473i | 0.0328998i | 0.999865 | + | 0.0164499i | \(0.00523640\pi\) | ||||
−0.999865 | + | 0.0164499i | \(0.994764\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 14.5441 | 0.131855 | 0.0659273 | − | 0.997824i | \(-0.478999\pi\) | ||||
0.0659273 | + | 0.997824i | \(0.478999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −70.6394 | −0.565115 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 167.061i | 1.06974i | 0.844935 | + | 0.534868i | \(0.179639\pi\) | ||||
−0.844935 | + | 0.534868i | \(0.820361\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 198.718 | 1.15132 | 0.575659 | − | 0.817690i | \(-0.304746\pi\) | ||||
0.575659 | + | 0.817690i | \(0.304746\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 154.737 | 0.816252 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 97.9098i | 0.472851i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 321.932i | 1.43041i | 0.698914 | + | 0.715206i | \(0.253667\pi\) | ||||
−0.698914 | + | 0.715206i | \(0.746333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 92.3834 | 0.379312 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 448.055 | 1.70669 | 0.853346 | − | 0.521345i | \(-0.174569\pi\) | ||||
0.853346 | + | 0.521345i | \(0.174569\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 86.5288i | 0.306872i | 0.988159 | + | 0.153436i | \(0.0490340\pi\) | ||||
−0.988159 | + | 0.153436i | \(0.950966\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 125.884i | − 0.417015i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −33.5268 | −0.104051 | −0.0520253 | − | 0.998646i | \(-0.516568\pi\) | ||||
−0.0520253 | + | 0.998646i | \(0.516568\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.738577i | 0.00202787i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 299.811i | 0.777022i | 0.921444 | + | 0.388511i | \(0.127010\pi\) | ||||
−0.921444 | + | 0.388511i | \(0.872990\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 721.443 | 1.76872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.17419 | −0.0189947 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 197.965i | 0.436827i | 0.975856 | + | 0.218414i | \(0.0700882\pi\) | ||||
−0.975856 | + | 0.218414i | \(0.929912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 476.996i | − 1.00120i | −0.865679 | − | 0.500599i | \(-0.833113\pi\) | ||||
0.865679 | − | 0.500599i | \(-0.166887\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 430.726 | 0.821922 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 824.500i | 1.50341i | 0.659497 | + | 0.751707i | \(0.270769\pi\) | ||||
−0.659497 | + | 0.751707i | \(0.729231\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 43.6323i | 0.0761263i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 503.994 | 0.842438 | 0.421219 | − | 0.906959i | \(-0.361602\pi\) | ||||
0.421219 | + | 0.906959i | \(0.361602\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1127.61 | −1.80791 | −0.903953 | − | 0.427631i | \(-0.859348\pi\) | ||||
−0.903953 | + | 0.427631i | \(0.859348\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 211.918i | − 0.326269i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 361.054i | − 0.534362i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 684.567 | 0.974934 | 0.487467 | − | 0.873141i | \(-0.337921\pi\) | ||||
0.487467 | + | 0.873141i | \(0.337921\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1119.55i | 1.48056i | 0.672297 | + | 0.740282i | \(0.265308\pi\) | ||||
−0.672297 | + | 0.740282i | \(0.734692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.44352i | 0.00439415i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −501.182 | −0.617613 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −643.835 | −0.766814 | −0.383407 | − | 0.923580i | \(-0.625249\pi\) | ||||
−0.383407 | + | 0.923580i | \(0.625249\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 215.561i | − 0.248318i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 596.154i | 0.664713i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −38.1111 | −0.0411591 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −168.589 | −0.176470 | −0.0882349 | − | 0.996100i | \(-0.528123\pi\) | ||||
−0.0882349 | + | 0.996100i | \(0.528123\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 464.212i | 0.471263i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 113.480i | 0.111799i | 0.998436 | + | 0.0558994i | \(0.0178026\pi\) | ||||
−0.998436 | + | 0.0558994i | \(0.982197\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1124.28 | −1.07552 | −0.537760 | − | 0.843098i | \(-0.680729\pi\) | ||||
−0.537760 | + | 0.843098i | \(0.680729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −293.729 | −0.273001 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1073.84i | − 0.970210i | −0.874456 | − | 0.485105i | \(-0.838781\pi\) | ||||
0.874456 | − | 0.485105i | \(-0.161219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1681.57i | − 1.47767i | −0.673888 | − | 0.738833i | \(-0.735377\pi\) | ||||
0.673888 | − | 0.738833i | \(-0.264623\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −965.795 | −0.825849 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1711.39 | −1.42473 | −0.712363 | − | 0.701812i | \(-0.752375\pi\) | ||||
−0.712363 | + | 0.701812i | \(0.752375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 203.430i | 0.164956i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 277.150i | 0.218996i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.72335 | 0.00132755 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1329.40 | −0.998801 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1344.16i | 0.985359i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 760.348i | 0.544061i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1279.16 | 0.893755 | 0.446878 | − | 0.894595i | \(-0.352536\pi\) | ||||
0.446878 | + | 0.894595i | \(0.352536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −259.586 | −0.177173 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2380.09i | 1.58740i | 0.608311 | + | 0.793699i | \(0.291847\pi\) | ||||
−0.608311 | + | 0.793699i | \(0.708153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.0731i | 0.0124349i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 377.652 | 0.240764 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1271.94 | 0.793206 | 0.396603 | − | 0.917990i | \(-0.370189\pi\) | ||||
0.396603 | + | 0.917990i | \(0.370189\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 788.385i | − 0.481079i | −0.970639 | − | 0.240539i | \(-0.922676\pi\) | ||||
0.970639 | − | 0.240539i | \(-0.0773243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 100.580i | − 0.0600737i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1588.35 | −0.928843 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2336.70 | −1.33829 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1976.18i | 1.08655i | 0.839556 | + | 0.543273i | \(0.182815\pi\) | ||||
−0.839556 | + | 0.543273i | \(0.817185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 670.640 | 0.361430 | 0.180715 | − | 0.983536i | \(-0.442159\pi\) | ||||
0.180715 | + | 0.983536i | \(0.442159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.21573 | −0.00117079 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2779.49i | 1.44035i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 337.739i | 0.171685i | 0.996309 | + | 0.0858423i | \(0.0273581\pi\) | ||||
−0.996309 | + | 0.0858423i | \(0.972642\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −899.432 | −0.448614 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 101.809 | 0.0498364 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 149.606i | − 0.0718899i | −0.999354 | − | 0.0359450i | \(-0.988556\pi\) | ||||
0.999354 | − | 0.0359450i | \(-0.0114441\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2164.33i | 1.02117i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3347.04 | 1.55091 | 0.775453 | − | 0.631405i | \(-0.217521\pi\) | ||||
0.775453 | + | 0.631405i | \(0.217521\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1248.70 | 0.568367 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 24.5226i | − 0.0109666i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 86.6015i | − 0.0380589i | −0.999819 | − | 0.0190295i | \(-0.993942\pi\) | ||||
0.999819 | − | 0.0190295i | \(-0.00605763\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −494.476 | −0.213593 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −593.894 | −0.252202 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2306.58i | 0.963140i | 0.876408 | + | 0.481570i | \(0.159933\pi\) | ||||
−0.876408 | + | 0.481570i | \(0.840067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2101.18i | − 0.862869i | −0.902144 | − | 0.431434i | \(-0.858008\pi\) | ||||
0.902144 | − | 0.431434i | \(-0.141992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1430.99 | 0.578042 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4502.89 | −1.78951 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 12.6984i | − 0.00496577i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 189.000i | − 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1515.51 | 0.574129 | 0.287064 | − | 0.957911i | \(-0.407321\pi\) | ||||
0.287064 | + | 0.957911i | \(0.407321\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1380.38 | −0.514830 | −0.257415 | − | 0.966301i | \(-0.582871\pi\) | ||||
−0.257415 | + | 0.966301i | \(0.582871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1292.18i | 0.474537i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1057.44i | − 0.382435i | −0.981548 | − | 0.191217i | \(-0.938756\pi\) | ||||
0.981548 | − | 0.191217i | \(-0.0612436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 982.569 | 0.350012 | 0.175006 | − | 0.984567i | \(-0.444005\pi\) | ||||
0.175006 | + | 0.984567i | \(0.444005\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2473.50 | −0.867996 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1169.42i | 0.404323i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6266.99i | 2.13515i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −130.897 | −0.0439516 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 140.539 | 0.0465134 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1332.78i | 0.434846i | 0.976078 | + | 0.217423i | \(0.0697651\pi\) | ||||
−0.976078 | + | 0.217423i | \(0.930235\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1511.98i | 0.486382i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1210.29 | −0.383911 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1391.03 | 0.435157 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 3382.84i | − 1.04380i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 7.58136i | − 0.00230759i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2802.74 | 0.841640 | 0.420820 | − | 0.907144i | \(-0.361742\pi\) | ||||
0.420820 | + | 0.907144i | \(0.361742\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 635.755 | 0.188372 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2933.73i | − 0.857792i | −0.903354 | − | 0.428896i | \(-0.858903\pi\) | ||||
0.903354 | − | 0.428896i | \(-0.141097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3742.19i | 1.07987i | 0.841706 | + | 0.539936i | \(0.181552\pi\) | ||||
−0.841706 | + | 0.539936i | \(0.818448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1083.16 | 0.308514 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1170.74 | −0.329176 | −0.164588 | − | 0.986362i | \(-0.552629\pi\) | ||||
−0.164588 | + | 0.986362i | \(0.552629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 468.943i | − 0.130172i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2053.70i | 0.562878i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1609.75 | 0.435675 | 0.217838 | − | 0.975985i | \(-0.430100\pi\) | ||||
0.217838 | + | 0.975985i | \(0.430100\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5408.12 | −1.44551 | −0.722755 | − | 0.691104i | \(-0.757124\pi\) | ||||
−0.722755 | + | 0.691104i | \(0.757124\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 685.369i | 0.178721i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 83.9066 | 0.0216148 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3358.66 | −0.854804 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5299.79i | 1.33275i | 0.745617 | + | 0.666374i | \(0.232155\pi\) | ||||
−0.745617 | + | 0.666374i | \(0.767845\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 750.173i | − 0.186415i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.3306 | −0.00253696 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 42.9014 | 0.0104129 | 0.00520645 | − | 0.999986i | \(-0.498343\pi\) | ||||
0.00520645 | + | 0.999986i | \(0.498343\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2253.52i | 0.540645i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 1503.55i | − 0.356579i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3563.82 | 0.835569 | 0.417784 | − | 0.908546i | \(-0.362807\pi\) | ||||
0.417784 | + | 0.908546i | \(0.362807\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4193.49 | −0.972090 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1931.51i | − 0.442720i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5293.26i | 1.19976i | 0.800089 | + | 0.599881i | \(0.204785\pi\) | ||||
−0.800089 | + | 0.599881i | \(0.795215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2544.94 | −0.570457 | −0.285229 | − | 0.958459i | \(-0.592070\pi\) | ||||
−0.285229 | + | 0.958459i | \(0.592070\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 646.684 | 0.143367 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3643.52i | 0.798954i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5360.35i | 1.16272i | 0.813648 | + | 0.581358i | \(0.197478\pi\) | ||||
−0.813648 | + | 0.581358i | \(0.802522\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1788.46 | −0.383772 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3851.63 | 0.817684 | 0.408842 | − | 0.912605i | \(-0.365933\pi\) | ||||
0.408842 | + | 0.912605i | \(0.365933\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 8884.40i | − 1.86616i | −0.359670 | − | 0.933080i | \(-0.617111\pi\) | ||||
0.359670 | − | 0.933080i | \(-0.382889\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 114.333i | − 0.0237632i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3136.38 | 0.645069 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4912.94 | −0.999988 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 505.766i | − 0.101885i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4308.01i | 0.858965i | 0.903075 | + | 0.429482i | \(0.141304\pi\) | ||||
−0.903075 | + | 0.429482i | \(0.858696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2768.95 | −0.546491 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1392.64 | −0.272084 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 447.878i | − 0.0866270i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 605.701i | 0.115987i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −340.440 | −0.0645471 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6671.80 | 1.25254 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3920.97i | 0.728930i | 0.931217 | + | 0.364465i | \(0.118748\pi\) | ||||
−0.931217 | + | 0.364465i | \(0.881252\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 3372.84i | − 0.620952i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7152.81 | 1.30418 | 0.652088 | − | 0.758143i | \(-0.273893\pi\) | ||||
0.652088 | + | 0.758143i | \(0.273893\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 754.226 | 0.136202 | 0.0681012 | − | 0.997678i | \(-0.478306\pi\) | ||||
0.0681012 | + | 0.997678i | \(0.478306\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 881.188i | − 0.157617i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 7954.23i | − 1.40932i | −0.709545 | − | 0.704660i | \(-0.751100\pi\) | ||||
0.709545 | − | 0.704660i | \(-0.248900\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8616.83 | 1.51238 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3221.53 | 0.560151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.670808i | 0 0.000115557i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2175.30i | 0.371274i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5044.72 | 0.853131 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −234.687 | −0.0393275 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8919.36i | 1.48113i | 0.671987 | + | 0.740563i | \(0.265441\pi\) | ||||
−0.671987 | + | 0.740563i | \(0.734559\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2897.38i | − 0.476804i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11532.4 | −1.88084 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3689.51 | −0.596381 | −0.298191 | − | 0.954506i | \(-0.596383\pi\) | ||||
−0.298191 | + | 0.954506i | \(0.596383\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 5134.17i | − 0.822566i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 10249.7i | − 1.62772i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −610.291 | −0.0952375 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5809.87i | 0.898819i | 0.893326 | + | 0.449410i | \(0.148366\pi\) | ||||
−0.893326 | + | 0.449410i | \(0.851634\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 5065.35i | − 0.776912i | −0.921467 | − | 0.388456i | \(-0.873009\pi\) | ||||
0.921467 | − | 0.388456i | \(-0.126991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −831.450 | −0.126437 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1513.12 | −0.228145 | −0.114072 | − | 0.993472i | \(-0.536390\pi\) | ||||
−0.114072 | + | 0.993472i | \(0.536390\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7049.42i | 1.05393i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.17004i | 0 0.000766464i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1919.55 | −0.282200 | −0.141100 | − | 0.989995i | \(-0.545064\pi\) | ||||
−0.141100 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6851.58 | 0.998918 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3988.21i | − 0.576658i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 15772.1i | − 2.26177i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10414.2 | −1.48125 | −0.740625 | − | 0.671918i | \(-0.765471\pi\) | ||||
−0.740625 | + | 0.671918i | \(0.765471\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4032.49 | −0.568897 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2098.67i | 0.293687i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9393.42i | 1.30395i | 0.758241 | + | 0.651975i | \(0.226059\pi\) | ||||
−0.758241 | + | 0.651975i | \(0.773941\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2281.04 | −0.314114 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5144.54 | 0.702804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13916.5i | 1.88613i | 0.332604 | + | 0.943067i | \(0.392073\pi\) | ||||
−0.332604 | + | 0.943067i | \(0.607927\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3837.47i | 0.516010i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1163.07 | −0.155170 | −0.0775852 | − | 0.996986i | \(-0.524721\pi\) | ||||
−0.0775852 | + | 0.996986i | \(0.524721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5050.10 | 0.668512 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 778.759i | − 0.102291i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 4008.53i | − 0.522469i | −0.965275 | − | 0.261234i | \(-0.915870\pi\) | ||||
0.965275 | − | 0.261234i | \(-0.0841295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.58065 | 0.000463124 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7140.26 | −0.916485 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9575.11i | 1.21969i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5436.43i | 0.687271i | 0.939103 | + | 0.343635i | \(0.111658\pi\) | ||||
−0.939103 | + | 0.343635i | \(0.888342\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −57.2193 | −0.00717932 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1337.79 | 0.166599 | 0.0832994 | − | 0.996525i | \(-0.473454\pi\) | ||||
0.0832994 | + | 0.996525i | \(0.473454\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6119.42i | − 0.756402i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1132.96i | 0.139005i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16604.9 | 2.02230 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5946.08 | 0.718863 | 0.359431 | − | 0.933172i | \(-0.382971\pi\) | ||||
0.359431 | + | 0.933172i | \(0.382971\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3815.82i | 0.457958i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1385.75i | 0.165105i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15659.3 | −1.85225 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2365.15 | 0.277751 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6475.08i | 0.754960i | 0.926018 | + | 0.377480i | \(0.123209\pi\) | ||||
−0.926018 | + | 0.377480i | \(0.876791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 148.460i | 0.0171865i | 0.999963 | + | 0.00859325i | \(0.00273535\pi\) | ||||
−0.999963 | + | 0.00859325i | \(0.997265\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 301.741 | 0.0346836 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.3909 | −0.00198490 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3338.97i | − 0.378417i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 4765.05i | − 0.536268i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3972.95 | 0.444014 | 0.222007 | − | 0.975045i | \(-0.428739\pi\) | ||||
0.222007 | + | 0.975045i | \(0.428739\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12727.5 | −1.41257 | −0.706287 | − | 0.707926i | \(-0.749631\pi\) | ||||
−0.706287 | + | 0.707926i | \(0.749631\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 7010.09i | − 0.772662i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 39.6288i | 0.00433799i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13699.0 | −1.48933 | −0.744666 | − | 0.667437i | \(-0.767391\pi\) | ||||
−0.744666 | + | 0.667437i | \(0.767391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −441.000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 11556.0i | − 1.23938i | −0.784848 | − | 0.619688i | \(-0.787259\pi\) | ||||
0.784848 | − | 0.619688i | \(-0.212741\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 9005.40i | − 0.959319i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5928.55 | −0.627317 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13286.6 | 1.39651 | 0.698256 | − | 0.715848i | \(-0.253960\pi\) | ||||
0.698256 | + | 0.715848i | \(0.253960\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 23110.3i | − 2.41290i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2011.92i | 0.208672i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3015.08 | 0.310657 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3989.44 | 0.408354 | 0.204177 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204177 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 6.64720i | 0 0.000675958i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 9542.23i | − 0.964048i | −0.876158 | − | 0.482024i | \(-0.839902\pi\) | ||||
0.876158 | − | 0.482024i | \(-0.160098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10466.6 | −1.05059 | −0.525295 | − | 0.850920i | \(-0.676045\pi\) | ||||
−0.525295 | + | 0.850920i | \(0.676045\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8338.48 | −0.831587 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2048.14i | 0.202947i | 0.994838 | + | 0.101474i | \(0.0323558\pi\) | ||||
−0.994838 | + | 0.101474i | \(0.967644\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5771.50i | 0.568237i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1013.22 | −0.0991222 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4463.08 | 0.433853 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 192.473i | − 0.0185922i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2698.30i | − 0.259007i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7566.57 | 0.721765 | 0.360883 | − | 0.932611i | \(-0.382475\pi\) | ||||
0.360883 | + | 0.932611i | \(0.382475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9913.71 | 0.939763 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 305.426i | 0.0287731i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2358.07i | − 0.220772i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7729.08 | 0.719174 | 0.359587 | − | 0.933111i | \(-0.382918\pi\) | ||||
0.359587 | + | 0.933111i | \(0.382918\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 448.818 | 0.0415057 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14478.6i | 1.33077i | 0.746500 | + | 0.665385i | \(0.231733\pi\) | ||||
−0.746500 | + | 0.665385i | \(0.768267\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 41.1291i | 0.00375732i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6492.99 | −0.589572 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3527.96 | 0.318412 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 833.888i | − 0.0748095i | −0.999300 | − | 0.0374047i | \(-0.988091\pi\) | ||||
0.999300 | − | 0.0374047i | \(-0.0119091\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10041.1i | 0.895416i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2969.77 | 0.263251 | 0.131626 | − | 0.991300i | \(-0.457980\pi\) | ||||
0.131626 | + | 0.991300i | \(0.457980\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1587.26 | −0.139865 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3746.10i | 0.328147i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17527.8i | 1.52634i | 0.646198 | + | 0.763170i | \(0.276358\pi\) | ||||
−0.646198 | + | 0.763170i | \(0.723642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7893.29 | −0.683324 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 73.5677 | 0.00633157 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 15725.4i | − 1.34552i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1729.28i | 0.147106i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 259.805 | 0.0219733 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5661.35 | 0.476062 | 0.238031 | − | 0.971258i | \(-0.423498\pi\) | ||||
0.238031 | + | 0.971258i | \(0.423498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 21827.1i | − 1.82492i | −0.409168 | − | 0.912459i | \(-0.634181\pi\) | ||||
0.409168 | − | 0.912459i | \(-0.365819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1483.43i | − 0.123318i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 48.9229 | 0.00404386 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11955.5 | −0.982614 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 1781.68i | − 0.145609i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13797.6i | − 1.12128i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15020.0 | 1.21378 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6919.75 | −0.556069 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 2527.38i | − 0.201970i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 729.984i | − 0.0580119i | −0.999579 | − | 0.0290060i | \(-0.990766\pi\) | ||||
0.999579 | − | 0.0290060i | \(-0.00923418\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6303.53 | 0.498178 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 23520.4 | 1.84863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 23541.6i | − 1.84016i | −0.391734 | − | 0.920078i | \(-0.628125\pi\) | ||||
0.391734 | − | 0.920078i | \(-0.371875\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4292.96i | 0.333733i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −455.195 | −0.0351941 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4791.97 | 0.368490 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 13508.7i | − 1.03317i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5392.39i | 0.410203i | 0.978741 | + | 0.205102i | \(0.0657525\pi\) | ||||
−0.978741 | + | 0.205102i | \(0.934248\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2664.61 | 0.201612 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 38.0952 | 0.00286699 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8566.71i | 0.641286i | 0.947200 | + | 0.320643i | \(0.103899\pi\) | ||||
−0.947200 | + | 0.320643i | \(0.896101\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 23937.4i | − 1.78240i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25605.4 | 1.88653 | 0.943263 | − | 0.332045i | \(-0.107739\pi\) | ||||
0.943263 | + | 0.332045i | \(0.107739\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 11694.6i | − 0.857102i | −0.903518 | − | 0.428551i | \(-0.859024\pi\) | ||||
0.903518 | − | 0.428551i | \(-0.140976\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4546.53i | 0.331473i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1027.39 | −0.0745131 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22162.0 | 1.59899 | 0.799495 | − | 0.600673i | \(-0.205101\pi\) | ||||
0.799495 | + | 0.600673i | \(0.205101\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 4141.15i | − 0.297237i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7836.86i | 0.559600i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15464.0 | 1.09855 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3876.53 | −0.273974 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 310.769i | − 0.0218515i | −0.999940 | − | 0.0109257i | \(-0.996522\pi\) | ||||
0.999940 | − | 0.0109257i | \(-0.00347784\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 541.453i | 0.0378781i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3172.33 | 0.220799 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10069.8 | 0.697328 | 0.348664 | − | 0.937248i | \(-0.386635\pi\) | ||||
0.348664 | + | 0.937248i | \(0.386635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.1047i | 0.00166083i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2947.71i | 0.202080i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9888.41 | 0.674507 | 0.337253 | − | 0.941414i | \(-0.390502\pi\) | ||||
0.337253 | + | 0.941414i | \(0.390502\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17962.8 | 1.21917 | 0.609584 | − | 0.792722i | \(-0.291337\pi\) | ||||
0.609584 | + | 0.792722i | \(0.291337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 7420.50i | − 0.501138i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 18594.5i | − 1.24955i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26295.5 | −1.75832 | −0.879160 | − | 0.476527i | \(-0.841895\pi\) | ||||
−0.879160 | + | 0.476527i | \(0.841895\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3508.27 | −0.233436 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1032.44i | 0.0683600i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3706.64i | − 0.244225i | −0.992516 | − | 0.122112i | \(-0.961033\pi\) | ||||
0.992516 | − | 0.122112i | \(-0.0389669\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18801.0 | −1.23273 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19879.0 | −1.29708 | −0.648539 | − | 0.761181i | \(-0.724620\pi\) | ||||
−0.648539 | + | 0.761181i | \(0.724620\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 4047.25i | − 0.262799i | −0.991330 | − | 0.131399i | \(-0.958053\pi\) | ||||
0.991330 | − | 0.131399i | \(-0.0419470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 392.691i | − 0.0253754i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4506.85 | −0.289828 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19465.0 | −1.24576 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 421.617i | 0.0268545i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 79.2571i | 0.00502415i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27715.5 | 1.74855 | 0.874277 | − | 0.485428i | \(-0.161336\pi\) | ||||
0.874277 | + | 0.485428i | \(0.161336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3998.34 | −0.251058 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17891.7i | 1.11813i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1508.93i | − 0.0938554i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4535.95 | −0.280813 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18708.7 | 1.15281 | 0.576405 | − | 0.817164i | \(-0.304455\pi\) | ||||
0.576405 | + | 0.817164i | \(0.304455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 15544.7i | − 0.953379i | −0.879072 | − | 0.476689i | \(-0.841837\pi\) | ||||
0.879072 | − | 0.476689i | \(-0.158163\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3630.86i | − 0.221651i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7016.63 | −0.426356 | −0.213178 | − | 0.977013i | \(-0.568381\pi\) | ||||
−0.213178 | + | 0.977013i | \(0.568381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10210.8 | 0.617582 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4173.08i | 0.251238i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11732.4i | 0.703102i | 0.936169 | + | 0.351551i | \(0.114346\pi\) | ||||
−0.936169 | + | 0.351551i | \(0.885654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33290.5 | −1.98591 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10148.5 | 0.602636 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 30900.3i | − 1.82657i | −0.407327 | − | 0.913283i | \(-0.633539\pi\) | ||||
0.407327 | − | 0.913283i | \(-0.366461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 23522.3i | − 1.38413i | −0.721835 | − | 0.692065i | \(-0.756701\pi\) | ||||
0.721835 | − | 0.692065i | \(-0.243299\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 22.7441 | 0.00133229 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −266.778 | −0.0155567 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2429.75i | 0.141050i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8408.23i | 0.485921i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24603.0 | −1.41548 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31873.0 | −1.82558 | −0.912790 | − | 0.408429i | \(-0.866077\pi\) | ||||
−0.912790 | + | 0.408429i | \(0.866077\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1907.26i | 0.108756i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 28606.2i | − 1.62397i | −0.583681 | − | 0.811983i | \(-0.698388\pi\) | ||||
0.583681 | − | 0.811983i | \(-0.301612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1180.12 | −0.0666993 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8801.20 | 0.495246 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18459.6i | 1.03417i | 0.855935 | + | 0.517084i | \(0.172982\pi\) | ||||
−0.855935 | + | 0.517084i | \(0.827018\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17790.8i | 0.992337i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11226.6 | −0.623464 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9232.51 | 0.510494 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 750.319i | 0.0413075i | 0.999787 | + | 0.0206538i | \(0.00657476\pi\) | ||||
−0.999787 | + | 0.0206538i | \(0.993425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3249.48i | 0.178121i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11027.2 | 0.601851 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 110.308 | 0.00599455 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 3512.23i | − 0.190050i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12365.7i | 0.666257i | 0.942881 | + | 0.333129i | \(0.108104\pi\) | ||||
−0.942881 | + | 0.333129i | \(0.891896\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −877.177 | −0.0470602 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1406.83 | 0.0751549 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 794.360i | 0.0422560i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36658.2i | 1.94179i | 0.239511 | + | 0.970894i | \(0.423013\pi\) | ||||
−0.239511 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6161.10 | −0.324978 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2890.18 | 0.151807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 22216.4i | − 1.16202i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4829.26i | 0.251537i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22654.9 | −1.17508 | −0.587542 | − | 0.809194i | \(-0.699904\pi\) | ||||
−0.587542 | + | 0.809194i | \(0.699904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7869.96 | −0.406508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 16224.4i | − 0.834565i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 11801.1i | − 0.604524i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2446.73 | 0.124820 | 0.0624100 | − | 0.998051i | \(-0.480121\pi\) | ||||
0.0624100 | + | 0.998051i | \(0.480121\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.3027i | 0.00107785i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10555.2i | 0.531874i | 0.963990 | + | 0.265937i | \(0.0856813\pi\) | ||||
−0.963990 | + | 0.265937i | \(0.914319\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2056.11 | −0.103185 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42527.0 | 2.12551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 21756.1i | − 1.08296i | −0.840713 | − | 0.541481i | \(-0.817864\pi\) | ||||
0.840713 | − | 0.541481i | \(-0.182136\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 251.720i | 0.0124793i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4240.78 | −0.209393 | −0.104697 | − | 0.994504i | \(-0.533387\pi\) | ||||
−0.104697 | + | 0.994504i | \(0.533387\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27641.1 | −1.35932 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 10076.0i | − 0.493521i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 7516.91i | − 0.366705i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17371.5 | 0.844067 | 0.422034 | − | 0.906580i | \(-0.361316\pi\) | ||||
0.422034 | + | 0.906580i | \(0.361316\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −15899.4 | −0.769463 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9380.32i | 0.452165i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 33342.0i | − 1.60084i | −0.599439 | − | 0.800420i | \(-0.704610\pi\) | ||||
0.599439 | − | 0.800420i | \(-0.295390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2250.52 | 0.107627 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10831.6 | 0.515962 | 0.257981 | − | 0.966150i | \(-0.416943\pi\) | ||||
0.257981 | + | 0.966150i | \(0.416943\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 11771.0i | − 0.558505i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 30.9917i | − 0.00146472i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6096.21 | 0.286990 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19819.2 | −0.929389 | −0.464695 | − | 0.885471i | \(-0.653836\pi\) | ||||
−0.464695 | + | 0.885471i | \(0.653836\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 128.704i | 0.00601189i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 19421.7i | − 0.903685i | −0.892098 | − | 0.451843i | \(-0.850767\pi\) | ||||
0.892098 | − | 0.451843i | \(-0.149233\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14037.3 | −0.650627 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6760.56 | −0.312141 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1220.83i | 0.0561498i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 25995.6i | − 1.19103i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4510.64 | 0.205871 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4723.99 | −0.214785 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 634.033i | − 0.0287177i | −0.999897 | − | 0.0143589i | \(-0.995429\pi\) | ||||
0.999897 | − | 0.0143589i | \(-0.00457072\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10691.5i | 0.482416i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11979.7 | −0.538496 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14688.8 | −0.657775 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 12580.5i | − 0.561236i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26293.4i | 1.16858i | 0.811545 | + | 0.584290i | \(0.198627\pi\) | ||||
−0.811545 | + | 0.584290i | \(0.801373\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.25404 | −0.000365465 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5794.52 | 0.255605 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58161.3i | 2.55600i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1424.01i | 0.0623476i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15879.8 | −0.692683 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10342.5 | −0.449473 | −0.224737 | − | 0.974420i | \(-0.572152\pi\) | ||||
−0.224737 | + | 0.974420i | \(0.572152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16566.5i | 0.717298i | 0.933472 | + | 0.358649i | \(0.116763\pi\) | ||||
−0.933472 | + | 0.358649i | \(0.883237\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 7634.81i | − 0.329354i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2092.56 | 0.0899376 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −235.768 | −0.0100960 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1940.05i | 0.0827727i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 28950.0i | − 1.23065i | −0.788275 | − | 0.615323i | \(-0.789025\pi\) | ||||
0.788275 | − | 0.615323i | \(-0.210975\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17682.2 | 0.748922 | 0.374461 | − | 0.927243i | \(-0.377828\pi\) | ||||
0.374461 | + | 0.927243i | \(0.377828\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10930.6 | −0.461276 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 40381.1i | − 1.69793i | −0.528449 | − | 0.848965i | \(-0.677226\pi\) | ||||
0.528449 | − | 0.848965i | \(-0.322774\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 37226.2i | − 1.55961i | −0.626022 | − | 0.779806i | \(-0.715318\pi\) | ||||
0.626022 | − | 0.779806i | \(-0.284682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16081.0 | −0.671294 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 12.0634 | 0.000501768 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46815.4i | 1.94025i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 5365.39i | − 0.221571i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19414.0 | 0.798862 | 0.399431 | − | 0.916763i | \(-0.369208\pi\) | ||||
0.399431 | + | 0.916763i | \(0.369208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3520.23 | −0.144337 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11554.9i | 0.472090i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17465.7i | 0.711053i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9305.83 | −0.377511 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26653.2 | 1.07743 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4682.21i | 0.188606i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11641.9i | 0.467304i | 0.972320 | + | 0.233652i | \(0.0750677\pi\) | ||||
−0.972320 | + | 0.233652i | \(0.924932\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 343.000 | 0.0137197 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18755.4 | 0.747575 | 0.373788 | − | 0.927514i | \(-0.378059\pi\) | ||||
0.373788 | + | 0.927514i | \(0.378059\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5477.43i | 0.217564i | 0.994066 | + | 0.108782i | \(0.0346951\pi\) | ||||
−0.994066 | + | 0.108782i | \(0.965305\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9409.15i | 0.372431i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −44169.7 | −1.74224 | −0.871120 | − | 0.491071i | \(-0.836606\pi\) | ||||
−0.871120 | + | 0.491071i | \(0.836606\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1211.31 | 0.0476134 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 14738.8i | − 0.577343i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 35309.3i | − 1.37835i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25390.0 | 0.987725 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1517.30 | 0.0588233 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5322.44i | 0.205636i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25235.0i | 0.971636i | 0.874060 | + | 0.485818i | \(0.161478\pi\) | ||||
−0.874060 | + | 0.485818i | \(0.838522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12924.0 | −0.495924 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14930.3 | 0.570957 | 0.285479 | − | 0.958385i | \(-0.407847\pi\) | ||||
0.285479 | + | 0.958385i | \(0.407847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9325.73i | 0.355420i | 0.984083 | + | 0.177710i | \(0.0568689\pi\) | ||||
−0.984083 | + | 0.177710i | \(0.943131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 8306.86i | − 0.315517i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13393.6 | 0.507006 | 0.253503 | − | 0.967335i | \(-0.418417\pi\) | ||||
0.253503 | + | 0.967335i | \(0.418417\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8954.10 | 0.337808 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 4177.91i | − 0.157088i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 91.3514i | − 0.00342324i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32262.4 | −1.20493 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1343.63 | 0.0500141 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33198.0i | 1.23161i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 73.8111i | 0.00272920i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1817.10 | −0.0669651 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29389.4 | 1.07949 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 34813.6i | − 1.27449i | −0.770660 | − | 0.637247i | \(-0.780073\pi\) | ||||
0.770660 | − | 0.637247i | \(-0.219927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1021.32i | − 0.0372663i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51367.2 | 1.86814 | 0.934068 | − | 0.357096i | \(-0.116233\pi\) | ||||
0.934068 | + | 0.357096i | \(0.116233\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57745.5 | 2.09321 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20015.4i | 0.723157i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16660.6i | 0.599980i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25493.9 | 0.915089 | 0.457545 | − | 0.889187i | \(-0.348729\pi\) | ||||
0.457545 | + | 0.889187i | \(0.348729\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11762.9 | −0.420848 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 15520.2i | − 0.553472i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 22741.1i | − 0.808347i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10118.5 | 0.358507 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13198.9 | −0.466139 | −0.233069 | − | 0.972460i | \(-0.574877\pi\) | ||||
−0.233069 | + | 0.972460i | \(0.574877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 133.512i | 0.00469997i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21458.4i | 0.752966i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 177.614 | 0.00621240 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25935.6 | −0.904245 | −0.452123 | − | 0.891956i | \(-0.649333\pi\) | ||||
−0.452123 | + | 0.891956i | \(0.649333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2262.68i | 0.0786365i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 51952.9i | − 1.79980i | −0.436093 | − | 0.899901i | \(-0.643638\pi\) | ||||
0.436093 | − | 0.899901i | \(-0.356362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6516.56 | 0.225035 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2643.56 | 0.0910002 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27316.9i | 0.937359i | 0.883368 | + | 0.468680i | \(0.155270\pi\) | ||||
−0.883368 | + | 0.468680i | \(0.844730\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34724.2i | 1.18777i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23862.7 | 0.813671 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2017.13 | 0.0685636 | 0.0342818 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342818 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21197.6i | 0.718261i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25850.5i | 0.873175i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8903.58 | 0.299804 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9697.89 | 0.325531 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9664.60i | 0.323403i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 19307.6i | − 0.644075i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35636.5 | 1.18510 | 0.592550 | − | 0.805534i | \(-0.298121\pi\) | ||||
0.592550 | + | 0.805534i | \(0.298121\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.01242 | −6.67166e−5 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10179.9i | 0.336445i | 0.985749 | + | 0.168222i | \(0.0538026\pi\) | ||||
−0.985749 | + | 0.168222i | \(0.946197\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 5518.69i | − 0.181831i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6525.90 | −0.214355 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −60124.9 | −1.96885 | −0.984425 | − | 0.175806i | \(-0.943747\pi\) | ||||
−0.984425 | + | 0.175806i | \(0.943747\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33208.5i | 1.08411i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15134.2i | 0.492555i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54363.0 | 1.76390 | 0.881948 | − | 0.471347i | \(-0.156232\pi\) | ||||
0.881948 | + | 0.471347i | \(0.156232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14790.6 | 0.478443 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 704.062i | − 0.0227057i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1258.48i | 0.0404626i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32372.1 | −1.03767 | −0.518836 | − | 0.854874i | \(-0.673635\pi\) | ||||
−0.518836 | + | 0.854874i | \(0.673635\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26758.1 | −0.855128 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13743.3i | 0.437882i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28233.4i | 0.896851i | 0.893820 | + | 0.448425i | \(0.148015\pi\) | ||||
−0.893820 | + | 0.448425i | \(0.851985\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8692.15 | 0.275283 |
(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 | 1344.4.c.g.673.11 | yes | 12 | |
4.3 | odd | 2 | 1344.4.c.f.673.5 | ✓ | 12 | ||
8.3 | odd | 2 | 1344.4.c.f.673.8 | yes | 12 | ||
8.5 | even | 2 | inner | 1344.4.c.g.673.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.c.f.673.5 | ✓ | 12 | 4.3 | odd | 2 | ||
1344.4.c.f.673.8 | yes | 12 | 8.3 | odd | 2 | ||
1344.4.c.g.673.2 | yes | 12 | 8.5 | even | 2 | inner | |
1344.4.c.g.673.11 | yes | 12 | 1.1 | even | 1 | trivial |