Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(62,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.62");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{111})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 112x^{2} + 3025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 62.4 | ||
Root | \(6.74273i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.62 |
Dual form | 63.4.c.b.62.2 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 21.0713 | 1.88468 | 0.942338 | − | 0.334664i | \(-0.108623\pi\) | ||||
0.942338 | + | 0.334664i | \(0.108623\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.0000 | − | 14.8997i | −0.593944 | − | 0.804506i | ||||
\(8\) | 22.6274i | 1.00000i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 59.5987i | 1.88468i | ||||||||
\(11\) | 15.5563i | 0.426401i | 0.977008 | + | 0.213201i | \(0.0683888\pi\) | ||||
−0.977008 | + | 0.213201i | \(0.931611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 29.7993i | 0.635757i | 0.948131 | + | 0.317879i | \(0.102970\pi\) | ||||
−0.948131 | + | 0.317879i | \(0.897030\pi\) | |||||||
\(14\) | 42.1426 | − | 31.1127i | 0.804506 | − | 0.593944i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | −63.2139 | −0.901860 | −0.450930 | − | 0.892559i | \(-0.648908\pi\) | ||||
−0.450930 | + | 0.892559i | \(0.648908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 89.3980i | − | 1.07944i | −0.841846 | − | 0.539719i | \(-0.818531\pi\) | ||
0.841846 | − | 0.539719i | \(-0.181469\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −44.0000 | −0.426401 | ||||||||
\(23\) | − | 77.7817i | − | 0.705157i | −0.935782 | − | 0.352579i | \(-0.885305\pi\) | ||
0.935782 | − | 0.352579i | \(-0.114695\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 319.000 | 2.55200 | ||||||||
\(26\) | −84.2852 | −0.635757 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 125.865i | 0.805950i | 0.915211 | + | 0.402975i | \(0.132024\pi\) | ||||
−0.915211 | + | 0.402975i | \(0.867976\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 238.395i | − | 1.38119i | −0.723241 | − | 0.690596i | \(-0.757348\pi\) | ||
0.723241 | − | 0.690596i | \(-0.242652\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 178.796i | − | 0.901860i | ||||||
\(35\) | −231.784 | − | 313.955i | −1.11939 | − | 1.51623i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −184.000 | −0.817552 | −0.408776 | − | 0.912635i | \(-0.634044\pi\) | ||||
−0.408776 | + | 0.912635i | \(0.634044\pi\) | |||||||
\(38\) | 252.856 | 1.07944 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 476.789i | 1.88468i | ||||||||
\(41\) | −105.357 | −0.401315 | −0.200658 | − | 0.979661i | \(-0.564308\pi\) | ||||
−0.200658 | + | 0.979661i | \(0.564308\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −190.000 | −0.673831 | −0.336915 | − | 0.941535i | \(-0.609384\pi\) | ||||
−0.336915 | + | 0.941535i | \(0.609384\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 220.000 | 0.705157 | ||||||||
\(47\) | 42.1426 | 0.130790 | 0.0653950 | − | 0.997859i | \(-0.479169\pi\) | ||||
0.0653950 | + | 0.997859i | \(0.479169\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −101.000 | + | 327.793i | −0.294461 | + | 0.955664i | ||||
\(50\) | 902.268i | 2.55200i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 357.796i | − | 0.927303i | −0.886018 | − | 0.463652i | \(-0.846539\pi\) | ||
0.886018 | − | 0.463652i | \(-0.153461\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 327.793i | 0.803628i | ||||||||
\(56\) | 337.141 | − | 248.902i | 0.804506 | − | 0.593944i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −356.000 | −0.805950 | ||||||||
\(59\) | 84.2852 | 0.185983 | 0.0929915 | − | 0.995667i | \(-0.470357\pi\) | ||||
0.0929915 | + | 0.995667i | \(0.470357\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 655.585i | − | 1.37605i | −0.725687 | − | 0.688025i | \(-0.758478\pi\) | ||
0.725687 | − | 0.688025i | \(-0.241522\pi\) | |||||||
\(62\) | 674.282 | 1.38119 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 627.911i | 1.19820i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 296.000 | 0.539734 | 0.269867 | − | 0.962898i | \(-0.413020\pi\) | ||||
0.269867 | + | 0.962898i | \(0.413020\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 888.000 | − | 655.585i | 1.51623 | − | 1.11939i | ||||
\(71\) | 329.512i | 0.550787i | 0.961332 | + | 0.275393i | \(0.0888081\pi\) | ||||
−0.961332 | + | 0.275393i | \(0.911192\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 804.582i | 1.28999i | 0.764187 | + | 0.644994i | \(0.223140\pi\) | ||||
−0.764187 | + | 0.644994i | \(0.776860\pi\) | |||||||
\(74\) | − | 520.431i | − | 0.817552i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 231.784 | − | 171.120i | 0.343043 | − | 0.253259i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 836.000 | 1.19060 | 0.595300 | − | 0.803504i | \(-0.297033\pi\) | ||||
0.595300 | + | 0.803504i | \(0.297033\pi\) | |||||||
\(80\) | −1348.56 | −1.88468 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 297.993i | − | 0.401315i | ||||||
\(83\) | −1222.14 | −1.61623 | −0.808113 | − | 0.589027i | \(-0.799511\pi\) | ||||
−0.808113 | + | 0.589027i | \(0.799511\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1332.00 | −1.69971 | ||||||||
\(86\) | − | 537.401i | − | 0.673831i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −352.000 | −0.426401 | ||||||||
\(89\) | 695.353 | 0.828172 | 0.414086 | − | 0.910238i | \(-0.364101\pi\) | ||||
0.414086 | + | 0.910238i | \(0.364101\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 444.000 | − | 327.793i | 0.511471 | − | 0.377604i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 119.197i | 0.130790i | ||||||||
\(95\) | − | 1883.73i | − | 2.03439i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 566.187i | − | 0.592656i | −0.955086 | − | 0.296328i | \(-0.904238\pi\) | ||
0.955086 | − | 0.296328i | \(-0.0957621\pi\) | |||||||
\(98\) | −927.138 | − | 285.671i | −0.955664 | − | 0.294461i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 737.496 | 0.726570 | 0.363285 | − | 0.931678i | \(-0.381655\pi\) | ||||
0.363285 | + | 0.931678i | \(0.381655\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 655.585i | 0.627153i | 0.949563 | + | 0.313576i | \(0.101527\pi\) | ||||
−0.949563 | + | 0.313576i | \(0.898473\pi\) | |||||||
\(104\) | −674.282 | −0.635757 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1012.00 | 0.927303 | ||||||||
\(107\) | 1984.14i | 1.79266i | 0.443391 | + | 0.896328i | \(0.353775\pi\) | ||||
−0.443391 | + | 0.896328i | \(0.646225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −844.000 | −0.741656 | −0.370828 | − | 0.928702i | \(-0.620926\pi\) | ||||
−0.370828 | + | 0.928702i | \(0.620926\pi\) | |||||||
\(110\) | −927.138 | −0.803628 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 704.000 | + | 953.579i | 0.593944 | + | 0.804506i | ||||
\(113\) | 575.585i | 0.479172i | 0.970875 | + | 0.239586i | \(0.0770118\pi\) | ||||
−0.970875 | + | 0.239586i | \(0.922988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1638.96i | − | 1.32899i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 238.395i | 0.185983i | ||||||||
\(119\) | 695.353 | + | 941.866i | 0.535655 | + | 0.725552i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1089.00 | 0.818182 | ||||||||
\(122\) | 1854.28 | 1.37605 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4087.83 | 2.92502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −220.000 | −0.153715 | −0.0768577 | − | 0.997042i | \(-0.524489\pi\) | ||||
−0.0768577 | + | 0.997042i | \(0.524489\pi\) | |||||||
\(128\) | − | 1448.15i | − | 1.00000i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1776.00 | −1.19820 | ||||||||
\(131\) | −1306.42 | −0.871317 | −0.435659 | − | 0.900112i | \(-0.643484\pi\) | ||||
−0.435659 | + | 0.900112i | \(0.643484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1332.00 | + | 983.378i | −0.868414 | + | 0.641125i | ||||
\(134\) | 837.214i | 0.539734i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 1430.37i | − | 0.901860i | ||||||
\(137\) | 1568.36i | 0.978060i | 0.872267 | + | 0.489030i | \(0.162649\pi\) | ||||
−0.872267 | + | 0.489030i | \(0.837351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 655.585i | 0.400043i | 0.979791 | + | 0.200022i | \(0.0641012\pi\) | ||||
−0.979791 | + | 0.200022i | \(0.935899\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −932.000 | −0.550787 | ||||||||
\(143\) | −463.569 | −0.271088 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2652.14i | 1.51895i | ||||||||
\(146\) | −2275.70 | −1.28999 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1466.54i | 0.806333i | 0.915127 | + | 0.403166i | \(0.132090\pi\) | ||||
−0.915127 | + | 0.403166i | \(0.867910\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1970.00 | 1.06170 | 0.530849 | − | 0.847467i | \(-0.321873\pi\) | ||||
0.530849 | + | 0.847467i | \(0.321873\pi\) | |||||||
\(152\) | 2022.85 | 1.07944 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 484.000 | + | 655.585i | 0.253259 | + | 0.343043i | ||||
\(155\) | − | 5023.29i | − | 2.60310i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2622.34i | 1.33303i | 0.745492 | + | 0.666515i | \(0.232215\pi\) | ||||
−0.745492 | + | 0.666515i | \(0.767785\pi\) | |||||||
\(158\) | 2364.57i | 1.19060i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1158.92 | + | 855.599i | −0.567303 | + | 0.418824i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1336.00 | −0.641985 | −0.320993 | − | 0.947082i | \(-0.604016\pi\) | ||||
−0.320993 | + | 0.947082i | \(0.604016\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 3456.72i | − | 1.61623i | ||||||
\(167\) | −2317.84 | −1.07401 | −0.537006 | − | 0.843578i | \(-0.680445\pi\) | ||||
−0.537006 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1309.00 | 0.595812 | ||||||||
\(170\) | − | 3767.46i | − | 1.69971i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 231.784 | 0.101863 | 0.0509313 | − | 0.998702i | \(-0.483781\pi\) | ||||
0.0509313 | + | 0.998702i | \(0.483781\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3509.00 | − | 4752.99i | −1.51575 | − | 2.05310i | ||||
\(176\) | − | 995.606i | − | 0.426401i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1966.76i | 0.828172i | ||||||||
\(179\) | 108.894i | 0.0454701i | 0.999742 | + | 0.0227351i | \(0.00723742\pi\) | ||||
−0.999742 | + | 0.0227351i | \(0.992763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2592.54i | − | 1.06465i | −0.846539 | − | 0.532326i | \(-0.821318\pi\) | ||
0.846539 | − | 0.532326i | \(-0.178682\pi\) | |||||||
\(182\) | 927.138 | + | 1255.82i | 0.377604 | + | 0.511471i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1760.00 | 0.705157 | ||||||||
\(185\) | −3877.12 | −1.54082 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 983.378i | − | 0.384555i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5328.00 | 2.03439 | ||||||||
\(191\) | − | 2224.56i | − | 0.842740i | −0.906889 | − | 0.421370i | \(-0.861549\pi\) | ||
0.906889 | − | 0.421370i | \(-0.138451\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3740.00 | 1.39488 | 0.697438 | − | 0.716645i | \(-0.254323\pi\) | ||||
0.697438 | + | 0.716645i | \(0.254323\pi\) | |||||||
\(194\) | 1601.42 | 0.592656 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1197.84i | − | 0.433211i | −0.976259 | − | 0.216605i | \(-0.930502\pi\) | ||
0.976259 | − | 0.216605i | \(-0.0694985\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 804.582i | − | 0.286610i | −0.989679 | − | 0.143305i | \(-0.954227\pi\) | ||
0.989679 | − | 0.143305i | \(-0.0457729\pi\) | |||||||
\(200\) | 7218.15i | 2.55200i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2085.95i | 0.726570i | ||||||||
\(203\) | 1875.35 | − | 1384.52i | 0.648392 | − | 0.478689i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2220.00 | −0.756349 | ||||||||
\(206\) | −1854.28 | −0.627153 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1907.16i | − | 0.635757i | ||||||
\(209\) | 1390.71 | 0.460274 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3590.00 | 1.17131 | 0.585654 | − | 0.810561i | \(-0.300838\pi\) | ||||
0.585654 | + | 0.810561i | \(0.300838\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5612.00 | −1.79266 | ||||||||
\(215\) | −4003.55 | −1.26995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3552.00 | + | 2622.34i | −1.11118 | + | 0.820351i | ||||
\(218\) | − | 2387.19i | − | 0.741656i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1883.73i | − | 0.573365i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3009.73i | 0.903796i | 0.892070 | + | 0.451898i | \(0.149253\pi\) | ||||
−0.892070 | + | 0.451898i | \(0.850747\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1628.00 | −0.479172 | ||||||||
\(227\) | 3708.55 | 1.08434 | 0.542170 | − | 0.840269i | \(-0.317603\pi\) | ||||
0.542170 | + | 0.840269i | \(0.317603\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 327.793i | − | 0.0945902i | −0.998881 | − | 0.0472951i | \(-0.984940\pi\) | ||
0.998881 | − | 0.0472951i | \(-0.0150601\pi\) | |||||||
\(230\) | 4635.69 | 1.32899 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2848.00 | −0.805950 | ||||||||
\(233\) | 643.467i | 0.180922i | 0.995900 | + | 0.0904612i | \(0.0288341\pi\) | ||||
−0.995900 | + | 0.0904612i | \(0.971166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 888.000 | 0.246497 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2664.00 | + | 1966.76i | −0.725552 | + | 0.535655i | ||||
\(239\) | − | 646.296i | − | 0.174918i | −0.996168 | − | 0.0874590i | \(-0.972125\pi\) | ||
0.996168 | − | 0.0874590i | \(-0.0278747\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 387.391i | − | 0.103544i | −0.998659 | − | 0.0517719i | \(-0.983513\pi\) | ||
0.998659 | − | 0.0517719i | \(-0.0164869\pi\) | |||||||
\(242\) | 3080.16i | 0.818182i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2128.20 | + | 6907.02i | −0.554963 | + | 1.80112i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2664.00 | 0.686260 | ||||||||
\(248\) | 5394.25 | 1.38119 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11562.1i | 2.92502i | ||||||||
\(251\) | −6194.96 | −1.55786 | −0.778930 | − | 0.627111i | \(-0.784237\pi\) | ||||
−0.778930 | + | 0.627111i | \(0.784237\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1210.00 | 0.300680 | ||||||||
\(254\) | − | 622.254i | − | 0.153715i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3561.05 | 0.864328 | 0.432164 | − | 0.901795i | \(-0.357750\pi\) | ||||
0.432164 | + | 0.901795i | \(0.357750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2024.00 | + | 2741.54i | 0.485580 | + | 0.657725i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 3695.12i | − | 0.871317i | ||||||
\(263\) | 601.041i | 0.140919i | 0.997515 | + | 0.0704596i | \(0.0224466\pi\) | ||||
−0.997515 | + | 0.0704596i | \(0.977553\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 7539.23i | − | 1.74767i | ||||||
\(266\) | −2781.41 | − | 3767.46i | −0.641125 | − | 0.868414i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4867.47 | 1.10325 | 0.551626 | − | 0.834091i | \(-0.314007\pi\) | ||||
0.551626 | + | 0.834091i | \(0.314007\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1787.96i | − | 0.400778i | −0.979716 | − | 0.200389i | \(-0.935779\pi\) | ||
0.979716 | − | 0.200389i | \(-0.0642206\pi\) | |||||||
\(272\) | 4045.69 | 0.901860 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4436.00 | −0.978060 | ||||||||
\(275\) | 4962.48i | 1.08818i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1126.00 | −0.244241 | −0.122121 | − | 0.992515i | \(-0.538969\pi\) | ||||
−0.122121 | + | 0.992515i | \(0.538969\pi\) | |||||||
\(278\) | −1854.28 | −0.400043 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7104.00 | − | 5244.68i | 1.51623 | − | 1.11939i | ||||
\(281\) | − | 5075.61i | − | 1.07753i | −0.842456 | − | 0.538765i | \(-0.818891\pi\) | ||
0.842456 | − | 0.538765i | \(-0.181109\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7122.04i | − | 1.49598i | −0.663712 | − | 0.747988i | \(-0.731020\pi\) | ||
0.663712 | − | 0.747988i | \(-0.268980\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 1311.17i | − | 0.271088i | ||||||
\(287\) | 1158.92 | + | 1569.78i | 0.238359 | + | 0.322861i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −917.000 | −0.186648 | ||||||||
\(290\) | −7501.39 | −1.51895 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −231.784 | −0.0462150 | −0.0231075 | − | 0.999733i | \(-0.507356\pi\) | ||||
−0.0231075 | + | 0.999733i | \(0.507356\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1776.00 | 0.350518 | ||||||||
\(296\) | − | 4163.44i | − | 0.817552i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4148.00 | −0.806333 | ||||||||
\(299\) | 2317.84 | 0.448309 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2090.00 | + | 2830.94i | 0.400218 | + | 0.542101i | ||||
\(302\) | 5572.00i | 1.06170i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5721.47i | 1.07944i | ||||||||
\(305\) | − | 13814.0i | − | 2.59341i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8850.40i | 1.64534i | 0.568520 | + | 0.822669i | \(0.307516\pi\) | ||||
−0.568520 | + | 0.822669i | \(0.692484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14208.0 | 2.60310 | ||||||||
\(311\) | −6489.96 | −1.18332 | −0.591659 | − | 0.806188i | \(-0.701527\pi\) | ||||
−0.591659 | + | 0.806188i | \(0.701527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10847.0i | − | 1.95881i | −0.201916 | − | 0.979403i | \(-0.564717\pi\) | ||
0.201916 | − | 0.979403i | \(-0.435283\pi\) | |||||||
\(314\) | −7417.10 | −1.33303 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1780.49i | 0.315465i | 0.987482 | + | 0.157733i | \(0.0504184\pi\) | ||||
−0.987482 | + | 0.157733i | \(0.949582\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1958.00 | −0.343658 | ||||||||
\(320\) | −10788.5 | −1.88468 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2420.00 | − | 3277.93i | −0.418824 | − | 0.567303i | ||||
\(323\) | 5651.20i | 0.973502i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9505.99i | 1.62245i | ||||||||
\(326\) | − | 3778.78i | − | 0.641985i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2383.95i | − | 0.401315i | ||||||
\(329\) | −463.569 | − | 627.911i | −0.0776820 | − | 0.105221i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9526.00 | −1.58186 | −0.790931 | − | 0.611905i | \(-0.790403\pi\) | ||||
−0.790931 | + | 0.611905i | \(0.790403\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6555.85i | − | 1.07401i | ||||||
\(335\) | 6237.11 | 1.01722 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8272.00 | −1.33711 | −0.668553 | − | 0.743665i | \(-0.733086\pi\) | ||||
−0.668553 | + | 0.743665i | \(0.733086\pi\) | |||||||
\(338\) | 3702.41i | 0.595812i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3708.55 | 0.588942 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5995.00 | − | 2100.85i | 0.943731 | − | 0.330715i | ||||
\(344\) | − | 4299.21i | − | 0.673831i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 655.585i | 0.101863i | ||||||||
\(347\) | − | 9784.94i | − | 1.51378i | −0.653540 | − | 0.756892i | \(-0.726717\pi\) | ||
0.653540 | − | 0.756892i | \(-0.273283\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6317.46i | 0.968956i | 0.874803 | + | 0.484478i | \(0.160990\pi\) | ||||
−0.874803 | + | 0.484478i | \(0.839010\pi\) | |||||||
\(350\) | 13443.5 | − | 9924.95i | 2.05310 | − | 1.51575i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5457.47 | −0.822866 | −0.411433 | − | 0.911440i | \(-0.634972\pi\) | ||||
−0.411433 | + | 0.911440i | \(0.634972\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6943.24i | 1.03805i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −308.000 | −0.0454701 | ||||||||
\(359\) | 10842.8i | 1.59404i | 0.603954 | + | 0.797019i | \(0.293591\pi\) | ||||
−0.603954 | + | 0.797019i | \(0.706409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1133.00 | −0.165184 | ||||||||
\(362\) | 7332.82 | 1.06465 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16953.6i | 2.43121i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3724.92i | 0.529807i | 0.964275 | + | 0.264903i | \(0.0853400\pi\) | ||||
−0.964275 | + | 0.264903i | \(0.914660\pi\) | |||||||
\(368\) | 4978.03i | 0.705157i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 10966.2i | − | 1.54082i | ||||||
\(371\) | −5331.04 | + | 3935.76i | −0.746021 | + | 0.550766i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4202.00 | 0.583301 | 0.291651 | − | 0.956525i | \(-0.405796\pi\) | ||||
0.291651 | + | 0.956525i | \(0.405796\pi\) | |||||||
\(374\) | 2781.41 | 0.384555 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 953.579i | 0.130790i | ||||||||
\(377\) | −3750.69 | −0.512389 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2506.00 | −0.339643 | −0.169821 | − | 0.985475i | \(-0.554319\pi\) | ||||
−0.169821 | + | 0.985475i | \(0.554319\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6292.00 | 0.842740 | ||||||||
\(383\) | 13106.4 | 1.74857 | 0.874286 | − | 0.485410i | \(-0.161330\pi\) | ||||
0.874286 | + | 0.485410i | \(0.161330\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4884.00 | − | 3605.72i | 0.646524 | − | 0.477310i | ||||
\(386\) | 10578.3i | 1.39488i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4631.55i | 0.603673i | 0.953360 | + | 0.301837i | \(0.0975997\pi\) | ||||
−0.953360 | + | 0.301837i | \(0.902400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4916.89i | 0.635953i | ||||||||
\(392\) | −7417.10 | − | 2285.37i | −0.955664 | − | 0.294461i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3388.00 | 0.433211 | ||||||||
\(395\) | 17615.6 | 2.24389 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8045.82i | 1.01715i | 0.861018 | + | 0.508574i | \(0.169827\pi\) | ||||
−0.861018 | + | 0.508574i | \(0.830173\pi\) | |||||||
\(398\) | 2275.70 | 0.286610 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20416.0 | −2.55200 | ||||||||
\(401\) | − | 13552.4i | − | 1.68772i | −0.536565 | − | 0.843859i | \(-0.680278\pi\) | ||
0.536565 | − | 0.843859i | \(-0.319722\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7104.00 | 0.878103 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3916.00 | + | 5304.28i | 0.478689 | + | 0.648392i | ||||
\(407\) | − | 2862.37i | − | 0.348605i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10161.6i | − | 1.22850i | −0.789111 | − | 0.614251i | \(-0.789458\pi\) | ||
0.789111 | − | 0.614251i | \(-0.210542\pi\) | |||||||
\(410\) | − | 6279.11i | − | 0.756349i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −927.138 | − | 1255.82i | −0.110464 | − | 0.149625i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25752.0 | −3.04606 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3933.51i | 0.460274i | ||||||||
\(419\) | 8934.23 | 1.04168 | 0.520842 | − | 0.853653i | \(-0.325618\pi\) | ||||
0.520842 | + | 0.853653i | \(0.325618\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5606.00 | 0.648978 | 0.324489 | − | 0.945889i | \(-0.394808\pi\) | ||||
0.324489 | + | 0.945889i | \(0.394808\pi\) | |||||||
\(422\) | 10154.1i | 1.17131i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8096.00 | 0.927303 | ||||||||
\(425\) | −20165.2 | −2.30155 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9768.00 | + | 7211.44i | −1.10704 | + | 0.817297i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 11323.7i | − | 1.26995i | ||||||
\(431\) | − | 883.883i | − | 0.0987823i | −0.998780 | − | 0.0493911i | \(-0.984272\pi\) | ||
0.998780 | − | 0.0493911i | \(-0.0157281\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1966.76i | − | 0.218282i | −0.994026 | − | 0.109141i | \(-0.965190\pi\) | ||
0.994026 | − | 0.109141i | \(-0.0348101\pi\) | |||||||
\(434\) | −7417.10 | − | 10046.6i | −0.820351 | − | 1.11118i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6953.53 | −0.761173 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 387.391i | − | 0.0421166i | −0.999778 | − | 0.0210583i | \(-0.993296\pi\) | ||
0.999778 | − | 0.0210583i | \(-0.00670356\pi\) | |||||||
\(440\) | −7417.10 | −0.803628 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5328.00 | 0.573365 | ||||||||
\(443\) | − | 2623.37i | − | 0.281354i | −0.990056 | − | 0.140677i | \(-0.955072\pi\) | ||
0.990056 | − | 0.140677i | \(-0.0449279\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14652.0 | 1.56083 | ||||||||
\(446\) | −8512.81 | −0.903796 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5632.00 | + | 7628.63i | 0.593944 | + | 0.804506i | ||||
\(449\) | 5140.67i | 0.540319i | 0.962816 | + | 0.270159i | \(0.0870764\pi\) | ||||
−0.962816 | + | 0.270159i | \(0.912924\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1638.96i | − | 0.171121i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 10489.4i | 1.08434i | ||||||||
\(455\) | 9355.66 | − | 6907.02i | 0.963956 | − | 0.711662i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3608.00 | 0.369311 | 0.184655 | − | 0.982803i | \(-0.440883\pi\) | ||||
0.184655 | + | 0.982803i | \(0.440883\pi\) | |||||||
\(458\) | 927.138 | 0.0945902 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1538.21 | −0.155404 | −0.0777021 | − | 0.996977i | \(-0.524758\pi\) | ||||
−0.0777021 | + | 0.996977i | \(0.524758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1772.00 | 0.177866 | 0.0889329 | − | 0.996038i | \(-0.471654\pi\) | ||||
0.0889329 | + | 0.996038i | \(0.471654\pi\) | |||||||
\(464\) | − | 8055.36i | − | 0.805950i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1820.00 | −0.180922 | ||||||||
\(467\) | −12769.2 | −1.26529 | −0.632643 | − | 0.774443i | \(-0.718030\pi\) | ||||
−0.632643 | + | 0.774443i | \(0.718030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3256.00 | − | 4410.30i | −0.320572 | − | 0.434219i | ||||
\(470\) | 2511.64i | 0.246497i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1907.16i | 0.185983i | ||||||||
\(473\) | − | 2955.71i | − | 0.287322i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 28518.0i | − | 2.75472i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1828.00 | 0.174918 | ||||||||
\(479\) | −4635.69 | −0.442192 | −0.221096 | − | 0.975252i | \(-0.570963\pi\) | ||||
−0.221096 | + | 0.975252i | \(0.570963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5483.08i | − | 0.519765i | ||||||
\(482\) | 1095.71 | 0.103544 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 11930.3i | − | 1.11696i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1958.00 | 0.182188 | 0.0910939 | − | 0.995842i | \(-0.470964\pi\) | ||||
0.0910939 | + | 0.995842i | \(0.470964\pi\) | |||||||
\(488\) | 14834.2 | 1.37605 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19536.0 | − | 6019.46i | −1.80112 | − | 0.554963i | ||||
\(491\) | 7126.22i | 0.654994i | 0.944852 | + | 0.327497i | \(0.106205\pi\) | ||||
−0.944852 | + | 0.327497i | \(0.893795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 7956.42i | − | 0.726854i | ||||||
\(494\) | 7534.93i | 0.686260i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15257.3i | 1.38119i | ||||||||
\(497\) | 4909.61 | − | 3624.63i | 0.443111 | − | 0.327137i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10310.0 | 0.924928 | 0.462464 | − | 0.886638i | \(-0.346965\pi\) | ||||
0.462464 | + | 0.886638i | \(0.346965\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 17522.0i | − | 1.55786i | ||||||
\(503\) | −126.428 | −0.0112070 | −0.00560352 | − | 0.999984i | \(-0.501784\pi\) | ||||
−0.00560352 | + | 0.999984i | \(0.501784\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15540.0 | 1.36935 | ||||||||
\(506\) | 3422.40i | 0.300680i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7101.03 | 0.618365 | 0.309182 | − | 0.951003i | \(-0.399945\pi\) | ||||
0.309182 | + | 0.951003i | \(0.399945\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11988.0 | − | 8850.40i | 1.03780 | − | 0.766181i | ||||
\(512\) | − | 11585.2i | − | 1.00000i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10072.2i | 0.864328i | ||||||||
\(515\) | 13814.0i | 1.18198i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 655.585i | 0.0557691i | ||||||||
\(518\) | −7754.24 | + | 5724.74i | −0.657725 | + | 0.485580i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −14208.0 | −1.19820 | ||||||||
\(521\) | −4488.19 | −0.377411 | −0.188705 | − | 0.982034i | \(-0.560429\pi\) | ||||
−0.188705 | + | 0.982034i | \(0.560429\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9297.39i | 0.777336i | 0.921378 | + | 0.388668i | \(0.127065\pi\) | ||||
−0.921378 | + | 0.388668i | \(0.872935\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1700.00 | −0.140919 | ||||||||
\(527\) | 15069.9i | 1.24564i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6117.00 | 0.502753 | ||||||||
\(530\) | 21324.2 | 1.74767 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3139.55i | − | 0.255139i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 41808.5i | 3.37857i | ||||||||
\(536\) | 6697.72i | 0.539734i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13767.3i | 1.10325i | ||||||||
\(539\) | −5099.26 | − | 1571.19i | −0.407496 | − | 0.125558i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15646.0 | −1.24339 | −0.621695 | − | 0.783259i | \(-0.713556\pi\) | ||||
−0.621695 | + | 0.783259i | \(0.713556\pi\) | |||||||
\(542\) | 5057.11 | 0.400778 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17784.2 | −1.39778 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1880.00 | 0.146952 | 0.0734762 | − | 0.997297i | \(-0.476591\pi\) | ||||
0.0734762 | + | 0.997297i | \(0.476591\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14036.0 | −1.08818 | ||||||||
\(551\) | 11252.1 | 0.869972 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9196.00 | − | 12456.1i | −0.707150 | − | 0.957845i | ||||
\(554\) | − | 3184.81i | − | 0.244241i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7001.77i | − | 0.532629i | −0.963886 | − | 0.266315i | \(-0.914194\pi\) | ||
0.963886 | − | 0.266315i | \(-0.0858060\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5661.87i | − | 0.428393i | ||||||
\(560\) | 14834.2 | + | 20093.1i | 1.11939 | + | 1.51623i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14356.0 | 1.07753 | ||||||||
\(563\) | −8386.38 | −0.627786 | −0.313893 | − | 0.949458i | \(-0.601633\pi\) | ||||
−0.313893 | + | 0.949458i | \(0.601633\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12128.3i | 0.903084i | ||||||||
\(566\) | 20144.2 | 1.49598 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7456.00 | −0.550787 | ||||||||
\(569\) | − | 17905.4i | − | 1.31921i | −0.751612 | − | 0.659606i | \(-0.770723\pi\) | ||
0.751612 | − | 0.659606i | \(-0.229277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24736.0 | −1.81291 | −0.906453 | − | 0.422307i | \(-0.861221\pi\) | ||||
−0.906453 | + | 0.422307i | \(0.861221\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4440.00 | + | 3277.93i | −0.322861 | + | 0.238359i | ||||
\(575\) | − | 24812.4i | − | 1.79956i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 17343.2i | − | 1.25131i | −0.780099 | − | 0.625656i | \(-0.784831\pi\) | ||
0.780099 | − | 0.625656i | \(-0.215169\pi\) | |||||||
\(578\) | − | 2593.67i | − | 0.186648i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13443.5 | + | 18209.4i | 0.959949 | + | 1.30026i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5566.00 | 0.395403 | ||||||||
\(584\) | −18205.6 | −1.28999 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 655.585i | − | 0.0462150i | ||||||
\(587\) | 3329.27 | 0.234095 | 0.117047 | − | 0.993126i | \(-0.462657\pi\) | ||||
0.117047 | + | 0.993126i | \(0.462657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21312.0 | −1.49091 | ||||||||
\(590\) | 5023.29i | 0.350518i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11776.0 | 0.817552 | ||||||||
\(593\) | −22567.4 | −1.56278 | −0.781392 | − | 0.624041i | \(-0.785490\pi\) | ||||
−0.781392 | + | 0.624041i | \(0.785490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14652.0 | + | 19846.4i | 1.00954 | + | 1.36743i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6555.85i | 0.448309i | ||||||||
\(599\) | 25216.8i | 1.72009i | 0.510221 | + | 0.860044i | \(0.329564\pi\) | ||||
−0.510221 | + | 0.860044i | \(0.670436\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13290.5i | 0.902048i | 0.892512 | + | 0.451024i | \(0.148941\pi\) | ||||
−0.892512 | + | 0.451024i | \(0.851059\pi\) | |||||||
\(602\) | −8007.10 | + | 5911.41i | −0.542101 | + | 0.400218i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22946.7 | 1.54201 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 18386.2i | − | 1.22944i | −0.788744 | − | 0.614722i | \(-0.789268\pi\) | ||
0.788744 | − | 0.614722i | \(-0.210732\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39072.0 | 2.59341 | ||||||||
\(611\) | 1255.82i | 0.0831507i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26554.0 | −1.74960 | −0.874801 | − | 0.484483i | \(-0.839008\pi\) | ||||
−0.874801 | + | 0.484483i | \(0.839008\pi\) | |||||||
\(614\) | −25032.7 | −1.64534 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3872.00 | + | 5244.68i | 0.253259 | + | 0.343043i | ||||
\(617\) | − | 26475.5i | − | 1.72749i | −0.503927 | − | 0.863746i | \(-0.668112\pi\) | ||
0.503927 | − | 0.863746i | \(-0.331888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 16389.6i | − | 1.06422i | −0.846674 | − | 0.532112i | \(-0.821398\pi\) | ||
0.846674 | − | 0.532112i | \(-0.178602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 18356.4i | − | 1.18332i | ||||||
\(623\) | −7648.88 | − | 10360.5i | −0.491888 | − | 0.666269i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 46261.0 | 2.96070 | ||||||||
\(626\) | 30679.8 | 1.95881 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11631.4 | 0.737318 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24860.0 | 1.56840 | 0.784200 | − | 0.620508i | \(-0.213073\pi\) | ||||
0.784200 | + | 0.620508i | \(0.213073\pi\) | |||||||
\(632\) | 18916.5i | 1.19060i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5036.00 | −0.315465 | ||||||||
\(635\) | −4635.69 | −0.289703 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9768.00 | − | 3009.73i | −0.607570 | − | 0.187206i | ||||
\(638\) | − | 5538.06i | − | 0.343658i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 30514.5i | − | 1.88468i | ||||||
\(641\) | − | 5279.26i | − | 0.325301i | −0.986684 | − | 0.162651i | \(-0.947996\pi\) | ||
0.986684 | − | 0.162651i | \(-0.0520044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2652.14i | − | 0.162660i | −0.996687 | − | 0.0813299i | \(-0.974083\pi\) | ||
0.996687 | − | 0.0813299i | \(-0.0259167\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15984.0 | −0.973502 | ||||||||
\(647\) | −23009.9 | −1.39816 | −0.699081 | − | 0.715042i | \(-0.746407\pi\) | ||||
−0.699081 | + | 0.715042i | \(0.746407\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1311.17i | 0.0793035i | ||||||||
\(650\) | −26887.0 | −1.62245 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 5864.74i | − | 0.351463i | −0.984438 | − | 0.175731i | \(-0.943771\pi\) | ||
0.984438 | − | 0.175731i | \(-0.0562290\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27528.0 | −1.64215 | ||||||||
\(656\) | 6742.82 | 0.401315 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1776.00 | − | 1311.17i | 0.105221 | − | 0.0776820i | ||||
\(659\) | − | 2759.13i | − | 0.163096i | −0.996669 | − | 0.0815482i | \(-0.974014\pi\) | ||
0.996669 | − | 0.0815482i | \(-0.0259864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 20978.7i | − | 1.23446i | −0.786783 | − | 0.617230i | \(-0.788255\pi\) | ||
0.786783 | − | 0.617230i | \(-0.211745\pi\) | |||||||
\(662\) | − | 26943.6i | − | 1.58186i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 27653.8i | − | 1.61623i | ||||||
\(665\) | −28067.0 | + | 20721.1i | −1.63668 | + | 1.20831i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9790.00 | 0.568321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17641.2i | 1.01722i | ||||||||
\(671\) | 10198.5 | 0.586750 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13636.0 | −0.781024 | −0.390512 | − | 0.920598i | \(-0.627702\pi\) | ||||
−0.390512 | + | 0.920598i | \(0.627702\pi\) | |||||||
\(674\) | − | 23396.7i | − | 1.33711i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9966.73 | 0.565809 | 0.282904 | − | 0.959148i | \(-0.408702\pi\) | ||||
0.282904 | + | 0.959148i | \(0.408702\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8436.00 | + | 6228.06i | −0.476795 | + | 0.352004i | ||||
\(680\) | − | 30139.7i | − | 1.69971i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10489.4i | 0.588942i | ||||||||
\(683\) | 202.233i | 0.0113297i | 0.999984 | + | 0.00566487i | \(0.00180319\pi\) | ||||
−0.999984 | + | 0.00566487i | \(0.998197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33047.5i | 1.84333i | ||||||||
\(686\) | 5942.11 | + | 16956.4i | 0.330715 | + | 0.943731i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12160.0 | 0.673831 | ||||||||
\(689\) | 10662.1 | 0.589540 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20084.7i | 1.10573i | 0.833271 | + | 0.552865i | \(0.186466\pi\) | ||||
−0.833271 | + | 0.552865i | \(0.813534\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27676.0 | 1.51378 | ||||||||
\(695\) | 13814.0i | 0.753952i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6660.00 | 0.361930 | ||||||||
\(698\) | −17868.5 | −0.968956 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22883.4i | 1.23294i | 0.787377 | + | 0.616472i | \(0.211439\pi\) | ||||
−0.787377 | + | 0.616472i | \(0.788561\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16449.2i | 0.882496i | ||||||||
\(704\) | − | 7964.85i | − | 0.426401i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 15436.1i | − | 0.822866i | ||||||
\(707\) | −8112.45 | − | 10988.4i | −0.431542 | − | 0.584530i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12212.0 | 0.646871 | 0.323435 | − | 0.946250i | \(-0.395162\pi\) | ||||
0.323435 | + | 0.946250i | \(0.395162\pi\) | |||||||
\(710\) | −19638.5 | −1.03805 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15734.0i | 0.828172i | ||||||||
\(713\) | −18542.8 | −0.973957 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9768.00 | −0.510913 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −30668.0 | −1.59404 | ||||||||
\(719\) | 28825.5 | 1.49515 | 0.747574 | − | 0.664178i | \(-0.231218\pi\) | ||||
0.747574 | + | 0.664178i | \(0.231218\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9768.00 | − | 7211.44i | 0.504548 | − | 0.372494i | ||||
\(722\) | − | 3204.61i | − | 0.165184i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40150.9i | 2.05678i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3277.93i | 0.167224i | 0.996498 | + | 0.0836118i | \(0.0266456\pi\) | ||||
−0.996498 | + | 0.0836118i | \(0.973354\pi\) | |||||||
\(728\) | 7417.10 | + | 10046.6i | 0.377604 | + | 0.511471i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −47952.0 | −2.43121 | ||||||||
\(731\) | 12010.6 | 0.607701 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 12128.3i | − | 0.611146i | −0.952169 | − | 0.305573i | \(-0.901152\pi\) | ||
0.952169 | − | 0.305573i | \(-0.0988480\pi\) | |||||||
\(734\) | −10535.7 | −0.529807 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4604.68i | 0.230143i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1760.00 | 0.0876085 | 0.0438042 | − | 0.999040i | \(-0.486052\pi\) | ||||
0.0438042 | + | 0.999040i | \(0.486052\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11132.0 | − | 15078.5i | −0.550766 | − | 0.746021i | ||||
\(743\) | − | 22436.5i | − | 1.10783i | −0.832574 | − | 0.553913i | \(-0.813134\pi\) | ||
0.832574 | − | 0.553913i | \(-0.186866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30901.9i | 1.51968i | ||||||||
\(746\) | 11885.1i | 0.583301i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29563.0 | − | 21825.6i | 1.44220 | − | 1.06474i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5122.00 | −0.248874 | −0.124437 | − | 0.992228i | \(-0.539712\pi\) | ||||
−0.124437 | + | 0.992228i | \(0.539712\pi\) | |||||||
\(752\) | −2697.13 | −0.130790 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 10608.6i | − | 0.512389i | ||||||
\(755\) | 41510.5 | 2.00095 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18772.0 | −0.901295 | −0.450647 | − | 0.892702i | \(-0.648807\pi\) | ||||
−0.450647 | + | 0.892702i | \(0.648807\pi\) | |||||||
\(758\) | − | 7088.04i | − | 0.339643i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 42624.0 | 2.03439 | ||||||||
\(761\) | 28973.0 | 1.38012 | 0.690061 | − | 0.723752i | \(-0.257584\pi\) | ||||
0.690061 | + | 0.723752i | \(0.257584\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9284.00 | + | 12575.3i | 0.440502 | + | 0.596667i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37070.4i | 1.74857i | ||||||||
\(767\) | 2511.64i | 0.118240i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11740.9i | 0.550571i | 0.961363 | + | 0.275285i | \(0.0887724\pi\) | ||||
−0.961363 | + | 0.275285i | \(0.911228\pi\) | |||||||
\(770\) | 10198.5 | + | 13814.0i | 0.477310 | + | 0.646524i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12706.0 | 0.591207 | 0.295603 | − | 0.955311i | \(-0.404479\pi\) | ||||
0.295603 | + | 0.955311i | \(0.404479\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 76047.9i | − | 3.52480i | ||||||
\(776\) | 12811.4 | 0.592656 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13100.0 | −0.603673 | ||||||||
\(779\) | 9418.66i | 0.433195i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5126.00 | −0.234856 | ||||||||
\(782\) | −13907.1 | −0.635953 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6464.00 | − | 20978.7i | 0.294461 | − | 0.955664i | ||||
\(785\) | 55256.2i | 2.51233i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 26342.6i | − | 1.19315i | −0.802556 | − | 0.596577i | \(-0.796527\pi\) | ||
0.802556 | − | 0.596577i | \(-0.203473\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 49824.5i | 2.24389i | ||||||||
\(791\) | 8576.02 | − | 6331.43i | 0.385497 | − | 0.284602i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19536.0 | 0.874834 | ||||||||
\(794\) | −22757.0 | −1.01715 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19448.8 | −0.864382 | −0.432191 | − | 0.901782i | \(-0.642259\pi\) | ||||
−0.432191 | + | 0.901782i | \(0.642259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2664.00 | −0.117954 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38332.0 | 1.68772 | ||||||||
\(803\) | −12516.4 | −0.550053 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −24420.0 | + | 18028.6i | −1.06918 | + | 0.789347i | ||||
\(806\) | 20093.1i | 0.878103i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16687.6i | 0.726570i | ||||||||
\(809\) | 34593.1i | 1.50337i | 0.659521 | + | 0.751686i | \(0.270759\pi\) | ||||
−0.659521 | + | 0.751686i | \(0.729241\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28607.4i | − | 1.23864i | −0.785137 | − | 0.619322i | \(-0.787408\pi\) | ||
0.785137 | − | 0.619322i | \(-0.212592\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8096.00 | 0.348605 | ||||||||
\(815\) | −28151.3 | −1.20993 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16985.6i | 0.727358i | ||||||||
\(818\) | 28741.3 | 1.22850 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 28469.5i | − | 1.21022i | −0.796141 | − | 0.605112i | \(-0.793128\pi\) | ||
0.796141 | − | 0.605112i | \(-0.206872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23468.0 | 0.993977 | 0.496988 | − | 0.867757i | \(-0.334439\pi\) | ||||
0.496988 | + | 0.867757i | \(0.334439\pi\) | |||||||
\(824\) | −14834.2 | −0.627153 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3552.00 | − | 2622.34i | 0.149625 | − | 0.110464i | ||||
\(827\) | − | 37447.0i | − | 1.57456i | −0.616598 | − | 0.787278i | \(-0.711489\pi\) | ||
0.616598 | − | 0.787278i | \(-0.288511\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10817.2i | 0.453191i | 0.973989 | + | 0.226596i | \(0.0727595\pi\) | ||||
−0.973989 | + | 0.226596i | \(0.927240\pi\) | |||||||
\(830\) | − | 72837.7i | − | 3.04606i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 15257.3i | − | 0.635757i | ||||||
\(833\) | 6384.61 | − | 20721.1i | 0.265562 | − | 0.861875i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −48840.0 | −2.02417 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25269.8i | 1.04168i | ||||||||
\(839\) | −42690.5 | −1.75666 | −0.878331 | − | 0.478054i | \(-0.841342\pi\) | ||||
−0.878331 | + | 0.478054i | \(0.841342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8547.00 | 0.350445 | ||||||||
\(842\) | 15856.2i | 0.648978i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27582.3 | 1.12291 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11979.0 | − | 16225.7i | −0.485954 | − | 0.658232i | ||||
\(848\) | 22898.9i | 0.927303i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 57035.9i | − | 2.30155i | ||||||
\(851\) | 14311.8i | 0.576502i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 4589.10i | − | 0.184206i | −0.995749 | − | 0.0921030i | \(-0.970641\pi\) | ||
0.995749 | − | 0.0921030i | \(-0.0293589\pi\) | |||||||
\(854\) | −20397.0 | − | 27628.1i | −0.817297 | − | 1.10704i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −44896.0 | −1.79266 | ||||||||
\(857\) | 4783.19 | 0.190654 | 0.0953270 | − | 0.995446i | \(-0.469610\pi\) | ||||
0.0953270 | + | 0.995446i | \(0.469610\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37040.6i | 1.47125i | 0.677386 | + | 0.735627i | \(0.263113\pi\) | ||||
−0.677386 | + | 0.735627i | \(0.736887\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2500.00 | 0.0987823 | ||||||||
\(863\) | 1195.01i | 0.0471363i | 0.999722 | + | 0.0235682i | \(0.00750267\pi\) | ||||
−0.999722 | + | 0.0235682i | \(0.992497\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4884.00 | 0.191978 | ||||||||
\(866\) | 5562.83 | 0.218282 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13005.1i | 0.507673i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8820.60i | 0.343140i | ||||||||
\(872\) | − | 19097.5i | − | 0.741656i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 19667.6i | − | 0.761173i | ||||||
\(875\) | −44966.2 | − | 60907.3i | −1.73730 | − | 2.35319i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34298.0 | 1.32059 | 0.660297 | − | 0.751004i | \(-0.270430\pi\) | ||||
0.660297 | + | 0.751004i | \(0.270430\pi\) | |||||||
\(878\) | 1095.71 | 0.0421166 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 20978.7i | − | 0.803628i | ||||||
\(881\) | −21682.4 | −0.829169 | −0.414584 | − | 0.910011i | \(-0.636073\pi\) | ||||
−0.414584 | + | 0.910011i | \(0.636073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16034.0 | 0.611084 | 0.305542 | − | 0.952179i | \(-0.401162\pi\) | ||||
0.305542 | + | 0.952179i | \(0.401162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7420.00 | 0.281354 | ||||||||
\(887\) | −46820.4 | −1.77235 | −0.886176 | − | 0.463348i | \(-0.846648\pi\) | ||||
−0.886176 | + | 0.463348i | \(0.846648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2420.00 | + | 3277.93i | 0.0912983 | + | 0.123665i | ||||
\(890\) | 41442.1i | 1.56083i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 3767.46i | − | 0.141180i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2294.55i | 0.0856964i | ||||||||
\(896\) | −21577.0 | + | 15929.7i | −0.804506 | + | 0.593944i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14540.0 | −0.540319 | ||||||||
\(899\) | 30005.5 | 1.11317 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22617.7i | 0.836298i | ||||||||
\(902\) | 4635.69 | 0.171121 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13024.0 | −0.479172 | ||||||||
\(905\) | − | 54628.2i | − | 2.00652i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51722.0 | 1.89350 | 0.946748 | − | 0.321976i | \(-0.104347\pi\) | ||||
0.946748 | + | 0.321976i | \(0.104347\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 19536.0 | + | 26461.8i | 0.711662 | + | 0.963956i | ||||
\(911\) | 38564.2i | 1.40251i | 0.712909 | + | 0.701256i | \(0.247377\pi\) | ||||
−0.712909 | + | 0.701256i | \(0.752623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 19012.0i | − | 0.689161i | ||||||
\(914\) | 10205.0i | 0.369311i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14370.6 | + | 19465.2i | 0.517514 | + | 0.700980i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30470.0 | 1.09370 | 0.546851 | − | 0.837230i | \(-0.315826\pi\) | ||||
0.546851 | + | 0.837230i | \(0.315826\pi\) | |||||||
\(920\) | 37085.5 | 1.32899 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 4350.70i | − | 0.155404i | ||||||
\(923\) | −9819.23 | −0.350167 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −58696.0 | −2.08639 | ||||||||
\(926\) | 5011.97i | 0.177866i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26444.5 | −0.933924 | −0.466962 | − | 0.884277i | \(-0.654652\pi\) | ||||
−0.466962 | + | 0.884277i | \(0.654652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29304.0 | + | 9029.20i | 1.03158 | + | 0.317852i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 36116.8i | − | 1.26529i | ||||||
\(935\) | − | 20721.1i | − | 0.724760i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19667.6i | − | 0.685711i | −0.939388 | − | 0.342855i | \(-0.888606\pi\) | ||
0.939388 | − | 0.342855i | \(-0.111394\pi\) | |||||||
\(938\) | 12474.2 | − | 9209.36i | 0.434219 | − | 0.320572i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3940.33 | 0.136505 | 0.0682525 | − | 0.997668i | \(-0.478258\pi\) | ||||
0.0682525 | + | 0.997668i | \(0.478258\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8194.82i | 0.282990i | ||||||||
\(944\) | −5394.25 | −0.185983 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8360.00 | 0.287322 | ||||||||
\(947\) | 52081.2i | 1.78713i | 0.448933 | + | 0.893565i | \(0.351804\pi\) | ||||
−0.448933 | + | 0.893565i | \(0.648196\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23976.0 | −0.820120 | ||||||||
\(950\) | 80661.0 | 2.75472 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21312.0 | + | 15734.0i | −0.725552 | + | 0.535655i | ||||
\(953\) | 15993.3i | 0.543626i | 0.962350 | + | 0.271813i | \(0.0876231\pi\) | ||||
−0.962350 | + | 0.271813i | \(0.912377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 46874.3i | − | 1.58829i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 13111.7i | − | 0.442192i | ||||||
\(959\) | 23368.1 | − | 17252.0i | 0.786856 | − | 0.580913i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27041.0 | −0.907690 | ||||||||
\(962\) | 15508.5 | 0.519765 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 78806.7 | 2.62889 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24772.0 | −0.823799 | −0.411900 | − | 0.911229i | \(-0.635135\pi\) | ||||
−0.411900 | + | 0.911229i | \(0.635135\pi\) | |||||||
\(968\) | 24641.3i | 0.818182i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 33744.0 | 1.11696 | ||||||||
\(971\) | −55122.5 | −1.82180 | −0.910899 | − | 0.412629i | \(-0.864611\pi\) | ||||
−0.910899 | + | 0.412629i | \(0.864611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9768.00 | − | 7211.44i | 0.321837 | − | 0.237603i | ||||
\(974\) | 5538.06i | 0.182188i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 41957.5i | 1.37605i | ||||||||
\(977\) | − | 45160.1i | − | 1.47881i | −0.673260 | − | 0.739406i | \(-0.735107\pi\) | ||
0.673260 | − | 0.739406i | \(-0.264893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10817.2i | 0.353134i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20156.0 | −0.654994 | ||||||||
\(983\) | −33840.5 | −1.09801 | −0.549006 | − | 0.835819i | \(-0.684993\pi\) | ||||
−0.549006 | + | 0.835819i | \(0.684993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 25240.0i | − | 0.816461i | ||||||
\(986\) | 22504.2 | 0.726854 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 14778.5i | 0.475157i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18382.0 | −0.589227 | −0.294613 | − | 0.955617i | \(-0.595191\pi\) | ||||
−0.294613 | + | 0.955617i | \(0.595191\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10252.0 | + | 13886.5i | 0.327137 | + | 0.443111i | ||||
\(995\) | − | 16953.6i | − | 0.540166i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38679.5i | 1.22868i | 0.789042 | + | 0.614340i | \(0.210577\pi\) | ||||
−0.789042 | + | 0.614340i | \(0.789423\pi\) | |||||||
\(998\) | 29161.1i | 0.924928i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 63.4.c.b.62.4 | yes | 4 | |
3.2 | odd | 2 | inner | 63.4.c.b.62.1 | ✓ | 4 | |
4.3 | odd | 2 | 1008.4.k.b.881.4 | 4 | |||
7.2 | even | 3 | 441.4.p.a.80.3 | 8 | |||
7.3 | odd | 6 | 441.4.p.a.215.2 | 8 | |||
7.4 | even | 3 | 441.4.p.a.215.1 | 8 | |||
7.5 | odd | 6 | 441.4.p.a.80.4 | 8 | |||
7.6 | odd | 2 | inner | 63.4.c.b.62.3 | yes | 4 | |
12.11 | even | 2 | 1008.4.k.b.881.2 | 4 | |||
21.2 | odd | 6 | 441.4.p.a.80.2 | 8 | |||
21.5 | even | 6 | 441.4.p.a.80.1 | 8 | |||
21.11 | odd | 6 | 441.4.p.a.215.4 | 8 | |||
21.17 | even | 6 | 441.4.p.a.215.3 | 8 | |||
21.20 | even | 2 | inner | 63.4.c.b.62.2 | yes | 4 | |
28.27 | even | 2 | 1008.4.k.b.881.1 | 4 | |||
84.83 | odd | 2 | 1008.4.k.b.881.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.c.b.62.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
63.4.c.b.62.2 | yes | 4 | 21.20 | even | 2 | inner | |
63.4.c.b.62.3 | yes | 4 | 7.6 | odd | 2 | inner | |
63.4.c.b.62.4 | yes | 4 | 1.1 | even | 1 | trivial | |
441.4.p.a.80.1 | 8 | 21.5 | even | 6 | |||
441.4.p.a.80.2 | 8 | 21.2 | odd | 6 | |||
441.4.p.a.80.3 | 8 | 7.2 | even | 3 | |||
441.4.p.a.80.4 | 8 | 7.5 | odd | 6 | |||
441.4.p.a.215.1 | 8 | 7.4 | even | 3 | |||
441.4.p.a.215.2 | 8 | 7.3 | odd | 6 | |||
441.4.p.a.215.3 | 8 | 21.17 | even | 6 | |||
441.4.p.a.215.4 | 8 | 21.11 | odd | 6 | |||
1008.4.k.b.881.1 | 4 | 28.27 | even | 2 | |||
1008.4.k.b.881.2 | 4 | 12.11 | even | 2 | |||
1008.4.k.b.881.3 | 4 | 84.83 | odd | 2 | |||
1008.4.k.b.881.4 | 4 | 4.3 | odd | 2 |