Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (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: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.36 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.17 |
$q$-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 \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.08125 | + | 0.817560i | 0.930763 | + | 0.365624i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.41849i | − | 1.29207i | −0.763308 | − | 0.646034i | \(-0.776426\pi\) | ||
0.763308 | − | 0.646034i | \(-0.223574\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.18352 | 1.56289 | 0.781446 | − | 0.623973i | \(-0.214483\pi\) | ||||
0.781446 | + | 0.623973i | \(0.214483\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.24487i | 1.45467i | 0.686285 | + | 0.727333i | \(0.259240\pi\) | ||||
−0.686285 | + | 0.727333i | \(0.740760\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.817560 | + | 2.08125i | −0.211093 | + | 0.537376i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.93273i | − | 1.92397i | −0.273105 | − | 0.961984i | \(-0.588051\pi\) | ||
0.273105 | − | 0.961984i | \(-0.411949\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.59836 | 0.366688 | 0.183344 | − | 0.983049i | \(-0.441308\pi\) | ||||
0.183344 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.41849 | 0.745976 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.16283i | − | 1.49355i | −0.665075 | − | 0.746777i | \(-0.731600\pi\) | ||
0.665075 | − | 0.746777i | \(-0.268400\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.66319 | + | 3.40309i | 0.732638 | + | 0.680619i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.58679 | 1.22314 | 0.611568 | − | 0.791192i | \(-0.290539\pi\) | ||||
0.611568 | + | 0.791192i | \(0.290539\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.96221 | −1.07085 | −0.535423 | − | 0.844584i | \(-0.679848\pi\) | ||||
−0.535423 | + | 0.844584i | \(0.679848\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.18352i | 0.902336i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.79482 | − | 7.11473i | 0.472412 | − | 1.20261i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.2629i | − | 1.68720i | −0.536969 | − | 0.843602i | \(-0.680431\pi\) | ||
0.536969 | − | 0.843602i | \(-0.319569\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.24487 | −0.839852 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.07835 | −1.26163 | −0.630813 | − | 0.775935i | \(-0.717279\pi\) | ||||
−0.630813 | + | 0.775935i | \(0.717279\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 0.663360i | − | 0.101161i | −0.998720 | − | 0.0505807i | \(-0.983893\pi\) | ||
0.998720 | − | 0.0505807i | \(-0.0161072\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.08125 | − | 0.817560i | −0.310254 | − | 0.121875i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 7.08264i | − | 1.03311i | −0.856254 | − | 0.516555i | \(-0.827214\pi\) | ||
0.856254 | − | 0.516555i | \(-0.172786\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.68609 | −0.669442 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.93273 | 1.11080 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5654i | 1.58863i | 0.607504 | + | 0.794316i | \(0.292171\pi\) | ||||
−0.607504 | + | 0.794316i | \(0.707829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.7882 | + | 4.23784i | 1.45468 | + | 0.571431i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.59836i | 0.211707i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.90150 | 0.247554 | 0.123777 | − | 0.992310i | \(-0.460499\pi\) | ||||
0.123777 | + | 0.992310i | \(0.460499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.14296 | 0.146341 | 0.0731705 | − | 0.997319i | \(-0.476688\pi\) | ||||
0.0731705 | + | 0.997319i | \(0.476688\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.41849i | 0.430690i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.28800 | + | 10.9159i | −0.531861 | + | 1.35395i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.16283 | 0.862303 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.39500 | 0.165556 | 0.0827780 | − | 0.996568i | \(-0.473621\pi\) | ||||
0.0827780 | + | 0.996568i | \(0.473621\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.22878i | 0.729023i | 0.931199 | + | 0.364512i | \(0.118764\pi\) | ||||
−0.931199 | + | 0.364512i | \(0.881236\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.40309 | + | 3.66319i | −0.392955 | + | 0.422989i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 17.7198i | − | 2.01936i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.75892 | −0.197894 | −0.0989469 | − | 0.995093i | \(-0.531547\pi\) | ||||
−0.0989469 | + | 0.995093i | \(0.531547\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.9936i | − | 1.42624i | −0.701044 | − | 0.713118i | \(-0.747282\pi\) | ||
0.701044 | − | 0.713118i | \(-0.252718\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.48548 | − | 16.5100i | 0.703449 | − | 1.79076i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.58679i | 0.706178i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.29938 | −0.667733 | −0.333867 | − | 0.942620i | \(-0.608354\pi\) | ||||
−0.333867 | + | 0.942620i | \(0.608354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.9296 | 1.87953 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5.96221i | − | 0.618253i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.32658 | + | 1.30675i | 0.341300 | + | 0.134070i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 4.62505i | − | 0.469603i | −0.972043 | − | 0.234801i | \(-0.924556\pi\) | ||
0.972043 | − | 0.234801i | \(-0.0754440\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.18352 | −0.520964 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.37470 | 0.932818 | 0.466409 | − | 0.884569i | \(-0.345548\pi\) | ||||
0.466409 | + | 0.884569i | \(0.345548\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.81662i | − | 0.770194i | −0.922876 | − | 0.385097i | \(-0.874168\pi\) | ||
0.922876 | − | 0.385097i | \(-0.125832\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 7.11473 | + | 2.79482i | 0.694327 | + | 0.272747i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.25657i | 0.894867i | 0.894317 | + | 0.447433i | \(0.147662\pi\) | ||||
−0.894317 | + | 0.447433i | \(0.852338\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.7849 | −1.60770 | −0.803849 | − | 0.594834i | \(-0.797218\pi\) | ||||
−0.803849 | + | 0.594834i | \(0.797218\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.2629 | 0.974108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.985409i | − | 0.0926995i | −0.998925 | − | 0.0463497i | \(-0.985241\pi\) | ||
0.998925 | − | 0.0463497i | \(-0.0147589\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.85605 | − | 14.9076i | 0.546079 | − | 1.39014i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 5.24487i | − | 0.484889i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −27.1180 | −2.48590 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.8689 | 1.44263 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.07835i | − | 0.728400i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.84177 | + | 10.0776i | 0.433061 | + | 0.901364i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.93033i | 0.348760i | 0.984678 | + | 0.174380i | \(0.0557921\pi\) | ||||
−0.984678 | + | 0.174380i | \(0.944208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.663360 | 0.0584056 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.9128 | −1.56504 | −0.782522 | − | 0.622622i | \(-0.786067\pi\) | ||||
−0.782522 | + | 0.622622i | \(0.786067\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.46397i | − | 0.473786i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.817560 | − | 2.08125i | 0.0703644 | − | 0.179125i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 5.44440i | − | 0.465146i | −0.972579 | − | 0.232573i | \(-0.925286\pi\) | ||
0.972579 | − | 0.232573i | \(-0.0747145\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.3886 | 1.05079 | 0.525395 | − | 0.850858i | \(-0.323917\pi\) | ||||
0.525395 | + | 0.850858i | \(0.323917\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.08264 | 0.596466 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 27.1869i | 2.27349i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.7088 | + | 5.38510i | 1.13845 | + | 0.447208i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 4.68609i | − | 0.386502i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.4378 | 0.855094 | 0.427547 | − | 0.903993i | \(-0.359378\pi\) | ||||
0.427547 | + | 0.903993i | \(0.359378\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.58130 | 0.210064 | 0.105032 | − | 0.994469i | \(-0.466506\pi\) | ||||
0.105032 | + | 0.994469i | \(0.466506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.93273i | 0.641323i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.4088 | − | 4.87447i | −0.996703 | − | 0.391527i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.37987i | − | 0.189934i | −0.995480 | − | 0.0949672i | \(-0.969725\pi\) | ||
0.995480 | − | 0.0949672i | \(-0.0302746\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.5654 | −0.917197 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.4861 | −1.92977 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.42295i | 0.659737i | 0.944027 | + | 0.329868i | \(0.107004\pi\) | ||||
−0.944027 | + | 0.329868i | \(0.892996\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.23784 | + | 10.7882i | −0.329916 | + | 0.839860i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.31683i | − | 0.411428i | −0.978612 | − | 0.205714i | \(-0.934048\pi\) | ||
0.978612 | − | 0.205714i | \(-0.0659517\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −14.5087 | −1.11605 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.59836 | −0.122229 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.2214i | 1.15726i | 0.815591 | + | 0.578629i | \(0.196412\pi\) | ||||
−0.815591 | + | 0.578629i | \(0.803588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.6334 | − | 12.5226i | 0.879406 | − | 0.946619i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.90150i | 0.142925i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.6194 | 1.01796 | 0.508980 | − | 0.860779i | \(-0.330023\pi\) | ||||
0.508980 | + | 0.860779i | \(0.330023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.42287 | −0.403079 | −0.201539 | − | 0.979480i | \(-0.564594\pi\) | ||||
−0.201539 | + | 0.979480i | \(0.564594\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.14296i | 0.0844900i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.39051 | − | 21.3596i | 0.616883 | − | 1.57039i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 41.1195i | − | 3.00695i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.41849 | −0.248659 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.71059 | 0.268489 | 0.134244 | − | 0.990948i | \(-0.457139\pi\) | ||||
0.134244 | + | 0.990948i | \(0.457139\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.66970i | − | 0.336133i | −0.985776 | − | 0.168066i | \(-0.946248\pi\) | ||
0.985776 | − | 0.168066i | \(-0.0537523\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.9159 | − | 4.28800i | −0.781703 | − | 0.307070i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 21.7808i | − | 1.55182i | −0.630844 | − | 0.775909i | \(-0.717291\pi\) | ||
0.630844 | − | 0.775909i | \(-0.282709\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0873 | 1.84928 | 0.924641 | − | 0.380840i | \(-0.124365\pi\) | ||||
0.924641 | + | 0.380840i | \(0.124365\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 22.5169i | − | 1.58038i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.8131 | − | 6.60454i | −1.17427 | − | 0.461281i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.16283i | 0.497851i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.28512 | 0.573094 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 25.5255 | 1.75725 | 0.878626 | − | 0.477511i | \(-0.158461\pi\) | ||||
0.878626 | + | 0.477511i | \(0.158461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.39500i | 0.0955838i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.542337 | − | 1.38062i | 0.0369871 | − | 0.0941573i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3818i | 1.38361i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.22878 | −0.420902 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 41.6061 | 2.79873 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.1864i | 1.15089i | 0.817842 | + | 0.575443i | \(0.195170\pi\) | ||||
−0.817842 | + | 0.575443i | \(0.804830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.66319 | − | 3.40309i | −0.244213 | − | 0.226873i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.5003i | 0.696926i | 0.937322 | + | 0.348463i | \(0.113296\pi\) | ||||
−0.937322 | + | 0.348463i | \(0.886704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.29601 | 0.416052 | 0.208026 | − | 0.978123i | \(-0.433296\pi\) | ||||
0.208026 | + | 0.978123i | \(0.433296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 17.7198 | 1.16588 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.9039i | 1.82804i | 0.405664 | + | 0.914022i | \(0.367040\pi\) | ||||
−0.405664 | + | 0.914022i | \(0.632960\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.79049 | − | 14.7407i | 0.377730 | − | 0.961580i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.75892i | − | 0.114254i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.3664 | 1.51145 | 0.755725 | − | 0.654889i | \(-0.227285\pi\) | ||||
0.755725 | + | 0.654889i | \(0.227285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.9579 | −1.35002 | −0.675009 | − | 0.737810i | \(-0.735860\pi\) | ||||
−0.675009 | + | 0.737810i | \(0.735860\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.75292 | − | 3.83116i | −0.623091 | − | 0.244764i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.38318i | 0.533409i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.9936 | 0.823438 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0003 | −0.694336 | −0.347168 | − | 0.937803i | \(-0.612857\pi\) | ||||
−0.347168 | + | 0.937803i | \(0.612857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 37.1287i | − | 2.33426i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.5100 | + | 6.48548i | 1.03389 | + | 0.406137i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.4819i | 1.40238i | 0.712974 | + | 0.701190i | \(0.247348\pi\) | ||||
−0.712974 | + | 0.701190i | \(0.752652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.0835 | −2.17998 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.58679 | −0.407712 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.3224i | 1.19147i | 0.803181 | + | 0.595735i | \(0.203139\pi\) | ||||
−0.803181 | + | 0.595735i | \(0.796861\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.45543 | + | 24.0705i | −0.580842 | + | 1.47864i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 6.29938i | − | 0.385516i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.71965 | −0.226791 | −0.113396 | − | 0.993550i | \(-0.536173\pi\) | ||||
−0.113396 | + | 0.993550i | \(0.536173\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3434 | 0.932043 | 0.466022 | − | 0.884773i | \(-0.345687\pi\) | ||||
0.466022 | + | 0.884773i | \(0.345687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 17.9296i | 1.08515i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 18.9882 | + | 17.6400i | 1.14503 | + | 1.06373i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.6005i | 1.53818i | 0.639138 | + | 0.769092i | \(0.279291\pi\) | ||||
−0.639138 | + | 0.769092i | \(0.720709\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.96221 | 0.356948 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1995 | 1.44362 | 0.721811 | − | 0.692090i | \(-0.243310\pi\) | ||||
0.721811 | + | 0.692090i | \(0.243310\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.3634i | − | 0.616037i | −0.951380 | − | 0.308019i | \(-0.900334\pi\) | ||
0.951380 | − | 0.308019i | \(-0.0996659\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.30675 | + | 3.32658i | −0.0774054 | + | 0.197049i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.6158i | 1.63011i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −45.9281 | −2.70166 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.62505 | 0.271125 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.91431i | − | 0.287097i | −0.989643 | − | 0.143549i | \(-0.954149\pi\) | ||
0.989643 | − | 0.143549i | \(-0.0458513\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.95749 | + | 1.55459i | 0.230414 | + | 0.0905116i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.18352i | − | 0.300779i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.5681 | 2.17262 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.26769 | −0.130708 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.37470i | 0.538563i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.37878 | + | 0.934439i | 0.136209 | + | 0.0535058i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.87657i | 0.164175i | 0.996625 | + | 0.0820873i | \(0.0261586\pi\) | ||||
−0.996625 | + | 0.0820873i | \(0.973841\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.81662 | 0.444672 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.15003 | 0.348736 | 0.174368 | − | 0.984681i | \(-0.444212\pi\) | ||||
0.174368 | + | 0.984681i | \(0.444212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.46096i | − | 0.252149i | −0.992021 | − | 0.126074i | \(-0.959762\pi\) | ||
0.992021 | − | 0.126074i | \(-0.0402378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.79482 | + | 7.11473i | −0.157471 | + | 0.400870i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.7678i | 0.829444i | 0.909948 | + | 0.414722i | \(0.136121\pi\) | ||||
−0.909948 | + | 0.414722i | \(0.863879\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.1428 | 1.91163 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.25657 | −0.516652 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12.6793i | − | 0.705496i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.8488 | + | 19.2130i | −0.990073 | + | 1.06574i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 16.7849i | − | 0.928205i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.2120 | −1.33485 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0188 | 0.715578 | 0.357789 | − | 0.933802i | \(-0.383531\pi\) | ||||
0.357789 | + | 0.933802i | \(0.383531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.2629i | 0.562401i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.817560 | + | 2.08125i | −0.0446681 | + | 0.113711i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.35694i | − | 0.291811i | −0.989299 | − | 0.145906i | \(-0.953390\pi\) | ||
0.989299 | − | 0.145906i | \(-0.0466096\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.985409 | 0.0535201 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.9053 | −1.67362 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.91008i | − | 0.427104i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.9076 | + | 5.85605i | 0.802600 | + | 0.315279i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.3748i | 1.52324i | 0.648025 | + | 0.761619i | \(0.275595\pi\) | ||||
−0.648025 | + | 0.761619i | \(0.724405\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.6940 | −1.00067 | −0.500335 | − | 0.865832i | \(-0.666790\pi\) | ||||
−0.500335 | + | 0.865832i | \(0.666790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.24487 | 0.279951 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5467i | 0.827465i | 0.910399 | + | 0.413732i | \(0.135775\pi\) | ||||
−0.910399 | + | 0.413732i | \(0.864225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.90334 | + | 1.14050i | 0.154093 | + | 0.0605313i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 27.1180i | − | 1.43523i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.8793 | 1.84086 | 0.920430 | − | 0.390908i | \(-0.127839\pi\) | ||||
0.920430 | + | 0.390908i | \(0.127839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4453 | −0.865540 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.8689i | 0.832903i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.09240 | + | 12.9636i | −0.266549 | + | 0.678548i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.4800i | 0.651452i | 0.945464 | + | 0.325726i | \(0.105609\pi\) | ||||
−0.945464 | + | 0.325726i | \(0.894391\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.07835 | 0.420542 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 39.5363 | 2.05262 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 5.61837i | − | 0.290908i | −0.989365 | − | 0.145454i | \(-0.953536\pi\) | ||
0.989365 | − | 0.145454i | \(-0.0464643\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.0776 | + | 4.84177i | −0.520403 | + | 0.250028i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.5469i | 1.77926i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.6866 | 0.651669 | 0.325834 | − | 0.945427i | \(-0.394355\pi\) | ||||
0.325834 | + | 0.945427i | \(0.394355\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.93033 | −0.201357 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 22.8508i | − | 1.16762i | −0.811889 | − | 0.583811i | \(-0.801561\pi\) | ||
0.811889 | − | 0.583811i | \(-0.198439\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.4870 | − | 36.8794i | 0.738328 | − | 1.87955i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.663360i | 0.0337205i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.2207 | 1.88716 | 0.943581 | − | 0.331142i | \(-0.107434\pi\) | ||||
0.943581 | + | 0.331142i | \(0.107434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −56.8208 | −2.87355 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 17.9128i | − | 0.903579i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.66075 | − | 1.43802i | −0.184192 | − | 0.0723548i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.301013i | 0.0151074i | 0.999971 | + | 0.00755370i | \(0.00240444\pi\) | ||||
−0.999971 | + | 0.00755370i | \(0.997596\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.46397 | 0.273541 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.0301904 | 0.00150764 | 0.000753818 | − | 1.00000i | \(-0.499760\pi\) | ||||
0.000753818 | 1.00000i | \(0.499760\pi\) | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 31.2711i | − | 1.55772i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.08125 | + | 0.817560i | 0.103418 | + | 0.0406249i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 53.1978i | − | 2.63692i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.13879 | −0.451884 | −0.225942 | − | 0.974141i | \(-0.572546\pi\) | ||||
−0.225942 | + | 0.974141i | \(0.572546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.44440 | 0.268552 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.50025i | − | 0.319856i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.6231 | − | 27.0430i | 0.521466 | − | 1.32749i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.3886i | 0.606674i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.473003 | 0.0231077 | 0.0115539 | − | 0.999933i | \(-0.496322\pi\) | ||||
0.0115539 | + | 0.999933i | \(0.496322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.6592 | −1.54297 | −0.771487 | − | 0.636245i | \(-0.780487\pi\) | ||||
−0.771487 | + | 0.636245i | \(0.780487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.08264i | 0.344370i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 26.9958 | − | 29.0591i | 1.30949 | − | 1.40957i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.90720i | − | 0.189083i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.1869 | −1.31260 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.9666 | −0.769084 | −0.384542 | − | 0.923108i | \(-0.625641\pi\) | ||||
−0.384542 | + | 0.923108i | \(0.625641\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11.5387i | − | 0.554516i | −0.960795 | − | 0.277258i | \(-0.910574\pi\) | ||
0.960795 | − | 0.277258i | \(-0.0894257\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.38510 | + | 13.7088i | −0.258196 | + | 0.657284i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 11.4488i | − | 0.547668i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.1762 | −0.867501 | −0.433750 | − | 0.901033i | \(-0.642810\pi\) | ||||
−0.433750 | + | 0.901033i | \(0.642810\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.68609 | 0.223147 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.0286i | 0.714032i | 0.934098 | + | 0.357016i | \(0.116206\pi\) | ||||
−0.934098 | + | 0.357016i | \(0.883794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.1106 | − | 5.15013i | −0.621501 | − | 0.244139i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4378i | 0.493689i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.19596 | −0.292405 | −0.146203 | − | 0.989255i | \(-0.546705\pi\) | ||||
−0.146203 | + | 0.989255i | \(0.546705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.8743 | −1.97178 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.58130i | 0.121280i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 37.3159 | + | 14.6585i | 1.74939 | + | 0.687201i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.21675i | − | 0.103695i | −0.998655 | − | 0.0518476i | \(-0.983489\pi\) | ||
0.998655 | − | 0.0518476i | \(-0.0165110\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.93273 | −0.370268 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.01529 | −0.326735 | −0.163367 | − | 0.986565i | \(-0.552236\pi\) | ||||
−0.163367 | + | 0.986565i | \(0.552236\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 6.89526i | − | 0.320450i | −0.987081 | − | 0.160225i | \(-0.948778\pi\) | ||
0.987081 | − | 0.160225i | \(-0.0512219\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.87447 | − | 12.4088i | 0.226048 | − | 0.575447i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 2.92697i | − | 0.135444i | −0.997704 | − | 0.0677220i | \(-0.978427\pi\) | ||
0.997704 | − | 0.0677220i | \(-0.0215731\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.41849 | 0.157851 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.37987 | 0.109659 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 3.43854i | − | 0.158104i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.85508 | + | 5.43936i | 0.268650 | + | 0.249575i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 11.5654i | − | 0.529544i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −28.3826 | −1.29684 | −0.648418 | − | 0.761285i | \(-0.724569\pi\) | ||||
−0.648418 | + | 0.761285i | \(0.724569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 53.8274 | 2.45432 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 24.4861i | − | 1.11416i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.78126 | − | 9.62588i | 0.171698 | − | 0.437089i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0285i | 0.907579i | 0.891109 | + | 0.453789i | \(0.149928\pi\) | ||||
−0.891109 | + | 0.453789i | \(0.850072\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −8.42295 | −0.380899 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.61015 | 0.253183 | 0.126591 | − | 0.991955i | \(-0.459596\pi\) | ||||
0.126591 | + | 0.991955i | \(0.459596\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 52.2512i | − | 2.35328i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.7882 | − | 4.23784i | −0.484894 | − | 0.190477i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4.76880i | − | 0.213910i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.1619 | −0.633974 | −0.316987 | − | 0.948430i | \(-0.602671\pi\) | ||||
−0.316987 | + | 0.948430i | \(0.602671\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.31683 | 0.237538 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.705378i | 0.0314513i | 0.999876 | + | 0.0157256i | \(0.00500583\pi\) | ||||
−0.999876 | + | 0.0157256i | \(0.994994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.5111 | + | 7.66439i | 0.868232 | + | 0.341061i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 14.5087i | − | 0.644354i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.4309 | 1.79207 | 0.896035 | − | 0.443984i | \(-0.146435\pi\) | ||||
0.896035 | + | 0.443984i | \(0.146435\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.2930 | 0.941948 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1.59836i | − | 0.0705692i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.39056 | − | 16.2683i | 0.281602 | − | 0.716868i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 36.7131i | − | 1.61464i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.2214 | −0.668143 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.4333 | −0.939011 | −0.469506 | − | 0.882929i | \(-0.655568\pi\) | ||||
−0.469506 | + | 0.882929i | \(0.655568\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.4820i | 1.50779i | 0.656994 | + | 0.753895i | \(0.271828\pi\) | ||||
−0.656994 | + | 0.753895i | \(0.728172\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.5226 | + | 11.6334i | 0.546530 | + | 0.507725i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 47.2966i | 2.06027i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.3061 | −1.23070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.90150 | −0.0825179 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 42.3699i | − | 1.83524i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.56781 | + | 19.2652i | −0.327185 | + | 0.832908i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.6194i | 0.587719i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.2905 | −1.04626 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.74511 | −0.332988 | −0.166494 | − | 0.986042i | \(-0.553245\pi\) | ||||
−0.166494 | + | 0.986042i | \(0.553245\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 5.42287i | − | 0.232718i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −34.9335 | − | 13.7226i | −1.49638 | − | 0.587813i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.58452i | − | 0.238777i | −0.992848 | − | 0.119388i | \(-0.961907\pi\) | ||
0.992848 | − | 0.119388i | \(-0.0380934\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.14296 | −0.0487803 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.5280 | 0.448510 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.01285i | 0.255692i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.3596 | + | 8.39051i | 0.906663 | + | 0.356157i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 4.65576i | − | 0.197271i | −0.995124 | − | 0.0986355i | \(-0.968552\pi\) | ||
0.995124 | − | 0.0986355i | \(-0.0314478\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.47924 | 0.147156 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 41.1195 | 1.73607 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 7.52137i | − | 0.316988i | −0.987360 | − | 0.158494i | \(-0.949336\pi\) | ||
0.987360 | − | 0.158494i | \(-0.0506639\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.805631 | − | 2.05088i | 0.0338932 | − | 0.0862812i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 3.41849i | − | 0.143563i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −47.1101 | −1.97496 | −0.987479 | − | 0.157752i | \(-0.949575\pi\) | ||||
−0.987479 | + | 0.157752i | \(0.949575\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 47.2241 | 1.97627 | 0.988133 | − | 0.153600i | \(-0.0490868\pi\) | ||||
0.988133 | + | 0.153600i | \(0.0490868\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.71059i | 0.155012i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.3758 | − | 26.2388i | 1.01654 | − | 1.09423i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 31.2367i | − | 1.30040i | −0.759762 | − | 0.650201i | \(-0.774685\pi\) | ||
0.759762 | − | 0.650201i | \(-0.225315\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.66970 | 0.194066 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −44.4186 | −1.84279 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 59.9496i | 2.48286i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.28800 | − | 10.9159i | 0.177287 | − | 0.451316i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.6525i | 0.604772i | 0.953186 | + | 0.302386i | \(0.0977832\pi\) | ||||
−0.953186 | + | 0.302386i | \(0.902217\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.52975 | −0.392666 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.7808 | 0.895943 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 43.6008i | − | 1.79047i | −0.445593 | − | 0.895236i | \(-0.647007\pi\) | ||
0.445593 | − | 0.895236i | \(-0.352993\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −56.4392 | − | 22.1706i | −2.31378 | − | 0.908905i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.0873i | 1.06768i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.8903 | −0.935271 | −0.467636 | − | 0.883921i | \(-0.654894\pi\) | ||||
−0.467636 | + | 0.883921i | \(0.654894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4901 | 0.672645 | 0.336322 | − | 0.941747i | \(-0.390817\pi\) | ||||
0.336322 | + | 0.941747i | \(0.390817\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 33.0272 | + | 12.9738i | 1.34275 | + | 0.527460i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 10.0851i | − | 0.409344i | −0.978831 | − | 0.204672i | \(-0.934387\pi\) | ||
0.978831 | − | 0.204672i | \(-0.0656127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.5169 | 0.912431 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.1476 | 1.50283 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.8535i | − | 0.963434i | −0.876327 | − | 0.481717i | \(-0.840013\pi\) | ||
0.876327 | − | 0.481717i | \(-0.159987\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.60454 | − | 16.8131i | 0.266321 | − | 0.677968i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.706932i | 0.0284600i | 0.999899 | + | 0.0142300i | \(0.00452971\pi\) | ||||
−0.999899 | + | 0.0142300i | \(0.995470\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.6278 | 1.47220 | 0.736099 | − | 0.676874i | \(-0.236666\pi\) | ||||
0.736099 | + | 0.676874i | \(0.236666\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.16283 | −0.287434 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.5344i | 0.862757i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.83792 | + | 24.9323i | 0.0735167 | + | 0.997294i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.28512i | 0.330876i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −81.4125 | −3.24613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4962 | −1.45289 | −0.726445 | − | 0.687225i | \(-0.758829\pi\) | ||||
−0.726445 | + | 0.687225i | \(0.758829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.5255i | 1.01455i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.21328 | + | 8.17999i | −0.127515 | + | 0.324613i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 24.5780i | − | 0.973814i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.39500 | −0.0551853 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.86090 | 0.231492 | 0.115746 | − | 0.993279i | \(-0.463074\pi\) | ||||
0.115746 | + | 0.993279i | \(0.463074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.6775i | 0.578825i | 0.957205 | + | 0.289412i | \(0.0934599\pi\) | ||||
−0.957205 | + | 0.289412i | \(0.906540\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.38062 | + | 0.542337i | 0.0543617 | + | 0.0213545i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.5924i | 0.691630i | 0.938303 | + | 0.345815i | \(0.112397\pi\) | ||||
−0.938303 | + | 0.345815i | \(0.887603\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.85645 | 0.386900 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.3818 | −0.798825 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.97398i | 0.390312i | 0.980772 | + | 0.195156i | \(0.0625213\pi\) | ||||
−0.980772 | + | 0.195156i | \(0.937479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −37.2809 | − | 14.6448i | −1.45669 | − | 0.572218i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.22878i | − | 0.243008i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.5427 | −0.488595 | −0.244298 | − | 0.969700i | \(-0.578557\pi\) | ||||
−0.244298 | + | 0.969700i | \(0.578557\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.99415 | 0.349832 | 0.174916 | − | 0.984583i | \(-0.444035\pi\) | ||||
0.174916 | + | 0.984583i | \(0.444035\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.6061i | 1.61585i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.46713 | − | 11.3719i | 0.173228 | − | 0.440983i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 47.1801i | − | 1.82682i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.1864 | −0.664464 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.92456 | 0.228715 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.182820i | 0.00704719i | 0.999994 | + | 0.00352360i | \(0.00112160\pi\) | ||||
−0.999994 | + | 0.00352360i | \(0.998878\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.40309 | − | 3.66319i | 0.130985 | − | 0.140996i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.2910i | 1.85598i | 0.372610 | + | 0.927988i | \(0.378463\pi\) | ||||
−0.372610 | + | 0.927988i | \(0.621537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.8107 | −0.606759 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.5003 | −0.402371 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.2104i | 1.72993i | 0.501833 | + | 0.864965i | \(0.332659\pi\) | ||||
−0.501833 | + | 0.864965i | \(0.667341\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.45112 | − | 11.3311i | 0.170069 | − | 0.432941i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.29601i | 0.240208i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −60.6592 | −2.31093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.6390 | −1.01339 | −0.506697 | − | 0.862124i | \(-0.669134\pi\) | ||||
−0.506697 | + | 0.862124i | \(0.669134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.7198i | 0.673121i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.7838 | + | 10.1285i | 0.978037 | + | 0.384194i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64.0833i | 2.42733i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.9039 | −1.05542 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.7808 | −1.38919 | −0.694596 | − | 0.719400i | \(-0.744417\pi\) | ||||
−0.694596 | + | 0.719400i | \(0.744417\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 16.4037i | − | 0.618678i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.7407 | + | 5.79049i | 0.555168 | + | 0.218082i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 32.0474i | − | 1.20526i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.39744 | −0.315372 | −0.157686 | − | 0.987489i | \(-0.550403\pi\) | ||||
−0.157686 | + | 0.987489i | \(0.550403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.75892 | 0.0659646 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42.7063i | 1.59936i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.2270 | + | 56.5828i | −0.831241 | + | 2.11608i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.3664i | 0.872636i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.8620 | −1.67307 | −0.836536 | − | 0.547913i | \(-0.815423\pi\) | ||||
−0.836536 | + | 0.547913i | \(0.815423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.7210 | −0.995144 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 20.9579i | − | 0.779433i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.1287 | + | 22.4155i | 0.896116 | + | 0.832490i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.2720i | − | 1.45652i | −0.685301 | − | 0.728260i | \(-0.740329\pi\) | ||
0.685301 | − | 0.728260i | \(-0.259671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.26225 | −0.194631 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 20.9749i | − | 0.774726i | −0.921927 | − | 0.387363i | \(-0.873386\pi\) | ||
0.921927 | − | 0.387363i | \(-0.126614\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.83116 | − | 9.75292i | 0.141315 | − | 0.359742i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.18352i | 0.190938i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.13014 | −0.0415728 | −0.0207864 | − | 0.999784i | \(-0.506617\pi\) | ||||
−0.0207864 | + | 0.999784i | \(0.506617\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.38318 | −0.307964 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 48.0720i | − | 1.76359i | −0.471633 | − | 0.881795i | \(-0.656335\pi\) | ||
0.471633 | − | 0.881795i | \(-0.343665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 21.7236 | + | 8.53349i | 0.795889 | + | 0.312643i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.9936i | 0.475412i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 31.6435 | 1.15623 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0475 | 1.24241 | 0.621206 | − | 0.783647i | \(-0.286643\pi\) | ||||
0.621206 | + | 0.783647i | \(0.286643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 11.0003i | − | 0.400875i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.37233 | + | 2.11037i | 0.195519 | + | 0.0768043i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.62146i | − | 0.0589329i | −0.999566 | − | 0.0294665i | \(-0.990619\pi\) | ||
0.999566 | − | 0.0294665i | \(-0.00938082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37.1287 | 1.34769 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.62522 | −0.348914 | −0.174457 | − | 0.984665i | \(-0.555817\pi\) | ||||
−0.174457 | + | 0.984665i | \(0.555817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.3789i | 2.07726i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.48548 | + | 16.5100i | −0.234483 | + | 0.596919i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.97311i | 0.360108i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.3671 | −1.56386 | −0.781929 | − | 0.623367i | \(-0.785764\pi\) | ||||
−0.781929 | + | 0.623367i | \(0.785764\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.4819 | −0.809665 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.1785i | 0.833672i | 0.908982 | + | 0.416836i | \(0.136861\pi\) | ||||
−0.908982 | + | 0.416836i | \(0.863139\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.8407 | − | 20.2900i | −0.784542 | − | 0.728837i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 35.0835i | − | 1.25861i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.9121 | −0.462623 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.23102 | 0.258746 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.58679i | − | 0.235393i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.94569 | − | 4.95310i | 0.0694446 | − | 0.176784i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 23.5640i | − | 0.839967i | −0.907532 | − | 0.419984i | \(-0.862036\pi\) | ||
0.907532 | − | 0.419984i | \(-0.137964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −19.3224 | −0.687895 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.36861 | −0.119774 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.99468i | 0.212877i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −24.0705 | − | 9.45543i | −0.853693 | − | 0.335350i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.39253i | − | 0.0493258i | −0.999696 | − | 0.0246629i | \(-0.992149\pi\) | ||
0.999696 | − | 0.0246629i | \(-0.00785124\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −56.1847 | −1.98767 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.29938 | 0.222578 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.2870i | 1.13938i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.9616 | − | 20.0188i | −1.79616 | − | 0.705572i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3.71965i | − | 0.130938i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31.3071 | 1.10070 | 0.550350 | − | 0.834934i | \(-0.314494\pi\) | ||||
0.550350 | + | 0.834934i | \(0.314494\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.7145 | 0.867844 | 0.433922 | − | 0.900950i | \(-0.357129\pi\) | ||||
0.433922 | + | 0.900950i | \(0.357129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.3434i | 0.538115i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.88627 | + | 17.5303i | −0.241216 | + | 0.614058i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.06029i | − | 0.0370947i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.9296 | −0.626510 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.0688 | 1.53801 | 0.769006 | − | 0.639242i | \(-0.220752\pi\) | ||||
0.769006 | + | 0.639242i | \(0.220752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.3790i | 1.09380i | 0.837197 | + | 0.546902i | \(0.184193\pi\) | ||||
−0.837197 | + | 0.546902i | \(0.815807\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −17.6400 | + | 18.9882i | −0.614146 | + | 0.661085i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 41.9888i | 1.46009i | 0.683397 | + | 0.730047i | \(0.260502\pi\) | ||||
−0.683397 | + | 0.730047i | \(0.739498\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.45124 | 0.0504037 | 0.0252018 | − | 0.999682i | \(-0.491977\pi\) | ||||
0.0252018 | + | 0.999682i | \(0.491977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.6005 | −0.888071 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.1735i | 1.28798i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.34683 | − | 11.0656i | 0.150428 | − | 0.382942i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.96221i | 0.206084i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.9161 | 0.549487 | 0.274743 | − | 0.961518i | \(-0.411407\pi\) | ||||
0.274743 | + | 0.961518i | \(0.411407\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3858 | 0.496063 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 24.1995i | 0.833476i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.1962 | − | 11.8617i | −1.03878 | − | 0.408056i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 54.2478i | − | 1.86398i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.3634 | 0.355669 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −73.5111 | −2.51993 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.1330i | − | 0.929015i | −0.885569 | − | 0.464507i | \(-0.846231\pi\) | ||
0.885569 | − | 0.464507i | \(-0.153769\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.32658 | − | 1.30675i | −0.113767 | − | 0.0446900i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.8254i | 1.42873i | 0.699774 | + | 0.714364i | \(0.253284\pi\) | ||||
−0.699774 | + | 0.714364i | \(0.746716\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.8125 | 0.880710 | 0.440355 | − | 0.897824i | \(-0.354853\pi\) | ||||
0.440355 | + | 0.897824i | \(0.354853\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.6158 | −0.941143 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.31036i | − | 0.0786455i | −0.999227 | − | 0.0393227i | \(-0.987480\pi\) | ||
0.999227 | − | 0.0393227i | \(-0.0125200\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −12.4444 | + | 31.6794i | −0.423121 | + | 1.07713i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 45.9281i | − | 1.55980i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.11740 | −0.309287 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.24487 | −0.177716 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.62505i | 0.156534i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 34.4501 | − | 16.5516i | 1.16462 | − | 0.559545i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.6911i | 1.34027i | 0.742237 | + | 0.670137i | \(0.233765\pi\) | ||||
−0.742237 | + | 0.670137i | \(0.766235\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.91431 | 0.165756 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.8795 | −0.770830 | −0.385415 | − | 0.922743i | \(-0.625942\pi\) | ||||
−0.385415 | + | 0.922743i | \(0.625942\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.8762i | 0.837152i | 0.908182 | + | 0.418576i | \(0.137471\pi\) | ||||
−0.908182 | + | 0.418576i | \(0.862529\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.55459 | + | 3.95749i | −0.0522569 | + | 0.133029i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 49.3187i | − | 1.65596i | −0.560759 | − | 0.827979i | \(-0.689491\pi\) | ||
0.560759 | − | 0.827979i | \(-0.310509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.4358 | 0.450622 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.18352 | 0.173655 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 11.3206i | − | 0.378829i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.3453 | + | 11.1347i | 0.947478 | + | 0.372190i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.5681i | 1.25436i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −39.2719 | −1.30979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 91.7453 | 3.05648 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.26769i | − | 0.0754640i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.2863 | − | 4.43353i | −0.375171 | − | 0.147375i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 15.1653i | − | 0.503556i | −0.967785 | − | 0.251778i | \(-0.918985\pi\) | ||
0.967785 | − | 0.251778i | \(-0.0810153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.37470 | −0.310939 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.8443 | −0.922524 | −0.461262 | − | 0.887264i | \(-0.652603\pi\) | ||||
−0.461262 | + | 0.887264i | \(0.652603\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 67.3528i | − | 2.22905i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.934439 | + | 2.37878i | −0.0308916 | + | 0.0786401i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 61.2346i | 2.02215i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −50.9981 | −1.68227 | −0.841135 | − | 0.540825i | \(-0.818112\pi\) | ||||
−0.841135 | + | 0.540825i | \(0.818112\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.87657 | −0.0947862 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.31660i | 0.240829i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.9255 | − | 37.5948i | 1.14834 | − | 1.23611i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.81662i | 0.256731i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.0324 | −1.37904 | −0.689519 | − | 0.724268i | \(-0.742178\pi\) | ||||
−0.689519 | + | 0.724268i | \(0.742178\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.49004 | −0.245476 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.15003i | 0.201343i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.6177 | − | 85.5798i | 1.09942 | − | 2.79876i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.16094i | − | 0.0379264i | −0.999820 | − | 0.0189632i | \(-0.993963\pi\) | ||
0.999820 | − | 0.0189632i | \(-0.00603653\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.46096 | 0.145578 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −48.5340 | −1.58216 | −0.791082 | − | 0.611710i | \(-0.790482\pi\) | ||||
−0.791082 | + | 0.611710i | \(0.790482\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.8638i | 1.88431i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.11473 | − | 2.79482i | −0.231442 | − | 0.0909156i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.3681i | 1.63674i | 0.574689 | + | 0.818372i | \(0.305123\pi\) | ||||
−0.574689 | + | 0.818372i | \(0.694877\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.6692 | −1.06049 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.7678 | −0.478880 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.4655i | 1.79670i | 0.439277 | + | 0.898352i | \(0.355235\pi\) | ||||
−0.439277 | + | 0.898352i | \(0.644765\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.72266 | + | 3.03363i | 0.249899 | + | 0.0981660i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 34.1428i | 1.10368i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.6116 | −0.601001 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.54801 | 0.146710 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 9.25657i | − | 0.298289i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.81777 | − | 9.71881i | 0.122898 | − | 0.312860i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 53.8961i | − | 1.73318i | −0.499019 | − | 0.866591i | \(-0.666306\pi\) | ||
0.499019 | − | 0.866591i | \(-0.333694\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.6793 | 0.407319 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.3151 | 0.331028 | 0.165514 | − | 0.986207i | \(-0.447072\pi\) | ||||
0.165514 | + | 0.986207i | \(0.447072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 42.3505i | − | 1.35769i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.2130 | − | 17.8488i | −0.615307 | − | 0.571619i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.3713i | 1.13163i | 0.824533 | + | 0.565814i | \(0.191438\pi\) | ||||
−0.824533 | + | 0.565814i | \(0.808562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.6530 | −1.04359 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.7849 | 0.535899 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 31.7285i | − | 1.01198i | −0.862539 | − | 0.505991i | \(-0.831127\pi\) | ||
0.862539 | − | 0.505991i | \(-0.168873\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.8071 | − | 45.3313i | 0.567383 | − | 1.44438i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 24.2120i | − | 0.770675i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.75153 | −0.151090 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.7206 | 0.467617 | 0.233808 | − | 0.972283i | \(-0.424881\pi\) | ||||
0.233808 | + | 0.972283i | \(0.424881\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.0188i | 0.413139i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 54.2942 | + | 21.3280i | 1.72124 | + | 0.676142i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 17.8245i | − | 0.564506i | −0.959340 | − | 0.282253i | \(-0.908918\pi\) | ||
0.959340 | − | 0.282253i | \(-0.0910818\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.2629 | −0.324703 |
(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 | 4020.2.g.c.1609.36 | yes | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.17 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.17 | ✓ | 38 | 5.4 | even | 2 | inner | |
4020.2.g.c.1609.36 | yes | 38 | 1.1 | even | 1 | trivial |