Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,4,Mod(1133,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("2268.1133");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(133.816331893\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1133.11 | ||
Character | \(\chi\) | \(=\) | 2268.1133 |
Dual form | 2268.4.f.a.1133.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.9938 | −0.983316 | −0.491658 | − | 0.870788i | \(-0.663609\pi\) | ||||
−0.491658 | + | 0.870788i | \(0.663609\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.4708 | − | 14.5403i | 0.619365 | − | 0.785103i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 15.9659i | − | 0.437626i | −0.975767 | − | 0.218813i | \(-0.929781\pi\) | ||
0.975767 | − | 0.218813i | \(-0.0702185\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 89.4072i | − | 1.90747i | −0.300650 | − | 0.953734i | \(-0.597204\pi\) | ||
0.300650 | − | 0.953734i | \(-0.402796\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −106.953 | −1.52588 | −0.762939 | − | 0.646471i | \(-0.776244\pi\) | ||||
−0.762939 | + | 0.646471i | \(0.776244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.31634i | 0.100416i | 0.998739 | + | 0.0502079i | \(0.0159884\pi\) | ||||
−0.998739 | + | 0.0502079i | \(0.984012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 143.059i | − | 1.29695i | −0.761237 | − | 0.648474i | \(-0.775407\pi\) | ||
0.761237 | − | 0.648474i | \(-0.224593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.13623 | −0.0330899 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 149.789i | − | 0.959140i | −0.877504 | − | 0.479570i | \(-0.840793\pi\) | ||
0.877504 | − | 0.479570i | \(-0.159207\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 42.9493i | − | 0.248836i | −0.992230 | − | 0.124418i | \(-0.960294\pi\) | ||
0.992230 | − | 0.124418i | \(-0.0397064\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −126.108 | + | 159.853i | −0.609031 | + | 0.772004i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 390.706 | 1.73599 | 0.867997 | − | 0.496570i | \(-0.165407\pi\) | ||||
0.867997 | + | 0.496570i | \(0.165407\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −344.973 | −1.31404 | −0.657021 | − | 0.753873i | \(-0.728184\pi\) | ||||
−0.657021 | + | 0.753873i | \(0.728184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −57.1185 | −0.202570 | −0.101285 | − | 0.994857i | \(-0.532295\pi\) | ||||
−0.101285 | + | 0.994857i | \(0.532295\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −16.2656 | −0.0504806 | −0.0252403 | − | 0.999681i | \(-0.508035\pi\) | ||||
−0.0252403 | + | 0.999681i | \(0.508035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −79.8415 | − | 333.578i | −0.232774 | − | 0.972531i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 445.230i | − | 1.15391i | −0.816777 | − | 0.576954i | \(-0.804241\pi\) | ||
0.816777 | − | 0.576954i | \(-0.195759\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 175.526i | 0.430325i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −386.700 | −0.853288 | −0.426644 | − | 0.904420i | \(-0.640304\pi\) | ||||
−0.426644 | + | 0.904420i | \(0.640304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 485.964i | 1.02002i | 0.860168 | + | 0.510011i | \(0.170359\pi\) | ||||
−0.860168 | + | 0.510011i | \(0.829641\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 982.925i | 1.87564i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 503.642 | 0.918354 | 0.459177 | − | 0.888345i | \(-0.348144\pi\) | ||||
0.459177 | + | 0.888345i | \(0.348144\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 751.418i | 1.25601i | 0.778208 | + | 0.628007i | \(0.216129\pi\) | ||||
−0.778208 | + | 0.628007i | \(0.783871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 507.533i | − | 0.813729i | −0.913489 | − | 0.406865i | \(-0.866622\pi\) | ||
0.913489 | − | 0.406865i | \(-0.133378\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −232.149 | − | 183.141i | −0.343582 | − | 0.271050i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −763.141 | −1.08684 | −0.543418 | − | 0.839462i | \(-0.682870\pi\) | ||||
−0.543418 | + | 0.839462i | \(0.682870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1214.48 | 1.60610 | 0.803052 | − | 0.595908i | \(-0.203208\pi\) | ||||
0.803052 | + | 0.595908i | \(0.203208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1175.82 | 1.50042 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 425.727 | 0.507045 | 0.253523 | − | 0.967329i | \(-0.418411\pi\) | ||||
0.253523 | + | 0.967329i | \(0.418411\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1300.01 | − | 1025.57i | −1.49756 | − | 1.18142i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 91.4282i | − | 0.0987404i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 571.094i | − | 0.597792i | −0.954286 | − | 0.298896i | \(-0.903382\pi\) | ||
0.954286 | − | 0.298896i | \(-0.0966184\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −706.770 | −0.696299 | −0.348150 | − | 0.937439i | \(-0.613190\pi\) | ||||
−0.348150 | + | 0.937439i | \(0.613190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 251.271i | − | 0.240373i | −0.992751 | − | 0.120187i | \(-0.961651\pi\) | ||
0.992751 | − | 0.120187i | \(-0.0383493\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 739.962i | 0.668549i | 0.942476 | + | 0.334275i | \(0.108491\pi\) | ||||
−0.942476 | + | 0.334275i | \(0.891509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1497.38 | 1.31580 | 0.657902 | − | 0.753104i | \(-0.271444\pi\) | ||||
0.657902 | + | 0.753104i | \(0.271444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 995.254i | − | 0.828546i | −0.910153 | − | 0.414273i | \(-0.864036\pi\) | ||
0.910153 | − | 0.414273i | \(-0.135964\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1572.76i | 1.27531i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1226.84 | + | 1555.13i | −0.945075 | + | 1.19797i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1076.09 | 0.808483 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1419.70 | 1.01585 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2469.41 | 1.72539 | 0.862696 | − | 0.505724i | \(-0.168774\pi\) | ||||
0.862696 | + | 0.505724i | \(0.168774\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1539.57 | −1.02682 | −0.513409 | − | 0.858144i | \(-0.671618\pi\) | ||||
−0.513409 | + | 0.858144i | \(0.671618\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 120.922 | + | 95.3951i | 0.0788367 | + | 0.0621940i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1639.44i | 1.02239i | 0.859465 | + | 0.511194i | \(0.170797\pi\) | ||||
−0.859465 | + | 0.511194i | \(0.829203\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1038.69i | − | 0.633817i | −0.948456 | − | 0.316909i | \(-0.897355\pi\) | ||
0.948456 | − | 0.316909i | \(-0.102645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1427.46 | −0.834759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1646.75i | 0.943137i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1758.80i | − | 0.967025i | −0.875337 | − | 0.483512i | \(-0.839361\pi\) | ||
0.875337 | − | 0.483512i | \(-0.160639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −704.801 | −0.379841 | −0.189920 | − | 0.981800i | \(-0.560823\pi\) | ||||
−0.189920 | + | 0.981800i | \(0.560823\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 472.177i | 0.244685i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 668.631i | 0.339889i | 0.985454 | + | 0.169944i | \(0.0543588\pi\) | ||||
−0.985454 | + | 0.169944i | \(0.945641\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2080.12 | − | 1641.00i | −1.01824 | − | 0.803285i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3926.19 | −1.88665 | −0.943323 | − | 0.331877i | \(-0.892318\pi\) | ||||
−0.943323 | + | 0.331877i | \(0.892318\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1933.60 | 0.895967 | 0.447984 | − | 0.894042i | \(-0.352142\pi\) | ||||
0.447984 | + | 0.894042i | \(0.352142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5796.65 | −2.63844 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1700.04 | 0.747118 | 0.373559 | − | 0.927606i | \(-0.378137\pi\) | ||||
0.373559 | + | 0.927606i | \(0.378137\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −47.4459 | + | 60.1421i | −0.0204947 | + | 0.0259790i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1175.15i | 0.490697i | 0.969435 | + | 0.245349i | \(0.0789024\pi\) | ||||
−0.969435 | + | 0.245349i | \(0.921098\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3506.89i | − | 1.44014i | −0.693902 | − | 0.720070i | \(-0.744110\pi\) | ||
0.693902 | − | 0.720070i | \(-0.255890\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4295.35 | −1.70703 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1707.60i | 0.667764i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1418.14i | − | 0.537239i | −0.963246 | − | 0.268620i | \(-0.913433\pi\) | ||
0.963246 | − | 0.268620i | \(-0.0865674\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1493.64 | −0.557070 | −0.278535 | − | 0.960426i | \(-0.589849\pi\) | ||||
−0.278535 | + | 0.960426i | \(0.589849\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2384.42i | 0.862351i | 0.902268 | + | 0.431175i | \(0.141901\pi\) | ||||
−0.902268 | + | 0.431175i | \(0.858099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4960.24i | 1.76695i | 0.468482 | + | 0.883473i | \(0.344801\pi\) | ||||
−0.468482 | + | 0.883473i | \(0.655199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2177.97 | − | 1718.20i | −0.753024 | − | 0.594057i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3792.56 | 1.29212 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 132.778 | 0.0439446 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3947.29 | −1.28788 | −0.643939 | − | 0.765077i | \(-0.722701\pi\) | ||||
−0.643939 | + | 0.765077i | \(0.722701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 627.950 | 0.199190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −624.497 | − | 492.663i | −0.195362 | − | 0.154121i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9562.37i | 2.91056i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1613.65i | 0.484565i | 0.970206 | + | 0.242283i | \(0.0778961\pi\) | ||||
−0.970206 | + | 0.242283i | \(0.922104\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3499.91 | −1.02334 | −0.511668 | − | 0.859183i | \(-0.670972\pi\) | ||||
−0.511668 | + | 0.859183i | \(0.670972\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1910.16i | − | 0.551208i | −0.961271 | − | 0.275604i | \(-0.911122\pi\) | ||
0.961271 | − | 0.275604i | \(-0.0888778\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4408.26i | 1.23946i | 0.784814 | + | 0.619731i | \(0.212758\pi\) | ||||
−0.784814 | + | 0.619731i | \(0.787242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 178.821 | 0.0496383 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4290.45i | 1.16120i | 0.814190 | + | 0.580599i | \(0.197182\pi\) | ||||
−0.814190 | + | 0.580599i | \(0.802818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1632.09i | 0.436234i | 0.975923 | + | 0.218117i | \(0.0699914\pi\) | ||||
−0.975923 | + | 0.218117i | \(0.930009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 877.762 | + | 3667.29i | 0.228891 | + | 0.956305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 743.541 | 0.191540 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3912.60 | −0.983908 | −0.491954 | − | 0.870621i | \(-0.663717\pi\) | ||||
−0.491954 | + | 0.870621i | \(0.663717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2284.06 | −0.567579 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2109.22 | −0.511943 | −0.255971 | − | 0.966684i | \(-0.582395\pi\) | ||||
−0.255971 | + | 0.966684i | \(0.582395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4481.72 | − | 5681.00i | 1.07521 | − | 1.36293i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4419.90i | − | 1.03628i | −0.855295 | − | 0.518142i | \(-0.826624\pi\) | ||
0.855295 | − | 0.518142i | \(-0.173376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4894.78i | 1.13466i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4557.94 | −1.03309 | −0.516547 | − | 0.856259i | \(-0.672783\pi\) | ||||
−0.516547 | + | 0.856259i | \(0.672783\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 128.189i | − | 0.0287341i | −0.999897 | − | 0.0143671i | \(-0.995427\pi\) | ||
0.999897 | − | 0.0143671i | \(-0.00457334\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 66.0385i | 0.0144810i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2040.02 | −0.442502 | −0.221251 | − | 0.975217i | \(-0.571014\pi\) | ||||
−0.221251 | + | 0.975217i | \(0.571014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1739.64i | − | 0.369318i | −0.982803 | − | 0.184659i | \(-0.940882\pi\) | ||
0.982803 | − | 0.184659i | \(-0.0591180\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1247.67i | 0.262072i | 0.991378 | + | 0.131036i | \(0.0418303\pi\) | ||||
−0.991378 | + | 0.131036i | \(0.958170\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3957.11 | + | 5016.01i | −0.813871 | + | 1.03166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6525.95 | 1.32830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4791.18 | 0.955302 | 0.477651 | − | 0.878550i | \(-0.341488\pi\) | ||||
0.477651 | + | 0.878550i | \(0.341488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4251.30 | 0.839052 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12790.5 | −2.47389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −655.195 | + | 830.521i | −0.125465 | + | 0.159038i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5342.59i | − | 1.00300i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4679.41i | 0.869929i | 0.900448 | + | 0.434965i | \(0.143239\pi\) | ||||
−0.900448 | + | 0.434965i | \(0.856761\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1838.33 | −0.335183 | −0.167592 | − | 0.985856i | \(-0.553599\pi\) | ||||
−0.167592 | + | 0.985856i | \(0.553599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 5958.40i | − | 1.07600i | −0.842944 | − | 0.538001i | \(-0.819179\pi\) | ||
0.842944 | − | 0.538001i | \(-0.180821\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10376.3i | 1.83846i | 0.393716 | + | 0.919232i | \(0.371189\pi\) | ||||
−0.393716 | + | 0.919232i | \(0.628811\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2391.51 | −0.419745 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 889.458i | − | 0.153222i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 369.809i | 0.0631179i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −186.580 | + | 236.507i | −0.0312659 | + | 0.0396324i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4843.30 | 0.804265 | 0.402132 | − | 0.915582i | \(-0.368269\pi\) | ||||
0.402132 | + | 0.915582i | \(0.368269\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5536.94 | −0.903032 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1118.03 | 0.180720 | 0.0903602 | − | 0.995909i | \(-0.471198\pi\) | ||||
0.0903602 | + | 0.995909i | \(0.471198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −685.723 | −0.108897 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5766.18 | − | 2665.49i | −0.907709 | − | 0.419600i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4428.11i | 0.685052i | 0.939508 | + | 0.342526i | \(0.111283\pi\) | ||||
−0.939508 | + | 0.342526i | \(0.888717\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2286.45i | − | 0.350691i | −0.984507 | − | 0.175345i | \(-0.943896\pi\) | ||
0.984507 | − | 0.175345i | \(-0.0561042\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8055.77 | −1.21463 | −0.607316 | − | 0.794460i | \(-0.707754\pi\) | ||||
−0.607316 | + | 0.794460i | \(0.707754\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 8260.95i | − | 1.23506i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5537.25i | − | 0.814053i | −0.913416 | − | 0.407027i | \(-0.866566\pi\) | ||
0.913416 | − | 0.407027i | \(-0.133434\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6789.84 | 0.989917 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5579.72i | 0.800153i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 5391.15i | − | 0.766800i | −0.923582 | − | 0.383400i | \(-0.874753\pi\) | ||
0.923582 | − | 0.383400i | \(-0.125247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6473.79 | − | 5107.15i | −0.905936 | − | 0.714690i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2124.17 | −0.294866 | −0.147433 | − | 0.989072i | \(-0.547101\pi\) | ||||
−0.147433 | + | 0.989072i | \(0.547101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13392.2 | −1.82953 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5358.80 | −0.726288 | −0.363144 | − | 0.931733i | \(-0.618297\pi\) | ||||
−0.363144 | + | 0.931733i | \(0.618297\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5458.46 | −0.728235 | −0.364118 | − | 0.931353i | \(-0.618629\pi\) | ||||
−0.364118 | + | 0.931353i | \(0.618629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2552.20 | + | 2013.42i | 0.337850 | + | 0.266528i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 1635.34i | − | 0.213149i | −0.994305 | − | 0.106575i | \(-0.966012\pi\) | ||
0.994305 | − | 0.106575i | \(-0.0339883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15300.6i | 1.97899i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8389.82 | 1.06870 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 7694.41i | − | 0.972724i | −0.873757 | − | 0.486362i | \(-0.838324\pi\) | ||
0.873757 | − | 0.486362i | \(-0.161676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5543.10i | 0.690297i | 0.938548 | + | 0.345148i | \(0.112171\pi\) | ||||
−0.938548 | + | 0.345148i | \(0.887829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3839.98 | −0.474648 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6237.97i | − | 0.759716i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7345.86i | 0.888091i | 0.896004 | + | 0.444045i | \(0.146457\pi\) | ||||
−0.896004 | + | 0.444045i | \(0.853543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4435.75 | + | 5622.74i | −0.528497 | + | 0.669920i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13351.8 | −1.57931 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3434.91 | −0.400492 | −0.200246 | − | 0.979746i | \(-0.564174\pi\) | ||||
−0.200246 | + | 0.979746i | \(0.564174\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14482.3 | 1.67654 | 0.838269 | − | 0.545257i | \(-0.183568\pi\) | ||||
0.838269 | + | 0.545257i | \(0.183568\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 442.383 | 0.0504911 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7066.07 | + | 5574.40i | 0.800822 | + | 0.631766i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13632.5i | 1.52356i | 0.647839 | + | 0.761778i | \(0.275673\pi\) | ||||
−0.647839 | + | 0.761778i | \(0.724327\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6735.48i | − | 0.747544i | −0.927521 | − | 0.373772i | \(-0.878064\pi\) | ||
0.927521 | − | 0.373772i | \(-0.121936\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1189.73 | 0.130234 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 10601.5i | − | 1.15258i | −0.817246 | − | 0.576289i | \(-0.804500\pi\) | ||
0.817246 | − | 0.576289i | \(-0.195500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3593.27i | 0.385376i | 0.981260 | + | 0.192688i | \(0.0617205\pi\) | ||||
−0.981260 | + | 0.192688i | \(0.938280\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4680.36 | −0.498586 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8675.98i | − | 0.911904i | −0.890004 | − | 0.455952i | \(-0.849299\pi\) | ||
0.890004 | − | 0.455952i | \(-0.150701\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5507.79i | 0.575059i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14292.0 | + | 11274.9i | 1.47257 | + | 1.16171i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2932.69 | 0.300187 | 0.150094 | − | 0.988672i | \(-0.452042\pi\) | ||||
0.150094 | + | 0.988672i | \(0.452042\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6031.61 | −0.609371 | −0.304686 | − | 0.952453i | \(-0.598551\pi\) | ||||
−0.304686 | + | 0.952453i | \(0.598551\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −591.276 | −0.0593497 | −0.0296748 | − | 0.999560i | \(-0.509447\pi\) | ||||
−0.0296748 | + | 0.999560i | \(0.509447\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16674.6 | 1.65227 | 0.826134 | − | 0.563473i | \(-0.190535\pi\) | ||||
0.826134 | + | 0.563473i | \(0.190535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5777.18 | − | 7323.12i | 0.568796 | − | 0.721002i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 911.947i | 0.0886498i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 34.3983i | − | 0.00332274i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17217.5 | 1.64235 | 0.821175 | − | 0.570677i | \(-0.193319\pi\) | ||||
0.821175 | + | 0.570677i | \(0.193319\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 34932.0i | − | 3.31135i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6278.50i | 0.587818i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8745.94 | 0.813792 | 0.406896 | − | 0.913475i | \(-0.366611\pi\) | ||||
0.406896 | + | 0.913475i | \(0.366611\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 754.388i | 0.0693382i | 0.999399 | + | 0.0346691i | \(0.0110377\pi\) | ||||
−0.999399 | + | 0.0346691i | \(0.988962\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16020.3i | 1.46353i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10925.9 | + | 8619.37i | 0.986100 | + | 0.777931i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4960.47 | 0.445013 | 0.222506 | − | 0.974931i | \(-0.428576\pi\) | ||||
0.222506 | + | 0.974931i | \(0.428576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5299.83 | −0.469797 | −0.234898 | − | 0.972020i | \(-0.575476\pi\) | ||||
−0.234898 | + | 0.972020i | \(0.575476\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7770.09 | 0.684682 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18689.6 | −1.62751 | −0.813755 | − | 0.581207i | \(-0.802580\pi\) | ||||
−0.813755 | + | 0.581207i | \(0.802580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7379.69 | − | 5821.81i | −0.638861 | − | 0.503995i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2762.42i | 0.236363i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 259.695i | 0.0220916i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8964.93 | −0.753859 | −0.376930 | − | 0.926242i | \(-0.623020\pi\) | ||||
−0.376930 | + | 0.926242i | \(0.623020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20614.1i | 1.72350i | 0.507330 | + | 0.861752i | \(0.330633\pi\) | ||||
−0.507330 | + | 0.861752i | \(0.669367\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4593.56i | 0.379694i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8298.82 | −0.682076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30843.0i | 2.50649i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8134.99i | − | 0.657395i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5325.86 | + | 1274.74i | −0.425605 | + | 0.101868i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9376.65 | 0.745164 | 0.372582 | − | 0.927999i | \(-0.378473\pi\) | ||||
0.372582 | + | 0.927999i | \(0.378473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16461.9 | −1.29385 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2344.50 | −0.183261 | −0.0916305 | − | 0.995793i | \(-0.529208\pi\) | ||||
−0.0916305 | + | 0.995793i | \(0.529208\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1245.69 | 0.0963127 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8753.83 | + | 11096.3i | −0.673148 | + | 0.853278i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15368.4i | 1.16908i | 0.811364 | + | 0.584541i | \(0.198725\pi\) | ||||
−0.811364 | + | 0.584541i | \(0.801275\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5106.81i | 0.386395i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12895.5 | 0.965327 | 0.482664 | − | 0.875806i | \(-0.339669\pi\) | ||||
0.482664 | + | 0.875806i | \(0.339669\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10941.6i | 0.814722i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 24236.2i | − | 1.78565i | −0.450406 | − | 0.892824i | \(-0.648721\pi\) | ||
0.450406 | − | 0.892824i | \(-0.351279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7356.76 | 0.539178 | 0.269589 | − | 0.962975i | \(-0.413112\pi\) | ||||
0.269589 | + | 0.962975i | \(0.413112\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 591.724i | 0.0429158i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11928.2i | 0.860617i | 0.902682 | + | 0.430308i | \(0.141595\pi\) | ||||
−0.902682 | + | 0.430308i | \(0.858405\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13931.1 | − | 17658.9i | 0.994765 | − | 1.26096i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7108.49 | −0.504980 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5276.72 | 0.371028 | 0.185514 | − | 0.982642i | \(-0.440605\pi\) | ||||
0.185514 | + | 0.982642i | \(0.440605\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 357.181 | 0.0249871 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5290.53 | 0.366367 | 0.183184 | − | 0.983079i | \(-0.441360\pi\) | ||||
0.183184 | + | 0.983079i | \(0.441360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13487.6 | − | 17096.8i | 0.929308 | − | 1.17798i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 9894.37i | − | 0.674913i | −0.941341 | − | 0.337457i | \(-0.890433\pi\) | ||
0.941341 | − | 0.337457i | \(-0.109567\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2662.24i | − | 0.180691i | −0.995910 | − | 0.0903454i | \(-0.971203\pi\) | ||
0.995910 | − | 0.0903454i | \(-0.0287971\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11830.3 | −0.794994 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 11313.4i | − | 0.756499i | −0.925704 | − | 0.378249i | \(-0.876526\pi\) | ||
0.925704 | − | 0.378249i | \(-0.123474\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1454.26i | 0.0962901i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23984.5 | −1.58030 | −0.790151 | − | 0.612912i | \(-0.789998\pi\) | ||||
−0.790151 | + | 0.612912i | \(0.789998\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 16238.6i | − | 1.05955i | −0.848138 | − | 0.529775i | \(-0.822276\pi\) | ||
0.848138 | − | 0.529775i | \(-0.177724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17287.8i | 1.12254i | 0.827632 | + | 0.561271i | \(0.189687\pi\) | ||||
−0.827632 | + | 0.561271i | \(0.810313\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4883.43 | − | 6190.21i | 0.314046 | − | 0.398083i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15090.9 | −0.965815 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −41787.2 | −2.64891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 348.827 | 0.0220073 | 0.0110036 | − | 0.999939i | \(-0.496497\pi\) | ||||
0.0110036 | + | 0.999939i | \(0.496497\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27148.2 | −1.69660 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29824.3 | + | 7138.41i | −1.85507 | + | 0.444009i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16753.3i | 1.03232i | 0.856493 | + | 0.516158i | \(0.172638\pi\) | ||||
−0.856493 | + | 0.516158i | \(0.827362\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12309.7i | 0.754975i | 0.926015 | + | 0.377487i | \(0.123212\pi\) | ||||
−0.926015 | + | 0.377487i | \(0.876788\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32197.6 | 1.95644 | 0.978220 | − | 0.207570i | \(-0.0665555\pi\) | ||||
0.978220 | + | 0.207570i | \(0.0665555\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6174.00i | 0.373422i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 17824.6i | − | 1.06820i | −0.845422 | − | 0.534098i | \(-0.820651\pi\) | ||
0.845422 | − | 0.534098i | \(-0.179349\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16925.8 | 1.00969 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20533.9i | − | 1.21379i | −0.794782 | − | 0.606895i | \(-0.792415\pi\) | ||
0.794782 | − | 0.606895i | \(-0.207585\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10184.0i | 0.599261i | 0.954055 | + | 0.299630i | \(0.0968634\pi\) | ||||
−0.954055 | + | 0.299630i | \(0.903137\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1329.40 | − | 1048.75i | −0.0775214 | − | 0.0611563i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21428.6 | −1.24395 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7758.84 | 0.446388 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17547.2 | −1.00504 | −0.502521 | − | 0.864565i | \(-0.667594\pi\) | ||||
−0.502521 | + | 0.864565i | \(0.667594\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9665.66 | −0.548717 | −0.274358 | − | 0.961627i | \(-0.588465\pi\) | ||||
−0.274358 | + | 0.961627i | \(0.588465\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8303.89 | − | 6550.91i | −0.469329 | − | 0.370251i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 4376.97i | − | 0.245213i | −0.992455 | − | 0.122606i | \(-0.960875\pi\) | ||
0.992455 | − | 0.122606i | \(-0.0391253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 18023.7i | − | 1.00533i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39806.8 | −2.20104 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20238.2i | 1.11418i | 0.830453 | + | 0.557088i | \(0.188082\pi\) | ||||
−0.830453 | + | 0.557088i | \(0.811918\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11419.2i | 0.623243i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36895.9 | 2.00507 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 33130.3i | − | 1.78504i | −0.451004 | − | 0.892522i | \(-0.648934\pi\) | ||
0.451004 | − | 0.892522i | \(-0.351066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3249.25i | 0.174321i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8107.22 | + | 10276.7i | −0.431263 | + | 0.546667i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35213.2 | −1.86525 | −0.932623 | − | 0.360852i | \(-0.882486\pi\) | ||||
−0.932623 | + | 0.360852i | \(0.882486\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6144.28 | −0.322728 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15693.3 | 0.820831 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21789.0 | 1.13017 | 0.565086 | − | 0.825032i | \(-0.308843\pi\) | ||||
0.565086 | + | 0.825032i | \(0.308843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3653.55 | − | 2882.28i | −0.188718 | − | 0.148879i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 619.560i | 0.0317378i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 791.178i | − | 0.0403620i | −0.999796 | − | 0.0201810i | \(-0.993576\pi\) | ||
0.999796 | − | 0.0201810i | \(-0.00642425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6109.00 | 0.309097 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 225.319i | 0.0113538i | 0.999984 | + | 0.00567691i | \(0.00180703\pi\) | ||||
−0.999984 | + | 0.00567691i | \(0.998193\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 8041.08i | − | 0.401896i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2564.36 | −0.127648 | −0.0638238 | − | 0.997961i | \(-0.520330\pi\) | ||||
−0.0638238 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 35125.9i | − | 1.73438i | −0.497977 | − | 0.867190i | \(-0.665924\pi\) | ||
0.497977 | − | 0.867190i | \(-0.334076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19335.9i | 0.950891i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10759.3 | + | 8487.95i | 0.524880 | + | 0.414076i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10427.5 | 0.506666 | 0.253333 | − | 0.967379i | \(-0.418473\pi\) | ||||
0.253333 | + | 0.967379i | \(0.418473\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7748.45 | 0.373503 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14031.2 | −0.673677 | −0.336838 | − | 0.941562i | \(-0.609358\pi\) | ||||
−0.336838 | + | 0.941562i | \(0.609358\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10871.3 | −0.517849 | −0.258924 | − | 0.965898i | \(-0.583368\pi\) | ||||
−0.258924 | + | 0.965898i | \(0.583368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17176.1 | − | 21772.3i | 0.814963 | − | 1.03304i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34573.7i | 1.62762i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20740.7i | 0.972599i | 0.873792 | + | 0.486299i | \(0.161654\pi\) | ||||
−0.873792 | + | 0.486299i | \(0.838346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7445.62 | 0.346443 | 0.173221 | − | 0.984883i | \(-0.444582\pi\) | ||||
0.173221 | + | 0.984883i | \(0.444582\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 177.648i | 0.00823396i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 2868.91i | − | 0.131950i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11997.0 | 0.549665 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7350.79i | − | 0.334218i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16648.0i | − | 0.754049i | −0.926203 | − | 0.377024i | \(-0.876947\pi\) | ||
0.926203 | − | 0.377024i | \(-0.123053\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14471.3 | − | 11416.4i | −0.650494 | − | 0.513172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43448.7 | 1.94566 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28637.6 | 1.27277 | 0.636383 | − | 0.771373i | \(-0.280430\pi\) | ||||
0.636383 | + | 0.771373i | \(0.280430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1739.66 | 0.0770272 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8103.20 | −0.356109 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22868.4 | + | 18040.8i | 1.00125 | + | 0.789882i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.4260i | 0.00214799i | 0.999999 | + | 0.00107400i | \(0.000341863\pi\) | ||||
−0.999999 | + | 0.00107400i | \(0.999658\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37292.7i | − | 1.61470i | −0.590072 | − | 0.807350i | \(-0.700901\pi\) | ||
0.590072 | − | 0.807350i | \(-0.299099\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43163.8 | 1.85517 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 475.017i | − | 0.0203412i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 807.586i | 0.0343300i | 0.999853 | + | 0.0171650i | \(0.00546406\pi\) | ||||
−0.999853 | + | 0.0171650i | \(0.994536\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20680.5 | −0.875913 | −0.437957 | − | 0.898996i | \(-0.644298\pi\) | ||||
−0.437957 | + | 0.898996i | \(0.644298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 44485.5i | 1.87051i | 0.353976 | + | 0.935255i | \(0.384830\pi\) | ||||
−0.353976 | + | 0.935255i | \(0.615170\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7797.19i | 0.326668i | 0.986571 | + | 0.163334i | \(0.0522248\pi\) | ||||
−0.986571 | + | 0.163334i | \(0.947775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8539.30 | + | 35677.2i | 0.355185 | + | 1.48396i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21257.6 | −0.881019 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29475.4 | 1.21288 | 0.606439 | − | 0.795130i | \(-0.292598\pi\) | ||||
0.606439 | + | 0.795130i | \(0.292598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1952.37 | 0.0800512 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 63727.2 | 2.59442 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12343.6 | − | 15646.7i | 0.500746 | − | 0.634743i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 55894.0i | − | 2.25149i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9768.10i | 0.392091i | 0.980595 | + | 0.196045i | \(0.0628100\pi\) | ||||
−0.980595 | + | 0.196045i | \(0.937190\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22812.3 | 0.909281 | 0.454641 | − | 0.890675i | \(-0.349768\pi\) | ||||
0.454641 | + | 0.890675i | \(0.349768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 35568.7i | − | 1.41279i | −0.707817 | − | 0.706396i | \(-0.750320\pi\) | ||
0.707817 | − | 0.706396i | \(-0.249680\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 34594.9i | − | 1.36457i | −0.731087 | − | 0.682285i | \(-0.760986\pi\) | ||
0.731087 | − | 0.682285i | \(-0.239014\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18689.9 | −0.734653 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12184.2i | 0.475628i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 45029.2i | − | 1.75173i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16285.1 | − | 20642.9i | 0.629184 | − | 0.797550i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23303.7 | −0.897275 | −0.448637 | − | 0.893714i | \(-0.648091\pi\) | ||||
−0.448637 | + | 0.893714i | \(0.648091\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8387.34 | 0.320745 | 0.160373 | − | 0.987057i | \(-0.448730\pi\) | ||||
0.160373 | + | 0.987057i | \(0.448730\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4287.17 | 0.163391 | 0.0816957 | − | 0.996657i | \(-0.473966\pi\) | ||||
0.0816957 | + | 0.996657i | \(0.473966\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13461.3 | 0.509569 | 0.254784 | − | 0.966998i | \(-0.417996\pi\) | ||||
0.254784 | + | 0.966998i | \(0.417996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28326.1 | − | 35906.0i | 1.06865 | − | 1.35461i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 135.271i | − | 0.00506904i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 12919.4i | − | 0.482510i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6433.32 | −0.238669 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47618.7i | 1.76072i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38554.1i | 1.41611i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13884.6 | 0.508304 | 0.254152 | − | 0.967164i | \(-0.418204\pi\) | ||||
0.254152 | + | 0.967164i | \(0.418204\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 52493.2i | − | 1.90909i | −0.298073 | − | 0.954543i | \(-0.596344\pi\) | ||
0.298073 | − | 0.954543i | \(-0.403656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 19390.3i | − | 0.702874i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17660.1 | + | 22385.9i | −0.635975 | + | 0.806158i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29789.5 | 1.06928 | 0.534639 | − | 0.845081i | \(-0.320448\pi\) | ||||
0.534639 | + | 0.845081i | \(0.320448\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67182.2 | 2.39581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1616.05 | −0.0574438 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 18314.2 | 0.646792 | 0.323396 | − | 0.946264i | \(-0.395175\pi\) | ||||
0.323396 | + | 0.946264i | \(0.395175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2774.15 | − | 663.989i | 0.0976574 | − | 0.0233742i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 18773.0i | − | 0.656623i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4717.18i | 0.164465i | 0.996613 | + | 0.0822325i | \(0.0262050\pi\) | ||||
−0.996613 | + | 0.0822325i | \(0.973795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40928.9 | −1.41790 | −0.708950 | − | 0.705259i | \(-0.750831\pi\) | ||||
−0.708950 | + | 0.705259i | \(0.750831\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 49351.4i | 1.70424i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 24971.8i | − | 0.856890i | −0.903568 | − | 0.428445i | \(-0.859062\pi\) | ||
0.903568 | − | 0.428445i | \(-0.140938\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45377.1 | −1.55216 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14607.3i | 0.496512i | 0.968694 | + | 0.248256i | \(0.0798574\pi\) | ||||
−0.968694 | + | 0.248256i | \(0.920143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15590.7i | 0.528276i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 23838.0 | + | 18805.7i | 0.802680 | + | 0.633231i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27946.4 | 0.938080 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16420.8 | 0.547775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27656.3 | −0.919717 | −0.459859 | − | 0.887992i | \(-0.652100\pi\) | ||||
−0.459859 | + | 0.887992i | \(0.652100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5235.20 | 0.173023 | 0.0865117 | − | 0.996251i | \(-0.472428\pi\) | ||||
0.0865117 | + | 0.996251i | \(0.472428\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15102.9 | − | 11914.6i | −0.497612 | − | 0.392564i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4586.77i | 0.150198i | 0.997176 | + | 0.0750991i | \(0.0239273\pi\) | ||||
−0.997176 | + | 0.0750991i | \(0.976073\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 6797.11i | − | 0.221896i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3934.28 | −0.127654 | −0.0638270 | − | 0.997961i | \(-0.520331\pi\) | ||||
−0.0638270 | + | 0.997961i | \(0.520331\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 26213.9i | − | 0.847963i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8171.31i | 0.262722i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17434.1 | −0.558841 | −0.279421 | − | 0.960169i | \(-0.590142\pi\) | ||||
−0.279421 | + | 0.960169i | \(0.590142\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 54531.9i | − | 1.73747i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 14149.8i | − | 0.449476i | −0.974419 | − | 0.224738i | \(-0.927847\pi\) | ||
0.974419 | − | 0.224738i | \(-0.0721526\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2268.4.f.a.1133.11 | 48 | ||
3.2 | odd | 2 | inner | 2268.4.f.a.1133.38 | 48 | ||
7.6 | odd | 2 | inner | 2268.4.f.a.1133.37 | 48 | ||
9.2 | odd | 6 | 252.4.x.a.41.11 | ✓ | 48 | ||
9.4 | even | 3 | 252.4.x.a.209.14 | yes | 48 | ||
9.5 | odd | 6 | 756.4.x.a.629.6 | 48 | |||
9.7 | even | 3 | 756.4.x.a.125.19 | 48 | |||
21.20 | even | 2 | inner | 2268.4.f.a.1133.12 | 48 | ||
63.13 | odd | 6 | 252.4.x.a.209.11 | yes | 48 | ||
63.20 | even | 6 | 252.4.x.a.41.14 | yes | 48 | ||
63.34 | odd | 6 | 756.4.x.a.125.6 | 48 | |||
63.41 | even | 6 | 756.4.x.a.629.19 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.11 | ✓ | 48 | 9.2 | odd | 6 | ||
252.4.x.a.41.14 | yes | 48 | 63.20 | even | 6 | ||
252.4.x.a.209.11 | yes | 48 | 63.13 | odd | 6 | ||
252.4.x.a.209.14 | yes | 48 | 9.4 | even | 3 | ||
756.4.x.a.125.6 | 48 | 63.34 | odd | 6 | |||
756.4.x.a.125.19 | 48 | 9.7 | even | 3 | |||
756.4.x.a.629.6 | 48 | 9.5 | odd | 6 | |||
756.4.x.a.629.19 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.11 | 48 | 1.1 | even | 1 | trivial | ||
2268.4.f.a.1133.12 | 48 | 21.20 | even | 2 | inner | ||
2268.4.f.a.1133.37 | 48 | 7.6 | odd | 2 | inner | ||
2268.4.f.a.1133.38 | 48 | 3.2 | odd | 2 | inner |