Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(4409,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.4409");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.d (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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4409.7 | ||
Character | \(\chi\) | \(=\) | 4410.4409 |
Dual form | 4410.2.d.c.4409.8 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.12606 | − | 1.93184i | −0.503590 | − | 0.863943i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.12606 | + | 1.93184i | 0.356092 | + | 0.610900i | ||||
\(11\) | 0.602126i | 0.181548i | 0.995872 | + | 0.0907739i | \(0.0289341\pi\) | ||||
−0.995872 | + | 0.0907739i | \(0.971066\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0571454 | 0.0158493 | 0.00792464 | − | 0.999969i | \(-0.497477\pi\) | ||||
0.00792464 | + | 0.999969i | \(0.497477\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.347217i | − | 0.0842124i | −0.999113 | − | 0.0421062i | \(-0.986593\pi\) | ||
0.999113 | − | 0.0421062i | \(-0.0134068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.92239i | 1.12927i | 0.825339 | + | 0.564637i | \(0.190984\pi\) | ||||
−0.825339 | + | 0.564637i | \(0.809016\pi\) | |||||||
\(20\) | −1.12606 | − | 1.93184i | −0.251795 | − | 0.431972i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.602126i | − | 0.128374i | ||||||
\(23\) | 1.45795 | 0.304004 | 0.152002 | − | 0.988380i | \(-0.451428\pi\) | ||||
0.152002 | + | 0.988380i | \(0.451428\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46398 | + | 4.35073i | −0.492795 | + | 0.870145i | ||||
\(26\) | −0.0571454 | −0.0112071 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.49327i | − | 1.20577i | −0.797828 | − | 0.602885i | \(-0.794018\pi\) | ||
0.797828 | − | 0.602885i | \(-0.205982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.05969i | 0.908748i | 0.890811 | + | 0.454374i | \(0.150137\pi\) | ||||
−0.890811 | + | 0.454374i | \(0.849863\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.347217i | 0.0595472i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 1.16480i | − | 0.191493i | −0.995406 | − | 0.0957464i | \(-0.969476\pi\) | ||
0.995406 | − | 0.0957464i | \(-0.0305238\pi\) | |||||||
\(38\) | − | 4.92239i | − | 0.798517i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.12606 | + | 1.93184i | 0.178046 | + | 0.305450i | ||||
\(41\) | −2.64008 | −0.412311 | −0.206156 | − | 0.978519i | \(-0.566095\pi\) | ||||
−0.206156 | + | 0.978519i | \(0.566095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 12.0070i | − | 1.83105i | −0.402260 | − | 0.915526i | \(-0.631775\pi\) | ||
0.402260 | − | 0.915526i | \(-0.368225\pi\) | |||||||
\(44\) | 0.602126i | 0.0907739i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.45795 | −0.214963 | ||||||||
\(47\) | − | 7.74571i | − | 1.12983i | −0.825150 | − | 0.564914i | \(-0.808909\pi\) | ||
0.825150 | − | 0.564914i | \(-0.191091\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.46398 | − | 4.35073i | 0.348459 | − | 0.615286i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0571454 | 0.00792464 | ||||||||
\(53\) | 5.55299 | 0.762762 | 0.381381 | − | 0.924418i | \(-0.375449\pi\) | ||||
0.381381 | + | 0.924418i | \(0.375449\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.16321 | − | 0.678030i | 0.156847 | − | 0.0914256i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.49327i | 0.852608i | ||||||||
\(59\) | 0.890569 | 0.115942 | 0.0579711 | − | 0.998318i | \(-0.481537\pi\) | ||||
0.0579711 | + | 0.998318i | \(0.481537\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.72460i | 0.732959i | 0.930426 | + | 0.366480i | \(0.119437\pi\) | ||||
−0.930426 | + | 0.366480i | \(0.880563\pi\) | |||||||
\(62\) | − | 5.05969i | − | 0.642582i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.0643492 | − | 0.110395i | −0.00798153 | − | 0.0136929i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.110634i | − | 0.0135160i | −0.999977 | − | 0.00675802i | \(-0.997849\pi\) | ||
0.999977 | − | 0.00675802i | \(-0.00215116\pi\) | |||||||
\(68\) | − | 0.347217i | − | 0.0421062i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.7816i | − | 1.51689i | −0.651735 | − | 0.758447i | \(-0.725959\pi\) | ||
0.651735 | − | 0.758447i | \(-0.274041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.914240 | 0.107004 | 0.0535018 | − | 0.998568i | \(-0.482962\pi\) | ||||
0.0535018 | + | 0.998568i | \(0.482962\pi\) | |||||||
\(74\) | 1.16480i | 0.135406i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.92239i | 0.564637i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.38275 | 0.155572 | 0.0777860 | − | 0.996970i | \(-0.475215\pi\) | ||||
0.0777860 | + | 0.996970i | \(0.475215\pi\) | |||||||
\(80\) | −1.12606 | − | 1.93184i | −0.125897 | − | 0.215986i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.64008 | 0.291548 | ||||||||
\(83\) | 0.429722i | 0.0471681i | 0.999722 | + | 0.0235841i | \(0.00750774\pi\) | ||||
−0.999722 | + | 0.0235841i | \(0.992492\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.670765 | + | 0.390987i | −0.0727547 | + | 0.0424085i | ||||
\(86\) | 12.0070i | 1.29475i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 0.602126i | − | 0.0641868i | ||||||
\(89\) | −15.9541 | −1.69113 | −0.845563 | − | 0.533875i | \(-0.820735\pi\) | ||||
−0.845563 | + | 0.533875i | \(0.820735\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.45795 | 0.152002 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.74571i | 0.798909i | ||||||||
\(95\) | 9.50925 | − | 5.54291i | 0.975629 | − | 0.568691i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1539 | 1.33558 | 0.667788 | − | 0.744351i | \(-0.267241\pi\) | ||||
0.667788 | + | 0.744351i | \(0.267241\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.46398 | + | 4.35073i | −0.246398 | + | 0.435073i | ||||
\(101\) | −13.3448 | −1.32786 | −0.663928 | − | 0.747796i | \(-0.731112\pi\) | ||||
−0.663928 | + | 0.747796i | \(0.731112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.58914 | −0.649248 | −0.324624 | − | 0.945843i | \(-0.605238\pi\) | ||||
−0.324624 | + | 0.945843i | \(0.605238\pi\) | |||||||
\(104\) | −0.0571454 | −0.00560357 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.55299 | −0.539354 | ||||||||
\(107\) | −3.66504 | −0.354313 | −0.177156 | − | 0.984183i | \(-0.556690\pi\) | ||||
−0.177156 | + | 0.984183i | \(0.556690\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6104 | −1.20785 | −0.603926 | − | 0.797040i | \(-0.706398\pi\) | ||||
−0.603926 | + | 0.797040i | \(0.706398\pi\) | |||||||
\(110\) | −1.16321 | + | 0.678030i | −0.110908 | + | 0.0646476i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.87823 | −0.270761 | −0.135381 | − | 0.990794i | \(-0.543226\pi\) | ||||
−0.135381 | + | 0.990794i | \(0.543226\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.64174 | − | 2.81652i | −0.153093 | − | 0.262642i | ||||
\(116\) | − | 6.49327i | − | 0.602885i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.890569 | −0.0819836 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6374 | 0.967040 | ||||||||
\(122\) | − | 5.72460i | − | 0.518281i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.05969i | 0.454374i | ||||||||
\(125\) | 11.1795 | − | 0.139188i | 0.999923 | − | 0.0124493i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.2456i | − | 1.26409i | −0.774931 | − | 0.632046i | \(-0.782215\pi\) | ||
0.774931 | − | 0.632046i | \(-0.217785\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0643492 | + | 0.110395i | 0.00564380 | + | 0.00968232i | ||||
\(131\) | −8.52449 | −0.744788 | −0.372394 | − | 0.928075i | \(-0.621463\pi\) | ||||
−0.372394 | + | 0.928075i | \(0.621463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.110634i | 0.00955729i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.347217i | 0.0297736i | ||||||||
\(137\) | 8.54900 | 0.730391 | 0.365195 | − | 0.930931i | \(-0.381002\pi\) | ||||
0.365195 | + | 0.930931i | \(0.381002\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50047i | 0.551362i | 0.961249 | + | 0.275681i | \(0.0889034\pi\) | ||||
−0.961249 | + | 0.275681i | \(0.911097\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.7816i | 1.07261i | ||||||||
\(143\) | 0.0344087i | 0.00287740i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.5439 | + | 7.31181i | −1.04172 | + | 0.607213i | ||||
\(146\) | −0.914240 | −0.0756630 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.16480i | − | 0.0957464i | ||||||
\(149\) | 9.98512i | 0.818013i | 0.912532 | + | 0.409006i | \(0.134125\pi\) | ||||
−0.912532 | + | 0.409006i | \(0.865875\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.36685 | −0.762263 | −0.381132 | − | 0.924521i | \(-0.624466\pi\) | ||||
−0.381132 | + | 0.924521i | \(0.624466\pi\) | |||||||
\(152\) | − | 4.92239i | − | 0.399259i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.77449 | − | 5.69752i | 0.785106 | − | 0.457636i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.4850 | −1.87430 | −0.937152 | − | 0.348921i | \(-0.886548\pi\) | ||||
−0.937152 | + | 0.348921i | \(0.886548\pi\) | |||||||
\(158\) | −1.38275 | −0.110006 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.12606 | + | 1.93184i | 0.0890229 | + | 0.152725i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.209681i | 0.0164235i | 0.999966 | + | 0.00821173i | \(0.00261391\pi\) | ||||
−0.999966 | + | 0.00821173i | \(0.997386\pi\) | |||||||
\(164\) | −2.64008 | −0.206156 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 0.429722i | − | 0.0333529i | ||||||
\(167\) | − | 11.7957i | − | 0.912779i | −0.889780 | − | 0.456390i | \(-0.849142\pi\) | ||
0.889780 | − | 0.456390i | \(-0.150858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9967 | −0.999749 | ||||||||
\(170\) | 0.670765 | − | 0.390987i | 0.0514454 | − | 0.0299873i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 12.0070i | − | 0.915526i | ||||||
\(173\) | − | 19.8493i | − | 1.50911i | −0.656236 | − | 0.754556i | \(-0.727852\pi\) | ||
0.656236 | − | 0.754556i | \(-0.272148\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.602126i | 0.0453869i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.9541 | 1.19581 | ||||||||
\(179\) | − | 6.96012i | − | 0.520224i | −0.965578 | − | 0.260112i | \(-0.916241\pi\) | ||
0.965578 | − | 0.260112i | \(-0.0837595\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3113i | 0.989422i | 0.869057 | + | 0.494711i | \(0.164726\pi\) | ||||
−0.869057 | + | 0.494711i | \(0.835274\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.45795 | −0.107482 | ||||||||
\(185\) | −2.25021 | + | 1.31164i | −0.165439 | + | 0.0964337i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.209068 | 0.0152886 | ||||||||
\(188\) | − | 7.74571i | − | 0.564914i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.50925 | + | 5.54291i | −0.689874 | + | 0.402125i | ||||
\(191\) | 25.0941i | 1.81575i | 0.419243 | + | 0.907874i | \(0.362296\pi\) | ||||
−0.419243 | + | 0.907874i | \(0.637704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5745i | 1.19306i | 0.802592 | + | 0.596529i | \(0.203454\pi\) | ||||
−0.802592 | + | 0.596529i | \(0.796546\pi\) | |||||||
\(194\) | −13.1539 | −0.944395 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.440156 | 0.0313598 | 0.0156799 | − | 0.999877i | \(-0.495009\pi\) | ||||
0.0156799 | + | 0.999877i | \(0.495009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.7109i | − | 1.46815i | −0.679066 | − | 0.734077i | \(-0.737615\pi\) | ||
0.679066 | − | 0.734077i | \(-0.262385\pi\) | |||||||
\(200\) | 2.46398 | − | 4.35073i | 0.174229 | − | 0.307643i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.3448 | 0.938936 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.97289 | + | 5.10020i | 0.207636 | + | 0.356213i | ||||
\(206\) | 6.58914 | 0.459087 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0571454 | 0.00396232 | ||||||||
\(209\) | −2.96390 | −0.205017 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4319 | −0.718164 | −0.359082 | − | 0.933306i | \(-0.616910\pi\) | ||||
−0.359082 | + | 0.933306i | \(0.616910\pi\) | |||||||
\(212\) | 5.55299 | 0.381381 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.66504 | 0.250537 | ||||||||
\(215\) | −23.1956 | + | 13.5206i | −1.58192 | + | 0.922098i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.6104 | 0.854081 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.16321 | − | 0.678030i | 0.0784235 | − | 0.0457128i | ||||
\(221\) | − | 0.0198418i | − | 0.00133471i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3950 | −0.763067 | −0.381533 | − | 0.924355i | \(-0.624604\pi\) | ||||
−0.381533 | + | 0.924355i | \(0.624604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.87823 | 0.191457 | ||||||||
\(227\) | 27.4366i | 1.82103i | 0.413475 | + | 0.910516i | \(0.364315\pi\) | ||||
−0.413475 | + | 0.910516i | \(0.635685\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.2770i | 0.943452i | 0.881745 | + | 0.471726i | \(0.156369\pi\) | ||||
−0.881745 | + | 0.471726i | \(0.843631\pi\) | |||||||
\(230\) | 1.64174 | + | 2.81652i | 0.108253 | + | 0.185716i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.49327i | 0.426304i | ||||||||
\(233\) | −25.2801 | −1.65616 | −0.828078 | − | 0.560613i | \(-0.810565\pi\) | ||||
−0.828078 | + | 0.560613i | \(0.810565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.9634 | + | 8.72214i | −0.976107 | + | 0.568969i | ||||
\(236\) | 0.890569 | 0.0579711 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 19.6427i | − | 1.27058i | −0.772274 | − | 0.635289i | \(-0.780881\pi\) | ||
0.772274 | − | 0.635289i | \(-0.219119\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.467621i | − | 0.0301221i | −0.999887 | − | 0.0150611i | \(-0.995206\pi\) | ||
0.999887 | − | 0.0150611i | \(-0.00479427\pi\) | |||||||
\(242\) | −10.6374 | −0.683801 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.72460i | 0.366480i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.281292i | 0.0178982i | ||||||||
\(248\) | − | 5.05969i | − | 0.321291i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.1795 | + | 0.139188i | −0.707052 | + | 0.00880300i | ||||
\(251\) | −12.1113 | −0.764460 | −0.382230 | − | 0.924067i | \(-0.624844\pi\) | ||||
−0.382230 | + | 0.924067i | \(0.624844\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.877870i | 0.0551912i | ||||||||
\(254\) | 14.2456i | 0.893848i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 16.4198i | − | 1.02424i | −0.858914 | − | 0.512120i | \(-0.828860\pi\) | ||
0.858914 | − | 0.512120i | \(-0.171140\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0643492 | − | 0.110395i | −0.00399077 | − | 0.00684644i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.52449 | 0.526645 | ||||||||
\(263\) | 19.0087 | 1.17212 | 0.586062 | − | 0.810266i | \(-0.300677\pi\) | ||||
0.586062 | + | 0.810266i | \(0.300677\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.25300 | − | 10.7275i | −0.384119 | − | 0.658983i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 0.110634i | − | 0.00675802i | ||||||
\(269\) | 1.59449 | 0.0972175 | 0.0486088 | − | 0.998818i | \(-0.484521\pi\) | ||||
0.0486088 | + | 0.998818i | \(0.484521\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.99015i | − | 0.485367i | −0.970106 | − | 0.242683i | \(-0.921972\pi\) | ||
0.970106 | − | 0.242683i | \(-0.0780276\pi\) | |||||||
\(272\) | − | 0.347217i | − | 0.0210531i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.54900 | −0.516464 | ||||||||
\(275\) | −2.61969 | − | 1.48362i | −0.157973 | − | 0.0894658i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 19.8876i | − | 1.19493i | −0.801894 | − | 0.597466i | \(-0.796174\pi\) | ||
0.801894 | − | 0.597466i | \(-0.203826\pi\) | |||||||
\(278\) | − | 6.50047i | − | 0.389872i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.28665i | 0.494340i | 0.968972 | + | 0.247170i | \(0.0795007\pi\) | ||||
−0.968972 | + | 0.247170i | \(0.920499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.939284 | −0.0558347 | −0.0279173 | − | 0.999610i | \(-0.508888\pi\) | ||||
−0.0279173 | + | 0.999610i | \(0.508888\pi\) | |||||||
\(284\) | − | 12.7816i | − | 0.758447i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.0344087i | − | 0.00203463i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8794 | 0.992908 | ||||||||
\(290\) | 12.5439 | − | 7.31181i | 0.736605 | − | 0.429365i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.914240 | 0.0535018 | ||||||||
\(293\) | 13.4622i | 0.786469i | 0.919438 | + | 0.393235i | \(0.128644\pi\) | ||||
−0.919438 | + | 0.393235i | \(0.871356\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.00283 | − | 1.72043i | −0.0583873 | − | 0.100167i | ||||
\(296\) | 1.16480i | 0.0677029i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 9.98512i | − | 0.578422i | ||||||
\(299\) | 0.0833152 | 0.00481824 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.36685 | 0.539002 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.92239i | 0.282319i | ||||||||
\(305\) | 11.0590 | − | 6.44624i | 0.633235 | − | 0.369111i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.59205 | −0.490374 | −0.245187 | − | 0.969476i | \(-0.578849\pi\) | ||||
−0.245187 | + | 0.969476i | \(0.578849\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.77449 | + | 5.69752i | −0.555154 | + | 0.323597i | ||||
\(311\) | −21.5290 | −1.22080 | −0.610398 | − | 0.792095i | \(-0.708990\pi\) | ||||
−0.610398 | + | 0.792095i | \(0.708990\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.77206 | 0.156686 | 0.0783429 | − | 0.996926i | \(-0.475037\pi\) | ||||
0.0783429 | + | 0.996926i | \(0.475037\pi\) | |||||||
\(314\) | 23.4850 | 1.32533 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.38275 | 0.0777860 | ||||||||
\(317\) | −27.6421 | −1.55254 | −0.776268 | − | 0.630403i | \(-0.782890\pi\) | ||||
−0.776268 | + | 0.630403i | \(0.782890\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.90977 | 0.218905 | ||||||||
\(320\) | −1.12606 | − | 1.93184i | −0.0629487 | − | 0.107993i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.70914 | 0.0950989 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.140805 | + | 0.248624i | −0.00781045 | + | 0.0137912i | ||||
\(326\) | − | 0.209681i | − | 0.0116131i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.64008 | 0.145774 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.8909 | 1.86281 | 0.931406 | − | 0.363981i | \(-0.118583\pi\) | ||||
0.931406 | + | 0.363981i | \(0.118583\pi\) | |||||||
\(332\) | 0.429722i | 0.0235841i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.7957i | 0.645433i | ||||||||
\(335\) | −0.213726 | + | 0.124580i | −0.0116771 | + | 0.00680654i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.42365i | − | 0.186498i | −0.995643 | − | 0.0932492i | \(-0.970275\pi\) | ||
0.995643 | − | 0.0932492i | \(-0.0297253\pi\) | |||||||
\(338\) | 12.9967 | 0.706929 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.670765 | + | 0.390987i | −0.0363774 | + | 0.0212042i | ||||
\(341\) | −3.04657 | −0.164981 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 12.0070i | 0.647374i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.8493i | 1.06710i | ||||||||
\(347\) | −25.9747 | −1.39439 | −0.697196 | − | 0.716880i | \(-0.745569\pi\) | ||||
−0.697196 | + | 0.716880i | \(0.745569\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 16.0984i | − | 0.861726i | −0.902417 | − | 0.430863i | \(-0.858209\pi\) | ||
0.902417 | − | 0.430863i | \(-0.141791\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 0.602126i | − | 0.0320934i | ||||||
\(353\) | − | 21.3823i | − | 1.13807i | −0.822315 | − | 0.569033i | \(-0.807318\pi\) | ||
0.822315 | − | 0.569033i | \(-0.192682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.6919 | + | 14.3928i | −1.31051 | + | 0.763892i | ||||
\(356\) | −15.9541 | −0.845563 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.96012i | 0.367854i | ||||||||
\(359\) | − | 19.0185i | − | 1.00376i | −0.864938 | − | 0.501878i | \(-0.832643\pi\) | ||
0.864938 | − | 0.501878i | \(-0.167357\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.22995 | −0.275260 | ||||||||
\(362\) | − | 13.3113i | − | 0.699627i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.02949 | − | 1.76616i | −0.0538859 | − | 0.0924451i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.1510 | −1.88707 | −0.943533 | − | 0.331280i | \(-0.892520\pi\) | ||||
−0.943533 | + | 0.331280i | \(0.892520\pi\) | |||||||
\(368\) | 1.45795 | 0.0760009 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.25021 | − | 1.31164i | 0.116983 | − | 0.0681890i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 21.5031i | − | 1.11339i | −0.830718 | − | 0.556693i | \(-0.812070\pi\) | ||
0.830718 | − | 0.556693i | \(-0.187930\pi\) | |||||||
\(374\) | −0.209068 | −0.0108107 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.74571i | 0.399454i | ||||||||
\(377\) | − | 0.371060i | − | 0.0191106i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.31543 | 0.273035 | 0.136518 | − | 0.990638i | \(-0.456409\pi\) | ||||
0.136518 | + | 0.990638i | \(0.456409\pi\) | |||||||
\(380\) | 9.50925 | − | 5.54291i | 0.487814 | − | 0.284345i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 25.0941i | − | 1.28393i | ||||||
\(383\) | 26.3353i | 1.34567i | 0.739793 | + | 0.672835i | \(0.234923\pi\) | ||||
−0.739793 | + | 0.672835i | \(0.765077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 16.5745i | − | 0.843619i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.1539 | 0.667788 | ||||||||
\(389\) | − | 3.43842i | − | 0.174335i | −0.996194 | − | 0.0871674i | \(-0.972219\pi\) | ||
0.996194 | − | 0.0871674i | \(-0.0277815\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.506225i | − | 0.0256009i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.440156 | −0.0221747 | ||||||||
\(395\) | −1.55707 | − | 2.67125i | −0.0783445 | − | 0.134405i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.9177 | 1.40115 | 0.700576 | − | 0.713578i | \(-0.252927\pi\) | ||||
0.700576 | + | 0.713578i | \(0.252927\pi\) | |||||||
\(398\) | 20.7109i | 1.03814i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.46398 | + | 4.35073i | −0.123199 | + | 0.217536i | ||||
\(401\) | 24.2952i | 1.21325i | 0.794990 | + | 0.606623i | \(0.207476\pi\) | ||||
−0.794990 | + | 0.606623i | \(0.792524\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.289138i | 0.0144030i | ||||||||
\(404\) | −13.3448 | −0.663928 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.701359 | 0.0347651 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.1853i | 0.701420i | 0.936484 | + | 0.350710i | \(0.114060\pi\) | ||||
−0.936484 | + | 0.350710i | \(0.885940\pi\) | |||||||
\(410\) | −2.97289 | − | 5.10020i | −0.146821 | − | 0.251881i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.58914 | −0.324624 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.830152 | − | 0.483893i | 0.0407506 | − | 0.0237534i | ||||
\(416\) | −0.0571454 | −0.00280178 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.96390 | 0.144969 | ||||||||
\(419\) | −17.9730 | −0.878036 | −0.439018 | − | 0.898478i | \(-0.644674\pi\) | ||||
−0.439018 | + | 0.898478i | \(0.644674\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.9077 | 0.629084 | 0.314542 | − | 0.949244i | \(-0.398149\pi\) | ||||
0.314542 | + | 0.949244i | \(0.398149\pi\) | |||||||
\(422\) | 10.4319 | 0.507819 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.55299 | −0.269677 | ||||||||
\(425\) | 1.51064 | + | 0.855533i | 0.0732770 | + | 0.0414995i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.66504 | −0.177156 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 23.1956 | − | 13.5206i | 1.11859 | − | 0.652022i | ||||
\(431\) | − | 7.13005i | − | 0.343442i | −0.985146 | − | 0.171721i | \(-0.945067\pi\) | ||
0.985146 | − | 0.171721i | \(-0.0549328\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.1054 | −1.35066 | −0.675330 | − | 0.737516i | \(-0.735999\pi\) | ||||
−0.675330 | + | 0.737516i | \(0.735999\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.6104 | −0.603926 | ||||||||
\(437\) | 7.17661i | 0.343304i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 21.2538i | − | 1.01439i | −0.861831 | − | 0.507195i | \(-0.830682\pi\) | ||
0.861831 | − | 0.507195i | \(-0.169318\pi\) | |||||||
\(440\) | −1.16321 | + | 0.678030i | −0.0554538 | + | 0.0323238i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.0198418i | 0.000943780i | ||||||||
\(443\) | −8.94032 | −0.424768 | −0.212384 | − | 0.977186i | \(-0.568123\pi\) | ||||
−0.212384 | + | 0.977186i | \(0.568123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.9652 | + | 30.8206i | 0.851634 | + | 1.46104i | ||||
\(446\) | 11.3950 | 0.539570 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.6014i | − | 0.972241i | −0.873892 | − | 0.486121i | \(-0.838412\pi\) | ||
0.873892 | − | 0.486121i | \(-0.161588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.58966i | − | 0.0748542i | ||||||
\(452\) | −2.87823 | −0.135381 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 27.4366i | − | 1.28766i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.8747i | − | 1.25715i | −0.777750 | − | 0.628573i | \(-0.783639\pi\) | ||
0.777750 | − | 0.628573i | \(-0.216361\pi\) | |||||||
\(458\) | − | 14.2770i | − | 0.667122i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.64174 | − | 2.81652i | −0.0765466 | − | 0.131321i | ||||
\(461\) | −25.0610 | −1.16721 | −0.583603 | − | 0.812039i | \(-0.698357\pi\) | ||||
−0.583603 | + | 0.812039i | \(0.698357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.7470i | − | 1.19656i | −0.801286 | − | 0.598282i | \(-0.795850\pi\) | ||
0.801286 | − | 0.598282i | \(-0.204150\pi\) | |||||||
\(464\) | − | 6.49327i | − | 0.301442i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.2801 | 1.17108 | ||||||||
\(467\) | 0.198229i | 0.00917293i | 0.999989 | + | 0.00458647i | \(0.00145992\pi\) | ||||
−0.999989 | + | 0.00458647i | \(0.998540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 14.9634 | − | 8.72214i | 0.690212 | − | 0.402322i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.890569 | −0.0409918 | ||||||||
\(473\) | 7.22973 | 0.332423 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.4160 | − | 12.1287i | −0.982633 | − | 0.556501i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.6427i | 0.898435i | ||||||||
\(479\) | 8.78904 | 0.401581 | 0.200791 | − | 0.979634i | \(-0.435649\pi\) | ||||
0.200791 | + | 0.979634i | \(0.435649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 0.0665632i | − | 0.00303502i | ||||||
\(482\) | 0.467621i | 0.0212996i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.6374 | 0.483520 | ||||||||
\(485\) | −14.8121 | − | 25.4112i | −0.672582 | − | 1.15386i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 42.7286i | − | 1.93622i | −0.250527 | − | 0.968110i | \(-0.580604\pi\) | ||
0.250527 | − | 0.968110i | \(-0.419396\pi\) | |||||||
\(488\) | − | 5.72460i | − | 0.259140i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.45933i | − | 0.156117i | −0.996949 | − | 0.0780587i | \(-0.975128\pi\) | ||
0.996949 | − | 0.0780587i | \(-0.0248722\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.25457 | −0.101541 | ||||||||
\(494\) | − | 0.281292i | − | 0.0126559i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.05969i | 0.227187i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.9942 | −1.16366 | −0.581830 | − | 0.813311i | \(-0.697663\pi\) | ||||
−0.581830 | + | 0.813311i | \(0.697663\pi\) | |||||||
\(500\) | 11.1795 | − | 0.139188i | 0.499961 | − | 0.00622466i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.1113 | 0.540555 | ||||||||
\(503\) | 9.37901i | 0.418189i | 0.977895 | + | 0.209095i | \(0.0670517\pi\) | ||||
−0.977895 | + | 0.209095i | \(0.932948\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0270 | + | 25.7799i | 0.668695 | + | 1.14719i | ||||
\(506\) | − | 0.877870i | − | 0.0390261i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 14.2456i | − | 0.632046i | ||||||
\(509\) | 7.20399 | 0.319311 | 0.159656 | − | 0.987173i | \(-0.448962\pi\) | ||||
0.159656 | + | 0.987173i | \(0.448962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.4198i | 0.724248i | ||||||||
\(515\) | 7.41978 | + | 12.7291i | 0.326954 | + | 0.560913i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.66389 | 0.205118 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.0643492 | + | 0.110395i | 0.00282190 | + | 0.00484116i | ||||
\(521\) | −5.21234 | −0.228357 | −0.114178 | − | 0.993460i | \(-0.536424\pi\) | ||||
−0.114178 | + | 0.993460i | \(0.536424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.7249 | −1.29978 | −0.649890 | − | 0.760028i | \(-0.725185\pi\) | ||||
−0.649890 | + | 0.760028i | \(0.725185\pi\) | |||||||
\(524\) | −8.52449 | −0.372394 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.0087 | −0.828817 | ||||||||
\(527\) | 1.75681 | 0.0765278 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.8744 | −0.907582 | ||||||||
\(530\) | 6.25300 | + | 10.7275i | 0.271613 | + | 0.465971i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.150868 | −0.00653484 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.12705 | + | 7.08025i | 0.178428 | + | 0.306106i | ||||
\(536\) | 0.110634i | 0.00477864i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.59449 | −0.0687432 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.2785 | 1.21579 | 0.607895 | − | 0.794018i | \(-0.292014\pi\) | ||||
0.607895 | + | 0.794018i | \(0.292014\pi\) | |||||||
\(542\) | 7.99015i | 0.343206i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.347217i | 0.0148868i | ||||||||
\(545\) | 14.2000 | + | 24.3611i | 0.608262 | + | 1.04352i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.7288i | − | 0.800786i | −0.916343 | − | 0.400393i | \(-0.868874\pi\) | ||
0.916343 | − | 0.400393i | \(-0.131126\pi\) | |||||||
\(548\) | 8.54900 | 0.365195 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.61969 | + | 1.48362i | 0.111704 | + | 0.0632619i | ||||
\(551\) | 31.9624 | 1.36164 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 19.8876i | 0.844945i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.50047i | 0.275681i | ||||||||
\(557\) | −34.0649 | −1.44338 | −0.721688 | − | 0.692219i | \(-0.756633\pi\) | ||||
−0.721688 | + | 0.692219i | \(0.756633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.686145i | − | 0.0290208i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 8.28665i | − | 0.349551i | ||||||
\(563\) | 24.6170i | 1.03748i | 0.854931 | + | 0.518741i | \(0.173599\pi\) | ||||
−0.854931 | + | 0.518741i | \(0.826401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.24106 | + | 5.56027i | 0.136353 | + | 0.233922i | ||||
\(566\) | 0.939284 | 0.0394811 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.7816i | 0.536303i | ||||||||
\(569\) | − | 35.1245i | − | 1.47249i | −0.676713 | − | 0.736247i | \(-0.736596\pi\) | ||
0.676713 | − | 0.736247i | \(-0.263404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.0787 | 1.13321 | 0.566605 | − | 0.823990i | \(-0.308257\pi\) | ||||
0.566605 | + | 0.823990i | \(0.308257\pi\) | |||||||
\(572\) | 0.0344087i | 0.00143870i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.59235 | + | 6.34315i | −0.149812 | + | 0.264527i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0688 | −0.793845 | −0.396923 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396923 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(578\) | −16.8794 | −0.702092 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −12.5439 | + | 7.31181i | −0.520858 | + | 0.303607i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.34360i | 0.138478i | ||||||||
\(584\) | −0.914240 | −0.0378315 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 13.4622i | − | 0.556118i | ||||||
\(587\) | − | 9.47721i | − | 0.391166i | −0.980687 | − | 0.195583i | \(-0.937340\pi\) | ||
0.980687 | − | 0.195583i | \(-0.0626599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.9058 | −1.02623 | ||||||||
\(590\) | 1.00283 | + | 1.72043i | 0.0412861 | + | 0.0708291i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 1.16480i | − | 0.0478732i | ||||||
\(593\) | 23.4238i | 0.961902i | 0.876748 | + | 0.480951i | \(0.159708\pi\) | ||||
−0.876748 | + | 0.480951i | \(0.840292\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.98512i | 0.409006i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.0833152 | −0.00340701 | ||||||||
\(599\) | 0.818609i | 0.0334474i | 0.999860 | + | 0.0167237i | \(0.00532357\pi\) | ||||
−0.999860 | + | 0.0167237i | \(0.994676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7.66116i | − | 0.312505i | −0.987717 | − | 0.156253i | \(-0.950059\pi\) | ||
0.987717 | − | 0.156253i | \(-0.0499414\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.36685 | −0.381132 | ||||||||
\(605\) | −11.9784 | − | 20.5498i | −0.486991 | − | 0.835468i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.6746 | 0.920334 | 0.460167 | − | 0.887832i | \(-0.347789\pi\) | ||||
0.460167 | + | 0.887832i | \(0.347789\pi\) | |||||||
\(608\) | − | 4.92239i | − | 0.199629i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.0590 | + | 6.44624i | −0.447765 | + | 0.261001i | ||||
\(611\) | − | 0.442631i | − | 0.0179070i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.2088i | 0.775837i | 0.921694 | + | 0.387919i | \(0.126806\pi\) | ||||
−0.921694 | + | 0.387919i | \(0.873194\pi\) | |||||||
\(614\) | 8.59205 | 0.346747 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.1200 | −0.769744 | −0.384872 | − | 0.922970i | \(-0.625754\pi\) | ||||
−0.384872 | + | 0.922970i | \(0.625754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 27.2018i | − | 1.09333i | −0.837351 | − | 0.546666i | \(-0.815897\pi\) | ||
0.837351 | − | 0.546666i | \(-0.184103\pi\) | |||||||
\(620\) | 9.77449 | − | 5.69752i | 0.392553 | − | 0.228818i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.5290 | 0.863232 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.8577 | − | 21.4402i | −0.514306 | − | 0.857607i | ||||
\(626\) | −2.77206 | −0.110794 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.4850 | −0.937152 | ||||||||
\(629\) | −0.404440 | −0.0161261 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.7018 | 1.30184 | 0.650918 | − | 0.759148i | \(-0.274384\pi\) | ||||
0.650918 | + | 0.759148i | \(0.274384\pi\) | |||||||
\(632\) | −1.38275 | −0.0550030 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.6421 | 1.09781 | ||||||||
\(635\) | −27.5201 | + | 16.0414i | −1.09210 | + | 0.636583i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.90977 | −0.154789 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.12606 | + | 1.93184i | 0.0445115 | + | 0.0763625i | ||||
\(641\) | 42.5112i | 1.67909i | 0.543290 | + | 0.839545i | \(0.317178\pi\) | ||||
−0.543290 | + | 0.839545i | \(0.682822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.8265 | −1.17624 | −0.588121 | − | 0.808773i | \(-0.700132\pi\) | ||||
−0.588121 | + | 0.808773i | \(0.700132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.70914 | −0.0672451 | ||||||||
\(647\) | 23.0895i | 0.907741i | 0.891068 | + | 0.453871i | \(0.149957\pi\) | ||||
−0.891068 | + | 0.453871i | \(0.850043\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.536235i | 0.0210491i | ||||||||
\(650\) | 0.140805 | − | 0.248624i | 0.00552282 | − | 0.00975184i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.209681i | 0.00821173i | ||||||||
\(653\) | 21.1582 | 0.827986 | 0.413993 | − | 0.910280i | \(-0.364134\pi\) | ||||
0.413993 | + | 0.910280i | \(0.364134\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.59910 | + | 16.4679i | 0.375068 | + | 0.643455i | ||||
\(656\) | −2.64008 | −0.103078 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 0.985920i | − | 0.0384060i | −0.999816 | − | 0.0192030i | \(-0.993887\pi\) | ||
0.999816 | − | 0.0192030i | \(-0.00611288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.37369i | 0.286803i | 0.989665 | + | 0.143402i | \(0.0458041\pi\) | ||||
−0.989665 | + | 0.143402i | \(0.954196\pi\) | |||||||
\(662\) | −33.8909 | −1.31721 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 0.429722i | − | 0.0166765i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 9.46687i | − | 0.366559i | ||||||
\(668\) | − | 11.7957i | − | 0.456390i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.213726 | − | 0.124580i | 0.00825695 | − | 0.00481295i | ||||
\(671\) | −3.44693 | −0.133067 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.3692i | 1.09355i | 0.837279 | + | 0.546776i | \(0.184145\pi\) | ||||
−0.837279 | + | 0.546776i | \(0.815855\pi\) | |||||||
\(674\) | 3.42365i | 0.131874i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9967 | −0.499874 | ||||||||
\(677\) | − | 38.2412i | − | 1.46973i | −0.678213 | − | 0.734865i | \(-0.737245\pi\) | ||
0.678213 | − | 0.734865i | \(-0.262755\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.670765 | − | 0.390987i | 0.0257227 | − | 0.0149937i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.04657 | 0.116659 | ||||||||
\(683\) | −28.0427 | −1.07302 | −0.536512 | − | 0.843893i | \(-0.680258\pi\) | ||||
−0.536512 | + | 0.843893i | \(0.680258\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.62670 | − | 16.5153i | −0.367817 | − | 0.631016i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 12.0070i | − | 0.457763i | ||||||
\(689\) | 0.317328 | 0.0120892 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 34.3370i | − | 1.30624i | −0.757254 | − | 0.653120i | \(-0.773460\pi\) | ||
0.757254 | − | 0.653120i | \(-0.226540\pi\) | |||||||
\(692\) | − | 19.8493i | − | 0.754556i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.9747 | 0.985984 | ||||||||
\(695\) | 12.5578 | − | 7.31992i | 0.476346 | − | 0.277660i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.916680i | 0.0347217i | ||||||||
\(698\) | 16.0984i | 0.609332i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 49.6503i | 1.87527i | 0.347628 | + | 0.937633i | \(0.386987\pi\) | ||||
−0.347628 | + | 0.937633i | \(0.613013\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.73363 | 0.216248 | ||||||||
\(704\) | 0.602126i | 0.0226935i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.3823i | 0.804734i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.141183 | −0.00530223 | −0.00265111 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265111 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(710\) | 24.6919 | − | 14.3928i | 0.926670 | − | 0.540153i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.9541 | 0.597904 | ||||||||
\(713\) | 7.37678i | 0.276263i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0664720 | − | 0.0387463i | 0.00248591 | − | 0.00144903i | ||||
\(716\) | − | 6.96012i | − | 0.260112i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 19.0185i | 0.709763i | ||||||||
\(719\) | 18.8949 | 0.704660 | 0.352330 | − | 0.935876i | \(-0.385389\pi\) | ||||
0.352330 | + | 0.935876i | \(0.385389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.22995 | 0.194638 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.3113i | 0.494711i | ||||||||
\(725\) | 28.2504 | + | 15.9993i | 1.04920 | + | 0.594197i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.1018 | 1.56147 | 0.780735 | − | 0.624862i | \(-0.214845\pi\) | ||||
0.780735 | + | 0.624862i | \(0.214845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.02949 | + | 1.76616i | 0.0381031 | + | 0.0653685i | ||||
\(731\) | −4.16903 | −0.154197 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.2332 | −0.377974 | −0.188987 | − | 0.981980i | \(-0.560520\pi\) | ||||
−0.188987 | + | 0.981980i | \(0.560520\pi\) | |||||||
\(734\) | 36.1510 | 1.33436 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.45795 | −0.0537408 | ||||||||
\(737\) | 0.0666154 | 0.00245381 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.0324 | 0.773688 | 0.386844 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386844 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(740\) | −2.25021 | + | 1.31164i | −0.0827194 | + | 0.0482169i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.0317 | −0.514774 | −0.257387 | − | 0.966308i | \(-0.582861\pi\) | ||||
−0.257387 | + | 0.966308i | \(0.582861\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.2896 | − | 11.2438i | 0.706716 | − | 0.411943i | ||||
\(746\) | 21.5031i | 0.787283i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.209068 | 0.00764429 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.7407 | −1.41367 | −0.706835 | − | 0.707379i | \(-0.749878\pi\) | ||||
−0.706835 | + | 0.707379i | \(0.749878\pi\) | |||||||
\(752\) | − | 7.74571i | − | 0.282457i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.371060i | 0.0135132i | ||||||||
\(755\) | 10.5476 | + | 18.0952i | 0.383868 | + | 0.658552i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1568i | 0.659919i | 0.943995 | + | 0.329960i | \(0.107035\pi\) | ||||
−0.943995 | + | 0.329960i | \(0.892965\pi\) | |||||||
\(758\) | −5.31543 | −0.193065 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.50925 | + | 5.54291i | −0.344937 | + | 0.201063i | ||||
\(761\) | 25.0314 | 0.907386 | 0.453693 | − | 0.891158i | \(-0.350106\pi\) | ||||
0.453693 | + | 0.891158i | \(0.350106\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 25.0941i | 0.907874i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 26.3353i | − | 0.951532i | ||||||
\(767\) | 0.0508919 | 0.00183760 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.6902i | 1.03460i | 0.855805 | + | 0.517298i | \(0.173062\pi\) | ||||
−0.855805 | + | 0.517298i | \(0.826938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 16.5745i | 0.596529i | ||||||||
\(773\) | 19.3034i | 0.694294i | 0.937811 | + | 0.347147i | \(0.112850\pi\) | ||||
−0.937811 | + | 0.347147i | \(0.887150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −22.0133 | − | 12.4670i | −0.790743 | − | 0.447826i | ||||
\(776\) | −13.1539 | −0.472197 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.43842i | 0.123273i | ||||||||
\(779\) | − | 12.9955i | − | 0.465612i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.69611 | 0.275389 | ||||||||
\(782\) | 0.506225i | 0.0181026i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.4455 | + | 45.3691i | 0.943880 | + | 1.61929i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −41.4238 | −1.47660 | −0.738300 | − | 0.674473i | \(-0.764371\pi\) | ||||
−0.738300 | + | 0.674473i | \(0.764371\pi\) | |||||||
\(788\) | 0.440156 | 0.0156799 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.55707 | + | 2.67125i | 0.0553979 | + | 0.0950390i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.327134i | 0.0116169i | ||||||||
\(794\) | −27.9177 | −0.990764 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 20.7109i | − | 0.734077i | ||||||
\(797\) | − | 24.9918i | − | 0.885253i | −0.896706 | − | 0.442627i | \(-0.854047\pi\) | ||
0.896706 | − | 0.442627i | \(-0.145953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.68944 | −0.0951455 | ||||||||
\(800\) | 2.46398 | − | 4.35073i | 0.0871147 | − | 0.153821i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 24.2952i | − | 0.857895i | ||||||
\(803\) | 0.550487i | 0.0194263i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 0.289138i | − | 0.0101845i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13.3448 | 0.469468 | ||||||||
\(809\) | − | 6.63517i | − | 0.233280i | −0.993174 | − | 0.116640i | \(-0.962788\pi\) | ||
0.993174 | − | 0.116640i | \(-0.0372124\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.77141i | − | 0.0973173i | −0.998815 | − | 0.0486587i | \(-0.984505\pi\) | ||
0.998815 | − | 0.0486587i | \(-0.0154946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.701359 | −0.0245826 | ||||||||
\(815\) | 0.405069 | − | 0.236113i | 0.0141889 | − | 0.00827069i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.1032 | 2.06776 | ||||||||
\(818\) | − | 14.1853i | − | 0.495979i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.97289 | + | 5.10020i | 0.103818 | + | 0.178107i | ||||
\(821\) | − | 20.9012i | − | 0.729457i | −0.931114 | − | 0.364728i | \(-0.881162\pi\) | ||
0.931114 | − | 0.364728i | \(-0.118838\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.9867i | 1.21956i | 0.792571 | + | 0.609780i | \(0.208742\pi\) | ||||
−0.792571 | + | 0.609780i | \(0.791258\pi\) | |||||||
\(824\) | 6.58914 | 0.229544 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.8919 | −1.10899 | −0.554495 | − | 0.832187i | \(-0.687089\pi\) | ||||
−0.554495 | + | 0.832187i | \(0.687089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 50.1802i | − | 1.74283i | −0.490547 | − | 0.871415i | \(-0.663203\pi\) | ||
0.490547 | − | 0.871415i | \(-0.336797\pi\) | |||||||
\(830\) | −0.830152 | + | 0.483893i | −0.0288150 | + | 0.0167962i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.0571454 | 0.00198116 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22.7874 | + | 13.2827i | −0.788589 | + | 0.459666i | ||||
\(836\) | −2.96390 | −0.102509 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.9730 | 0.620865 | ||||||||
\(839\) | 21.7782 | 0.751866 | 0.375933 | − | 0.926647i | \(-0.377322\pi\) | ||||
0.375933 | + | 0.926647i | \(0.377322\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.1625 | −0.453881 | ||||||||
\(842\) | −12.9077 | −0.444829 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.4319 | −0.359082 | ||||||||
\(845\) | 14.6351 | + | 25.1076i | 0.503463 | + | 0.863726i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.55299 | 0.190690 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.51064 | − | 0.855533i | −0.0518147 | − | 0.0293445i | ||||
\(851\) | − | 1.69823i | − | 0.0582145i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 41.3403 | 1.41547 | 0.707733 | − | 0.706480i | \(-0.249718\pi\) | ||||
0.707733 | + | 0.706480i | \(0.249718\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.66504 | 0.125268 | ||||||||
\(857\) | 40.9455i | 1.39867i | 0.714793 | + | 0.699336i | \(0.246521\pi\) | ||||
−0.714793 | + | 0.699336i | \(0.753479\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 39.8993i | − | 1.36135i | −0.732587 | − | 0.680673i | \(-0.761687\pi\) | ||
0.732587 | − | 0.680673i | \(-0.238313\pi\) | |||||||
\(860\) | −23.1956 | + | 13.5206i | −0.790962 | + | 0.461049i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.13005i | 0.242850i | ||||||||
\(863\) | 31.9325 | 1.08700 | 0.543498 | − | 0.839410i | \(-0.317100\pi\) | ||||
0.543498 | + | 0.839410i | \(0.317100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.3455 | + | 22.3515i | −1.30379 | + | 0.759973i | ||||
\(866\) | 28.1054 | 0.955060 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.832592i | 0.0282438i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.00632220i | − | 0.000214220i | ||||||
\(872\) | 12.6104 | 0.427040 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 7.17661i | − | 0.242752i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 44.3366i | − | 1.49714i | −0.663055 | − | 0.748571i | \(-0.730741\pi\) | ||
0.663055 | − | 0.748571i | \(-0.269259\pi\) | |||||||
\(878\) | 21.2538i | 0.717282i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.16321 | − | 0.678030i | 0.0392117 | − | 0.0228564i | ||||
\(881\) | 18.8931 | 0.636526 | 0.318263 | − | 0.948003i | \(-0.396901\pi\) | ||||
0.318263 | + | 0.948003i | \(0.396901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.2866i | 1.12018i | 0.828430 | + | 0.560092i | \(0.189234\pi\) | ||||
−0.828430 | + | 0.560092i | \(0.810766\pi\) | |||||||
\(884\) | − | 0.0198418i | − | 0.000667353i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.94032 | 0.300356 | ||||||||
\(887\) | 32.5007i | 1.09127i | 0.838024 | + | 0.545633i | \(0.183711\pi\) | ||||
−0.838024 | + | 0.545633i | \(0.816289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −17.9652 | − | 30.8206i | −0.602196 | − | 1.03311i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.3950 | −0.381533 | ||||||||
\(893\) | 38.1274 | 1.27589 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.4458 | + | 7.83752i | −0.449444 | + | 0.261979i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.6014i | 0.687478i | ||||||||
\(899\) | 32.8540 | 1.09574 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.92809i | − | 0.0642340i | ||||||
\(902\) | 1.58966i | 0.0529299i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.87823 | 0.0957286 | ||||||||
\(905\) | 25.7153 | − | 14.9893i | 0.854804 | − | 0.498263i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 57.4699i | − | 1.90826i | −0.299396 | − | 0.954129i | \(-0.596785\pi\) | ||
0.299396 | − | 0.954129i | \(-0.403215\pi\) | |||||||
\(908\) | 27.4366i | 0.910516i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.7785i | 0.522766i | 0.965235 | + | 0.261383i | \(0.0841785\pi\) | ||||
−0.965235 | + | 0.261383i | \(0.915822\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.258747 | −0.00856327 | ||||||||
\(914\) | 26.8747i | 0.888937i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.2770i | 0.471726i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.9710 | −0.427873 | −0.213937 | − | 0.976848i | \(-0.568629\pi\) | ||||
−0.213937 | + | 0.976848i | \(0.568629\pi\) | |||||||
\(920\) | 1.64174 | + | 2.81652i | 0.0541266 | + | 0.0928579i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.0610 | 0.825339 | ||||||||
\(923\) | − | 0.730408i | − | 0.0240417i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.06775 | + | 2.87005i | 0.166627 | + | 0.0943667i | ||||
\(926\) | 25.7470i | 0.846098i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.49327i | 0.213152i | ||||||||
\(929\) | 51.1394 | 1.67783 | 0.838914 | − | 0.544264i | \(-0.183191\pi\) | ||||
0.838914 | + | 0.544264i | \(0.183191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −25.2801 | −0.828078 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 0.198229i | − | 0.00648624i | ||||||
\(935\) | −0.235423 | − | 0.403885i | −0.00769917 | − | 0.0132085i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0919 | 1.21174 | 0.605870 | − | 0.795564i | \(-0.292825\pi\) | ||||
0.605870 | + | 0.795564i | \(0.292825\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.9634 | + | 8.72214i | −0.488053 | + | 0.284485i | ||||
\(941\) | 15.2864 | 0.498322 | 0.249161 | − | 0.968462i | \(-0.419845\pi\) | ||||
0.249161 | + | 0.968462i | \(0.419845\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.84911 | −0.125344 | ||||||||
\(944\) | 0.890569 | 0.0289856 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.22973 | −0.235059 | ||||||||
\(947\) | 24.2177 | 0.786970 | 0.393485 | − | 0.919331i | \(-0.371269\pi\) | ||||
0.393485 | + | 0.919331i | \(0.371269\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0522446 | 0.00169593 | ||||||||
\(950\) | 21.4160 | + | 12.1287i | 0.694826 | + | 0.393505i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.3359 | 0.626352 | 0.313176 | − | 0.949695i | \(-0.398607\pi\) | ||||
0.313176 | + | 0.949695i | \(0.398607\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.4777 | − | 28.2575i | 1.56870 | − | 0.914392i | ||||
\(956\) | − | 19.6427i | − | 0.635289i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.78904 | −0.283961 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.39950 | 0.174178 | ||||||||
\(962\) | 0.0665632i | 0.00214608i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 0.467621i | − | 0.0150611i | ||||||
\(965\) | 32.0192 | − | 18.6639i | 1.03073 | − | 0.600811i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 46.7895i | − | 1.50465i | −0.658792 | − | 0.752325i | \(-0.728932\pi\) | ||
0.658792 | − | 0.752325i | \(-0.271068\pi\) | |||||||
\(968\) | −10.6374 | −0.341900 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.8121 | + | 25.4112i | 0.475587 | + | 0.815903i | ||||
\(971\) | 5.69948 | 0.182905 | 0.0914525 | − | 0.995809i | \(-0.470849\pi\) | ||||
0.0914525 | + | 0.995809i | \(0.470849\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 42.7286i | 1.36911i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.72460i | 0.183240i | ||||||||
\(977\) | −35.5489 | −1.13731 | −0.568656 | − | 0.822576i | \(-0.692536\pi\) | ||||
−0.568656 | + | 0.822576i | \(0.692536\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.60635i | − | 0.307020i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.45933i | 0.110392i | ||||||||
\(983\) | − | 34.6900i | − | 1.10644i | −0.833035 | − | 0.553220i | \(-0.813399\pi\) | ||
0.833035 | − | 0.553220i | \(-0.186601\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.495642 | − | 0.850309i | −0.0157925 | − | 0.0270931i | ||||
\(986\) | 2.25457 | 0.0718002 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.281292i | 0.00894909i | ||||||||
\(989\) | − | 17.5056i | − | 0.556646i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.8763 | −1.01258 | −0.506292 | − | 0.862362i | \(-0.668984\pi\) | ||||
−0.506292 | + | 0.862362i | \(0.668984\pi\) | |||||||
\(992\) | − | 5.05969i | − | 0.160645i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.0100 | + | 23.3217i | −1.26840 | + | 0.739347i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.2004 | 0.354720 | 0.177360 | − | 0.984146i | \(-0.443244\pi\) | ||||
0.177360 | + | 0.984146i | \(0.443244\pi\) | |||||||
\(998\) | 25.9942 | 0.822831 | ||||||||
\(999\) | 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 | 4410.2.d.c.4409.7 | ✓ | 24 | |
3.2 | odd | 2 | 4410.2.d.d.4409.18 | yes | 24 | ||
5.4 | even | 2 | 4410.2.d.d.4409.8 | yes | 24 | ||
7.6 | odd | 2 | inner | 4410.2.d.c.4409.18 | yes | 24 | |
15.14 | odd | 2 | inner | 4410.2.d.c.4409.17 | yes | 24 | |
21.20 | even | 2 | 4410.2.d.d.4409.7 | yes | 24 | ||
35.34 | odd | 2 | 4410.2.d.d.4409.17 | yes | 24 | ||
105.104 | even | 2 | inner | 4410.2.d.c.4409.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4410.2.d.c.4409.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
4410.2.d.c.4409.8 | yes | 24 | 105.104 | even | 2 | inner | |
4410.2.d.c.4409.17 | yes | 24 | 15.14 | odd | 2 | inner | |
4410.2.d.c.4409.18 | yes | 24 | 7.6 | odd | 2 | inner | |
4410.2.d.d.4409.7 | yes | 24 | 21.20 | even | 2 | ||
4410.2.d.d.4409.8 | yes | 24 | 5.4 | even | 2 | ||
4410.2.d.d.4409.17 | yes | 24 | 35.34 | odd | 2 | ||
4410.2.d.d.4409.18 | yes | 24 | 3.2 | odd | 2 |