Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.f (of order \(2\), degree \(1\), not 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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + 25x^{8} - 16x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-0.404496 - 1.35513i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.g.199.3 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.75963 | − | 0.950636i | −0.879814 | − | 0.475318i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.19258 | + | 3.34553i | 0.548146 | + | 0.836383i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.98982 | −0.569975 | −0.284987 | − | 0.958531i | \(-0.591989\pi\) | ||||
−0.284987 | + | 0.958531i | \(0.591989\pi\) | |||||||
\(8\) | −0.677747 | − | 7.97124i | −0.0847184 | − | 0.996405i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 8.39401i | − | 0.763091i | −0.924350 | − | 0.381546i | \(-0.875392\pi\) | ||
0.924350 | − | 0.381546i | \(-0.124608\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 9.77033i | − | 0.751564i | −0.926708 | − | 0.375782i | \(-0.877374\pi\) | ||
0.926708 | − | 0.375782i | \(-0.122626\pi\) | |||||||
\(14\) | 7.02060 | + | 3.79287i | 0.501472 | + | 0.270919i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.38516 | + | 14.6707i | −0.399073 | + | 0.916919i | ||||
\(17\) | − | 12.1399i | − | 0.714114i | −0.934083 | − | 0.357057i | \(-0.883780\pi\) | ||
0.934083 | − | 0.357057i | \(-0.116220\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 17.3719i | 0.914313i | 0.889386 | + | 0.457157i | \(0.151132\pi\) | ||||
−0.889386 | + | 0.457157i | \(0.848868\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.97964 | + | 14.7703i | −0.362711 | + | 0.671379i | ||||
\(23\) | −2.97203 | −0.129219 | −0.0646094 | − | 0.997911i | \(-0.520580\pi\) | ||||
−0.0646094 | + | 0.997911i | \(0.520580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.28803 | + | 17.1921i | −0.357232 | + | 0.661236i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.74801 | − | 13.3481i | −0.312429 | − | 0.476717i | ||||
\(29\) | 51.6300 | 1.78034 | 0.890172 | − | 0.455624i | \(-0.150584\pi\) | ||||
0.890172 | + | 0.455624i | \(0.150584\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 30.7541i | 0.992067i | 0.868303 | + | 0.496033i | \(0.165211\pi\) | ||||
−0.868303 | + | 0.496033i | \(0.834789\pi\) | |||||||
\(32\) | 25.1820 | − | 19.7450i | 0.786938 | − | 0.617032i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −11.5407 | + | 21.3618i | −0.339431 | + | 0.628287i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.5407i | 0.528126i | 0.964505 | + | 0.264063i | \(0.0850627\pi\) | ||||
−0.964505 | + | 0.264063i | \(0.914937\pi\) | |||||||
\(38\) | 16.5144 | − | 30.5682i | 0.434589 | − | 0.804426i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.5603 | −1.03806 | −0.519028 | − | 0.854757i | \(-0.673706\pi\) | ||||
−0.519028 | + | 0.854757i | \(0.673706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −62.9208 | −1.46327 | −0.731637 | − | 0.681694i | \(-0.761244\pi\) | ||||
−0.731637 | + | 0.681694i | \(0.761244\pi\) | |||||||
\(44\) | 28.0824 | − | 18.4046i | 0.638237 | − | 0.418285i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.22967 | + | 2.82532i | 0.113688 | + | 0.0614200i | ||||
\(47\) | −39.5201 | −0.840853 | −0.420426 | − | 0.907327i | \(-0.638120\pi\) | ||||
−0.420426 | + | 0.907327i | \(0.638120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −33.0813 | −0.675129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 32.6869 | − | 21.4223i | 0.628595 | − | 0.411966i | ||||
\(53\) | − | 21.2096i | − | 0.400182i | −0.979777 | − | 0.200091i | \(-0.935876\pi\) | ||
0.979777 | − | 0.200091i | \(-0.0641237\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.70409 | + | 31.8038i | 0.0482873 | + | 0.567926i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −90.8496 | − | 49.0813i | −1.56637 | − | 0.846230i | ||||
\(59\) | 50.3640i | 0.853628i | 0.904339 | + | 0.426814i | \(0.140364\pi\) | ||||
−0.904339 | + | 0.426814i | \(0.859636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −70.3923 | −1.15397 | −0.576986 | − | 0.816754i | \(-0.695771\pi\) | ||||
−0.576986 | + | 0.816754i | \(0.695771\pi\) | |||||||
\(62\) | 29.2359 | − | 54.1157i | 0.471547 | − | 0.872834i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −63.0813 | + | 10.8050i | −0.985646 | + | 0.168828i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 94.8394 | 1.41551 | 0.707757 | − | 0.706456i | \(-0.249707\pi\) | ||||
0.707757 | + | 0.706456i | \(0.249707\pi\) | |||||||
\(68\) | 40.6145 | − | 26.6178i | 0.597273 | − | 0.391438i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 132.376i | − | 1.86445i | −0.361874 | − | 0.932227i | \(-0.617863\pi\) | ||
0.361874 | − | 0.932227i | \(-0.382137\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 77.7033i | − | 1.06443i | −0.846610 | − | 0.532214i | \(-0.821360\pi\) | ||
0.846610 | − | 0.532214i | \(-0.178640\pi\) | |||||||
\(74\) | 18.5761 | − | 34.3843i | 0.251028 | − | 0.464653i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −58.1184 | + | 38.0894i | −0.764716 | + | 0.501177i | ||||
\(77\) | 33.4906i | 0.434943i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 48.3742i | 0.612331i | 0.951978 | + | 0.306166i | \(0.0990462\pi\) | ||||
−0.951978 | + | 0.306166i | \(0.900954\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 74.8903 | + | 40.4593i | 0.913296 | + | 0.493407i | ||||
\(83\) | −140.248 | −1.68974 | −0.844868 | − | 0.534974i | \(-0.820321\pi\) | ||||
−0.844868 | + | 0.534974i | \(0.820321\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 110.717 | + | 59.8148i | 1.28741 | + | 0.695521i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −66.9106 | + | 5.68901i | −0.760348 | + | 0.0646479i | ||||
\(89\) | −18.1394 | −0.203813 | −0.101907 | − | 0.994794i | \(-0.532494\pi\) | ||||
−0.101907 | + | 0.994794i | \(0.532494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 38.9819i | 0.428372i | ||||||||
\(92\) | −6.51642 | − | 9.94303i | −0.0708307 | − | 0.108076i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 69.5407 | + | 37.5692i | 0.739794 | + | 0.399673i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 15.0000i | − | 0.154639i | −0.997006 | − | 0.0773196i | \(-0.975364\pi\) | ||
0.997006 | − | 0.0773196i | \(-0.0246362\pi\) | |||||||
\(98\) | 58.2108 | + | 31.4483i | 0.593988 | + | 0.320901i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −118.611 | −1.17437 | −0.587184 | − | 0.809453i | \(-0.699763\pi\) | ||||
−0.587184 | + | 0.809453i | \(0.699763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −165.740 | −1.60912 | −0.804562 | − | 0.593868i | \(-0.797600\pi\) | ||||
−0.804562 | + | 0.593868i | \(0.797600\pi\) | |||||||
\(104\) | −77.8816 | + | 6.62181i | −0.748862 | + | 0.0636712i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.1626 | + | 37.3211i | −0.190214 | + | 0.352085i | ||||
\(107\) | −104.222 | −0.974039 | −0.487020 | − | 0.873391i | \(-0.661916\pi\) | ||||
−0.487020 | + | 0.873391i | \(0.661916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −60.8516 | −0.558272 | −0.279136 | − | 0.960252i | \(-0.590048\pi\) | ||||
−0.279136 | + | 0.960252i | \(0.590048\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 25.4757 | − | 58.5335i | 0.227461 | − | 0.522621i | ||||
\(113\) | 139.821i | 1.23735i | 0.785646 | + | 0.618676i | \(0.212331\pi\) | ||||
−0.785646 | + | 0.618676i | \(0.787669\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 113.203 | + | 172.730i | 0.975888 | + | 1.48905i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 47.8779 | − | 88.6220i | 0.405745 | − | 0.751034i | ||||
\(119\) | 48.4362i | 0.407027i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 50.5407 | 0.417691 | ||||||||
\(122\) | 123.864 | + | 66.9175i | 1.01528 | + | 0.548504i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −102.889 | + | 67.4308i | −0.829748 | + | 0.543797i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −63.8372 | −0.502655 | −0.251327 | − | 0.967902i | \(-0.580867\pi\) | ||||
−0.251327 | + | 0.967902i | \(0.580867\pi\) | |||||||
\(128\) | 121.271 | + | 40.9547i | 0.947432 | + | 0.319958i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 205.994i | − | 1.57248i | −0.617923 | − | 0.786238i | \(-0.712026\pi\) | ||
0.617923 | − | 0.786238i | \(-0.287974\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 69.3110i | − | 0.521135i | ||||||
\(134\) | −166.882 | − | 90.1577i | −1.24539 | − | 0.672819i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −96.7703 | + | 8.22780i | −0.711547 | + | 0.0604985i | ||||
\(137\) | 243.081i | 1.77431i | 0.461470 | + | 0.887156i | \(0.347322\pi\) | ||||
−0.461470 | + | 0.887156i | \(0.652678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 122.520i | 0.881439i | 0.897645 | + | 0.440719i | \(0.145277\pi\) | ||||
−0.897645 | + | 0.440719i | \(0.854723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −125.842 | + | 232.933i | −0.886209 | + | 1.64037i | ||||
\(143\) | −82.0122 | −0.573512 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −73.8676 | + | 136.729i | −0.505942 | + | 0.936499i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −65.3739 | + | 42.8445i | −0.441716 | + | 0.289490i | ||||
\(149\) | −121.399 | −0.814761 | −0.407380 | − | 0.913259i | \(-0.633558\pi\) | ||||
−0.407380 | + | 0.913259i | \(0.633558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 113.376i | 0.750833i | 0.926856 | + | 0.375417i | \(0.122500\pi\) | ||||
−0.926856 | + | 0.375417i | \(0.877500\pi\) | |||||||
\(152\) | 138.476 | − | 11.7738i | 0.911026 | − | 0.0774591i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 31.8374 | − | 58.9310i | 0.206736 | − | 0.382669i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 117.933i | 0.751165i | 0.926789 | + | 0.375583i | \(0.122557\pi\) | ||||
−0.926789 | + | 0.375583i | \(0.877443\pi\) | |||||||
\(158\) | 45.9862 | − | 85.1206i | 0.291052 | − | 0.538738i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.8579 | 0.0736514 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 158.677 | 0.973476 | 0.486738 | − | 0.873548i | \(-0.338187\pi\) | ||||
0.486738 | + | 0.873548i | \(0.338187\pi\) | |||||||
\(164\) | −93.3169 | − | 142.387i | −0.569006 | − | 0.868212i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 246.785 | + | 133.325i | 1.48665 | + | 0.803162i | ||||
\(167\) | −260.736 | −1.56130 | −0.780648 | − | 0.624972i | \(-0.785111\pi\) | ||||
−0.780648 | + | 0.624972i | \(0.785111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 73.5407 | 0.435152 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −137.959 | − | 210.504i | −0.802088 | − | 1.22386i | ||||
\(173\) | 294.711i | 1.70353i | 0.523924 | + | 0.851765i | \(0.324468\pi\) | ||||
−0.523924 | + | 0.851765i | \(0.675532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 123.146 | + | 53.5971i | 0.699693 | + | 0.304529i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 31.9186 | + | 17.2440i | 0.179318 | + | 0.0968762i | ||||
\(179\) | 147.236i | 0.822550i | 0.911511 | + | 0.411275i | \(0.134916\pi\) | ||||
−0.911511 | + | 0.411275i | \(0.865084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −71.7703 | −0.396521 | −0.198261 | − | 0.980149i | \(-0.563529\pi\) | ||||
−0.198261 | + | 0.980149i | \(0.563529\pi\) | |||||||
\(182\) | 37.0576 | − | 68.5936i | 0.203613 | − | 0.376888i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.01428 | + | 23.6908i | 0.0109472 | + | 0.128754i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −101.903 | −0.544934 | ||||||||
\(188\) | −86.6510 | − | 132.216i | −0.460910 | − | 0.703275i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 333.832i | − | 1.74781i | −0.486094 | − | 0.873907i | \(-0.661579\pi\) | ||
0.486094 | − | 0.873907i | \(-0.338421\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 192.703i | 0.998463i | 0.866469 | + | 0.499231i | \(0.166384\pi\) | ||||
−0.866469 | + | 0.499231i | \(0.833616\pi\) | |||||||
\(194\) | −14.2595 | + | 26.3944i | −0.0735028 | + | 0.136054i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −72.5335 | − | 110.675i | −0.370069 | − | 0.564666i | ||||
\(197\) | 36.5608i | 0.185588i | 0.995685 | + | 0.0927940i | \(0.0295798\pi\) | ||||
−0.995685 | + | 0.0927940i | \(0.970420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 230.742i | − | 1.15951i | −0.814793 | − | 0.579753i | \(-0.803149\pi\) | ||
0.814793 | − | 0.579753i | \(-0.196851\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 208.712 | + | 112.756i | 1.03323 | + | 0.558198i | ||||
\(203\) | −205.994 | −1.01475 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 291.640 | + | 157.558i | 1.41573 | + | 0.764846i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 143.338 | + | 62.3852i | 0.689123 | + | 0.299929i | ||||
\(209\) | 145.820 | 0.697705 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 177.957i | − | 0.843400i | −0.906735 | − | 0.421700i | \(-0.861433\pi\) | ||
0.906735 | − | 0.421700i | \(-0.138567\pi\) | |||||||
\(212\) | 70.9575 | − | 46.5039i | 0.334705 | − | 0.219358i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 183.392 | + | 99.0774i | 0.856973 | + | 0.462978i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 122.703i | − | 0.565453i | ||||||
\(218\) | 107.076 | + | 57.8478i | 0.491176 | + | 0.265357i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −118.611 | −0.536702 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 175.877 | 0.788684 | 0.394342 | − | 0.918964i | \(-0.370972\pi\) | ||||
0.394342 | + | 0.918964i | \(0.370972\pi\) | |||||||
\(224\) | −100.472 | + | 78.7791i | −0.448535 | + | 0.351693i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 132.919 | − | 246.033i | 0.588136 | − | 1.08864i | ||||
\(227\) | −76.5902 | −0.337402 | −0.168701 | − | 0.985667i | \(-0.553957\pi\) | ||||
−0.168701 | + | 0.985667i | \(0.553957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 77.6363 | 0.339023 | 0.169511 | − | 0.985528i | \(-0.445781\pi\) | ||||
0.169511 | + | 0.985528i | \(0.445781\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −34.9921 | − | 411.555i | −0.150828 | − | 1.77394i | ||||
\(233\) | − | 133.539i | − | 0.573130i | −0.958061 | − | 0.286565i | \(-0.907487\pi\) | ||
0.958061 | − | 0.286565i | \(-0.0925134\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −168.494 | + | 110.427i | −0.713960 | + | 0.467912i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 46.0452 | − | 85.2297i | 0.193467 | − | 0.358108i | ||||
\(239\) | − | 14.8602i | − | 0.0621764i | −0.999517 | − | 0.0310882i | \(-0.990103\pi\) | ||
0.999517 | − | 0.0310882i | \(-0.00989727\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 125.622 | 0.521253 | 0.260627 | − | 0.965440i | \(-0.416071\pi\) | ||||
0.260627 | + | 0.965440i | \(0.416071\pi\) | |||||||
\(242\) | −88.9328 | − | 48.0458i | −0.367491 | − | 0.198536i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −154.341 | − | 235.500i | −0.632545 | − | 0.965163i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 169.730 | 0.687165 | ||||||||
\(248\) | 245.148 | − | 20.8435i | 0.988500 | − | 0.0840463i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 164.024i | − | 0.653484i | −0.945114 | − | 0.326742i | \(-0.894049\pi\) | ||
0.945114 | − | 0.326742i | \(-0.105951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.9473i | 0.0986057i | ||||||||
\(254\) | 112.330 | + | 60.6859i | 0.442243 | + | 0.238921i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −174.459 | − | 187.350i | −0.681482 | − | 0.731835i | ||||
\(257\) | − | 188.098i | − | 0.731901i | −0.930634 | − | 0.365950i | \(-0.880744\pi\) | ||
0.930634 | − | 0.365950i | \(-0.119256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 77.9638i | − | 0.301018i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −195.826 | + | 362.474i | −0.747426 | + | 1.38349i | ||||
\(263\) | −114.544 | −0.435529 | −0.217764 | − | 0.976001i | \(-0.569876\pi\) | ||||
−0.217764 | + | 0.976001i | \(0.569876\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −65.8895 | + | 121.962i | −0.247705 | + | 0.458502i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 207.943 | + | 317.288i | 0.775907 | + | 1.18391i | ||||
\(269\) | 221.871 | 0.824800 | 0.412400 | − | 0.911003i | \(-0.364691\pi\) | ||||
0.412400 | + | 0.911003i | \(0.364691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 390.163i | − | 1.43971i | −0.694122 | − | 0.719857i | \(-0.744207\pi\) | ||
0.694122 | − | 0.719857i | \(-0.255793\pi\) | |||||||
\(272\) | 178.101 | + | 77.5155i | 0.654785 | + | 0.284983i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 231.081 | − | 427.732i | 0.843362 | − | 1.56106i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 272.421i | − | 0.983469i | −0.870745 | − | 0.491734i | \(-0.836363\pi\) | ||
0.870745 | − | 0.491734i | \(-0.163637\pi\) | |||||||
\(278\) | 116.472 | − | 215.590i | 0.418964 | − | 0.775502i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −473.740 | −1.68591 | −0.842953 | − | 0.537987i | \(-0.819185\pi\) | ||||
−0.842953 | + | 0.537987i | \(0.819185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 164.824 | 0.582415 | 0.291208 | − | 0.956660i | \(-0.405943\pi\) | ||||
0.291208 | + | 0.956660i | \(0.405943\pi\) | |||||||
\(284\) | 442.869 | − | 290.246i | 1.55940 | − | 1.02199i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 144.311 | + | 77.9638i | 0.504584 | + | 0.272601i | ||||
\(287\) | 169.808 | 0.591665 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 141.622 | 0.490041 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 259.959 | − | 170.371i | 0.890270 | − | 0.583462i | ||||
\(293\) | − | 273.219i | − | 0.932488i | −0.884656 | − | 0.466244i | \(-0.845607\pi\) | ||
0.884656 | − | 0.466244i | \(-0.154393\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 155.763 | − | 13.2436i | 0.526227 | − | 0.0447420i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 213.618 | + | 115.407i | 0.716838 | + | 0.387270i | ||||
\(299\) | 29.0377i | 0.0971161i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 251.043 | 0.834029 | ||||||||
\(302\) | 107.779 | − | 199.499i | 0.356885 | − | 0.660594i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −254.859 | − | 110.923i | −0.838351 | − | 0.364877i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −132.905 | −0.432915 | −0.216458 | − | 0.976292i | \(-0.569450\pi\) | ||||
−0.216458 | + | 0.976292i | \(0.569450\pi\) | |||||||
\(308\) | −112.044 | + | 73.4309i | −0.363779 | + | 0.238412i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 235.032i | 0.755730i | 0.925861 | + | 0.377865i | \(0.123342\pi\) | ||||
−0.925861 | + | 0.377865i | \(0.876658\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 497.651i | 1.58994i | 0.606650 | + | 0.794969i | \(0.292513\pi\) | ||||
−0.606650 | + | 0.794969i | \(0.707487\pi\) | |||||||
\(314\) | 112.111 | − | 207.518i | 0.357042 | − | 0.660886i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −161.837 | + | 106.064i | −0.512144 | + | 0.335647i | ||||
\(317\) | 169.959i | 0.536149i | 0.963398 | + | 0.268074i | \(0.0863873\pi\) | ||||
−0.963398 | + | 0.268074i | \(0.913613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 433.382i | − | 1.35857i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.8655 | − | 11.2725i | −0.0647996 | − | 0.0350078i | ||||
\(323\) | 210.894 | 0.652924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −279.212 | − | 150.844i | −0.856478 | − | 0.462711i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28.8451 | + | 339.258i | 0.0879424 | + | 1.03432i | ||||
\(329\) | 157.678 | 0.479265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.3086i | − | 0.0311440i | −0.999879 | − | 0.0155720i | \(-0.995043\pi\) | ||
0.999879 | − | 0.0155720i | \(-0.00495691\pi\) | |||||||
\(332\) | −307.506 | − | 469.205i | −0.926222 | − | 1.41327i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 458.799 | + | 247.865i | 1.37365 | + | 0.742112i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 109.029i | 0.323527i | 0.986830 | + | 0.161763i | \(0.0517182\pi\) | ||||
−0.986830 | + | 0.161763i | \(0.948282\pi\) | |||||||
\(338\) | −129.404 | − | 69.9104i | −0.382853 | − | 0.206835i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 258.150 | 0.757038 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 327.490 | 0.954781 | ||||||||
\(344\) | 42.6444 | + | 501.557i | 0.123966 | + | 1.45801i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 280.163 | − | 518.581i | 0.809719 | − | 1.49879i | ||||
\(347\) | −173.824 | −0.500934 | −0.250467 | − | 0.968125i | \(-0.580584\pi\) | ||||
−0.250467 | + | 0.968125i | \(0.580584\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −259.244 | −0.742819 | −0.371410 | − | 0.928469i | \(-0.621125\pi\) | ||||
−0.371410 | + | 0.928469i | \(0.621125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −165.740 | − | 211.378i | −0.470852 | − | 0.600506i | ||||
\(353\) | − | 115.400i | − | 0.326912i | −0.986551 | − | 0.163456i | \(-0.947736\pi\) | ||
0.986551 | − | 0.163456i | \(-0.0522642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −39.7721 | − | 60.6859i | −0.111719 | − | 0.170466i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 139.968 | − | 259.081i | 0.390973 | − | 0.723691i | ||||
\(359\) | 333.832i | 0.929895i | 0.885338 | + | 0.464948i | \(0.153927\pi\) | ||||
−0.885338 | + | 0.464948i | \(0.846073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 59.2154 | 0.164032 | ||||||||
\(362\) | 126.289 | + | 68.2275i | 0.348865 | + | 0.188474i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −130.415 | + | 85.4710i | −0.358283 | + | 0.234810i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −525.148 | −1.43092 | −0.715461 | − | 0.698653i | \(-0.753783\pi\) | ||||
−0.715461 | + | 0.698653i | \(0.753783\pi\) | |||||||
\(368\) | 18.9769 | − | 43.6018i | 0.0515677 | − | 0.118483i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 84.6227i | 0.228093i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 417.014i | − | 1.11800i | −0.829167 | − | 0.559000i | \(-0.811185\pi\) | ||
0.829167 | − | 0.559000i | \(-0.188815\pi\) | |||||||
\(374\) | 179.311 | + | 96.8724i | 0.479441 | + | 0.259017i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.7846 | + | 315.024i | 0.0712357 | + | 0.837830i | ||||
\(377\) | − | 504.442i | − | 1.33804i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 126.758i | 0.334454i | 0.985918 | + | 0.167227i | \(0.0534812\pi\) | ||||
−0.985918 | + | 0.167227i | \(0.946519\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −317.353 | + | 587.421i | −0.830767 | + | 1.53775i | ||||
\(383\) | −129.404 | −0.337870 | −0.168935 | − | 0.985627i | \(-0.554033\pi\) | ||||
−0.168935 | + | 0.985627i | \(0.554033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 183.191 | − | 339.086i | 0.474587 | − | 0.878462i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 50.1830 | − | 32.8887i | 0.129338 | − | 0.0847648i | ||||
\(389\) | 87.9088 | 0.225987 | 0.112993 | − | 0.993596i | \(-0.463956\pi\) | ||||
0.112993 | + | 0.993596i | \(0.463956\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0803i | 0.0922769i | ||||||||
\(392\) | 22.4208 | + | 263.699i | 0.0571958 | + | 0.672702i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 34.7560 | − | 64.3335i | 0.0882133 | − | 0.163283i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 239.770i | 0.603955i | 0.953315 | + | 0.301978i | \(0.0976468\pi\) | ||||
−0.953315 | + | 0.301978i | \(0.902353\pi\) | |||||||
\(398\) | −219.351 | + | 406.019i | −0.551134 | + | 1.02015i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 383.043 | 0.955218 | 0.477609 | − | 0.878572i | \(-0.341503\pi\) | ||||
0.477609 | + | 0.878572i | \(0.341503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 300.477 | 0.745602 | ||||||||
\(404\) | −260.065 | − | 396.817i | −0.643725 | − | 0.982221i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 362.474 | + | 195.826i | 0.892792 | + | 0.482329i | ||||
\(407\) | 164.024 | 0.403008 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 731.976 | 1.78967 | 0.894836 | − | 0.446395i | \(-0.147292\pi\) | ||||
0.894836 | + | 0.446395i | \(0.147292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −363.398 | − | 554.488i | −0.882035 | − | 1.34584i | ||||
\(413\) | − | 200.944i | − | 0.486546i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −192.915 | − | 246.037i | −0.463739 | − | 0.591434i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −256.589 | − | 138.622i | −0.613850 | − | 0.331632i | ||||
\(419\) | − | 692.847i | − | 1.65357i | −0.562516 | − | 0.826786i | \(-0.690167\pi\) | ||
0.562516 | − | 0.826786i | \(-0.309833\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −326.622 | −0.775824 | −0.387912 | − | 0.921696i | \(-0.626804\pi\) | ||||
−0.387912 | + | 0.921696i | \(0.626804\pi\) | |||||||
\(422\) | −169.173 | + | 313.139i | −0.400883 | + | 0.742035i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −169.067 | + | 14.3748i | −0.398743 | + | 0.0339027i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 280.853 | 0.657735 | ||||||||
\(428\) | −228.516 | − | 348.679i | −0.533915 | − | 0.814670i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 367.408i | 0.852456i | 0.904616 | + | 0.426228i | \(0.140158\pi\) | ||||
−0.904616 | + | 0.426228i | \(0.859842\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 493.622i | 1.14000i | 0.821643 | + | 0.570002i | \(0.193058\pi\) | ||||
−0.821643 | + | 0.570002i | \(0.806942\pi\) | |||||||
\(434\) | −116.646 | + | 215.912i | −0.268770 | + | 0.497493i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −133.422 | − | 203.581i | −0.306014 | − | 0.466929i | ||||
\(437\) | − | 51.6300i | − | 0.118146i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 658.970i | 1.50107i | 0.660831 | + | 0.750535i | \(0.270204\pi\) | ||||
−0.660831 | + | 0.750535i | \(0.729796\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 208.712 | + | 112.756i | 0.472198 | + | 0.255104i | ||||
\(443\) | 623.245 | 1.40687 | 0.703437 | − | 0.710758i | \(-0.251648\pi\) | ||||
0.703437 | + | 0.710758i | \(0.251648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −309.477 | − | 167.195i | −0.693896 | − | 0.374876i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 251.683 | − | 43.1099i | 0.561793 | − | 0.0962274i | ||||
\(449\) | −364.198 | −0.811132 | −0.405566 | − | 0.914066i | \(-0.632925\pi\) | ||||
−0.405566 | + | 0.914066i | \(0.632925\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 357.251i | 0.792132i | ||||||||
\(452\) | −467.775 | + | 306.569i | −1.03490 | + | 0.678249i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 134.770 | + | 72.8094i | 0.296851 | + | 0.160373i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 215.866i | − | 0.472354i | −0.971710 | − | 0.236177i | \(-0.924105\pi\) | ||
0.971710 | − | 0.236177i | \(-0.0758946\pi\) | |||||||
\(458\) | −136.611 | − | 73.8038i | −0.298277 | − | 0.161144i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.9142 | 0.0605515 | 0.0302757 | − | 0.999542i | \(-0.490361\pi\) | ||||
0.0302757 | + | 0.999542i | \(0.490361\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −369.545 | −0.798154 | −0.399077 | − | 0.916917i | \(-0.630669\pi\) | ||||
−0.399077 | + | 0.916917i | \(0.630669\pi\) | |||||||
\(464\) | −329.666 | + | 757.448i | −0.710487 | + | 1.63243i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −126.947 | + | 234.979i | −0.272419 | + | 0.504248i | ||||
\(467\) | 741.443 | 1.58767 | 0.793837 | − | 0.608131i | \(-0.208080\pi\) | ||||
0.793837 | + | 0.608131i | \(0.208080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −378.392 | −0.806807 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 401.464 | − | 34.1341i | 0.850559 | − | 0.0723179i | ||||
\(473\) | 528.158i | 1.11661i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −162.045 | + | 106.200i | −0.340430 | + | 0.223110i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.1266 | + | 26.1484i | −0.0295536 | + | 0.0547037i | ||||
\(479\) | − | 419.700i | − | 0.876201i | −0.898926 | − | 0.438101i | \(-0.855651\pi\) | ||
0.898926 | − | 0.438101i | \(-0.144349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 190.919 | 0.396920 | ||||||||
\(482\) | −221.048 | − | 119.421i | −0.458606 | − | 0.247761i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 110.815 | + | 169.085i | 0.228956 | + | 0.349350i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 195.501 | 0.401440 | 0.200720 | − | 0.979649i | \(-0.435672\pi\) | ||||
0.200720 | + | 0.979649i | \(0.435672\pi\) | |||||||
\(488\) | 47.7082 | + | 561.114i | 0.0977626 | + | 1.14982i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 676.741i | 1.37829i | 0.724623 | + | 0.689146i | \(0.242014\pi\) | ||||
−0.724623 | + | 0.689146i | \(0.757986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 626.785i | − | 1.27137i | ||||||
\(494\) | −298.661 | − | 161.351i | −0.604577 | − | 0.326622i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −451.184 | − | 196.370i | −0.909645 | − | 0.395907i | ||||
\(497\) | 528.158i | 1.06269i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 628.139i | − | 1.25880i | −0.777083 | − | 0.629398i | \(-0.783302\pi\) | ||
0.777083 | − | 0.629398i | \(-0.216698\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −155.928 | + | 288.622i | −0.310613 | + | 0.574944i | ||||
\(503\) | 514.645 | 1.02315 | 0.511575 | − | 0.859238i | \(-0.329062\pi\) | ||||
0.511575 | + | 0.859238i | \(0.329062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 23.7158 | − | 43.8979i | 0.0468691 | − | 0.0867547i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −139.968 | − | 213.569i | −0.275528 | − | 0.420412i | ||||
\(509\) | −802.364 | −1.57635 | −0.788177 | − | 0.615449i | \(-0.788975\pi\) | ||||
−0.788177 | + | 0.615449i | \(0.788975\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 310.022i | 0.606697i | ||||||||
\(512\) | 128.882 | + | 495.513i | 0.251723 | + | 0.967799i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −178.813 | + | 330.983i | −0.347886 | + | 0.643937i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 331.732i | 0.641648i | ||||||||
\(518\) | −74.1152 | + | 137.187i | −0.143079 | + | 0.264840i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 917.482 | 1.76100 | 0.880501 | − | 0.474045i | \(-0.157207\pi\) | ||||
0.880501 | + | 0.474045i | \(0.157207\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −957.290 | −1.83038 | −0.915191 | − | 0.403020i | \(-0.867960\pi\) | ||||
−0.915191 | + | 0.403020i | \(0.867960\pi\) | |||||||
\(524\) | 689.161 | − | 451.660i | 1.31519 | − | 0.861946i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 201.555 | + | 108.890i | 0.383184 | + | 0.207015i | ||||
\(527\) | 373.352 | 0.708449 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −520.167 | −0.983303 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 231.882 | − | 151.970i | 0.435869 | − | 0.285658i | ||||
\(533\) | 415.828i | 0.780165i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −64.2771 | − | 755.987i | −0.119920 | − | 1.41042i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −390.411 | − | 210.919i | −0.725670 | − | 0.392042i | ||||
\(539\) | 277.685i | 0.515185i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −329.014 | −0.608159 | −0.304080 | − | 0.952647i | \(-0.598349\pi\) | ||||
−0.304080 | + | 0.952647i | \(0.598349\pi\) | |||||||
\(542\) | −370.903 | + | 686.541i | −0.684322 | + | 1.26668i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −239.703 | − | 305.708i | −0.440631 | − | 0.561963i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.7716 | 0.0471145 | 0.0235572 | − | 0.999722i | \(-0.492501\pi\) | ||||
0.0235572 | + | 0.999722i | \(0.492501\pi\) | |||||||
\(548\) | −813.234 | + | 532.975i | −1.48400 | + | 0.972581i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 896.913i | 1.62779i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 193.004i | − | 0.349013i | ||||||
\(554\) | −258.973 | + | 479.359i | −0.467460 | + | 0.865270i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −409.895 | + | 268.635i | −0.737220 | + | 0.483157i | ||||
\(557\) | − | 632.405i | − | 1.13538i | −0.823244 | − | 0.567688i | \(-0.807838\pi\) | ||
0.823244 | − | 0.567688i | \(-0.192162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 614.757i | 1.09974i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 833.605 | + | 450.354i | 1.48328 | + | 0.801341i | ||||
\(563\) | 156.675 | 0.278285 | 0.139143 | − | 0.990272i | \(-0.455565\pi\) | ||||
0.139143 | + | 0.990272i | \(0.455565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −290.028 | − | 156.687i | −0.512417 | − | 0.276832i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1055.20 | + | 89.7176i | −1.85775 | + | 0.157953i | ||||
\(569\) | −522.581 | −0.918421 | −0.459210 | − | 0.888328i | \(-0.651868\pi\) | ||||
−0.459210 | + | 0.888328i | \(0.651868\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 855.387i | − | 1.49805i | −0.662541 | − | 0.749026i | \(-0.730522\pi\) | ||
0.662541 | − | 0.749026i | \(-0.269478\pi\) | |||||||
\(572\) | −179.819 | − | 274.374i | −0.314368 | − | 0.479676i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −298.799 | − | 161.426i | −0.520556 | − | 0.281229i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 484.081i | − | 0.838962i | −0.907764 | − | 0.419481i | \(-0.862212\pi\) | ||
0.907764 | − | 0.419481i | \(-0.137788\pi\) | |||||||
\(578\) | −249.202 | − | 134.631i | −0.431145 | − | 0.232926i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 559.565 | 0.963107 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −178.034 | −0.305375 | ||||||||
\(584\) | −619.392 | + | 52.6632i | −1.06060 | + | 0.0901766i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −259.732 | + | 480.764i | −0.443228 | + | 0.820416i | ||||
\(587\) | −134.666 | −0.229413 | −0.114707 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114707 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −534.258 | −0.907060 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −286.675 | − | 124.770i | −0.484249 | − | 0.210761i | ||||
\(593\) | − | 960.465i | − | 1.61967i | −0.586657 | − | 0.809836i | \(-0.699556\pi\) | ||
0.586657 | − | 0.809836i | \(-0.300444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −266.178 | − | 406.145i | −0.446608 | − | 0.681452i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 27.6043 | − | 51.0956i | 0.0461611 | − | 0.0854442i | ||||
\(599\) | − | 492.073i | − | 0.821491i | −0.911750 | − | 0.410746i | \(-0.865268\pi\) | ||
0.911750 | − | 0.410746i | \(-0.134732\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 152.187 | 0.253223 | 0.126611 | − | 0.991952i | \(-0.459590\pi\) | ||||
0.126611 | + | 0.991952i | \(0.459590\pi\) | |||||||
\(602\) | −441.742 | − | 238.650i | −0.733791 | − | 0.396429i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −379.302 | + | 248.586i | −0.627984 | + | 0.411566i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1032.50 | 1.70100 | 0.850498 | − | 0.525978i | \(-0.176301\pi\) | ||||
0.850498 | + | 0.525978i | \(0.176301\pi\) | |||||||
\(608\) | 343.010 | + | 437.461i | 0.564160 | + | 0.719508i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 386.124i | 0.631955i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 774.029i | − | 1.26269i | −0.775502 | − | 0.631345i | \(-0.782503\pi\) | ||
0.775502 | − | 0.631345i | \(-0.217497\pi\) | |||||||
\(614\) | 233.863 | + | 126.344i | 0.380885 | + | 0.205772i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 266.962 | − | 22.6981i | 0.433379 | − | 0.0368476i | ||||
\(617\) | 594.857i | 0.964112i | 0.876141 | + | 0.482056i | \(0.160110\pi\) | ||||
−0.876141 | + | 0.482056i | \(0.839890\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 158.333i | 0.255788i | 0.991788 | + | 0.127894i | \(0.0408217\pi\) | ||||
−0.991788 | + | 0.127894i | \(0.959178\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 223.430 | − | 413.569i | 0.359212 | − | 0.664902i | ||||
\(623\) | 72.3729 | 0.116168 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 473.085 | − | 875.680i | 0.755726 | − | 1.39885i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −394.548 | + | 258.578i | −0.628262 | + | 0.411748i | ||||
\(629\) | 237.222 | 0.377142 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 832.689i | 1.31963i | 0.751426 | + | 0.659817i | \(0.229366\pi\) | ||||
−0.751426 | + | 0.659817i | \(0.770634\pi\) | |||||||
\(632\) | 385.602 | − | 32.7854i | 0.610130 | − | 0.0518757i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 161.569 | − | 299.065i | 0.254841 | − | 0.471711i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 323.215i | 0.507402i | ||||||||
\(638\) | −411.989 | + | 762.592i | −0.645751 | + | 1.19529i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.7158 | −0.0369981 | −0.0184990 | − | 0.999829i | \(-0.505889\pi\) | ||||
−0.0184990 | + | 0.999829i | \(0.505889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −637.188 | −0.990961 | −0.495480 | − | 0.868619i | \(-0.665008\pi\) | ||||
−0.495480 | + | 0.868619i | \(0.665008\pi\) | |||||||
\(644\) | 25.9994 | + | 39.6709i | 0.0403717 | + | 0.0616008i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −371.096 | − | 200.484i | −0.574451 | − | 0.310346i | ||||
\(647\) | 462.353 | 0.714610 | 0.357305 | − | 0.933988i | \(-0.383696\pi\) | ||||
0.357305 | + | 0.933988i | \(0.383696\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 422.756 | 0.651396 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 347.911 | + | 530.857i | 0.533606 | + | 0.814198i | ||||
\(653\) | − | 661.697i | − | 1.01332i | −0.862146 | − | 0.506659i | \(-0.830880\pi\) | ||
0.862146 | − | 0.506659i | \(-0.169120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 271.754 | − | 624.390i | 0.414260 | − | 0.951813i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −277.455 | − | 149.895i | −0.421664 | − | 0.227803i | ||||
\(659\) | − | 248.647i | − | 0.377310i | −0.982043 | − | 0.188655i | \(-0.939587\pi\) | ||
0.982043 | − | 0.188655i | \(-0.0604127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1022.35 | −1.54668 | −0.773339 | − | 0.633993i | \(-0.781415\pi\) | ||||
−0.773339 | + | 0.633993i | \(0.781415\pi\) | |||||||
\(662\) | −9.79977 | + | 18.1394i | −0.0148033 | + | 0.0274009i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 95.0527 | + | 1117.95i | 0.143152 | + | 1.68366i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −153.446 | −0.230054 | ||||||||
\(668\) | −571.686 | − | 872.301i | −0.855817 | − | 1.30584i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 590.873i | 0.880586i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 683.215i | 1.01518i | 0.861599 | + | 0.507589i | \(0.169463\pi\) | ||||
−0.861599 | + | 0.507589i | \(0.830537\pi\) | |||||||
\(674\) | 103.646 | − | 191.850i | 0.153778 | − | 0.284644i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 161.244 | + | 246.033i | 0.238527 | + | 0.363954i | ||||
\(677\) | − | 707.751i | − | 1.04542i | −0.852510 | − | 0.522711i | \(-0.824921\pi\) | ||
0.852510 | − | 0.522711i | \(-0.175079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 59.8473i | 0.0881404i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −454.248 | − | 245.407i | −0.666053 | − | 0.359834i | ||||
\(683\) | 597.701 | 0.875112 | 0.437556 | − | 0.899191i | \(-0.355844\pi\) | ||||
0.437556 | + | 0.899191i | \(0.355844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −576.260 | − | 311.324i | −0.840030 | − | 0.453825i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 401.760 | − | 923.093i | 0.583953 | − | 1.34170i | ||||
\(689\) | −207.225 | −0.300762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1280.71i | 1.85342i | 0.375777 | + | 0.926710i | \(0.377376\pi\) | ||||
−0.375777 | + | 0.926710i | \(0.622624\pi\) | |||||||
\(692\) | −985.964 | + | 646.178i | −1.42480 | + | 0.933783i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 305.866 | + | 165.244i | 0.440729 | + | 0.238103i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 516.679i | 0.741290i | ||||||||
\(698\) | 456.173 | + | 246.447i | 0.653543 | + | 0.353075i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −312.568 | −0.445889 | −0.222944 | − | 0.974831i | \(-0.571567\pi\) | ||||
−0.222944 | + | 0.974831i | \(0.571567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −339.459 | −0.482872 | ||||||||
\(704\) | 90.6969 | + | 529.505i | 0.128831 | + | 0.752138i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −109.703 | + | 203.061i | −0.155387 | + | 0.287622i | ||||
\(707\) | 473.237 | 0.669360 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −265.120 | −0.373935 | −0.186967 | − | 0.982366i | \(-0.559866\pi\) | ||||
−0.186967 | + | 0.982366i | \(0.559866\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.2939 | + | 144.593i | 0.0172667 | + | 0.203081i | ||||
\(713\) | − | 91.4021i | − | 0.128194i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −492.584 | + | 322.828i | −0.687967 | + | 0.450877i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 317.353 | − | 587.421i | 0.441996 | − | 0.818135i | ||||
\(719\) | 430.705i | 0.599033i | 0.954091 | + | 0.299517i | \(0.0968254\pi\) | ||||
−0.954091 | + | 0.299517i | \(0.903175\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 661.273 | 0.917160 | ||||||||
\(722\) | −104.197 | − | 56.2923i | −0.144317 | − | 0.0779671i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −157.362 | − | 240.110i | −0.217351 | − | 0.331644i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −679.243 | −0.934310 | −0.467155 | − | 0.884176i | \(-0.654721\pi\) | ||||
−0.467155 | + | 0.884176i | \(0.654721\pi\) | |||||||
\(728\) | 310.734 | − | 26.4198i | 0.426832 | − | 0.0362910i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 763.855i | 1.04494i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1045.41i | − | 1.42620i | −0.701061 | − | 0.713101i | \(-0.747290\pi\) | ||
0.701061 | − | 0.713101i | \(-0.252710\pi\) | |||||||
\(734\) | 924.066 | + | 499.225i | 1.25895 | + | 0.680143i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −74.8418 | + | 58.6828i | −0.101687 | + | 0.0797321i | ||||
\(737\) | − | 796.082i | − | 1.08017i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 846.147i | 1.14499i | 0.819908 | + | 0.572495i | \(0.194024\pi\) | ||||
−0.819908 | + | 0.572495i | \(0.805976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 80.4453 | − | 148.904i | 0.108417 | − | 0.200680i | ||||
\(743\) | 322.828 | 0.434493 | 0.217246 | − | 0.976117i | \(-0.430293\pi\) | ||||
0.217246 | + | 0.976117i | \(0.430293\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −396.429 | + | 733.790i | −0.531406 | + | 0.983633i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −223.430 | − | 340.919i | −0.298703 | − | 0.455774i | ||||
\(749\) | 415.828 | 0.555178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 716.488i | − | 0.954045i | −0.878891 | − | 0.477023i | \(-0.841716\pi\) | ||
0.878891 | − | 0.477023i | \(-0.158284\pi\) | |||||||
\(752\) | 252.342 | − | 579.788i | 0.335562 | − | 0.770994i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −479.541 | + | 887.630i | −0.635996 | + | 1.17723i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 375.636i | 0.496217i | 0.968732 | + | 0.248108i | \(0.0798089\pi\) | ||||
−0.968732 | + | 0.248108i | \(0.920191\pi\) | |||||||
\(758\) | 120.501 | − | 223.047i | 0.158972 | − | 0.294257i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 97.6836 | 0.128362 | 0.0641811 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641811 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 242.787 | 0.318201 | ||||||||
\(764\) | 1116.85 | − | 731.955i | 1.46184 | − | 0.958056i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 227.703 | + | 123.016i | 0.297263 | + | 0.160596i | ||||
\(767\) | 492.073 | 0.641556 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 665.651 | 0.865605 | 0.432803 | − | 0.901489i | \(-0.357525\pi\) | ||||
0.432803 | + | 0.901489i | \(0.357525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −644.695 | + | 422.518i | −0.835097 | + | 0.547303i | ||||
\(773\) | − | 167.735i | − | 0.216992i | −0.994097 | − | 0.108496i | \(-0.965396\pi\) | ||
0.994097 | − | 0.108496i | \(-0.0346035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −119.569 | + | 10.1662i | −0.154083 | + | 0.0131008i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −154.687 | − | 83.5692i | −0.198826 | − | 0.107415i | ||||
\(779\) | − | 739.355i | − | 0.949108i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1111.17 | −1.42275 | ||||||||
\(782\) | 34.2992 | − | 63.4879i | 0.0438609 | − | 0.0811865i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 211.230 | − | 485.326i | 0.269426 | − | 0.619039i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 185.097 | 0.235193 | 0.117597 | − | 0.993061i | \(-0.462481\pi\) | ||||
0.117597 | + | 0.993061i | \(0.462481\pi\) | |||||||
\(788\) | −122.315 | + | 80.1626i | −0.155223 | + | 0.101729i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 557.860i | − | 0.705259i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 687.756i | 0.867284i | ||||||||
\(794\) | 227.934 | − | 421.907i | 0.287071 | − | 0.531369i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 771.953 | − | 505.920i | 0.969790 | − | 0.635578i | ||||
\(797\) | 529.145i | 0.663921i | 0.943293 | + | 0.331960i | \(0.107710\pi\) | ||||
−0.943293 | + | 0.331960i | \(0.892290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 479.771i | 0.600465i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −674.013 | − | 364.134i | −0.840415 | − | 0.454033i | ||||
\(803\) | −652.242 | −0.812256 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −528.729 | − | 285.645i | −0.655991 | − | 0.354398i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 80.3883 | + | 945.478i | 0.0994905 | + | 1.17015i | ||||
\(809\) | 1306.81 | 1.61533 | 0.807667 | − | 0.589638i | \(-0.200730\pi\) | ||||
0.807667 | + | 0.589638i | \(0.200730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 582.743i | 0.718549i | 0.933232 | + | 0.359274i | \(0.116976\pi\) | ||||
−0.933232 | + | 0.359274i | \(0.883024\pi\) | |||||||
\(812\) | −451.660 | − | 689.161i | −0.556231 | − | 0.848720i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −288.622 | − | 155.928i | −0.354572 | − | 0.191557i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1093.06i | − | 1.33789i | ||||||
\(818\) | −1288.01 | − | 695.843i | −1.57458 | − | 0.850663i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 224.659 | 0.273641 | 0.136821 | − | 0.990596i | \(-0.456312\pi\) | ||||
0.136821 | + | 0.990596i | \(0.456312\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 680.427 | 0.826764 | 0.413382 | − | 0.910558i | \(-0.364347\pi\) | ||||
0.413382 | + | 0.910558i | \(0.364347\pi\) | |||||||
\(824\) | 112.330 | + | 1321.15i | 0.136322 | + | 1.60334i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −191.024 | + | 353.586i | −0.231264 | + | 0.428070i | ||||
\(827\) | 594.207 | 0.718509 | 0.359255 | − | 0.933240i | \(-0.383031\pi\) | ||||
0.359255 | + | 0.933240i | \(0.383031\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −546.029 | −0.658659 | −0.329330 | − | 0.944215i | \(-0.606823\pi\) | ||||
−0.329330 | + | 0.944215i | \(0.606823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 105.568 | + | 616.325i | 0.126885 | + | 0.740776i | ||||
\(833\) | 401.605i | 0.482119i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 319.723 | + | 487.846i | 0.382444 | + | 0.583548i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −658.645 | + | 1219.15i | −0.785973 | + | 1.45484i | ||||
\(839\) | − | 279.613i | − | 0.333269i | −0.986019 | − | 0.166634i | \(-0.946710\pi\) | ||
0.986019 | − | 0.166634i | \(-0.0532900\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1824.65 | 2.16963 | ||||||||
\(842\) | 574.733 | + | 310.499i | 0.682581 | + | 0.368763i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 595.362 | − | 390.186i | 0.705406 | − | 0.462306i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −201.648 | −0.238073 | ||||||||
\(848\) | 311.160 | + | 135.427i | 0.366934 | + | 0.159702i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 58.0755i | − | 0.0682438i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 422.173i | − | 0.494927i | −0.968897 | − | 0.247463i | \(-0.920403\pi\) | ||
0.968897 | − | 0.247463i | \(-0.0795970\pi\) | |||||||
\(854\) | −494.196 | − | 266.989i | −0.578684 | − | 0.312633i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 70.6363 | + | 830.780i | 0.0825190 | + | 0.970537i | ||||
\(857\) | − | 1609.18i | − | 1.87768i | −0.344347 | − | 0.938842i | \(-0.611900\pi\) | ||
0.344347 | − | 0.938842i | \(-0.388100\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1146.70i | − | 1.33493i | −0.744643 | − | 0.667463i | \(-0.767380\pi\) | ||
0.744643 | − | 0.667463i | \(-0.232620\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 349.272 | − | 646.502i | 0.405188 | − | 0.750003i | ||||
\(863\) | 1318.54 | 1.52786 | 0.763929 | − | 0.645300i | \(-0.223268\pi\) | ||||
0.763929 | + | 0.645300i | \(0.223268\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 469.255 | − | 868.591i | 0.541865 | − | 1.00299i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 410.508 | − | 269.037i | 0.472935 | − | 0.309951i | ||||
\(869\) | 406.053 | 0.467265 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 926.612i | − | 1.06385i | ||||||
\(872\) | 41.2420 | + | 485.063i | 0.0472959 | + | 0.556265i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −49.0813 | + | 90.8496i | −0.0561571 | + | 0.103947i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1194.61i | 1.36216i | 0.732210 | + | 0.681079i | \(0.238489\pi\) | ||||
−0.732210 | + | 0.681079i | \(0.761511\pi\) | |||||||
\(878\) | 626.440 | − | 1159.54i | 0.713485 | − | 1.32066i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1008.88 | −1.14516 | −0.572579 | − | 0.819850i | \(-0.694057\pi\) | ||||
−0.572579 | + | 0.819850i | \(0.694057\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 210.869 | 0.238809 | 0.119405 | − | 0.992846i | \(-0.461901\pi\) | ||||
0.119405 | + | 0.992846i | \(0.461901\pi\) | |||||||
\(884\) | −260.065 | − | 396.817i | −0.294191 | − | 0.448888i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1096.68 | − | 592.479i | −1.23779 | − | 0.668712i | ||||
\(887\) | −1682.25 | −1.89657 | −0.948283 | − | 0.317425i | \(-0.897182\pi\) | ||||
−0.948283 | + | 0.317425i | \(0.897182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 254.699 | 0.286500 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 385.624 | + | 588.401i | 0.432314 | + | 0.659642i | ||||
\(893\) | − | 686.541i | − | 0.768803i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −483.851 | − | 163.402i | −0.540012 | − | 0.182368i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 640.853 | + | 346.220i | 0.713645 | + | 0.385545i | ||||
\(899\) | 1587.83i | 1.76622i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −257.484 | −0.285775 | ||||||||
\(902\) | 339.616 | − | 628.629i | 0.376514 | − | 0.696928i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1114.55 | − | 94.7631i | 1.23290 | − | 0.104826i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1198.24 | −1.32111 | −0.660554 | − | 0.750779i | \(-0.729678\pi\) | ||||
−0.660554 | + | 0.750779i | \(0.729678\pi\) | |||||||
\(908\) | −167.930 | − | 256.235i | −0.184945 | − | 0.282197i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 647.021i | − | 0.710232i | −0.934822 | − | 0.355116i | \(-0.884441\pi\) | ||
0.934822 | − | 0.355116i | \(-0.115559\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1177.24i | 1.28942i | ||||||||
\(914\) | −205.210 | + | 379.844i | −0.224519 | + | 0.415584i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 170.224 | + | 259.735i | 0.185834 | + | 0.283553i | ||||
\(917\) | 821.881i | 0.896272i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1316.77i | − | 1.43283i | −0.697672 | − | 0.716417i | \(-0.745781\pi\) | ||
0.697672 | − | 0.716417i | \(-0.254219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −49.1187 | − | 26.5363i | −0.0532740 | − | 0.0287812i | ||||
\(923\) | −1293.36 | −1.40126 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 650.262 | + | 351.303i | 0.702227 | + | 0.379377i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1300.15 | − | 1019.44i | 1.40102 | − | 1.09853i | ||||
\(929\) | 29.9973 | 0.0322898 | 0.0161449 | − | 0.999870i | \(-0.494861\pi\) | ||||
0.0161449 | + | 0.999870i | \(0.494861\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 574.687i | − | 0.617279i | ||||||
\(932\) | 446.760 | − | 292.796i | 0.479356 | − | 0.314159i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1304.66 | − | 704.843i | −1.39686 | − | 0.754650i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1023.87i | − | 1.09271i | −0.837553 | − | 0.546356i | \(-0.816015\pi\) | ||
0.837553 | − | 0.546356i | \(-0.183985\pi\) | |||||||
\(938\) | 665.830 | + | 359.713i | 0.709840 | + | 0.383490i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 746.535 | 0.793343 | 0.396671 | − | 0.917961i | \(-0.370165\pi\) | ||||
0.396671 | + | 0.917961i | \(0.370165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 126.491 | 0.134136 | ||||||||
\(944\) | −738.876 | − | 321.583i | −0.782708 | − | 0.340660i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 502.086 | − | 929.361i | 0.530746 | − | 0.982411i | ||||
\(947\) | −1070.22 | −1.13011 | −0.565056 | − | 0.825053i | \(-0.691145\pi\) | ||||
−0.565056 | + | 0.825053i | \(0.691145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −759.187 | −0.799986 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 386.096 | − | 32.8275i | 0.405563 | − | 0.0344826i | ||||
\(953\) | − | 121.117i | − | 0.127091i | −0.997979 | − | 0.0635453i | \(-0.979759\pi\) | ||
0.997979 | − | 0.0635453i | \(-0.0202407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 49.7151 | − | 32.5821i | 0.0520033 | − | 0.0340817i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −398.982 | + | 738.516i | −0.416474 | + | 0.770894i | ||||
\(959\) | − | 969.849i | − | 1.01131i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1868 | 0.0158031 | ||||||||
\(962\) | −335.946 | − | 181.494i | −0.349216 | − | 0.188663i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 275.437 | + | 420.272i | 0.285723 | + | 0.435967i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1543.20 | 1.59587 | 0.797933 | − | 0.602747i | \(-0.205927\pi\) | ||||
0.797933 | + | 0.602747i | \(0.205927\pi\) | |||||||
\(968\) | −34.2538 | − | 402.872i | −0.0353861 | − | 0.416190i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 945.350i | − | 0.973584i | −0.873518 | − | 0.486792i | \(-0.838167\pi\) | ||
0.873518 | − | 0.486792i | \(-0.161833\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 488.833i | − | 0.502398i | ||||||
\(974\) | −344.010 | − | 185.851i | −0.353193 | − | 0.190812i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 449.466 | − | 1032.70i | 0.460519 | − | 1.05810i | ||||
\(977\) | 419.744i | 0.429626i | 0.976655 | + | 0.214813i | \(0.0689142\pi\) | ||||
−0.976655 | + | 0.214813i | \(0.931086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 152.262i | 0.155528i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 643.335 | − | 1190.81i | 0.655127 | − | 1.21264i | ||||
\(983\) | −645.254 | −0.656413 | −0.328206 | − | 0.944606i | \(-0.606444\pi\) | ||||
−0.328206 | + | 0.944606i | \(0.606444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −595.844 | + | 1102.91i | −0.604304 | + | 1.11857i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 372.146 | + | 567.836i | 0.376666 | + | 0.574733i | ||||
\(989\) | 187.003 | 0.189083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 994.611i | − | 1.00364i | −0.864971 | − | 0.501822i | \(-0.832663\pi\) | ||
0.864971 | − | 0.501822i | \(-0.167337\pi\) | |||||||
\(992\) | 607.240 | + | 774.450i | 0.612137 | + | 0.780695i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 502.086 | − | 929.361i | 0.505116 | − | 0.934971i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1027.03i | − | 1.03012i | −0.857153 | − | 0.515062i | \(-0.827769\pi\) | ||
0.857153 | − | 0.515062i | \(-0.172231\pi\) | |||||||
\(998\) | −597.132 | + | 1105.29i | −0.598328 | + | 1.10751i | ||||
\(999\) | 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 | 900.3.f.g.199.1 | 16 | ||
3.2 | odd | 2 | inner | 900.3.f.g.199.15 | 16 | ||
4.3 | odd | 2 | inner | 900.3.f.g.199.14 | 16 | ||
5.2 | odd | 4 | 900.3.c.q.451.5 | yes | 8 | ||
5.3 | odd | 4 | 900.3.c.p.451.4 | yes | 8 | ||
5.4 | even | 2 | inner | 900.3.f.g.199.16 | 16 | ||
12.11 | even | 2 | inner | 900.3.f.g.199.4 | 16 | ||
15.2 | even | 4 | 900.3.c.q.451.4 | yes | 8 | ||
15.8 | even | 4 | 900.3.c.p.451.5 | yes | 8 | ||
15.14 | odd | 2 | inner | 900.3.f.g.199.2 | 16 | ||
20.3 | even | 4 | 900.3.c.p.451.3 | ✓ | 8 | ||
20.7 | even | 4 | 900.3.c.q.451.6 | yes | 8 | ||
20.19 | odd | 2 | inner | 900.3.f.g.199.3 | 16 | ||
60.23 | odd | 4 | 900.3.c.p.451.6 | yes | 8 | ||
60.47 | odd | 4 | 900.3.c.q.451.3 | yes | 8 | ||
60.59 | even | 2 | inner | 900.3.f.g.199.13 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.c.p.451.3 | ✓ | 8 | 20.3 | even | 4 | ||
900.3.c.p.451.4 | yes | 8 | 5.3 | odd | 4 | ||
900.3.c.p.451.5 | yes | 8 | 15.8 | even | 4 | ||
900.3.c.p.451.6 | yes | 8 | 60.23 | odd | 4 | ||
900.3.c.q.451.3 | yes | 8 | 60.47 | odd | 4 | ||
900.3.c.q.451.4 | yes | 8 | 15.2 | even | 4 | ||
900.3.c.q.451.5 | yes | 8 | 5.2 | odd | 4 | ||
900.3.c.q.451.6 | yes | 8 | 20.7 | even | 4 | ||
900.3.f.g.199.1 | 16 | 1.1 | even | 1 | trivial | ||
900.3.f.g.199.2 | 16 | 15.14 | odd | 2 | inner | ||
900.3.f.g.199.3 | 16 | 20.19 | odd | 2 | inner | ||
900.3.f.g.199.4 | 16 | 12.11 | even | 2 | inner | ||
900.3.f.g.199.13 | 16 | 60.59 | even | 2 | inner | ||
900.3.f.g.199.14 | 16 | 4.3 | odd | 2 | inner | ||
900.3.f.g.199.15 | 16 | 3.2 | odd | 2 | inner | ||
900.3.f.g.199.16 | 16 | 5.4 | even | 2 | inner |