Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,3,Mod(159,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, 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("160.159");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.h (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: | \(4.35968422976\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1827904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 159.6 | ||
Root | \(-0.273891i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.159 |
Dual form | 160.3.h.b.159.5 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 5.30219 | 1.76740 | 0.883698 | − | 0.468058i | \(-0.155046\pi\) | ||||
0.883698 | + | 0.468058i | \(0.155046\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.54778 | + | 4.75441i | −0.309556 | + | 0.950881i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.206625 | −0.0295178 | −0.0147589 | − | 0.999891i | \(-0.504698\pi\) | ||||
−0.0147589 | + | 0.999891i | \(0.504698\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 19.1132 | 2.12369 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.0176i | 1.36524i | 0.730774 | + | 0.682619i | \(0.239159\pi\) | ||||
−0.730774 | + | 0.682619i | \(0.760841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 11.6999i | − | 0.899995i | −0.893030 | − | 0.449998i | \(-0.851425\pi\) | ||
0.893030 | − | 0.449998i | \(-0.148575\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.20662 | + | 25.2087i | −0.547108 | + | 1.68058i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 18.1911i | − | 1.07007i | −0.844831 | − | 0.535033i | \(-0.820299\pi\) | ||
0.844831 | − | 0.535033i | \(-0.179701\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.3999i | − | 1.02105i | −0.859864 | − | 0.510523i | \(-0.829452\pi\) | ||
0.859864 | − | 0.510523i | \(-0.170548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.09556 | −0.0521696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −27.2242 | −1.18366 | −0.591831 | − | 0.806062i | \(-0.701595\pi\) | ||||
−0.591831 | + | 0.806062i | \(0.701595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.2087 | − | 14.7176i | −0.808350 | − | 0.588702i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 53.6220 | 1.98600 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 44.4175 | 1.53164 | 0.765819 | − | 0.643056i | \(-0.222334\pi\) | ||||
0.765819 | + | 0.643056i | \(0.222334\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.3822i | 0.657492i | 0.944418 | + | 0.328746i | \(0.106626\pi\) | ||||
−0.944418 | + | 0.328746i | \(0.893374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 79.6262i | 2.41292i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.319810 | − | 0.982377i | 0.00913742 | − | 0.0280679i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 18.1089i | − | 0.489431i | −0.969595 | − | 0.244715i | \(-0.921305\pi\) | ||
0.969595 | − | 0.244715i | \(-0.0786945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 62.0352i | − | 1.59065i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −32.3043 | −0.787910 | −0.393955 | − | 0.919130i | \(-0.628893\pi\) | ||||
−0.393955 | + | 0.919130i | \(0.628893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.06244 | −0.0944753 | −0.0472377 | − | 0.998884i | \(-0.515042\pi\) | ||||
−0.0472377 | + | 0.998884i | \(0.515042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −29.5830 | + | 90.8718i | −0.657401 | + | 2.01937i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.37588 | 0.114380 | 0.0571902 | − | 0.998363i | \(-0.481786\pi\) | ||||
0.0571902 | + | 0.998363i | \(0.481786\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.9573 | −0.999129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 96.4527i | − | 1.89123i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 79.1703i | − | 1.49378i | −0.664948 | − | 0.746890i | \(-0.731546\pi\) | ||
0.664948 | − | 0.746890i | \(-0.268454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −71.3999 | − | 23.2440i | −1.29818 | − | 0.422618i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 102.862i | − | 1.80459i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 83.3999i | 1.41356i | 0.707435 | + | 0.706779i | \(0.249852\pi\) | ||||
−0.707435 | + | 0.706779i | \(0.750148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.7486 | −0.602435 | −0.301218 | − | 0.953555i | \(-0.597393\pi\) | ||||
−0.301218 | + | 0.953555i | \(0.597393\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.94925 | −0.0626866 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 55.6262 | + | 18.1089i | 0.855788 | + | 0.278599i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.51518 | −0.0673907 | −0.0336954 | − | 0.999432i | \(-0.510728\pi\) | ||||
−0.0336954 | + | 0.999432i | \(0.510728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −144.348 | −2.09200 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 41.6530i | 0.586662i | 0.956011 | + | 0.293331i | \(0.0947638\pi\) | ||||
−0.956011 | + | 0.293331i | \(0.905236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.5910i | 0.569740i | 0.958566 | + | 0.284870i | \(0.0919504\pi\) | ||||
−0.958566 | + | 0.284870i | \(0.908050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −107.151 | − | 78.0352i | −1.42867 | − | 1.04047i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.10301i | − | 0.0402988i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.5473i | − | 0.196801i | −0.995147 | − | 0.0984004i | \(-0.968627\pi\) | ||
0.995147 | − | 0.0984004i | \(-0.0313726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 112.295 | 1.38636 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −50.9862 | −0.614291 | −0.307146 | − | 0.951663i | \(-0.599374\pi\) | ||||
−0.307146 | + | 0.951663i | \(0.599374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 86.4880 | + | 28.1559i | 1.01751 | + | 0.331246i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 235.510 | 2.70701 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8885 | 0.122343 | 0.0611713 | − | 0.998127i | \(-0.480516\pi\) | ||||
0.0611713 | + | 0.998127i | \(0.480516\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.41749i | 0.0265659i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 108.070i | 1.16205i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 92.2349 | + | 30.0268i | 0.970893 | + | 0.316071i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.1559i | − | 0.125318i | −0.998035 | − | 0.0626592i | \(-0.980042\pi\) | ||
0.998035 | − | 0.0626592i | \(-0.0199581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 287.035i | 2.89934i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 127.723 | 1.26459 | 0.632294 | − | 0.774728i | \(-0.282113\pi\) | ||||
0.632294 | + | 0.774728i | \(0.282113\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.77575 | 0.0463665 | 0.0231833 | − | 0.999731i | \(-0.492620\pi\) | ||||
0.0231833 | + | 0.999731i | \(0.492620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.69569 | − | 5.20875i | 0.0161494 | − | 0.0496071i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 107.213 | 1.00199 | 0.500997 | − | 0.865449i | \(-0.332967\pi\) | ||||
0.500997 | + | 0.865449i | \(0.332967\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 53.6689 | 0.492376 | 0.246188 | − | 0.969222i | \(-0.420822\pi\) | ||||
0.246188 | + | 0.969222i | \(0.420822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 96.0170i | − | 0.865018i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.5063i | 0.181471i | 0.995875 | + | 0.0907356i | \(0.0289218\pi\) | ||||
−0.995875 | + | 0.0907356i | \(0.971078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 42.1372 | − | 129.435i | 0.366410 | − | 1.12552i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 223.623i | − | 1.91131i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.75873i | 0.0315860i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −104.529 | −0.863876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −171.283 | −1.39255 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 101.252 | − | 73.3010i | 0.810016 | − | 0.586408i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −138.477 | −1.09037 | −0.545184 | − | 0.838316i | \(-0.683540\pi\) | ||||
−0.545184 | + | 0.838316i | \(0.683540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.5398 | −0.166975 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 219.105i | 1.67256i | 0.548304 | + | 0.836279i | \(0.315274\pi\) | ||||
−0.548304 | + | 0.836279i | \(0.684726\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00849i | 0.0301390i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −82.9951 | + | 254.941i | −0.614779 | + | 1.88845i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 59.7821i | − | 0.436366i | −0.975908 | − | 0.218183i | \(-0.929987\pi\) | ||
0.975908 | − | 0.218183i | \(-0.0700129\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 26.6524i | − | 0.191744i | −0.995394 | − | 0.0958718i | \(-0.969436\pi\) | ||
0.995394 | − | 0.0958718i | \(-0.0305639\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 28.5039 | 0.202155 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 175.705 | 1.22871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −68.7486 | + | 211.179i | −0.474128 | + | 1.45641i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −259.581 | −1.76586 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 143.463 | 0.962838 | 0.481419 | − | 0.876490i | \(-0.340121\pi\) | ||||
0.481419 | + | 0.876490i | \(0.340121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 83.4937i | 0.552939i | 0.961023 | + | 0.276469i | \(0.0891644\pi\) | ||||
−0.961023 | + | 0.276469i | \(0.910836\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 347.690i | − | 2.27249i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −96.9055 | − | 31.5473i | −0.625197 | − | 0.203531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 169.673i | 1.08072i | 0.841434 | + | 0.540360i | \(0.181712\pi\) | ||||
−0.841434 | + | 0.540360i | \(0.818288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 419.776i | − | 2.64010i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.62520 | 0.0349391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 275.478 | 1.69005 | 0.845026 | − | 0.534726i | \(-0.179585\pi\) | ||||
0.845026 | + | 0.534726i | \(0.179585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −378.575 | − | 123.244i | −2.29440 | − | 0.746933i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 132.481 | 0.793299 | 0.396650 | − | 0.917970i | \(-0.370173\pi\) | ||||
0.396650 | + | 0.917970i | \(0.370173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.1115 | 0.190009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 370.793i | − | 2.16838i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 272.614i | 1.57580i | 0.615801 | + | 0.787901i | \(0.288832\pi\) | ||||
−0.615801 | + | 0.787901i | \(0.711168\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.17562 | + | 3.04101i | 0.0238607 | + | 0.0173772i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 442.202i | 2.49831i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 157.523i | − | 0.880014i | −0.897994 | − | 0.440007i | \(-0.854976\pi\) | ||
0.897994 | − | 0.440007i | \(-0.145024\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −335.063 | −1.85118 | −0.925590 | − | 0.378529i | \(-0.876430\pi\) | ||||
−0.925590 | + | 0.378529i | \(0.876430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −194.848 | −1.06474 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 86.0972 | + | 28.0287i | 0.465391 | + | 0.151506i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 273.187 | 1.46090 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.0796 | −0.0586223 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 298.575i | 1.56322i | 0.623766 | + | 0.781611i | \(0.285602\pi\) | ||||
−0.623766 | + | 0.781611i | \(0.714398\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 191.915i | − | 0.994376i | −0.867643 | − | 0.497188i | \(-0.834366\pi\) | ||
0.867643 | − | 0.497188i | \(-0.165634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 294.941 | + | 96.0170i | 1.51252 | + | 0.492395i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 59.2472i | 0.300747i | 0.988629 | + | 0.150374i | \(0.0480477\pi\) | ||||
−0.988629 | + | 0.150374i | \(0.951952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 309.100i | − | 1.55327i | −0.629953 | − | 0.776633i | \(-0.716926\pi\) | ||
0.629953 | − | 0.776633i | \(-0.283074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −23.9403 | −0.119106 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.17775 | −0.0452106 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 50.0000 | − | 153.588i | 0.243902 | − | 0.749209i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −520.342 | −2.51373 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 291.340 | 1.39397 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 205.693i | − | 0.974850i | −0.873165 | − | 0.487425i | \(-0.837936\pi\) | ||
0.873165 | − | 0.487425i | \(-0.162064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 220.852i | 1.03686i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.28777 | − | 19.3145i | 0.0292454 | − | 0.0898348i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.21147i | − | 0.0194077i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 220.523i | 1.00696i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −212.835 | −0.963054 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −228.723 | −1.02567 | −0.512833 | − | 0.858488i | \(-0.671404\pi\) | ||||
−0.512833 | + | 0.858488i | \(0.671404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −386.254 | − | 281.299i | −1.71668 | − | 1.25022i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −282.403 | −1.24407 | −0.622033 | − | 0.782991i | \(-0.713693\pi\) | ||||
−0.622033 | + | 0.782991i | \(0.713693\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 49.2525 | 0.215076 | 0.107538 | − | 0.994201i | \(-0.465703\pi\) | ||||
0.107538 | + | 0.994201i | \(0.465703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 16.4527i | − | 0.0712240i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 124.273i | 0.533363i | 0.963785 | + | 0.266681i | \(0.0859271\pi\) | ||||
−0.963785 | + | 0.266681i | \(0.914073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.32069 | + | 25.5591i | −0.0354072 | + | 0.108762i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 82.4345i | − | 0.347825i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 80.4527i | 0.336622i | 0.985734 | + | 0.168311i | \(0.0538313\pi\) | ||||
−0.985734 | + | 0.168311i | \(0.946169\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20979 | −0.00501988 | −0.00250994 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00250994 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 112.812 | 0.464247 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 75.7752 | − | 232.763i | 0.309287 | − | 0.950053i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −226.977 | −0.918936 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −270.338 | −1.08570 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 211.853i | 0.844034i | 0.906588 | + | 0.422017i | \(0.138678\pi\) | ||||
−0.906588 | + | 0.422017i | \(0.861322\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 408.843i | − | 1.61598i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 458.575 | + | 149.288i | 1.79834 | + | 0.585442i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 182.646i | − | 0.710685i | −0.934736 | − | 0.355342i | \(-0.884364\pi\) | ||
0.934736 | − | 0.355342i | \(-0.115636\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.74175i | 0.0144469i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 848.960 | 3.25272 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 74.6636 | 0.283892 | 0.141946 | − | 0.989874i | \(-0.454664\pi\) | ||||
0.141946 | + | 0.989874i | \(0.454664\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 376.408 | + | 122.538i | 1.42041 | + | 0.462409i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 57.7329 | 0.216228 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −184.089 | −0.684344 | −0.342172 | − | 0.939637i | \(-0.611163\pi\) | ||||
−0.342172 | + | 0.939637i | \(0.611163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 234.746i | 0.866222i | 0.901341 | + | 0.433111i | \(0.142584\pi\) | ||||
−0.901341 | + | 0.433111i | \(0.857416\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.8180i | 0.0469524i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 221.023 | − | 303.487i | 0.803719 | − | 1.10359i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 452.208i | 1.63252i | 0.577684 | + | 0.816260i | \(0.303957\pi\) | ||||
−0.577684 | + | 0.816260i | \(0.696043\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 389.570i | 1.39631i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −196.110 | −0.697900 | −0.348950 | − | 0.937141i | \(-0.613462\pi\) | ||||
−0.348950 | + | 0.937141i | \(0.613462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 418.449 | 1.47862 | 0.739309 | − | 0.673366i | \(-0.235152\pi\) | ||||
0.739309 | + | 0.673366i | \(0.235152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 489.046 | + | 159.207i | 1.71595 | + | 0.558623i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.67486 | 0.0232574 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −41.9170 | −0.145042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 64.4527i | − | 0.221487i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 286.666i | − | 0.978383i | −0.872176 | − | 0.489191i | \(-0.837292\pi\) | ||
0.872176 | − | 0.489191i | \(-0.162708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −396.517 | − | 129.085i | −1.34412 | − | 0.437575i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 805.275i | 2.71136i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 318.522i | 1.06529i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.839400 | 0.00278870 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 677.214 | 2.23503 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 56.8787 | − | 174.718i | 0.186488 | − | 0.572844i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −261.715 | −0.852493 | −0.426247 | − | 0.904607i | \(-0.640164\pi\) | ||||
−0.426247 | + | 0.904607i | \(0.640164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.3219 | 0.0819480 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 578.904i | − | 1.86143i | −0.365747 | − | 0.930714i | \(-0.619187\pi\) | ||
0.365747 | − | 0.930714i | \(-0.380813\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 99.3124i | − | 0.317292i | −0.987336 | − | 0.158646i | \(-0.949287\pi\) | ||
0.987336 | − | 0.158646i | \(-0.0507129\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.11258 | − | 18.7764i | 0.0194050 | − | 0.0596075i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 191.623i | 0.604489i | 0.953230 | + | 0.302245i | \(0.0977359\pi\) | ||||
−0.953230 | + | 0.302245i | \(0.902264\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 667.045i | 2.09105i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 568.466 | 1.77092 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −352.905 | −1.09259 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −172.194 | + | 236.441i | −0.529829 | + | 0.727511i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 284.563 | 0.870222 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.11079 | −0.00337626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 530.187i | 1.60177i | 0.598816 | + | 0.800886i | \(0.295638\pi\) | ||||
−0.598816 | + | 0.800886i | \(0.704362\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 346.120i | − | 1.03940i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.98851 | − | 21.4670i | 0.0208612 | − | 0.0640806i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 487.427i | − | 1.44637i | −0.690653 | − | 0.723186i | \(-0.742677\pi\) | ||
0.690653 | − | 0.723186i | \(-0.257323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 108.728i | 0.320731i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −306.093 | −0.897633 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.2404 | 0.0590099 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 223.419 | − | 686.289i | 0.647592 | − | 1.98924i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −310.497 | −0.894804 | −0.447402 | − | 0.894333i | \(-0.647651\pi\) | ||||
−0.447402 | + | 0.894333i | \(0.647651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −253.004 | −0.724941 | −0.362471 | − | 0.931995i | \(-0.618067\pi\) | ||||
−0.362471 | + | 0.931995i | \(0.618067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 627.374i | − | 1.78739i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 322.639i | 0.913992i | 0.889469 | + | 0.456996i | \(0.151075\pi\) | ||||
−0.889469 | + | 0.456996i | \(0.848925\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −198.035 | − | 64.4697i | −0.557846 | − | 0.181605i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.9295i | 0.0558250i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 254.975i | − | 0.710236i | −0.934822 | − | 0.355118i | \(-0.884441\pi\) | ||
0.934822 | − | 0.355118i | \(-0.115559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3550 | −0.0425347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −554.232 | −1.52681 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −197.740 | − | 64.3738i | −0.541755 | − | 0.176366i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −207.935 | −0.566581 | −0.283291 | − | 0.959034i | \(-0.591426\pi\) | ||||
−0.283291 | + | 0.959034i | \(0.591426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −617.438 | −1.67327 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.3585i | 0.0440931i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 203.826i | − | 0.546450i | −0.961950 | − | 0.273225i | \(-0.911910\pi\) | ||
0.961950 | − | 0.273225i | \(-0.0880903\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 536.857 | − | 388.656i | 1.43162 | − | 1.03642i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 519.682i | − | 1.37847i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 454.099i | − | 1.19815i | −0.800692 | − | 0.599076i | \(-0.795535\pi\) | ||
0.800692 | − | 0.599076i | \(-0.204465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −734.229 | −1.92711 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −541.569 | −1.41402 | −0.707009 | − | 0.707205i | \(-0.749956\pi\) | ||||
−0.707009 | + | 0.707205i | \(0.749956\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7530 | + | 4.80278i | 0.0383194 | + | 0.0124748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −77.6462 | −0.200636 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −423.431 | −1.08851 | −0.544256 | − | 0.838919i | \(-0.683188\pi\) | ||||
−0.544256 | + | 0.838919i | \(0.683188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 495.240i | 1.26660i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1161.74i | 2.95607i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 73.9180 | + | 24.0638i | 0.187134 | + | 0.0609209i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 11.7772i | − | 0.0296654i | −0.999890 | − | 0.0148327i | \(-0.995278\pi\) | ||
0.999890 | − | 0.0148327i | \(-0.00472157\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.2538i | 0.0532676i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 127.442 | 0.317809 | 0.158905 | − | 0.987294i | \(-0.449204\pi\) | ||||
0.158905 | + | 0.987294i | \(0.449204\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 238.471 | 0.591739 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −173.808 | + | 533.897i | −0.429156 | + | 1.31826i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 271.953 | 0.668190 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 608.012 | 1.48658 | 0.743290 | − | 0.668969i | \(-0.233264\pi\) | ||||
0.743290 | + | 0.668969i | \(0.233264\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 316.976i | − | 0.771231i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 17.2325i | − | 0.0417251i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 78.9155 | − | 242.409i | 0.190158 | − | 0.584118i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 141.316i | − | 0.338887i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 565.630i | − | 1.34995i | −0.737840 | − | 0.674976i | \(-0.764154\pi\) | ||
0.737840 | − | 0.674976i | \(-0.235846\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 711.356 | 1.68968 | 0.844841 | − | 0.535018i | \(-0.179695\pi\) | ||||
0.844841 | + | 0.535018i | \(0.179695\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 102.750 | 0.242908 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −267.729 | + | 367.620i | −0.629950 | + | 0.864988i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.59316 | 0.0177826 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 931.622 | 2.17161 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 309.254i | − | 0.717526i | −0.933429 | − | 0.358763i | \(-0.883199\pi\) | ||
0.933429 | − | 0.358763i | \(-0.116801\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 187.374i | − | 0.432735i | −0.976312 | − | 0.216368i | \(-0.930579\pi\) | ||
0.976312 | − | 0.216368i | \(-0.0694210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −364.518 | + | 1119.71i | −0.837972 | + | 2.57404i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 528.147i | 1.20857i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 289.657i | − | 0.659811i | −0.944014 | − | 0.329906i | \(-0.892983\pi\) | ||
0.944014 | − | 0.329906i | \(-0.107017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −935.730 | −2.12184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −295.516 | −0.667079 | −0.333539 | − | 0.942736i | \(-0.608243\pi\) | ||||
−0.333539 | + | 0.942736i | \(0.608243\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.8530 | + | 51.7683i | −0.0378719 | + | 0.116333i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 760.667 | 1.70172 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −604.409 | −1.34612 | −0.673061 | − | 0.739587i | \(-0.735021\pi\) | ||||
−0.673061 | + | 0.739587i | \(0.735021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 485.134i | − | 1.07569i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 442.699i | 0.977262i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.4937 | − | 3.74175i | −0.0252610 | − | 0.00822363i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 392.507i | 0.858877i | 0.903096 | + | 0.429438i | \(0.141288\pi\) | ||||
−0.903096 | + | 0.429438i | \(0.858712\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 975.444i | − | 2.12515i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −400.277 | −0.868279 | −0.434139 | − | 0.900846i | \(-0.642947\pi\) | ||||
−0.434139 | + | 0.900846i | \(0.642947\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 732.679 | 1.58246 | 0.791230 | − | 0.611518i | \(-0.209441\pi\) | ||||
0.791230 | + | 0.611518i | \(0.209441\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −513.811 | − | 167.269i | −1.10497 | − | 0.359719i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 592.126 | 1.26794 | 0.633968 | − | 0.773360i | \(-0.281425\pi\) | ||||
0.633968 | + | 0.773360i | \(0.281425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.932947 | 0.00198923 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 899.639i | 1.91006i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 61.0082i | − | 0.128981i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −285.519 | + | 392.047i | −0.601092 | + | 0.825362i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1513.20i | − | 3.17232i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 309.151i | − | 0.645409i | −0.946500 | − | 0.322705i | \(-0.895408\pi\) | ||
0.946500 | − | 0.322705i | \(-0.104592\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −211.873 | −0.440485 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.8259 | 0.0617513 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 57.7940 | + | 18.8146i | 0.119163 | + | 0.0387931i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −570.769 | −1.17201 | −0.586005 | − | 0.810307i | \(-0.699300\pi\) | ||||
−0.586005 | + | 0.810307i | \(0.699300\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1460.64 | 2.98699 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 301.659i | 0.614378i | 0.951649 | + | 0.307189i | \(0.0993883\pi\) | ||||
−0.951649 | + | 0.307189i | \(0.900612\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 808.004i | − | 1.63895i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1364.68 | − | 444.267i | −2.75693 | − | 0.897509i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 8.60653i | − | 0.0173170i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 517.758i | 1.03759i | 0.854898 | + | 0.518795i | \(0.173619\pi\) | ||||
−0.854898 | + | 0.518795i | \(0.826381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 702.439 | 1.40207 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −406.671 | −0.808491 | −0.404246 | − | 0.914650i | \(-0.632466\pi\) | ||||
−0.404246 | + | 0.914650i | \(0.632466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −197.688 | + | 607.249i | −0.391461 | + | 1.20247i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 170.261 | 0.335821 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 627.097 | 1.23202 | 0.616009 | − | 0.787739i | \(-0.288748\pi\) | ||||
0.616009 | + | 0.787739i | \(0.288748\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.59372i | − | 0.0168175i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 1040.26i | − | 2.02780i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.39182 | + | 22.7059i | −0.0143530 | + | 0.0440891i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 80.7330i | 0.156157i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1445.45i | 2.78507i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −111.743 | −0.214478 | −0.107239 | − | 0.994233i | \(-0.534201\pi\) | ||||
−0.107239 | + | 0.994233i | \(0.534201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 769.813 | 1.47192 | 0.735959 | − | 0.677027i | \(-0.236732\pi\) | ||||
0.735959 | + | 0.677027i | \(0.236732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 22.1399 | + | 16.1240i | 0.0421713 | + | 0.0307124i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 370.776 | 0.703560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 212.160 | 0.401058 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1594.04i | 3.00195i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 377.958i | 0.709115i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −165.943 | + | 509.736i | −0.310174 | + | 0.952778i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 835.214i | − | 1.55533i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 735.222i | − | 1.36405i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −225.558 | −0.416927 | −0.208463 | − | 0.978030i | \(-0.566846\pi\) | ||||
−0.208463 | + | 0.978030i | \(0.566846\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1776.57 | −3.27177 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −83.0678 | + | 255.164i | −0.152418 | + | 0.468191i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 882.346 | 1.61306 | 0.806532 | − | 0.591190i | \(-0.201342\pi\) | ||||
0.806532 | + | 0.591190i | \(0.201342\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −702.382 | −1.27938 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 861.694i | − | 1.56387i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.21245i | 0.00580913i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 456.504 | + | 148.613i | 0.822529 | + | 0.267772i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 303.119i | 0.544199i | 0.962269 | + | 0.272100i | \(0.0877180\pi\) | ||||
−0.962269 | + | 0.272100i | \(0.912282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.5303i | 0.0850273i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1448.49 | 2.58198 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −344.003 | −0.611017 | −0.305508 | − | 0.952189i | \(-0.598826\pi\) | ||||
−0.305508 | + | 0.952189i | \(0.598826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −97.4950 | − | 31.7392i | −0.172558 | − | 0.0561756i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.2029 | −0.0409223 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −228.925 | −0.402329 | −0.201165 | − | 0.979557i | \(-0.564473\pi\) | ||||
−0.201165 | + | 0.979557i | \(0.564473\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 371.169i | − | 0.650033i | −0.945708 | − | 0.325017i | \(-0.894630\pi\) | ||
0.945708 | − | 0.325017i | \(-0.105370\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1583.10i | 2.76283i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 550.168 | + | 400.674i | 0.956814 | + | 0.696825i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 580.289i | − | 1.00570i | −0.864374 | − | 0.502850i | \(-0.832285\pi\) | ||
0.864374 | − | 0.502850i | \(-0.167715\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 1017.57i | − | 1.75746i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.5350 | 0.0181325 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1188.95 | 2.03936 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1063.19 | + | 346.120i | 1.81743 | + | 0.591657i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 65.0801 | 0.110869 | 0.0554345 | − | 0.998462i | \(-0.482346\pi\) | ||||
0.0554345 | + | 0.998462i | \(0.482346\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 395.413 | 0.671329 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 314.140i | 0.531539i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1002.90i | 1.69124i | 0.533787 | + | 0.845619i | \(0.320768\pi\) | ||||
−0.533787 | + | 0.845619i | \(0.679232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.8705 | − | 5.81770i | −0.0300345 | − | 0.00977764i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1638.91i | − | 2.74524i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 888.567i | 1.48342i | 0.670722 | + | 0.741709i | \(0.265984\pi\) | ||||
−0.670722 | + | 0.741709i | \(0.734016\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 132.065 | 0.219742 | 0.109871 | − | 0.993946i | \(-0.464956\pi\) | ||||
0.109871 | + | 0.993946i | \(0.464956\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −86.2995 | −0.143117 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 161.788 | − | 496.973i | 0.267418 | − | 0.821443i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 700.090 | 1.15336 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −48.6621 | −0.0799050 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 62.8975i | − | 0.102942i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 727.420i | 1.18666i | 0.804961 | + | 0.593328i | \(0.202186\pi\) | ||||
−0.804961 | + | 0.593328i | \(0.797814\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 265.109 | − | 814.351i | 0.431072 | − | 1.32415i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 99.7137i | 0.161611i | 0.996730 | + | 0.0808053i | \(0.0257492\pi\) | ||||
−0.996730 | + | 0.0808053i | \(0.974251\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 721.349i | 1.16535i | 0.812707 | + | 0.582673i | \(0.197993\pi\) | ||||
−0.812707 | + | 0.582673i | \(0.802007\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1459.82 | −2.35075 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.24983 | −0.00361129 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 191.787 | + | 594.847i | 0.306859 | + | 0.951755i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1544.74 | 2.46370 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −329.422 | −0.523723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 796.856i | − | 1.26285i | −0.775438 | − | 0.631423i | \(-0.782471\pi\) | ||
0.775438 | − | 0.631423i | \(-0.217529\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1090.62i | − | 1.72295i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 214.332 | − | 658.375i | 0.337530 | − | 1.03681i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 572.797i | 0.899211i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 796.121i | 1.24589i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 205.013 | 0.319833 | 0.159917 | − | 0.987131i | \(-0.448877\pi\) | ||||
0.159917 | + | 0.987131i | \(0.448877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −495.044 | −0.769897 | −0.384949 | − | 0.922938i | \(-0.625781\pi\) | ||||
−0.384949 | + | 0.922938i | \(0.625781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 33.3389 | − | 102.409i | 0.0516882 | − | 0.158774i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1121.84 | −1.73391 | −0.866953 | − | 0.498389i | \(-0.833925\pi\) | ||||
−0.866953 | + | 0.498389i | \(0.833925\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1252.47 | −1.92984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 22.3300i | − | 0.0343011i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 622.987i | 0.954038i | 0.878893 | + | 0.477019i | \(0.158283\pi\) | ||||
−0.878893 | + | 0.477019i | \(0.841717\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1041.71 | − | 339.127i | −1.59040 | − | 0.517751i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 794.936i | 1.20995i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 264.030i | − | 0.400653i | −0.979729 | − | 0.200326i | \(-0.935800\pi\) | ||
0.979729 | − | 0.200326i | \(-0.0642002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1285.15 | 1.94425 | 0.972124 | − | 0.234469i | \(-0.0753352\pi\) | ||||
0.972124 | + | 0.234469i | \(0.0753352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1128.49 | −1.70210 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.0580 | − | 6.20427i | −0.0286586 | − | 0.00932972i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1209.23 | −1.81294 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1212.73 | −1.81276 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 551.876i | − | 0.822468i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1244.16i | − | 1.84868i | −0.381565 | − | 0.924342i | \(-0.624615\pi\) | ||
0.381565 | − | 0.924342i | \(-0.375385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1083.63 | − | 789.185i | −1.60538 | − | 1.16916i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 963.335i | − | 1.42295i | −0.702713 | − | 0.711473i | \(-0.748028\pi\) | ||
0.702713 | − | 0.711473i | \(-0.251972\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.51170i | 0.00369912i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1497.35 | −2.19876 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 770.819 | 1.12858 | 0.564289 | − | 0.825577i | \(-0.309150\pi\) | ||||
0.564289 | + | 0.825577i | \(0.309150\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 284.228 | + | 92.5296i | 0.414932 | + | 0.135080i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 261.146 | 0.380125 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −926.287 | −1.34439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 408.765i | − | 0.591555i | −0.955257 | − | 0.295778i | \(-0.904421\pi\) | ||
0.955257 | − | 0.295778i | \(-0.0955788\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 59.3084i | − | 0.0855821i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 126.716 | + | 41.2520i | 0.182325 | + | 0.0593554i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 587.652i | 0.843116i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 658.921i | 0.942663i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1335.62 | 1.90530 | 0.952650 | − | 0.304068i | \(-0.0983450\pi\) | ||||
0.952650 | + | 0.304068i | \(0.0983450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −351.311 | −0.499731 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −44.1178 | + | 135.519i | −0.0625785 | + | 0.192226i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −26.3908 | −0.0373279 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 362.956 | 0.511927 | 0.255964 | − | 0.966686i | \(-0.417607\pi\) | ||||
0.255964 | + | 0.966686i | \(0.417607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 297.158i | − | 0.417943i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 554.891i | − | 0.778249i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −271.953 | + | 835.374i | −0.380354 | + | 1.16836i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 426.575i | 0.594945i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 648.098i | 0.901388i | 0.892679 | + | 0.450694i | \(0.148823\pi\) | ||||
−0.892679 | + | 0.450694i | \(0.851177\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.986788 | −0.00136864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.41453 | −0.00887211 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −897.622 | − | 653.717i | −1.23810 | − | 0.901679i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 431.123 | 0.593017 | 0.296508 | − | 0.955030i | \(-0.404178\pi\) | ||||
0.296508 | + | 0.955030i | \(0.404178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −412.506 | −0.565852 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.9003i | 0.101095i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1464.87i | − | 1.99846i | −0.0392126 | − | 0.999231i | \(-0.512485\pi\) | ||
0.0392126 | − | 0.999231i | \(-0.487515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 401.774 | − | 1234.15i | 0.546632 | − | 1.67912i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 67.8073i | − | 0.0920044i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 99.1951i | − | 0.134229i | −0.997745 | − | 0.0671144i | \(-0.978621\pi\) | ||
0.997745 | − | 0.0671144i | \(-0.0213793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1203.48 | −1.62412 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 602.719 | 0.811196 | 0.405598 | − | 0.914052i | \(-0.367063\pi\) | ||||
0.405598 | + | 0.914052i | \(0.367063\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −222.049 | + | 682.081i | −0.298053 | + | 0.915545i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −974.508 | −1.30456 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.1529 | −0.0295767 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 541.472i | 0.721001i | 0.932759 | + | 0.360501i | \(0.117394\pi\) | ||||
−0.932759 | + | 0.360501i | \(0.882606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1123.28i | 1.49174i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −396.963 | − | 129.230i | −0.525779 | − | 0.171166i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1092.79i | 1.44358i | 0.692113 | + | 0.721789i | \(0.256680\pi\) | ||||
−0.692113 | + | 0.721789i | \(0.743320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2167.76i | − | 2.85608i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.7706 | −0.0246657 | −0.0123328 | − | 0.999924i | \(-0.503926\pi\) | ||||
−0.0123328 | + | 0.999924i | \(0.503926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0893 | −0.0145338 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1653.06 | + | 538.149i | 2.16086 | + | 0.703462i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 975.773 | 1.27219 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.0830 | 0.0508231 | 0.0254116 | − | 0.999677i | \(-0.491910\pi\) | ||||
0.0254116 | + | 0.999677i | \(0.491910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 968.423i | − | 1.25606i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 31.2171i | − | 0.0403843i | −0.999796 | − | 0.0201922i | \(-0.993572\pi\) | ||
0.999796 | − | 0.0201922i | \(-0.00642780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 299.977 | − | 411.900i | 0.387067 | − | 0.531484i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.8395i | 0.0255334i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 626.699i | 0.804492i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −625.529 | −0.800933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2381.75 | 3.04183 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −806.695 | − | 262.617i | −1.02764 | − | 0.334544i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −988.563 | −1.25612 | −0.628058 | − | 0.778167i | \(-0.716150\pi\) | ||||
−0.628058 | + | 0.778167i | \(0.716150\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 395.880 | 0.501750 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 4.23710i | − | 0.00535663i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 429.956i | 0.542189i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1995.78 | + | 649.721i | 2.51042 | + | 0.817259i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 118.920i | − | 0.149210i | −0.997213 | − | 0.0746048i | \(-0.976230\pi\) | ||
0.997213 | − | 0.0746048i | \(-0.0237695\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 97.7933i | − | 0.122395i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 208.114 | 0.259818 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −624.598 | −0.777831 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.70658 | + | 26.7445i | −0.0108156 | + | 0.0332230i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −976.072 | −1.20951 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1214.04 | 1.50067 | 0.750337 | − | 0.661056i | \(-0.229891\pi\) | ||||
0.750337 | + | 0.661056i | \(0.229891\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 706.666i | − | 0.871351i | −0.900104 | − | 0.435676i | \(-0.856509\pi\) | ||
0.900104 | − | 0.435676i | \(-0.143491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1244.67i | 1.53096i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −426.380 | + | 1309.74i | −0.523166 | + | 1.60704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 78.8108i | 0.0964636i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 46.2060i | 0.0564176i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 991.775 | 1.20801 | 0.604004 | − | 0.796981i | \(-0.293571\pi\) | ||||
0.604004 | + | 0.796981i | \(0.293571\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 523.998 | 0.636693 | 0.318347 | − | 0.947974i | \(-0.396872\pi\) | ||||
0.318347 | + | 0.947974i | \(0.396872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1171.90 | − | 1609.15i | 1.42049 | − | 1.95048i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 318.794 | 0.385483 | 0.192741 | − | 0.981250i | \(-0.438262\pi\) | ||||
0.192741 | + | 0.981250i | \(0.438262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1034.11 | −1.24742 | −0.623711 | − | 0.781655i | \(-0.714376\pi\) | ||||
−0.623711 | + | 0.781655i | \(0.714376\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2397.69i | 2.88531i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 890.588i | 1.06913i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −205.052 | + | 629.868i | −0.245571 | + | 0.754333i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1092.94i | 1.30578i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 445.284i | 0.530732i | 0.964148 | + | 0.265366i | \(0.0854928\pi\) | ||||
−0.964148 | + | 0.265366i | \(0.914507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1131.91 | 1.34591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1039.81 | −1.23346 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −49.7016 | + | 152.671i | −0.0588184 | + | 0.180676i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.5983 | 0.0254997 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2218.69 | 2.61330 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 493.002i | 0.579321i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1200.49i | − | 1.40737i | −0.710513 | − | 0.703684i | \(-0.751537\pi\) | ||
0.710513 | − | 0.703684i | \(-0.248463\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1762.90 | + | 573.907i | 2.06187 | + | 0.671236i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1223.15i | − | 1.42724i | −0.700531 | − | 0.713622i | \(-0.747054\pi\) | ||
0.700531 | − | 0.713622i | \(-0.252946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 210.033i | − | 0.244509i | −0.992499 | − | 0.122254i | \(-0.960988\pi\) | ||
0.992499 | − | 0.122254i | \(-0.0390124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.3914 | 0.0411050 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1560.47 | −1.80819 | −0.904095 | − | 0.427333i | \(-0.859453\pi\) | ||||
−0.904095 | + | 0.427333i | \(0.859453\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1296.12 | − | 421.947i | −1.49840 | − | 0.487800i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −222.252 | −0.256346 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 233.483 | 0.268680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.8273i | 0.0606513i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 232.338i | − | 0.266137i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.9211 | + | 15.1458i | −0.0239099 | + | 0.0173095i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1011.66i | − | 1.15354i | −0.816906 | − | 0.576771i | \(-0.804313\pi\) | ||
0.816906 | − | 0.576771i | \(-0.195687\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1519.96i | − | 1.72919i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 266.455 | 0.302446 | 0.151223 | − | 0.988500i | \(-0.451679\pi\) | ||||
0.151223 | + | 0.988500i | \(0.451679\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −469.871 | −0.532130 | −0.266065 | − | 0.963955i | \(-0.585724\pi\) | ||||
−0.266065 | + | 0.963955i | \(0.585724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2102.41 | − | 684.431i | −2.37560 | − | 0.773369i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −764.559 | −0.861961 | −0.430980 | − | 0.902361i | \(-0.641832\pi\) | ||||
−0.430980 | + | 0.902361i | \(0.641832\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.6127 | 0.0321853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1686.41i | 1.89271i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 104.291i | − | 0.116788i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 748.926 | + | 243.810i | 0.836789 | + | 0.272414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1688.86i | 1.88279i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 905.328i | 1.00704i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1440.20 | −1.59844 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.45065 | 0.00492874 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 518.605 | − | 1593.03i | 0.573044 | − | 1.76025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1333.20 | −1.46990 | −0.734948 | − | 0.678123i | \(-0.762794\pi\) | ||||
−0.734948 | + | 0.678123i | \(0.762794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2441.20 | 2.68559 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1496.11i | − | 1.64227i | −0.570736 | − | 0.821134i | \(-0.693342\pi\) | ||
0.570736 | − | 0.821134i | \(-0.306658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 765.691i | − | 0.838654i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 301.582 | − | 926.385i | 0.329597 | − | 1.01244i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 45.2725i | − | 0.0493702i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 564.228i | − | 0.613959i | −0.951716 | − | 0.306980i | \(-0.900682\pi\) | ||
0.951716 | − | 0.306980i | \(-0.0993183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1387.66 | −1.50669 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 487.337 | 0.527993 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −266.519 | + | 365.959i | −0.288129 | + | 0.395631i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 91.2798 | 0.0984680 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1449.16 | 1.55991 | 0.779957 | − | 0.625833i | \(-0.215241\pi\) | ||||
0.779957 | + | 0.625833i | \(0.215241\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 949.765i | 1.02016i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 3069.46i | − | 3.28988i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −422.834 | + | 1298.84i | −0.452229 | + | 1.38914i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 258.795i | − | 0.276196i | −0.990419 | − | 0.138098i | \(-0.955901\pi\) | ||
0.990419 | − | 0.138098i | \(-0.0440989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 526.573i | − | 0.560781i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.3444 | 0.0216200 | 0.0108100 | − | 0.999942i | \(-0.496559\pi\) | ||||
0.0108100 | + | 0.999942i | \(0.496559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 879.461 | 0.932620 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.1488 | − | 52.6770i | 0.0181469 | − | 0.0557429i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 613.539 | 0.647876 | 0.323938 | − | 0.946078i | \(-0.394993\pi\) | ||||
0.323938 | + | 0.946078i | \(0.394993\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 486.612 | 0.512763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1016.02i | 1.06837i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 81.6126i | − | 0.0856376i | −0.999083 | − | 0.0428188i | \(-0.986366\pi\) | ||
0.999083 | − | 0.0428188i | \(-0.0136338\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1419.55 | − | 462.129i | −1.48644 | − | 0.483905i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3536.80i | 3.69571i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.3525i | 0.0128806i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 545.564 | 0.567704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2049.19 | 2.12792 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 912.440 | + | 297.042i | 0.945534 | + | 0.307815i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −127.482 | −0.131833 | −0.0659165 | − | 0.997825i | \(-0.520997\pi\) | ||||
−0.0659165 | + | 0.997825i | \(0.520997\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1871.17 | −1.93103 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1122.62i | 1.15615i | 0.815983 | + | 0.578076i | \(0.196196\pi\) | ||||
−0.815983 | + | 0.578076i | \(0.803804\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.50703i | 0.00565985i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −913.007 | + | 1253.65i | −0.936418 | + | 1.28580i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 424.837i | 0.434838i | 0.976078 | + | 0.217419i | \(0.0697639\pi\) | ||||
−0.976078 | + | 0.217419i | \(0.930236\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 163.519i | 0.167027i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1025.78 | 1.04565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 663.324 | 0.674795 | 0.337398 | − | 0.941362i | \(-0.390453\pi\) | ||||
0.337398 | + | 0.941362i | \(0.390453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −281.685 | − | 91.7017i | −0.285975 | − | 0.0930982i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.88961 | −0.00596719 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 110.597 | 0.111827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1771.36i | − | 1.78745i | −0.448616 | − | 0.893724i | \(-0.648083\pi\) | ||
0.448616 | − | 0.893724i | \(-0.351917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2811.15i | 2.83097i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1469.59 | + | 478.419i | 1.47697 | + | 0.480823i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 447.066i | 0.448411i | 0.974542 | + | 0.224205i | \(0.0719786\pi\) | ||||
−0.974542 | + | 0.224205i | \(0.928021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 971.038i | − | 0.972010i |
(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 | 160.3.h.b.159.6 | yes | 6 | |
3.2 | odd | 2 | 1440.3.j.b.1279.3 | 6 | |||
4.3 | odd | 2 | 160.3.h.a.159.2 | yes | 6 | ||
5.2 | odd | 4 | 800.3.b.i.351.1 | 6 | |||
5.3 | odd | 4 | 800.3.b.h.351.6 | 6 | |||
5.4 | even | 2 | 160.3.h.a.159.1 | ✓ | 6 | ||
8.3 | odd | 2 | 320.3.h.g.319.5 | 6 | |||
8.5 | even | 2 | 320.3.h.f.319.1 | 6 | |||
12.11 | even | 2 | 1440.3.j.a.1279.3 | 6 | |||
15.14 | odd | 2 | 1440.3.j.a.1279.4 | 6 | |||
16.3 | odd | 4 | 1280.3.e.i.639.1 | 6 | |||
16.5 | even | 4 | 1280.3.e.f.639.1 | 6 | |||
16.11 | odd | 4 | 1280.3.e.g.639.6 | 6 | |||
16.13 | even | 4 | 1280.3.e.h.639.6 | 6 | |||
20.3 | even | 4 | 800.3.b.h.351.1 | 6 | |||
20.7 | even | 4 | 800.3.b.i.351.6 | 6 | |||
20.19 | odd | 2 | inner | 160.3.h.b.159.5 | yes | 6 | |
40.3 | even | 4 | 1600.3.b.v.1151.6 | 6 | |||
40.13 | odd | 4 | 1600.3.b.v.1151.1 | 6 | |||
40.19 | odd | 2 | 320.3.h.f.319.2 | 6 | |||
40.27 | even | 4 | 1600.3.b.w.1151.1 | 6 | |||
40.29 | even | 2 | 320.3.h.g.319.6 | 6 | |||
40.37 | odd | 4 | 1600.3.b.w.1151.6 | 6 | |||
60.59 | even | 2 | 1440.3.j.b.1279.4 | 6 | |||
80.19 | odd | 4 | 1280.3.e.f.639.6 | 6 | |||
80.29 | even | 4 | 1280.3.e.g.639.1 | 6 | |||
80.59 | odd | 4 | 1280.3.e.h.639.1 | 6 | |||
80.69 | even | 4 | 1280.3.e.i.639.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.1 | ✓ | 6 | 5.4 | even | 2 | ||
160.3.h.a.159.2 | yes | 6 | 4.3 | odd | 2 | ||
160.3.h.b.159.5 | yes | 6 | 20.19 | odd | 2 | inner | |
160.3.h.b.159.6 | yes | 6 | 1.1 | even | 1 | trivial | |
320.3.h.f.319.1 | 6 | 8.5 | even | 2 | |||
320.3.h.f.319.2 | 6 | 40.19 | odd | 2 | |||
320.3.h.g.319.5 | 6 | 8.3 | odd | 2 | |||
320.3.h.g.319.6 | 6 | 40.29 | even | 2 | |||
800.3.b.h.351.1 | 6 | 20.3 | even | 4 | |||
800.3.b.h.351.6 | 6 | 5.3 | odd | 4 | |||
800.3.b.i.351.1 | 6 | 5.2 | odd | 4 | |||
800.3.b.i.351.6 | 6 | 20.7 | even | 4 | |||
1280.3.e.f.639.1 | 6 | 16.5 | even | 4 | |||
1280.3.e.f.639.6 | 6 | 80.19 | odd | 4 | |||
1280.3.e.g.639.1 | 6 | 80.29 | even | 4 | |||
1280.3.e.g.639.6 | 6 | 16.11 | odd | 4 | |||
1280.3.e.h.639.1 | 6 | 80.59 | odd | 4 | |||
1280.3.e.h.639.6 | 6 | 16.13 | even | 4 | |||
1280.3.e.i.639.1 | 6 | 16.3 | odd | 4 | |||
1280.3.e.i.639.6 | 6 | 80.69 | even | 4 | |||
1440.3.j.a.1279.3 | 6 | 12.11 | even | 2 | |||
1440.3.j.a.1279.4 | 6 | 15.14 | odd | 2 | |||
1440.3.j.b.1279.3 | 6 | 3.2 | odd | 2 | |||
1440.3.j.b.1279.4 | 6 | 60.59 | even | 2 | |||
1600.3.b.v.1151.1 | 6 | 40.13 | odd | 4 | |||
1600.3.b.v.1151.6 | 6 | 40.3 | even | 4 | |||
1600.3.b.w.1151.1 | 6 | 40.27 | even | 4 | |||
1600.3.b.w.1151.6 | 6 | 40.37 | odd | 4 |