Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
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, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
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.c (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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.12239922073600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} + 4x^{4} - 32x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.3 | ||
Root | \(0.950636 + 1.75963i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.q.451.4 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.950636 | − | 1.75963i | −0.475318 | − | 0.879814i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.19258 | + | 3.34553i | −0.548146 | + | 0.836383i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.98982i | 0.569975i | 0.958531 | + | 0.284987i | \(0.0919894\pi\) | ||||
−0.958531 | + | 0.284987i | \(0.908011\pi\) | |||||||
\(8\) | 7.97124 | + | 0.677747i | 0.996405 | + | 0.0847184i | ||||
\(9\) | 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 | ||||||||
\(13\) | −9.77033 | −0.751564 | −0.375782 | − | 0.926708i | \(-0.622626\pi\) | ||||
−0.375782 | + | 0.926708i | \(0.622626\pi\) | |||||||
\(14\) | 7.02060 | − | 3.79287i | 0.501472 | − | 0.270919i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −6.38516 | − | 14.6707i | −0.399073 | − | 0.916919i | ||||
\(17\) | −12.1399 | −0.714114 | −0.357057 | − | 0.934083i | \(-0.616220\pi\) | ||||
−0.357057 | + | 0.934083i | \(0.616220\pi\) | |||||||
\(18\) | 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 | ||||||||
\(22\) | −14.7703 | + | 7.97964i | −0.671379 | + | 0.362711i | ||||
\(23\) | 2.97203i | 0.129219i | 0.997911 | + | 0.0646094i | \(0.0205801\pi\) | ||||
−0.997911 | + | 0.0646094i | \(0.979420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 9.28803 | + | 17.1921i | 0.357232 | + | 0.661236i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −13.3481 | − | 8.74801i | −0.476717 | − | 0.312429i | ||||
\(29\) | 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 | \(-0.834789\pi\) | ||
0.868303 | − | 0.496033i | \(-0.165211\pi\) | |||||||
\(32\) | −19.7450 | + | 25.1820i | −0.617032 | + | 0.786938i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.5407 | + | 21.3618i | 0.339431 | + | 0.628287i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −19.5407 | −0.528126 | −0.264063 | − | 0.964505i | \(-0.585063\pi\) | ||||
−0.264063 | + | 0.964505i | \(0.585063\pi\) | |||||||
\(38\) | 30.5682 | − | 16.5144i | 0.804426 | − | 0.434589i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 42.5603 | 1.03806 | 0.519028 | − | 0.854757i | \(-0.326294\pi\) | ||||
0.519028 | + | 0.854757i | \(0.326294\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 62.9208i | − | 1.46327i | −0.681694 | − | 0.731637i | \(-0.738756\pi\) | ||
0.681694 | − | 0.731637i | \(-0.261244\pi\) | |||||||
\(44\) | 28.0824 | + | 18.4046i | 0.638237 | + | 0.418285i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.22967 | − | 2.82532i | 0.113688 | − | 0.0614200i | ||||
\(47\) | − | 39.5201i | − | 0.840853i | −0.907327 | − | 0.420426i | \(-0.861880\pi\) | ||
0.907327 | − | 0.420426i | \(-0.138120\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 33.0813 | 0.675129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 21.4223 | − | 32.6869i | 0.411966 | − | 0.628595i | ||||
\(53\) | 21.2096 | 0.400182 | 0.200091 | − | 0.979777i | \(-0.435876\pi\) | ||||
0.200091 | + | 0.979777i | \(0.435876\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.70409 | + | 31.8038i | −0.0482873 | + | 0.567926i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −49.0813 | − | 90.8496i | −0.846230 | − | 1.56637i | ||||
\(59\) | − | 50.3640i | − | 0.853628i | −0.904339 | − | 0.426814i | \(-0.859636\pi\) | ||
0.904339 | − | 0.426814i | \(-0.140364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −70.3923 | −1.15397 | −0.576986 | − | 0.816754i | \(-0.695771\pi\) | ||||
−0.576986 | + | 0.816754i | \(0.695771\pi\) | |||||||
\(62\) | −54.1157 | + | 29.2359i | −0.872834 | + | 0.471547i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 63.0813 | + | 10.8050i | 0.985646 | + | 0.168828i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 94.8394i | − | 1.41551i | −0.706456 | − | 0.707757i | \(-0.749707\pi\) | ||
0.706456 | − | 0.707757i | \(-0.250293\pi\) | |||||||
\(68\) | 26.6178 | − | 40.6145i | 0.391438 | − | 0.597273i | ||||
\(69\) | 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 | ||||||||
\(73\) | −77.7033 | −1.06443 | −0.532214 | − | 0.846610i | \(-0.678640\pi\) | ||||
−0.532214 | + | 0.846610i | \(0.678640\pi\) | |||||||
\(74\) | 18.5761 | + | 34.3843i | 0.251028 | + | 0.464653i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −58.1184 | − | 38.0894i | −0.764716 | − | 0.501177i | ||||
\(77\) | 33.4906 | 0.434943 | ||||||||
\(78\) | 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 | ||||||||
\(82\) | −40.4593 | − | 74.8903i | −0.493407 | − | 0.913296i | ||||
\(83\) | 140.248i | 1.68974i | 0.534974 | + | 0.844868i | \(0.320321\pi\) | ||||
−0.534974 | + | 0.844868i | \(0.679679\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −110.717 | + | 59.8148i | −1.28741 | + | 0.695521i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.68901 | − | 66.9106i | 0.0646479 | − | 0.760348i | ||||
\(89\) | −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 | ||||||
\(92\) | −9.94303 | − | 6.51642i | −0.108076 | − | 0.0708307i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −69.5407 | + | 37.5692i | −0.739794 | + | 0.399673i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.0000 | 0.154639 | 0.0773196 | − | 0.997006i | \(-0.475364\pi\) | ||||
0.0773196 | + | 0.997006i | \(0.475364\pi\) | |||||||
\(98\) | −31.4483 | − | 58.2108i | −0.320901 | − | 0.593988i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 118.611 | 1.17437 | 0.587184 | − | 0.809453i | \(-0.300237\pi\) | ||||
0.587184 | + | 0.809453i | \(0.300237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 165.740i | − | 1.60912i | −0.593868 | − | 0.804562i | \(-0.702400\pi\) | ||
0.593868 | − | 0.804562i | \(-0.297600\pi\) | |||||||
\(104\) | −77.8816 | − | 6.62181i | −0.748862 | − | 0.0636712i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.1626 | − | 37.3211i | −0.190214 | − | 0.352085i | ||||
\(107\) | − | 104.222i | − | 0.974039i | −0.873391 | − | 0.487020i | \(-0.838084\pi\) | ||
0.873391 | − | 0.487020i | \(-0.161916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 60.8516 | 0.558272 | 0.279136 | − | 0.960252i | \(-0.409952\pi\) | ||||
0.279136 | + | 0.960252i | \(0.409952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 58.5335 | − | 25.4757i | 0.522621 | − | 0.227461i | ||||
\(113\) | −139.821 | −1.23735 | −0.618676 | − | 0.785646i | \(-0.712331\pi\) | ||||
−0.618676 | + | 0.785646i | \(0.712331\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −113.203 | + | 172.730i | −0.975888 | + | 1.48905i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −88.6220 | + | 47.8779i | −0.751034 | + | 0.405745i | ||||
\(119\) | − | 48.4362i | − | 0.407027i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 50.5407 | 0.417691 | ||||||||
\(122\) | 66.9175 | + | 123.864i | 0.548504 | + | 1.01528i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 102.889 | + | 67.4308i | 0.829748 | + | 0.543797i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 63.8372i | 0.502655i | 0.967902 | + | 0.251327i | \(0.0808671\pi\) | ||||
−0.967902 | + | 0.251327i | \(0.919133\pi\) | |||||||
\(128\) | −40.9547 | − | 121.271i | −0.319958 | − | 0.947432i | ||||
\(129\) | 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 | ||||||||
\(133\) | −69.3110 | −0.521135 | ||||||||
\(134\) | −166.882 | + | 90.1577i | −1.24539 | + | 0.672819i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −96.7703 | − | 8.22780i | −0.711547 | − | 0.0604985i | ||||
\(137\) | 243.081 | 1.77431 | 0.887156 | − | 0.461470i | \(-0.152678\pi\) | ||||
0.887156 | + | 0.461470i | \(0.152678\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −232.933 | + | 125.842i | −1.64037 | + | 0.886209i | ||||
\(143\) | 82.0122i | 0.573512i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 73.8676 | + | 136.729i | 0.505942 | + | 0.936499i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 42.8445 | − | 65.3739i | 0.289490 | − | 0.441716i | ||||
\(149\) | −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 | \(-0.877500\pi\) | ||
0.926856 | − | 0.375417i | \(-0.122500\pi\) | |||||||
\(152\) | −11.7738 | + | 138.476i | −0.0774591 | + | 0.911026i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −31.8374 | − | 58.9310i | −0.206736 | − | 0.382669i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −117.933 | −0.751165 | −0.375583 | − | 0.926789i | \(-0.622557\pi\) | ||||
−0.375583 | + | 0.926789i | \(0.622557\pi\) | |||||||
\(158\) | 85.1206 | − | 45.9862i | 0.538738 | − | 0.291052i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.8579 | −0.0736514 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 158.677i | 0.973476i | 0.873548 | + | 0.486738i | \(0.161813\pi\) | ||||
−0.873548 | + | 0.486738i | \(0.838187\pi\) | |||||||
\(164\) | −93.3169 | + | 142.387i | −0.569006 | + | 0.868212i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 246.785 | − | 133.325i | 1.48665 | − | 0.803162i | ||||
\(167\) | − | 260.736i | − | 1.56130i | −0.624972 | − | 0.780648i | \(-0.714889\pi\) | ||
0.624972 | − | 0.780648i | \(-0.285111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −73.5407 | −0.435152 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 210.504 | + | 137.959i | 1.22386 | + | 0.802088i | ||||
\(173\) | −294.711 | −1.70353 | −0.851765 | − | 0.523924i | \(-0.824468\pi\) | ||||
−0.851765 | + | 0.523924i | \(0.824468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −123.146 | + | 53.5971i | −0.699693 | + | 0.304529i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.2440 | + | 31.9186i | 0.0968762 | + | 0.179318i | ||||
\(179\) | − | 147.236i | − | 0.822550i | −0.911511 | − | 0.411275i | \(-0.865084\pi\) | ||
0.911511 | − | 0.411275i | \(-0.134916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −71.7703 | −0.396521 | −0.198261 | − | 0.980149i | \(-0.563529\pi\) | ||||
−0.198261 | + | 0.980149i | \(0.563529\pi\) | |||||||
\(182\) | −68.5936 | + | 37.0576i | −0.376888 | + | 0.203613i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.01428 | + | 23.6908i | −0.0109472 | + | 0.128754i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 101.903i | 0.544934i | ||||||||
\(188\) | 132.216 | + | 86.6510i | 0.703275 | + | 0.460910i | ||||
\(189\) | 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 | ||||||||
\(193\) | 192.703 | 0.998463 | 0.499231 | − | 0.866469i | \(-0.333616\pi\) | ||||
0.499231 | + | 0.866469i | \(0.333616\pi\) | |||||||
\(194\) | −14.2595 | − | 26.3944i | −0.0735028 | − | 0.136054i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −72.5335 | + | 110.675i | −0.370069 | + | 0.564666i | ||||
\(197\) | 36.5608 | 0.185588 | 0.0927940 | − | 0.995685i | \(-0.470420\pi\) | ||||
0.0927940 | + | 0.995685i | \(0.470420\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | −112.756 | − | 208.712i | −0.558198 | − | 1.03323i | ||||
\(203\) | 205.994i | 1.01475i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −291.640 | + | 157.558i | −1.41573 | + | 0.764846i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 62.3852 | + | 143.338i | 0.299929 | + | 0.689123i | ||||
\(209\) | 145.820 | 0.697705 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 177.957i | 0.843400i | 0.906735 | + | 0.421700i | \(0.138567\pi\) | ||||
−0.906735 | + | 0.421700i | \(0.861433\pi\) | |||||||
\(212\) | −46.5039 | + | 70.9575i | −0.219358 | + | 0.334705i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −183.392 | + | 99.0774i | −0.856973 | + | 0.462978i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 122.703 | 0.565453 | ||||||||
\(218\) | −57.8478 | − | 107.076i | −0.265357 | − | 0.491176i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 118.611 | 0.536702 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 175.877i | 0.788684i | 0.918964 | + | 0.394342i | \(0.129028\pi\) | ||||
−0.918964 | + | 0.394342i | \(0.870972\pi\) | |||||||
\(224\) | −100.472 | − | 78.7791i | −0.448535 | − | 0.351693i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 132.919 | + | 246.033i | 0.588136 | + | 1.08864i | ||||
\(227\) | − | 76.5902i | − | 0.337402i | −0.985667 | − | 0.168701i | \(-0.946043\pi\) | ||
0.985667 | − | 0.168701i | \(-0.0539572\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −77.6363 | −0.339023 | −0.169511 | − | 0.985528i | \(-0.554219\pi\) | ||||
−0.169511 | + | 0.985528i | \(0.554219\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 411.555 | + | 34.9921i | 1.77394 | + | 0.150828i | ||||
\(233\) | 133.539 | 0.573130 | 0.286565 | − | 0.958061i | \(-0.407487\pi\) | ||||
0.286565 | + | 0.958061i | \(0.407487\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 168.494 | + | 110.427i | 0.713960 | + | 0.467912i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −85.2297 | + | 46.0452i | −0.358108 | + | 0.193467i | ||||
\(239\) | 14.8602i | 0.0621764i | 0.999517 | + | 0.0310882i | \(0.00989727\pi\) | ||||
−0.999517 | + | 0.0310882i | \(0.990103\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 125.622 | 0.521253 | 0.260627 | − | 0.965440i | \(-0.416071\pi\) | ||||
0.260627 | + | 0.965440i | \(0.416071\pi\) | |||||||
\(242\) | −48.0458 | − | 88.9328i | −0.198536 | − | 0.367491i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 154.341 | − | 235.500i | 0.632545 | − | 0.965163i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 169.730i | − | 0.687165i | ||||||
\(248\) | 20.8435 | − | 245.148i | 0.0840463 | − | 0.988500i | ||||
\(249\) | 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 | ||||||||
\(253\) | 24.9473 | 0.0986057 | ||||||||
\(254\) | 112.330 | − | 60.6859i | 0.442243 | − | 0.238921i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −174.459 | + | 187.350i | −0.681482 | + | 0.731835i | ||||
\(257\) | −188.098 | −0.731901 | −0.365950 | − | 0.930634i | \(-0.619256\pi\) | ||||
−0.365950 | + | 0.930634i | \(0.619256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 77.9638i | − | 0.301018i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −362.474 | + | 195.826i | −1.38349 | + | 0.747426i | ||||
\(263\) | 114.544i | 0.435529i | 0.976001 | + | 0.217764i | \(0.0698764\pi\) | ||||
−0.976001 | + | 0.217764i | \(0.930124\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 65.8895 | + | 121.962i | 0.247705 | + | 0.458502i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 317.288 | + | 207.943i | 1.18391 | + | 0.775907i | ||||
\(269\) | 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 | \(0.255793\pi\) | ||||
−0.694122 | + | 0.719857i | \(0.744207\pi\) | |||||||
\(272\) | 77.5155 | + | 178.101i | 0.284983 | + | 0.654785i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −231.081 | − | 427.732i | −0.843362 | − | 1.56106i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 272.421 | 0.983469 | 0.491734 | − | 0.870745i | \(-0.336363\pi\) | ||||
0.491734 | + | 0.870745i | \(0.336363\pi\) | |||||||
\(278\) | 215.590 | − | 116.472i | 0.775502 | − | 0.418964i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 473.740 | 1.68591 | 0.842953 | − | 0.537987i | \(-0.180815\pi\) | ||||
0.842953 | + | 0.537987i | \(0.180815\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 164.824i | 0.582415i | 0.956660 | + | 0.291208i | \(0.0940570\pi\) | ||||
−0.956660 | + | 0.291208i | \(0.905943\pi\) | |||||||
\(284\) | 442.869 | + | 290.246i | 1.55940 | + | 1.02199i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 144.311 | − | 77.9638i | 0.504584 | − | 0.272601i | ||||
\(287\) | 169.808i | 0.591665i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −141.622 | −0.490041 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 170.371 | − | 259.959i | 0.583462 | − | 0.890270i | ||||
\(293\) | 273.219 | 0.932488 | 0.466244 | − | 0.884656i | \(-0.345607\pi\) | ||||
0.466244 | + | 0.884656i | \(0.345607\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −155.763 | − | 13.2436i | −0.526227 | − | 0.0447420i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 115.407 | + | 213.618i | 0.387270 | + | 0.716838i | ||||
\(299\) | − | 29.0377i | − | 0.0971161i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 251.043 | 0.834029 | ||||||||
\(302\) | −199.499 | + | 107.779i | −0.660594 | + | 0.356885i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 254.859 | − | 110.923i | 0.838351 | − | 0.364877i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 132.905i | 0.432915i | 0.976292 | + | 0.216458i | \(0.0694503\pi\) | ||||
−0.976292 | + | 0.216458i | \(0.930550\pi\) | |||||||
\(308\) | −73.4309 | + | 112.044i | −0.238412 | + | 0.363779i | ||||
\(309\) | 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 | ||||||||
\(313\) | 497.651 | 1.58994 | 0.794969 | − | 0.606650i | \(-0.207487\pi\) | ||||
0.794969 | + | 0.606650i | \(0.207487\pi\) | |||||||
\(314\) | 112.111 | + | 207.518i | 0.357042 | + | 0.660886i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −161.837 | − | 106.064i | −0.512144 | − | 0.335647i | ||||
\(317\) | 169.959 | 0.536149 | 0.268074 | − | 0.963398i | \(-0.413613\pi\) | ||||
0.268074 | + | 0.963398i | \(0.413613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 433.382i | − | 1.35857i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.2725 | + | 20.8655i | 0.0350078 | + | 0.0647996i | ||||
\(323\) | − | 210.894i | − | 0.652924i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 279.212 | − | 150.844i | 0.856478 | − | 0.462711i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 339.258 | + | 28.8451i | 1.03432 | + | 0.0879424i | ||||
\(329\) | 157.678 | 0.479265 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3086i | 0.0311440i | 0.999879 | + | 0.0155720i | \(0.00495691\pi\) | ||||
−0.999879 | + | 0.0155720i | \(0.995043\pi\) | |||||||
\(332\) | −469.205 | − | 307.506i | −1.41327 | − | 0.926222i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −458.799 | + | 247.865i | −1.37365 | + | 0.742112i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −109.029 | −0.323527 | −0.161763 | − | 0.986830i | \(-0.551718\pi\) | ||||
−0.161763 | + | 0.986830i | \(0.551718\pi\) | |||||||
\(338\) | 69.9104 | + | 129.404i | 0.206835 | + | 0.382853i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −258.150 | −0.757038 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 327.490i | 0.954781i | ||||||||
\(344\) | 42.6444 | − | 501.557i | 0.123966 | − | 1.45801i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 280.163 | + | 518.581i | 0.809719 | + | 1.49879i | ||||
\(347\) | − | 173.824i | − | 0.500934i | −0.968125 | − | 0.250467i | \(-0.919416\pi\) | ||
0.968125 | − | 0.250467i | \(-0.0805842\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 259.244 | 0.742819 | 0.371410 | − | 0.928469i | \(-0.378875\pi\) | ||||
0.371410 | + | 0.928469i | \(0.378875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 211.378 | + | 165.740i | 0.600506 | + | 0.470852i | ||||
\(353\) | 115.400 | 0.326912 | 0.163456 | − | 0.986551i | \(-0.447736\pi\) | ||||
0.163456 | + | 0.986551i | \(0.447736\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 39.7721 | − | 60.6859i | 0.111719 | − | 0.170466i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −259.081 | + | 139.968i | −0.723691 | + | 0.390973i | ||||
\(359\) | − | 333.832i | − | 0.929895i | −0.885338 | − | 0.464948i | \(-0.846073\pi\) | ||
0.885338 | − | 0.464948i | \(-0.153927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 59.2154 | 0.164032 | ||||||||
\(362\) | 68.2275 | + | 126.289i | 0.188474 | + | 0.348865i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 130.415 | + | 85.4710i | 0.358283 | + | 0.234810i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 525.148i | 1.43092i | 0.698653 | + | 0.715461i | \(0.253783\pi\) | ||||
−0.698653 | + | 0.715461i | \(0.746217\pi\) | |||||||
\(368\) | 43.6018 | − | 18.9769i | 0.118483 | − | 0.0515677i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 84.6227i | 0.228093i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −417.014 | −1.11800 | −0.559000 | − | 0.829167i | \(-0.688815\pi\) | ||||
−0.559000 | + | 0.829167i | \(0.688815\pi\) | |||||||
\(374\) | 179.311 | − | 96.8724i | 0.479441 | − | 0.259017i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.7846 | − | 315.024i | 0.0712357 | − | 0.837830i | ||||
\(377\) | −504.442 | −1.33804 | ||||||||
\(378\) | 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 | ||||||||
\(382\) | −587.421 | + | 317.353i | −1.53775 | + | 0.830767i | ||||
\(383\) | 129.404i | 0.337870i | 0.985627 | + | 0.168935i | \(0.0540328\pi\) | ||||
−0.985627 | + | 0.168935i | \(0.945967\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −183.191 | − | 339.086i | −0.474587 | − | 0.878462i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −32.8887 | + | 50.1830i | −0.0847648 | + | 0.129338i | ||||
\(389\) | 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 | ||||||
\(392\) | 263.699 | + | 22.4208i | 0.672702 | + | 0.0571958i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −34.7560 | − | 64.3335i | −0.0882133 | − | 0.163283i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −239.770 | −0.603955 | −0.301978 | − | 0.953315i | \(-0.597647\pi\) | ||||
−0.301978 | + | 0.953315i | \(0.597647\pi\) | |||||||
\(398\) | −406.019 | + | 219.351i | −1.02015 | + | 0.551134i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −383.043 | −0.955218 | −0.477609 | − | 0.878572i | \(-0.658497\pi\) | ||||
−0.477609 | + | 0.878572i | \(0.658497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 300.477i | 0.745602i | ||||||||
\(404\) | −260.065 | + | 396.817i | −0.643725 | + | 0.982221i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 362.474 | − | 195.826i | 0.892792 | − | 0.482329i | ||||
\(407\) | 164.024i | 0.403008i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −731.976 | −1.78967 | −0.894836 | − | 0.446395i | \(-0.852708\pi\) | ||||
−0.894836 | + | 0.446395i | \(0.852708\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 554.488 | + | 363.398i | 1.34584 | + | 0.882035i | ||||
\(413\) | 200.944 | 0.486546 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 192.915 | − | 246.037i | 0.463739 | − | 0.591434i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −138.622 | − | 256.589i | −0.331632 | − | 0.613850i | ||||
\(419\) | 692.847i | 1.65357i | 0.562516 | + | 0.826786i | \(0.309833\pi\) | ||||
−0.562516 | + | 0.826786i | \(0.690167\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −326.622 | −0.775824 | −0.387912 | − | 0.921696i | \(-0.626804\pi\) | ||||
−0.387912 | + | 0.921696i | \(0.626804\pi\) | |||||||
\(422\) | 313.139 | − | 169.173i | 0.742035 | − | 0.400883i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 169.067 | + | 14.3748i | 0.398743 | + | 0.0339027i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 280.853i | − | 0.657735i | ||||||
\(428\) | 348.679 | + | 228.516i | 0.814670 | + | 0.533915i | ||||
\(429\) | 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 | ||||||||
\(433\) | 493.622 | 1.14000 | 0.570002 | − | 0.821643i | \(-0.306942\pi\) | ||||
0.570002 | + | 0.821643i | \(0.306942\pi\) | |||||||
\(434\) | −116.646 | − | 215.912i | −0.268770 | − | 0.497493i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −133.422 | + | 203.581i | −0.306014 | + | 0.466929i | ||||
\(437\) | −51.6300 | −0.118146 | ||||||||
\(438\) | 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 | ||||||||
\(442\) | −112.756 | − | 208.712i | −0.255104 | − | 0.472198i | ||||
\(443\) | − | 623.245i | − | 1.40687i | −0.710758 | − | 0.703437i | \(-0.751648\pi\) | ||
0.710758 | − | 0.703437i | \(-0.248352\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 309.477 | − | 167.195i | 0.693896 | − | 0.374876i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −43.1099 | + | 251.683i | −0.0962274 | + | 0.561793i | ||||
\(449\) | −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 | ||||||
\(452\) | 306.569 | − | 467.775i | 0.678249 | − | 1.03490i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −134.770 | + | 72.8094i | −0.296851 | + | 0.160373i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 215.866 | 0.472354 | 0.236177 | − | 0.971710i | \(-0.424105\pi\) | ||||
0.236177 | + | 0.971710i | \(0.424105\pi\) | |||||||
\(458\) | 73.8038 | + | 136.611i | 0.161144 | + | 0.298277i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.9142 | −0.0605515 | −0.0302757 | − | 0.999542i | \(-0.509639\pi\) | ||||
−0.0302757 | + | 0.999542i | \(0.509639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 369.545i | − | 0.798154i | −0.916917 | − | 0.399077i | \(-0.869331\pi\) | ||
0.916917 | − | 0.399077i | \(-0.130669\pi\) | |||||||
\(464\) | −329.666 | − | 757.448i | −0.710487 | − | 1.63243i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −126.947 | − | 234.979i | −0.272419 | − | 0.504248i | ||||
\(467\) | 741.443i | 1.58767i | 0.608131 | + | 0.793837i | \(0.291920\pi\) | ||||
−0.608131 | + | 0.793837i | \(0.708080\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 378.392 | 0.806807 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.1341 | − | 401.464i | 0.0723179 | − | 0.850559i | ||||
\(473\) | −528.158 | −1.11661 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 162.045 | + | 106.200i | 0.340430 | + | 0.223110i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 26.1484 | − | 14.1266i | 0.0547037 | − | 0.0295536i | ||||
\(479\) | 419.700i | 0.876201i | 0.898926 | + | 0.438101i | \(0.144349\pi\) | ||||
−0.898926 | + | 0.438101i | \(0.855651\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 190.919 | 0.396920 | ||||||||
\(482\) | −119.421 | − | 221.048i | −0.247761 | − | 0.458606i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −110.815 | + | 169.085i | −0.228956 | + | 0.349350i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 195.501i | − | 0.401440i | −0.979649 | − | 0.200720i | \(-0.935672\pi\) | ||
0.979649 | − | 0.200720i | \(-0.0643281\pi\) | |||||||
\(488\) | −561.114 | − | 47.7082i | −1.14982 | − | 0.0977626i | ||||
\(489\) | 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 | ||||||||
\(493\) | −626.785 | −1.27137 | ||||||||
\(494\) | −298.661 | + | 161.351i | −0.604577 | + | 0.326622i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −451.184 | + | 196.370i | −0.909645 | + | 0.395907i | ||||
\(497\) | 528.158 | 1.06269 | ||||||||
\(498\) | 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 | ||||||||
\(502\) | −288.622 | + | 155.928i | −0.574944 | + | 0.310613i | ||||
\(503\) | − | 514.645i | − | 1.02315i | −0.859238 | − | 0.511575i | \(-0.829062\pi\) | ||
0.859238 | − | 0.511575i | \(-0.170938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −23.7158 | − | 43.8979i | −0.0468691 | − | 0.0867547i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −213.569 | − | 139.968i | −0.420412 | − | 0.275528i | ||||
\(509\) | −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 | ||||||
\(512\) | 495.513 | + | 128.882i | 0.967799 | + | 0.251723i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 178.813 | + | 330.983i | 0.347886 | + | 0.643937i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −331.732 | −0.641648 | ||||||||
\(518\) | −137.187 | + | 74.1152i | −0.264840 | + | 0.143079i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −917.482 | −1.76100 | −0.880501 | − | 0.474045i | \(-0.842793\pi\) | ||||
−0.880501 | + | 0.474045i | \(0.842793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 957.290i | − | 1.83038i | −0.403020 | − | 0.915191i | \(-0.632040\pi\) | ||
0.403020 | − | 0.915191i | \(-0.367960\pi\) | |||||||
\(524\) | 689.161 | + | 451.660i | 1.31519 | + | 0.861946i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 201.555 | − | 108.890i | 0.383184 | − | 0.207015i | ||||
\(527\) | 373.352i | 0.708449i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 520.167 | 0.983303 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 151.970 | − | 231.882i | 0.285658 | − | 0.435869i | ||||
\(533\) | −415.828 | −0.780165 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 64.2771 | − | 755.987i | 0.119920 | − | 1.41042i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −210.919 | − | 390.411i | −0.392042 | − | 0.725670i | ||||
\(539\) | − | 277.685i | − | 0.515185i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −329.014 | −0.608159 | −0.304080 | − | 0.952647i | \(-0.598349\pi\) | ||||
−0.304080 | + | 0.952647i | \(0.598349\pi\) | |||||||
\(542\) | 686.541 | − | 370.903i | 1.26668 | − | 0.684322i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 239.703 | − | 305.708i | 0.440631 | − | 0.561963i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 25.7716i | − | 0.0471145i | −0.999722 | − | 0.0235572i | \(-0.992501\pi\) | ||
0.999722 | − | 0.0235572i | \(-0.00749920\pi\) | |||||||
\(548\) | −532.975 | + | 813.234i | −0.972581 | + | 1.48400i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 896.913i | 1.62779i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −193.004 | −0.349013 | ||||||||
\(554\) | −258.973 | − | 479.359i | −0.467460 | − | 0.865270i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −409.895 | − | 268.635i | −0.737220 | − | 0.483157i | ||||
\(557\) | −632.405 | −1.13538 | −0.567688 | − | 0.823244i | \(-0.692162\pi\) | ||||
−0.567688 | + | 0.823244i | \(0.692162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 614.757i | 1.09974i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −450.354 | − | 833.605i | −0.801341 | − | 1.48328i | ||||
\(563\) | − | 156.675i | − | 0.278285i | −0.990272 | − | 0.139143i | \(-0.955565\pi\) | ||
0.990272 | − | 0.139143i | \(-0.0444346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 290.028 | − | 156.687i | 0.512417 | − | 0.276832i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 89.7176 | − | 1055.20i | 0.157953 | − | 1.85775i | ||||
\(569\) | −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 | \(0.269478\pi\) | ||||
−0.662541 | + | 0.749026i | \(0.730522\pi\) | |||||||
\(572\) | −274.374 | − | 179.819i | −0.479676 | − | 0.314368i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 298.799 | − | 161.426i | 0.520556 | − | 0.281229i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 484.081 | 0.838962 | 0.419481 | − | 0.907764i | \(-0.362212\pi\) | ||||
0.419481 | + | 0.907764i | \(0.362212\pi\) | |||||||
\(578\) | 134.631 | + | 249.202i | 0.232926 | + | 0.431145i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −559.565 | −0.963107 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 178.034i | − | 0.305375i | ||||||
\(584\) | −619.392 | − | 52.6632i | −1.06060 | − | 0.0901766i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −259.732 | − | 480.764i | −0.443228 | − | 0.820416i | ||||
\(587\) | − | 134.666i | − | 0.229413i | −0.993399 | − | 0.114707i | \(-0.963407\pi\) | ||
0.993399 | − | 0.114707i | \(-0.0365928\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 534.258 | 0.907060 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 124.770 | + | 286.675i | 0.210761 | + | 0.484249i | ||||
\(593\) | 960.465 | 1.61967 | 0.809836 | − | 0.586657i | \(-0.199556\pi\) | ||||
0.809836 | + | 0.586657i | \(0.199556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 266.178 | − | 406.145i | 0.446608 | − | 0.681452i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −51.0956 | + | 27.6043i | −0.0854442 | + | 0.0461611i | ||||
\(599\) | 492.073i | 0.821491i | 0.911750 | + | 0.410746i | \(0.134732\pi\) | ||||
−0.911750 | + | 0.410746i | \(0.865268\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 152.187 | 0.253223 | 0.126611 | − | 0.991952i | \(-0.459590\pi\) | ||||
0.126611 | + | 0.991952i | \(0.459590\pi\) | |||||||
\(602\) | −238.650 | − | 441.742i | −0.396429 | − | 0.733791i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 379.302 | + | 248.586i | 0.627984 | + | 0.411566i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1032.50i | − | 1.70100i | −0.525978 | − | 0.850498i | \(-0.676301\pi\) | ||
0.525978 | − | 0.850498i | \(-0.323699\pi\) | |||||||
\(608\) | −437.461 | − | 343.010i | −0.719508 | − | 0.564160i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 386.124i | 0.631955i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −774.029 | −1.26269 | −0.631345 | − | 0.775502i | \(-0.717497\pi\) | ||||
−0.631345 | + | 0.775502i | \(0.717497\pi\) | |||||||
\(614\) | 233.863 | − | 126.344i | 0.380885 | − | 0.205772i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 266.962 | + | 22.6981i | 0.433379 | + | 0.0368476i | ||||
\(617\) | 594.857 | 0.964112 | 0.482056 | − | 0.876141i | \(-0.339890\pi\) | ||||
0.482056 | + | 0.876141i | \(0.339890\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | 413.569 | − | 223.430i | 0.664902 | − | 0.359212i | ||||
\(623\) | − | 72.3729i | − | 0.116168i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −473.085 | − | 875.680i | −0.755726 | − | 1.39885i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 258.578 | − | 394.548i | 0.411748 | − | 0.628262i | ||||
\(629\) | 237.222 | 0.377142 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 832.689i | − | 1.31963i | −0.751426 | − | 0.659817i | \(-0.770634\pi\) | ||
0.751426 | − | 0.659817i | \(-0.229366\pi\) | |||||||
\(632\) | −32.7854 | + | 385.602i | −0.0518757 | + | 0.610130i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −161.569 | − | 299.065i | −0.254841 | − | 0.471711i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −323.215 | −0.507402 | ||||||||
\(638\) | −762.592 | + | 411.989i | −1.19529 | + | 0.645751i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7158 | 0.0369981 | 0.0184990 | − | 0.999829i | \(-0.494111\pi\) | ||||
0.0184990 | + | 0.999829i | \(0.494111\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 637.188i | − | 0.990961i | −0.868619 | − | 0.495480i | \(-0.834992\pi\) | ||
0.868619 | − | 0.495480i | \(-0.165008\pi\) | |||||||
\(644\) | 25.9994 | − | 39.6709i | 0.0403717 | − | 0.0616008i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −371.096 | + | 200.484i | −0.574451 | + | 0.310346i | ||||
\(647\) | 462.353i | 0.714610i | 0.933988 | + | 0.357305i | \(0.116304\pi\) | ||||
−0.933988 | + | 0.357305i | \(0.883696\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −422.756 | −0.651396 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −530.857 | − | 347.911i | −0.814198 | − | 0.533606i | ||||
\(653\) | 661.697 | 1.01332 | 0.506659 | − | 0.862146i | \(-0.330880\pi\) | ||||
0.506659 | + | 0.862146i | \(0.330880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −271.754 | − | 624.390i | −0.414260 | − | 0.951813i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −149.895 | − | 277.455i | −0.227803 | − | 0.421664i | ||||
\(659\) | 248.647i | 0.377310i | 0.982043 | + | 0.188655i | \(0.0604127\pi\) | ||||
−0.982043 | + | 0.188655i | \(0.939587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1022.35 | −1.54668 | −0.773339 | − | 0.633993i | \(-0.781415\pi\) | ||||
−0.773339 | + | 0.633993i | \(0.781415\pi\) | |||||||
\(662\) | 18.1394 | − | 9.79977i | 0.0274009 | − | 0.0148033i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −95.0527 | + | 1117.95i | −0.143152 | + | 1.68366i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 153.446i | 0.230054i | ||||||||
\(668\) | 872.301 | + | 571.686i | 1.30584 | + | 0.855817i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 590.873i | 0.880586i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 683.215 | 1.01518 | 0.507589 | − | 0.861599i | \(-0.330537\pi\) | ||||
0.507589 | + | 0.861599i | \(0.330537\pi\) | |||||||
\(674\) | 103.646 | + | 191.850i | 0.153778 | + | 0.284644i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 161.244 | − | 246.033i | 0.238527 | − | 0.363954i | ||||
\(677\) | −707.751 | −1.04542 | −0.522711 | − | 0.852510i | \(-0.675079\pi\) | ||||
−0.522711 | + | 0.852510i | \(0.675079\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 59.8473i | 0.0881404i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 245.407 | + | 454.248i | 0.359834 | + | 0.666053i | ||||
\(683\) | − | 597.701i | − | 0.875112i | −0.899191 | − | 0.437556i | \(-0.855844\pi\) | ||
0.899191 | − | 0.437556i | \(-0.144156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 576.260 | − | 311.324i | 0.840030 | − | 0.453825i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −923.093 | + | 401.760i | −1.34170 | + | 0.583953i | ||||
\(689\) | −207.225 | −0.300762 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1280.71i | − | 1.85342i | −0.375777 | − | 0.926710i | \(-0.622624\pi\) | ||
0.375777 | − | 0.926710i | \(-0.377376\pi\) | |||||||
\(692\) | 646.178 | − | 985.964i | 0.933783 | − | 1.42480i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −305.866 | + | 165.244i | −0.440729 | + | 0.238103i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −516.679 | −0.741290 | ||||||||
\(698\) | −246.447 | − | 456.173i | −0.353075 | − | 0.653543i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 312.568 | 0.445889 | 0.222944 | − | 0.974831i | \(-0.428433\pi\) | ||||
0.222944 | + | 0.974831i | \(0.428433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 339.459i | − | 0.482872i | ||||||
\(704\) | 90.6969 | − | 529.505i | 0.128831 | − | 0.752138i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −109.703 | − | 203.061i | −0.155387 | − | 0.287622i | ||||
\(707\) | 473.237i | 0.669360i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 265.120 | 0.373935 | 0.186967 | − | 0.982366i | \(-0.440134\pi\) | ||||
0.186967 | + | 0.982366i | \(0.440134\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −144.593 | − | 12.2939i | −0.203081 | − | 0.0172667i | ||||
\(713\) | 91.4021 | 0.128194 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 492.584 | + | 322.828i | 0.687967 | + | 0.450877i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −587.421 | + | 317.353i | −0.818135 | + | 0.441996i | ||||
\(719\) | − | 430.705i | − | 0.599033i | −0.954091 | − | 0.299517i | \(-0.903175\pi\) | ||
0.954091 | − | 0.299517i | \(-0.0968254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 661.273 | 0.917160 | ||||||||
\(722\) | −56.2923 | − | 104.197i | −0.0779671 | − | 0.144317i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 157.362 | − | 240.110i | 0.217351 | − | 0.331644i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 679.243i | 0.934310i | 0.884176 | + | 0.467155i | \(0.154721\pi\) | ||||
−0.884176 | + | 0.467155i | \(0.845279\pi\) | |||||||
\(728\) | 26.4198 | − | 310.734i | 0.0362910 | − | 0.426832i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 763.855i | 1.04494i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1045.41 | −1.42620 | −0.713101 | − | 0.701061i | \(-0.752710\pi\) | ||||
−0.713101 | + | 0.701061i | \(0.752710\pi\) | |||||||
\(734\) | 924.066 | − | 499.225i | 1.25895 | − | 0.680143i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −74.8418 | − | 58.6828i | −0.101687 | − | 0.0797321i | ||||
\(737\) | −796.082 | −1.08017 | ||||||||
\(738\) | 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 | ||||||||
\(742\) | 148.904 | − | 80.4453i | 0.200680 | − | 0.108417i | ||||
\(743\) | − | 322.828i | − | 0.434493i | −0.976117 | − | 0.217246i | \(-0.930293\pi\) | ||
0.976117 | − | 0.217246i | \(-0.0697075\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 396.429 | + | 733.790i | 0.531406 | + | 0.983633i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −340.919 | − | 223.430i | −0.455774 | − | 0.298703i | ||||
\(749\) | 415.828 | 0.555178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 716.488i | 0.954045i | 0.878891 | + | 0.477023i | \(0.158284\pi\) | ||||
−0.878891 | + | 0.477023i | \(0.841716\pi\) | |||||||
\(752\) | −579.788 | + | 252.342i | −0.770994 | + | 0.335562i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 479.541 | + | 887.630i | 0.635996 | + | 1.17723i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −375.636 | −0.496217 | −0.248108 | − | 0.968732i | \(-0.579809\pi\) | ||||
−0.248108 | + | 0.968732i | \(0.579809\pi\) | |||||||
\(758\) | 223.047 | − | 120.501i | 0.294257 | − | 0.158972i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −97.6836 | −0.128362 | −0.0641811 | − | 0.997938i | \(-0.520444\pi\) | ||||
−0.0641811 | + | 0.997938i | \(0.520444\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 242.787i | 0.318201i | ||||||||
\(764\) | 1116.85 | + | 731.955i | 1.46184 | + | 0.958056i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 227.703 | − | 123.016i | 0.297263 | − | 0.160596i | ||||
\(767\) | 492.073i | 0.641556i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −665.651 | −0.865605 | −0.432803 | − | 0.901489i | \(-0.642475\pi\) | ||||
−0.432803 | + | 0.901489i | \(0.642475\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −422.518 | + | 644.695i | −0.547303 | + | 0.835097i | ||||
\(773\) | 167.735 | 0.216992 | 0.108496 | − | 0.994097i | \(-0.465396\pi\) | ||||
0.108496 | + | 0.994097i | \(0.465396\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 119.569 | + | 10.1662i | 0.154083 | + | 0.0131008i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −83.5692 | − | 154.687i | −0.107415 | − | 0.198826i | ||||
\(779\) | 739.355i | 0.949108i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1111.17 | −1.42275 | ||||||||
\(782\) | −63.4879 | + | 34.2992i | −0.0811865 | + | 0.0438609i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −211.230 | − | 485.326i | −0.269426 | − | 0.619039i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 185.097i | − | 0.235193i | −0.993061 | − | 0.117597i | \(-0.962481\pi\) | ||
0.993061 | − | 0.117597i | \(-0.0375190\pi\) | |||||||
\(788\) | −80.1626 | + | 122.315i | −0.101729 | + | 0.155223i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 557.860i | − | 0.705259i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 687.756 | 0.867284 | ||||||||
\(794\) | 227.934 | + | 421.907i | 0.287071 | + | 0.531369i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 771.953 | + | 505.920i | 0.969790 | + | 0.635578i | ||||
\(797\) | 529.145 | 0.663921 | 0.331960 | − | 0.943293i | \(-0.392290\pi\) | ||||
0.331960 | + | 0.943293i | \(0.392290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 479.771i | 0.600465i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 364.134 | + | 674.013i | 0.454033 | + | 0.840415i | ||||
\(803\) | 652.242i | 0.812256i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 528.729 | − | 285.645i | 0.655991 | − | 0.354398i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 945.478 | + | 80.3883i | 1.17015 | + | 0.0994905i | ||||
\(809\) | 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 | \(-0.883024\pi\) | ||
0.933232 | − | 0.359274i | \(-0.116976\pi\) | |||||||
\(812\) | −689.161 | − | 451.660i | −0.848720 | − | 0.556231i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 288.622 | − | 155.928i | 0.354572 | − | 0.191557i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1093.06 | 1.33789 | ||||||||
\(818\) | 695.843 | + | 1288.01i | 0.850663 | + | 1.57458i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −224.659 | −0.273641 | −0.136821 | − | 0.990596i | \(-0.543688\pi\) | ||||
−0.136821 | + | 0.990596i | \(0.543688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 680.427i | 0.826764i | 0.910558 | + | 0.413382i | \(0.135653\pi\) | ||||
−0.910558 | + | 0.413382i | \(0.864347\pi\) | |||||||
\(824\) | 112.330 | − | 1321.15i | 0.136322 | − | 1.60334i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −191.024 | − | 353.586i | −0.231264 | − | 0.428070i | ||||
\(827\) | 594.207i | 0.718509i | 0.933240 | + | 0.359255i | \(0.116969\pi\) | ||||
−0.933240 | + | 0.359255i | \(0.883031\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 546.029 | 0.658659 | 0.329330 | − | 0.944215i | \(-0.393177\pi\) | ||||
0.329330 | + | 0.944215i | \(0.393177\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −616.325 | − | 105.568i | −0.740776 | − | 0.126885i | ||||
\(833\) | −401.605 | −0.482119 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −319.723 | + | 487.846i | −0.382444 | + | 0.583548i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1219.15 | − | 658.645i | 1.45484 | − | 0.785973i | ||||
\(839\) | 279.613i | 0.333269i | 0.986019 | + | 0.166634i | \(0.0532900\pi\) | ||||
−0.986019 | + | 0.166634i | \(0.946710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1824.65 | 2.16963 | ||||||||
\(842\) | 310.499 | + | 574.733i | 0.368763 | + | 0.682581i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −595.362 | − | 390.186i | −0.705406 | − | 0.462306i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 201.648i | 0.238073i | ||||||||
\(848\) | −135.427 | − | 311.160i | −0.159702 | − | 0.366934i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 58.0755i | − | 0.0682438i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −422.173 | −0.494927 | −0.247463 | − | 0.968897i | \(-0.579597\pi\) | ||||
−0.247463 | + | 0.968897i | \(0.579597\pi\) | |||||||
\(854\) | −494.196 | + | 266.989i | −0.578684 | + | 0.312633i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 70.6363 | − | 830.780i | 0.0825190 | − | 0.970537i | ||||
\(857\) | −1609.18 | −1.87768 | −0.938842 | − | 0.344347i | \(-0.888100\pi\) | ||||
−0.938842 | + | 0.344347i | \(0.888100\pi\) | |||||||
\(858\) | 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 | ||||||||
\(862\) | 646.502 | − | 349.272i | 0.750003 | − | 0.405188i | ||||
\(863\) | − | 1318.54i | − | 1.52786i | −0.645300 | − | 0.763929i | \(-0.723268\pi\) | ||
0.645300 | − | 0.763929i | \(-0.276732\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −469.255 | − | 868.591i | −0.541865 | − | 1.00299i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −269.037 | + | 410.508i | −0.309951 | + | 0.472935i | ||||
\(869\) | 406.053 | 0.467265 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 926.612i | 1.06385i | ||||||||
\(872\) | 485.063 | + | 41.2420i | 0.556265 | + | 0.0472959i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 49.0813 | + | 90.8496i | 0.0561571 | + | 0.103947i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1194.61 | −1.36216 | −0.681079 | − | 0.732210i | \(-0.738489\pi\) | ||||
−0.681079 | + | 0.732210i | \(0.738489\pi\) | |||||||
\(878\) | 1159.54 | − | 626.440i | 1.32066 | − | 0.713485i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1008.88 | 1.14516 | 0.572579 | − | 0.819850i | \(-0.305943\pi\) | ||||
0.572579 | + | 0.819850i | \(0.305943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 210.869i | 0.238809i | 0.992846 | + | 0.119405i | \(0.0380986\pi\) | ||||
−0.992846 | + | 0.119405i | \(0.961901\pi\) | |||||||
\(884\) | −260.065 | + | 396.817i | −0.294191 | + | 0.448888i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1096.68 | + | 592.479i | −1.23779 | + | 0.668712i | ||||
\(887\) | − | 1682.25i | − | 1.89657i | −0.317425 | − | 0.948283i | \(-0.602818\pi\) | ||
0.317425 | − | 0.948283i | \(-0.397182\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −254.699 | −0.286500 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −588.401 | − | 385.624i | −0.659642 | − | 0.432314i | ||||
\(893\) | 686.541 | 0.768803 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 483.851 | − | 163.402i | 0.540012 | − | 0.182368i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 346.220 | + | 640.853i | 0.385545 | + | 0.713645i | ||||
\(899\) | − | 1587.83i | − | 1.76622i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −257.484 | −0.285775 | ||||||||
\(902\) | −628.629 | + | 339.616i | −0.696928 | + | 0.376514i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1114.55 | − | 94.7631i | −1.23290 | − | 0.104826i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1198.24i | 1.32111i | 0.750779 | + | 0.660554i | \(0.229678\pi\) | ||||
−0.750779 | + | 0.660554i | \(0.770322\pi\) | |||||||
\(908\) | 256.235 | + | 167.930i | 0.282197 | + | 0.184945i | ||||
\(909\) | 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 | ||||||||
\(913\) | 1177.24 | 1.28942 | ||||||||
\(914\) | −205.210 | − | 379.844i | −0.224519 | − | 0.415584i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 170.224 | − | 259.735i | 0.185834 | − | 0.283553i | ||||
\(917\) | 821.881 | 0.896272 | ||||||||
\(918\) | 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 | ||||||||
\(922\) | 26.5363 | + | 49.1187i | 0.0287812 | + | 0.0532740i | ||||
\(923\) | 1293.36i | 1.40126i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −650.262 | + | 351.303i | −0.702227 | + | 0.379377i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1019.44 | + | 1300.15i | −1.09853 | + | 1.40102i | ||||
\(929\) | 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 | ||||||||
\(932\) | −292.796 | + | 446.760i | −0.314159 | + | 0.479356i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1304.66 | − | 704.843i | 1.39686 | − | 0.754650i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1023.87 | 1.09271 | 0.546356 | − | 0.837553i | \(-0.316015\pi\) | ||||
0.546356 | + | 0.837553i | \(0.316015\pi\) | |||||||
\(938\) | −359.713 | − | 665.830i | −0.383490 | − | 0.709840i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −746.535 | −0.793343 | −0.396671 | − | 0.917961i | \(-0.629835\pi\) | ||||
−0.396671 | + | 0.917961i | \(0.629835\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 126.491i | 0.134136i | ||||||||
\(944\) | −738.876 | + | 321.583i | −0.782708 | + | 0.340660i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 502.086 | + | 929.361i | 0.530746 | + | 0.982411i | ||||
\(947\) | − | 1070.22i | − | 1.13011i | −0.825053 | − | 0.565056i | \(-0.808855\pi\) | ||
0.825053 | − | 0.565056i | \(-0.191145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 759.187 | 0.799986 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32.8275 | − | 386.096i | 0.0344826 | − | 0.405563i | ||||
\(953\) | 121.117 | 0.127091 | 0.0635453 | − | 0.997979i | \(-0.479759\pi\) | ||||
0.0635453 | + | 0.997979i | \(0.479759\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −49.7151 | − | 32.5821i | −0.0520033 | − | 0.0340817i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 738.516 | − | 398.982i | 0.770894 | − | 0.416474i | ||||
\(959\) | 969.849i | 1.01131i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1868 | 0.0158031 | ||||||||
\(962\) | −181.494 | − | 335.946i | −0.188663 | − | 0.349216i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −275.437 | + | 420.272i | −0.285723 | + | 0.435967i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1543.20i | − | 1.59587i | −0.602747 | − | 0.797933i | \(-0.705927\pi\) | ||
0.602747 | − | 0.797933i | \(-0.294073\pi\) | |||||||
\(968\) | 402.872 | + | 34.2538i | 0.416190 | + | 0.0353861i | ||||
\(969\) | 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 | ||||||||
\(973\) | −488.833 | −0.502398 | ||||||||
\(974\) | −344.010 | + | 185.851i | −0.353193 | + | 0.190812i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 449.466 | + | 1032.70i | 0.460519 | + | 1.05810i | ||||
\(977\) | 419.744 | 0.429626 | 0.214813 | − | 0.976655i | \(-0.431086\pi\) | ||||
0.214813 | + | 0.976655i | \(0.431086\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 152.262i | 0.155528i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1190.81 | − | 643.335i | 1.21264 | − | 0.655127i | ||||
\(983\) | 645.254i | 0.656413i | 0.944606 | + | 0.328206i | \(0.106444\pi\) | ||||
−0.944606 | + | 0.328206i | \(0.893556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 595.844 | + | 1102.91i | 0.604304 | + | 1.11857i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 567.836 | + | 372.146i | 0.574733 | + | 0.376666i | ||||
\(989\) | 187.003 | 0.189083 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 994.611i | 1.00364i | 0.864971 | + | 0.501822i | \(0.167337\pi\) | ||||
−0.864971 | + | 0.501822i | \(0.832663\pi\) | |||||||
\(992\) | 774.450 | + | 607.240i | 0.780695 | + | 0.612137i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −502.086 | − | 929.361i | −0.505116 | − | 0.934971i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1027.03 | 1.03012 | 0.515062 | − | 0.857153i | \(-0.327769\pi\) | ||||
0.515062 | + | 0.857153i | \(0.327769\pi\) | |||||||
\(998\) | −1105.29 | + | 597.132i | −1.10751 | + | 0.598328i | ||||
\(999\) | 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.c.q.451.3 | yes | 8 | |
3.2 | odd | 2 | inner | 900.3.c.q.451.6 | yes | 8 | |
4.3 | odd | 2 | inner | 900.3.c.q.451.4 | yes | 8 | |
5.2 | odd | 4 | 900.3.f.g.199.13 | 16 | |||
5.3 | odd | 4 | 900.3.f.g.199.4 | 16 | |||
5.4 | even | 2 | 900.3.c.p.451.6 | yes | 8 | ||
12.11 | even | 2 | inner | 900.3.c.q.451.5 | yes | 8 | |
15.2 | even | 4 | 900.3.f.g.199.3 | 16 | |||
15.8 | even | 4 | 900.3.f.g.199.14 | 16 | |||
15.14 | odd | 2 | 900.3.c.p.451.3 | ✓ | 8 | ||
20.3 | even | 4 | 900.3.f.g.199.15 | 16 | |||
20.7 | even | 4 | 900.3.f.g.199.2 | 16 | |||
20.19 | odd | 2 | 900.3.c.p.451.5 | yes | 8 | ||
60.23 | odd | 4 | 900.3.f.g.199.1 | 16 | |||
60.47 | odd | 4 | 900.3.f.g.199.16 | 16 | |||
60.59 | even | 2 | 900.3.c.p.451.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
900.3.c.p.451.3 | ✓ | 8 | 15.14 | odd | 2 | ||
900.3.c.p.451.4 | yes | 8 | 60.59 | even | 2 | ||
900.3.c.p.451.5 | yes | 8 | 20.19 | odd | 2 | ||
900.3.c.p.451.6 | yes | 8 | 5.4 | even | 2 | ||
900.3.c.q.451.3 | yes | 8 | 1.1 | even | 1 | trivial | |
900.3.c.q.451.4 | yes | 8 | 4.3 | odd | 2 | inner | |
900.3.c.q.451.5 | yes | 8 | 12.11 | even | 2 | inner | |
900.3.c.q.451.6 | yes | 8 | 3.2 | odd | 2 | inner | |
900.3.f.g.199.1 | 16 | 60.23 | odd | 4 | |||
900.3.f.g.199.2 | 16 | 20.7 | even | 4 | |||
900.3.f.g.199.3 | 16 | 15.2 | even | 4 | |||
900.3.f.g.199.4 | 16 | 5.3 | odd | 4 | |||
900.3.f.g.199.13 | 16 | 5.2 | odd | 4 | |||
900.3.f.g.199.14 | 16 | 15.8 | even | 4 | |||
900.3.f.g.199.15 | 16 | 20.3 | even | 4 | |||
900.3.f.g.199.16 | 16 | 60.47 | odd | 4 |