Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(1149,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1149.20 | ||
Character | \(\chi\) | \(=\) | 1150.1149 |
Dual form | 1150.3.c.c.1149.19 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | − | 4.30716i | − | 1.43572i | −0.696187 | − | 0.717861i | \(-0.745121\pi\) | ||
0.696187 | − | 0.717861i | \(-0.254879\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.09125 | 1.01521 | ||||||||
\(7\) | 1.47532 | 0.210761 | 0.105380 | − | 0.994432i | \(-0.466394\pi\) | ||||
0.105380 | + | 0.994432i | \(0.466394\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −9.55167 | −1.06130 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.04959i | − | 0.549963i | −0.961450 | − | 0.274981i | \(-0.911328\pi\) | ||
0.961450 | − | 0.274981i | \(-0.0886717\pi\) | |||||||
\(12\) | 8.61433i | 0.717861i | ||||||||
\(13\) | 5.21324i | 0.401018i | 0.979692 | + | 0.200509i | \(0.0642597\pi\) | ||||
−0.979692 | + | 0.200509i | \(0.935740\pi\) | |||||||
\(14\) | 2.08642i | 0.149030i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −15.7063 | −0.923901 | −0.461951 | − | 0.886906i | \(-0.652850\pi\) | ||||
−0.461951 | + | 0.886906i | \(0.652850\pi\) | |||||||
\(18\) | − | 13.5081i | − | 0.750450i | ||||||
\(19\) | − | 4.82663i | − | 0.254033i | −0.991901 | − | 0.127017i | \(-0.959460\pi\) | ||
0.991901 | − | 0.127017i | \(-0.0405402\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 6.35447i | − | 0.302594i | ||||||
\(22\) | 8.55541 | 0.388882 | ||||||||
\(23\) | −22.8548 | + | 2.58013i | −0.993688 | + | 0.112180i | ||||
\(24\) | −12.1825 | −0.507604 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.37263 | −0.283563 | ||||||||
\(27\) | 2.37613i | 0.0880047i | ||||||||
\(28\) | −2.95065 | −0.105380 | ||||||||
\(29\) | 23.4711 | 0.809349 | 0.404674 | − | 0.914461i | \(-0.367385\pi\) | ||||
0.404674 | + | 0.914461i | \(0.367385\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −20.4887 | −0.660924 | −0.330462 | − | 0.943819i | \(-0.607205\pi\) | ||||
−0.330462 | + | 0.943819i | \(0.607205\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −26.0566 | −0.789593 | ||||||||
\(34\) | − | 22.2121i | − | 0.653297i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 19.1033 | 0.530648 | ||||||||
\(37\) | −15.5248 | −0.419589 | −0.209794 | − | 0.977746i | \(-0.567279\pi\) | ||||
−0.209794 | + | 0.977746i | \(0.567279\pi\) | |||||||
\(38\) | 6.82589 | 0.179629 | ||||||||
\(39\) | 22.4543 | 0.575751 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 20.3093 | 0.495348 | 0.247674 | − | 0.968843i | \(-0.420334\pi\) | ||||
0.247674 | + | 0.968843i | \(0.420334\pi\) | |||||||
\(42\) | 8.98657 | 0.213966 | ||||||||
\(43\) | −38.1696 | −0.887666 | −0.443833 | − | 0.896109i | \(-0.646382\pi\) | ||||
−0.443833 | + | 0.896109i | \(0.646382\pi\) | |||||||
\(44\) | 12.0992i | 0.274981i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.64885 | − | 32.3216i | −0.0793229 | − | 0.702643i | ||||
\(47\) | − | 13.8273i | − | 0.294198i | −0.989122 | − | 0.147099i | \(-0.953006\pi\) | ||
0.989122 | − | 0.147099i | \(-0.0469935\pi\) | |||||||
\(48\) | − | 17.2287i | − | 0.358930i | ||||||
\(49\) | −46.8234 | −0.955580 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 67.6497i | 1.32647i | ||||||||
\(52\) | − | 10.4265i | − | 0.200509i | ||||||
\(53\) | −38.2742 | −0.722154 | −0.361077 | − | 0.932536i | \(-0.617591\pi\) | ||||
−0.361077 | + | 0.932536i | \(0.617591\pi\) | |||||||
\(54\) | −3.36035 | −0.0622287 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 4.17285i | − | 0.0745152i | ||||||
\(57\) | −20.7891 | −0.364721 | ||||||||
\(58\) | 33.1932i | 0.572296i | ||||||||
\(59\) | 33.5696 | 0.568977 | 0.284488 | − | 0.958679i | \(-0.408176\pi\) | ||||
0.284488 | + | 0.958679i | \(0.408176\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 100.567i | 1.64864i | 0.566124 | + | 0.824320i | \(0.308442\pi\) | ||||
−0.566124 | + | 0.824320i | \(0.691558\pi\) | |||||||
\(62\) | − | 28.9753i | − | 0.467344i | ||||||
\(63\) | −14.0918 | −0.223680 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 36.8496i | − | 0.558327i | ||||||
\(67\) | 32.4469 | 0.484282 | 0.242141 | − | 0.970241i | \(-0.422150\pi\) | ||||
0.242141 | + | 0.970241i | \(0.422150\pi\) | |||||||
\(68\) | 31.4126 | 0.461951 | ||||||||
\(69\) | 11.1130 | + | 98.4395i | 0.161059 | + | 1.42666i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −24.1306 | −0.339868 | −0.169934 | − | 0.985455i | \(-0.554355\pi\) | ||||
−0.169934 | + | 0.985455i | \(0.554355\pi\) | |||||||
\(72\) | 27.0162i | 0.375225i | ||||||||
\(73\) | − | 15.1818i | − | 0.207969i | −0.994579 | − | 0.103985i | \(-0.966841\pi\) | ||
0.994579 | − | 0.103985i | \(-0.0331593\pi\) | |||||||
\(74\) | − | 21.9554i | − | 0.296694i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.65326i | 0.127017i | ||||||||
\(77\) | − | 8.92511i | − | 0.115910i | ||||||
\(78\) | 31.7552i | 0.407117i | ||||||||
\(79\) | 11.2095i | 0.141893i | 0.997480 | + | 0.0709463i | \(0.0226019\pi\) | ||||
−0.997480 | + | 0.0709463i | \(0.977398\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −75.7306 | −0.934946 | ||||||||
\(82\) | 28.7216i | 0.350264i | ||||||||
\(83\) | 44.1310 | 0.531698 | 0.265849 | − | 0.964015i | \(-0.414348\pi\) | ||||
0.265849 | + | 0.964015i | \(0.414348\pi\) | |||||||
\(84\) | 12.7089i | 0.151297i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 53.9800i | − | 0.627675i | ||||||
\(87\) | − | 101.094i | − | 1.16200i | ||||||
\(88\) | −17.1108 | −0.194441 | ||||||||
\(89\) | 111.039i | 1.24763i | 0.781572 | + | 0.623815i | \(0.214418\pi\) | ||||
−0.781572 | + | 0.623815i | \(0.785582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.69122i | 0.0845189i | ||||||||
\(92\) | 45.7096 | − | 5.16026i | 0.496844 | − | 0.0560898i | ||||
\(93\) | 88.2480i | 0.948903i | ||||||||
\(94\) | 19.5547 | 0.208029 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 24.3650 | 0.253802 | ||||||||
\(97\) | −154.126 | −1.58893 | −0.794463 | − | 0.607312i | \(-0.792248\pi\) | ||||
−0.794463 | + | 0.607312i | \(0.792248\pi\) | |||||||
\(98\) | − | 66.2183i | − | 0.675697i | ||||||
\(99\) | 57.7837i | 0.583673i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −58.8607 | −0.582779 | −0.291390 | − | 0.956604i | \(-0.594118\pi\) | ||||
−0.291390 | + | 0.956604i | \(0.594118\pi\) | |||||||
\(102\) | −95.6712 | −0.937952 | ||||||||
\(103\) | −54.2662 | −0.526856 | −0.263428 | − | 0.964679i | \(-0.584853\pi\) | ||||
−0.263428 | + | 0.964679i | \(0.584853\pi\) | |||||||
\(104\) | 14.7453 | 0.141781 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 54.1279i | − | 0.510640i | ||||||
\(107\) | −119.124 | −1.11331 | −0.556653 | − | 0.830745i | \(-0.687915\pi\) | ||||
−0.556653 | + | 0.830745i | \(0.687915\pi\) | |||||||
\(108\) | − | 4.75225i | − | 0.0440023i | ||||||
\(109\) | 149.223i | 1.36902i | 0.729003 | + | 0.684510i | \(0.239984\pi\) | ||||
−0.729003 | + | 0.684510i | \(0.760016\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 66.8678i | 0.602413i | ||||||||
\(112\) | 5.90130 | 0.0526902 | ||||||||
\(113\) | 35.3339 | 0.312690 | 0.156345 | − | 0.987703i | \(-0.450029\pi\) | ||||
0.156345 | + | 0.987703i | \(0.450029\pi\) | |||||||
\(114\) | − | 29.4002i | − | 0.257897i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −46.9422 | −0.404674 | ||||||||
\(117\) | − | 49.7951i | − | 0.425599i | ||||||
\(118\) | 47.4746i | 0.402327i | ||||||||
\(119\) | −23.1719 | −0.194722 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 84.4025 | 0.697541 | ||||||||
\(122\) | −142.223 | −1.16576 | ||||||||
\(123\) | − | 87.4753i | − | 0.711181i | ||||||
\(124\) | 40.9773 | 0.330462 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 19.9288i | − | 0.158165i | ||||||
\(127\) | 92.8398i | 0.731022i | 0.930807 | + | 0.365511i | \(0.119106\pi\) | ||||
−0.930807 | + | 0.365511i | \(0.880894\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 164.403i | 1.27444i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 151.709 | 1.15808 | 0.579042 | − | 0.815297i | \(-0.303427\pi\) | ||||
0.579042 | + | 0.815297i | \(0.303427\pi\) | |||||||
\(132\) | 52.1131 | 0.394797 | ||||||||
\(133\) | − | 7.12085i | − | 0.0535402i | ||||||
\(134\) | 45.8869i | 0.342439i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 44.4242i | 0.326648i | ||||||||
\(137\) | −267.464 | −1.95229 | −0.976145 | − | 0.217121i | \(-0.930333\pi\) | ||||
−0.976145 | + | 0.217121i | \(0.930333\pi\) | |||||||
\(138\) | −139.214 | + | 15.7162i | −1.00880 | + | 0.113886i | ||||
\(139\) | −239.779 | −1.72503 | −0.862516 | − | 0.506030i | \(-0.831112\pi\) | ||||
−0.862516 | + | 0.506030i | \(0.831112\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −59.5564 | −0.422386 | ||||||||
\(142\) | − | 34.1258i | − | 0.240323i | ||||||
\(143\) | 31.5380 | 0.220545 | ||||||||
\(144\) | −38.2067 | −0.265324 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 21.4703 | 0.147057 | ||||||||
\(147\) | 201.676i | 1.37195i | ||||||||
\(148\) | 31.0496 | 0.209794 | ||||||||
\(149\) | 201.647i | 1.35333i | 0.736290 | + | 0.676667i | \(0.236576\pi\) | ||||
−0.736290 | + | 0.676667i | \(0.763424\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 120.787 | 0.799912 | 0.399956 | − | 0.916534i | \(-0.369025\pi\) | ||||
0.399956 | + | 0.916534i | \(0.369025\pi\) | |||||||
\(152\) | −13.6518 | −0.0898143 | ||||||||
\(153\) | 150.022 | 0.980533 | ||||||||
\(154\) | 12.6220 | 0.0819611 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −44.9086 | −0.287875 | ||||||||
\(157\) | −194.897 | −1.24138 | −0.620692 | − | 0.784055i | \(-0.713148\pi\) | ||||
−0.620692 | + | 0.784055i | \(0.713148\pi\) | |||||||
\(158\) | −15.8526 | −0.100333 | ||||||||
\(159\) | 164.853i | 1.03681i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.7183 | + | 3.80653i | −0.209430 | + | 0.0236430i | ||||
\(162\) | − | 107.099i | − | 0.661107i | ||||||
\(163\) | − | 153.813i | − | 0.943635i | −0.881696 | − | 0.471817i | \(-0.843598\pi\) | ||
0.881696 | − | 0.471817i | \(-0.156402\pi\) | |||||||
\(164\) | −40.6185 | −0.247674 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62.4106i | 0.375967i | ||||||||
\(167\) | 48.4949i | 0.290389i | 0.989403 | + | 0.145194i | \(0.0463808\pi\) | ||||
−0.989403 | + | 0.145194i | \(0.953619\pi\) | |||||||
\(168\) | −17.9731 | −0.106983 | ||||||||
\(169\) | 141.822 | 0.839184 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.1024i | 0.269605i | ||||||||
\(172\) | 76.3393 | 0.443833 | ||||||||
\(173\) | 111.269i | 0.643174i | 0.946880 | + | 0.321587i | \(0.104216\pi\) | ||||
−0.946880 | + | 0.321587i | \(0.895784\pi\) | |||||||
\(174\) | 142.968 | 0.821658 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 24.1984i | − | 0.137491i | ||||||
\(177\) | − | 144.590i | − | 0.816892i | ||||||
\(178\) | −157.033 | −0.882207 | ||||||||
\(179\) | −262.590 | −1.46698 | −0.733492 | − | 0.679698i | \(-0.762111\pi\) | ||||
−0.733492 | + | 0.679698i | \(0.762111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 211.167i | − | 1.16667i | −0.812231 | − | 0.583335i | \(-0.801747\pi\) | ||
0.812231 | − | 0.583335i | \(-0.198253\pi\) | |||||||
\(182\) | −10.8770 | −0.0597639 | ||||||||
\(183\) | 433.159 | 2.36699 | ||||||||
\(184\) | 7.29771 | + | 64.6432i | 0.0396615 | + | 0.351322i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −124.802 | −0.670976 | ||||||||
\(187\) | 95.0168i | 0.508111i | ||||||||
\(188\) | 27.6546i | 0.147099i | ||||||||
\(189\) | 3.50556i | 0.0185479i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 72.8209i | − | 0.381261i | −0.981662 | − | 0.190631i | \(-0.938947\pi\) | ||
0.981662 | − | 0.190631i | \(-0.0610533\pi\) | |||||||
\(192\) | 34.4573i | 0.179465i | ||||||||
\(193\) | − | 198.550i | − | 1.02875i | −0.857564 | − | 0.514377i | \(-0.828023\pi\) | ||
0.857564 | − | 0.514377i | \(-0.171977\pi\) | |||||||
\(194\) | − | 217.967i | − | 1.12354i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 93.6468 | 0.477790 | ||||||||
\(197\) | 28.2055i | 0.143175i | 0.997434 | + | 0.0715876i | \(0.0228066\pi\) | ||||
−0.997434 | + | 0.0715876i | \(0.977193\pi\) | |||||||
\(198\) | −81.7184 | −0.412719 | ||||||||
\(199\) | − | 214.499i | − | 1.07788i | −0.842343 | − | 0.538941i | \(-0.818825\pi\) | ||
0.842343 | − | 0.538941i | \(-0.181175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 139.754i | − | 0.695295i | ||||||
\(202\) | − | 83.2416i | − | 0.412087i | ||||||
\(203\) | 34.6275 | 0.170579 | ||||||||
\(204\) | − | 135.299i | − | 0.663233i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 76.7439i | − | 0.372543i | ||||||
\(207\) | 218.302 | − | 24.6445i | 1.05460 | − | 0.119056i | ||||
\(208\) | 20.8530i | 0.100255i | ||||||||
\(209\) | −29.1991 | −0.139709 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 240.262 | 1.13868 | 0.569340 | − | 0.822102i | \(-0.307199\pi\) | ||||
0.569340 | + | 0.822102i | \(0.307199\pi\) | |||||||
\(212\) | 76.5483 | 0.361077 | ||||||||
\(213\) | 103.935i | 0.487956i | ||||||||
\(214\) | − | 168.466i | − | 0.787226i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.72070 | 0.0311144 | ||||||||
\(217\) | −30.2274 | −0.139297 | ||||||||
\(218\) | −211.034 | −0.968044 | ||||||||
\(219\) | −65.3904 | −0.298586 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 81.8808i | − | 0.370501i | ||||||
\(222\) | −94.5654 | −0.425970 | ||||||||
\(223\) | − | 257.402i | − | 1.15427i | −0.816648 | − | 0.577136i | \(-0.804170\pi\) | ||
0.816648 | − | 0.577136i | \(-0.195830\pi\) | |||||||
\(224\) | 8.34570i | 0.0372576i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 49.9697i | 0.221105i | ||||||||
\(227\) | 106.401 | 0.468727 | 0.234363 | − | 0.972149i | \(-0.424699\pi\) | ||||
0.234363 | + | 0.972149i | \(0.424699\pi\) | |||||||
\(228\) | 41.5782 | 0.182360 | ||||||||
\(229\) | − | 328.507i | − | 1.43453i | −0.696801 | − | 0.717265i | \(-0.745394\pi\) | ||
0.696801 | − | 0.717265i | \(-0.254606\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −38.4419 | −0.166415 | ||||||||
\(232\) | − | 66.3863i | − | 0.286148i | ||||||
\(233\) | 149.213i | 0.640400i | 0.947350 | + | 0.320200i | \(0.103750\pi\) | ||||
−0.947350 | + | 0.320200i | \(0.896250\pi\) | |||||||
\(234\) | 70.4210 | 0.300944 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −67.1393 | −0.284488 | ||||||||
\(237\) | 48.2812 | 0.203718 | ||||||||
\(238\) | − | 32.7701i | − | 0.137689i | ||||||
\(239\) | 343.168 | 1.43585 | 0.717925 | − | 0.696121i | \(-0.245092\pi\) | ||||
0.717925 | + | 0.696121i | \(0.245092\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 348.748i | − | 1.44709i | −0.690278 | − | 0.723544i | \(-0.742512\pi\) | ||
0.690278 | − | 0.723544i | \(-0.257488\pi\) | |||||||
\(242\) | 119.363i | 0.493236i | ||||||||
\(243\) | 347.570i | 1.43033i | ||||||||
\(244\) | − | 201.134i | − | 0.824320i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 123.709 | 0.502881 | ||||||||
\(247\) | 25.1624 | 0.101872 | ||||||||
\(248\) | 57.9507i | 0.233672i | ||||||||
\(249\) | − | 190.079i | − | 0.763371i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 225.099i | − | 0.896809i | −0.893831 | − | 0.448405i | \(-0.851992\pi\) | ||
0.893831 | − | 0.448405i | \(-0.148008\pi\) | |||||||
\(252\) | 28.1836 | 0.111840 | ||||||||
\(253\) | 15.6087 | + | 138.262i | 0.0616946 | + | 0.546491i | ||||
\(254\) | −131.295 | −0.516911 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 393.632i | − | 1.53164i | −0.643054 | − | 0.765821i | \(-0.722333\pi\) | ||
0.643054 | − | 0.765821i | \(-0.277667\pi\) | |||||||
\(258\) | −232.501 | −0.901166 | ||||||||
\(259\) | −22.9041 | −0.0884328 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −224.188 | −0.858959 | ||||||||
\(262\) | 214.549i | 0.818890i | ||||||||
\(263\) | 132.720 | 0.504640 | 0.252320 | − | 0.967644i | \(-0.418806\pi\) | ||||
0.252320 | + | 0.967644i | \(0.418806\pi\) | |||||||
\(264\) | 73.6991i | 0.279163i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 10.0704 | 0.0378586 | ||||||||
\(267\) | 478.263 | 1.79125 | ||||||||
\(268\) | −64.8938 | −0.242141 | ||||||||
\(269\) | 438.116 | 1.62868 | 0.814341 | − | 0.580386i | \(-0.197098\pi\) | ||||
0.814341 | + | 0.580386i | \(0.197098\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −204.698 | −0.755342 | −0.377671 | − | 0.925940i | \(-0.623275\pi\) | ||||
−0.377671 | + | 0.925940i | \(0.623275\pi\) | |||||||
\(272\) | −62.8253 | −0.230975 | ||||||||
\(273\) | 33.1274 | 0.121346 | ||||||||
\(274\) | − | 378.251i | − | 1.38048i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −22.2261 | − | 196.879i | −0.0805293 | − | 0.713330i | ||||
\(277\) | 173.804i | 0.627452i | 0.949514 | + | 0.313726i | \(0.101577\pi\) | ||||
−0.949514 | + | 0.313726i | \(0.898423\pi\) | |||||||
\(278\) | − | 339.099i | − | 1.21978i | ||||||
\(279\) | 195.701 | 0.701437 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 143.605i | − | 0.511051i | −0.966802 | − | 0.255526i | \(-0.917752\pi\) | ||
0.966802 | − | 0.255526i | \(-0.0822485\pi\) | |||||||
\(282\) | − | 84.2255i | − | 0.298672i | ||||||
\(283\) | 72.1714 | 0.255023 | 0.127511 | − | 0.991837i | \(-0.459301\pi\) | ||||
0.127511 | + | 0.991837i | \(0.459301\pi\) | |||||||
\(284\) | 48.2612 | 0.169934 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 44.6014i | 0.155949i | ||||||||
\(287\) | 29.9627 | 0.104400 | ||||||||
\(288\) | − | 54.0324i | − | 0.187612i | ||||||
\(289\) | −42.3114 | −0.146406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 663.845i | 2.28126i | ||||||||
\(292\) | 30.3635i | 0.103985i | ||||||||
\(293\) | 124.199 | 0.423889 | 0.211944 | − | 0.977282i | \(-0.432020\pi\) | ||||
0.211944 | + | 0.977282i | \(0.432020\pi\) | |||||||
\(294\) | −285.213 | −0.970113 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 43.9107i | 0.148347i | ||||||||
\(297\) | 14.3746 | 0.0483993 | ||||||||
\(298\) | −285.171 | −0.956951 | ||||||||
\(299\) | −13.4508 | − | 119.148i | −0.0449861 | − | 0.398487i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −56.3126 | −0.187085 | ||||||||
\(302\) | 170.818i | 0.565623i | ||||||||
\(303\) | 253.523i | 0.836709i | ||||||||
\(304\) | − | 19.3065i | − | 0.0635083i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 212.163i | 0.693342i | ||||||||
\(307\) | 219.717i | 0.715690i | 0.933781 | + | 0.357845i | \(0.116488\pi\) | ||||
−0.933781 | + | 0.357845i | \(0.883512\pi\) | |||||||
\(308\) | 17.8502i | 0.0579552i | ||||||||
\(309\) | 233.733i | 0.756418i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −317.069 | −1.01951 | −0.509757 | − | 0.860319i | \(-0.670265\pi\) | ||||
−0.509757 | + | 0.860319i | \(0.670265\pi\) | |||||||
\(312\) | − | 63.5103i | − | 0.203559i | ||||||
\(313\) | −484.654 | −1.54841 | −0.774207 | − | 0.632932i | \(-0.781851\pi\) | ||||
−0.774207 | + | 0.632932i | \(0.781851\pi\) | |||||||
\(314\) | − | 275.626i | − | 0.877791i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 22.4190i | − | 0.0709463i | ||||||
\(317\) | − | 521.910i | − | 1.64640i | −0.567748 | − | 0.823202i | \(-0.692185\pi\) | ||
0.567748 | − | 0.823202i | \(-0.307815\pi\) | |||||||
\(318\) | −233.138 | −0.733137 | ||||||||
\(319\) | − | 141.991i | − | 0.445111i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 513.086i | 1.59840i | ||||||||
\(322\) | −5.38325 | − | 47.6849i | −0.0167182 | − | 0.148090i | ||||
\(323\) | 75.8086i | 0.234702i | ||||||||
\(324\) | 151.461 | 0.467473 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 217.524 | 0.667251 | ||||||||
\(327\) | 642.729 | 1.96553 | ||||||||
\(328\) | − | 57.4432i | − | 0.175132i | ||||||
\(329\) | − | 20.3997i | − | 0.0620053i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −318.270 | −0.961540 | −0.480770 | − | 0.876847i | \(-0.659643\pi\) | ||||
−0.480770 | + | 0.876847i | \(0.659643\pi\) | |||||||
\(332\) | −88.2619 | −0.265849 | ||||||||
\(333\) | 148.288 | 0.445308 | ||||||||
\(334\) | −68.5822 | −0.205336 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 25.4179i | − | 0.0756484i | ||||||
\(337\) | −116.539 | −0.345812 | −0.172906 | − | 0.984938i | \(-0.555316\pi\) | ||||
−0.172906 | + | 0.984938i | \(0.555316\pi\) | |||||||
\(338\) | 200.567i | 0.593393i | ||||||||
\(339\) | − | 152.189i | − | 0.448935i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 123.948i | 0.363484i | ||||||||
\(342\) | −65.1986 | −0.190639 | ||||||||
\(343\) | −141.371 | −0.412159 | ||||||||
\(344\) | 107.960i | 0.313837i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −157.358 | −0.454793 | ||||||||
\(347\) | − | 100.715i | − | 0.290245i | −0.989414 | − | 0.145122i | \(-0.953642\pi\) | ||
0.989414 | − | 0.145122i | \(-0.0463576\pi\) | |||||||
\(348\) | 202.188i | 0.581000i | ||||||||
\(349\) | −143.476 | −0.411106 | −0.205553 | − | 0.978646i | \(-0.565899\pi\) | ||||
−0.205553 | + | 0.978646i | \(0.565899\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.3873 | −0.0352915 | ||||||||
\(352\) | 34.2216 | 0.0972206 | ||||||||
\(353\) | 274.394i | 0.777320i | 0.921381 | + | 0.388660i | \(0.127062\pi\) | ||||
−0.921381 | + | 0.388660i | \(0.872938\pi\) | |||||||
\(354\) | 204.481 | 0.577630 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 222.078i | − | 0.623815i | ||||||
\(357\) | 99.8053i | 0.279567i | ||||||||
\(358\) | − | 371.358i | − | 1.03731i | ||||||
\(359\) | 476.871i | 1.32833i | 0.747586 | + | 0.664166i | \(0.231213\pi\) | ||||
−0.747586 | + | 0.664166i | \(0.768787\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 337.704 | 0.935467 | ||||||||
\(362\) | 298.636 | 0.824961 | ||||||||
\(363\) | − | 363.535i | − | 1.00147i | ||||||
\(364\) | − | 15.3824i | − | 0.0422595i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 612.579i | 1.67371i | ||||||||
\(367\) | 14.0319 | 0.0382340 | 0.0191170 | − | 0.999817i | \(-0.493914\pi\) | ||||
0.0191170 | + | 0.999817i | \(0.493914\pi\) | |||||||
\(368\) | −91.4193 | + | 10.3205i | −0.248422 | + | 0.0280449i | ||||
\(369\) | −193.987 | −0.525711 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −56.4668 | −0.152202 | ||||||||
\(372\) | − | 176.496i | − | 0.474452i | ||||||
\(373\) | −105.662 | −0.283277 | −0.141639 | − | 0.989918i | \(-0.545237\pi\) | ||||
−0.141639 | + | 0.989918i | \(0.545237\pi\) | |||||||
\(374\) | −134.374 | −0.359289 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −39.1095 | −0.104015 | ||||||||
\(377\) | 122.361i | 0.324564i | ||||||||
\(378\) | −4.95761 | −0.0131154 | ||||||||
\(379\) | − | 339.983i | − | 0.897053i | −0.893770 | − | 0.448527i | \(-0.851949\pi\) | ||
0.893770 | − | 0.448527i | \(-0.148051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 399.876 | 1.04954 | ||||||||
\(382\) | 102.984 | 0.269592 | ||||||||
\(383\) | 699.796 | 1.82714 | 0.913572 | − | 0.406676i | \(-0.133312\pi\) | ||||
0.913572 | + | 0.406676i | \(0.133312\pi\) | |||||||
\(384\) | −48.7300 | −0.126901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 280.792 | 0.727439 | ||||||||
\(387\) | 364.584 | 0.942077 | ||||||||
\(388\) | 308.252 | 0.794463 | ||||||||
\(389\) | 124.817i | 0.320867i | 0.987047 | + | 0.160433i | \(0.0512892\pi\) | ||||
−0.987047 | + | 0.160433i | \(0.948711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 358.965 | − | 40.5244i | 0.918070 | − | 0.103643i | ||||
\(392\) | 132.437i | 0.337849i | ||||||||
\(393\) | − | 653.436i | − | 1.66269i | ||||||
\(394\) | −39.8886 | −0.101240 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 115.567i | − | 0.291837i | ||||||
\(397\) | − | 149.557i | − | 0.376719i | −0.982100 | − | 0.188360i | \(-0.939683\pi\) | ||
0.982100 | − | 0.188360i | \(-0.0603170\pi\) | |||||||
\(398\) | 303.347 | 0.762178 | ||||||||
\(399\) | −30.6707 | −0.0768688 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 426.696i | − | 1.06408i | −0.846719 | − | 0.532040i | \(-0.821426\pi\) | ||
0.846719 | − | 0.532040i | \(-0.178574\pi\) | |||||||
\(402\) | 197.642 | 0.491647 | ||||||||
\(403\) | − | 106.812i | − | 0.265043i | ||||||
\(404\) | 117.721 | 0.291390 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 48.9707i | 0.120617i | ||||||||
\(407\) | 93.9186i | 0.230758i | ||||||||
\(408\) | 191.342 | 0.468976 | ||||||||
\(409\) | −346.263 | −0.846610 | −0.423305 | − | 0.905987i | \(-0.639130\pi\) | ||||
−0.423305 | + | 0.905987i | \(0.639130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1152.01i | 2.80294i | ||||||||
\(412\) | 108.532 | 0.263428 | ||||||||
\(413\) | 49.5261 | 0.119918 | ||||||||
\(414\) | 34.8527 | + | 308.725i | 0.0841852 | + | 0.745713i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −29.4905 | −0.0708907 | ||||||||
\(417\) | 1032.77i | 2.47667i | ||||||||
\(418\) | − | 41.2938i | − | 0.0987890i | ||||||
\(419\) | 158.433i | 0.378121i | 0.981965 | + | 0.189060i | \(0.0605442\pi\) | ||||
−0.981965 | + | 0.189060i | \(0.939456\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 18.0568i | − | 0.0428902i | −0.999770 | − | 0.0214451i | \(-0.993173\pi\) | ||
0.999770 | − | 0.0214451i | \(-0.00682671\pi\) | |||||||
\(422\) | 339.781i | 0.805169i | ||||||||
\(423\) | 132.074i | 0.312231i | ||||||||
\(424\) | 108.256i | 0.255320i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −146.986 | −0.345037 | ||||||||
\(427\) | 148.369i | 0.347469i | ||||||||
\(428\) | 238.247 | 0.556653 | ||||||||
\(429\) | − | 135.839i | − | 0.316641i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 151.730i | − | 0.352041i | −0.984387 | − | 0.176020i | \(-0.943678\pi\) | ||
0.984387 | − | 0.176020i | \(-0.0563225\pi\) | |||||||
\(432\) | 9.50451i | 0.0220012i | ||||||||
\(433\) | 625.471 | 1.44451 | 0.722253 | − | 0.691629i | \(-0.243106\pi\) | ||||
0.722253 | + | 0.691629i | \(0.243106\pi\) | |||||||
\(434\) | − | 42.7480i | − | 0.0984978i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 298.447i | − | 0.684510i | ||||||
\(437\) | 12.4533 | + | 110.312i | 0.0284973 | + | 0.252430i | ||||
\(438\) | − | 92.4759i | − | 0.211132i | ||||||
\(439\) | −272.842 | −0.621509 | −0.310755 | − | 0.950490i | \(-0.600582\pi\) | ||||
−0.310755 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 447.242 | 1.01415 | ||||||||
\(442\) | 115.797 | 0.261984 | ||||||||
\(443\) | − | 5.57528i | − | 0.0125853i | −0.999980 | − | 0.00629264i | \(-0.997997\pi\) | ||
0.999980 | − | 0.00629264i | \(-0.00200302\pi\) | |||||||
\(444\) | − | 133.736i | − | 0.301206i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 364.022 | 0.816193 | ||||||||
\(447\) | 868.525 | 1.94301 | ||||||||
\(448\) | −11.8026 | −0.0263451 | ||||||||
\(449\) | −455.331 | −1.01410 | −0.507050 | − | 0.861916i | \(-0.669264\pi\) | ||||
−0.507050 | + | 0.861916i | \(0.669264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 122.863i | − | 0.272423i | ||||||
\(452\) | −70.6679 | −0.156345 | ||||||||
\(453\) | − | 520.248i | − | 1.14845i | ||||||
\(454\) | 150.474i | 0.331440i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 58.8004i | 0.128948i | ||||||||
\(457\) | −597.785 | −1.30806 | −0.654032 | − | 0.756467i | \(-0.726924\pi\) | ||||
−0.654032 | + | 0.756467i | \(0.726924\pi\) | |||||||
\(458\) | 464.579 | 1.01437 | ||||||||
\(459\) | − | 37.3202i | − | 0.0813077i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −340.556 | −0.738734 | −0.369367 | − | 0.929284i | \(-0.620425\pi\) | ||||
−0.369367 | + | 0.929284i | \(0.620425\pi\) | |||||||
\(462\) | − | 54.3651i | − | 0.117673i | ||||||
\(463\) | 471.395i | 1.01813i | 0.860727 | + | 0.509066i | \(0.170009\pi\) | ||||
−0.860727 | + | 0.509066i | \(0.829991\pi\) | |||||||
\(464\) | 93.8844 | 0.202337 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −211.019 | −0.452831 | ||||||||
\(467\) | 245.681 | 0.526084 | 0.263042 | − | 0.964784i | \(-0.415274\pi\) | ||||
0.263042 | + | 0.964784i | \(0.415274\pi\) | |||||||
\(468\) | 99.5903i | 0.212800i | ||||||||
\(469\) | 47.8697 | 0.102068 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 839.455i | 1.78228i | ||||||||
\(472\) | − | 94.9493i | − | 0.201164i | ||||||
\(473\) | 230.911i | 0.488183i | ||||||||
\(474\) | 68.2800i | 0.144051i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 46.3439 | 0.0973610 | ||||||||
\(477\) | 365.582 | 0.766420 | ||||||||
\(478\) | 485.313i | 1.01530i | ||||||||
\(479\) | − | 203.940i | − | 0.425763i | −0.977078 | − | 0.212881i | \(-0.931715\pi\) | ||
0.977078 | − | 0.212881i | \(-0.0682848\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 80.9345i | − | 0.168263i | ||||||
\(482\) | 493.205 | 1.02325 | ||||||||
\(483\) | 16.3954 | + | 145.230i | 0.0339448 | + | 0.300684i | ||||
\(484\) | −168.805 | −0.348771 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −491.538 | −1.01139 | ||||||||
\(487\) | − | 681.456i | − | 1.39929i | −0.714489 | − | 0.699647i | \(-0.753341\pi\) | ||
0.714489 | − | 0.699647i | \(-0.246659\pi\) | |||||||
\(488\) | 284.447 | 0.582882 | ||||||||
\(489\) | −662.496 | −1.35480 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −329.666 | −0.671417 | −0.335709 | − | 0.941966i | \(-0.608976\pi\) | ||||
−0.335709 | + | 0.941966i | \(0.608976\pi\) | |||||||
\(492\) | 174.951i | 0.355591i | ||||||||
\(493\) | −368.645 | −0.747758 | ||||||||
\(494\) | 35.5850i | 0.0720344i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −81.9546 | −0.165231 | ||||||||
\(497\) | −35.6005 | −0.0716308 | ||||||||
\(498\) | 268.813 | 0.539785 | ||||||||
\(499\) | 993.708 | 1.99140 | 0.995700 | − | 0.0926377i | \(-0.0295298\pi\) | ||||
0.995700 | + | 0.0926377i | \(0.0295298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 208.876 | 0.416918 | ||||||||
\(502\) | 318.338 | 0.634140 | ||||||||
\(503\) | 880.515 | 1.75053 | 0.875264 | − | 0.483646i | \(-0.160688\pi\) | ||||
0.875264 | + | 0.483646i | \(0.160688\pi\) | |||||||
\(504\) | 39.8577i | 0.0790827i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −195.532 | + | 22.0741i | −0.386428 | + | 0.0436246i | ||||
\(507\) | − | 610.851i | − | 1.20483i | ||||||
\(508\) | − | 185.680i | − | 0.365511i | ||||||
\(509\) | 689.907 | 1.35542 | 0.677708 | − | 0.735331i | \(-0.262973\pi\) | ||||
0.677708 | + | 0.735331i | \(0.262973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 22.3980i | − | 0.0438318i | ||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 11.4687 | 0.0223561 | ||||||||
\(514\) | 556.680 | 1.08303 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 328.806i | − | 0.637221i | ||||||
\(517\) | −83.6494 | −0.161798 | ||||||||
\(518\) | − | 32.3913i | − | 0.0625315i | ||||||
\(519\) | 479.255 | 0.923419 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 408.559i | − | 0.784183i | −0.919926 | − | 0.392092i | \(-0.871752\pi\) | ||
0.919926 | − | 0.392092i | \(-0.128248\pi\) | |||||||
\(522\) | − | 317.050i | − | 0.607376i | ||||||
\(523\) | −516.837 | −0.988216 | −0.494108 | − | 0.869400i | \(-0.664505\pi\) | ||||
−0.494108 | + | 0.869400i | \(0.664505\pi\) | |||||||
\(524\) | −303.418 | −0.579042 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 187.695i | 0.356834i | ||||||||
\(527\) | 321.801 | 0.610629 | ||||||||
\(528\) | −104.226 | −0.197398 | ||||||||
\(529\) | 515.686 | − | 117.937i | 0.974831 | − | 0.222943i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −320.646 | −0.603853 | ||||||||
\(532\) | 14.2417i | 0.0267701i | ||||||||
\(533\) | 105.877i | 0.198644i | ||||||||
\(534\) | 676.367i | 1.26660i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 91.7737i | − | 0.171220i | ||||||
\(537\) | 1131.02i | 2.10618i | ||||||||
\(538\) | 619.589i | 1.15165i | ||||||||
\(539\) | 283.262i | 0.525533i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −825.026 | −1.52500 | −0.762501 | − | 0.646987i | \(-0.776029\pi\) | ||||
−0.762501 | + | 0.646987i | \(0.776029\pi\) | |||||||
\(542\) | − | 289.486i | − | 0.534107i | ||||||
\(543\) | −909.533 | −1.67501 | ||||||||
\(544\) | − | 88.8484i | − | 0.163324i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 46.8492i | 0.0858043i | ||||||||
\(547\) | − | 749.566i | − | 1.37032i | −0.728392 | − | 0.685161i | \(-0.759732\pi\) | ||
0.728392 | − | 0.685161i | \(-0.240268\pi\) | |||||||
\(548\) | 534.927 | 0.976145 | ||||||||
\(549\) | − | 960.583i | − | 1.74970i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 113.286i | − | 0.205601i | ||||||
\(552\) | 278.429 | − | 31.4324i | 0.504400 | − | 0.0569428i | ||||
\(553\) | 16.5377i | 0.0299054i | ||||||||
\(554\) | −245.796 | −0.443675 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 479.559 | 0.862516 | ||||||||
\(557\) | −406.149 | −0.729173 | −0.364586 | − | 0.931170i | \(-0.618790\pi\) | ||||
−0.364586 | + | 0.931170i | \(0.618790\pi\) | |||||||
\(558\) | 276.763i | 0.495991i | ||||||||
\(559\) | − | 198.988i | − | 0.355971i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 409.253 | 0.729506 | ||||||||
\(562\) | 203.089 | 0.361368 | ||||||||
\(563\) | −285.771 | −0.507587 | −0.253793 | − | 0.967258i | \(-0.581678\pi\) | ||||
−0.253793 | + | 0.967258i | \(0.581678\pi\) | |||||||
\(564\) | 119.113 | 0.211193 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 102.066i | 0.180328i | ||||||||
\(567\) | −111.727 | −0.197050 | ||||||||
\(568\) | 68.2517i | 0.120161i | ||||||||
\(569\) | 315.624i | 0.554699i | 0.960769 | + | 0.277349i | \(0.0894560\pi\) | ||||
−0.960769 | + | 0.277349i | \(0.910544\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 383.907i | 0.672342i | 0.941801 | + | 0.336171i | \(0.109132\pi\) | ||||
−0.941801 | + | 0.336171i | \(0.890868\pi\) | |||||||
\(572\) | −63.0759 | −0.110273 | ||||||||
\(573\) | −313.652 | −0.547385 | ||||||||
\(574\) | 42.3737i | 0.0738218i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 76.4133 | 0.132662 | ||||||||
\(577\) | − | 717.832i | − | 1.24408i | −0.782987 | − | 0.622038i | \(-0.786305\pi\) | ||
0.782987 | − | 0.622038i | \(-0.213695\pi\) | |||||||
\(578\) | − | 59.8374i | − | 0.103525i | ||||||
\(579\) | −855.186 | −1.47701 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 65.1075 | 0.112061 | ||||||||
\(582\) | −938.819 | −1.61309 | ||||||||
\(583\) | 231.543i | 0.397158i | ||||||||
\(584\) | −42.9405 | −0.0735283 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 175.644i | 0.299735i | ||||||||
\(587\) | − | 296.393i | − | 0.504928i | −0.967606 | − | 0.252464i | \(-0.918759\pi\) | ||
0.967606 | − | 0.252464i | \(-0.0812410\pi\) | |||||||
\(588\) | − | 403.352i | − | 0.685973i | ||||||
\(589\) | 98.8912i | 0.167897i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 121.486 | 0.205560 | ||||||||
\(592\) | −62.0992 | −0.104897 | ||||||||
\(593\) | − | 654.259i | − | 1.10330i | −0.834075 | − | 0.551652i | \(-0.813998\pi\) | ||
0.834075 | − | 0.551652i | \(-0.186002\pi\) | |||||||
\(594\) | 20.3287i | 0.0342235i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 403.293i | − | 0.676667i | ||||||
\(597\) | −923.881 | −1.54754 | ||||||||
\(598\) | 168.500 | − | 19.0224i | 0.281773 | − | 0.0318100i | ||||
\(599\) | −368.673 | −0.615480 | −0.307740 | − | 0.951470i | \(-0.599573\pi\) | ||||
−0.307740 | + | 0.951470i | \(0.599573\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 148.316 | 0.246782 | 0.123391 | − | 0.992358i | \(-0.460623\pi\) | ||||
0.123391 | + | 0.992358i | \(0.460623\pi\) | |||||||
\(602\) | − | 79.6381i | − | 0.132289i | ||||||
\(603\) | −309.922 | −0.513967 | ||||||||
\(604\) | −241.573 | −0.399956 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −358.535 | −0.591643 | ||||||||
\(607\) | 939.932i | 1.54849i | 0.632887 | + | 0.774244i | \(0.281870\pi\) | ||||
−0.632887 | + | 0.774244i | \(0.718130\pi\) | |||||||
\(608\) | 27.3036 | 0.0449072 | ||||||||
\(609\) | − | 149.146i | − | 0.244904i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 72.0850 | 0.117979 | ||||||||
\(612\) | −300.043 | −0.490267 | ||||||||
\(613\) | −602.963 | −0.983626 | −0.491813 | − | 0.870701i | \(-0.663666\pi\) | ||||
−0.491813 | + | 0.870701i | \(0.663666\pi\) | |||||||
\(614\) | −310.727 | −0.506069 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25.2440 | −0.0409805 | ||||||||
\(617\) | −885.697 | −1.43549 | −0.717745 | − | 0.696306i | \(-0.754826\pi\) | ||||
−0.717745 | + | 0.696306i | \(0.754826\pi\) | |||||||
\(618\) | −330.549 | −0.534869 | ||||||||
\(619\) | − | 85.9838i | − | 0.138908i | −0.997585 | − | 0.0694538i | \(-0.977874\pi\) | ||
0.997585 | − | 0.0694538i | \(-0.0221257\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.13072 | − | 54.3060i | −0.00987233 | − | 0.0874492i | ||||
\(622\) | − | 448.403i | − | 0.720905i | ||||||
\(623\) | 163.819i | 0.262951i | ||||||||
\(624\) | 89.8171 | 0.143938 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 685.404i | − | 1.09489i | ||||||
\(627\) | 125.765i | 0.200583i | ||||||||
\(628\) | 389.794 | 0.620692 | ||||||||
\(629\) | 243.837 | 0.387659 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 645.385i | − | 1.02280i | −0.859344 | − | 0.511398i | \(-0.829128\pi\) | ||
0.859344 | − | 0.511398i | \(-0.170872\pi\) | |||||||
\(632\) | 31.7053 | 0.0501666 | ||||||||
\(633\) | − | 1034.85i | − | 1.63483i | ||||||
\(634\) | 738.092 | 1.16418 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 329.706i | − | 0.518406i | ||||||
\(637\) | − | 244.102i | − | 0.383205i | ||||||
\(638\) | 200.805 | 0.314741 | ||||||||
\(639\) | 230.488 | 0.360701 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 140.119i | − | 0.218594i | −0.994009 | − | 0.109297i | \(-0.965140\pi\) | ||
0.994009 | − | 0.109297i | \(-0.0348599\pi\) | |||||||
\(642\) | −725.613 | −1.13024 | ||||||||
\(643\) | −1028.11 | −1.59892 | −0.799461 | − | 0.600718i | \(-0.794882\pi\) | ||||
−0.799461 | + | 0.600718i | \(0.794882\pi\) | |||||||
\(644\) | 67.4366 | − | 7.61306i | 0.104715 | − | 0.0118215i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −107.210 | −0.165959 | ||||||||
\(647\) | 1248.29i | 1.92934i | 0.263455 | + | 0.964672i | \(0.415138\pi\) | ||||
−0.263455 | + | 0.964672i | \(0.584862\pi\) | |||||||
\(648\) | 214.199i | 0.330553i | ||||||||
\(649\) | − | 203.082i | − | 0.312916i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 130.194i | 0.199992i | ||||||||
\(652\) | 307.625i | 0.471817i | ||||||||
\(653\) | 457.504i | 0.700618i | 0.936634 | + | 0.350309i | \(0.113923\pi\) | ||||
−0.936634 | + | 0.350309i | \(0.886077\pi\) | |||||||
\(654\) | 908.956i | 1.38984i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 81.2370 | 0.123837 | ||||||||
\(657\) | 145.011i | 0.220717i | ||||||||
\(658\) | 28.8496 | 0.0438444 | ||||||||
\(659\) | − | 173.014i | − | 0.262540i | −0.991347 | − | 0.131270i | \(-0.958095\pi\) | ||
0.991347 | − | 0.131270i | \(-0.0419055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 582.673i | − | 0.881502i | −0.897629 | − | 0.440751i | \(-0.854712\pi\) | ||
0.897629 | − | 0.440751i | \(-0.145288\pi\) | |||||||
\(662\) | − | 450.101i | − | 0.679911i | ||||||
\(663\) | −352.674 | −0.531937 | ||||||||
\(664\) | − | 124.821i | − | 0.187984i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 209.710i | 0.314880i | ||||||||
\(667\) | −536.428 | + | 60.5585i | −0.804240 | + | 0.0907924i | ||||
\(668\) | − | 96.9899i | − | 0.145194i | ||||||
\(669\) | −1108.67 | −1.65721 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 608.389 | 0.906690 | ||||||||
\(672\) | 35.9463 | 0.0534915 | ||||||||
\(673\) | 390.678i | 0.580502i | 0.956951 | + | 0.290251i | \(0.0937388\pi\) | ||||
−0.956951 | + | 0.290251i | \(0.906261\pi\) | |||||||
\(674\) | − | 164.810i | − | 0.244526i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −283.644 | −0.419592 | ||||||||
\(677\) | 952.947 | 1.40760 | 0.703801 | − | 0.710397i | \(-0.251485\pi\) | ||||
0.703801 | + | 0.710397i | \(0.251485\pi\) | |||||||
\(678\) | 215.228 | 0.317445 | ||||||||
\(679\) | −227.386 | −0.334883 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 458.286i | − | 0.672961i | ||||||
\(682\) | −175.289 | −0.257022 | ||||||||
\(683\) | − | 299.732i | − | 0.438847i | −0.975630 | − | 0.219423i | \(-0.929582\pi\) | ||
0.975630 | − | 0.219423i | \(-0.0704176\pi\) | |||||||
\(684\) | − | 92.2048i | − | 0.134802i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 199.928i | − | 0.291441i | ||||||
\(687\) | −1414.93 | −2.05958 | ||||||||
\(688\) | −152.679 | −0.221917 | ||||||||
\(689\) | − | 199.532i | − | 0.289597i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 165.585 | 0.239631 | 0.119815 | − | 0.992796i | \(-0.461770\pi\) | ||||
0.119815 | + | 0.992796i | \(0.461770\pi\) | |||||||
\(692\) | − | 222.538i | − | 0.321587i | ||||||
\(693\) | 85.2497i | 0.123015i | ||||||||
\(694\) | 142.432 | 0.205234 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −285.937 | −0.410829 | ||||||||
\(697\) | −318.984 | −0.457652 | ||||||||
\(698\) | − | 202.906i | − | 0.290696i | ||||||
\(699\) | 642.685 | 0.919436 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 831.750i | − | 1.18652i | −0.805011 | − | 0.593260i | \(-0.797841\pi\) | ||
0.805011 | − | 0.593260i | \(-0.202159\pi\) | |||||||
\(702\) | − | 17.5183i | − | 0.0249549i | ||||||
\(703\) | 74.9324i | 0.106590i | ||||||||
\(704\) | 48.3967i | 0.0687453i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −388.052 | −0.549649 | ||||||||
\(707\) | −86.8387 | −0.122827 | ||||||||
\(708\) | 289.180i | 0.408446i | ||||||||
\(709\) | − | 835.784i | − | 1.17882i | −0.807834 | − | 0.589410i | \(-0.799360\pi\) | ||
0.807834 | − | 0.589410i | \(-0.200640\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 107.070i | − | 0.150590i | ||||||
\(712\) | 314.066 | 0.441104 | ||||||||
\(713\) | 468.265 | − | 52.8634i | 0.656753 | − | 0.0741422i | ||||
\(714\) | −141.146 | −0.197683 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 525.180 | 0.733492 | ||||||||
\(717\) | − | 1478.08i | − | 2.06148i | ||||||
\(718\) | −674.397 | −0.939272 | ||||||||
\(719\) | −881.656 | −1.22623 | −0.613113 | − | 0.789996i | \(-0.710083\pi\) | ||||
−0.613113 | + | 0.789996i | \(0.710083\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −80.0602 | −0.111041 | ||||||||
\(722\) | 477.585i | 0.661475i | ||||||||
\(723\) | −1502.12 | −2.07762 | ||||||||
\(724\) | 422.335i | 0.583335i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 514.117 | 0.708150 | ||||||||
\(727\) | 531.577 | 0.731193 | 0.365596 | − | 0.930774i | \(-0.380865\pi\) | ||||
0.365596 | + | 0.930774i | \(0.380865\pi\) | |||||||
\(728\) | 21.7541 | 0.0298820 | ||||||||
\(729\) | 815.463 | 1.11861 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 599.505 | 0.820116 | ||||||||
\(732\) | −866.318 | −1.18349 | ||||||||
\(733\) | −18.4847 | −0.0252178 | −0.0126089 | − | 0.999921i | \(-0.504014\pi\) | ||||
−0.0126089 | + | 0.999921i | \(0.504014\pi\) | |||||||
\(734\) | 19.8441i | 0.0270356i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −14.5954 | − | 129.286i | −0.0198307 | − | 0.175661i | ||||
\(737\) | − | 196.290i | − | 0.266337i | ||||||
\(738\) | − | 274.339i | − | 0.371734i | ||||||
\(739\) | 960.371 | 1.29955 | 0.649777 | − | 0.760125i | \(-0.274862\pi\) | ||||
0.649777 | + | 0.760125i | \(0.274862\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 108.379i | − | 0.146260i | ||||||
\(742\) | − | 79.8562i | − | 0.107623i | ||||||
\(743\) | 248.966 | 0.335082 | 0.167541 | − | 0.985865i | \(-0.446417\pi\) | ||||
0.167541 | + | 0.985865i | \(0.446417\pi\) | |||||||
\(744\) | 249.603 | 0.335488 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 149.429i | − | 0.200307i | ||||||
\(747\) | −421.524 | −0.564289 | ||||||||
\(748\) | − | 190.034i | − | 0.254056i | ||||||
\(749\) | −175.746 | −0.234641 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.0757i | 0.0320582i | 0.999872 | + | 0.0160291i | \(0.00510244\pi\) | ||||
−0.999872 | + | 0.0160291i | \(0.994898\pi\) | |||||||
\(752\) | − | 55.3091i | − | 0.0735494i | ||||||
\(753\) | −969.539 | −1.28757 | ||||||||
\(754\) | −173.044 | −0.229501 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 7.01112i | − | 0.00927396i | ||||||
\(757\) | −914.334 | −1.20784 | −0.603920 | − | 0.797045i | \(-0.706395\pi\) | ||||
−0.603920 | + | 0.797045i | \(0.706395\pi\) | |||||||
\(758\) | 480.809 | 0.634312 | ||||||||
\(759\) | 595.518 | − | 67.2294i | 0.784609 | − | 0.0885762i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 313.770 | 0.412312 | 0.206156 | − | 0.978519i | \(-0.433905\pi\) | ||||
0.206156 | + | 0.978519i | \(0.433905\pi\) | |||||||
\(762\) | 565.511i | 0.742140i | ||||||||
\(763\) | 220.153i | 0.288536i | ||||||||
\(764\) | 145.642i | 0.190631i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 989.662i | 1.29199i | ||||||||
\(767\) | 175.007i | 0.228170i | ||||||||
\(768\) | − | 68.9146i | − | 0.0897326i | ||||||
\(769\) | 309.335i | 0.402257i | 0.979565 | + | 0.201128i | \(0.0644608\pi\) | ||||
−0.979565 | + | 0.201128i | \(0.935539\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1695.44 | −2.19901 | ||||||||
\(772\) | 397.099i | 0.514377i | ||||||||
\(773\) | 233.356 | 0.301884 | 0.150942 | − | 0.988543i | \(-0.451769\pi\) | ||||
0.150942 | + | 0.988543i | \(0.451769\pi\) | |||||||
\(774\) | 515.599i | 0.666149i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 435.934i | 0.561770i | ||||||||
\(777\) | 98.6518i | 0.126965i | ||||||||
\(778\) | −176.518 | −0.226887 | ||||||||
\(779\) | − | 98.0253i | − | 0.125835i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 145.980i | 0.186915i | ||||||||
\(782\) | 57.3101 | + | 507.653i | 0.0732866 | + | 0.649173i | ||||
\(783\) | 55.7703i | 0.0712265i | ||||||||
\(784\) | −187.294 | −0.238895 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 924.098 | 1.17570 | ||||||||
\(787\) | −690.751 | −0.877702 | −0.438851 | − | 0.898560i | \(-0.644614\pi\) | ||||
−0.438851 | + | 0.898560i | \(0.644614\pi\) | |||||||
\(788\) | − | 56.4111i | − | 0.0715876i | ||||||
\(789\) | − | 571.648i | − | 0.724522i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 52.1290 | 0.0659027 | ||||||||
\(792\) | 163.437 | 0.206360 | ||||||||
\(793\) | −524.280 | −0.661135 | ||||||||
\(794\) | 211.506 | 0.266381 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 428.997i | 0.538941i | ||||||||
\(797\) | 91.6732 | 0.115023 | 0.0575114 | − | 0.998345i | \(-0.481683\pi\) | ||||
0.0575114 | + | 0.998345i | \(0.481683\pi\) | |||||||
\(798\) | − | 43.3749i | − | 0.0543545i | ||||||
\(799\) | 217.176i | 0.271810i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1060.61i | − | 1.32410i | ||||||
\(802\) | 603.439 | 0.752418 | ||||||||
\(803\) | −91.8434 | −0.114375 | ||||||||
\(804\) | 279.508i | 0.347647i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 151.055 | 0.187414 | ||||||||
\(807\) | − | 1887.04i | − | 2.33833i | ||||||
\(808\) | 166.483i | 0.206044i | ||||||||
\(809\) | −1071.73 | −1.32476 | −0.662382 | − | 0.749166i | \(-0.730454\pi\) | ||||
−0.662382 | + | 0.749166i | \(0.730454\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −257.388 | −0.317371 | −0.158685 | − | 0.987329i | \(-0.550726\pi\) | ||||
−0.158685 | + | 0.987329i | \(0.550726\pi\) | |||||||
\(812\) | −69.2550 | −0.0852894 | ||||||||
\(813\) | 881.666i | 1.08446i | ||||||||
\(814\) | −132.821 | −0.163171 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 270.599i | 0.331616i | ||||||||
\(817\) | 184.231i | 0.225497i | ||||||||
\(818\) | − | 489.690i | − | 0.598643i | ||||||
\(819\) | − | 73.4640i | − | 0.0896996i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −349.772 | −0.426032 | −0.213016 | − | 0.977049i | \(-0.568329\pi\) | ||||
−0.213016 | + | 0.977049i | \(0.568329\pi\) | |||||||
\(822\) | −1629.19 | −1.98198 | ||||||||
\(823\) | − | 1438.73i | − | 1.74815i | −0.485789 | − | 0.874076i | \(-0.661468\pi\) | ||
0.485789 | − | 0.874076i | \(-0.338532\pi\) | |||||||
\(824\) | 153.488i | 0.186272i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 70.0405i | 0.0847948i | ||||||||
\(827\) | 996.093 | 1.20447 | 0.602233 | − | 0.798320i | \(-0.294278\pi\) | ||||
0.602233 | + | 0.798320i | \(0.294278\pi\) | |||||||
\(828\) | −436.603 | + | 49.2891i | −0.527299 | + | 0.0595279i | ||||
\(829\) | 234.343 | 0.282681 | 0.141341 | − | 0.989961i | \(-0.454859\pi\) | ||||
0.141341 | + | 0.989961i | \(0.454859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 748.603 | 0.900846 | ||||||||
\(832\) | − | 41.7059i | − | 0.0501273i | ||||||
\(833\) | 735.424 | 0.882862 | ||||||||
\(834\) | −1460.56 | −1.75127 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 58.3983 | 0.0698544 | ||||||||
\(837\) | − | 48.6836i | − | 0.0581644i | ||||||
\(838\) | −224.058 | −0.267372 | ||||||||
\(839\) | 742.848i | 0.885397i | 0.896670 | + | 0.442699i | \(0.145979\pi\) | ||||
−0.896670 | + | 0.442699i | \(0.854021\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −290.107 | −0.344955 | ||||||||
\(842\) | 25.5361 | 0.0303280 | ||||||||
\(843\) | −618.532 | −0.733727 | ||||||||
\(844\) | −480.523 | −0.569340 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −186.780 | −0.220781 | ||||||||
\(847\) | 124.521 | 0.147014 | ||||||||
\(848\) | −153.097 | −0.180539 | ||||||||
\(849\) | − | 310.854i | − | 0.366142i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 354.816 | − | 40.0560i | 0.416940 | − | 0.0470693i | ||||
\(852\) | − | 207.869i | − | 0.243978i | ||||||
\(853\) | − | 482.186i | − | 0.565283i | −0.959226 | − | 0.282642i | \(-0.908789\pi\) | ||
0.959226 | − | 0.282642i | \(-0.0912107\pi\) | |||||||
\(854\) | −209.826 | −0.245697 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 336.933i | 0.393613i | ||||||||
\(857\) | 685.909i | 0.800361i | 0.916436 | + | 0.400180i | \(0.131053\pi\) | ||||
−0.916436 | + | 0.400180i | \(0.868947\pi\) | |||||||
\(858\) | 192.106 | 0.223899 | ||||||||
\(859\) | −670.668 | −0.780754 | −0.390377 | − | 0.920655i | \(-0.627655\pi\) | ||||
−0.390377 | + | 0.920655i | \(0.627655\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 129.054i | − | 0.149889i | ||||||
\(862\) | 214.578 | 0.248931 | ||||||||
\(863\) | − | 891.818i | − | 1.03339i | −0.856169 | − | 0.516696i | \(-0.827162\pi\) | ||
0.856169 | − | 0.516696i | \(-0.172838\pi\) | |||||||
\(864\) | −13.4414 | −0.0155572 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 884.550i | 1.02142i | ||||||||
\(867\) | 182.242i | 0.210199i | ||||||||
\(868\) | 60.4548 | 0.0696484 | ||||||||
\(869\) | 67.8129 | 0.0780356 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 169.154i | 0.194206i | ||||||||
\(872\) | 422.067 | 0.484022 | ||||||||
\(873\) | 1472.16 | 1.68632 | ||||||||
\(874\) | −156.004 | + | 17.6117i | −0.178495 | + | 0.0201507i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 130.781 | 0.149293 | ||||||||
\(877\) | 181.676i | 0.207156i | 0.994621 | + | 0.103578i | \(0.0330291\pi\) | ||||
−0.994621 | + | 0.103578i | \(0.966971\pi\) | |||||||
\(878\) | − | 385.858i | − | 0.439473i | ||||||
\(879\) | − | 534.947i | − | 0.608586i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 316.887i | 0.359691i | 0.983695 | + | 0.179845i | \(0.0575597\pi\) | ||||
−0.983695 | + | 0.179845i | \(0.942440\pi\) | |||||||
\(882\) | 632.495i | 0.717115i | ||||||||
\(883\) | 1361.85i | 1.54230i | 0.636656 | + | 0.771148i | \(0.280317\pi\) | ||||
−0.636656 | + | 0.771148i | \(0.719683\pi\) | |||||||
\(884\) | 163.762i | 0.185251i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.88463 | 0.00889914 | ||||||||
\(887\) | 1628.63i | 1.83611i | 0.396449 | + | 0.918057i | \(0.370242\pi\) | ||||
−0.396449 | + | 0.918057i | \(0.629758\pi\) | |||||||
\(888\) | 189.131 | 0.212985 | ||||||||
\(889\) | 136.969i | 0.154071i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 458.139i | 0.514185i | ||||||||
\(892\) | 514.805i | 0.577136i | ||||||||
\(893\) | −66.7392 | −0.0747360 | ||||||||
\(894\) | 1228.28i | 1.37392i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 16.6914i | − | 0.0186288i | ||||||
\(897\) | −513.189 | + | 57.9350i | −0.572117 | + | 0.0645875i | ||||
\(898\) | − | 643.936i | − | 0.717078i | ||||||
\(899\) | −480.891 | −0.534918 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 601.146 | 0.667199 | ||||||||
\(902\) | 173.754 | 0.192632 | ||||||||
\(903\) | 242.548i | 0.268602i | ||||||||
\(904\) | − | 99.9395i | − | 0.110552i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 735.742 | 0.812077 | ||||||||
\(907\) | −1551.21 | −1.71026 | −0.855130 | − | 0.518413i | \(-0.826523\pi\) | ||||
−0.855130 | + | 0.518413i | \(0.826523\pi\) | |||||||
\(908\) | −212.802 | −0.234363 | ||||||||
\(909\) | 562.218 | 0.618502 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1672.31i | − | 1.83569i | −0.396937 | − | 0.917846i | \(-0.629927\pi\) | ||
0.396937 | − | 0.917846i | \(-0.370073\pi\) | |||||||
\(912\) | −83.1564 | −0.0911802 | ||||||||
\(913\) | − | 266.974i | − | 0.292414i | ||||||
\(914\) | − | 845.396i | − | 0.924941i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 657.014i | 0.717265i | ||||||||
\(917\) | 223.820 | 0.244079 | ||||||||
\(918\) | 52.7788 | 0.0574932 | ||||||||
\(919\) | 1670.00i | 1.81719i | 0.417673 | + | 0.908597i | \(0.362846\pi\) | ||||
−0.417673 | + | 0.908597i | \(0.637154\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 946.357 | 1.02753 | ||||||||
\(922\) | − | 481.619i | − | 0.522364i | ||||||
\(923\) | − | 125.799i | − | 0.136293i | ||||||
\(924\) | 76.8838 | 0.0832076 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −666.653 | −0.719928 | ||||||||
\(927\) | 518.332 | 0.559150 | ||||||||
\(928\) | 132.773i | 0.143074i | ||||||||
\(929\) | 877.260 | 0.944306 | 0.472153 | − | 0.881517i | \(-0.343477\pi\) | ||||
0.472153 | + | 0.881517i | \(0.343477\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 225.999i | 0.242749i | ||||||||
\(932\) | − | 298.426i | − | 0.320200i | ||||||
\(933\) | 1365.67i | 1.46374i | ||||||||
\(934\) | 347.445i | 0.371997i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −140.842 | −0.150472 | ||||||||
\(937\) | 726.689 | 0.775549 | 0.387774 | − | 0.921754i | \(-0.373244\pi\) | ||||
0.387774 | + | 0.921754i | \(0.373244\pi\) | |||||||
\(938\) | 67.6980i | 0.0721727i | ||||||||
\(939\) | 2087.48i | 2.22309i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 289.839i | − | 0.308011i | −0.988070 | − | 0.154006i | \(-0.950783\pi\) | ||
0.988070 | − | 0.154006i | \(-0.0492174\pi\) | |||||||
\(942\) | −1187.17 | −1.26026 | ||||||||
\(943\) | −464.164 | + | 52.4005i | −0.492221 | + | 0.0555679i | ||||
\(944\) | 134.279 | 0.142244 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −326.557 | −0.345198 | ||||||||
\(947\) | − | 1420.59i | − | 1.50010i | −0.661381 | − | 0.750050i | \(-0.730030\pi\) | ||
0.661381 | − | 0.750050i | \(-0.269970\pi\) | |||||||
\(948\) | −96.5624 | −0.101859 | ||||||||
\(949\) | 79.1462 | 0.0833996 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2247.95 | −2.36378 | ||||||||
\(952\) | 65.5401i | 0.0688446i | ||||||||
\(953\) | 1465.45 | 1.53772 | 0.768860 | − | 0.639418i | \(-0.220824\pi\) | ||||
0.768860 | + | 0.639418i | \(0.220824\pi\) | |||||||
\(954\) | 517.011i | 0.541941i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −686.336 | −0.717925 | ||||||||
\(957\) | −611.577 | −0.639056 | ||||||||
\(958\) | 288.415 | 0.301060 | ||||||||
\(959\) | −394.596 | −0.411466 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −541.215 | −0.563179 | ||||||||
\(962\) | 114.459 | 0.118980 | ||||||||
\(963\) | 1137.83 | 1.18155 | ||||||||
\(964\) | 697.497i | 0.723544i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −205.387 | + | 23.1865i | −0.212615 | + | 0.0240026i | ||||
\(967\) | − | 1536.47i | − | 1.58890i | −0.607328 | − | 0.794451i | \(-0.707759\pi\) | ||
0.607328 | − | 0.794451i | \(-0.292241\pi\) | |||||||
\(968\) | − | 238.726i | − | 0.246618i | ||||||
\(969\) | 326.520 | 0.336966 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1693.09i | 1.74366i | 0.489812 | + | 0.871828i | \(0.337065\pi\) | ||||
−0.489812 | + | 0.871828i | \(0.662935\pi\) | |||||||
\(972\) | − | 695.139i | − | 0.715164i | ||||||
\(973\) | −353.752 | −0.363569 | ||||||||
\(974\) | 963.724 | 0.989450 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 402.268i | 0.412160i | ||||||||
\(977\) | 1295.96 | 1.32647 | 0.663235 | − | 0.748411i | \(-0.269183\pi\) | ||||
0.663235 | + | 0.748411i | \(0.269183\pi\) | |||||||
\(978\) | − | 936.911i | − | 0.957986i | ||||||
\(979\) | 671.740 | 0.686150 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1425.33i | − | 1.45294i | ||||||
\(982\) | − | 466.218i | − | 0.474764i | ||||||
\(983\) | 1692.07 | 1.72133 | 0.860667 | − | 0.509168i | \(-0.170047\pi\) | ||||
0.860667 | + | 0.509168i | \(0.170047\pi\) | |||||||
\(984\) | −247.418 | −0.251441 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 521.343i | − | 0.528745i | ||||||
\(987\) | −87.8650 | −0.0890223 | ||||||||
\(988\) | −50.3248 | −0.0509360 | ||||||||
\(989\) | 872.361 | − | 98.4827i | 0.882063 | − | 0.0995780i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.3192 | 0.0457308 | 0.0228654 | − | 0.999739i | \(-0.492721\pi\) | ||||
0.0228654 | + | 0.999739i | \(0.492721\pi\) | |||||||
\(992\) | − | 115.901i | − | 0.116836i | ||||||
\(993\) | 1370.84i | 1.38050i | ||||||||
\(994\) | − | 50.3467i | − | 0.0506506i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 380.159i | 0.381685i | ||||||||
\(997\) | 1358.89i | 1.36298i | 0.731830 | + | 0.681488i | \(0.238667\pi\) | ||||
−0.731830 | + | 0.681488i | \(0.761333\pi\) | |||||||
\(998\) | 1405.32i | 1.40813i | ||||||||
\(999\) | − | 36.8889i | − | 0.0369258i |
(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 | 1150.3.c.c.1149.20 | 32 | ||
5.2 | odd | 4 | 1150.3.d.b.551.2 | 16 | |||
5.3 | odd | 4 | 230.3.d.a.91.16 | yes | 16 | ||
5.4 | even | 2 | inner | 1150.3.c.c.1149.13 | 32 | ||
15.8 | even | 4 | 2070.3.c.a.91.2 | 16 | |||
20.3 | even | 4 | 1840.3.k.d.321.4 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.c.c.1149.14 | 32 | ||
115.22 | even | 4 | 1150.3.d.b.551.1 | 16 | |||
115.68 | even | 4 | 230.3.d.a.91.15 | ✓ | 16 | ||
115.114 | odd | 2 | inner | 1150.3.c.c.1149.19 | 32 | ||
345.68 | odd | 4 | 2070.3.c.a.91.7 | 16 | |||
460.183 | odd | 4 | 1840.3.k.d.321.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.15 | ✓ | 16 | 115.68 | even | 4 | ||
230.3.d.a.91.16 | yes | 16 | 5.3 | odd | 4 | ||
1150.3.c.c.1149.13 | 32 | 5.4 | even | 2 | inner | ||
1150.3.c.c.1149.14 | 32 | 23.22 | odd | 2 | inner | ||
1150.3.c.c.1149.19 | 32 | 115.114 | odd | 2 | inner | ||
1150.3.c.c.1149.20 | 32 | 1.1 | even | 1 | trivial | ||
1150.3.d.b.551.1 | 16 | 115.22 | even | 4 | |||
1150.3.d.b.551.2 | 16 | 5.2 | odd | 4 | |||
1840.3.k.d.321.3 | 16 | 460.183 | odd | 4 | |||
1840.3.k.d.321.4 | 16 | 20.3 | even | 4 | |||
2070.3.c.a.91.2 | 16 | 15.8 | even | 4 | |||
2070.3.c.a.91.7 | 16 | 345.68 | odd | 4 |