Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,4,Mod(99,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("490.99");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(28.9109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 438 x^{18} + 80439 x^{16} + 8097428 x^{14} + 488971671 x^{12} + 18162509334 x^{10} + \cdots + 9871083181584 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{23}\cdot 5^{2}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.17 | ||
Root | \(-3.69313i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.4.c.g.99.4 |
$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000i | 0.707107i | ||||||||
\(3\) | 4.69313i | 0.903194i | 0.892222 | + | 0.451597i | \(0.149146\pi\) | ||||
−0.892222 | + | 0.451597i | \(0.850854\pi\) | |||||||
\(4\) | −4.00000 | −0.500000 | ||||||||
\(5\) | −1.54203 | − | 11.0735i | −0.137923 | − | 0.990443i | ||||
\(6\) | −9.38627 | −0.638655 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 8.00000i | − | 0.353553i | ||||||
\(9\) | 4.97448 | 0.184240 | ||||||||
\(10\) | 22.1470 | − | 3.08406i | 0.700349 | − | 0.0975265i | ||||
\(11\) | 1.37696 | 0.0377427 | 0.0188714 | − | 0.999822i | \(-0.493993\pi\) | ||||
0.0188714 | + | 0.999822i | \(0.493993\pi\) | |||||||
\(12\) | − | 18.7725i | − | 0.451597i | ||||||
\(13\) | 69.4841i | 1.48242i | 0.671275 | + | 0.741209i | \(0.265747\pi\) | ||||
−0.671275 | + | 0.741209i | \(0.734253\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 51.9694 | − | 7.23695i | 0.894562 | − | 0.124571i | ||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | − | 26.3126i | − | 0.375397i | −0.982227 | − | 0.187699i | \(-0.939897\pi\) | ||
0.982227 | − | 0.187699i | \(-0.0601028\pi\) | |||||||
\(18\) | 9.94897i | 0.130277i | ||||||||
\(19\) | 14.1726 | 0.171127 | 0.0855637 | − | 0.996333i | \(-0.472731\pi\) | ||||
0.0855637 | + | 0.996333i | \(0.472731\pi\) | |||||||
\(20\) | 6.16812 | + | 44.2940i | 0.0689616 | + | 0.495221i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.75393i | 0.0266881i | ||||||||
\(23\) | 29.6889i | 0.269155i | 0.990903 | + | 0.134577i | \(0.0429677\pi\) | ||||
−0.990903 | + | 0.134577i | \(0.957032\pi\) | |||||||
\(24\) | 37.5451 | 0.319327 | ||||||||
\(25\) | −120.244 | + | 34.1513i | −0.961954 | + | 0.273210i | ||||
\(26\) | −138.968 | −1.04823 | ||||||||
\(27\) | 150.061i | 1.06960i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 75.5596 | 0.483830 | 0.241915 | − | 0.970297i | \(-0.422224\pi\) | ||||
0.241915 | + | 0.970297i | \(0.422224\pi\) | |||||||
\(30\) | 14.4739 | + | 103.939i | 0.0880853 | + | 0.632551i | ||||
\(31\) | −245.058 | −1.41980 | −0.709898 | − | 0.704304i | \(-0.751259\pi\) | ||||
−0.709898 | + | 0.704304i | \(0.751259\pi\) | |||||||
\(32\) | 32.0000i | 0.176777i | ||||||||
\(33\) | 6.46227i | 0.0340890i | ||||||||
\(34\) | 52.6253 | 0.265446 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −19.8979 | −0.0921201 | ||||||||
\(37\) | 245.100i | 1.08903i | 0.838750 | + | 0.544517i | \(0.183287\pi\) | ||||
−0.838750 | + | 0.544517i | \(0.816713\pi\) | |||||||
\(38\) | 28.3452i | 0.121005i | ||||||||
\(39\) | −326.098 | −1.33891 | ||||||||
\(40\) | −88.5879 | + | 12.3362i | −0.350174 | + | 0.0487632i | ||||
\(41\) | −238.438 | −0.908239 | −0.454119 | − | 0.890941i | \(-0.650046\pi\) | ||||
−0.454119 | + | 0.890941i | \(0.650046\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 194.636i | 0.690271i | 0.938553 | + | 0.345136i | \(0.112167\pi\) | ||||
−0.938553 | + | 0.345136i | \(0.887833\pi\) | |||||||
\(44\) | −5.50785 | −0.0188714 | ||||||||
\(45\) | −7.67080 | − | 55.0849i | −0.0254110 | − | 0.182479i | ||||
\(46\) | −59.3777 | −0.190321 | ||||||||
\(47\) | 375.460i | 1.16524i | 0.812743 | + | 0.582622i | \(0.197973\pi\) | ||||
−0.812743 | + | 0.582622i | \(0.802027\pi\) | |||||||
\(48\) | 75.0902i | 0.225799i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −68.3026 | − | 240.489i | −0.193189 | − | 0.680204i | ||||
\(51\) | 123.489 | 0.339057 | ||||||||
\(52\) | − | 277.936i | − | 0.741209i | ||||||
\(53\) | − | 511.930i | − | 1.32677i | −0.748277 | − | 0.663387i | \(-0.769118\pi\) | ||
0.748277 | − | 0.663387i | \(-0.230882\pi\) | |||||||
\(54\) | −300.121 | −0.756321 | ||||||||
\(55\) | −2.12332 | − | 15.2478i | −0.00520560 | − | 0.0373820i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 66.5140i | 0.154561i | ||||||||
\(58\) | 151.119i | 0.342120i | ||||||||
\(59\) | −656.810 | −1.44931 | −0.724655 | − | 0.689111i | \(-0.758001\pi\) | ||||
−0.724655 | + | 0.689111i | \(0.758001\pi\) | |||||||
\(60\) | −207.878 | + | 28.9478i | −0.447281 | + | 0.0622857i | ||||
\(61\) | −809.766 | −1.69967 | −0.849836 | − | 0.527047i | \(-0.823299\pi\) | ||||
−0.849836 | + | 0.527047i | \(0.823299\pi\) | |||||||
\(62\) | − | 490.116i | − | 1.00395i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −64.0000 | −0.125000 | ||||||||
\(65\) | 769.431 | − | 107.146i | 1.46825 | − | 0.204460i | ||||
\(66\) | −12.9245 | −0.0241046 | ||||||||
\(67\) | − | 220.579i | − | 0.402210i | −0.979570 | − | 0.201105i | \(-0.935547\pi\) | ||
0.979570 | − | 0.201105i | \(-0.0644532\pi\) | |||||||
\(68\) | 105.251i | 0.187699i | ||||||||
\(69\) | −139.334 | −0.243099 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1106.75 | 1.84995 | 0.924976 | − | 0.380027i | \(-0.124085\pi\) | ||||
0.924976 | + | 0.380027i | \(0.124085\pi\) | |||||||
\(72\) | − | 39.7959i | − | 0.0651387i | ||||||
\(73\) | 898.681i | 1.44086i | 0.693528 | + | 0.720429i | \(0.256055\pi\) | ||||
−0.693528 | + | 0.720429i | \(0.743945\pi\) | |||||||
\(74\) | −490.201 | −0.770063 | ||||||||
\(75\) | −160.277 | − | 564.323i | −0.246762 | − | 0.868832i | ||||
\(76\) | −56.6905 | −0.0855637 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 652.197i | − | 0.946753i | ||||||
\(79\) | 708.811 | 1.00946 | 0.504731 | − | 0.863277i | \(-0.331592\pi\) | ||||
0.504731 | + | 0.863277i | \(0.331592\pi\) | |||||||
\(80\) | −24.6725 | − | 177.176i | −0.0344808 | − | 0.247611i | ||||
\(81\) | −569.943 | −0.781815 | ||||||||
\(82\) | − | 476.876i | − | 0.642222i | ||||||
\(83\) | − | 419.279i | − | 0.554481i | −0.960801 | − | 0.277240i | \(-0.910580\pi\) | ||
0.960801 | − | 0.277240i | \(-0.0894198\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −291.373 | + | 40.5749i | −0.371810 | + | 0.0517760i | ||||
\(86\) | −389.271 | −0.488096 | ||||||||
\(87\) | 354.612i | 0.436993i | ||||||||
\(88\) | − | 11.0157i | − | 0.0133441i | ||||||
\(89\) | −393.760 | −0.468972 | −0.234486 | − | 0.972119i | \(-0.575341\pi\) | ||||
−0.234486 | + | 0.972119i | \(0.575341\pi\) | |||||||
\(90\) | 110.170 | − | 15.3416i | 0.129032 | − | 0.0179683i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 118.755i | − | 0.134577i | ||||||
\(93\) | − | 1150.09i | − | 1.28235i | ||||||
\(94\) | −750.920 | −0.823952 | ||||||||
\(95\) | −21.8546 | − | 156.940i | −0.0236024 | − | 0.169492i | ||||
\(96\) | −150.180 | −0.159664 | ||||||||
\(97\) | − | 152.826i | − | 0.159971i | −0.996796 | − | 0.0799853i | \(-0.974513\pi\) | ||
0.996796 | − | 0.0799853i | \(-0.0254873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.84968 | 0.00695372 | ||||||||
\(100\) | 480.977 | − | 136.605i | 0.480977 | − | 0.136605i | ||||
\(101\) | 351.090 | 0.345888 | 0.172944 | − | 0.984932i | \(-0.444672\pi\) | ||||
0.172944 | + | 0.984932i | \(0.444672\pi\) | |||||||
\(102\) | 246.978i | 0.239749i | ||||||||
\(103\) | − | 375.433i | − | 0.359151i | −0.983744 | − | 0.179576i | \(-0.942528\pi\) | ||
0.983744 | − | 0.179576i | \(-0.0574724\pi\) | |||||||
\(104\) | 555.873 | 0.524114 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1023.86 | 0.938170 | ||||||||
\(107\) | − | 514.577i | − | 0.464917i | −0.972606 | − | 0.232458i | \(-0.925323\pi\) | ||
0.972606 | − | 0.232458i | \(-0.0746769\pi\) | |||||||
\(108\) | − | 600.242i | − | 0.534799i | ||||||
\(109\) | −1795.57 | −1.57784 | −0.788918 | − | 0.614499i | \(-0.789358\pi\) | ||||
−0.788918 | + | 0.614499i | \(0.789358\pi\) | |||||||
\(110\) | 30.4956 | − | 4.24663i | 0.0264331 | − | 0.00368091i | ||||
\(111\) | −1150.29 | −0.983609 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 925.436i | 0.770422i | 0.922828 | + | 0.385211i | \(0.125871\pi\) | ||||
−0.922828 | + | 0.385211i | \(0.874129\pi\) | |||||||
\(114\) | −133.028 | −0.109291 | ||||||||
\(115\) | 328.759 | − | 45.7811i | 0.266582 | − | 0.0371227i | ||||
\(116\) | −302.239 | −0.241915 | ||||||||
\(117\) | 345.648i | 0.273121i | ||||||||
\(118\) | − | 1313.62i | − | 1.02482i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −57.8956 | − | 415.755i | −0.0440427 | − | 0.316276i | ||||
\(121\) | −1329.10 | −0.998575 | ||||||||
\(122\) | − | 1619.53i | − | 1.20185i | ||||||
\(123\) | − | 1119.02i | − | 0.820316i | ||||||
\(124\) | 980.231 | 0.709898 | ||||||||
\(125\) | 563.594 | + | 1278.86i | 0.403275 | + | 0.915079i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2780.44i | 1.94271i | 0.237636 | + | 0.971354i | \(0.423627\pi\) | ||||
−0.237636 | + | 0.971354i | \(0.576373\pi\) | |||||||
\(128\) | − | 128.000i | − | 0.0883883i | ||||||
\(129\) | −913.452 | −0.623449 | ||||||||
\(130\) | 214.293 | + | 1538.86i | 0.144575 | + | 1.03821i | ||||
\(131\) | −1747.06 | −1.16520 | −0.582601 | − | 0.812759i | \(-0.697965\pi\) | ||||
−0.582601 | + | 0.812759i | \(0.697965\pi\) | |||||||
\(132\) | − | 25.8491i | − | 0.0170445i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 441.159 | 0.284405 | ||||||||
\(135\) | 1661.69 | − | 231.398i | 1.05938 | − | 0.147523i | ||||
\(136\) | −210.501 | −0.132723 | ||||||||
\(137\) | 2067.80i | 1.28952i | 0.764386 | + | 0.644759i | \(0.223042\pi\) | ||||
−0.764386 | + | 0.644759i | \(0.776958\pi\) | |||||||
\(138\) | − | 278.668i | − | 0.171897i | ||||||
\(139\) | 2336.91 | 1.42600 | 0.713001 | − | 0.701163i | \(-0.247336\pi\) | ||||
0.713001 | + | 0.701163i | \(0.247336\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1762.08 | −1.05244 | ||||||||
\(142\) | 2213.49i | 1.30811i | ||||||||
\(143\) | 95.6770i | 0.0559504i | ||||||||
\(144\) | 79.5918 | 0.0460600 | ||||||||
\(145\) | −116.515 | − | 836.709i | −0.0667314 | − | 0.479206i | ||||
\(146\) | −1797.36 | −1.01884 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 980.401i | − | 0.544517i | ||||||
\(149\) | −2230.70 | −1.22648 | −0.613241 | − | 0.789896i | \(-0.710135\pi\) | ||||
−0.613241 | + | 0.789896i | \(0.710135\pi\) | |||||||
\(150\) | 1128.65 | − | 320.553i | 0.614357 | − | 0.174487i | ||||
\(151\) | 2572.46 | 1.38638 | 0.693192 | − | 0.720753i | \(-0.256204\pi\) | ||||
0.693192 | + | 0.720753i | \(0.256204\pi\) | |||||||
\(152\) | − | 113.381i | − | 0.0605027i | ||||||
\(153\) | − | 130.892i | − | 0.0691633i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 377.886 | + | 2713.64i | 0.195823 | + | 1.40623i | ||||
\(156\) | 1304.39 | 0.669455 | ||||||||
\(157\) | 1083.02i | 0.550535i | 0.961368 | + | 0.275268i | \(0.0887664\pi\) | ||||
−0.961368 | + | 0.275268i | \(0.911234\pi\) | |||||||
\(158\) | 1417.62i | 0.713797i | ||||||||
\(159\) | 2402.56 | 1.19833 | ||||||||
\(160\) | 354.352 | − | 49.3449i | 0.175087 | − | 0.0243816i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1139.89i | − | 0.552827i | ||||||
\(163\) | 1368.56i | 0.657633i | 0.944394 | + | 0.328816i | \(0.106650\pi\) | ||||
−0.944394 | + | 0.328816i | \(0.893350\pi\) | |||||||
\(164\) | 953.753 | 0.454119 | ||||||||
\(165\) | 71.5599 | − | 9.96501i | 0.0337632 | − | 0.00470167i | ||||
\(166\) | 838.559 | 0.392077 | ||||||||
\(167\) | 2268.75i | 1.05126i | 0.850712 | + | 0.525632i | \(0.176171\pi\) | ||||
−0.850712 | + | 0.525632i | \(0.823829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2631.04 | −1.19756 | ||||||||
\(170\) | −81.1497 | − | 582.746i | −0.0366112 | − | 0.262909i | ||||
\(171\) | 70.5015 | 0.0315285 | ||||||||
\(172\) | − | 778.543i | − | 0.345136i | ||||||
\(173\) | 2365.83i | 1.03972i | 0.854252 | + | 0.519859i | \(0.174015\pi\) | ||||
−0.854252 | + | 0.519859i | \(0.825985\pi\) | |||||||
\(174\) | −709.223 | −0.309000 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22.0314 | 0.00943568 | ||||||||
\(177\) | − | 3082.50i | − | 1.30901i | ||||||
\(178\) | − | 787.521i | − | 0.331613i | ||||||
\(179\) | 2007.64 | 0.838313 | 0.419156 | − | 0.907914i | \(-0.362326\pi\) | ||||
0.419156 | + | 0.907914i | \(0.362326\pi\) | |||||||
\(180\) | 30.6832 | + | 220.340i | 0.0127055 | + | 0.0912397i | ||||
\(181\) | −2030.01 | −0.833645 | −0.416822 | − | 0.908988i | \(-0.636856\pi\) | ||||
−0.416822 | + | 0.908988i | \(0.636856\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3800.34i | − | 1.53513i | ||||||
\(184\) | 237.511 | 0.0951605 | ||||||||
\(185\) | 2714.12 | − | 377.952i | 1.07863 | − | 0.150203i | ||||
\(186\) | 2300.18 | 0.906760 | ||||||||
\(187\) | − | 36.2315i | − | 0.0141685i | ||||||
\(188\) | − | 1501.84i | − | 0.582622i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 313.881 | − | 43.7092i | 0.119849 | − | 0.0166895i | ||||
\(191\) | −1509.50 | −0.571849 | −0.285925 | − | 0.958252i | \(-0.592301\pi\) | ||||
−0.285925 | + | 0.958252i | \(0.592301\pi\) | |||||||
\(192\) | − | 300.361i | − | 0.112899i | ||||||
\(193\) | − | 4067.79i | − | 1.51713i | −0.651599 | − | 0.758564i | \(-0.725901\pi\) | ||
0.651599 | − | 0.758564i | \(-0.274099\pi\) | |||||||
\(194\) | 305.652 | 0.113116 | ||||||||
\(195\) | 502.853 | + | 3611.05i | 0.184667 | + | 1.32611i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 919.891i | − | 0.332688i | −0.986068 | − | 0.166344i | \(-0.946804\pi\) | ||
0.986068 | − | 0.166344i | \(-0.0531962\pi\) | |||||||
\(198\) | 13.6994i | 0.00491703i | ||||||||
\(199\) | −1769.06 | −0.630177 | −0.315088 | − | 0.949062i | \(-0.602034\pi\) | ||||
−0.315088 | + | 0.949062i | \(0.602034\pi\) | |||||||
\(200\) | 273.210 | + | 961.954i | 0.0965944 | + | 0.340102i | ||||
\(201\) | 1035.21 | 0.363274 | ||||||||
\(202\) | 702.179i | 0.244580i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −493.955 | −0.169528 | ||||||||
\(205\) | 367.679 | + | 2640.34i | 0.125267 | + | 0.899559i | ||||
\(206\) | 750.867 | 0.253958 | ||||||||
\(207\) | 147.687i | 0.0495891i | ||||||||
\(208\) | 1111.75i | 0.370604i | ||||||||
\(209\) | 19.5152 | 0.00645881 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1377.05 | −0.449290 | −0.224645 | − | 0.974441i | \(-0.572122\pi\) | ||||
−0.224645 | + | 0.974441i | \(0.572122\pi\) | |||||||
\(212\) | 2047.72i | 0.663387i | ||||||||
\(213\) | 5194.11i | 1.67087i | ||||||||
\(214\) | 1029.15 | 0.328746 | ||||||||
\(215\) | 2155.30 | − | 300.134i | 0.683674 | − | 0.0952045i | ||||
\(216\) | 1200.48 | 0.378160 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 3591.13i | − | 1.11570i | ||||||
\(219\) | −4217.63 | −1.30138 | ||||||||
\(220\) | 8.49326 | + | 60.9911i | 0.00260280 | + | 0.0186910i | ||||
\(221\) | 1828.31 | 0.556495 | ||||||||
\(222\) | − | 2300.58i | − | 0.695517i | ||||||
\(223\) | − | 5623.92i | − | 1.68881i | −0.535702 | − | 0.844407i | \(-0.679953\pi\) | ||
0.535702 | − | 0.844407i | \(-0.320047\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −598.153 | + | 169.885i | −0.177231 | + | 0.0503363i | ||||
\(226\) | −1850.87 | −0.544771 | ||||||||
\(227\) | 2236.97i | 0.654066i | 0.945013 | + | 0.327033i | \(0.106049\pi\) | ||||
−0.945013 | + | 0.327033i | \(0.893951\pi\) | |||||||
\(228\) | − | 266.056i | − | 0.0772806i | ||||||
\(229\) | 5538.87 | 1.59833 | 0.799167 | − | 0.601108i | \(-0.205274\pi\) | ||||
0.799167 | + | 0.601108i | \(0.205274\pi\) | |||||||
\(230\) | 91.5622 | + | 657.519i | 0.0262497 | + | 0.188502i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 604.477i | − | 0.171060i | ||||||
\(233\) | − | 1190.21i | − | 0.334649i | −0.985902 | − | 0.167325i | \(-0.946487\pi\) | ||
0.985902 | − | 0.167325i | \(-0.0535128\pi\) | |||||||
\(234\) | −691.295 | −0.193126 | ||||||||
\(235\) | 4157.65 | − | 578.970i | 1.15411 | − | 0.160714i | ||||
\(236\) | 2627.24 | 0.724655 | ||||||||
\(237\) | 3326.55i | 0.911740i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1602.92 | 0.433824 | 0.216912 | − | 0.976191i | \(-0.430401\pi\) | ||||
0.216912 | + | 0.976191i | \(0.430401\pi\) | |||||||
\(240\) | 831.510 | − | 115.791i | 0.223641 | − | 0.0311429i | ||||
\(241\) | 4523.89 | 1.20917 | 0.604583 | − | 0.796542i | \(-0.293340\pi\) | ||||
0.604583 | + | 0.796542i | \(0.293340\pi\) | |||||||
\(242\) | − | 2658.21i | − | 0.706099i | ||||||
\(243\) | 1376.81i | 0.363468i | ||||||||
\(244\) | 3239.07 | 0.849836 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2238.05 | 0.580051 | ||||||||
\(247\) | 984.771i | 0.253682i | ||||||||
\(248\) | 1960.46i | 0.501974i | ||||||||
\(249\) | 1967.74 | 0.500804 | ||||||||
\(250\) | −2557.72 | + | 1127.19i | −0.647058 | + | 0.285159i | ||||
\(251\) | 6421.20 | 1.61475 | 0.807376 | − | 0.590038i | \(-0.200887\pi\) | ||||
0.807376 | + | 0.590038i | \(0.200887\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 40.8805i | 0.0101586i | ||||||||
\(254\) | −5560.88 | −1.37370 | ||||||||
\(255\) | −190.423 | − | 1367.45i | −0.0467638 | − | 0.335816i | ||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4221.71i | 1.02468i | 0.858782 | + | 0.512341i | \(0.171221\pi\) | ||||
−0.858782 | + | 0.512341i | \(0.828779\pi\) | |||||||
\(258\) | − | 1826.90i | − | 0.440845i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3077.73 | + | 428.586i | −0.734125 | + | 0.102230i | ||||
\(261\) | 375.870 | 0.0891410 | ||||||||
\(262\) | − | 3494.12i | − | 0.823922i | ||||||
\(263\) | − | 6969.60i | − | 1.63408i | −0.576579 | − | 0.817041i | \(-0.695613\pi\) | ||
0.576579 | − | 0.817041i | \(-0.304387\pi\) | |||||||
\(264\) | 51.6982 | 0.0120523 | ||||||||
\(265\) | −5668.85 | + | 789.411i | −1.31409 | + | 0.182993i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1847.97i | − | 0.423573i | ||||||
\(268\) | 882.317i | 0.201105i | ||||||||
\(269\) | 757.838 | 0.171770 | 0.0858851 | − | 0.996305i | \(-0.472628\pi\) | ||||
0.0858851 | + | 0.996305i | \(0.472628\pi\) | |||||||
\(270\) | 462.795 | + | 3323.39i | 0.104314 | + | 0.749092i | ||||
\(271\) | 1198.66 | 0.268684 | 0.134342 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134342 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(272\) | − | 421.002i | − | 0.0938493i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4135.60 | −0.911828 | ||||||||
\(275\) | −165.572 | + | 47.0250i | −0.0363068 | + | 0.0103117i | ||||
\(276\) | 557.335 | 0.121549 | ||||||||
\(277\) | 5216.82i | 1.13158i | 0.824549 | + | 0.565791i | \(0.191429\pi\) | ||||
−0.824549 | + | 0.565791i | \(0.808571\pi\) | |||||||
\(278\) | 4673.82i | 1.00834i | ||||||||
\(279\) | −1219.04 | −0.261584 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2533.29 | 0.537805 | 0.268902 | − | 0.963167i | \(-0.413339\pi\) | ||||
0.268902 | + | 0.963167i | \(0.413339\pi\) | |||||||
\(282\) | − | 3524.17i | − | 0.744189i | ||||||
\(283\) | − | 2453.49i | − | 0.515353i | −0.966231 | − | 0.257676i | \(-0.917043\pi\) | ||
0.966231 | − | 0.257676i | \(-0.0829569\pi\) | |||||||
\(284\) | −4426.98 | −0.924976 | ||||||||
\(285\) | 736.542 | − | 102.566i | 0.153084 | − | 0.0213176i | ||||
\(286\) | −191.354 | −0.0395629 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 159.184i | 0.0325694i | ||||||||
\(289\) | 4220.64 | 0.859077 | ||||||||
\(290\) | 1673.42 | − | 233.030i | 0.338850 | − | 0.0471862i | ||||
\(291\) | 717.233 | 0.144484 | ||||||||
\(292\) | − | 3594.73i | − | 0.720429i | ||||||
\(293\) | − | 8109.93i | − | 1.61702i | −0.588482 | − | 0.808510i | \(-0.700274\pi\) | ||
0.588482 | − | 0.808510i | \(-0.299726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1012.82 | + | 7273.17i | 0.199894 | + | 1.43546i | ||||
\(296\) | 1960.80 | 0.385032 | ||||||||
\(297\) | 206.628i | 0.0403696i | ||||||||
\(298\) | − | 4461.40i | − | 0.867254i | ||||||
\(299\) | −2062.90 | −0.398999 | ||||||||
\(300\) | 641.106 | + | 2257.29i | 0.123381 | + | 0.434416i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5144.92i | 0.980321i | ||||||||
\(303\) | 1647.71i | 0.312404i | ||||||||
\(304\) | 226.762 | 0.0427819 | ||||||||
\(305\) | 1248.68 | + | 8966.94i | 0.234424 | + | 1.68343i | ||||
\(306\) | 261.784 | 0.0489058 | ||||||||
\(307\) | 2741.20i | 0.509605i | 0.966993 | + | 0.254803i | \(0.0820105\pi\) | ||||
−0.966993 | + | 0.254803i | \(0.917990\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1761.96 | 0.324383 | ||||||||
\(310\) | −5427.29 | + | 755.772i | −0.994353 | + | 0.138468i | ||||
\(311\) | 5851.31 | 1.06687 | 0.533437 | − | 0.845840i | \(-0.320900\pi\) | ||||
0.533437 | + | 0.845840i | \(0.320900\pi\) | |||||||
\(312\) | 2608.79i | 0.473376i | ||||||||
\(313\) | 3252.21i | 0.587302i | 0.955913 | + | 0.293651i | \(0.0948704\pi\) | ||||
−0.955913 | + | 0.293651i | \(0.905130\pi\) | |||||||
\(314\) | −2166.03 | −0.389287 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2835.24 | −0.504731 | ||||||||
\(317\) | 9.59340i | 0.00169974i | 1.00000 | 0.000849872i | \(0.000270523\pi\) | |||||
−1.00000 | 0.000849872i | \(0.999729\pi\) | ||||||||
\(318\) | 4805.11i | 0.847350i | ||||||||
\(319\) | 104.043 | 0.0182611 | ||||||||
\(320\) | 98.6899 | + | 708.703i | 0.0172404 | + | 0.123805i | ||||
\(321\) | 2414.98 | 0.419910 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 372.919i | − | 0.0642408i | ||||||
\(324\) | 2279.77 | 0.390908 | ||||||||
\(325\) | −2372.97 | − | 8355.07i | −0.405012 | − | 1.42602i | ||||
\(326\) | −2737.13 | −0.465017 | ||||||||
\(327\) | − | 8426.84i | − | 1.42509i | ||||||
\(328\) | 1907.51i | 0.321111i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 19.9300 | + | 143.120i | 0.00332458 | + | 0.0238742i | ||||
\(331\) | 5067.12 | 0.841433 | 0.420716 | − | 0.907192i | \(-0.361779\pi\) | ||||
0.420716 | + | 0.907192i | \(0.361779\pi\) | |||||||
\(332\) | 1677.12i | 0.277240i | ||||||||
\(333\) | 1219.25i | 0.200644i | ||||||||
\(334\) | −4537.50 | −0.743355 | ||||||||
\(335\) | −2442.58 | + | 340.140i | −0.398366 | + | 0.0554741i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3099.47i | − | 0.501006i | −0.968116 | − | 0.250503i | \(-0.919404\pi\) | ||
0.968116 | − | 0.250503i | \(-0.0805960\pi\) | |||||||
\(338\) | − | 5262.08i | − | 0.846803i | ||||||
\(339\) | −4343.20 | −0.695841 | ||||||||
\(340\) | 1165.49 | − | 162.299i | 0.185905 | − | 0.0258880i | ||||
\(341\) | −337.435 | −0.0535870 | ||||||||
\(342\) | 141.003i | 0.0222940i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1557.09 | 0.244048 | ||||||||
\(345\) | 214.857 | + | 1542.91i | 0.0335290 | + | 0.240776i | ||||
\(346\) | −4731.67 | −0.735191 | ||||||||
\(347\) | 5206.13i | 0.805417i | 0.915328 | + | 0.402709i | \(0.131931\pi\) | ||||
−0.915328 | + | 0.402709i | \(0.868069\pi\) | |||||||
\(348\) | − | 1418.45i | − | 0.218496i | ||||||
\(349\) | −4727.17 | −0.725043 | −0.362521 | − | 0.931975i | \(-0.618084\pi\) | ||||
−0.362521 | + | 0.931975i | \(0.618084\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10426.8 | −1.58559 | ||||||||
\(352\) | 44.0628i | 0.00667203i | ||||||||
\(353\) | 6737.46i | 1.01586i | 0.861398 | + | 0.507930i | \(0.169589\pi\) | ||||
−0.861398 | + | 0.507930i | \(0.830411\pi\) | |||||||
\(354\) | 6164.99 | 0.925609 | ||||||||
\(355\) | −1706.63 | − | 12255.5i | −0.255151 | − | 1.83227i | ||||
\(356\) | 1575.04 | 0.234486 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4015.28i | 0.592777i | ||||||||
\(359\) | −1429.57 | −0.210167 | −0.105083 | − | 0.994463i | \(-0.533511\pi\) | ||||
−0.105083 | + | 0.994463i | \(0.533511\pi\) | |||||||
\(360\) | −440.679 | + | 61.3664i | −0.0645162 | + | 0.00898415i | ||||
\(361\) | −6658.14 | −0.970715 | ||||||||
\(362\) | − | 4060.03i | − | 0.589476i | ||||||
\(363\) | − | 6237.66i | − | 0.901908i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9951.54 | − | 1385.79i | 1.42709 | − | 0.198728i | ||||
\(366\) | 7600.69 | 1.08550 | ||||||||
\(367\) | − | 10595.2i | − | 1.50699i | −0.657455 | − | 0.753493i | \(-0.728367\pi\) | ||
0.657455 | − | 0.753493i | \(-0.271633\pi\) | |||||||
\(368\) | 475.022i | 0.0672887i | ||||||||
\(369\) | −1186.11 | −0.167334 | ||||||||
\(370\) | 755.904 | + | 5428.23i | 0.106210 | + | 0.762704i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 4600.36i | 0.641176i | ||||||||
\(373\) | − | 12340.9i | − | 1.71311i | −0.516057 | − | 0.856554i | \(-0.672601\pi\) | ||
0.516057 | − | 0.856554i | \(-0.327399\pi\) | |||||||
\(374\) | 72.4631 | 0.0100187 | ||||||||
\(375\) | −6001.87 | + | 2645.02i | −0.826494 | + | 0.364236i | ||||
\(376\) | 3003.68 | 0.411976 | ||||||||
\(377\) | 5250.19i | 0.717238i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2953.93 | 0.400352 | 0.200176 | − | 0.979760i | \(-0.435849\pi\) | ||||
0.200176 | + | 0.979760i | \(0.435849\pi\) | |||||||
\(380\) | 87.4183 | + | 627.761i | 0.0118012 | + | 0.0847460i | ||||
\(381\) | −13049.0 | −1.75464 | ||||||||
\(382\) | − | 3018.99i | − | 0.404359i | ||||||
\(383\) | − | 2952.33i | − | 0.393883i | −0.980415 | − | 0.196941i | \(-0.936899\pi\) | ||
0.980415 | − | 0.196941i | \(-0.0631009\pi\) | |||||||
\(384\) | 600.721 | 0.0798318 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8135.57 | 1.07277 | ||||||||
\(387\) | 968.213i | 0.127176i | ||||||||
\(388\) | 611.304i | 0.0799853i | ||||||||
\(389\) | −10036.7 | −1.30818 | −0.654088 | − | 0.756418i | \(-0.726948\pi\) | ||||
−0.654088 | + | 0.756418i | \(0.726948\pi\) | |||||||
\(390\) | −7222.09 | + | 1005.71i | −0.937705 | + | 0.130579i | ||||
\(391\) | 781.193 | 0.101040 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 8199.19i | − | 1.05240i | ||||||
\(394\) | 1839.78 | 0.235246 | ||||||||
\(395\) | −1093.01 | − | 7849.01i | −0.139228 | − | 0.999814i | ||||
\(396\) | −27.3987 | −0.00347686 | ||||||||
\(397\) | 1702.16i | 0.215187i | 0.994195 | + | 0.107593i | \(0.0343144\pi\) | ||||
−0.994195 | + | 0.107593i | \(0.965686\pi\) | |||||||
\(398\) | − | 3538.11i | − | 0.445602i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1923.91 | + | 546.420i | −0.240489 | + | 0.0683026i | ||||
\(401\) | 5463.99 | 0.680446 | 0.340223 | − | 0.940345i | \(-0.389497\pi\) | ||||
0.340223 | + | 0.940345i | \(0.389497\pi\) | |||||||
\(402\) | 2070.42i | 0.256873i | ||||||||
\(403\) | − | 17027.6i | − | 2.10473i | ||||||
\(404\) | −1404.36 | −0.172944 | ||||||||
\(405\) | 878.869 | + | 6311.26i | 0.107831 | + | 0.774344i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 337.494i | 0.0411031i | ||||||||
\(408\) | − | 987.910i | − | 0.119875i | ||||||
\(409\) | −1295.75 | −0.156652 | −0.0783262 | − | 0.996928i | \(-0.524958\pi\) | ||||
−0.0783262 | + | 0.996928i | \(0.524958\pi\) | |||||||
\(410\) | −5280.68 | + | 735.357i | −0.636084 | + | 0.0885773i | ||||
\(411\) | −9704.47 | −1.16469 | ||||||||
\(412\) | 1501.73i | 0.179576i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −295.374 | −0.0350648 | ||||||||
\(415\) | −4642.89 | + | 646.541i | −0.549182 | + | 0.0764758i | ||||
\(416\) | −2223.49 | −0.262057 | ||||||||
\(417\) | 10967.4i | 1.28796i | ||||||||
\(418\) | 39.0303i | 0.00456707i | ||||||||
\(419\) | 1699.48 | 0.198150 | 0.0990750 | − | 0.995080i | \(-0.468412\pi\) | ||||
0.0990750 | + | 0.995080i | \(0.468412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11127.8 | −1.28820 | −0.644102 | − | 0.764940i | \(-0.722769\pi\) | ||||
−0.644102 | + | 0.764940i | \(0.722769\pi\) | |||||||
\(422\) | − | 2754.10i | − | 0.317696i | ||||||
\(423\) | 1867.72i | 0.214685i | ||||||||
\(424\) | −4095.44 | −0.469085 | ||||||||
\(425\) | 898.611 | + | 3163.95i | 0.102562 | + | 0.361115i | ||||
\(426\) | −10388.2 | −1.18148 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2058.31i | 0.232458i | ||||||||
\(429\) | −449.025 | −0.0505341 | ||||||||
\(430\) | 600.268 | + | 4310.59i | 0.0673197 | + | 0.483431i | ||||
\(431\) | −16330.1 | −1.82504 | −0.912519 | − | 0.409035i | \(-0.865865\pi\) | ||||
−0.912519 | + | 0.409035i | \(0.865865\pi\) | |||||||
\(432\) | 2400.97i | 0.267400i | ||||||||
\(433\) | − | 14851.9i | − | 1.64835i | −0.566334 | − | 0.824176i | \(-0.691639\pi\) | ||
0.566334 | − | 0.824176i | \(-0.308361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3926.79 | − | 546.821i | 0.432816 | − | 0.0602714i | ||||
\(436\) | 7182.27 | 0.788918 | ||||||||
\(437\) | 420.769i | 0.0460597i | ||||||||
\(438\) | − | 8435.27i | − | 0.920211i | ||||||
\(439\) | −10095.5 | −1.09757 | −0.548786 | − | 0.835963i | \(-0.684910\pi\) | ||||
−0.548786 | + | 0.835963i | \(0.684910\pi\) | |||||||
\(440\) | −121.982 | + | 16.9865i | −0.0132165 | + | 0.00184046i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3656.62i | 0.393502i | ||||||||
\(443\) | 13256.2i | 1.42171i | 0.703336 | + | 0.710857i | \(0.251693\pi\) | ||||
−0.703336 | + | 0.710857i | \(0.748307\pi\) | |||||||
\(444\) | 4601.16 | 0.491805 | ||||||||
\(445\) | 607.190 | + | 4360.30i | 0.0646822 | + | 0.464490i | ||||
\(446\) | 11247.8 | 1.19417 | ||||||||
\(447\) | − | 10469.0i | − | 1.10775i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15773.7 | 1.65792 | 0.828962 | − | 0.559306i | \(-0.188932\pi\) | ||||
0.828962 | + | 0.559306i | \(0.188932\pi\) | |||||||
\(450\) | −339.770 | − | 1196.31i | −0.0355931 | − | 0.125321i | ||||
\(451\) | −328.320 | −0.0342794 | ||||||||
\(452\) | − | 3701.75i | − | 0.385211i | ||||||
\(453\) | 12072.9i | 1.25217i | ||||||||
\(454\) | −4473.94 | −0.462494 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 532.112 | 0.0546457 | ||||||||
\(457\) | 7088.20i | 0.725540i | 0.931879 | + | 0.362770i | \(0.118169\pi\) | ||||
−0.931879 | + | 0.362770i | \(0.881831\pi\) | |||||||
\(458\) | 11077.7i | 1.13019i | ||||||||
\(459\) | 3948.49 | 0.401525 | ||||||||
\(460\) | −1315.04 | + | 183.124i | −0.133291 | + | 0.0185613i | ||||
\(461\) | 17395.7 | 1.75748 | 0.878739 | − | 0.477303i | \(-0.158386\pi\) | ||||
0.878739 | + | 0.477303i | \(0.158386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13350.8i | − | 1.34010i | −0.742316 | − | 0.670050i | \(-0.766273\pi\) | ||
0.742316 | − | 0.670050i | \(-0.233727\pi\) | |||||||
\(464\) | 1208.95 | 0.120958 | ||||||||
\(465\) | −12735.5 | + | 1773.47i | −1.27010 | + | 0.176866i | ||||
\(466\) | 2380.42 | 0.236633 | ||||||||
\(467\) | − | 1522.43i | − | 0.150856i | −0.997151 | − | 0.0754281i | \(-0.975968\pi\) | ||
0.997151 | − | 0.0754281i | \(-0.0240323\pi\) | |||||||
\(468\) | − | 1382.59i | − | 0.136560i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1157.94 | + | 8315.30i | 0.113642 | + | 0.816077i | ||||
\(471\) | −5082.74 | −0.497240 | ||||||||
\(472\) | 5254.48i | 0.512409i | ||||||||
\(473\) | 268.006i | 0.0260527i | ||||||||
\(474\) | −6653.09 | −0.644697 | ||||||||
\(475\) | −1704.18 | + | 484.013i | −0.164617 | + | 0.0467538i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2546.59i | − | 0.244445i | ||||||
\(478\) | 3205.83i | 0.306760i | ||||||||
\(479\) | 15526.6 | 1.48106 | 0.740529 | − | 0.672024i | \(-0.234575\pi\) | ||||
0.740529 | + | 0.672024i | \(0.234575\pi\) | |||||||
\(480\) | 231.582 | + | 1663.02i | 0.0220213 | + | 0.158138i | ||||
\(481\) | −17030.6 | −1.61440 | ||||||||
\(482\) | 9047.77i | 0.855010i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5316.42 | 0.499288 | ||||||||
\(485\) | −1692.32 | + | 235.662i | −0.158442 | + | 0.0220637i | ||||
\(486\) | −2753.63 | −0.257011 | ||||||||
\(487\) | − | 12837.5i | − | 1.19450i | −0.802055 | − | 0.597250i | \(-0.796260\pi\) | ||
0.802055 | − | 0.597250i | \(-0.203740\pi\) | |||||||
\(488\) | 6478.13i | 0.600925i | ||||||||
\(489\) | −6422.85 | −0.593970 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6619.17 | 0.608389 | 0.304194 | − | 0.952610i | \(-0.401613\pi\) | ||||
0.304194 | + | 0.952610i | \(0.401613\pi\) | |||||||
\(492\) | 4476.09i | 0.410158i | ||||||||
\(493\) | − | 1988.17i | − | 0.181629i | ||||||
\(494\) | −1969.54 | −0.179380 | ||||||||
\(495\) | −10.5624 | − | 75.8498i | −0.000959080 | − | 0.00688727i | ||||
\(496\) | −3920.93 | −0.354949 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3935.47i | 0.354122i | ||||||||
\(499\) | 16221.6 | 1.45527 | 0.727633 | − | 0.685966i | \(-0.240620\pi\) | ||||
0.727633 | + | 0.685966i | \(0.240620\pi\) | |||||||
\(500\) | −2254.38 | − | 5115.45i | −0.201638 | − | 0.457539i | ||||
\(501\) | −10647.5 | −0.949495 | ||||||||
\(502\) | 12842.4i | 1.14180i | ||||||||
\(503\) | − | 3242.95i | − | 0.287467i | −0.989616 | − | 0.143734i | \(-0.954089\pi\) | ||
0.989616 | − | 0.143734i | \(-0.0459109\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −541.390 | − | 3887.79i | −0.0477061 | − | 0.342583i | ||||
\(506\) | −81.7609 | −0.00718323 | ||||||||
\(507\) | − | 12347.8i | − | 1.08163i | ||||||
\(508\) | − | 11121.8i | − | 0.971354i | ||||||
\(509\) | −10885.0 | −0.947878 | −0.473939 | − | 0.880558i | \(-0.657168\pi\) | ||||
−0.473939 | + | 0.880558i | \(0.657168\pi\) | |||||||
\(510\) | 2734.90 | − | 380.847i | 0.237458 | − | 0.0330670i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000i | 0.0441942i | ||||||||
\(513\) | 2126.75i | 0.183038i | ||||||||
\(514\) | −8443.42 | −0.724559 | ||||||||
\(515\) | −4157.36 | + | 578.929i | −0.355719 | + | 0.0495353i | ||||
\(516\) | 3653.81 | 0.311725 | ||||||||
\(517\) | 516.994i | 0.0439795i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11103.2 | −0.939066 | ||||||||
\(520\) | −857.172 | − | 6155.45i | −0.0722875 | − | 0.519105i | ||||
\(521\) | 16284.5 | 1.36936 | 0.684679 | − | 0.728845i | \(-0.259943\pi\) | ||||
0.684679 | + | 0.728845i | \(0.259943\pi\) | |||||||
\(522\) | 751.741i | 0.0630322i | ||||||||
\(523\) | − | 2243.58i | − | 0.187581i | −0.995592 | − | 0.0937907i | \(-0.970102\pi\) | ||
0.995592 | − | 0.0937907i | \(-0.0298985\pi\) | |||||||
\(524\) | 6988.24 | 0.582601 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13939.2 | 1.15547 | ||||||||
\(527\) | 6448.12i | 0.532988i | ||||||||
\(528\) | 103.396i | 0.00852225i | ||||||||
\(529\) | 11285.6 | 0.927556 | ||||||||
\(530\) | −1578.82 | − | 11337.7i | −0.129396 | − | 0.929204i | ||||
\(531\) | −3267.29 | −0.267021 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 16567.7i | − | 1.34639i | ||||||
\(534\) | 3695.94 | 0.299511 | ||||||||
\(535\) | −5698.17 | + | 793.493i | −0.460473 | + | 0.0641228i | ||||
\(536\) | −1764.63 | −0.142203 | ||||||||
\(537\) | 9422.12i | 0.757159i | ||||||||
\(538\) | 1515.68i | 0.121460i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6646.78 | + | 925.591i | −0.529688 | + | 0.0737613i | ||||
\(541\) | −12207.7 | −0.970147 | −0.485073 | − | 0.874473i | \(-0.661207\pi\) | ||||
−0.485073 | + | 0.874473i | \(0.661207\pi\) | |||||||
\(542\) | 2397.32i | 0.189988i | ||||||||
\(543\) | − | 9527.13i | − | 0.752943i | ||||||
\(544\) | 842.005 | 0.0663615 | ||||||||
\(545\) | 2768.82 | + | 19883.2i | 0.217620 | + | 1.56276i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12789.6i | 0.999716i | 0.866107 | + | 0.499858i | \(0.166614\pi\) | ||||
−0.866107 | + | 0.499858i | \(0.833386\pi\) | |||||||
\(548\) | − | 8271.20i | − | 0.644759i | ||||||
\(549\) | −4028.17 | −0.313148 | ||||||||
\(550\) | −94.0501 | − | 331.144i | −0.00729147 | − | 0.0256728i | ||||
\(551\) | 1070.88 | 0.0827966 | ||||||||
\(552\) | 1114.67i | 0.0859484i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10433.6 | −0.800149 | ||||||||
\(555\) | 1773.78 | + | 12737.7i | 0.135663 | + | 0.974209i | ||||
\(556\) | −9347.64 | −0.713001 | ||||||||
\(557\) | 7623.39i | 0.579917i | 0.957039 | + | 0.289958i | \(0.0936414\pi\) | ||||
−0.957039 | + | 0.289958i | \(0.906359\pi\) | |||||||
\(558\) | − | 2438.07i | − | 0.184967i | ||||||
\(559\) | −13524.1 | −1.02327 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 170.039 | 0.0127969 | ||||||||
\(562\) | 5066.57i | 0.380285i | ||||||||
\(563\) | 3329.24i | 0.249220i | 0.992206 | + | 0.124610i | \(0.0397679\pi\) | ||||
−0.992206 | + | 0.124610i | \(0.960232\pi\) | |||||||
\(564\) | 7048.34 | 0.526221 | ||||||||
\(565\) | 10247.8 | − | 1427.05i | 0.763059 | − | 0.106259i | ||||
\(566\) | 4906.98 | 0.364410 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 8853.96i | − | 0.654056i | ||||||
\(569\) | 12728.9 | 0.937828 | 0.468914 | − | 0.883244i | \(-0.344645\pi\) | ||||
0.468914 | + | 0.883244i | \(0.344645\pi\) | |||||||
\(570\) | 205.133 | + | 1473.08i | 0.0150738 | + | 0.108247i | ||||
\(571\) | 12084.5 | 0.885672 | 0.442836 | − | 0.896603i | \(-0.353972\pi\) | ||||
0.442836 | + | 0.896603i | \(0.353972\pi\) | |||||||
\(572\) | − | 382.708i | − | 0.0279752i | ||||||
\(573\) | − | 7084.26i | − | 0.516491i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1013.91 | − | 3569.92i | −0.0735358 | − | 0.258914i | ||||
\(576\) | −318.367 | −0.0230300 | ||||||||
\(577\) | 1738.58i | 0.125438i | 0.998031 | + | 0.0627192i | \(0.0199773\pi\) | ||||
−0.998031 | + | 0.0627192i | \(0.980023\pi\) | |||||||
\(578\) | 8441.29i | 0.607459i | ||||||||
\(579\) | 19090.7 | 1.37026 | ||||||||
\(580\) | 466.061 | + | 3346.84i | 0.0333657 | + | 0.239603i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1434.47i | 0.102166i | ||||||||
\(583\) | − | 704.908i | − | 0.0500760i | ||||||
\(584\) | 7189.45 | 0.509421 | ||||||||
\(585\) | 3827.52 | − | 532.999i | 0.270511 | − | 0.0376697i | ||||
\(586\) | 16219.9 | 1.14341 | ||||||||
\(587\) | 5392.62i | 0.379177i | 0.981864 | + | 0.189589i | \(0.0607154\pi\) | ||||
−0.981864 | + | 0.189589i | \(0.939285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3473.11 | −0.242966 | ||||||||
\(590\) | −14546.3 | + | 2025.64i | −1.01502 | + | 0.141346i | ||||
\(591\) | 4317.17 | 0.300482 | ||||||||
\(592\) | 3921.61i | 0.272258i | ||||||||
\(593\) | − | 5429.42i | − | 0.375986i | −0.982170 | − | 0.187993i | \(-0.939802\pi\) | ||
0.982170 | − | 0.187993i | \(-0.0601982\pi\) | |||||||
\(594\) | −413.256 | −0.0285456 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8922.79 | 0.613241 | ||||||||
\(597\) | − | 8302.42i | − | 0.569172i | ||||||
\(598\) | − | 4125.81i | − | 0.282135i | ||||||
\(599\) | −10220.4 | −0.697151 | −0.348575 | − | 0.937281i | \(-0.613334\pi\) | ||||
−0.348575 | + | 0.937281i | \(0.613334\pi\) | |||||||
\(600\) | −4514.58 | + | 1282.21i | −0.307178 | + | 0.0872435i | ||||
\(601\) | 1659.74 | 0.112649 | 0.0563247 | − | 0.998413i | \(-0.482062\pi\) | ||||
0.0563247 | + | 0.998413i | \(0.482062\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1097.27i | − | 0.0741032i | ||||||
\(604\) | −10289.8 | −0.693192 | ||||||||
\(605\) | 2049.52 | + | 14717.8i | 0.137727 | + | 0.989032i | ||||
\(606\) | −3295.42 | −0.220903 | ||||||||
\(607\) | − | 24030.5i | − | 1.60686i | −0.595396 | − | 0.803432i | \(-0.703005\pi\) | ||
0.595396 | − | 0.803432i | \(-0.296995\pi\) | |||||||
\(608\) | 453.524i | 0.0302513i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −17933.9 | + | 2497.37i | −1.19036 | + | 0.165763i | ||||
\(611\) | −26088.5 | −1.72738 | ||||||||
\(612\) | 523.567i | 0.0345816i | ||||||||
\(613\) | 28438.2i | 1.87375i | 0.349666 | + | 0.936874i | \(0.386295\pi\) | ||||
−0.349666 | + | 0.936874i | \(0.613705\pi\) | |||||||
\(614\) | −5482.41 | −0.360345 | ||||||||
\(615\) | −12391.5 | + | 1725.57i | −0.812476 | + | 0.113141i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 3296.92i | − | 0.215120i | −0.994199 | − | 0.107560i | \(-0.965696\pi\) | ||
0.994199 | − | 0.107560i | \(-0.0343038\pi\) | |||||||
\(618\) | 3523.92i | 0.229374i | ||||||||
\(619\) | −1357.63 | −0.0881549 | −0.0440774 | − | 0.999028i | \(-0.514035\pi\) | ||||
−0.0440774 | + | 0.999028i | \(0.514035\pi\) | |||||||
\(620\) | −1511.54 | − | 10854.6i | −0.0979115 | − | 0.703114i | ||||
\(621\) | −4455.13 | −0.287887 | ||||||||
\(622\) | 11702.6i | 0.754393i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5217.57 | −0.334728 | ||||||||
\(625\) | 13292.4 | − | 8212.99i | 0.850712 | − | 0.525632i | ||||
\(626\) | −6504.41 | −0.415285 | ||||||||
\(627\) | 91.5873i | 0.00583356i | ||||||||
\(628\) | − | 4332.06i | − | 0.275268i | ||||||
\(629\) | 6449.24 | 0.408820 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21289.4 | −1.34314 | −0.671568 | − | 0.740943i | \(-0.734379\pi\) | ||||
−0.671568 | + | 0.740943i | \(0.734379\pi\) | |||||||
\(632\) | − | 5670.49i | − | 0.356899i | ||||||
\(633\) | − | 6462.69i | − | 0.405796i | ||||||
\(634\) | −19.1868 | −0.00120190 | ||||||||
\(635\) | 30789.1 | − | 4287.52i | 1.92414 | − | 0.267945i | ||||
\(636\) | −9610.23 | −0.599167 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 208.086i | 0.0129125i | ||||||||
\(639\) | 5505.49 | 0.340835 | ||||||||
\(640\) | −1417.41 | + | 197.380i | −0.0875436 | + | 0.0121908i | ||||
\(641\) | 29433.2 | 1.81364 | 0.906819 | − | 0.421520i | \(-0.138503\pi\) | ||||
0.906819 | + | 0.421520i | \(0.138503\pi\) | |||||||
\(642\) | 4829.96i | 0.296921i | ||||||||
\(643\) | 13351.4i | 0.818862i | 0.912341 | + | 0.409431i | \(0.134273\pi\) | ||||
−0.912341 | + | 0.409431i | \(0.865727\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1408.57 | + | 10115.1i | 0.0859881 | + | 0.617491i | ||||
\(646\) | 745.838 | 0.0454251 | ||||||||
\(647\) | − | 8985.21i | − | 0.545974i | −0.962018 | − | 0.272987i | \(-0.911988\pi\) | ||
0.962018 | − | 0.272987i | \(-0.0880116\pi\) | |||||||
\(648\) | 4559.55i | 0.276413i | ||||||||
\(649\) | −904.402 | −0.0547009 | ||||||||
\(650\) | 16710.1 | − | 4745.94i | 1.00835 | − | 0.286386i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 5474.25i | − | 0.328816i | ||||||
\(653\) | − | 12069.4i | − | 0.723298i | −0.932314 | − | 0.361649i | \(-0.882214\pi\) | ||
0.932314 | − | 0.361649i | \(-0.117786\pi\) | |||||||
\(654\) | 16853.7 | 1.00769 | ||||||||
\(655\) | 2694.02 | + | 19346.1i | 0.160708 | + | 1.15407i | ||||
\(656\) | −3815.01 | −0.227060 | ||||||||
\(657\) | 4470.48i | 0.265464i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23236.3 | 1.37353 | 0.686765 | − | 0.726880i | \(-0.259030\pi\) | ||||
0.686765 | + | 0.726880i | \(0.259030\pi\) | |||||||
\(660\) | −286.240 | + | 39.8600i | −0.0168816 | + | 0.00235083i | ||||
\(661\) | −11281.7 | −0.663856 | −0.331928 | − | 0.943305i | \(-0.607699\pi\) | ||||
−0.331928 | + | 0.943305i | \(0.607699\pi\) | |||||||
\(662\) | 10134.2i | 0.594983i | ||||||||
\(663\) | 8580.51i | 0.502623i | ||||||||
\(664\) | −3354.24 | −0.196039 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2438.50 | −0.141877 | ||||||||
\(667\) | 2243.28i | 0.130225i | ||||||||
\(668\) | − | 9074.99i | − | 0.525632i | ||||||
\(669\) | 26393.8 | 1.52533 | ||||||||
\(670\) | −680.279 | − | 4885.17i | −0.0392261 | − | 0.281687i | ||||
\(671\) | −1115.02 | −0.0641502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2558.69i | 0.146553i | 0.997312 | + | 0.0732766i | \(0.0233456\pi\) | ||||
−0.997312 | + | 0.0732766i | \(0.976654\pi\) | |||||||
\(674\) | 6198.95 | 0.354265 | ||||||||
\(675\) | −5124.76 | − | 18043.9i | −0.292225 | − | 1.02891i | ||||
\(676\) | 10524.2 | 0.598780 | ||||||||
\(677\) | 9567.49i | 0.543144i | 0.962418 | + | 0.271572i | \(0.0875435\pi\) | ||||
−0.962418 | + | 0.271572i | \(0.912457\pi\) | |||||||
\(678\) | − | 8686.40i | − | 0.492034i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 324.599 | + | 2330.98i | 0.0183056 | + | 0.131455i | ||||
\(681\) | −10498.4 | −0.590749 | ||||||||
\(682\) | − | 674.871i | − | 0.0378917i | ||||||
\(683\) | − | 26825.8i | − | 1.50287i | −0.659807 | − | 0.751435i | \(-0.729362\pi\) | ||
0.659807 | − | 0.751435i | \(-0.270638\pi\) | |||||||
\(684\) | −282.006 | −0.0157643 | ||||||||
\(685\) | 22897.8 | − | 3188.61i | 1.27719 | − | 0.177855i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25994.7i | 1.44361i | ||||||||
\(688\) | 3114.17i | 0.172568i | ||||||||
\(689\) | 35571.0 | 1.96683 | ||||||||
\(690\) | −3085.82 | + | 429.714i | −0.170254 | + | 0.0237086i | ||||
\(691\) | 8541.18 | 0.470220 | 0.235110 | − | 0.971969i | \(-0.424455\pi\) | ||||
0.235110 | + | 0.971969i | \(0.424455\pi\) | |||||||
\(692\) | − | 9463.34i | − | 0.519859i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10412.3 | −0.569516 | ||||||||
\(695\) | −3603.58 | − | 25877.8i | −0.196679 | − | 1.41237i | ||||
\(696\) | 2836.89 | 0.154500 | ||||||||
\(697\) | 6273.94i | 0.340950i | ||||||||
\(698\) | − | 9454.35i | − | 0.512682i | ||||||
\(699\) | 5585.82 | 0.302253 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3409.68 | 0.183711 | 0.0918557 | − | 0.995772i | \(-0.470720\pi\) | ||||
0.0918557 | + | 0.995772i | \(0.470720\pi\) | |||||||
\(702\) | − | 20853.6i | − | 1.12118i | ||||||
\(703\) | 3473.71i | 0.186364i | ||||||||
\(704\) | −88.1256 | −0.00471784 | ||||||||
\(705\) | 2717.18 | + | 19512.4i | 0.145156 | + | 1.04238i | ||||
\(706\) | −13474.9 | −0.718322 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12330.0i | 0.654505i | ||||||||
\(709\) | −8364.26 | −0.443056 | −0.221528 | − | 0.975154i | \(-0.571104\pi\) | ||||
−0.221528 | + | 0.975154i | \(0.571104\pi\) | |||||||
\(710\) | 24511.1 | − | 3413.27i | 1.29561 | − | 0.180419i | ||||
\(711\) | 3525.97 | 0.185983 | ||||||||
\(712\) | 3150.08i | 0.165807i | ||||||||
\(713\) | − | 7275.49i | − | 0.382145i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1059.48 | − | 147.537i | 0.0554157 | − | 0.00771687i | ||||
\(716\) | −8030.56 | −0.419156 | ||||||||
\(717\) | 7522.70i | 0.391828i | ||||||||
\(718\) | − | 2859.14i | − | 0.148610i | ||||||
\(719\) | 31967.1 | 1.65810 | 0.829049 | − | 0.559176i | \(-0.188882\pi\) | ||||
0.829049 | + | 0.559176i | \(0.188882\pi\) | |||||||
\(720\) | −122.733 | − | 881.358i | −0.00635275 | − | 0.0456198i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 13316.3i | − | 0.686399i | ||||||
\(723\) | 21231.2i | 1.09211i | ||||||||
\(724\) | 8120.05 | 0.416822 | ||||||||
\(725\) | −9085.62 | + | 2580.46i | −0.465423 | + | 0.132187i | ||||
\(726\) | 12475.3 | 0.637745 | ||||||||
\(727\) | − | 27903.4i | − | 1.42349i | −0.702437 | − | 0.711746i | \(-0.747905\pi\) | ||
0.702437 | − | 0.711746i | \(-0.252095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21850.0 | −1.11010 | ||||||||
\(730\) | 2771.59 | + | 19903.1i | 0.140522 | + | 1.00910i | ||||
\(731\) | 5121.38 | 0.259126 | ||||||||
\(732\) | 15201.4i | 0.767567i | ||||||||
\(733\) | 1029.02i | 0.0518521i | 0.999664 | + | 0.0259261i | \(0.00825345\pi\) | ||||
−0.999664 | + | 0.0259261i | \(0.991747\pi\) | |||||||
\(734\) | 21190.4 | 1.06560 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −950.044 | −0.0475803 | ||||||||
\(737\) | − | 303.730i | − | 0.0151805i | ||||||
\(738\) | − | 2372.21i | − | 0.118323i | ||||||
\(739\) | 22515.6 | 1.12077 | 0.560385 | − | 0.828232i | \(-0.310653\pi\) | ||||
0.560385 | + | 0.828232i | \(0.310653\pi\) | |||||||
\(740\) | −10856.5 | + | 1511.81i | −0.539313 | + | 0.0751016i | ||||
\(741\) | −4621.66 | −0.229124 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34792.5i | 1.71792i | 0.512045 | + | 0.858958i | \(0.328888\pi\) | ||||
−0.512045 | + | 0.858958i | \(0.671112\pi\) | |||||||
\(744\) | −9200.72 | −0.453380 | ||||||||
\(745\) | 3439.80 | + | 24701.6i | 0.169161 | + | 1.21476i | ||||
\(746\) | 24681.9 | 1.21135 | ||||||||
\(747\) | − | 2085.70i | − | 0.102158i | ||||||
\(748\) | 144.926i | 0.00708426i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −5290.05 | − | 12003.7i | −0.257554 | − | 0.584419i | ||||
\(751\) | −8250.40 | −0.400881 | −0.200440 | − | 0.979706i | \(-0.564237\pi\) | ||||
−0.200440 | + | 0.979706i | \(0.564237\pi\) | |||||||
\(752\) | 6007.36i | 0.291311i | ||||||||
\(753\) | 30135.6i | 1.45843i | ||||||||
\(754\) | −10500.4 | −0.507164 | ||||||||
\(755\) | −3966.81 | − | 28486.1i | −0.191215 | − | 1.37313i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 437.145i | − | 0.0209885i | −0.999945 | − | 0.0104943i | \(-0.996660\pi\) | ||
0.999945 | − | 0.0104943i | \(-0.00334049\pi\) | |||||||
\(758\) | 5907.86i | 0.283091i | ||||||||
\(759\) | −191.857 | −0.00917521 | ||||||||
\(760\) | −1255.52 | + | 174.837i | −0.0599244 | + | 0.00834473i | ||||
\(761\) | −20973.4 | −0.999063 | −0.499531 | − | 0.866296i | \(-0.666494\pi\) | ||||
−0.499531 | + | 0.866296i | \(0.666494\pi\) | |||||||
\(762\) | − | 26097.9i | − | 1.24072i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 6037.98 | 0.285925 | ||||||||
\(765\) | −1449.43 | + | 201.839i | −0.0685023 | + | 0.00953922i | ||||
\(766\) | 5904.66 | 0.278517 | ||||||||
\(767\) | − | 45637.8i | − | 2.14848i | ||||||
\(768\) | 1201.44i | 0.0564496i | ||||||||
\(769\) | −3186.01 | −0.149402 | −0.0747012 | − | 0.997206i | \(-0.523800\pi\) | ||||
−0.0747012 | + | 0.997206i | \(0.523800\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19813.1 | −0.925486 | ||||||||
\(772\) | 16271.1i | 0.758564i | ||||||||
\(773\) | 11968.5i | 0.556894i | 0.960452 | + | 0.278447i | \(0.0898196\pi\) | ||||
−0.960452 | + | 0.278447i | \(0.910180\pi\) | |||||||
\(774\) | −1936.43 | −0.0899268 | ||||||||
\(775\) | 29466.8 | − | 8369.04i | 1.36578 | − | 0.387903i | ||||
\(776\) | −1222.61 | −0.0565581 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 20073.4i | − | 0.925021i | ||||||
\(779\) | −3379.29 | −0.155425 | ||||||||
\(780\) | −2011.41 | − | 14444.2i | −0.0923335 | − | 0.663057i | ||||
\(781\) | 1523.95 | 0.0698222 | ||||||||
\(782\) | 1562.39i | 0.0714460i | ||||||||
\(783\) | 11338.5i | 0.517504i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11992.8 | − | 1670.04i | 0.545274 | − | 0.0759316i | ||||
\(786\) | 16398.4 | 0.744161 | ||||||||
\(787\) | 14961.3i | 0.677653i | 0.940849 | + | 0.338827i | \(0.110030\pi\) | ||||
−0.940849 | + | 0.338827i | \(0.889970\pi\) | |||||||
\(788\) | 3679.56i | 0.166344i | ||||||||
\(789\) | 32709.3 | 1.47589 | ||||||||
\(790\) | 15698.0 | − | 2186.01i | 0.706975 | − | 0.0984492i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 54.7974i | − | 0.00245851i | ||||||
\(793\) | − | 56265.9i | − | 2.51962i | ||||||
\(794\) | −3404.32 | −0.152160 | ||||||||
\(795\) | −3704.81 | − | 26604.7i | −0.165278 | − | 1.18688i | ||||
\(796\) | 7076.23 | 0.315088 | ||||||||
\(797\) | 23075.5i | 1.02556i | 0.858519 | + | 0.512782i | \(0.171385\pi\) | ||||
−0.858519 | + | 0.512782i | \(0.828615\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9879.34 | 0.437429 | ||||||||
\(800\) | −1092.84 | − | 3847.82i | −0.0482972 | − | 0.170051i | ||||
\(801\) | −1958.76 | −0.0864035 | ||||||||
\(802\) | 10928.0i | 0.481148i | ||||||||
\(803\) | 1237.45i | 0.0543819i | ||||||||
\(804\) | −4140.83 | −0.181637 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 34055.2 | 1.48827 | ||||||||
\(807\) | 3556.63i | 0.155142i | ||||||||
\(808\) | − | 2808.72i | − | 0.122290i | ||||||
\(809\) | −31847.6 | −1.38405 | −0.692027 | − | 0.721871i | \(-0.743282\pi\) | ||||
−0.692027 | + | 0.721871i | \(0.743282\pi\) | |||||||
\(810\) | −12622.5 | + | 1757.74i | −0.547544 | + | 0.0762477i | ||||
\(811\) | −9375.21 | −0.405929 | −0.202964 | − | 0.979186i | \(-0.565058\pi\) | ||||
−0.202964 | + | 0.979186i | \(0.565058\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5625.48i | 0.242674i | ||||||||
\(814\) | −674.988 | −0.0290643 | ||||||||
\(815\) | 15154.8 | − | 2110.36i | 0.651348 | − | 0.0907028i | ||||
\(816\) | 1975.82 | 0.0847642 | ||||||||
\(817\) | 2758.50i | 0.118124i | ||||||||
\(818\) | − | 2591.50i | − | 0.110770i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1470.71 | − | 10561.4i | −0.0626336 | − | 0.449779i | ||||
\(821\) | −35109.2 | −1.49247 | −0.746237 | − | 0.665681i | \(-0.768141\pi\) | ||||
−0.746237 | + | 0.665681i | \(0.768141\pi\) | |||||||
\(822\) | − | 19408.9i | − | 0.823557i | ||||||
\(823\) | 6387.04i | 0.270520i | 0.990810 | + | 0.135260i | \(0.0431870\pi\) | ||||
−0.990810 | + | 0.135260i | \(0.956813\pi\) | |||||||
\(824\) | −3003.47 | −0.126979 | ||||||||
\(825\) | −220.695 | − | 777.051i | −0.00931346 | − | 0.0327921i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 32401.5i | − | 1.36241i | −0.732095 | − | 0.681203i | \(-0.761457\pi\) | ||
0.732095 | − | 0.681203i | \(-0.238543\pi\) | |||||||
\(828\) | − | 590.747i | − | 0.0247945i | ||||||
\(829\) | −38188.2 | −1.59991 | −0.799957 | − | 0.600057i | \(-0.795145\pi\) | ||||
−0.799957 | + | 0.600057i | \(0.795145\pi\) | |||||||
\(830\) | −1293.08 | − | 9285.77i | −0.0540766 | − | 0.388330i | ||||
\(831\) | −24483.2 | −1.02204 | ||||||||
\(832\) | − | 4446.98i | − | 0.185302i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −21934.9 | −0.910723 | ||||||||
\(835\) | 25123.0 | − | 3498.47i | 1.04122 | − | 0.144994i | ||||
\(836\) | −78.0606 | −0.00322941 | ||||||||
\(837\) | − | 36773.5i | − | 1.51861i | ||||||
\(838\) | 3398.95i | 0.140113i | ||||||||
\(839\) | 11555.7 | 0.475503 | 0.237751 | − | 0.971326i | \(-0.423590\pi\) | ||||
0.237751 | + | 0.971326i | \(0.423590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18679.7 | −0.765908 | ||||||||
\(842\) | − | 22255.5i | − | 0.910897i | ||||||
\(843\) | 11889.1i | 0.485742i | ||||||||
\(844\) | 5508.20 | 0.224645 | ||||||||
\(845\) | 4057.14 | + | 29134.8i | 0.165171 | + | 1.18612i | ||||
\(846\) | −3735.44 | −0.151805 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 8190.88i | − | 0.331693i | ||||||
\(849\) | 11514.6 | 0.465464 | ||||||||
\(850\) | −6327.89 | + | 1797.22i | −0.255347 | + | 0.0725226i | ||||
\(851\) | −7276.75 | −0.293118 | ||||||||
\(852\) | − | 20776.4i | − | 0.835433i | ||||||
\(853\) | 15910.9i | 0.638661i | 0.947643 | + | 0.319331i | \(0.103458\pi\) | ||||
−0.947643 | + | 0.319331i | \(0.896542\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −108.715 | − | 780.697i | −0.00434852 | − | 0.0312272i | ||||
\(856\) | −4116.62 | −0.164373 | ||||||||
\(857\) | 18769.1i | 0.748120i | 0.927404 | + | 0.374060i | \(0.122035\pi\) | ||||
−0.927404 | + | 0.374060i | \(0.877965\pi\) | |||||||
\(858\) | − | 898.050i | − | 0.0357330i | ||||||
\(859\) | −25394.0 | −1.00865 | −0.504327 | − | 0.863513i | \(-0.668259\pi\) | ||||
−0.504327 | + | 0.863513i | \(0.668259\pi\) | |||||||
\(860\) | −8621.19 | + | 1200.54i | −0.341837 | + | 0.0476022i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 32660.1i | − | 1.29050i | ||||||
\(863\) | 7314.11i | 0.288500i | 0.989541 | + | 0.144250i | \(0.0460769\pi\) | ||||
−0.989541 | + | 0.144250i | \(0.953923\pi\) | |||||||
\(864\) | −4801.94 | −0.189080 | ||||||||
\(865\) | 26198.0 | − | 3648.18i | 1.02978 | − | 0.143401i | ||||
\(866\) | 29703.8 | 1.16556 | ||||||||
\(867\) | 19808.1i | 0.775913i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 976.006 | 0.0380998 | ||||||||
\(870\) | 1093.64 | + | 7853.58i | 0.0426183 | + | 0.306047i | ||||
\(871\) | 15326.8 | 0.596243 | ||||||||
\(872\) | 14364.5i | 0.557849i | ||||||||
\(873\) | − | 760.231i | − | 0.0294730i | ||||||
\(874\) | −841.538 | −0.0325691 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16870.5 | 0.650688 | ||||||||
\(877\) | − | 823.666i | − | 0.0317140i | −0.999874 | − | 0.0158570i | \(-0.994952\pi\) | ||
0.999874 | − | 0.0158570i | \(-0.00504766\pi\) | |||||||
\(878\) | − | 20191.1i | − | 0.776100i | ||||||
\(879\) | 38061.0 | 1.46048 | ||||||||
\(880\) | −33.9731 | − | 243.964i | −0.00130140 | − | 0.00934550i | ||||
\(881\) | 14893.3 | 0.569543 | 0.284772 | − | 0.958595i | \(-0.408082\pi\) | ||||
0.284772 | + | 0.958595i | \(0.408082\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25856.7i | 0.985443i | 0.870187 | + | 0.492722i | \(0.163998\pi\) | ||||
−0.870187 | + | 0.492722i | \(0.836002\pi\) | |||||||
\(884\) | −7313.24 | −0.278248 | ||||||||
\(885\) | −34134.0 | + | 4753.30i | −1.29650 | + | 0.180543i | ||||
\(886\) | −26512.3 | −1.00530 | ||||||||
\(887\) | − | 33095.8i | − | 1.25282i | −0.779495 | − | 0.626408i | \(-0.784524\pi\) | ||
0.779495 | − | 0.626408i | \(-0.215476\pi\) | |||||||
\(888\) | 9202.31i | 0.347758i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8720.60 | + | 1214.38i | −0.328444 | + | 0.0457372i | ||||
\(891\) | −784.791 | −0.0295078 | ||||||||
\(892\) | 22495.7i | 0.844407i | ||||||||
\(893\) | 5321.25i | 0.199405i | ||||||||
\(894\) | 20937.9 | 0.783299 | ||||||||
\(895\) | −3095.84 | − | 22231.6i | −0.115623 | − | 0.830301i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 9681.49i | − | 0.360374i | ||||||
\(898\) | 31547.4i | 1.17233i | ||||||||
\(899\) | −18516.5 | −0.686940 | ||||||||
\(900\) | 2392.61 | − | 679.540i | 0.0886153 | − | 0.0251682i | ||||
\(901\) | −13470.2 | −0.498067 | ||||||||
\(902\) | − | 656.641i | − | 0.0242392i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7403.49 | 0.272385 | ||||||||
\(905\) | 3130.34 | + | 22479.3i | 0.114979 | + | 0.825677i | ||||
\(906\) | −24145.8 | −0.885421 | ||||||||
\(907\) | 21942.3i | 0.803288i | 0.915796 | + | 0.401644i | \(0.131561\pi\) | ||||
−0.915796 | + | 0.401644i | \(0.868439\pi\) | |||||||
\(908\) | − | 8947.88i | − | 0.327033i | ||||||
\(909\) | 1746.49 | 0.0637265 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24393.5 | 0.887150 | 0.443575 | − | 0.896237i | \(-0.353710\pi\) | ||||
0.443575 | + | 0.896237i | \(0.353710\pi\) | |||||||
\(912\) | 1064.22i | 0.0386403i | ||||||||
\(913\) | − | 577.332i | − | 0.0209276i | ||||||
\(914\) | −14176.4 | −0.513035 | ||||||||
\(915\) | −42083.1 | + | 5860.24i | −1.52046 | + | 0.211731i | ||||
\(916\) | −22155.5 | −0.799167 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 7896.98i | 0.283921i | ||||||||
\(919\) | 3024.68 | 0.108569 | 0.0542845 | − | 0.998526i | \(-0.482712\pi\) | ||||
0.0542845 | + | 0.998526i | \(0.482712\pi\) | |||||||
\(920\) | −366.249 | − | 2630.07i | −0.0131249 | − | 0.0942511i | ||||
\(921\) | −12864.8 | −0.460272 | ||||||||
\(922\) | 34791.3i | 1.24272i | ||||||||
\(923\) | 76901.2i | 2.74240i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8370.49 | − | 29471.9i | −0.297535 | − | 1.04760i | ||||
\(926\) | 26701.7 | 0.947594 | ||||||||
\(927\) | − | 1867.59i | − | 0.0661701i | ||||||
\(928\) | 2417.91i | 0.0855299i | ||||||||
\(929\) | −10167.2 | −0.359068 | −0.179534 | − | 0.983752i | \(-0.557459\pi\) | ||||
−0.179534 | + | 0.983752i | \(0.557459\pi\) | |||||||
\(930\) | −3546.94 | − | 25471.0i | −0.125063 | − | 0.898094i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4760.84i | 0.167325i | ||||||||
\(933\) | 27461.0i | 0.963594i | ||||||||
\(934\) | 3044.87 | 0.106671 | ||||||||
\(935\) | −401.209 | + | 55.8701i | −0.0140331 | + | 0.00195417i | ||||
\(936\) | 2765.18 | 0.0965628 | ||||||||
\(937\) | − | 9820.83i | − | 0.342404i | −0.985236 | − | 0.171202i | \(-0.945235\pi\) | ||
0.985236 | − | 0.171202i | \(-0.0547651\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15263.0 | −0.530448 | ||||||||
\(940\) | −16630.6 | + | 2315.88i | −0.577054 | + | 0.0803571i | ||||
\(941\) | 33497.1 | 1.16044 | 0.580220 | − | 0.814460i | \(-0.302967\pi\) | ||||
0.580220 | + | 0.814460i | \(0.302967\pi\) | |||||||
\(942\) | − | 10165.5i | − | 0.351602i | ||||||
\(943\) | − | 7078.96i | − | 0.244457i | ||||||
\(944\) | −10509.0 | −0.362328 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −536.012 | −0.0184221 | ||||||||
\(947\) | 12844.3i | 0.440742i | 0.975416 | + | 0.220371i | \(0.0707268\pi\) | ||||
−0.975416 | + | 0.220371i | \(0.929273\pi\) | |||||||
\(948\) | − | 13306.2i | − | 0.455870i | ||||||
\(949\) | −62444.1 | −2.13595 | ||||||||
\(950\) | −968.026 | − | 3408.35i | −0.0330599 | − | 0.116402i | ||||
\(951\) | −45.0231 | −0.00153520 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42080.9i | 1.43036i | 0.698939 | + | 0.715181i | \(0.253656\pi\) | ||||
−0.698939 | + | 0.715181i | \(0.746344\pi\) | |||||||
\(954\) | 5093.18 | 0.172849 | ||||||||
\(955\) | 2327.69 | + | 16715.4i | 0.0788713 | + | 0.566384i | ||||
\(956\) | −6411.67 | −0.216912 | ||||||||
\(957\) | 488.287i | 0.0164933i | ||||||||
\(958\) | 31053.1i | 1.04727i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3326.04 | + | 463.165i | −0.111820 | + | 0.0155714i | ||||
\(961\) | 30262.3 | 1.01582 | ||||||||
\(962\) | − | 34061.2i | − | 1.14155i | ||||||
\(963\) | − | 2559.76i | − | 0.0856563i | ||||||
\(964\) | −18095.5 | −0.604583 | ||||||||
\(965\) | −45044.6 | + | 6272.65i | −1.50263 | + | 0.209247i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27707.6i | 0.921422i | 0.887550 | + | 0.460711i | \(0.152405\pi\) | ||||
−0.887550 | + | 0.460711i | \(0.847595\pi\) | |||||||
\(968\) | 10632.8i | 0.353050i | ||||||||
\(969\) | 1750.16 | 0.0580219 | ||||||||
\(970\) | −471.325 | − | 3384.64i | −0.0156014 | − | 0.112035i | ||||
\(971\) | −33481.8 | −1.10657 | −0.553286 | − | 0.832991i | \(-0.686626\pi\) | ||||
−0.553286 | + | 0.832991i | \(0.686626\pi\) | |||||||
\(972\) | − | 5507.26i | − | 0.181734i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 25675.0 | 0.844640 | ||||||||
\(975\) | 39211.5 | − | 11136.7i | 1.28797 | − | 0.365804i | ||||
\(976\) | −12956.3 | −0.424918 | ||||||||
\(977\) | − | 15829.2i | − | 0.518342i | −0.965831 | − | 0.259171i | \(-0.916551\pi\) | ||
0.965831 | − | 0.259171i | \(-0.0834494\pi\) | |||||||
\(978\) | − | 12845.7i | − | 0.420000i | ||||||
\(979\) | −542.193 | −0.0177003 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8932.02 | −0.290701 | ||||||||
\(982\) | 13238.3i | 0.430196i | ||||||||
\(983\) | − | 17743.6i | − | 0.575720i | −0.957672 | − | 0.287860i | \(-0.907056\pi\) | ||
0.957672 | − | 0.287860i | \(-0.0929438\pi\) | |||||||
\(984\) | −8952.18 | −0.290025 | ||||||||
\(985\) | −10186.4 | + | 1418.50i | −0.329508 | + | 0.0458854i | ||||
\(986\) | 3976.35 | 0.128431 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 3939.09i | − | 0.126841i | ||||||
\(989\) | −5778.51 | −0.185790 | ||||||||
\(990\) | 151.700 | − | 21.1248i | 0.00487003 | − | 0.000678172i | ||||
\(991\) | −23864.5 | −0.764966 | −0.382483 | − | 0.923962i | \(-0.624931\pi\) | ||||
−0.382483 | + | 0.923962i | \(0.624931\pi\) | |||||||
\(992\) | − | 7841.85i | − | 0.250987i | ||||||
\(993\) | 23780.7i | 0.759977i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2727.94 | + | 19589.6i | 0.0869160 | + | 0.624154i | ||||
\(996\) | −7870.94 | −0.250402 | ||||||||
\(997\) | 9649.90i | 0.306535i | 0.988185 | + | 0.153268i | \(0.0489796\pi\) | ||||
−0.988185 | + | 0.153268i | \(0.951020\pi\) | |||||||
\(998\) | 32443.2i | 1.02903i | ||||||||
\(999\) | −36779.9 | −1.16483 |
(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 | 490.4.c.g.99.17 | yes | 20 | |
5.2 | odd | 4 | 2450.4.a.db.1.7 | 10 | |||
5.3 | odd | 4 | 2450.4.a.dc.1.4 | 10 | |||
5.4 | even | 2 | inner | 490.4.c.g.99.4 | ✓ | 20 | |
7.6 | odd | 2 | inner | 490.4.c.g.99.14 | yes | 20 | |
35.13 | even | 4 | 2450.4.a.dc.1.7 | 10 | |||
35.27 | even | 4 | 2450.4.a.db.1.4 | 10 | |||
35.34 | odd | 2 | inner | 490.4.c.g.99.7 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
490.4.c.g.99.4 | ✓ | 20 | 5.4 | even | 2 | inner | |
490.4.c.g.99.7 | yes | 20 | 35.34 | odd | 2 | inner | |
490.4.c.g.99.14 | yes | 20 | 7.6 | odd | 2 | inner | |
490.4.c.g.99.17 | yes | 20 | 1.1 | even | 1 | trivial | |
2450.4.a.db.1.4 | 10 | 35.27 | even | 4 | |||
2450.4.a.db.1.7 | 10 | 5.2 | odd | 4 | |||
2450.4.a.dc.1.4 | 10 | 5.3 | odd | 4 | |||
2450.4.a.dc.1.7 | 10 | 35.13 | even | 4 |