Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(25,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.25");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.b (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: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.1362828.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 23x^{2} + 48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 25.3 | ||
Root | \(1.52356i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.25 |
Dual form | 39.4.b.b.25.2 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52356i | 0.538658i | 0.963048 | + | 0.269329i | \(0.0868019\pi\) | ||||
−0.963048 | + | 0.269329i | \(0.913198\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 5.67878 | 0.709847 | ||||||||
\(5\) | − | 9.65841i | − | 0.863874i | −0.901904 | − | 0.431937i | \(-0.857830\pi\) | ||
0.901904 | − | 0.431937i | \(-0.142170\pi\) | |||||||
\(6\) | 4.57067i | 0.310994i | ||||||||
\(7\) | 22.3639i | 1.20754i | 0.797159 | + | 0.603769i | \(0.206335\pi\) | ||||
−0.797159 | + | 0.603769i | \(0.793665\pi\) | |||||||
\(8\) | 20.8404i | 0.921023i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 14.7151 | 0.465333 | ||||||||
\(11\) | − | 50.3050i | − | 1.37887i | −0.724349 | − | 0.689433i | \(-0.757860\pi\) | ||
0.724349 | − | 0.689433i | \(-0.242140\pi\) | |||||||
\(12\) | 17.0363 | 0.409831 | ||||||||
\(13\) | −39.7151 | + | 24.8940i | −0.847307 | + | 0.531103i | ||||
\(14\) | −34.0727 | −0.650450 | ||||||||
\(15\) | − | 28.9752i | − | 0.498758i | ||||||
\(16\) | 13.6788 | 0.213731 | ||||||||
\(17\) | −86.1454 | −1.22902 | −0.614509 | − | 0.788910i | \(-0.710646\pi\) | ||||
−0.614509 | + | 0.788910i | \(0.710646\pi\) | |||||||
\(18\) | 13.7120i | 0.179553i | ||||||||
\(19\) | − | 116.880i | − | 1.41127i | −0.708578 | − | 0.705633i | \(-0.750663\pi\) | ||
0.708578 | − | 0.705633i | \(-0.249337\pi\) | |||||||
\(20\) | − | 54.8480i | − | 0.613219i | ||||||
\(21\) | 67.0918i | 0.697173i | ||||||||
\(22\) | 76.6424 | 0.742737 | ||||||||
\(23\) | −72.0000 | −0.652741 | −0.326370 | − | 0.945242i | \(-0.605826\pi\) | ||||
−0.326370 | + | 0.945242i | \(0.605826\pi\) | |||||||
\(24\) | 62.5211i | 0.531753i | ||||||||
\(25\) | 31.7151 | 0.253721 | ||||||||
\(26\) | −37.9273 | − | 60.5082i | −0.286083 | − | 0.456409i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 127.000i | 0.857168i | ||||||||
\(29\) | 14.1454 | 0.0905768 | 0.0452884 | − | 0.998974i | \(-0.485579\pi\) | ||||
0.0452884 | + | 0.998974i | \(0.485579\pi\) | |||||||
\(30\) | 44.1454 | 0.268660 | ||||||||
\(31\) | 196.215i | 1.13682i | 0.822747 | + | 0.568408i | \(0.192441\pi\) | ||||
−0.822747 | + | 0.568408i | \(0.807559\pi\) | |||||||
\(32\) | 187.563i | 1.03615i | ||||||||
\(33\) | − | 150.915i | − | 0.796089i | ||||||
\(34\) | − | 131.247i | − | 0.662021i | ||||||
\(35\) | 216.000 | 1.04316 | ||||||||
\(36\) | 51.1090 | 0.236616 | ||||||||
\(37\) | − | 154.424i | − | 0.686138i | −0.939310 | − | 0.343069i | \(-0.888533\pi\) | ||
0.939310 | − | 0.343069i | \(-0.111467\pi\) | |||||||
\(38\) | 178.073 | 0.760190 | ||||||||
\(39\) | −119.145 | + | 74.6819i | −0.489193 | + | 0.306633i | ||||
\(40\) | 201.285 | 0.795648 | ||||||||
\(41\) | 265.726i | 1.01218i | 0.862480 | + | 0.506091i | \(0.168910\pi\) | ||||
−0.862480 | + | 0.506091i | \(0.831090\pi\) | |||||||
\(42\) | −102.218 | −0.375538 | ||||||||
\(43\) | −211.855 | −0.751338 | −0.375669 | − | 0.926754i | \(-0.622587\pi\) | ||||
−0.375669 | + | 0.926754i | \(0.622587\pi\) | |||||||
\(44\) | − | 285.671i | − | 0.978785i | ||||||
\(45\) | − | 86.9257i | − | 0.287958i | ||||||
\(46\) | − | 109.696i | − | 0.351604i | ||||||
\(47\) | 67.5535i | 0.209653i | 0.994491 | + | 0.104827i | \(0.0334287\pi\) | ||||
−0.994491 | + | 0.104827i | \(0.966571\pi\) | |||||||
\(48\) | 41.0363 | 0.123398 | ||||||||
\(49\) | −157.145 | −0.458150 | ||||||||
\(50\) | 48.3197i | 0.136669i | ||||||||
\(51\) | −258.436 | −0.709574 | ||||||||
\(52\) | −225.533 | + | 141.367i | −0.601459 | + | 0.377002i | ||||
\(53\) | 686.581 | 1.77942 | 0.889710 | − | 0.456527i | \(-0.150907\pi\) | ||||
0.889710 | + | 0.456527i | \(0.150907\pi\) | |||||||
\(54\) | 41.1360i | 0.103665i | ||||||||
\(55\) | −485.866 | −1.19117 | ||||||||
\(56\) | −466.073 | −1.11217 | ||||||||
\(57\) | − | 350.639i | − | 0.814795i | ||||||
\(58\) | 21.5512i | 0.0487899i | ||||||||
\(59\) | − | 91.9304i | − | 0.202853i | −0.994843 | − | 0.101426i | \(-0.967659\pi\) | ||
0.994843 | − | 0.101426i | \(-0.0323406\pi\) | |||||||
\(60\) | − | 164.544i | − | 0.354042i | ||||||
\(61\) | 329.006 | 0.690572 | 0.345286 | − | 0.938498i | \(-0.387782\pi\) | ||||
0.345286 | + | 0.938498i | \(0.387782\pi\) | |||||||
\(62\) | −298.945 | −0.612355 | ||||||||
\(63\) | 201.275i | 0.402513i | ||||||||
\(64\) | −176.333 | −0.344400 | ||||||||
\(65\) | 240.436 | + | 383.585i | 0.458807 | + | 0.731967i | ||||
\(66\) | 229.927 | 0.428820 | ||||||||
\(67\) | − | 768.370i | − | 1.40106i | −0.713621 | − | 0.700532i | \(-0.752946\pi\) | ||
0.713621 | − | 0.700532i | \(-0.247054\pi\) | |||||||
\(68\) | −489.201 | −0.872416 | ||||||||
\(69\) | −216.000 | −0.376860 | ||||||||
\(70\) | 329.088i | 0.561908i | ||||||||
\(71\) | − | 264.969i | − | 0.442902i | −0.975171 | − | 0.221451i | \(-0.928921\pi\) | ||
0.975171 | − | 0.221451i | \(-0.0710793\pi\) | |||||||
\(72\) | 187.563i | 0.307008i | ||||||||
\(73\) | 771.306i | 1.23664i | 0.785927 | + | 0.618319i | \(0.212186\pi\) | ||||
−0.785927 | + | 0.618319i | \(0.787814\pi\) | |||||||
\(74\) | 235.273 | 0.369594 | ||||||||
\(75\) | 95.1454 | 0.146486 | ||||||||
\(76\) | − | 663.734i | − | 1.00178i | ||||||
\(77\) | 1125.02 | 1.66503 | ||||||||
\(78\) | −113.782 | − | 181.525i | −0.165170 | − | 0.263508i | ||||
\(79\) | 1226.86 | 1.74725 | 0.873624 | − | 0.486602i | \(-0.161764\pi\) | ||||
0.873624 | + | 0.486602i | \(0.161764\pi\) | |||||||
\(80\) | − | 132.115i | − | 0.184637i | ||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −404.849 | −0.545220 | ||||||||
\(83\) | 514.019i | 0.679771i | 0.940467 | + | 0.339885i | \(0.110388\pi\) | ||||
−0.940467 | + | 0.339885i | \(0.889612\pi\) | |||||||
\(84\) | 381.000i | 0.494886i | ||||||||
\(85\) | 832.027i | 1.06172i | ||||||||
\(86\) | − | 322.772i | − | 0.404714i | ||||||
\(87\) | 42.4361 | 0.0522945 | ||||||||
\(88\) | 1048.38 | 1.26997 | ||||||||
\(89\) | 527.889i | 0.628720i | 0.949304 | + | 0.314360i | \(0.101790\pi\) | ||||
−0.949304 | + | 0.314360i | \(0.898210\pi\) | |||||||
\(90\) | 132.436 | 0.155111 | ||||||||
\(91\) | −556.727 | − | 888.186i | −0.641328 | − | 1.02316i | ||||
\(92\) | −408.872 | −0.463346 | ||||||||
\(93\) | 588.646i | 0.656341i | ||||||||
\(94\) | −102.921 | −0.112931 | ||||||||
\(95\) | −1128.87 | −1.21916 | ||||||||
\(96\) | 562.690i | 0.598222i | ||||||||
\(97\) | 74.2755i | 0.0777478i | 0.999244 | + | 0.0388739i | \(0.0123771\pi\) | ||||
−0.999244 | + | 0.0388739i | \(0.987623\pi\) | |||||||
\(98\) | − | 239.420i | − | 0.246786i | ||||||
\(99\) | − | 452.745i | − | 0.459622i | ||||||
\(100\) | 180.103 | 0.180103 | ||||||||
\(101\) | −609.419 | −0.600390 | −0.300195 | − | 0.953878i | \(-0.597052\pi\) | ||||
−0.300195 | + | 0.953878i | \(0.597052\pi\) | |||||||
\(102\) | − | 393.742i | − | 0.382218i | ||||||
\(103\) | 32.4361 | 0.0310293 | 0.0155147 | − | 0.999880i | \(-0.495061\pi\) | ||||
0.0155147 | + | 0.999880i | \(0.495061\pi\) | |||||||
\(104\) | −518.799 | − | 827.678i | −0.489158 | − | 0.780389i | ||||
\(105\) | 648.000 | 0.602270 | ||||||||
\(106\) | 1046.04i | 0.958498i | ||||||||
\(107\) | −1725.45 | −1.55893 | −0.779467 | − | 0.626444i | \(-0.784510\pi\) | ||||
−0.779467 | + | 0.626444i | \(0.784510\pi\) | |||||||
\(108\) | 153.327 | 0.136610 | ||||||||
\(109\) | − | 1273.43i | − | 1.11902i | −0.828825 | − | 0.559508i | \(-0.810990\pi\) | ||
0.828825 | − | 0.559508i | \(-0.189010\pi\) | |||||||
\(110\) | − | 740.244i | − | 0.641632i | ||||||
\(111\) | − | 463.271i | − | 0.396142i | ||||||
\(112\) | 305.911i | 0.258088i | ||||||||
\(113\) | 1114.73 | 0.928006 | 0.464003 | − | 0.885834i | \(-0.346413\pi\) | ||||
0.464003 | + | 0.885834i | \(0.346413\pi\) | |||||||
\(114\) | 534.218 | 0.438896 | ||||||||
\(115\) | 695.406i | 0.563886i | ||||||||
\(116\) | 80.3284 | 0.0642957 | ||||||||
\(117\) | −357.436 | + | 224.046i | −0.282436 | + | 0.177034i | ||||
\(118\) | 140.061 | 0.109268 | ||||||||
\(119\) | − | 1926.55i | − | 1.48409i | ||||||
\(120\) | 603.855 | 0.459368 | ||||||||
\(121\) | −1199.59 | −0.901272 | ||||||||
\(122\) | 501.259i | 0.371982i | ||||||||
\(123\) | 797.179i | 0.584384i | ||||||||
\(124\) | 1114.26i | 0.806966i | ||||||||
\(125\) | − | 1513.62i | − | 1.08306i | ||||||
\(126\) | −306.654 | −0.216817 | ||||||||
\(127\) | −1174.01 | −0.820289 | −0.410144 | − | 0.912021i | \(-0.634522\pi\) | ||||
−0.410144 | + | 0.912021i | \(0.634522\pi\) | |||||||
\(128\) | 1231.85i | 0.850637i | ||||||||
\(129\) | −635.564 | −0.433785 | ||||||||
\(130\) | −584.413 | + | 366.318i | −0.394280 | + | 0.247140i | ||||
\(131\) | −1445.16 | −0.963851 | −0.481925 | − | 0.876212i | \(-0.660062\pi\) | ||||
−0.481925 | + | 0.876212i | \(0.660062\pi\) | |||||||
\(132\) | − | 857.013i | − | 0.565102i | ||||||
\(133\) | 2613.89 | 1.70416 | ||||||||
\(134\) | 1170.65 | 0.754695 | ||||||||
\(135\) | − | 260.777i | − | 0.166253i | ||||||
\(136\) | − | 1795.30i | − | 1.13195i | ||||||
\(137\) | 508.793i | 0.317293i | 0.987335 | + | 0.158646i | \(0.0507130\pi\) | ||||
−0.987335 | + | 0.158646i | \(0.949287\pi\) | |||||||
\(138\) | − | 329.088i | − | 0.202999i | ||||||
\(139\) | −757.018 | −0.461938 | −0.230969 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230969 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(140\) | 1226.62 | 0.740486 | ||||||||
\(141\) | 202.661i | 0.121043i | ||||||||
\(142\) | 403.695 | 0.238573 | ||||||||
\(143\) | 1252.29 | + | 1997.87i | 0.732320 | + | 1.16832i | ||||
\(144\) | 123.109 | 0.0712436 | ||||||||
\(145\) | − | 136.622i | − | 0.0782470i | ||||||
\(146\) | −1175.13 | −0.666125 | ||||||||
\(147\) | −471.436 | −0.264513 | ||||||||
\(148\) | − | 876.939i | − | 0.487054i | ||||||
\(149\) | 3247.79i | 1.78570i | 0.450352 | + | 0.892851i | \(0.351298\pi\) | ||||
−0.450352 | + | 0.892851i | \(0.648702\pi\) | |||||||
\(150\) | 144.959i | 0.0789058i | ||||||||
\(151\) | 795.296i | 0.428611i | 0.976767 | + | 0.214305i | \(0.0687488\pi\) | ||||
−0.976767 | + | 0.214305i | \(0.931251\pi\) | |||||||
\(152\) | 2435.82 | 1.29981 | ||||||||
\(153\) | −775.308 | −0.409673 | ||||||||
\(154\) | 1714.03i | 0.896884i | ||||||||
\(155\) | 1895.13 | 0.982067 | ||||||||
\(156\) | −676.600 | + | 424.102i | −0.347252 | + | 0.217662i | ||||
\(157\) | −65.2732 | −0.0331807 | −0.0165903 | − | 0.999862i | \(-0.505281\pi\) | ||||
−0.0165903 | + | 0.999862i | \(0.505281\pi\) | |||||||
\(158\) | 1869.19i | 0.941169i | ||||||||
\(159\) | 2059.74 | 1.02735 | ||||||||
\(160\) | 1811.56 | 0.895104 | ||||||||
\(161\) | − | 1610.20i | − | 0.788210i | ||||||
\(162\) | 123.408i | 0.0598509i | ||||||||
\(163\) | − | 1855.39i | − | 0.891568i | −0.895140 | − | 0.445784i | \(-0.852925\pi\) | ||
0.895140 | − | 0.445784i | \(-0.147075\pi\) | |||||||
\(164\) | 1509.00i | 0.718495i | ||||||||
\(165\) | −1457.60 | −0.687721 | ||||||||
\(166\) | −783.137 | −0.366164 | ||||||||
\(167\) | − | 3532.54i | − | 1.63686i | −0.574604 | − | 0.818432i | \(-0.694844\pi\) | ||
0.574604 | − | 0.818432i | \(-0.305156\pi\) | |||||||
\(168\) | −1398.22 | −0.642112 | ||||||||
\(169\) | 957.581 | − | 1977.33i | 0.435859 | − | 0.900015i | ||||
\(170\) | −1267.64 | −0.571903 | ||||||||
\(171\) | − | 1051.92i | − | 0.470422i | ||||||
\(172\) | −1203.08 | −0.533335 | ||||||||
\(173\) | 3178.36 | 1.39680 | 0.698400 | − | 0.715708i | \(-0.253896\pi\) | ||||
0.698400 | + | 0.715708i | \(0.253896\pi\) | |||||||
\(174\) | 64.6537i | 0.0281689i | ||||||||
\(175\) | 709.275i | 0.306378i | ||||||||
\(176\) | − | 688.111i | − | 0.294706i | ||||||
\(177\) | − | 275.791i | − | 0.117117i | ||||||
\(178\) | −804.267 | −0.338665 | ||||||||
\(179\) | −2741.16 | −1.14460 | −0.572302 | − | 0.820043i | \(-0.693950\pi\) | ||||
−0.572302 | + | 0.820043i | \(0.693950\pi\) | |||||||
\(180\) | − | 493.632i | − | 0.204406i | ||||||
\(181\) | −3871.09 | −1.58970 | −0.794850 | − | 0.606806i | \(-0.792450\pi\) | ||||
−0.794850 | + | 0.606806i | \(0.792450\pi\) | |||||||
\(182\) | 1353.20 | − | 848.204i | 0.551131 | − | 0.345456i | ||||
\(183\) | 987.018 | 0.398702 | ||||||||
\(184\) | − | 1500.51i | − | 0.601189i | ||||||
\(185\) | −1491.49 | −0.592737 | ||||||||
\(186\) | −896.834 | −0.353544 | ||||||||
\(187\) | 4333.54i | 1.69465i | ||||||||
\(188\) | 383.621i | 0.148822i | ||||||||
\(189\) | 603.826i | 0.232391i | ||||||||
\(190\) | − | 1719.90i | − | 0.656708i | ||||||
\(191\) | −928.291 | −0.351669 | −0.175834 | − | 0.984420i | \(-0.556262\pi\) | ||||
−0.175834 | + | 0.984420i | \(0.556262\pi\) | |||||||
\(192\) | −528.999 | −0.198840 | ||||||||
\(193\) | − | 2261.51i | − | 0.843456i | −0.906722 | − | 0.421728i | \(-0.861424\pi\) | ||
0.906722 | − | 0.421728i | \(-0.138576\pi\) | |||||||
\(194\) | −113.163 | −0.0418795 | ||||||||
\(195\) | 721.308 | + | 1150.75i | 0.264892 | + | 0.422601i | ||||
\(196\) | −892.394 | −0.325216 | ||||||||
\(197\) | 2265.59i | 0.819374i | 0.912226 | + | 0.409687i | \(0.134362\pi\) | ||||
−0.912226 | + | 0.409687i | \(0.865638\pi\) | |||||||
\(198\) | 689.782 | 0.247579 | ||||||||
\(199\) | 260.895 | 0.0929366 | 0.0464683 | − | 0.998920i | \(-0.485203\pi\) | ||||
0.0464683 | + | 0.998920i | \(0.485203\pi\) | |||||||
\(200\) | 660.955i | 0.233683i | ||||||||
\(201\) | − | 2305.11i | − | 0.808905i | ||||||
\(202\) | − | 928.483i | − | 0.323405i | ||||||
\(203\) | 316.346i | 0.109375i | ||||||||
\(204\) | −1467.60 | −0.503690 | ||||||||
\(205\) | 2566.49 | 0.874399 | ||||||||
\(206\) | 49.4181i | 0.0167142i | ||||||||
\(207\) | −648.000 | −0.217580 | ||||||||
\(208\) | −543.254 | + | 340.519i | −0.181096 | + | 0.113513i | ||||
\(209\) | −5879.63 | −1.94595 | ||||||||
\(210\) | 987.264i | 0.324417i | ||||||||
\(211\) | 5851.22 | 1.90907 | 0.954537 | − | 0.298092i | \(-0.0963502\pi\) | ||||
0.954537 | + | 0.298092i | \(0.0963502\pi\) | |||||||
\(212\) | 3898.94 | 1.26312 | ||||||||
\(213\) | − | 794.907i | − | 0.255710i | ||||||
\(214\) | − | 2628.82i | − | 0.839732i | ||||||
\(215\) | 2046.18i | 0.649062i | ||||||||
\(216\) | 562.690i | 0.177251i | ||||||||
\(217\) | −4388.15 | −1.37275 | ||||||||
\(218\) | 1940.15 | 0.602767 | ||||||||
\(219\) | 2313.92i | 0.713973i | ||||||||
\(220\) | −2759.13 | −0.845547 | ||||||||
\(221\) | 3421.27 | − | 2144.50i | 1.04136 | − | 0.652736i | ||||
\(222\) | 705.820 | 0.213385 | ||||||||
\(223\) | 3463.60i | 1.04009i | 0.854139 | + | 0.520045i | \(0.174085\pi\) | ||||
−0.854139 | + | 0.520045i | \(0.825915\pi\) | |||||||
\(224\) | −4194.65 | −1.25119 | ||||||||
\(225\) | 285.436 | 0.0845737 | ||||||||
\(226\) | 1698.35i | 0.499878i | ||||||||
\(227\) | − | 5329.15i | − | 1.55819i | −0.626908 | − | 0.779093i | \(-0.715680\pi\) | ||
0.626908 | − | 0.779093i | \(-0.284320\pi\) | |||||||
\(228\) | − | 1991.20i | − | 0.578380i | ||||||
\(229\) | 4773.95i | 1.37761i | 0.724949 | + | 0.688803i | \(0.241863\pi\) | ||||
−0.724949 | + | 0.688803i | \(0.758137\pi\) | |||||||
\(230\) | −1059.49 | −0.303742 | ||||||||
\(231\) | 3375.05 | 0.961308 | ||||||||
\(232\) | 294.795i | 0.0834233i | ||||||||
\(233\) | 4813.78 | 1.35348 | 0.676741 | − | 0.736221i | \(-0.263392\pi\) | ||||
0.676741 | + | 0.736221i | \(0.263392\pi\) | |||||||
\(234\) | −341.346 | − | 544.574i | −0.0953610 | − | 0.152136i | ||||
\(235\) | 652.459 | 0.181114 | ||||||||
\(236\) | − | 522.052i | − | 0.143995i | ||||||
\(237\) | 3680.58 | 1.00877 | ||||||||
\(238\) | 2935.20 | 0.799416 | ||||||||
\(239\) | − | 1683.19i | − | 0.455549i | −0.973714 | − | 0.227775i | \(-0.926855\pi\) | ||
0.973714 | − | 0.227775i | \(-0.0731449\pi\) | |||||||
\(240\) | − | 396.346i | − | 0.106600i | ||||||
\(241\) | − | 664.861i | − | 0.177707i | −0.996045 | − | 0.0888537i | \(-0.971680\pi\) | ||
0.996045 | − | 0.0888537i | \(-0.0283204\pi\) | |||||||
\(242\) | − | 1827.65i | − | 0.485477i | ||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1868.35 | 0.490201 | ||||||||
\(245\) | 1517.77i | 0.395784i | ||||||||
\(246\) | −1214.55 | −0.314783 | ||||||||
\(247\) | 2909.60 | + | 4641.89i | 0.749528 | + | 1.19578i | ||||
\(248\) | −4089.20 | −1.04703 | ||||||||
\(249\) | 1542.06i | 0.392466i | ||||||||
\(250\) | 2306.08 | 0.583398 | ||||||||
\(251\) | −2142.04 | −0.538662 | −0.269331 | − | 0.963048i | \(-0.586802\pi\) | ||||
−0.269331 | + | 0.963048i | \(0.586802\pi\) | |||||||
\(252\) | 1143.00i | 0.285723i | ||||||||
\(253\) | 3621.96i | 0.900042i | ||||||||
\(254\) | − | 1788.67i | − | 0.441855i | ||||||
\(255\) | 2496.08i | 0.612983i | ||||||||
\(256\) | −3287.46 | −0.802603 | ||||||||
\(257\) | −3152.62 | −0.765194 | −0.382597 | − | 0.923915i | \(-0.624970\pi\) | ||||
−0.382597 | + | 0.923915i | \(0.624970\pi\) | |||||||
\(258\) | − | 968.317i | − | 0.233662i | ||||||
\(259\) | 3453.52 | 0.828539 | ||||||||
\(260\) | 1365.38 | + | 2178.29i | 0.325683 | + | 0.519585i | ||||
\(261\) | 127.308 | 0.0301923 | ||||||||
\(262\) | − | 2201.79i | − | 0.519186i | ||||||
\(263\) | −2167.71 | −0.508238 | −0.254119 | − | 0.967173i | \(-0.581786\pi\) | ||||
−0.254119 | + | 0.967173i | \(0.581786\pi\) | |||||||
\(264\) | 3145.13 | 0.733216 | ||||||||
\(265\) | − | 6631.28i | − | 1.53719i | ||||||
\(266\) | 3982.40i | 0.917958i | ||||||||
\(267\) | 1583.67i | 0.362992i | ||||||||
\(268\) | − | 4363.40i | − | 0.994542i | ||||||
\(269\) | −3248.98 | −0.736409 | −0.368204 | − | 0.929745i | \(-0.620027\pi\) | ||||
−0.368204 | + | 0.929745i | \(0.620027\pi\) | |||||||
\(270\) | 397.308 | 0.0895534 | ||||||||
\(271\) | − | 4897.70i | − | 1.09784i | −0.835876 | − | 0.548919i | \(-0.815040\pi\) | ||
0.835876 | − | 0.548919i | \(-0.184960\pi\) | |||||||
\(272\) | −1178.36 | −0.262679 | ||||||||
\(273\) | −1670.18 | − | 2664.56i | −0.370271 | − | 0.590719i | ||||
\(274\) | −775.175 | −0.170912 | ||||||||
\(275\) | − | 1595.43i | − | 0.349847i | ||||||
\(276\) | −1226.62 | −0.267513 | ||||||||
\(277\) | −2900.33 | −0.629111 | −0.314555 | − | 0.949239i | \(-0.601855\pi\) | ||||
−0.314555 | + | 0.949239i | \(0.601855\pi\) | |||||||
\(278\) | − | 1153.36i | − | 0.248827i | ||||||
\(279\) | 1765.94i | 0.378939i | ||||||||
\(280\) | 4501.52i | 0.960776i | ||||||||
\(281\) | 4396.53i | 0.933364i | 0.884425 | + | 0.466682i | \(0.154551\pi\) | ||||
−0.884425 | + | 0.466682i | \(0.845449\pi\) | |||||||
\(282\) | −308.764 | −0.0652009 | ||||||||
\(283\) | 559.151 | 0.117449 | 0.0587245 | − | 0.998274i | \(-0.481297\pi\) | ||||
0.0587245 | + | 0.998274i | \(0.481297\pi\) | |||||||
\(284\) | − | 1504.70i | − | 0.314393i | ||||||
\(285\) | −3386.62 | −0.703880 | ||||||||
\(286\) | −3043.86 | + | 1907.93i | −0.629327 | + | 0.394470i | ||||
\(287\) | −5942.69 | −1.22225 | ||||||||
\(288\) | 1688.07i | 0.345384i | ||||||||
\(289\) | 2508.02 | 0.510487 | ||||||||
\(290\) | 208.151 | 0.0421484 | ||||||||
\(291\) | 222.827i | 0.0448877i | ||||||||
\(292\) | 4380.08i | 0.877825i | ||||||||
\(293\) | − | 6918.65i | − | 1.37950i | −0.724050 | − | 0.689748i | \(-0.757722\pi\) | ||
0.724050 | − | 0.689748i | \(-0.242278\pi\) | |||||||
\(294\) | − | 718.259i | − | 0.142482i | ||||||
\(295\) | −887.901 | −0.175239 | ||||||||
\(296\) | 3218.25 | 0.631949 | ||||||||
\(297\) | − | 1358.24i | − | 0.265363i | ||||||
\(298\) | −4948.19 | −0.961883 | ||||||||
\(299\) | 2859.49 | − | 1792.37i | 0.553072 | − | 0.346673i | ||||
\(300\) | 540.310 | 0.103983 | ||||||||
\(301\) | − | 4737.90i | − | 0.907270i | ||||||
\(302\) | −1211.68 | −0.230875 | ||||||||
\(303\) | −1828.26 | −0.346635 | ||||||||
\(304\) | − | 1598.77i | − | 0.301631i | ||||||
\(305\) | − | 3177.67i | − | 0.596567i | ||||||
\(306\) | − | 1181.22i | − | 0.220674i | ||||||
\(307\) | − | 8980.94i | − | 1.66961i | −0.550548 | − | 0.834803i | \(-0.685581\pi\) | ||
0.550548 | − | 0.834803i | \(-0.314419\pi\) | |||||||
\(308\) | 6388.73 | 1.18192 | ||||||||
\(309\) | 97.3082 | 0.0179148 | ||||||||
\(310\) | 2887.33i | 0.528998i | ||||||||
\(311\) | 7943.13 | 1.44827 | 0.724137 | − | 0.689656i | \(-0.242238\pi\) | ||||
0.724137 | + | 0.689656i | \(0.242238\pi\) | |||||||
\(312\) | −1556.40 | − | 2483.03i | −0.282416 | − | 0.450558i | ||||
\(313\) | −5059.57 | −0.913686 | −0.456843 | − | 0.889547i | \(-0.651020\pi\) | ||||
−0.456843 | + | 0.889547i | \(0.651020\pi\) | |||||||
\(314\) | − | 99.4473i | − | 0.0178730i | ||||||
\(315\) | 1944.00 | 0.347721 | ||||||||
\(316\) | 6967.07 | 1.24028 | ||||||||
\(317\) | 8702.12i | 1.54183i | 0.636939 | + | 0.770914i | \(0.280200\pi\) | ||||
−0.636939 | + | 0.770914i | \(0.719800\pi\) | |||||||
\(318\) | 3138.13i | 0.553389i | ||||||||
\(319\) | − | 711.582i | − | 0.124893i | ||||||
\(320\) | 1703.10i | 0.297519i | ||||||||
\(321\) | −5176.36 | −0.900051 | ||||||||
\(322\) | 2453.23 | 0.424576 | ||||||||
\(323\) | 10068.6i | 1.73447i | ||||||||
\(324\) | 459.981 | 0.0788719 | ||||||||
\(325\) | −1259.57 | + | 789.515i | −0.214980 | + | 0.134752i | ||||
\(326\) | 2826.79 | 0.480250 | ||||||||
\(327\) | − | 3820.30i | − | 0.646064i | ||||||
\(328\) | −5537.84 | −0.932244 | ||||||||
\(329\) | −1510.76 | −0.253164 | ||||||||
\(330\) | − | 2220.73i | − | 0.370446i | ||||||
\(331\) | 1737.65i | 0.288549i | 0.989538 | + | 0.144275i | \(0.0460848\pi\) | ||||
−0.989538 | + | 0.144275i | \(0.953915\pi\) | |||||||
\(332\) | 2919.00i | 0.482533i | ||||||||
\(333\) | − | 1389.81i | − | 0.228713i | ||||||
\(334\) | 5382.02 | 0.881710 | ||||||||
\(335\) | −7421.23 | −1.21034 | ||||||||
\(336\) | 917.734i | 0.149007i | ||||||||
\(337\) | −2917.47 | −0.471586 | −0.235793 | − | 0.971803i | \(-0.575769\pi\) | ||||
−0.235793 | + | 0.971803i | \(0.575769\pi\) | |||||||
\(338\) | 3012.58 | + | 1458.93i | 0.484800 | + | 0.234779i | ||||
\(339\) | 3344.18 | 0.535785 | ||||||||
\(340\) | 4724.90i | 0.753658i | ||||||||
\(341\) | 9870.61 | 1.56752 | ||||||||
\(342\) | 1602.65 | 0.253397 | ||||||||
\(343\) | 4156.44i | 0.654305i | ||||||||
\(344\) | − | 4415.13i | − | 0.692000i | ||||||
\(345\) | 2086.22i | 0.325560i | ||||||||
\(346\) | 4842.41i | 0.752397i | ||||||||
\(347\) | 5081.23 | 0.786095 | 0.393047 | − | 0.919518i | \(-0.371421\pi\) | ||||
0.393047 | + | 0.919518i | \(0.371421\pi\) | |||||||
\(348\) | 240.985 | 0.0371211 | ||||||||
\(349\) | 4266.14i | 0.654330i | 0.944967 | + | 0.327165i | \(0.106093\pi\) | ||||
−0.944967 | + | 0.327165i | \(0.893907\pi\) | |||||||
\(350\) | −1080.62 | −0.165033 | ||||||||
\(351\) | −1072.31 | + | 672.137i | −0.163064 | + | 0.102211i | ||||
\(352\) | 9435.38 | 1.42871 | ||||||||
\(353\) | − | 3264.49i | − | 0.492213i | −0.969243 | − | 0.246106i | \(-0.920849\pi\) | ||
0.969243 | − | 0.246106i | \(-0.0791513\pi\) | |||||||
\(354\) | 420.183 | 0.0630861 | ||||||||
\(355\) | −2559.18 | −0.382612 | ||||||||
\(356\) | 2997.76i | 0.446295i | ||||||||
\(357\) | − | 5779.65i | − | 0.856838i | ||||||
\(358\) | − | 4176.31i | − | 0.616550i | ||||||
\(359\) | − | 4416.98i | − | 0.649357i | −0.945824 | − | 0.324679i | \(-0.894744\pi\) | ||
0.945824 | − | 0.324679i | \(-0.105256\pi\) | |||||||
\(360\) | 1811.56 | 0.265216 | ||||||||
\(361\) | −6801.87 | −0.991670 | ||||||||
\(362\) | − | 5897.82i | − | 0.856305i | ||||||
\(363\) | −3598.78 | −0.520350 | ||||||||
\(364\) | −3161.53 | − | 5043.81i | −0.455245 | − | 0.726285i | ||||
\(365\) | 7449.59 | 1.06830 | ||||||||
\(366\) | 1503.78i | 0.214764i | ||||||||
\(367\) | −1740.22 | −0.247516 | −0.123758 | − | 0.992312i | \(-0.539495\pi\) | ||||
−0.123758 | + | 0.992312i | \(0.539495\pi\) | |||||||
\(368\) | −984.872 | −0.139511 | ||||||||
\(369\) | 2391.54i | 0.337394i | ||||||||
\(370\) | − | 2272.37i | − | 0.319283i | ||||||
\(371\) | 15354.7i | 2.14872i | ||||||||
\(372\) | 3342.79i | 0.465902i | ||||||||
\(373\) | 1176.28 | 0.163285 | 0.0816427 | − | 0.996662i | \(-0.473983\pi\) | ||||
0.0816427 | + | 0.996662i | \(0.473983\pi\) | |||||||
\(374\) | −6602.39 | −0.912838 | ||||||||
\(375\) | − | 4540.86i | − | 0.625304i | ||||||
\(376\) | −1407.84 | −0.193095 | ||||||||
\(377\) | −561.785 | + | 352.134i | −0.0767464 | + | 0.0481056i | ||||
\(378\) | −919.962 | −0.125179 | ||||||||
\(379\) | 7135.54i | 0.967092i | 0.875319 | + | 0.483546i | \(0.160651\pi\) | ||||
−0.875319 | + | 0.483546i | \(0.839349\pi\) | |||||||
\(380\) | −6410.62 | −0.865415 | ||||||||
\(381\) | −3522.04 | −0.473594 | ||||||||
\(382\) | − | 1414.30i | − | 0.189429i | ||||||
\(383\) | − | 1942.87i | − | 0.259207i | −0.991566 | − | 0.129603i | \(-0.958630\pi\) | ||
0.991566 | − | 0.129603i | \(-0.0413704\pi\) | |||||||
\(384\) | 3695.56i | 0.491116i | ||||||||
\(385\) | − | 10865.9i | − | 1.43838i | ||||||
\(386\) | 3445.53 | 0.454334 | ||||||||
\(387\) | −1906.69 | −0.250446 | ||||||||
\(388\) | 421.794i | 0.0551891i | ||||||||
\(389\) | 7545.92 | 0.983531 | 0.491766 | − | 0.870728i | \(-0.336352\pi\) | ||||
0.491766 | + | 0.870728i | \(0.336352\pi\) | |||||||
\(390\) | −1753.24 | + | 1098.95i | −0.227638 | + | 0.142686i | ||||
\(391\) | 6202.47 | 0.802231 | ||||||||
\(392\) | − | 3274.97i | − | 0.421967i | ||||||
\(393\) | −4335.49 | −0.556480 | ||||||||
\(394\) | −3451.75 | −0.441362 | ||||||||
\(395\) | − | 11849.5i | − | 1.50940i | ||||||
\(396\) | − | 2571.04i | − | 0.326262i | ||||||
\(397\) | − | 415.922i | − | 0.0525806i | −0.999654 | − | 0.0262903i | \(-0.991631\pi\) | ||
0.999654 | − | 0.0262903i | \(-0.00836943\pi\) | |||||||
\(398\) | 397.489i | 0.0500611i | ||||||||
\(399\) | 7841.67 | 0.983896 | ||||||||
\(400\) | 433.824 | 0.0542280 | ||||||||
\(401\) | 958.178i | 0.119324i | 0.998219 | + | 0.0596622i | \(0.0190024\pi\) | ||||
−0.998219 | + | 0.0596622i | \(0.980998\pi\) | |||||||
\(402\) | 3511.96 | 0.435723 | ||||||||
\(403\) | −4884.58 | − | 7792.71i | −0.603767 | − | 0.963233i | ||||
\(404\) | −3460.75 | −0.426185 | ||||||||
\(405\) | − | 782.331i | − | 0.0959860i | ||||||
\(406\) | −481.970 | −0.0589157 | ||||||||
\(407\) | −7768.29 | −0.946093 | ||||||||
\(408\) | − | 5385.90i | − | 0.653534i | ||||||
\(409\) | 4284.83i | 0.518022i | 0.965874 | + | 0.259011i | \(0.0833966\pi\) | ||||
−0.965874 | + | 0.259011i | \(0.916603\pi\) | |||||||
\(410\) | 3910.20i | 0.471002i | ||||||||
\(411\) | 1526.38i | 0.183189i | ||||||||
\(412\) | 184.197 | 0.0220261 | ||||||||
\(413\) | 2055.92 | 0.244953 | ||||||||
\(414\) | − | 987.264i | − | 0.117201i | ||||||
\(415\) | 4964.61 | 0.587236 | ||||||||
\(416\) | −4669.20 | − | 7449.10i | −0.550303 | − | 0.877938i | ||||
\(417\) | −2271.05 | −0.266700 | ||||||||
\(418\) | − | 8957.95i | − | 1.04820i | ||||||
\(419\) | −9949.01 | −1.16000 | −0.580001 | − | 0.814616i | \(-0.696948\pi\) | ||||
−0.580001 | + | 0.814616i | \(0.696948\pi\) | |||||||
\(420\) | 3679.85 | 0.427520 | ||||||||
\(421\) | − | 377.250i | − | 0.0436724i | −0.999762 | − | 0.0218362i | \(-0.993049\pi\) | ||
0.999762 | − | 0.0218362i | \(-0.00695122\pi\) | |||||||
\(422\) | 8914.66i | 1.02834i | ||||||||
\(423\) | 607.982i | 0.0698843i | ||||||||
\(424\) | 14308.6i | 1.63889i | ||||||||
\(425\) | −2732.11 | −0.311828 | ||||||||
\(426\) | 1211.08 | 0.137740 | ||||||||
\(427\) | 7357.86i | 0.833892i | ||||||||
\(428\) | −9798.47 | −1.10661 | ||||||||
\(429\) | 3756.87 | + | 5993.61i | 0.422805 | + | 0.674532i | ||||
\(430\) | −3117.47 | −0.349622 | ||||||||
\(431\) | 2437.13i | 0.272373i | 0.990683 | + | 0.136186i | \(0.0434846\pi\) | ||||
−0.990683 | + | 0.136186i | \(0.956515\pi\) | |||||||
\(432\) | 369.327 | 0.0411325 | ||||||||
\(433\) | −11215.1 | −1.24471 | −0.622357 | − | 0.782733i | \(-0.713825\pi\) | ||||
−0.622357 | + | 0.782733i | \(0.713825\pi\) | |||||||
\(434\) | − | 6685.58i | − | 0.739443i | ||||||
\(435\) | − | 409.865i | − | 0.0451759i | ||||||
\(436\) | − | 7231.55i | − | 0.794331i | ||||||
\(437\) | 8415.34i | 0.921191i | ||||||||
\(438\) | −3525.38 | −0.384588 | ||||||||
\(439\) | 1835.19 | 0.199519 | 0.0997596 | − | 0.995012i | \(-0.468193\pi\) | ||||
0.0997596 | + | 0.995012i | \(0.468193\pi\) | |||||||
\(440\) | − | 10125.6i | − | 1.09709i | ||||||
\(441\) | −1414.31 | −0.152717 | ||||||||
\(442\) | 3267.26 | + | 5212.50i | 0.351601 | + | 0.560935i | ||||
\(443\) | 11610.1 | 1.24518 | 0.622588 | − | 0.782550i | \(-0.286081\pi\) | ||||
0.622588 | + | 0.782550i | \(0.286081\pi\) | |||||||
\(444\) | − | 2630.82i | − | 0.281201i | ||||||
\(445\) | 5098.56 | 0.543135 | ||||||||
\(446\) | −5276.99 | −0.560253 | ||||||||
\(447\) | 9743.38i | 1.03098i | ||||||||
\(448\) | − | 3943.50i | − | 0.415877i | ||||||
\(449\) | − | 14087.0i | − | 1.48064i | −0.672255 | − | 0.740319i | \(-0.734674\pi\) | ||
0.672255 | − | 0.740319i | \(-0.265326\pi\) | |||||||
\(450\) | 434.878i | 0.0455563i | ||||||||
\(451\) | 13367.4 | 1.39566 | ||||||||
\(452\) | 6330.29 | 0.658743 | ||||||||
\(453\) | 2385.89i | 0.247459i | ||||||||
\(454\) | 8119.26 | 0.839330 | ||||||||
\(455\) | −8578.47 | + | 5377.10i | −0.883878 | + | 0.554027i | ||||
\(456\) | 7307.45 | 0.750445 | ||||||||
\(457\) | − | 2375.01i | − | 0.243103i | −0.992585 | − | 0.121552i | \(-0.961213\pi\) | ||
0.992585 | − | 0.121552i | \(-0.0387870\pi\) | |||||||
\(458\) | −7273.38 | −0.742058 | ||||||||
\(459\) | −2325.92 | −0.236525 | ||||||||
\(460\) | 3949.05i | 0.400273i | ||||||||
\(461\) | 6372.06i | 0.643766i | 0.946779 | + | 0.321883i | \(0.104316\pi\) | ||||
−0.946779 | + | 0.321883i | \(0.895684\pi\) | |||||||
\(462\) | 5142.08i | 0.517816i | ||||||||
\(463\) | − | 63.4732i | − | 0.00637117i | −0.999995 | − | 0.00318558i | \(-0.998986\pi\) | ||
0.999995 | − | 0.00318558i | \(-0.00101400\pi\) | |||||||
\(464\) | 193.491 | 0.0193591 | ||||||||
\(465\) | 5685.38 | 0.566996 | ||||||||
\(466\) | 7334.06i | 0.729064i | ||||||||
\(467\) | 7855.78 | 0.778420 | 0.389210 | − | 0.921149i | \(-0.372748\pi\) | ||||
0.389210 | + | 0.921149i | \(0.372748\pi\) | |||||||
\(468\) | −2029.80 | + | 1272.31i | −0.200486 | + | 0.125667i | ||||
\(469\) | 17183.8 | 1.69184 | ||||||||
\(470\) | 994.058i | 0.0975584i | ||||||||
\(471\) | −195.820 | −0.0191569 | ||||||||
\(472\) | 1915.86 | 0.186832 | ||||||||
\(473\) | 10657.3i | 1.03599i | ||||||||
\(474\) | 5607.57i | 0.543384i | ||||||||
\(475\) | − | 3706.85i | − | 0.358068i | ||||||
\(476\) | − | 10940.4i | − | 1.05348i | ||||||
\(477\) | 6179.23 | 0.593140 | ||||||||
\(478\) | 2564.43 | 0.245385 | ||||||||
\(479\) | − | 13033.3i | − | 1.24323i | −0.783324 | − | 0.621613i | \(-0.786477\pi\) | ||
0.783324 | − | 0.621613i | \(-0.213523\pi\) | |||||||
\(480\) | 5434.69 | 0.516789 | ||||||||
\(481\) | 3844.22 | + | 6132.96i | 0.364410 | + | 0.581370i | ||||
\(482\) | 1012.95 | 0.0957235 | ||||||||
\(483\) | − | 4830.61i | − | 0.455073i | ||||||
\(484\) | −6812.23 | −0.639766 | ||||||||
\(485\) | 717.384 | 0.0671643 | ||||||||
\(486\) | 370.224i | 0.0345549i | ||||||||
\(487\) | 69.8976i | 0.00650383i | 0.999995 | + | 0.00325191i | \(0.00103512\pi\) | ||||
−0.999995 | + | 0.00325191i | \(0.998965\pi\) | |||||||
\(488\) | 6856.60i | 0.636033i | ||||||||
\(489\) | − | 5566.18i | − | 0.514747i | ||||||
\(490\) | −2312.41 | −0.213192 | ||||||||
\(491\) | 2625.66 | 0.241333 | 0.120667 | − | 0.992693i | \(-0.461497\pi\) | ||||
0.120667 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(492\) | 4527.01i | 0.414823i | ||||||||
\(493\) | −1218.56 | −0.111321 | ||||||||
\(494\) | −7072.18 | + | 4432.93i | −0.644114 | + | 0.403739i | ||||
\(495\) | −4372.80 | −0.397056 | ||||||||
\(496\) | 2683.99i | 0.242973i | ||||||||
\(497\) | 5925.75 | 0.534821 | ||||||||
\(498\) | −2349.41 | −0.211405 | ||||||||
\(499\) | − | 7631.34i | − | 0.684621i | −0.939587 | − | 0.342310i | \(-0.888791\pi\) | ||
0.939587 | − | 0.342310i | \(-0.111209\pi\) | |||||||
\(500\) | − | 8595.51i | − | 0.768806i | ||||||
\(501\) | − | 10597.6i | − | 0.945044i | ||||||
\(502\) | − | 3263.51i | − | 0.290154i | ||||||
\(503\) | −4320.14 | −0.382953 | −0.191477 | − | 0.981497i | \(-0.561328\pi\) | ||||
−0.191477 | + | 0.981497i | \(0.561328\pi\) | |||||||
\(504\) | −4194.65 | −0.370724 | ||||||||
\(505\) | 5886.01i | 0.518662i | ||||||||
\(506\) | −5518.26 | −0.484815 | ||||||||
\(507\) | 2872.74 | − | 5932.00i | 0.251643 | − | 0.519624i | ||||
\(508\) | −6666.95 | −0.582280 | ||||||||
\(509\) | 12450.7i | 1.08422i | 0.840308 | + | 0.542109i | \(0.182374\pi\) | ||||
−0.840308 | + | 0.542109i | \(0.817626\pi\) | |||||||
\(510\) | −3802.92 | −0.330188 | ||||||||
\(511\) | −17249.4 | −1.49329 | ||||||||
\(512\) | 4846.21i | 0.418309i | ||||||||
\(513\) | − | 3155.75i | − | 0.271598i | ||||||
\(514\) | − | 4803.18i | − | 0.412178i | ||||||
\(515\) | − | 313.281i | − | 0.0268054i | ||||||
\(516\) | −3609.23 | −0.307921 | ||||||||
\(517\) | 3398.28 | 0.289083 | ||||||||
\(518\) | 5261.63i | 0.446299i | ||||||||
\(519\) | 9535.08 | 0.806443 | ||||||||
\(520\) | −7994.05 | + | 5010.78i | −0.674158 | + | 0.422571i | ||||
\(521\) | 14373.1 | 1.20863 | 0.604314 | − | 0.796746i | \(-0.293447\pi\) | ||||
0.604314 | + | 0.796746i | \(0.293447\pi\) | |||||||
\(522\) | 193.961i | 0.0162633i | ||||||||
\(523\) | −16946.7 | −1.41688 | −0.708439 | − | 0.705772i | \(-0.750600\pi\) | ||||
−0.708439 | + | 0.705772i | \(0.750600\pi\) | |||||||
\(524\) | −8206.76 | −0.684187 | ||||||||
\(525\) | 2127.82i | 0.176887i | ||||||||
\(526\) | − | 3302.62i | − | 0.273767i | ||||||
\(527\) | − | 16903.0i | − | 1.39717i | ||||||
\(528\) | − | 2064.33i | − | 0.170149i | ||||||
\(529\) | −6983.00 | −0.573929 | ||||||||
\(530\) | 10103.1 | 0.828022 | ||||||||
\(531\) | − | 827.373i | − | 0.0676176i | ||||||
\(532\) | 14843.7 | 1.20969 | ||||||||
\(533\) | −6614.98 | − | 10553.4i | −0.537574 | − | 0.857630i | ||||
\(534\) | −2412.80 | −0.195528 | ||||||||
\(535\) | 16665.1i | 1.34672i | ||||||||
\(536\) | 16013.1 | 1.29041 | ||||||||
\(537\) | −8223.49 | −0.660837 | ||||||||
\(538\) | − | 4950.00i | − | 0.396673i | ||||||
\(539\) | 7905.20i | 0.631727i | ||||||||
\(540\) | − | 1480.90i | − | 0.118014i | ||||||
\(541\) | 815.667i | 0.0648212i | 0.999475 | + | 0.0324106i | \(0.0103184\pi\) | ||||
−0.999475 | + | 0.0324106i | \(0.989682\pi\) | |||||||
\(542\) | 7461.92 | 0.591359 | ||||||||
\(543\) | −11613.3 | −0.917814 | ||||||||
\(544\) | − | 16157.7i | − | 1.27345i | ||||||
\(545\) | −12299.3 | −0.966689 | ||||||||
\(546\) | 4059.60 | − | 2544.61i | 0.318196 | − | 0.199449i | ||||
\(547\) | −17971.4 | −1.40476 | −0.702378 | − | 0.711804i | \(-0.747878\pi\) | ||||
−0.702378 | + | 0.711804i | \(0.747878\pi\) | |||||||
\(548\) | 2889.32i | 0.225230i | ||||||||
\(549\) | 2961.05 | 0.230191 | ||||||||
\(550\) | 2430.72 | 0.188448 | ||||||||
\(551\) | − | 1653.31i | − | 0.127828i | ||||||
\(552\) | − | 4501.52i | − | 0.347097i | ||||||
\(553\) | 27437.4i | 2.10987i | ||||||||
\(554\) | − | 4418.81i | − | 0.338876i | ||||||
\(555\) | −4474.47 | −0.342217 | ||||||||
\(556\) | −4298.94 | −0.327906 | ||||||||
\(557\) | 6760.83i | 0.514301i | 0.966371 | + | 0.257151i | \(0.0827836\pi\) | ||||
−0.966371 | + | 0.257151i | \(0.917216\pi\) | |||||||
\(558\) | −2690.50 | −0.204118 | ||||||||
\(559\) | 8413.83 | − | 5273.90i | 0.636614 | − | 0.399038i | ||||
\(560\) | 2954.62 | 0.222956 | ||||||||
\(561\) | 13000.6i | 0.978408i | ||||||||
\(562\) | −6698.36 | −0.502764 | ||||||||
\(563\) | 12962.7 | 0.970359 | 0.485179 | − | 0.874415i | \(-0.338754\pi\) | ||||
0.485179 | + | 0.874415i | \(0.338754\pi\) | |||||||
\(564\) | 1150.86i | 0.0859222i | ||||||||
\(565\) | − | 10766.5i | − | 0.801681i | ||||||
\(566\) | 851.898i | 0.0632649i | ||||||||
\(567\) | 1811.48i | 0.134171i | ||||||||
\(568\) | 5522.05 | 0.407923 | ||||||||
\(569\) | 164.757 | 0.0121388 | 0.00606938 | − | 0.999982i | \(-0.498068\pi\) | ||||
0.00606938 | + | 0.999982i | \(0.498068\pi\) | |||||||
\(570\) | − | 5159.70i | − | 0.379151i | ||||||
\(571\) | −5216.55 | −0.382322 | −0.191161 | − | 0.981559i | \(-0.561225\pi\) | ||||
−0.191161 | + | 0.981559i | \(0.561225\pi\) | |||||||
\(572\) | 7111.48 | + | 11345.5i | 0.519836 | + | 0.829331i | ||||
\(573\) | −2784.87 | −0.203036 | ||||||||
\(574\) | − | 9054.01i | − | 0.658375i | ||||||
\(575\) | −2283.49 | −0.165614 | ||||||||
\(576\) | −1587.00 | −0.114800 | ||||||||
\(577\) | − | 12753.3i | − | 0.920151i | −0.887880 | − | 0.460076i | \(-0.847822\pi\) | ||
0.887880 | − | 0.460076i | \(-0.152178\pi\) | |||||||
\(578\) | 3821.11i | 0.274978i | ||||||||
\(579\) | − | 6784.53i | − | 0.486970i | ||||||
\(580\) | − | 775.844i | − | 0.0555434i | ||||||
\(581\) | −11495.5 | −0.820849 | ||||||||
\(582\) | −339.489 | −0.0241791 | ||||||||
\(583\) | − | 34538.5i | − | 2.45358i | ||||||
\(584\) | −16074.3 | −1.13897 | ||||||||
\(585\) | 2163.92 | + | 3452.26i | 0.152936 | + | 0.243989i | ||||
\(586\) | 10540.9 | 0.743076 | ||||||||
\(587\) | − | 1575.38i | − | 0.110771i | −0.998465 | − | 0.0553857i | \(-0.982361\pi\) | ||
0.998465 | − | 0.0553857i | \(-0.0176388\pi\) | |||||||
\(588\) | −2677.18 | −0.187764 | ||||||||
\(589\) | 22933.6 | 1.60435 | ||||||||
\(590\) | − | 1352.77i | − | 0.0943941i | ||||||
\(591\) | 6796.77i | 0.473066i | ||||||||
\(592\) | − | 2112.33i | − | 0.146649i | ||||||
\(593\) | 3845.95i | 0.266331i | 0.991094 | + | 0.133165i | \(0.0425142\pi\) | ||||
−0.991094 | + | 0.133165i | \(0.957486\pi\) | |||||||
\(594\) | 2069.35 | 0.142940 | ||||||||
\(595\) | −18607.4 | −1.28207 | ||||||||
\(596\) | 18443.5i | 1.26758i | ||||||||
\(597\) | 782.686 | 0.0536570 | ||||||||
\(598\) | 2730.77 | + | 4356.59i | 0.186738 | + | 0.297917i | ||||
\(599\) | 6107.20 | 0.416583 | 0.208292 | − | 0.978067i | \(-0.433210\pi\) | ||||
0.208292 | + | 0.978067i | \(0.433210\pi\) | |||||||
\(600\) | 1982.86i | 0.134917i | ||||||||
\(601\) | 9638.90 | 0.654208 | 0.327104 | − | 0.944988i | \(-0.393927\pi\) | ||||
0.327104 | + | 0.944988i | \(0.393927\pi\) | |||||||
\(602\) | 7218.46 | 0.488708 | ||||||||
\(603\) | − | 6915.33i | − | 0.467022i | ||||||
\(604\) | 4516.31i | 0.304248i | ||||||||
\(605\) | 11586.2i | 0.778586i | ||||||||
\(606\) | − | 2785.45i | − | 0.186718i | ||||||
\(607\) | 11821.7 | 0.790489 | 0.395244 | − | 0.918576i | \(-0.370660\pi\) | ||||
0.395244 | + | 0.918576i | \(0.370660\pi\) | |||||||
\(608\) | 21922.4 | 1.46228 | ||||||||
\(609\) | 949.037i | 0.0631477i | ||||||||
\(610\) | 4841.36 | 0.321346 | ||||||||
\(611\) | −1681.67 | − | 2682.90i | −0.111347 | − | 0.177640i | ||||
\(612\) | −4402.80 | −0.290805 | ||||||||
\(613\) | − | 8107.86i | − | 0.534214i | −0.963667 | − | 0.267107i | \(-0.913932\pi\) | ||
0.963667 | − | 0.267107i | \(-0.0860677\pi\) | |||||||
\(614\) | 13683.0 | 0.899347 | ||||||||
\(615\) | 7699.48 | 0.504834 | ||||||||
\(616\) | 23445.8i | 1.53354i | ||||||||
\(617\) | − | 27647.6i | − | 1.80397i | −0.431768 | − | 0.901985i | \(-0.642110\pi\) | ||
0.431768 | − | 0.901985i | \(-0.357890\pi\) | |||||||
\(618\) | 148.254i | 0.00964995i | ||||||||
\(619\) | 29181.9i | 1.89486i | 0.319956 | + | 0.947432i | \(0.396332\pi\) | ||||
−0.319956 | + | 0.947432i | \(0.603668\pi\) | |||||||
\(620\) | 10762.0 | 0.697118 | ||||||||
\(621\) | −1944.00 | −0.125620 | ||||||||
\(622\) | 12101.8i | 0.780125i | ||||||||
\(623\) | −11805.7 | −0.759204 | ||||||||
\(624\) | −1629.76 | + | 1021.56i | −0.104556 | + | 0.0655369i | ||||
\(625\) | −10654.8 | −0.681905 | ||||||||
\(626\) | − | 7708.53i | − | 0.492165i | ||||||
\(627\) | −17638.9 | −1.12349 | ||||||||
\(628\) | −370.672 | −0.0235532 | ||||||||
\(629\) | 13302.9i | 0.843277i | ||||||||
\(630\) | 2961.79i | 0.187303i | ||||||||
\(631\) | − | 2209.34i | − | 0.139386i | −0.997569 | − | 0.0696928i | \(-0.977798\pi\) | ||
0.997569 | − | 0.0696928i | \(-0.0222019\pi\) | |||||||
\(632\) | 25568.2i | 1.60926i | ||||||||
\(633\) | 17553.7 | 1.10220 | ||||||||
\(634\) | −13258.2 | −0.830518 | ||||||||
\(635\) | 11339.1i | 0.708627i | ||||||||
\(636\) | 11696.8 | 0.729260 | ||||||||
\(637\) | 6241.05 | − | 3911.97i | 0.388194 | − | 0.243325i | ||||
\(638\) | 1084.13 | 0.0672748 | ||||||||
\(639\) | − | 2384.72i | − | 0.147634i | ||||||
\(640\) | 11897.8 | 0.734844 | ||||||||
\(641\) | 18256.0 | 1.12491 | 0.562455 | − | 0.826828i | \(-0.309857\pi\) | ||||
0.562455 | + | 0.826828i | \(0.309857\pi\) | |||||||
\(642\) | − | 7886.47i | − | 0.484820i | ||||||
\(643\) | − | 1281.61i | − | 0.0786033i | −0.999227 | − | 0.0393016i | \(-0.987487\pi\) | ||
0.999227 | − | 0.0393016i | \(-0.0125133\pi\) | |||||||
\(644\) | − | 9143.99i | − | 0.559509i | ||||||
\(645\) | 6138.54i | 0.374736i | ||||||||
\(646\) | −15340.1 | −0.934287 | ||||||||
\(647\) | −16393.2 | −0.996107 | −0.498054 | − | 0.867146i | \(-0.665952\pi\) | ||||
−0.498054 | + | 0.867146i | \(0.665952\pi\) | |||||||
\(648\) | 1688.07i | 0.102336i | ||||||||
\(649\) | −4624.56 | −0.279707 | ||||||||
\(650\) | −1202.87 | − | 1919.02i | −0.0725853 | − | 0.115800i | ||||
\(651\) | −13164.4 | −0.792557 | ||||||||
\(652\) | − | 10536.4i | − | 0.632878i | ||||||
\(653\) | 16759.2 | 1.00434 | 0.502172 | − | 0.864768i | \(-0.332534\pi\) | ||||
0.502172 | + | 0.864768i | \(0.332534\pi\) | |||||||
\(654\) | 5820.44 | 0.348008 | ||||||||
\(655\) | 13958.0i | 0.832646i | ||||||||
\(656\) | 3634.81i | 0.216335i | ||||||||
\(657\) | 6941.76i | 0.412213i | ||||||||
\(658\) | − | 2301.73i | − | 0.136369i | ||||||
\(659\) | −29659.3 | −1.75320 | −0.876601 | − | 0.481217i | \(-0.840195\pi\) | ||||
−0.876601 | + | 0.481217i | \(0.840195\pi\) | |||||||
\(660\) | −8277.38 | −0.488177 | ||||||||
\(661\) | − | 10386.0i | − | 0.611147i | −0.952169 | − | 0.305573i | \(-0.901152\pi\) | ||
0.952169 | − | 0.305573i | \(-0.0988481\pi\) | |||||||
\(662\) | −2647.40 | −0.155429 | ||||||||
\(663\) | 10263.8 | − | 6433.50i | 0.601227 | − | 0.376857i | ||||
\(664\) | −10712.4 | −0.626084 | ||||||||
\(665\) | − | 25246.0i | − | 1.47218i | ||||||
\(666\) | 2117.46 | 0.123198 | ||||||||
\(667\) | −1018.47 | −0.0591232 | ||||||||
\(668\) | − | 20060.5i | − | 1.16192i | ||||||
\(669\) | 10390.8i | 0.600496i | ||||||||
\(670\) | − | 11306.7i | − | 0.651962i | ||||||
\(671\) | − | 16550.6i | − | 0.952206i | ||||||
\(672\) | −12584.0 | −0.722376 | ||||||||
\(673\) | 19449.6 | 1.11400 | 0.557002 | − | 0.830511i | \(-0.311951\pi\) | ||||
0.557002 | + | 0.830511i | \(0.311951\pi\) | |||||||
\(674\) | − | 4444.92i | − | 0.254024i | ||||||
\(675\) | 856.308 | 0.0488286 | ||||||||
\(676\) | 5437.89 | − | 11228.8i | 0.309393 | − | 0.638873i | ||||
\(677\) | −6629.48 | −0.376354 | −0.188177 | − | 0.982135i | \(-0.560258\pi\) | ||||
−0.188177 | + | 0.982135i | \(0.560258\pi\) | |||||||
\(678\) | 5095.04i | 0.288605i | ||||||||
\(679\) | −1661.09 | −0.0938835 | ||||||||
\(680\) | −17339.8 | −0.977867 | ||||||||
\(681\) | − | 15987.5i | − | 0.899619i | ||||||
\(682\) | 15038.4i | 0.844356i | ||||||||
\(683\) | − | 2526.40i | − | 0.141537i | −0.997493 | − | 0.0707687i | \(-0.977455\pi\) | ||
0.997493 | − | 0.0707687i | \(-0.0225452\pi\) | |||||||
\(684\) | − | 5973.61i | − | 0.333928i | ||||||
\(685\) | 4914.13 | 0.274101 | ||||||||
\(686\) | −6332.57 | −0.352447 | ||||||||
\(687\) | 14321.9i | 0.795361i | ||||||||
\(688\) | −2897.91 | −0.160584 | ||||||||
\(689\) | −27267.7 | + | 17091.7i | −1.50771 | + | 0.945055i | ||||
\(690\) | −3178.47 | −0.175365 | ||||||||
\(691\) | − | 3808.76i | − | 0.209685i | −0.994489 | − | 0.104842i | \(-0.966566\pi\) | ||
0.994489 | − | 0.104842i | \(-0.0334338\pi\) | |||||||
\(692\) | 18049.2 | 0.991515 | ||||||||
\(693\) | 10125.2 | 0.555011 | ||||||||
\(694\) | 7741.54i | 0.423436i | ||||||||
\(695\) | 7311.59i | 0.399056i | ||||||||
\(696\) | 884.384i | 0.0481645i | ||||||||
\(697\) | − | 22891.1i | − | 1.24399i | ||||||
\(698\) | −6499.69 | −0.352460 | ||||||||
\(699\) | 14441.3 | 0.781433 | ||||||||
\(700\) | 4027.81i | 0.217482i | ||||||||
\(701\) | −33617.8 | −1.81131 | −0.905655 | − | 0.424015i | \(-0.860620\pi\) | ||||
−0.905655 | + | 0.424015i | \(0.860620\pi\) | |||||||
\(702\) | −1024.04 | − | 1633.72i | −0.0550567 | − | 0.0878359i | ||||
\(703\) | −18049.0 | −0.968323 | ||||||||
\(704\) | 8870.43i | 0.474882i | ||||||||
\(705\) | 1957.38 | 0.104566 | ||||||||
\(706\) | 4973.63 | 0.265134 | ||||||||
\(707\) | − | 13629.0i | − | 0.724994i | ||||||
\(708\) | − | 1566.16i | − | 0.0831353i | ||||||
\(709\) | 26606.5i | 1.40935i | 0.709530 | + | 0.704675i | \(0.248907\pi\) | ||||
−0.709530 | + | 0.704675i | \(0.751093\pi\) | |||||||
\(710\) | − | 3899.05i | − | 0.206097i | ||||||
\(711\) | 11041.7 | 0.582416 | ||||||||
\(712\) | −11001.4 | −0.579066 | ||||||||
\(713\) | − | 14127.5i | − | 0.742046i | ||||||
\(714\) | 8805.61 | 0.461543 | ||||||||
\(715\) | 19296.2 | − | 12095.1i | 1.00928 | − | 0.632633i | ||||
\(716\) | −15566.5 | −0.812494 | ||||||||
\(717\) | − | 5049.56i | − | 0.263011i | ||||||
\(718\) | 6729.51 | 0.349781 | ||||||||
\(719\) | 16539.3 | 0.857877 | 0.428939 | − | 0.903334i | \(-0.358888\pi\) | ||||
0.428939 | + | 0.903334i | \(0.358888\pi\) | |||||||
\(720\) | − | 1189.04i | − | 0.0615456i | ||||||
\(721\) | 725.398i | 0.0374691i | ||||||||
\(722\) | − | 10363.0i | − | 0.534171i | ||||||
\(723\) | − | 1994.58i | − | 0.102599i | ||||||
\(724\) | −21983.1 | −1.12844 | ||||||||
\(725\) | 448.622 | 0.0229812 | ||||||||
\(726\) | − | 5482.94i | − | 0.280291i | ||||||
\(727\) | 12757.5 | 0.650823 | 0.325411 | − | 0.945573i | \(-0.394497\pi\) | ||||
0.325411 | + | 0.945573i | \(0.394497\pi\) | |||||||
\(728\) | 18510.1 | − | 11602.4i | 0.942350 | − | 0.590678i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 11349.9i | 0.575448i | ||||||||
\(731\) | 18250.3 | 0.923408 | ||||||||
\(732\) | 5605.06 | 0.283017 | ||||||||
\(733\) | 20523.4i | 1.03417i | 0.855933 | + | 0.517087i | \(0.172984\pi\) | ||||
−0.855933 | + | 0.517087i | \(0.827016\pi\) | |||||||
\(734\) | − | 2651.31i | − | 0.133327i | ||||||
\(735\) | 4553.32i | 0.228506i | ||||||||
\(736\) | − | 13504.6i | − | 0.676338i | ||||||
\(737\) | −38652.9 | −1.93188 | ||||||||
\(738\) | −3643.64 | −0.181740 | ||||||||
\(739\) | 7462.66i | 0.371473i | 0.982600 | + | 0.185736i | \(0.0594670\pi\) | ||||
−0.982600 | + | 0.185736i | \(0.940533\pi\) | |||||||
\(740\) | −8469.84 | −0.420753 | ||||||||
\(741\) | 8728.80 | + | 13925.7i | 0.432740 | + | 0.690381i | ||||
\(742\) | −23393.7 | −1.15742 | ||||||||
\(743\) | 18847.8i | 0.930632i | 0.885145 | + | 0.465316i | \(0.154059\pi\) | ||||
−0.885145 | + | 0.465316i | \(0.845941\pi\) | |||||||
\(744\) | −12267.6 | −0.604506 | ||||||||
\(745\) | 31368.5 | 1.54262 | ||||||||
\(746\) | 1792.13i | 0.0879549i | ||||||||
\(747\) | 4626.17i | 0.226590i | ||||||||
\(748\) | 24609.2i | 1.20294i | ||||||||
\(749\) | − | 38587.9i | − | 1.88247i | ||||||
\(750\) | 6918.25 | 0.336825 | ||||||||
\(751\) | 20832.6 | 1.01224 | 0.506119 | − | 0.862464i | \(-0.331080\pi\) | ||||
0.506119 | + | 0.862464i | \(0.331080\pi\) | |||||||
\(752\) | 924.050i | 0.0448093i | ||||||||
\(753\) | −6426.11 | −0.310996 | ||||||||
\(754\) | −536.496 | − | 855.910i | −0.0259125 | − | 0.0413400i | ||||
\(755\) | 7681.29 | 0.370266 | ||||||||
\(756\) | 3429.00i | 0.164962i | ||||||||
\(757\) | −20860.9 | −1.00159 | −0.500795 | − | 0.865566i | \(-0.666959\pi\) | ||||
−0.500795 | + | 0.865566i | \(0.666959\pi\) | |||||||
\(758\) | −10871.4 | −0.520932 | ||||||||
\(759\) | 10865.9i | 0.519640i | ||||||||
\(760\) | − | 23526.1i | − | 1.12287i | ||||||
\(761\) | 4464.86i | 0.212682i | 0.994330 | + | 0.106341i | \(0.0339135\pi\) | ||||
−0.994330 | + | 0.106341i | \(0.966086\pi\) | |||||||
\(762\) | − | 5366.01i | − | 0.255105i | ||||||
\(763\) | 28479.0 | 1.35126 | ||||||||
\(764\) | −5271.56 | −0.249631 | ||||||||
\(765\) | 7488.24i | 0.353906i | ||||||||
\(766\) | 2960.08 | 0.139624 | ||||||||
\(767\) | 2288.51 | + | 3651.03i | 0.107736 | + | 0.171879i | ||||
\(768\) | −9862.38 | −0.463383 | ||||||||
\(769\) | 23797.7i | 1.11595i | 0.829857 | + | 0.557977i | \(0.188422\pi\) | ||||
−0.829857 | + | 0.557977i | \(0.811578\pi\) | |||||||
\(770\) | 16554.8 | 0.774795 | ||||||||
\(771\) | −9457.85 | −0.441785 | ||||||||
\(772\) | − | 12842.6i | − | 0.598725i | ||||||
\(773\) | 29418.7i | 1.36885i | 0.729085 | + | 0.684423i | \(0.239946\pi\) | ||||
−0.729085 | + | 0.684423i | \(0.760054\pi\) | |||||||
\(774\) | − | 2904.95i | − | 0.134905i | ||||||
\(775\) | 6222.99i | 0.288434i | ||||||||
\(776\) | −1547.93 | −0.0716075 | ||||||||
\(777\) | 10360.6 | 0.478357 | ||||||||
\(778\) | 11496.6i | 0.529787i | ||||||||
\(779\) | 31058.0 | 1.42846 | ||||||||
\(780\) | 4096.15 | + | 6534.88i | 0.188033 | + | 0.299982i | ||||
\(781\) | −13329.3 | −0.610703 | ||||||||
\(782\) | 9449.80i | 0.432128i | ||||||||
\(783\) | 381.925 | 0.0174315 | ||||||||
\(784\) | −2149.56 | −0.0979208 | ||||||||
\(785\) | 630.435i | 0.0286640i | ||||||||
\(786\) | − | 6605.36i | − | 0.299752i | ||||||
\(787\) | − | 23896.0i | − | 1.08234i | −0.840913 | − | 0.541170i | \(-0.817982\pi\) | ||
0.840913 | − | 0.541170i | \(-0.182018\pi\) | |||||||
\(788\) | 12865.8i | 0.581630i | ||||||||
\(789\) | −6503.13 | −0.293432 | ||||||||
\(790\) | 18053.4 | 0.813052 | ||||||||
\(791\) | 24929.7i | 1.12060i | ||||||||
\(792\) | 9435.38 | 0.423323 | ||||||||
\(793\) | −13066.5 | + | 8190.26i | −0.585126 | + | 0.366765i | ||||
\(794\) | 633.680 | 0.0283230 | ||||||||
\(795\) | − | 19893.9i | − | 0.887500i | ||||||
\(796\) | 1481.57 | 0.0659708 | ||||||||
\(797\) | 1034.67 | 0.0459847 | 0.0229923 | − | 0.999736i | \(-0.492681\pi\) | ||||
0.0229923 | + | 0.999736i | \(0.492681\pi\) | |||||||
\(798\) | 11947.2i | 0.529983i | ||||||||
\(799\) | − | 5819.42i | − | 0.257667i | ||||||
\(800\) | 5948.59i | 0.262893i | ||||||||
\(801\) | 4751.00i | 0.209573i | ||||||||
\(802\) | −1459.84 | −0.0642751 | ||||||||
\(803\) | 38800.6 | 1.70516 | ||||||||
\(804\) | − | 13090.2i | − | 0.574199i | ||||||
\(805\) | −15552.0 | −0.680914 | ||||||||
\(806\) | 11872.6 | − | 7441.92i | 0.518853 | − | 0.325224i | ||||
\(807\) | −9746.95 | −0.425166 | ||||||||
\(808\) | − | 12700.5i | − | 0.552973i | ||||||
\(809\) | 29557.9 | 1.28455 | 0.642275 | − | 0.766474i | \(-0.277991\pi\) | ||||
0.642275 | + | 0.766474i | \(0.277991\pi\) | |||||||
\(810\) | 1191.92 | 0.0517037 | ||||||||
\(811\) | − | 30268.9i | − | 1.31058i | −0.755376 | − | 0.655292i | \(-0.772546\pi\) | ||
0.755376 | − | 0.655292i | \(-0.227454\pi\) | |||||||
\(812\) | 1796.46i | 0.0776396i | ||||||||
\(813\) | − | 14693.1i | − | 0.633837i | ||||||
\(814\) | − | 11835.4i | − | 0.509621i | ||||||
\(815\) | −17920.2 | −0.770203 | ||||||||
\(816\) | −3535.09 | −0.151658 | ||||||||
\(817\) | 24761.5i | 1.06034i | ||||||||
\(818\) | −6528.17 | −0.279037 | ||||||||
\(819\) | −5010.54 | − | 7993.68i | −0.213776 | − | 0.341052i | ||||
\(820\) | 14574.6 | 0.620690 | ||||||||
\(821\) | − | 39292.7i | − | 1.67031i | −0.550013 | − | 0.835156i | \(-0.685377\pi\) | ||
0.550013 | − | 0.835156i | \(-0.314623\pi\) | |||||||
\(822\) | −2325.52 | −0.0986763 | ||||||||
\(823\) | 25988.8 | 1.10074 | 0.550372 | − | 0.834920i | \(-0.314486\pi\) | ||||
0.550372 | + | 0.834920i | \(0.314486\pi\) | |||||||
\(824\) | 675.980i | 0.0285787i | ||||||||
\(825\) | − | 4786.29i | − | 0.201984i | ||||||
\(826\) | 3132.31i | 0.131946i | ||||||||
\(827\) | 19585.1i | 0.823508i | 0.911295 | + | 0.411754i | \(0.135084\pi\) | ||||
−0.911295 | + | 0.411754i | \(0.864916\pi\) | |||||||
\(828\) | −3679.85 | −0.154449 | ||||||||
\(829\) | −666.472 | −0.0279222 | −0.0139611 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139611 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(830\) | 7563.86i | 0.316320i | ||||||||
\(831\) | −8700.98 | −0.363217 | ||||||||
\(832\) | 7003.08 | − | 4389.62i | 0.291813 | − | 0.182912i | ||||
\(833\) | 13537.3 | 0.563075 | ||||||||
\(834\) | − | 3460.07i | − | 0.143660i | ||||||
\(835\) | −34118.7 | −1.41404 | ||||||||
\(836\) | −33389.1 | −1.38133 | ||||||||
\(837\) | 5297.81i | 0.218780i | ||||||||
\(838\) | − | 15157.9i | − | 0.624845i | ||||||
\(839\) | 36379.7i | 1.49698i | 0.663146 | + | 0.748490i | \(0.269221\pi\) | ||||
−0.663146 | + | 0.748490i | \(0.730779\pi\) | |||||||
\(840\) | 13504.6i | 0.554704i | ||||||||
\(841\) | −24188.9 | −0.991796 | ||||||||
\(842\) | 574.762 | 0.0235245 | ||||||||
\(843\) | 13189.6i | 0.538878i | ||||||||
\(844\) | 33227.8 | 1.35515 | ||||||||
\(845\) | −19097.9 | − | 9248.71i | −0.777500 | − | 0.376527i | ||||
\(846\) | −926.293 | −0.0376438 | ||||||||
\(847\) | − | 26827.6i | − | 1.08832i | ||||||
\(848\) | 9391.60 | 0.380317 | ||||||||
\(849\) | 1677.45 | 0.0678093 | ||||||||
\(850\) | − | 4162.52i | − | 0.167969i | ||||||
\(851\) | 11118.5i | 0.447871i | ||||||||
\(852\) | − | 4514.10i | − | 0.181515i | ||||||
\(853\) | 39951.4i | 1.60364i | 0.597563 | + | 0.801822i | \(0.296136\pi\) | ||||
−0.597563 | + | 0.801822i | \(0.703864\pi\) | |||||||
\(854\) | −11210.1 | −0.449183 | ||||||||
\(855\) | −10159.8 | −0.406385 | ||||||||
\(856\) | − | 35959.1i | − | 1.43581i | ||||||
\(857\) | −17226.4 | −0.686629 | −0.343314 | − | 0.939221i | \(-0.611550\pi\) | ||||
−0.343314 | + | 0.939221i | \(0.611550\pi\) | |||||||
\(858\) | −9131.59 | + | 5723.80i | −0.363342 | + | 0.227748i | ||||
\(859\) | −33392.3 | −1.32634 | −0.663172 | − | 0.748467i | \(-0.730790\pi\) | ||||
−0.663172 | + | 0.748467i | \(0.730790\pi\) | |||||||
\(860\) | 11619.8i | 0.460735i | ||||||||
\(861\) | −17828.1 | −0.705666 | ||||||||
\(862\) | −3713.11 | −0.146716 | ||||||||
\(863\) | 17381.9i | 0.685614i | 0.939406 | + | 0.342807i | \(0.111378\pi\) | ||||
−0.939406 | + | 0.342807i | \(0.888622\pi\) | |||||||
\(864\) | 5064.21i | 0.199407i | ||||||||
\(865\) | − | 30697.9i | − | 1.20666i | ||||||
\(866\) | − | 17086.8i | − | 0.670476i | ||||||
\(867\) | 7524.07 | 0.294730 | ||||||||
\(868\) | −24919.3 | −0.974443 | ||||||||
\(869\) | − | 61717.2i | − | 2.40922i | ||||||
\(870\) | 624.452 | 0.0243344 | ||||||||
\(871\) | 19127.8 | + | 30515.9i | 0.744110 | + | 1.18713i | ||||
\(872\) | 26538.8 | 1.03064 | ||||||||
\(873\) | 668.480i | 0.0259159i | ||||||||
\(874\) | −12821.2 | −0.496207 | ||||||||
\(875\) | 33850.5 | 1.30783 | ||||||||
\(876\) | 13140.2i | 0.506812i | ||||||||
\(877\) | − | 14335.6i | − | 0.551970i | −0.961162 | − | 0.275985i | \(-0.910996\pi\) | ||
0.961162 | − | 0.275985i | \(-0.0890040\pi\) | |||||||
\(878\) | 2796.02i | 0.107473i | ||||||||
\(879\) | − | 20756.0i | − | 0.796452i | ||||||
\(880\) | −6646.06 | −0.254589 | ||||||||
\(881\) | −5436.53 | −0.207901 | −0.103951 | − | 0.994582i | \(-0.533148\pi\) | ||||
−0.103951 | + | 0.994582i | \(0.533148\pi\) | |||||||
\(882\) | − | 2154.78i | − | 0.0822620i | ||||||
\(883\) | −21185.9 | −0.807430 | −0.403715 | − | 0.914885i | \(-0.632281\pi\) | ||||
−0.403715 | + | 0.914885i | \(0.632281\pi\) | |||||||
\(884\) | 19428.7 | − | 12178.1i | 0.739204 | − | 0.463343i | ||||
\(885\) | −2663.70 | −0.101174 | ||||||||
\(886\) | 17688.6i | 0.670724i | ||||||||
\(887\) | −12661.4 | −0.479287 | −0.239644 | − | 0.970861i | \(-0.577031\pi\) | ||||
−0.239644 | + | 0.970861i | \(0.577031\pi\) | |||||||
\(888\) | 9654.75 | 0.364856 | ||||||||
\(889\) | − | 26255.5i | − | 0.990531i | ||||||
\(890\) | 7767.94i | 0.292564i | ||||||||
\(891\) | − | 4074.71i | − | 0.153207i | ||||||
\(892\) | 19669.0i | 0.738305i | ||||||||
\(893\) | 7895.63 | 0.295876 | ||||||||
\(894\) | −14844.6 | −0.555343 | ||||||||
\(895\) | 26475.3i | 0.988794i | ||||||||
\(896\) | −27549.1 | −1.02718 | ||||||||
\(897\) | 8578.47 | − | 5377.10i | 0.319316 | − | 0.200152i | ||||
\(898\) | 21462.3 | 0.797558 | ||||||||
\(899\) | 2775.54i | 0.102969i | ||||||||
\(900\) | 1620.93 | 0.0600344 | ||||||||
\(901\) | −59145.8 | −2.18694 | ||||||||
\(902\) | 20365.9i | 0.751786i | ||||||||
\(903\) | − | 14213.7i | − | 0.523812i | ||||||
\(904\) | 23231.3i | 0.854715i | ||||||||
\(905\) | 37388.6i | 1.37330i | ||||||||
\(906\) | −3635.03 | −0.133296 | ||||||||
\(907\) | −3545.27 | −0.129789 | −0.0648946 | − | 0.997892i | \(-0.520671\pi\) | ||||
−0.0648946 | + | 0.997892i | \(0.520671\pi\) | |||||||
\(908\) | − | 30263.1i | − | 1.10607i | ||||||
\(909\) | −5484.77 | −0.200130 | ||||||||
\(910\) | −8192.30 | − | 13069.8i | −0.298431 | − | 0.476108i | ||||
\(911\) | −3913.88 | −0.142341 | −0.0711706 | − | 0.997464i | \(-0.522673\pi\) | ||||
−0.0711706 | + | 0.997464i | \(0.522673\pi\) | |||||||
\(912\) | − | 4796.32i | − | 0.174147i | ||||||
\(913\) | 25857.7 | 0.937313 | ||||||||
\(914\) | 3618.46 | 0.130950 | ||||||||
\(915\) | − | 9533.02i | − | 0.344428i | ||||||
\(916\) | 27110.2i | 0.977890i | ||||||||
\(917\) | − | 32319.5i | − | 1.16389i | ||||||
\(918\) | − | 3543.67i | − | 0.127406i | ||||||
\(919\) | 6917.79 | 0.248310 | 0.124155 | − | 0.992263i | \(-0.460378\pi\) | ||||
0.124155 | + | 0.992263i | \(0.460378\pi\) | |||||||
\(920\) | −14492.5 | −0.519352 | ||||||||
\(921\) | − | 26942.8i | − | 0.963948i | ||||||
\(922\) | −9708.18 | −0.346770 | ||||||||
\(923\) | 6596.13 | + | 10523.3i | 0.235227 | + | 0.375274i | ||||
\(924\) | 19166.2 | 0.682382 | ||||||||
\(925\) | − | 4897.57i | − | 0.174088i | ||||||
\(926\) | 96.7050 | 0.00343188 | ||||||||
\(927\) | 291.925 | 0.0103431 | ||||||||
\(928\) | 2653.15i | 0.0938512i | ||||||||
\(929\) | 3753.03i | 0.132543i | 0.997802 | + | 0.0662717i | \(0.0211104\pi\) | ||||
−0.997802 | + | 0.0662717i | \(0.978890\pi\) | |||||||
\(930\) | 8662.00i | 0.305417i | ||||||||
\(931\) | 18367.1i | 0.646571i | ||||||||
\(932\) | 27336.4 | 0.960765 | ||||||||
\(933\) | 23829.4 | 0.836162 | ||||||||
\(934\) | 11968.7i | 0.419302i | ||||||||
\(935\) | 41855.1 | 1.46397 | ||||||||
\(936\) | −4669.20 | − | 7449.10i | −0.163053 | − | 0.260130i | ||||
\(937\) | 48189.0 | 1.68011 | 0.840056 | − | 0.542499i | \(-0.182522\pi\) | ||||
0.840056 | + | 0.542499i | \(0.182522\pi\) | |||||||
\(938\) | 26180.4i | 0.911323i | ||||||||
\(939\) | −15178.7 | −0.527517 | ||||||||
\(940\) | 3705.17 | 0.128563 | ||||||||
\(941\) | − | 26656.4i | − | 0.923456i | −0.887022 | − | 0.461728i | \(-0.847230\pi\) | ||
0.887022 | − | 0.461728i | \(-0.152770\pi\) | |||||||
\(942\) | − | 298.342i | − | 0.0103190i | ||||||
\(943\) | − | 19132.3i | − | 0.660693i | ||||||
\(944\) | − | 1257.50i | − | 0.0433559i | ||||||
\(945\) | 5832.00 | 0.200757 | ||||||||
\(946\) | −16237.1 | −0.558047 | ||||||||
\(947\) | 31258.9i | 1.07263i | 0.844018 | + | 0.536314i | \(0.180184\pi\) | ||||
−0.844018 | + | 0.536314i | \(0.819816\pi\) | |||||||
\(948\) | 20901.2 | 0.716076 | ||||||||
\(949\) | −19200.9 | − | 30632.5i | −0.656783 | − | 1.04781i | ||||
\(950\) | 5647.60 | 0.192876 | ||||||||
\(951\) | 26106.4i | 0.890175i | ||||||||
\(952\) | 40150.0 | 1.36688 | ||||||||
\(953\) | −10602.4 | −0.360382 | −0.180191 | − | 0.983632i | \(-0.557672\pi\) | ||||
−0.180191 | + | 0.983632i | \(0.557672\pi\) | |||||||
\(954\) | 9414.40i | 0.319499i | ||||||||
\(955\) | 8965.81i | 0.303798i | ||||||||
\(956\) | − | 9558.44i | − | 0.323370i | ||||||
\(957\) | − | 2134.75i | − | 0.0721072i | ||||||
\(958\) | 19856.9 | 0.669674 | ||||||||
\(959\) | −11378.6 | −0.383144 | ||||||||
\(960\) | 5109.29i | 0.171772i | ||||||||
\(961\) | −8709.45 | −0.292352 | ||||||||
\(962\) | −9343.90 | + | 5856.88i | −0.313160 | + | 0.196293i | ||||
\(963\) | −15529.1 | −0.519645 | ||||||||
\(964\) | − | 3775.60i | − | 0.126145i | ||||||
\(965\) | −21842.6 | −0.728640 | ||||||||
\(966\) | 7359.70 | 0.245129 | ||||||||
\(967\) | 4815.93i | 0.160155i | 0.996789 | + | 0.0800774i | \(0.0255168\pi\) | ||||
−0.996789 | + | 0.0800774i | \(0.974483\pi\) | |||||||
\(968\) | − | 25000.0i | − | 0.830092i | ||||||
\(969\) | 30205.9i | 1.00140i | ||||||||
\(970\) | 1092.97i | 0.0361786i | ||||||||
\(971\) | 56729.5 | 1.87491 | 0.937454 | − | 0.348109i | \(-0.113176\pi\) | ||||
0.937454 | + | 0.348109i | \(0.113176\pi\) | |||||||
\(972\) | 1379.94 | 0.0455367 | ||||||||
\(973\) | − | 16929.9i | − | 0.557808i | ||||||
\(974\) | −106.493 | −0.00350334 | ||||||||
\(975\) | −3778.71 | + | 2368.54i | −0.124119 | + | 0.0777991i | ||||
\(976\) | 4500.40 | 0.147597 | ||||||||
\(977\) | 55246.2i | 1.80909i | 0.426375 | + | 0.904546i | \(0.359790\pi\) | ||||
−0.426375 | + | 0.904546i | \(0.640210\pi\) | |||||||
\(978\) | 8480.38 | 0.277273 | ||||||||
\(979\) | 26555.4 | 0.866921 | ||||||||
\(980\) | 8619.11i | 0.280946i | ||||||||
\(981\) | − | 11460.9i | − | 0.373005i | ||||||
\(982\) | 4000.34i | 0.129996i | ||||||||
\(983\) | − | 22820.6i | − | 0.740451i | −0.928942 | − | 0.370226i | \(-0.879280\pi\) | ||
0.928942 | − | 0.370226i | \(-0.120720\pi\) | |||||||
\(984\) | −16613.5 | −0.538231 | ||||||||
\(985\) | 21882.0 | 0.707836 | ||||||||
\(986\) | − | 1856.54i | − | 0.0599637i | ||||||
\(987\) | −4532.29 | −0.146164 | ||||||||
\(988\) | 16523.0 | + | 26360.3i | 0.532050 | + | 0.848818i | ||||
\(989\) | 15253.5 | 0.490429 | ||||||||
\(990\) | − | 6662.20i | − | 0.213877i | ||||||
\(991\) | −46490.4 | −1.49023 | −0.745115 | − | 0.666936i | \(-0.767605\pi\) | ||||
−0.745115 | + | 0.666936i | \(0.767605\pi\) | |||||||
\(992\) | −36802.8 | −1.17791 | ||||||||
\(993\) | 5212.94i | 0.166594i | ||||||||
\(994\) | 9028.21i | 0.288086i | ||||||||
\(995\) | − | 2519.84i | − | 0.0802856i | ||||||
\(996\) | 8757.01i | 0.278591i | ||||||||
\(997\) | 24943.4 | 0.792344 | 0.396172 | − | 0.918176i | \(-0.370338\pi\) | ||||
0.396172 | + | 0.918176i | \(0.370338\pi\) | |||||||
\(998\) | 11626.8 | 0.368777 | ||||||||
\(999\) | − | 4169.44i | − | 0.132047i |
(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 | 39.4.b.b.25.3 | yes | 4 | |
3.2 | odd | 2 | 117.4.b.e.64.2 | 4 | |||
4.3 | odd | 2 | 624.4.c.c.337.2 | 4 | |||
13.5 | odd | 4 | 507.4.a.l.1.3 | 4 | |||
13.8 | odd | 4 | 507.4.a.l.1.2 | 4 | |||
13.12 | even | 2 | inner | 39.4.b.b.25.2 | ✓ | 4 | |
39.5 | even | 4 | 1521.4.a.w.1.2 | 4 | |||
39.8 | even | 4 | 1521.4.a.w.1.3 | 4 | |||
39.38 | odd | 2 | 117.4.b.e.64.3 | 4 | |||
52.51 | odd | 2 | 624.4.c.c.337.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.b.b.25.2 | ✓ | 4 | 13.12 | even | 2 | inner | |
39.4.b.b.25.3 | yes | 4 | 1.1 | even | 1 | trivial | |
117.4.b.e.64.2 | 4 | 3.2 | odd | 2 | |||
117.4.b.e.64.3 | 4 | 39.38 | odd | 2 | |||
507.4.a.l.1.2 | 4 | 13.8 | odd | 4 | |||
507.4.a.l.1.3 | 4 | 13.5 | odd | 4 | |||
624.4.c.c.337.2 | 4 | 4.3 | odd | 2 | |||
624.4.c.c.337.3 | 4 | 52.51 | odd | 2 | |||
1521.4.a.w.1.2 | 4 | 39.5 | even | 4 | |||
1521.4.a.w.1.3 | 4 | 39.8 | even | 4 |