Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,4,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.89109359028\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.5922408960000.19 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 54x^{6} + 176x^{5} + 1307x^{4} - 2912x^{3} - 15314x^{2} + 16800x + 86044 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 18.3 | ||
Root | \(-2.82402 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.18 |
Dual form | 49.4.c.e.30.3 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.76556 | + | 3.05805i | 0.624221 | + | 1.08118i | 0.988691 | + | 0.149968i | \(0.0479170\pi\) |
−0.364470 | + | 0.931215i | \(0.618750\pi\) | |||||||
\(3\) | −3.91110 | + | 6.77422i | −0.752691 | + | 1.30370i | 0.193823 | + | 0.981037i | \(0.437911\pi\) |
−0.946514 | + | 0.322663i | \(0.895422\pi\) | |||||||
\(4\) | −2.23444 | + | 3.87016i | −0.279304 | + | 0.483769i | ||||
\(5\) | −1.03865 | − | 1.79899i | −0.0928996 | − | 0.160907i | 0.815830 | − | 0.578291i | \(-0.196280\pi\) |
−0.908730 | + | 0.417384i | \(0.862947\pi\) | |||||||
\(6\) | −27.6212 | −1.87938 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 12.4689 | 0.551051 | ||||||||
\(9\) | −17.0934 | − | 29.6066i | −0.633088 | − | 1.09654i | ||||
\(10\) | 3.66760 | − | 6.35247i | 0.115980 | − | 0.200883i | ||||
\(11\) | −24.5934 | + | 42.5970i | −0.674108 | + | 1.16759i | 0.302621 | + | 0.953111i | \(0.402138\pi\) |
−0.976729 | + | 0.214478i | \(0.931195\pi\) | |||||||
\(12\) | −17.4782 | − | 30.2731i | −0.420460 | − | 0.728258i | ||||
\(13\) | 44.8559 | 0.956983 | 0.478492 | − | 0.878092i | \(-0.341184\pi\) | ||||
0.478492 | + | 0.878092i | \(0.341184\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 16.2490 | 0.279699 | ||||||||
\(16\) | 39.8901 | + | 69.0916i | 0.623282 | + | 1.07956i | ||||
\(17\) | 13.2589 | − | 22.9652i | 0.189163 | − | 0.327639i | −0.755809 | − | 0.654793i | \(-0.772756\pi\) |
0.944971 | + | 0.327153i | \(0.106089\pi\) | |||||||
\(18\) | 60.3590 | − | 104.545i | 0.790375 | − | 1.36897i | ||||
\(19\) | 38.8675 | + | 67.3205i | 0.469306 | + | 0.812862i | 0.999384 | − | 0.0350869i | \(-0.0111708\pi\) |
−0.530078 | + | 0.847949i | \(0.677837\pi\) | |||||||
\(20\) | 9.28317 | 0.103789 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −173.685 | −1.68317 | ||||||||
\(23\) | −27.8755 | − | 48.2818i | −0.252715 | − | 0.437715i | 0.711558 | − | 0.702628i | \(-0.247990\pi\) |
−0.964272 | + | 0.264913i | \(0.914657\pi\) | |||||||
\(24\) | −48.7670 | + | 84.4669i | −0.414772 | + | 0.718406i | ||||
\(25\) | 60.3424 | − | 104.516i | 0.482739 | − | 0.836129i | ||||
\(26\) | 79.1960 | + | 137.171i | 0.597369 | + | 1.03467i | ||||
\(27\) | 56.2164 | 0.400698 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 121.436 | 0.777588 | 0.388794 | − | 0.921325i | \(-0.372892\pi\) | ||||
0.388794 | + | 0.921325i | \(0.372892\pi\) | |||||||
\(30\) | 28.6887 | + | 49.6903i | 0.174594 | + | 0.302406i | ||||
\(31\) | 152.776 | − | 264.616i | 0.885143 | − | 1.53311i | 0.0395940 | − | 0.999216i | \(-0.487394\pi\) |
0.845549 | − | 0.533897i | \(-0.179273\pi\) | |||||||
\(32\) | −90.9815 | + | 157.585i | −0.502607 | + | 0.870540i | ||||
\(33\) | −192.374 | − | 333.202i | −1.01479 | − | 1.75767i | ||||
\(34\) | 93.6380 | 0.472317 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 152.776 | 0.707298 | ||||||||
\(37\) | −38.5934 | − | 66.8457i | −0.171479 | − | 0.297010i | 0.767458 | − | 0.641099i | \(-0.221521\pi\) |
−0.938937 | + | 0.344089i | \(0.888188\pi\) | |||||||
\(38\) | −137.246 | + | 237.717i | −0.585902 | + | 1.01481i | ||||
\(39\) | −175.436 | + | 303.864i | −0.720313 | + | 1.24762i | ||||
\(40\) | −12.9508 | − | 22.4314i | −0.0511924 | − | 0.0886679i | ||||
\(41\) | −248.720 | −0.947403 | −0.473702 | − | 0.880685i | \(-0.657083\pi\) | ||||
−0.473702 | + | 0.880685i | \(0.657083\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −147.179 | −0.521967 | −0.260984 | − | 0.965343i | \(-0.584047\pi\) | ||||
−0.260984 | + | 0.965343i | \(0.584047\pi\) | |||||||
\(44\) | −109.905 | − | 190.360i | −0.376563 | − | 0.652226i | ||||
\(45\) | −35.5080 | + | 61.5017i | −0.117627 | + | 0.203736i | ||||
\(46\) | 98.4319 | − | 170.489i | 0.315500 | − | 0.546462i | ||||
\(47\) | 134.925 | + | 233.698i | 0.418742 | + | 0.725283i | 0.995813 | − | 0.0914112i | \(-0.0291378\pi\) |
−0.577071 | + | 0.816694i | \(0.695804\pi\) | |||||||
\(48\) | −624.056 | −1.87656 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 426.154 | 1.20534 | ||||||||
\(51\) | 103.714 | + | 179.638i | 0.284762 | + | 0.493222i | ||||
\(52\) | −100.228 | + | 173.599i | −0.267290 | + | 0.462959i | ||||
\(53\) | 70.5603 | − | 122.214i | 0.182872 | − | 0.316743i | −0.759986 | − | 0.649940i | \(-0.774794\pi\) |
0.942857 | + | 0.333197i | \(0.108127\pi\) | |||||||
\(54\) | 99.2536 | + | 171.912i | 0.250124 | + | 0.433228i | ||||
\(55\) | 102.176 | 0.250497 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −608.058 | −1.41297 | ||||||||
\(58\) | 214.403 | + | 371.356i | 0.485387 | + | 0.840715i | ||||
\(59\) | −212.417 | + | 367.917i | −0.468717 | + | 0.811842i | −0.999361 | − | 0.0357532i | \(-0.988617\pi\) |
0.530643 | + | 0.847595i | \(0.321950\pi\) | |||||||
\(60\) | −36.3074 | + | 62.8863i | −0.0781211 | + | 0.135310i | ||||
\(61\) | −293.998 | − | 509.220i | −0.617092 | − | 1.06883i | −0.990014 | − | 0.140972i | \(-0.954977\pi\) |
0.372922 | − | 0.927863i | \(-0.378356\pi\) | |||||||
\(62\) | 1078.95 | 2.21010 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.29373 | −0.00838618 | ||||||||
\(65\) | −46.5895 | − | 80.6954i | −0.0889033 | − | 0.153985i | ||||
\(66\) | 679.299 | − | 1176.58i | 1.26691 | − | 2.19435i | ||||
\(67\) | 89.8171 | − | 155.568i | 0.163775 | − | 0.283666i | −0.772445 | − | 0.635082i | \(-0.780966\pi\) |
0.936219 | + | 0.351416i | \(0.114300\pi\) | |||||||
\(68\) | 59.2525 | + | 102.628i | 0.105668 | + | 0.183022i | ||||
\(69\) | 436.095 | 0.760865 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 674.872 | 1.12806 | 0.564032 | − | 0.825753i | \(-0.309250\pi\) | ||||
0.564032 | + | 0.825753i | \(0.309250\pi\) | |||||||
\(72\) | −213.135 | − | 369.161i | −0.348864 | − | 0.604251i | ||||
\(73\) | 118.744 | − | 205.671i | 0.190383 | − | 0.329754i | −0.754994 | − | 0.655732i | \(-0.772360\pi\) |
0.945377 | + | 0.325978i | \(0.105694\pi\) | |||||||
\(74\) | 136.278 | − | 236.041i | 0.214081 | − | 0.370800i | ||||
\(75\) | 472.010 | + | 817.546i | 0.726707 | + | 1.25869i | ||||
\(76\) | −347.388 | −0.524317 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1238.97 | −1.79854 | ||||||||
\(79\) | −247.926 | − | 429.421i | −0.353087 | − | 0.611564i | 0.633702 | − | 0.773578i | \(-0.281535\pi\) |
−0.986789 | + | 0.162013i | \(0.948201\pi\) | |||||||
\(80\) | 82.8636 | − | 143.524i | 0.115805 | − | 0.200581i | ||||
\(81\) | 241.654 | − | 418.556i | 0.331487 | − | 0.574152i | ||||
\(82\) | −439.131 | − | 760.598i | −0.591389 | − | 1.02432i | ||||
\(83\) | 24.4406 | 0.0323217 | 0.0161609 | − | 0.999869i | \(-0.494856\pi\) | ||||
0.0161609 | + | 0.999869i | \(0.494856\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −55.0855 | −0.0702925 | ||||||||
\(86\) | −259.854 | − | 450.080i | −0.325823 | − | 0.564342i | ||||
\(87\) | −474.947 | + | 822.633i | −0.585284 | + | 1.01374i | ||||
\(88\) | −306.652 | + | 531.136i | −0.371468 | + | 0.643402i | ||||
\(89\) | 536.144 | + | 928.628i | 0.638552 | + | 1.10600i | 0.985751 | + | 0.168213i | \(0.0537996\pi\) |
−0.347199 | + | 0.937792i | \(0.612867\pi\) | |||||||
\(90\) | −250.767 | −0.293702 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 249.144 | 0.282337 | ||||||||
\(93\) | 1195.05 | + | 2069.88i | 1.33248 | + | 2.30792i | ||||
\(94\) | −476.439 | + | 825.216i | −0.522776 | + | 0.905474i | ||||
\(95\) | 80.7393 | − | 139.845i | 0.0871966 | − | 0.151029i | ||||
\(96\) | −711.675 | − | 1232.66i | −0.756615 | − | 1.31050i | ||||
\(97\) | −1667.43 | −1.74538 | −0.872690 | − | 0.488275i | \(-0.837626\pi\) | ||||
−0.872690 | + | 0.488275i | \(0.837626\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1681.54 | 1.70708 | ||||||||
\(100\) | 269.662 | + | 467.069i | 0.269662 | + | 0.467069i | ||||
\(101\) | −38.5593 | + | 66.7867i | −0.0379881 | + | 0.0657973i | −0.884394 | − | 0.466740i | \(-0.845428\pi\) |
0.846406 | + | 0.532538i | \(0.178762\pi\) | |||||||
\(102\) | −366.228 | + | 634.325i | −0.355509 | + | 0.615760i | ||||
\(103\) | 82.3463 | + | 142.628i | 0.0787749 | + | 0.136442i | 0.902722 | − | 0.430225i | \(-0.141566\pi\) |
−0.823947 | + | 0.566667i | \(0.808232\pi\) | |||||||
\(104\) | 559.302 | 0.527347 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 498.315 | 0.456610 | ||||||||
\(107\) | −511.311 | − | 885.617i | −0.461966 | − | 0.800148i | 0.537093 | − | 0.843523i | \(-0.319522\pi\) |
−0.999059 | + | 0.0433749i | \(0.986189\pi\) | |||||||
\(108\) | −125.612 | + | 217.566i | −0.111917 | + | 0.193845i | ||||
\(109\) | −681.259 | + | 1179.97i | −0.598649 | + | 1.03689i | 0.394372 | + | 0.918951i | \(0.370962\pi\) |
−0.993021 | + | 0.117940i | \(0.962371\pi\) | |||||||
\(110\) | 180.398 | + | 312.458i | 0.156366 | + | 0.270833i | ||||
\(111\) | 603.770 | 0.516282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1538.41 | −1.28072 | −0.640360 | − | 0.768075i | \(-0.721215\pi\) | ||||
−0.640360 | + | 0.768075i | \(0.721215\pi\) | |||||||
\(114\) | −1073.57 | − | 1859.47i | −0.882006 | − | 1.52768i | ||||
\(115\) | −57.9057 | + | 100.296i | −0.0469542 | + | 0.0813270i | ||||
\(116\) | −271.340 | + | 469.975i | −0.217184 | + | 0.376174i | ||||
\(117\) | −766.739 | − | 1328.03i | −0.605855 | − | 1.04937i | ||||
\(118\) | −1500.14 | −1.17033 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 202.607 | 0.154128 | ||||||||
\(121\) | −544.169 | − | 942.529i | −0.408842 | − | 0.708136i | ||||
\(122\) | 1038.15 | − | 1798.12i | 0.770404 | − | 1.33438i | ||||
\(123\) | 972.769 | − | 1684.88i | 0.713102 | − | 1.23513i | ||||
\(124\) | 682.738 | + | 1182.54i | 0.494449 | + | 0.856411i | ||||
\(125\) | −510.360 | −0.365184 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −170.358 | −0.119030 | −0.0595151 | − | 0.998227i | \(-0.518955\pi\) | ||||
−0.0595151 | + | 0.998227i | \(0.518955\pi\) | |||||||
\(128\) | 720.271 | + | 1247.55i | 0.497372 | + | 0.861473i | ||||
\(129\) | 575.632 | − | 997.023i | 0.392880 | − | 0.680488i | ||||
\(130\) | 164.514 | − | 284.946i | 0.110991 | − | 0.192242i | ||||
\(131\) | −375.968 | − | 651.195i | −0.250751 | − | 0.434314i | 0.712981 | − | 0.701183i | \(-0.247344\pi\) |
−0.963733 | + | 0.266869i | \(0.914011\pi\) | |||||||
\(132\) | 1719.39 | 1.13374 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 634.312 | 0.408927 | ||||||||
\(135\) | −58.3891 | − | 101.133i | −0.0372247 | − | 0.0644750i | ||||
\(136\) | 165.324 | − | 286.350i | 0.104238 | − | 0.180546i | ||||
\(137\) | −259.311 | + | 449.140i | −0.161711 | + | 0.280092i | −0.935483 | − | 0.353373i | \(-0.885035\pi\) |
0.773771 | + | 0.633465i | \(0.218368\pi\) | |||||||
\(138\) | 769.954 | + | 1333.60i | 0.474948 | + | 0.822634i | ||||
\(139\) | 2975.72 | 1.81581 | 0.907905 | − | 0.419177i | \(-0.137681\pi\) | ||||
0.907905 | + | 0.419177i | \(0.137681\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2110.83 | −1.26073 | ||||||||
\(142\) | 1191.53 | + | 2063.79i | 0.704161 | + | 1.21964i | ||||
\(143\) | −1103.16 | + | 1910.73i | −0.645110 | + | 1.11736i | ||||
\(144\) | 1363.71 | − | 2362.02i | 0.789186 | − | 1.36691i | ||||
\(145\) | −126.129 | − | 218.462i | −0.0722376 | − | 0.125119i | ||||
\(146\) | 838.604 | 0.475365 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 344.938 | 0.191579 | ||||||||
\(149\) | 1358.97 | + | 2353.80i | 0.747188 | + | 1.29417i | 0.949165 | + | 0.314778i | \(0.101930\pi\) |
−0.201977 | + | 0.979390i | \(0.564737\pi\) | |||||||
\(150\) | −1666.73 | + | 2886.86i | −0.907252 | + | 1.57141i | ||||
\(151\) | −353.825 | + | 612.843i | −0.190688 | + | 0.330281i | −0.945478 | − | 0.325685i | \(-0.894405\pi\) |
0.754791 | + | 0.655966i | \(0.227738\pi\) | |||||||
\(152\) | 484.634 | + | 839.410i | 0.258612 | + | 0.447929i | ||||
\(153\) | −906.561 | −0.479027 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −634.724 | −0.328918 | ||||||||
\(156\) | −784.000 | − | 1357.93i | −0.402373 | − | 0.696931i | ||||
\(157\) | 1558.96 | − | 2700.19i | 0.792473 | − | 1.37260i | −0.131958 | − | 0.991255i | \(-0.542126\pi\) |
0.924431 | − | 0.381349i | \(-0.124540\pi\) | |||||||
\(158\) | 875.459 | − | 1516.34i | 0.440809 | − | 0.763503i | ||||
\(159\) | 551.937 | + | 955.983i | 0.275292 | + | 0.476820i | ||||
\(160\) | 377.991 | 0.186768 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1706.62 | 0.827684 | ||||||||
\(163\) | −904.387 | − | 1566.44i | −0.434583 | − | 0.752720i | 0.562678 | − | 0.826676i | \(-0.309771\pi\) |
−0.997262 | + | 0.0739557i | \(0.976438\pi\) | |||||||
\(164\) | 555.749 | − | 962.585i | 0.264614 | − | 0.458325i | ||||
\(165\) | −399.619 | + | 692.160i | −0.188547 | + | 0.326573i | ||||
\(166\) | 43.1514 | + | 74.7404i | 0.0201759 | + | 0.0349457i | ||||
\(167\) | −3147.38 | −1.45839 | −0.729197 | − | 0.684303i | \(-0.760106\pi\) | ||||
−0.729197 | + | 0.684303i | \(0.760106\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −184.949 | −0.0841827 | ||||||||
\(170\) | −97.2570 | − | 168.454i | −0.0438781 | − | 0.0759991i | ||||
\(171\) | 1328.75 | − | 2301.47i | 0.594224 | − | 1.02923i | ||||
\(172\) | 328.862 | − | 569.606i | 0.145788 | − | 0.252512i | ||||
\(173\) | −1642.18 | − | 2844.34i | −0.721691 | − | 1.25001i | −0.960322 | − | 0.278895i | \(-0.910032\pi\) |
0.238631 | − | 0.971110i | \(-0.423301\pi\) | |||||||
\(174\) | −3354.20 | −1.46139 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3924.13 | −1.68064 | ||||||||
\(177\) | −1661.57 | − | 2877.92i | −0.705599 | − | 1.22213i | ||||
\(178\) | −1893.19 | + | 3279.11i | −0.797196 | + | 1.38078i | ||||
\(179\) | −1399.41 | + | 2423.85i | −0.584341 | + | 1.01211i | 0.410616 | + | 0.911808i | \(0.365314\pi\) |
−0.994957 | + | 0.100300i | \(0.968020\pi\) | |||||||
\(180\) | −158.681 | − | 274.843i | −0.0657076 | − | 0.113809i | ||||
\(181\) | 3723.04 | 1.52890 | 0.764451 | − | 0.644682i | \(-0.223010\pi\) | ||||
0.764451 | + | 0.644682i | \(0.223010\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4599.42 | 1.85792 | ||||||||
\(184\) | −347.576 | − | 602.019i | −0.139259 | − | 0.241203i | ||||
\(185\) | −80.1699 | + | 138.858i | −0.0318606 | + | 0.0551842i | ||||
\(186\) | −4219.86 | + | 7309.02i | −1.66352 | + | 2.88131i | ||||
\(187\) | 652.164 | + | 1129.58i | 0.255032 | + | 0.441728i | ||||
\(188\) | −1205.93 | −0.467826 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 570.202 | 0.217720 | ||||||||
\(191\) | −479.825 | − | 831.081i | −0.181774 | − | 0.314842i | 0.760710 | − | 0.649091i | \(-0.224851\pi\) |
−0.942485 | + | 0.334249i | \(0.891517\pi\) | |||||||
\(192\) | 16.7932 | − | 29.0867i | 0.00631221 | − | 0.0109331i | ||||
\(193\) | 1895.12 | − | 3282.45i | 0.706808 | − | 1.22423i | −0.259227 | − | 0.965816i | \(-0.583468\pi\) |
0.966035 | − | 0.258411i | \(-0.0831988\pi\) | |||||||
\(194\) | −2943.95 | − | 5099.08i | −1.08950 | − | 1.88707i | ||||
\(195\) | 728.865 | 0.267667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5117.99 | 1.85097 | 0.925487 | − | 0.378779i | \(-0.123656\pi\) | ||||
0.925487 | + | 0.378779i | \(0.123656\pi\) | |||||||
\(198\) | 2968.86 | + | 5142.22i | 1.06560 | + | 1.84566i | ||||
\(199\) | 432.427 | − | 748.986i | 0.154040 | − | 0.266805i | −0.778669 | − | 0.627435i | \(-0.784105\pi\) |
0.932709 | + | 0.360630i | \(0.117438\pi\) | |||||||
\(200\) | 752.402 | − | 1303.20i | 0.266014 | − | 0.460750i | ||||
\(201\) | 702.567 | + | 1216.88i | 0.246544 | + | 0.427026i | ||||
\(202\) | −272.316 | −0.0948519 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −926.969 | −0.318141 | ||||||||
\(205\) | 258.333 | + | 447.445i | 0.0880134 | + | 0.152444i | ||||
\(206\) | −290.775 | + | 503.637i | −0.0983460 | + | 0.170340i | ||||
\(207\) | −952.973 | + | 1650.60i | −0.319982 | + | 0.554224i | ||||
\(208\) | 1789.30 | + | 3099.17i | 0.596471 | + | 1.03312i | ||||
\(209\) | −3823.53 | −1.26545 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1344.61 | −0.438707 | −0.219353 | − | 0.975645i | \(-0.570395\pi\) | ||||
−0.219353 | + | 0.975645i | \(0.570395\pi\) | |||||||
\(212\) | 315.325 | + | 546.159i | 0.102154 | + | 0.176936i | ||||
\(213\) | −2639.49 | + | 4571.73i | −0.849084 | + | 1.47066i | ||||
\(214\) | 1805.51 | − | 3127.23i | 0.576738 | − | 0.998939i | ||||
\(215\) | 152.867 | + | 264.774i | 0.0484905 | + | 0.0839881i | ||||
\(216\) | 700.955 | 0.220805 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4811.23 | −1.49476 | ||||||||
\(219\) | 928.842 | + | 1608.80i | 0.286600 | + | 0.496405i | ||||
\(220\) | −228.305 | + | 395.435i | −0.0699650 | + | 0.121183i | ||||
\(221\) | 594.741 | − | 1030.12i | 0.181026 | − | 0.313545i | ||||
\(222\) | 1066.00 | + | 1846.36i | 0.322274 | + | 0.558196i | ||||
\(223\) | 864.916 | 0.259727 | 0.129863 | − | 0.991532i | \(-0.458546\pi\) | ||||
0.129863 | + | 0.991532i | \(0.458546\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4125.83 | −1.22247 | ||||||||
\(226\) | −2716.16 | − | 4704.53i | −0.799452 | − | 1.38469i | ||||
\(227\) | 857.672 | − | 1485.53i | 0.250774 | − | 0.434353i | −0.712965 | − | 0.701200i | \(-0.752648\pi\) |
0.963739 | + | 0.266846i | \(0.0859815\pi\) | |||||||
\(228\) | 1358.67 | − | 2353.28i | 0.394649 | − | 0.683552i | ||||
\(229\) | 522.729 | + | 905.394i | 0.150842 | + | 0.261267i | 0.931537 | − | 0.363646i | \(-0.118468\pi\) |
−0.780695 | + | 0.624912i | \(0.785135\pi\) | |||||||
\(230\) | −408.945 | −0.117239 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1514.17 | 0.428491 | ||||||||
\(233\) | −724.335 | − | 1254.58i | −0.203660 | − | 0.352749i | 0.746045 | − | 0.665895i | \(-0.231950\pi\) |
−0.949705 | + | 0.313146i | \(0.898617\pi\) | |||||||
\(234\) | 2707.45 | − | 4689.45i | 0.756375 | − | 1.31008i | ||||
\(235\) | 280.280 | − | 485.459i | 0.0778019 | − | 0.134757i | ||||
\(236\) | −949.263 | − | 1644.17i | −0.261830 | − | 0.453502i | ||||
\(237\) | 3878.65 | 1.06306 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3153.12 | −0.853383 | −0.426691 | − | 0.904397i | \(-0.640321\pi\) | ||||
−0.426691 | + | 0.904397i | \(0.640321\pi\) | |||||||
\(240\) | 648.175 | + | 1122.67i | 0.174331 | + | 0.301951i | ||||
\(241\) | 190.506 | − | 329.966i | 0.0509194 | − | 0.0881950i | −0.839442 | − | 0.543449i | \(-0.817118\pi\) |
0.890362 | + | 0.455254i | \(0.150451\pi\) | |||||||
\(242\) | 1921.53 | − | 3328.19i | 0.510416 | − | 0.884067i | ||||
\(243\) | 2649.18 | + | 4588.52i | 0.699363 | + | 1.21133i | ||||
\(244\) | 2627.68 | 0.689426 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6869.94 | 1.78053 | ||||||||
\(247\) | 1743.44 | + | 3019.72i | 0.449118 | + | 0.777895i | ||||
\(248\) | 1904.95 | − | 3299.47i | 0.487759 | − | 0.844824i | ||||
\(249\) | −95.5895 | + | 165.566i | −0.0243283 | + | 0.0421378i | ||||
\(250\) | −901.074 | − | 1560.71i | −0.227956 | − | 0.394831i | ||||
\(251\) | 3776.23 | 0.949617 | 0.474808 | − | 0.880089i | \(-0.342517\pi\) | ||||
0.474808 | + | 0.880089i | \(0.342517\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2742.21 | 0.681428 | ||||||||
\(254\) | −300.778 | − | 520.963i | −0.0743012 | − | 0.128693i | ||||
\(255\) | 215.445 | − | 373.161i | 0.0529086 | − | 0.0916403i | ||||
\(256\) | −2560.55 | + | 4435.00i | −0.625133 | + | 1.08276i | ||||
\(257\) | −2129.21 | − | 3687.90i | −0.516795 | − | 0.895116i | −0.999810 | − | 0.0195034i | \(-0.993791\pi\) |
0.483014 | − | 0.875612i | \(-0.339542\pi\) | |||||||
\(258\) | 4065.26 | 0.980977 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 416.405 | 0.0993244 | ||||||||
\(261\) | −2075.75 | − | 3595.30i | −0.492282 | − | 0.852658i | ||||
\(262\) | 1327.59 | − | 2299.45i | 0.313049 | − | 0.542216i | ||||
\(263\) | −2099.41 | + | 3636.29i | −0.492226 | + | 0.852560i | −0.999960 | − | 0.00895400i | \(-0.997150\pi\) |
0.507734 | + | 0.861514i | \(0.330483\pi\) | |||||||
\(264\) | −2398.69 | − | 4154.65i | −0.559202 | − | 0.968565i | ||||
\(265\) | −293.150 | −0.0679548 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8387.65 | −1.92253 | ||||||||
\(268\) | 401.381 | + | 695.212i | 0.0914860 | + | 0.158458i | ||||
\(269\) | −1870.29 | + | 3239.44i | −0.423917 | + | 0.734247i | −0.996319 | − | 0.0857271i | \(-0.972679\pi\) |
0.572401 | + | 0.819974i | \(0.306012\pi\) | |||||||
\(270\) | 206.179 | − | 357.113i | 0.0464729 | − | 0.0804933i | ||||
\(271\) | −2178.15 | − | 3772.66i | −0.488240 | − | 0.845656i | 0.511669 | − | 0.859183i | \(-0.329028\pi\) |
−0.999909 | + | 0.0135265i | \(0.995694\pi\) | |||||||
\(272\) | 2115.60 | 0.471607 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1831.32 | −0.403775 | ||||||||
\(275\) | 2968.05 | + | 5140.81i | 0.650837 | + | 1.12728i | ||||
\(276\) | −974.426 | + | 1687.76i | −0.212513 | + | 0.368083i | ||||
\(277\) | 672.152 | − | 1164.20i | 0.145797 | − | 0.252527i | −0.783873 | − | 0.620921i | \(-0.786759\pi\) |
0.929670 | + | 0.368394i | \(0.120092\pi\) | |||||||
\(278\) | 5253.83 | + | 9099.90i | 1.13347 | + | 1.96322i | ||||
\(279\) | −10445.9 | −2.24150 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4205.54 | 0.892817 | 0.446408 | − | 0.894829i | \(-0.352703\pi\) | ||||
0.446408 | + | 0.894829i | \(0.352703\pi\) | |||||||
\(282\) | −3726.80 | − | 6455.00i | −0.786977 | − | 1.36308i | ||||
\(283\) | −2376.02 | + | 4115.38i | −0.499079 | + | 0.864431i | −0.999999 | − | 0.00106280i | \(-0.999662\pi\) |
0.500920 | + | 0.865494i | \(0.332995\pi\) | |||||||
\(284\) | −1507.96 | + | 2611.86i | −0.315073 | + | 0.545723i | ||||
\(285\) | 631.559 | + | 1093.89i | 0.131264 | + | 0.227356i | ||||
\(286\) | −7790.79 | −1.61077 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6220.73 | 1.27278 | ||||||||
\(289\) | 2104.90 | + | 3645.80i | 0.428435 | + | 0.742071i | ||||
\(290\) | 445.378 | − | 771.418i | 0.0901845 | − | 0.156204i | ||||
\(291\) | 6521.48 | − | 11295.5i | 1.31373 | − | 2.27545i | ||||
\(292\) | 530.654 | + | 919.119i | 0.106350 | + | 0.184203i | ||||
\(293\) | −4961.17 | −0.989196 | −0.494598 | − | 0.869122i | \(-0.664685\pi\) | ||||
−0.494598 | + | 0.869122i | \(0.664685\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 882.506 | 0.174174 | ||||||||
\(296\) | −481.216 | − | 833.490i | −0.0944936 | − | 0.163668i | ||||
\(297\) | −1382.55 | + | 2394.65i | −0.270114 | + | 0.467850i | ||||
\(298\) | −4798.69 | + | 8311.58i | −0.932822 | + | 1.61569i | ||||
\(299\) | −1250.38 | − | 2165.72i | −0.241844 | − | 0.418886i | ||||
\(300\) | −4218.71 | −0.811890 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2498.80 | −0.476126 | ||||||||
\(303\) | −301.619 | − | 522.419i | −0.0571866 | − | 0.0990501i | ||||
\(304\) | −3100.85 | + | 5370.84i | −0.585020 | + | 1.01329i | ||||
\(305\) | −610.722 | + | 1057.80i | −0.114655 | + | 0.198589i | ||||
\(306\) | −1600.59 | − | 2772.31i | −0.299019 | − | 0.517915i | ||||
\(307\) | −4234.00 | −0.787124 | −0.393562 | − | 0.919298i | \(-0.628757\pi\) | ||||
−0.393562 | + | 0.919298i | \(0.628757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1288.26 | −0.237173 | ||||||||
\(310\) | −1120.65 | − | 1941.02i | −0.205317 | − | 0.355620i | ||||
\(311\) | 342.350 | − | 592.968i | 0.0624209 | − | 0.108116i | −0.833126 | − | 0.553083i | \(-0.813451\pi\) |
0.895547 | + | 0.444967i | \(0.146785\pi\) | |||||||
\(312\) | −2187.49 | + | 3788.84i | −0.396930 | + | 0.687502i | ||||
\(313\) | 2972.04 | + | 5147.72i | 0.536707 | + | 0.929604i | 0.999079 | + | 0.0429180i | \(0.0136654\pi\) |
−0.462371 | + | 0.886686i | \(0.653001\pi\) | |||||||
\(314\) | 11009.8 | 1.97872 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2215.90 | 0.394475 | ||||||||
\(317\) | 1411.95 | + | 2445.56i | 0.250166 | + | 0.433301i | 0.963571 | − | 0.267451i | \(-0.0861813\pi\) |
−0.713405 | + | 0.700752i | \(0.752848\pi\) | |||||||
\(318\) | −1948.96 | + | 3375.70i | −0.343686 | + | 0.595282i | ||||
\(319\) | −2986.52 | + | 5172.80i | −0.524178 | + | 0.907904i | ||||
\(320\) | 4.45967 | + | 7.72438i | 0.000779073 | + | 0.00134939i | ||||
\(321\) | 7999.16 | 1.39087 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2061.37 | 0.355101 | ||||||||
\(324\) | 1079.92 | + | 1870.48i | 0.185171 | + | 0.320726i | ||||
\(325\) | 2706.71 | − | 4688.16i | 0.461974 | − | 0.800162i | ||||
\(326\) | 3193.51 | − | 5531.32i | 0.542552 | − | 0.939728i | ||||
\(327\) | −5328.94 | − | 9230.00i | −0.901196 | − | 1.56092i | ||||
\(328\) | −3101.26 | −0.522068 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2822.21 | −0.470780 | ||||||||
\(331\) | 1406.48 | + | 2436.10i | 0.233557 | + | 0.404533i | 0.958852 | − | 0.283905i | \(-0.0916301\pi\) |
−0.725295 | + | 0.688438i | \(0.758297\pi\) | |||||||
\(332\) | −54.6109 | + | 94.5888i | −0.00902760 | + | 0.0156363i | ||||
\(333\) | −1319.38 | + | 2285.24i | −0.217122 | + | 0.376067i | ||||
\(334\) | −5556.91 | − | 9624.85i | −0.910361 | − | 1.57679i | ||||
\(335\) | −373.154 | −0.0608584 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4260.10 | 0.688612 | 0.344306 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344306 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(338\) | −326.540 | − | 565.584i | −0.0525486 | − | 0.0910169i | ||||
\(339\) | 6016.87 | − | 10421.5i | 0.963986 | − | 1.66967i | ||||
\(340\) | 123.085 | − | 213.190i | 0.0196330 | − | 0.0340054i | ||||
\(341\) | 7514.58 | + | 13015.6i | 1.19336 | + | 2.06697i | ||||
\(342\) | 9384.00 | 1.48371 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1835.16 | −0.287631 | ||||||||
\(345\) | −452.950 | − | 784.532i | −0.0706840 | − | 0.122428i | ||||
\(346\) | 5798.74 | − | 10043.7i | 0.900990 | − | 1.56056i | ||||
\(347\) | −18.0292 | + | 31.2275i | −0.00278922 | + | 0.00483106i | −0.867417 | − | 0.497583i | \(-0.834221\pi\) |
0.864627 | + | 0.502414i | \(0.167555\pi\) | |||||||
\(348\) | −2122.48 | − | 3676.24i | −0.326945 | − | 0.566285i | ||||
\(349\) | −242.692 | −0.0372236 | −0.0186118 | − | 0.999827i | \(-0.505925\pi\) | ||||
−0.0186118 | + | 0.999827i | \(0.505925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2521.63 | 0.383461 | ||||||||
\(352\) | −4475.09 | − | 7751.08i | −0.677622 | − | 1.17368i | ||||
\(353\) | 54.9949 | − | 95.2539i | 0.00829201 | − | 0.0143622i | −0.861850 | − | 0.507164i | \(-0.830694\pi\) |
0.870142 | + | 0.492802i | \(0.164027\pi\) | |||||||
\(354\) | 5867.20 | − | 10162.3i | 0.880899 | − | 1.52576i | ||||
\(355\) | −700.955 | − | 1214.09i | −0.104797 | − | 0.181513i | ||||
\(356\) | −4791.92 | −0.713402 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9883.01 | −1.45903 | ||||||||
\(359\) | −6202.23 | − | 10742.6i | −0.911814 | − | 1.57931i | −0.811500 | − | 0.584352i | \(-0.801349\pi\) |
−0.100314 | − | 0.994956i | \(-0.531985\pi\) | |||||||
\(360\) | −442.745 | + | 766.857i | −0.0648187 | + | 0.112269i | ||||
\(361\) | 408.136 | − | 706.913i | 0.0595038 | − | 0.103064i | ||||
\(362\) | 6573.26 | + | 11385.2i | 0.954373 | + | 1.65302i | ||||
\(363\) | 8513.20 | 1.23093 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −493.335 | −0.0707461 | ||||||||
\(366\) | 8120.58 | + | 14065.3i | 1.15975 | + | 2.00875i | ||||
\(367\) | −6929.81 | + | 12002.8i | −0.985649 | + | 1.70719i | −0.346634 | + | 0.938001i | \(0.612675\pi\) |
−0.639015 | + | 0.769194i | \(0.720658\pi\) | |||||||
\(368\) | 2223.91 | − | 3851.93i | 0.315025 | − | 0.545640i | ||||
\(369\) | 4251.47 | + | 7363.76i | 0.599790 | + | 1.03887i | ||||
\(370\) | −566.181 | −0.0795523 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −10681.0 | −1.48867 | ||||||||
\(373\) | −2449.03 | − | 4241.85i | −0.339963 | − | 0.588832i | 0.644463 | − | 0.764636i | \(-0.277081\pi\) |
−0.984425 | + | 0.175803i | \(0.943748\pi\) | |||||||
\(374\) | −2302.88 | + | 3988.70i | −0.318393 | + | 0.551472i | ||||
\(375\) | 1996.07 | − | 3457.30i | 0.274871 | − | 0.476091i | ||||
\(376\) | 1682.37 | + | 2913.94i | 0.230748 | + | 0.399668i | ||||
\(377\) | 5447.11 | 0.744139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9806.25 | −1.32906 | −0.664530 | − | 0.747262i | \(-0.731368\pi\) | ||||
−0.664530 | + | 0.747262i | \(0.731368\pi\) | |||||||
\(380\) | 360.814 | + | 624.948i | 0.0487088 | + | 0.0843662i | ||||
\(381\) | 666.287 | − | 1154.04i | 0.0895930 | − | 0.155180i | ||||
\(382\) | 1694.32 | − | 2934.65i | 0.226935 | − | 0.393063i | ||||
\(383\) | −5364.84 | − | 9292.18i | −0.715746 | − | 1.23971i | −0.962671 | − | 0.270673i | \(-0.912754\pi\) |
0.246926 | − | 0.969034i | \(-0.420580\pi\) | |||||||
\(384\) | −11268.2 | −1.49747 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13383.8 | 1.76482 | ||||||||
\(387\) | 2515.79 | + | 4357.47i | 0.330451 | + | 0.572359i | ||||
\(388\) | 3725.76 | − | 6453.21i | 0.487492 | − | 0.844361i | ||||
\(389\) | −2632.03 | + | 4558.80i | −0.343057 | + | 0.594191i | −0.984999 | − | 0.172562i | \(-0.944796\pi\) |
0.641942 | + | 0.766753i | \(0.278129\pi\) | |||||||
\(390\) | 1286.86 | + | 2228.90i | 0.167084 | + | 0.289397i | ||||
\(391\) | −1478.40 | −0.191217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5881.79 | 0.754954 | ||||||||
\(394\) | 9036.15 | + | 15651.1i | 1.15542 | + | 2.00124i | ||||
\(395\) | −515.016 | + | 892.034i | −0.0656032 | + | 0.113628i | ||||
\(396\) | −3757.29 | + | 6507.81i | −0.476795 | + | 0.825833i | ||||
\(397\) | −607.450 | − | 1052.13i | −0.0767935 | − | 0.133010i | 0.825071 | − | 0.565029i | \(-0.191135\pi\) |
−0.901865 | + | 0.432018i | \(0.857802\pi\) | |||||||
\(398\) | 3053.91 | 0.384620 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9628.26 | 1.20353 | ||||||||
\(401\) | −1147.73 | − | 1987.92i | −0.142929 | − | 0.247561i | 0.785669 | − | 0.618647i | \(-0.212319\pi\) |
−0.928599 | + | 0.371086i | \(0.878986\pi\) | |||||||
\(402\) | −2480.86 | + | 4296.97i | −0.307796 | + | 0.533117i | ||||
\(403\) | 6852.92 | − | 11869.6i | 0.847067 | − | 1.46716i | ||||
\(404\) | −172.317 | − | 298.461i | −0.0212205 | − | 0.0367550i | ||||
\(405\) | −1003.97 | −0.123180 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3796.57 | 0.462381 | ||||||||
\(408\) | 1293.20 | + | 2239.88i | 0.156919 | + | 0.271791i | ||||
\(409\) | −2323.27 | + | 4024.03i | −0.280876 | + | 0.486492i | −0.971601 | − | 0.236626i | \(-0.923958\pi\) |
0.690724 | + | 0.723118i | \(0.257292\pi\) | |||||||
\(410\) | −912.206 | + | 1579.99i | −0.109880 | + | 0.190317i | ||||
\(411\) | −2028.38 | − | 3513.26i | −0.243437 | − | 0.421646i | ||||
\(412\) | −735.990 | −0.0880087 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6730.14 | −0.798957 | ||||||||
\(415\) | −25.3852 | − | 43.9684i | −0.00300267 | − | 0.00520078i | ||||
\(416\) | −4081.06 | + | 7068.60i | −0.480986 | + | 0.833093i | ||||
\(417\) | −11638.3 | + | 20158.2i | −1.36674 | + | 2.36727i | ||||
\(418\) | −6750.69 | − | 11692.5i | −0.789922 | − | 1.36818i | ||||
\(419\) | 7541.24 | 0.879269 | 0.439634 | − | 0.898177i | \(-0.355108\pi\) | ||||
0.439634 | + | 0.898177i | \(0.355108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6243.63 | −0.722794 | −0.361397 | − | 0.932412i | \(-0.617700\pi\) | ||||
−0.361397 | + | 0.932412i | \(0.617700\pi\) | |||||||
\(422\) | −2374.00 | − | 4111.90i | −0.273850 | − | 0.474322i | ||||
\(423\) | 4612.66 | − | 7989.36i | 0.530202 | − | 0.918336i | ||||
\(424\) | 879.808 | − | 1523.87i | 0.100772 | − | 0.174542i | ||||
\(425\) | −1600.15 | − | 2771.55i | −0.182632 | − | 0.316329i | ||||
\(426\) | −18640.8 | −2.12006 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4569.97 | 0.516116 | ||||||||
\(429\) | −8629.12 | − | 14946.1i | −0.971137 | − | 1.68206i | ||||
\(430\) | −539.794 | + | 934.951i | −0.0605376 | + | 0.104854i | ||||
\(431\) | −5732.90 | + | 9929.68i | −0.640706 | + | 1.10974i | 0.344570 | + | 0.938761i | \(0.388025\pi\) |
−0.985275 | + | 0.170974i | \(0.945309\pi\) | |||||||
\(432\) | 2242.48 | + | 3884.08i | 0.249748 | + | 0.432576i | ||||
\(433\) | 5156.40 | 0.572289 | 0.286144 | − | 0.958187i | \(-0.407626\pi\) | ||||
0.286144 | + | 0.958187i | \(0.407626\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1973.21 | 0.217491 | ||||||||
\(436\) | −3044.46 | − | 5273.16i | −0.334411 | − | 0.579216i | ||||
\(437\) | 2166.90 | − | 3753.18i | 0.237201 | − | 0.410844i | ||||
\(438\) | −3279.86 | + | 5680.89i | −0.357803 | + | 0.619734i | ||||
\(439\) | 2532.12 | + | 4385.77i | 0.275289 | + | 0.476814i | 0.970208 | − | 0.242274i | \(-0.0778932\pi\) |
−0.694919 | + | 0.719088i | \(0.744560\pi\) | |||||||
\(440\) | 1274.01 | 0.138037 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4200.22 | 0.452000 | ||||||||
\(443\) | −6351.82 | − | 11001.7i | −0.681228 | − | 1.17992i | −0.974606 | − | 0.223925i | \(-0.928113\pi\) |
0.293378 | − | 0.955996i | \(-0.405220\pi\) | |||||||
\(444\) | −1349.09 | + | 2336.68i | −0.144200 | + | 0.249762i | ||||
\(445\) | 1113.73 | − | 1929.04i | 0.118642 | − | 0.205495i | ||||
\(446\) | 1527.06 | + | 2644.95i | 0.162127 | + | 0.280812i | ||||
\(447\) | −21260.2 | −2.24961 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13942.2 | 1.46542 | 0.732709 | − | 0.680542i | \(-0.238256\pi\) | ||||
0.732709 | + | 0.680542i | \(0.238256\pi\) | |||||||
\(450\) | −7284.41 | − | 12617.0i | −0.763090 | − | 1.32171i | ||||
\(451\) | 6116.87 | − | 10594.7i | 0.638652 | − | 1.10618i | ||||
\(452\) | 3437.48 | − | 5953.88i | 0.357711 | − | 0.619573i | ||||
\(453\) | −2767.69 | − | 4793.78i | −0.287058 | − | 0.497199i | ||||
\(454\) | 6057.10 | 0.626154 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7581.80 | −0.778619 | ||||||||
\(457\) | 7607.01 | + | 13175.7i | 0.778646 | + | 1.34865i | 0.932722 | + | 0.360595i | \(0.117426\pi\) |
−0.154077 | + | 0.988059i | \(0.549240\pi\) | |||||||
\(458\) | −1845.82 | + | 3197.06i | −0.188318 | + | 0.326177i | ||||
\(459\) | 745.369 | − | 1291.02i | 0.0757971 | − | 0.131284i | ||||
\(460\) | −258.773 | − | 448.208i | −0.0262290 | − | 0.0454300i | ||||
\(461\) | −11430.2 | −1.15479 | −0.577394 | − | 0.816465i | \(-0.695930\pi\) | ||||
−0.577394 | + | 0.816465i | \(0.695930\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9347.88 | −0.938300 | −0.469150 | − | 0.883119i | \(-0.655440\pi\) | ||||
−0.469150 | + | 0.883119i | \(0.655440\pi\) | |||||||
\(464\) | 4844.08 | + | 8390.20i | 0.484657 | + | 0.839451i | ||||
\(465\) | 2482.47 | − | 4299.76i | 0.247574 | − | 0.428810i | ||||
\(466\) | 2557.72 | − | 4430.10i | 0.254258 | − | 0.440387i | ||||
\(467\) | −1815.42 | − | 3144.40i | −0.179888 | − | 0.311575i | 0.761954 | − | 0.647631i | \(-0.224240\pi\) |
−0.941842 | + | 0.336056i | \(0.890907\pi\) | |||||||
\(468\) | 6852.92 | 0.676872 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1979.41 | 0.194262 | ||||||||
\(471\) | 12194.5 | + | 21121.4i | 1.19298 | + | 2.06629i | ||||
\(472\) | −2648.60 | + | 4587.51i | −0.258287 | + | 0.447367i | ||||
\(473\) | 3619.63 | − | 6269.38i | 0.351862 | − | 0.609443i | ||||
\(474\) | 6848.01 | + | 11861.1i | 0.663586 | + | 1.14936i | ||||
\(475\) | 9381.43 | 0.906210 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4824.46 | −0.463096 | ||||||||
\(478\) | −5567.04 | − | 9642.39i | −0.532700 | − | 0.922663i | ||||
\(479\) | −3260.62 | + | 5647.57i | −0.311027 | + | 0.538714i | −0.978585 | − | 0.205844i | \(-0.934006\pi\) |
0.667558 | + | 0.744557i | \(0.267339\pi\) | |||||||
\(480\) | −1478.36 | + | 2560.60i | −0.140578 | + | 0.243489i | ||||
\(481\) | −1731.14 | − | 2998.42i | −0.164102 | − | 0.284234i | ||||
\(482\) | 1345.40 | 0.127140 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4863.65 | 0.456766 | ||||||||
\(485\) | 1731.87 | + | 2999.69i | 0.162145 | + | 0.280843i | ||||
\(486\) | −9354.61 | + | 16202.7i | −0.873115 | + | 1.51228i | ||||
\(487\) | 1833.14 | − | 3175.10i | 0.170570 | − | 0.295436i | −0.768049 | − | 0.640391i | \(-0.778772\pi\) |
0.938619 | + | 0.344955i | \(0.112106\pi\) | |||||||
\(488\) | −3665.83 | − | 6349.40i | −0.340049 | − | 0.588983i | ||||
\(489\) | 14148.6 | 1.30843 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12470.7 | −1.14623 | −0.573113 | − | 0.819476i | \(-0.694264\pi\) | ||||
−0.573113 | + | 0.819476i | \(0.694264\pi\) | |||||||
\(492\) | 4347.18 | + | 7529.53i | 0.398345 | + | 0.689954i | ||||
\(493\) | 1610.11 | − | 2788.79i | 0.147091 | − | 0.254768i | ||||
\(494\) | −6156.30 | + | 10663.0i | −0.560698 | + | 0.971158i | ||||
\(495\) | −1746.53 | − | 3025.07i | −0.158587 | − | 0.274681i | ||||
\(496\) | 24377.0 | 2.20678 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −675.078 | −0.0607449 | ||||||||
\(499\) | 1151.97 | + | 1995.26i | 0.103345 | + | 0.178998i | 0.913061 | − | 0.407824i | \(-0.133712\pi\) |
−0.809716 | + | 0.586822i | \(0.800379\pi\) | |||||||
\(500\) | 1140.37 | − | 1975.17i | 0.101998 | − | 0.176665i | ||||
\(501\) | 12309.7 | − | 21321.1i | 1.09772 | − | 1.90131i | ||||
\(502\) | 6667.18 | + | 11547.9i | 0.592771 | + | 1.02671i | ||||
\(503\) | −10520.4 | −0.932570 | −0.466285 | − | 0.884635i | \(-0.654408\pi\) | ||||
−0.466285 | + | 0.884635i | \(0.654408\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 160.198 | 0.0141163 | ||||||||
\(506\) | 4841.55 | + | 8385.81i | 0.425362 | + | 0.736748i | ||||
\(507\) | 723.355 | − | 1252.89i | 0.0633636 | − | 0.109749i | ||||
\(508\) | 380.654 | − | 659.312i | 0.0332457 | − | 0.0575832i | ||||
\(509\) | 4831.11 | + | 8367.73i | 0.420698 | + | 0.728670i | 0.996008 | − | 0.0892655i | \(-0.0284520\pi\) |
−0.575310 | + | 0.817935i | \(0.695119\pi\) | |||||||
\(510\) | 1521.53 | 0.132107 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6558.89 | −0.566142 | ||||||||
\(513\) | 2184.99 | + | 3784.51i | 0.188050 | + | 0.325712i | ||||
\(514\) | 7518.51 | − | 13022.4i | 0.645189 | − | 1.11750i | ||||
\(515\) | 171.058 | − | 296.281i | 0.0146363 | − | 0.0253508i | ||||
\(516\) | 2572.42 | + | 4455.57i | 0.219466 | + | 0.380127i | ||||
\(517\) | −13273.1 | −1.12911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25690.9 | 2.17284 | ||||||||
\(520\) | −580.919 | − | 1006.18i | −0.0489903 | − | 0.0848537i | ||||
\(521\) | −4303.90 | + | 7454.58i | −0.361914 | + | 0.626854i | −0.988276 | − | 0.152679i | \(-0.951210\pi\) |
0.626361 | + | 0.779533i | \(0.284543\pi\) | |||||||
\(522\) | 7329.74 | − | 12695.5i | 0.614586 | − | 1.06449i | ||||
\(523\) | 5241.36 | + | 9078.30i | 0.438219 | + | 0.759018i | 0.997552 | − | 0.0699250i | \(-0.0222760\pi\) |
−0.559333 | + | 0.828943i | \(0.688943\pi\) | |||||||
\(524\) | 3360.30 | 0.280144 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14826.6 | −1.22903 | ||||||||
\(527\) | −4051.30 | − | 7017.06i | −0.334872 | − | 0.580015i | ||||
\(528\) | 15347.7 | − | 26582.9i | 1.26500 | − | 2.19105i | ||||
\(529\) | 4529.41 | − | 7845.18i | 0.372270 | − | 0.644791i | ||||
\(530\) | −517.574 | − | 896.465i | −0.0424189 | − | 0.0734716i | ||||
\(531\) | 14523.7 | 1.18696 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11156.6 | −0.906649 | ||||||||
\(534\) | −14808.9 | − | 25649.8i | −1.20008 | − | 2.07861i | ||||
\(535\) | −1062.15 | + | 1839.69i | −0.0858328 | + | 0.148667i | ||||
\(536\) | 1119.92 | − | 1939.75i | 0.0902483 | − | 0.156315i | ||||
\(537\) | −10946.5 | − | 18959.9i | −0.879656 | − | 1.52361i | ||||
\(538\) | −13208.5 | −1.05847 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 521.866 | 0.0415881 | ||||||||
\(541\) | −10361.3 | − | 17946.3i | −0.823416 | − | 1.42620i | −0.903124 | − | 0.429380i | \(-0.858732\pi\) |
0.0797082 | − | 0.996818i | \(-0.474601\pi\) | |||||||
\(542\) | 7691.32 | − | 13321.8i | 0.609540 | − | 1.05575i | ||||
\(543\) | −14561.2 | + | 25220.7i | −1.15079 | + | 1.99323i | ||||
\(544\) | 2412.64 | + | 4178.81i | 0.190149 | + | 0.329347i | ||||
\(545\) | 2830.35 | 0.222457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4175.09 | −0.326351 | −0.163176 | − | 0.986597i | \(-0.552174\pi\) | ||||
−0.163176 | + | 0.986597i | \(0.552174\pi\) | |||||||
\(548\) | −1158.83 | − | 2007.15i | −0.0903334 | − | 0.156462i | ||||
\(549\) | −10050.9 | + | 17408.6i | −0.781348 | + | 1.35333i | ||||
\(550\) | −10480.6 | + | 18152.9i | −0.812532 | + | 1.40735i | ||||
\(551\) | 4719.91 | + | 8175.12i | 0.364927 | + | 0.632072i | ||||
\(552\) | 5437.61 | 0.419276 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4746.91 | 0.364038 | ||||||||
\(555\) | −627.105 | − | 1086.18i | −0.0479624 | − | 0.0830733i | ||||
\(556\) | −6649.06 | + | 11516.5i | −0.507164 | + | 0.878433i | ||||
\(557\) | 5080.87 | − | 8800.33i | 0.386505 | − | 0.669447i | −0.605472 | − | 0.795867i | \(-0.707015\pi\) |
0.991977 | + | 0.126420i | \(0.0403488\pi\) | |||||||
\(558\) | −18442.8 | − | 31943.9i | −1.39919 | − | 2.42347i | ||||
\(559\) | −6601.85 | −0.499514 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10202.7 | −0.767841 | ||||||||
\(562\) | 7425.15 | + | 12860.7i | 0.557315 | + | 0.965298i | ||||
\(563\) | 8552.22 | − | 14812.9i | 0.640201 | − | 1.10886i | −0.345187 | − | 0.938534i | \(-0.612184\pi\) |
0.985388 | − | 0.170326i | \(-0.0544822\pi\) | |||||||
\(564\) | 4716.50 | − | 8169.22i | 0.352129 | − | 0.609905i | ||||
\(565\) | 1597.87 | + | 2767.59i | 0.118978 | + | 0.206076i | ||||
\(566\) | −16780.0 | −1.24614 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8414.89 | 0.621621 | ||||||||
\(569\) | 9128.79 | + | 15811.5i | 0.672581 | + | 1.16495i | 0.977170 | + | 0.212461i | \(0.0681479\pi\) |
−0.304588 | + | 0.952484i | \(0.598519\pi\) | |||||||
\(570\) | −2230.12 | + | 3862.68i | −0.163876 | + | 0.283841i | ||||
\(571\) | −6815.25 | + | 11804.4i | −0.499491 | + | 0.865143i | −1.00000 | 0.000587868i | \(-0.999813\pi\) | |
0.500509 | + | 0.865731i | \(0.333146\pi\) | |||||||
\(572\) | −4929.87 | − | 8538.79i | −0.360364 | − | 0.624169i | ||||
\(573\) | 7506.57 | 0.547280 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6728.30 | −0.487981 | ||||||||
\(576\) | 73.3943 | + | 127.123i | 0.00530920 | + | 0.00919580i | ||||
\(577\) | −2221.04 | + | 3846.96i | −0.160248 | + | 0.277558i | −0.934958 | − | 0.354759i | \(-0.884563\pi\) |
0.774709 | + | 0.632317i | \(0.217896\pi\) | |||||||
\(578\) | −7432.68 | + | 12873.8i | −0.534877 | + | 0.926433i | ||||
\(579\) | 14824.0 | + | 25676.0i | 1.06402 | + | 1.84293i | ||||
\(580\) | 1127.31 | 0.0807052 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 46056.4 | 3.28024 | ||||||||
\(583\) | 3470.63 | + | 6011.32i | 0.246551 | + | 0.427038i | ||||
\(584\) | 1480.61 | − | 2564.49i | 0.104911 | − | 0.181711i | ||||
\(585\) | −1592.75 | + | 2758.72i | −0.112567 | + | 0.194972i | ||||
\(586\) | −8759.26 | − | 15171.5i | −0.617477 | − | 1.06950i | ||||
\(587\) | 3103.38 | 0.218211 | 0.109106 | − | 0.994030i | \(-0.465201\pi\) | ||||
0.109106 | + | 0.994030i | \(0.465201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23752.1 | 1.66161 | ||||||||
\(590\) | 1558.12 | + | 2698.74i | 0.108723 | + | 0.188314i | ||||
\(591\) | −20017.0 | + | 34670.4i | −1.39321 | + | 2.41311i | ||||
\(592\) | 3078.99 | − | 5332.96i | 0.213759 | − | 0.370242i | ||||
\(593\) | −2968.86 | − | 5142.21i | −0.205592 | − | 0.356096i | 0.744729 | − | 0.667367i | \(-0.232579\pi\) |
−0.950321 | + | 0.311271i | \(0.899245\pi\) | |||||||
\(594\) | −9763.93 | −0.674443 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12146.1 | −0.834772 | ||||||||
\(597\) | 3382.53 | + | 5858.72i | 0.231889 | + | 0.401644i | ||||
\(598\) | 4415.25 | − | 7647.44i | 0.301928 | − | 0.522955i | ||||
\(599\) | 1300.16 | − | 2251.95i | 0.0886866 | − | 0.153610i | −0.818270 | − | 0.574835i | \(-0.805066\pi\) |
0.906956 | + | 0.421225i | \(0.138400\pi\) | |||||||
\(600\) | 5885.44 | + | 10193.9i | 0.400453 | + | 0.693605i | ||||
\(601\) | −13881.4 | −0.942156 | −0.471078 | − | 0.882092i | \(-0.656135\pi\) | ||||
−0.471078 | + | 0.882092i | \(0.656135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6141.11 | −0.414735 | ||||||||
\(604\) | −1581.20 | − | 2738.71i | −0.106520 | − | 0.184498i | ||||
\(605\) | −1130.40 | + | 1957.91i | −0.0759626 | + | 0.131571i | ||||
\(606\) | 1065.05 | − | 1844.73i | 0.0713942 | − | 0.123658i | ||||
\(607\) | 6142.28 | + | 10638.7i | 0.410721 | + | 0.711389i | 0.994969 | − | 0.100186i | \(-0.0319438\pi\) |
−0.584248 | + | 0.811575i | \(0.698610\pi\) | |||||||
\(608\) | −14144.9 | −0.943505 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4313.07 | −0.286281 | ||||||||
\(611\) | 6052.20 | + | 10482.7i | 0.400729 | + | 0.694084i | ||||
\(612\) | 2025.65 | − | 3508.53i | 0.133794 | − | 0.231738i | ||||
\(613\) | −11031.0 | + | 19106.2i | −0.726815 | + | 1.25888i | 0.231408 | + | 0.972857i | \(0.425667\pi\) |
−0.958223 | + | 0.286023i | \(0.907666\pi\) | |||||||
\(614\) | −7475.40 | − | 12947.8i | −0.491340 | − | 0.851025i | ||||
\(615\) | −4041.46 | −0.264988 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12182.2 | −0.794871 | −0.397436 | − | 0.917630i | \(-0.630100\pi\) | ||||
−0.397436 | + | 0.917630i | \(0.630100\pi\) | |||||||
\(618\) | −2274.50 | − | 3939.55i | −0.148048 | − | 0.256427i | ||||
\(619\) | −11624.3 | + | 20133.9i | −0.754799 | + | 1.30735i | 0.190675 | + | 0.981653i | \(0.438932\pi\) |
−0.945474 | + | 0.325698i | \(0.894401\pi\) | |||||||
\(620\) | 1418.25 | − | 2456.48i | 0.0918682 | − | 0.159120i | ||||
\(621\) | −1567.06 | − | 2714.22i | −0.101262 | − | 0.175391i | ||||
\(622\) | 2417.76 | 0.155858 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −27992.6 | −1.79583 | ||||||||
\(625\) | −7012.72 | − | 12146.4i | −0.448814 | − | 0.777368i | ||||
\(626\) | −10494.6 | + | 18177.3i | −0.670048 | + | 1.16056i | ||||
\(627\) | 14954.2 | − | 25901.5i | 0.952494 | − | 1.64977i | ||||
\(628\) | 6966.78 | + | 12066.8i | 0.442683 | + | 0.766749i | ||||
\(629\) | −2046.83 | −0.129749 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19184.4 | 1.21033 | 0.605165 | − | 0.796100i | \(-0.293107\pi\) | ||||
0.605165 | + | 0.796100i | \(0.293107\pi\) | |||||||
\(632\) | −3091.36 | − | 5354.39i | −0.194569 | − | 0.337004i | ||||
\(633\) | 5258.92 | − | 9108.72i | 0.330211 | − | 0.571942i | ||||
\(634\) | −4985.76 | + | 8635.59i | −0.312318 | + | 0.540951i | ||||
\(635\) | 176.942 | + | 306.473i | 0.0110579 | + | 0.0191528i | ||||
\(636\) | −4933.07 | −0.307561 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21091.6 | −1.30881 | ||||||||
\(639\) | −11535.8 | − | 19980.7i | −0.714164 | − | 1.23697i | ||||
\(640\) | 1496.22 | − | 2591.53i | 0.0924113 | − | 0.160061i | ||||
\(641\) | 9716.68 | − | 16829.8i | 0.598730 | − | 1.03703i | −0.394279 | − | 0.918991i | \(-0.629006\pi\) |
0.993009 | − | 0.118040i | \(-0.0376611\pi\) | |||||||
\(642\) | 14123.0 | + | 24461.8i | 0.868211 | + | 1.50379i | ||||
\(643\) | 5777.47 | 0.354341 | 0.177170 | − | 0.984180i | \(-0.443306\pi\) | ||||
0.177170 | + | 0.984180i | \(0.443306\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2391.52 | −0.145994 | ||||||||
\(646\) | 3639.48 | + | 6303.76i | 0.221661 | + | 0.383929i | ||||
\(647\) | 14615.7 | − | 25315.2i | 0.888106 | − | 1.53824i | 0.0459932 | − | 0.998942i | \(-0.485355\pi\) |
0.842112 | − | 0.539302i | \(-0.181312\pi\) | |||||||
\(648\) | 3013.15 | − | 5218.93i | 0.182666 | − | 0.316387i | ||||
\(649\) | −10448.1 | − | 18096.6i | −0.631932 | − | 1.09454i | ||||
\(650\) | 19115.5 | 1.15349 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8083.18 | 0.485524 | ||||||||
\(653\) | 3546.63 | + | 6142.95i | 0.212543 | + | 0.368135i | 0.952510 | − | 0.304508i | \(-0.0984922\pi\) |
−0.739967 | + | 0.672643i | \(0.765159\pi\) | |||||||
\(654\) | 18817.2 | − | 32592.3i | 1.12509 | − | 1.94872i | ||||
\(655\) | −780.997 | + | 1352.73i | −0.0465894 | + | 0.0806952i | ||||
\(656\) | −9921.46 | − | 17184.5i | −0.590500 | − | 1.02278i | ||||
\(657\) | −8118.98 | −0.482118 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19014.2 | 1.12396 | 0.561980 | − | 0.827151i | \(-0.310040\pi\) | ||||
0.561980 | + | 0.827151i | \(0.310040\pi\) | |||||||
\(660\) | −1785.84 | − | 3093.17i | −0.105324 | − | 0.182427i | ||||
\(661\) | 10529.2 | − | 18237.1i | 0.619573 | − | 1.07313i | −0.369990 | − | 0.929036i | \(-0.620639\pi\) |
0.989564 | − | 0.144097i | \(-0.0460277\pi\) | |||||||
\(662\) | −4966.48 | + | 8602.19i | −0.291583 | + | 0.505036i | ||||
\(663\) | 4652.18 | + | 8057.82i | 0.272513 | + | 0.472006i | ||||
\(664\) | 304.746 | 0.0178109 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −9317.83 | −0.542130 | ||||||||
\(667\) | −3385.08 | − | 5863.13i | −0.196508 | − | 0.340362i | ||||
\(668\) | 7032.63 | − | 12180.9i | 0.407336 | − | 0.705527i | ||||
\(669\) | −3382.77 | + | 5859.13i | −0.195494 | + | 0.338605i | ||||
\(670\) | −658.827 | − | 1141.12i | −0.0379891 | − | 0.0657991i | ||||
\(671\) | 28921.6 | 1.66395 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9634.87 | 0.551853 | 0.275926 | − | 0.961179i | \(-0.411015\pi\) | ||||
0.275926 | + | 0.961179i | \(0.411015\pi\) | |||||||
\(674\) | 7521.48 | + | 13027.6i | 0.429846 | + | 0.744516i | ||||
\(675\) | 3392.23 | − | 5875.52i | 0.193433 | − | 0.335035i | ||||
\(676\) | 413.257 | − | 715.783i | 0.0235126 | − | 0.0407250i | ||||
\(677\) | −4185.66 | − | 7249.77i | −0.237619 | − | 0.411568i | 0.722412 | − | 0.691463i | \(-0.243034\pi\) |
−0.960030 | + | 0.279895i | \(0.909700\pi\) | |||||||
\(678\) | 42492.7 | 2.40696 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −686.854 | −0.0387348 | ||||||||
\(681\) | 6708.88 | + | 11620.1i | 0.377511 | + | 0.653868i | ||||
\(682\) | −26534.9 | + | 45959.9i | −1.48985 | + | 2.58049i | ||||
\(683\) | 6034.42 | − | 10451.9i | 0.338069 | − | 0.585552i | −0.646001 | − | 0.763337i | \(-0.723560\pi\) |
0.984069 | + | 0.177785i | \(0.0568931\pi\) | |||||||
\(684\) | 5938.03 | + | 10285.0i | 0.331939 | + | 0.574935i | ||||
\(685\) | 1077.33 | 0.0600917 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8177.78 | −0.454151 | ||||||||
\(688\) | −5870.98 | − | 10168.8i | −0.325333 | − | 0.563493i | ||||
\(689\) | 3165.05 | − | 5482.02i | 0.175005 | − | 0.303118i | ||||
\(690\) | 1599.42 | − | 2770.28i | 0.0882449 | − | 0.152845i | ||||
\(691\) | −1490.64 | − | 2581.87i | −0.0820648 | − | 0.142140i | 0.822072 | − | 0.569384i | \(-0.192818\pi\) |
−0.904137 | + | 0.427243i | \(0.859485\pi\) | |||||||
\(692\) | 14677.4 | 0.806286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −127.327 | −0.00696435 | ||||||||
\(695\) | −3090.73 | − | 5353.30i | −0.168688 | − | 0.292176i | ||||
\(696\) | −5922.06 | + | 10257.3i | −0.322522 | + | 0.558624i | ||||
\(697\) | −3297.76 | + | 5711.89i | −0.179213 | + | 0.310407i | ||||
\(698\) | −428.489 | − | 742.165i | −0.0232357 | − | 0.0402455i | ||||
\(699\) | 11331.8 | 0.613172 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28978.0 | −1.56132 | −0.780660 | − | 0.624956i | \(-0.785117\pi\) | ||||
−0.780660 | + | 0.624956i | \(0.785117\pi\) | |||||||
\(702\) | 4452.11 | + | 7711.28i | 0.239365 | + | 0.414592i | ||||
\(703\) | 3000.06 | − | 5196.25i | 0.160952 | − | 0.278777i | ||||
\(704\) | 105.597 | − | 182.900i | 0.00565319 | − | 0.00979161i | ||||
\(705\) | 2192.41 | + | 3797.36i | 0.117122 | + | 0.202861i | ||||
\(706\) | 388.388 | 0.0207042 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 14850.7 | 0.788307 | ||||||||
\(709\) | 8186.22 | + | 14178.9i | 0.433625 | + | 0.751060i | 0.997182 | − | 0.0750169i | \(-0.0239011\pi\) |
−0.563558 | + | 0.826077i | \(0.690568\pi\) | |||||||
\(710\) | 2475.16 | − | 4287.10i | 0.130833 | − | 0.226609i | ||||
\(711\) | −8475.79 | + | 14680.5i | −0.447070 | + | 0.774349i | ||||
\(712\) | 6685.11 | + | 11578.9i | 0.351875 | + | 0.609465i | ||||
\(713\) | −17034.9 | −0.894755 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4583.18 | 0.239722 | ||||||||
\(716\) | −6253.79 | − | 10831.9i | −0.326418 | − | 0.565373i | ||||
\(717\) | 12332.2 | − | 21359.9i | 0.642334 | − | 1.11255i | ||||
\(718\) | 21900.9 | − | 37933.4i | 1.13835 | − | 1.97168i | ||||
\(719\) | −11505.3 | − | 19927.7i | −0.596765 | − | 1.03363i | −0.993295 | − | 0.115605i | \(-0.963119\pi\) |
0.396530 | − | 0.918022i | \(-0.370214\pi\) | |||||||
\(720\) | −5665.68 | −0.293260 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2882.36 | 0.148574 | ||||||||
\(723\) | 1490.18 | + | 2581.06i | 0.0766532 | + | 0.132767i | ||||
\(724\) | −8318.89 | + | 14408.7i | −0.427029 | + | 0.739636i | ||||
\(725\) | 7327.73 | − | 12692.0i | 0.375372 | − | 0.650164i | ||||
\(726\) | 15030.6 | + | 26033.8i | 0.768372 | + | 1.33086i | ||||
\(727\) | −24636.8 | −1.25685 | −0.628423 | − | 0.777872i | \(-0.716299\pi\) | ||||
−0.628423 | + | 0.777872i | \(0.716299\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28395.6 | −1.44264 | ||||||||
\(730\) | −871.015 | − | 1508.64i | −0.0441612 | − | 0.0764895i | ||||
\(731\) | −1951.44 | + | 3379.99i | −0.0987367 | + | 0.171017i | ||||
\(732\) | −10277.1 | + | 17800.5i | −0.518925 | + | 0.898805i | ||||
\(733\) | −3452.38 | − | 5979.70i | −0.173965 | − | 0.301317i | 0.765837 | − | 0.643034i | \(-0.222325\pi\) |
−0.939803 | + | 0.341718i | \(0.888991\pi\) | |||||||
\(734\) | −48940.1 | −2.46105 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10144.6 | 0.508065 | ||||||||
\(737\) | 4417.81 | + | 7651.88i | 0.220804 | + | 0.382443i | ||||
\(738\) | −15012.5 | + | 26002.4i | −0.748804 | + | 1.29697i | ||||
\(739\) | 4617.44 | − | 7997.65i | 0.229845 | − | 0.398103i | −0.727917 | − | 0.685665i | \(-0.759511\pi\) |
0.957762 | + | 0.287562i | \(0.0928448\pi\) | |||||||
\(740\) | −358.269 | − | 620.540i | −0.0177976 | − | 0.0308264i | ||||
\(741\) | −27275.0 | −1.35219 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20216.9 | 0.998232 | 0.499116 | − | 0.866535i | \(-0.333658\pi\) | ||||
0.499116 | + | 0.866535i | \(0.333658\pi\) | |||||||
\(744\) | 14900.9 | + | 25809.1i | 0.734265 | + | 1.27178i | ||||
\(745\) | 2822.98 | − | 4889.55i | 0.138827 | − | 0.240455i | ||||
\(746\) | 8647.84 | − | 14978.5i | 0.424424 | − | 0.735123i | ||||
\(747\) | −417.772 | − | 723.603i | −0.0204625 | − | 0.0354421i | ||||
\(748\) | −5828.88 | −0.284926 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14096.8 | 0.686321 | ||||||||
\(751\) | −12027.5 | − | 20832.2i | −0.584405 | − | 1.01222i | −0.994949 | − | 0.100378i | \(-0.967995\pi\) |
0.410544 | − | 0.911841i | \(-0.365339\pi\) | |||||||
\(752\) | −10764.4 | + | 18644.4i | −0.521989 | + | 0.904112i | ||||
\(753\) | −14769.2 | + | 25581.0i | −0.714768 | + | 1.23801i | ||||
\(754\) | 9617.23 | + | 16657.5i | 0.464508 | + | 0.804551i | ||||
\(755\) | 1470.00 | 0.0708593 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30328.2 | −1.45614 | −0.728069 | − | 0.685504i | \(-0.759582\pi\) | ||||
−0.728069 | + | 0.685504i | \(0.759582\pi\) | |||||||
\(758\) | −17313.6 | − | 29988.0i | −0.829627 | − | 1.43696i | ||||
\(759\) | −10725.1 | + | 18576.3i | −0.512905 | + | 0.888377i | ||||
\(760\) | 1006.73 | − | 1743.70i | 0.0480498 | − | 0.0832248i | ||||
\(761\) | 16917.1 | + | 29301.2i | 0.805839 | + | 1.39575i | 0.915723 | + | 0.401810i | \(0.131619\pi\) |
−0.109884 | + | 0.993944i | \(0.535048\pi\) | |||||||
\(762\) | 4705.49 | 0.223703 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4288.55 | 0.203082 | ||||||||
\(765\) | 941.598 | + | 1630.90i | 0.0445014 | + | 0.0770786i | ||||
\(766\) | 18943.9 | − | 32811.9i | 0.893567 | − | 1.54770i | ||||
\(767\) | −9528.14 | + | 16503.2i | −0.448555 | + | 0.776919i | ||||
\(768\) | −20029.1 | − | 34691.4i | −0.941065 | − | 1.62997i | ||||
\(769\) | 31738.1 | 1.48830 | 0.744151 | − | 0.668011i | \(-0.232854\pi\) | ||||
0.744151 | + | 0.668011i | \(0.232854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33310.2 | 1.55595 | ||||||||
\(772\) | 8469.06 | + | 14668.8i | 0.394829 | + | 0.683864i | ||||
\(773\) | −13747.1 | + | 23810.7i | −0.639650 | + | 1.10791i | 0.345860 | + | 0.938286i | \(0.387587\pi\) |
−0.985510 | + | 0.169619i | \(0.945746\pi\) | |||||||
\(774\) | −8883.57 | + | 15386.8i | −0.412550 | + | 0.714557i | ||||
\(775\) | −18437.8 | − | 31935.2i | −0.854587 | − | 1.48019i | ||||
\(776\) | −20791.0 | −0.961794 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18588.0 | −0.856573 | ||||||||
\(779\) | −9667.12 | − | 16743.9i | −0.444622 | − | 0.770108i | ||||
\(780\) | −1628.60 | + | 2820.82i | −0.0747606 | + | 0.129489i | ||||
\(781\) | −16597.4 | + | 28747.5i | −0.760436 | + | 1.31711i | ||||
\(782\) | −2610.21 | − | 4521.01i | −0.119362 | − | 0.206740i | ||||
\(783\) | 6826.68 | 0.311578 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6476.84 | −0.294482 | ||||||||
\(786\) | 10384.7 | + | 17986.8i | 0.471258 | + | 0.816243i | ||||
\(787\) | 234.178 | − | 405.608i | 0.0106068 | − | 0.0183715i | −0.860673 | − | 0.509158i | \(-0.829957\pi\) |
0.871280 | + | 0.490786i | \(0.163290\pi\) | |||||||
\(788\) | −11435.8 | + | 19807.4i | −0.516985 | + | 0.895445i | ||||
\(789\) | −16422.0 | − | 28443.8i | −0.740988 | − | 1.28343i | ||||
\(790\) | −3637.18 | −0.163804 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 20966.9 | 0.940688 | ||||||||
\(793\) | −13187.6 | − | 22841.5i | −0.590547 | − | 1.02286i | ||||
\(794\) | 2144.98 | − | 3715.22i | 0.0958723 | − | 0.166056i | ||||
\(795\) | 1146.54 | − | 1985.86i | 0.0511490 | − | 0.0885927i | ||||
\(796\) | 1932.46 | + | 3347.12i | 0.0860481 | + | 0.149040i | ||||
\(797\) | 37723.8 | 1.67659 | 0.838297 | − | 0.545214i | \(-0.183551\pi\) | ||||
0.838297 | + | 0.545214i | \(0.183551\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7155.87 | 0.316841 | ||||||||
\(800\) | 10980.1 | + | 19018.1i | 0.485256 | + | 0.840488i | ||||
\(801\) | 18329.0 | − | 31746.8i | 0.808520 | − | 1.40040i | ||||
\(802\) | 4052.77 | − | 7019.60i | 0.178439 | − | 0.309066i | ||||
\(803\) | 5840.66 | + | 10116.3i | 0.256678 | + | 0.444579i | ||||
\(804\) | −6279.36 | −0.275443 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 48397.1 | 2.11503 | ||||||||
\(807\) | −14629.8 | − | 25339.6i | −0.638158 | − | 1.10532i | ||||
\(808\) | −480.791 | + | 832.755i | −0.0209334 | + | 0.0362577i | ||||
\(809\) | 3898.57 | − | 6752.51i | 0.169427 | − | 0.293456i | −0.768792 | − | 0.639499i | \(-0.779142\pi\) |
0.938218 | + | 0.346043i | \(0.112475\pi\) | |||||||
\(810\) | −1772.58 | − | 3070.20i | −0.0768915 | − | 0.133180i | ||||
\(811\) | 16925.9 | 0.732860 | 0.366430 | − | 0.930446i | \(-0.380580\pi\) | ||||
0.366430 | + | 0.930446i | \(0.380580\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34075.8 | 1.46998 | ||||||||
\(814\) | 6703.09 | + | 11610.1i | 0.288628 | + | 0.499918i | ||||
\(815\) | −1878.68 | + | 3253.97i | −0.0807452 | + | 0.139855i | ||||
\(816\) | −8274.32 | + | 14331.5i | −0.354975 | + | 0.614834i | ||||
\(817\) | −5720.48 | − | 9908.16i | −0.244962 | − | 0.424287i | ||||
\(818\) | −16407.5 | −0.701316 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2308.91 | −0.0983301 | ||||||||
\(821\) | 15004.7 | + | 25988.8i | 0.637840 | + | 1.10477i | 0.985906 | + | 0.167301i | \(0.0535051\pi\) |
−0.348066 | + | 0.937470i | \(0.613162\pi\) | |||||||
\(822\) | 7162.49 | − | 12405.8i | 0.303918 | − | 0.526401i | ||||
\(823\) | 11692.8 | − | 20252.5i | 0.495243 | − | 0.857786i | −0.504742 | − | 0.863270i | \(-0.668412\pi\) |
0.999985 | + | 0.00548398i | \(0.00174562\pi\) | |||||||
\(824\) | 1026.76 | + | 1778.41i | 0.0434090 | + | 0.0751867i | ||||
\(825\) | −46433.3 | −1.95952 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −37325.9 | −1.56947 | −0.784734 | − | 0.619833i | \(-0.787200\pi\) | ||||
−0.784734 | + | 0.619833i | \(0.787200\pi\) | |||||||
\(828\) | −4258.71 | − | 7376.31i | −0.178745 | − | 0.309595i | ||||
\(829\) | 12335.7 | − | 21366.0i | 0.516809 | − | 0.895140i | −0.483000 | − | 0.875620i | \(-0.660453\pi\) |
0.999809 | − | 0.0195199i | \(-0.00621377\pi\) | |||||||
\(830\) | 89.6383 | − | 155.258i | 0.00374866 | − | 0.00649288i | ||||
\(831\) | 5257.70 | + | 9106.61i | 0.219480 | + | 0.380150i | ||||
\(832\) | −192.599 | −0.00802544 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −82193.0 | −3.41260 | ||||||||
\(835\) | 3269.03 | + | 5662.12i | 0.135484 | + | 0.234666i | ||||
\(836\) | 8543.44 | − | 14797.7i | 0.353446 | − | 0.612187i | ||||
\(837\) | 8588.53 | − | 14875.8i | 0.354675 | − | 0.614315i | ||||
\(838\) | 13314.5 | + | 23061.5i | 0.548858 | + | 0.950650i | ||||
\(839\) | 14147.4 | 0.582147 | 0.291074 | − | 0.956701i | \(-0.405987\pi\) | ||||
0.291074 | + | 0.956701i | \(0.405987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9642.35 | −0.395356 | ||||||||
\(842\) | −11023.5 | − | 19093.3i | −0.451183 | − | 0.781472i | ||||
\(843\) | −16448.3 | + | 28489.3i | −0.672015 | + | 1.16396i | ||||
\(844\) | 3004.46 | − | 5203.87i | 0.122533 | − | 0.212233i | ||||
\(845\) | 192.097 | + | 332.723i | 0.00782054 | + | 0.0135456i | ||||
\(846\) | 32575.8 | 1.32385 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11258.6 | 0.455923 | ||||||||
\(849\) | −18585.7 | − | 32191.3i | −0.751305 | − | 1.30130i | ||||
\(850\) | 5650.35 | − | 9786.69i | 0.228006 | − | 0.394918i | ||||
\(851\) | −2151.62 | + | 3726.71i | −0.0866704 | + | 0.150118i | ||||
\(852\) | −11795.5 | − | 20430.5i | −0.474306 | − | 0.821522i | ||||
\(853\) | 27963.6 | 1.12246 | 0.561229 | − | 0.827661i | \(-0.310329\pi\) | ||||
0.561229 | + | 0.827661i | \(0.310329\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5520.44 | −0.220813 | ||||||||
\(856\) | −6375.47 | − | 11042.6i | −0.254567 | − | 0.440923i | ||||
\(857\) | −16927.9 | + | 29320.0i | −0.674734 | + | 1.16867i | 0.301813 | + | 0.953367i | \(0.402408\pi\) |
−0.976547 | + | 0.215306i | \(0.930925\pi\) | |||||||
\(858\) | 30470.5 | − | 52776.5i | 1.21241 | − | 2.09995i | ||||
\(859\) | 12141.3 | + | 21029.4i | 0.482255 | + | 0.835291i | 0.999793 | − | 0.0203699i | \(-0.00648439\pi\) |
−0.517537 | + | 0.855661i | \(0.673151\pi\) | |||||||
\(860\) | −1366.29 | −0.0541745 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40487.2 | −1.59977 | ||||||||
\(863\) | 9833.49 | + | 17032.1i | 0.387875 | + | 0.671819i | 0.992163 | − | 0.124947i | \(-0.0398760\pi\) |
−0.604289 | + | 0.796765i | \(0.706543\pi\) | |||||||
\(864\) | −5114.65 | + | 8858.83i | −0.201393 | + | 0.348824i | ||||
\(865\) | −3411.29 | + | 5908.53i | −0.134090 | + | 0.232250i | ||||
\(866\) | 9103.96 | + | 15768.5i | 0.357235 | + | 0.618749i | ||||
\(867\) | −32929.9 | −1.28992 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24389.4 | 0.952075 | ||||||||
\(870\) | 3483.84 | + | 6034.18i | 0.135762 | + | 0.235147i | ||||
\(871\) | 4028.83 | − | 6978.13i | 0.156730 | − | 0.271464i | ||||
\(872\) | −8494.53 | + | 14713.0i | −0.329887 | + | 0.571380i | ||||
\(873\) | 28502.0 | + | 49366.9i | 1.10498 | + | 1.91388i | ||||
\(874\) | 15303.2 | 0.592264 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8301.75 | −0.320194 | ||||||||
\(877\) | 18030.5 | + | 31229.8i | 0.694238 | + | 1.20246i | 0.970437 | + | 0.241355i | \(0.0775919\pi\) |
−0.276199 | + | 0.961101i | \(0.589075\pi\) | |||||||
\(878\) | −8941.26 | + | 15486.7i | −0.343682 | + | 0.595275i | ||||
\(879\) | 19403.6 | − | 33608.1i | 0.744560 | − | 1.28962i | ||||
\(880\) | 4075.79 | + | 7059.48i | 0.156131 | + | 0.270426i | ||||
\(881\) | −15889.7 | −0.607646 | −0.303823 | − | 0.952728i | \(-0.598263\pi\) | ||||
−0.303823 | + | 0.952728i | \(0.598263\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14861.3 | 0.566390 | 0.283195 | − | 0.959062i | \(-0.408606\pi\) | ||||
0.283195 | + | 0.959062i | \(0.408606\pi\) | |||||||
\(884\) | 2657.82 | + | 4603.48i | 0.101122 | + | 0.175149i | ||||
\(885\) | −3451.57 | + | 5978.29i | −0.131100 | + | 0.227071i | ||||
\(886\) | 22429.1 | − | 38848.3i | 0.850474 | − | 1.47306i | ||||
\(887\) | 19094.9 | + | 33073.4i | 0.722824 | + | 1.25197i | 0.959863 | + | 0.280468i | \(0.0904896\pi\) |
−0.237039 | + | 0.971500i | \(0.576177\pi\) | |||||||
\(888\) | 7528.33 | 0.284498 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7865.45 | 0.296237 | ||||||||
\(891\) | 11886.2 | + | 20587.4i | 0.446915 | + | 0.774080i | ||||
\(892\) | −1932.60 | + | 3347.36i | −0.0725428 | + | 0.125648i | ||||
\(893\) | −10488.4 | + | 18166.5i | −0.393036 | + | 0.680759i | ||||
\(894\) | −37536.3 | − | 65014.8i | −1.40425 | − | 2.43224i | ||||
\(895\) | 5813.99 | 0.217140 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19561.4 | 0.728135 | ||||||||
\(898\) | 24615.8 | + | 42635.9i | 0.914745 | + | 1.58438i | ||||
\(899\) | 18552.5 | − | 32133.9i | 0.688277 | − | 1.19213i | ||||
\(900\) | 9218.89 | − | 15967.6i | 0.341440 | − | 0.591392i | ||||
\(901\) | −1871.11 | − | 3240.86i | −0.0691850 | − | 0.119832i | ||||
\(902\) | 43198.9 | 1.59464 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19182.2 | −0.705742 | ||||||||
\(905\) | −3866.93 | − | 6697.72i | −0.142034 | − | 0.246011i | ||||
\(906\) | 9773.06 | − | 16927.4i | 0.358376 | − | 0.620725i | ||||
\(907\) | −8432.75 | + | 14606.0i | −0.308715 | + | 0.534711i | −0.978082 | − | 0.208222i | \(-0.933232\pi\) |
0.669366 | + | 0.742933i | \(0.266566\pi\) | |||||||
\(908\) | 3832.83 | + | 6638.65i | 0.140085 | + | 0.242634i | ||||
\(909\) | 2636.44 | 0.0961993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26754.1 | 0.973000 | 0.486500 | − | 0.873681i | \(-0.338273\pi\) | ||||
0.486500 | + | 0.873681i | \(0.338273\pi\) | |||||||
\(912\) | −24255.5 | − | 42011.8i | −0.880680 | − | 1.52538i | ||||
\(913\) | −601.077 | + | 1041.10i | −0.0217883 | + | 0.0377385i | ||||
\(914\) | −26861.3 | + | 46525.2i | −0.972095 | + | 1.68372i | ||||
\(915\) | −4777.19 | − | 8274.33i | −0.172600 | − | 0.298952i | ||||
\(916\) | −4672.02 | −0.168524 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5263.99 | 0.189257 | ||||||||
\(919\) | 20763.8 | + | 35963.9i | 0.745303 | + | 1.29090i | 0.950053 | + | 0.312088i | \(0.101028\pi\) |
−0.204750 | + | 0.978814i | \(0.565638\pi\) | |||||||
\(920\) | −722.018 | + | 1250.57i | −0.0258742 | + | 0.0448154i | ||||
\(921\) | 16559.6 | − | 28682.1i | 0.592461 | − | 1.02617i | ||||
\(922\) | −20180.8 | − | 34954.1i | −0.720844 | − | 1.24854i | ||||
\(923\) | 30272.0 | 1.07954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9315.27 | −0.331118 | ||||||||
\(926\) | −16504.3 | − | 28586.2i | −0.585707 | − | 1.01447i | ||||
\(927\) | 2815.15 | − | 4875.99i | 0.0997430 | − | 0.172760i | ||||
\(928\) | −11048.4 | + | 19136.4i | −0.390821 | + | 0.676922i | ||||
\(929\) | −2292.34 | − | 3970.45i | −0.0809572 | − | 0.140222i | 0.822704 | − | 0.568470i | \(-0.192464\pi\) |
−0.903661 | + | 0.428248i | \(0.859131\pi\) | |||||||
\(930\) | 17531.8 | 0.618163 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6473.92 | 0.227532 | ||||||||
\(933\) | 2677.93 | + | 4638.31i | 0.0939673 | + | 0.162756i | ||||
\(934\) | 6410.48 | − | 11103.3i | 0.224580 | − | 0.388983i | ||||
\(935\) | 1354.74 | − | 2346.48i | 0.0473847 | − | 0.0820727i | ||||
\(936\) | −9560.37 | − | 16559.0i | −0.333857 | − | 0.578258i | ||||
\(937\) | −6928.18 | −0.241552 | −0.120776 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120776 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −46495.7 | −1.61590 | ||||||||
\(940\) | 1252.54 | + | 2169.45i | 0.0434609 | + | 0.0752764i | ||||
\(941\) | −10472.5 | + | 18138.9i | −0.362798 | + | 0.628384i | −0.988420 | − | 0.151742i | \(-0.951512\pi\) |
0.625622 | + | 0.780126i | \(0.284845\pi\) | |||||||
\(942\) | −43060.3 | + | 74582.5i | −1.48936 | + | 2.57965i | ||||
\(943\) | 6933.19 | + | 12008.6i | 0.239423 | + | 0.414693i | ||||
\(944\) | −33893.3 | −1.16857 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25562.8 | 0.878559 | ||||||||
\(947\) | −14639.5 | − | 25356.3i | −0.502342 | − | 0.870082i | −0.999996 | − | 0.00270685i | \(-0.999138\pi\) |
0.497654 | − | 0.867376i | \(-0.334195\pi\) | |||||||
\(948\) | −8666.60 | + | 15011.0i | −0.296918 | + | 0.514277i | ||||
\(949\) | 5326.39 | − | 9225.57i | 0.182194 | − | 0.315569i | ||||
\(950\) | 16563.5 | + | 28688.9i | 0.565676 | + | 0.979779i | ||||
\(951\) | −22089.0 | −0.753192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2136.81 | 0.0726316 | 0.0363158 | − | 0.999340i | \(-0.488438\pi\) | ||||
0.0363158 | + | 0.999340i | \(0.488438\pi\) | |||||||
\(954\) | −8517.89 | − | 14753.4i | −0.289074 | − | 0.500692i | ||||
\(955\) | −996.739 | + | 1726.40i | −0.0337735 | + | 0.0584975i | ||||
\(956\) | 7045.45 | − | 12203.1i | 0.238354 | − | 0.412840i | ||||
\(957\) | −23361.1 | − | 40462.7i | −0.789089 | − | 1.36674i | ||||
\(958\) | −23027.4 | −0.776597 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −69.7689 | −0.00234561 | ||||||||
\(961\) | −31785.7 | − | 55054.5i | −1.06696 | − | 1.84802i | ||||
\(962\) | 6112.88 | − | 10587.8i | 0.204872 | − | 0.354849i | ||||
\(963\) | −17480.1 | + | 30276.4i | −0.584930 | + | 1.01313i | ||||
\(964\) | 851.348 | + | 1474.58i | 0.0284440 | + | 0.0492665i | ||||
\(965\) | −7873.47 | −0.262649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3921.32 | −0.130405 | −0.0652023 | − | 0.997872i | \(-0.520769\pi\) | ||||
−0.0652023 | + | 0.997872i | \(0.520769\pi\) | |||||||
\(968\) | −6785.18 | − | 11752.3i | −0.225293 | − | 0.390219i | ||||
\(969\) | −8062.21 | + | 13964.2i | −0.267281 | + | 0.462945i | ||||
\(970\) | −6115.47 | + | 10592.3i | −0.202429 | + | 0.350617i | ||||
\(971\) | −23904.5 | − | 41403.9i | −0.790045 | − | 1.36840i | −0.925939 | − | 0.377674i | \(-0.876724\pi\) |
0.135894 | − | 0.990723i | \(-0.456609\pi\) | |||||||
\(972\) | −23677.7 | −0.781341 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 12946.1 | 0.425894 | ||||||||
\(975\) | 21172.4 | + | 36671.7i | 0.695447 | + | 1.20455i | ||||
\(976\) | 23455.2 | − | 40625.6i | 0.769245 | − | 1.33237i | ||||
\(977\) | 25664.6 | − | 44452.3i | 0.840411 | − | 1.45563i | −0.0491363 | − | 0.998792i | \(-0.515647\pi\) |
0.889547 | − | 0.456843i | \(-0.151020\pi\) | |||||||
\(978\) | 24980.2 | + | 43267.1i | 0.816749 | + | 1.41465i | ||||
\(979\) | −52742.4 | −1.72181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46580.1 | 1.51599 | ||||||||
\(982\) | −22017.9 | − | 38136.1i | −0.715499 | − | 1.23928i | ||||
\(983\) | 8163.16 | − | 14139.0i | 0.264867 | − | 0.458763i | −0.702662 | − | 0.711524i | \(-0.748005\pi\) |
0.967529 | + | 0.252761i | \(0.0813385\pi\) | |||||||
\(984\) | 12129.3 | − | 21008.6i | 0.392956 | − | 0.680620i | ||||
\(985\) | −5315.80 | − | 9207.23i | −0.171955 | − | 0.297834i | ||||
\(986\) | 11371.0 | 0.367268 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15582.4 | −0.501763 | ||||||||
\(989\) | 4102.69 | + | 7106.06i | 0.131909 | + | 0.228473i | ||||
\(990\) | 6167.21 | − | 10681.9i | 0.197987 | − | 0.342923i | ||||
\(991\) | −16885.0 | + | 29245.7i | −0.541242 | + | 0.937458i | 0.457592 | + | 0.889163i | \(0.348712\pi\) |
−0.998833 | + | 0.0482954i | \(0.984621\pi\) | |||||||
\(992\) | 27799.7 | + | 48150.4i | 0.889758 | + | 1.54111i | ||||
\(993\) | −22003.6 | −0.703185 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1796.56 | −0.0572410 | ||||||||
\(996\) | −427.177 | − | 739.893i | −0.0135900 | − | 0.0235385i | ||||
\(997\) | −25347.7 | + | 43903.5i | −0.805185 | + | 1.39462i | 0.110981 | + | 0.993823i | \(0.464601\pi\) |
−0.916166 | + | 0.400799i | \(0.868733\pi\) | |||||||
\(998\) | −4067.74 | + | 7045.53i | −0.129020 | + | 0.223469i | ||||
\(999\) | −2169.58 | − | 3757.82i | −0.0687112 | − | 0.119011i |
(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 | 49.4.c.e.18.3 | 8 | ||
3.2 | odd | 2 | 441.4.e.y.361.2 | 8 | |||
7.2 | even | 3 | inner | 49.4.c.e.30.3 | 8 | ||
7.3 | odd | 6 | 49.4.a.e.1.1 | ✓ | 4 | ||
7.4 | even | 3 | 49.4.a.e.1.2 | yes | 4 | ||
7.5 | odd | 6 | inner | 49.4.c.e.30.4 | 8 | ||
7.6 | odd | 2 | inner | 49.4.c.e.18.4 | 8 | ||
21.2 | odd | 6 | 441.4.e.y.226.2 | 8 | |||
21.5 | even | 6 | 441.4.e.y.226.1 | 8 | |||
21.11 | odd | 6 | 441.4.a.u.1.3 | 4 | |||
21.17 | even | 6 | 441.4.a.u.1.4 | 4 | |||
21.20 | even | 2 | 441.4.e.y.361.1 | 8 | |||
28.3 | even | 6 | 784.4.a.bf.1.4 | 4 | |||
28.11 | odd | 6 | 784.4.a.bf.1.1 | 4 | |||
35.4 | even | 6 | 1225.4.a.bb.1.3 | 4 | |||
35.24 | odd | 6 | 1225.4.a.bb.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.4.a.e.1.1 | ✓ | 4 | 7.3 | odd | 6 | ||
49.4.a.e.1.2 | yes | 4 | 7.4 | even | 3 | ||
49.4.c.e.18.3 | 8 | 1.1 | even | 1 | trivial | ||
49.4.c.e.18.4 | 8 | 7.6 | odd | 2 | inner | ||
49.4.c.e.30.3 | 8 | 7.2 | even | 3 | inner | ||
49.4.c.e.30.4 | 8 | 7.5 | odd | 6 | inner | ||
441.4.a.u.1.3 | 4 | 21.11 | odd | 6 | |||
441.4.a.u.1.4 | 4 | 21.17 | even | 6 | |||
441.4.e.y.226.1 | 8 | 21.5 | even | 6 | |||
441.4.e.y.226.2 | 8 | 21.2 | odd | 6 | |||
441.4.e.y.361.1 | 8 | 21.20 | even | 2 | |||
441.4.e.y.361.2 | 8 | 3.2 | odd | 2 | |||
784.4.a.bf.1.1 | 4 | 28.11 | odd | 6 | |||
784.4.a.bf.1.4 | 4 | 28.3 | even | 6 | |||
1225.4.a.bb.1.3 | 4 | 35.4 | even | 6 | |||
1225.4.a.bb.1.4 | 4 | 35.24 | odd | 6 |