Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [983,4,Mod(1,983)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(983, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("983.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 983 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 983.a (trivial) |
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: | yes |
Analytic conductor: | \(57.9988775356\) |
Analytic rank: | \(1\) |
Dimension: | \(109\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 983.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.58646 | −1.97511 | −0.987556 | − | 0.157267i | \(-0.949732\pi\) | ||||
−0.987556 | + | 0.157267i | \(0.949732\pi\) | |||||||
\(3\) | −0.724275 | −0.139387 | −0.0696934 | − | 0.997568i | \(-0.522202\pi\) | ||||
−0.0696934 | + | 0.997568i | \(0.522202\pi\) | |||||||
\(4\) | 23.2085 | 2.90107 | ||||||||
\(5\) | 15.1603 | 1.35598 | 0.677991 | − | 0.735071i | \(-0.262851\pi\) | ||||
0.677991 | + | 0.735071i | \(0.262851\pi\) | |||||||
\(6\) | 4.04613 | 0.275304 | ||||||||
\(7\) | 11.0308 | 0.595605 | 0.297803 | − | 0.954628i | \(-0.403746\pi\) | ||||
0.297803 | + | 0.954628i | \(0.403746\pi\) | |||||||
\(8\) | −84.9620 | −3.75482 | ||||||||
\(9\) | −26.4754 | −0.980571 | ||||||||
\(10\) | −84.6926 | −2.67822 | ||||||||
\(11\) | 7.32055 | 0.200657 | 0.100329 | − | 0.994954i | \(-0.468011\pi\) | ||||
0.100329 | + | 0.994954i | \(0.468011\pi\) | |||||||
\(12\) | −16.8094 | −0.404371 | ||||||||
\(13\) | 32.4287 | 0.691853 | 0.345927 | − | 0.938262i | \(-0.387565\pi\) | ||||
0.345927 | + | 0.938262i | \(0.387565\pi\) | |||||||
\(14\) | −61.6229 | −1.17639 | ||||||||
\(15\) | −10.9802 | −0.189006 | ||||||||
\(16\) | 288.968 | 4.51513 | ||||||||
\(17\) | −2.28267 | −0.0325664 | −0.0162832 | − | 0.999867i | \(-0.505183\pi\) | ||||
−0.0162832 | + | 0.999867i | \(0.505183\pi\) | |||||||
\(18\) | 147.904 | 1.93674 | ||||||||
\(19\) | −96.9959 | −1.17118 | −0.585589 | − | 0.810608i | \(-0.699137\pi\) | ||||
−0.585589 | + | 0.810608i | \(0.699137\pi\) | |||||||
\(20\) | 351.849 | 3.93379 | ||||||||
\(21\) | −7.98930 | −0.0830195 | ||||||||
\(22\) | −40.8960 | −0.396321 | ||||||||
\(23\) | 59.6538 | 0.540812 | 0.270406 | − | 0.962746i | \(-0.412842\pi\) | ||||
0.270406 | + | 0.962746i | \(0.412842\pi\) | |||||||
\(24\) | 61.5358 | 0.523373 | ||||||||
\(25\) | 104.836 | 0.838685 | ||||||||
\(26\) | −181.161 | −1.36649 | ||||||||
\(27\) | 38.7309 | 0.276065 | ||||||||
\(28\) | 256.008 | 1.72789 | ||||||||
\(29\) | 3.94482 | 0.0252598 | 0.0126299 | − | 0.999920i | \(-0.495980\pi\) | ||||
0.0126299 | + | 0.999920i | \(0.495980\pi\) | |||||||
\(30\) | 61.3407 | 0.373308 | ||||||||
\(31\) | −74.1438 | −0.429568 | −0.214784 | − | 0.976662i | \(-0.568905\pi\) | ||||
−0.214784 | + | 0.976662i | \(0.568905\pi\) | |||||||
\(32\) | −934.614 | −5.16306 | ||||||||
\(33\) | −5.30209 | −0.0279690 | ||||||||
\(34\) | 12.7520 | 0.0643222 | ||||||||
\(35\) | 167.230 | 0.807629 | ||||||||
\(36\) | −614.456 | −2.84470 | ||||||||
\(37\) | −245.467 | −1.09066 | −0.545331 | − | 0.838221i | \(-0.683596\pi\) | ||||
−0.545331 | + | 0.838221i | \(0.683596\pi\) | |||||||
\(38\) | 541.864 | 2.31321 | ||||||||
\(39\) | −23.4873 | −0.0964352 | ||||||||
\(40\) | −1288.05 | −5.09147 | ||||||||
\(41\) | 23.1593 | 0.0882164 | 0.0441082 | − | 0.999027i | \(-0.485955\pi\) | ||||
0.0441082 | + | 0.999027i | \(0.485955\pi\) | |||||||
\(42\) | 44.6319 | 0.163973 | ||||||||
\(43\) | −548.328 | −1.94463 | −0.972316 | − | 0.233670i | \(-0.924926\pi\) | ||||
−0.972316 | + | 0.233670i | \(0.924926\pi\) | |||||||
\(44\) | 169.899 | 0.582120 | ||||||||
\(45\) | −401.376 | −1.32964 | ||||||||
\(46\) | −333.254 | −1.06817 | ||||||||
\(47\) | 38.2747 | 0.118786 | 0.0593929 | − | 0.998235i | \(-0.481084\pi\) | ||||
0.0593929 | + | 0.998235i | \(0.481084\pi\) | |||||||
\(48\) | −209.292 | −0.629349 | ||||||||
\(49\) | −221.322 | −0.645255 | ||||||||
\(50\) | −585.660 | −1.65650 | ||||||||
\(51\) | 1.65328 | 0.00453932 | ||||||||
\(52\) | 752.622 | 2.00711 | ||||||||
\(53\) | 108.848 | 0.282103 | 0.141051 | − | 0.990002i | \(-0.454952\pi\) | ||||
0.141051 | + | 0.990002i | \(0.454952\pi\) | |||||||
\(54\) | −216.369 | −0.545260 | ||||||||
\(55\) | 110.982 | 0.272087 | ||||||||
\(56\) | −937.195 | −2.23639 | ||||||||
\(57\) | 70.2517 | 0.163247 | ||||||||
\(58\) | −22.0376 | −0.0498909 | ||||||||
\(59\) | −440.251 | −0.971454 | −0.485727 | − | 0.874110i | \(-0.661445\pi\) | ||||
−0.485727 | + | 0.874110i | \(0.661445\pi\) | |||||||
\(60\) | −254.836 | −0.548319 | ||||||||
\(61\) | −625.110 | −1.31208 | −0.656042 | − | 0.754725i | \(-0.727770\pi\) | ||||
−0.656042 | + | 0.754725i | \(0.727770\pi\) | |||||||
\(62\) | 414.201 | 0.848446 | ||||||||
\(63\) | −292.044 | −0.584033 | ||||||||
\(64\) | 2909.44 | 5.68250 | ||||||||
\(65\) | 491.629 | 0.938140 | ||||||||
\(66\) | 29.6199 | 0.0552418 | ||||||||
\(67\) | 93.2093 | 0.169960 | 0.0849801 | − | 0.996383i | \(-0.472917\pi\) | ||||
0.0849801 | + | 0.996383i | \(0.472917\pi\) | |||||||
\(68\) | −52.9774 | −0.0944772 | ||||||||
\(69\) | −43.2058 | −0.0753821 | ||||||||
\(70\) | −934.224 | −1.59516 | ||||||||
\(71\) | 648.102 | 1.08332 | 0.541659 | − | 0.840598i | \(-0.317796\pi\) | ||||
0.541659 | + | 0.840598i | \(0.317796\pi\) | |||||||
\(72\) | 2249.40 | 3.68187 | ||||||||
\(73\) | −870.388 | −1.39550 | −0.697748 | − | 0.716344i | \(-0.745814\pi\) | ||||
−0.697748 | + | 0.716344i | \(0.745814\pi\) | |||||||
\(74\) | 1371.29 | 2.15418 | ||||||||
\(75\) | −75.9298 | −0.116902 | ||||||||
\(76\) | −2251.13 | −3.39767 | ||||||||
\(77\) | 80.7512 | 0.119512 | ||||||||
\(78\) | 131.211 | 0.190470 | ||||||||
\(79\) | 174.114 | 0.247967 | 0.123983 | − | 0.992284i | \(-0.460433\pi\) | ||||
0.123983 | + | 0.992284i | \(0.460433\pi\) | |||||||
\(80\) | 4380.85 | 6.12243 | ||||||||
\(81\) | 686.785 | 0.942091 | ||||||||
\(82\) | −129.378 | −0.174237 | ||||||||
\(83\) | −594.841 | −0.786654 | −0.393327 | − | 0.919399i | \(-0.628676\pi\) | ||||
−0.393327 | + | 0.919399i | \(0.628676\pi\) | |||||||
\(84\) | −185.420 | −0.240845 | ||||||||
\(85\) | −34.6060 | −0.0441594 | ||||||||
\(86\) | 3063.21 | 3.84087 | ||||||||
\(87\) | −2.85713 | −0.00352088 | ||||||||
\(88\) | −621.968 | −0.753432 | ||||||||
\(89\) | −482.862 | −0.575093 | −0.287546 | − | 0.957767i | \(-0.592840\pi\) | ||||
−0.287546 | + | 0.957767i | \(0.592840\pi\) | |||||||
\(90\) | 2242.27 | 2.62618 | ||||||||
\(91\) | 357.713 | 0.412071 | ||||||||
\(92\) | 1384.48 | 1.56893 | ||||||||
\(93\) | 53.7005 | 0.0598761 | ||||||||
\(94\) | −213.820 | −0.234615 | ||||||||
\(95\) | −1470.49 | −1.58810 | ||||||||
\(96\) | 676.918 | 0.719663 | ||||||||
\(97\) | 1346.35 | 1.40929 | 0.704644 | − | 0.709561i | \(-0.251107\pi\) | ||||
0.704644 | + | 0.709561i | \(0.251107\pi\) | |||||||
\(98\) | 1236.41 | 1.27445 | ||||||||
\(99\) | −193.815 | −0.196759 | ||||||||
\(100\) | 2433.08 | 2.43308 | ||||||||
\(101\) | 657.588 | 0.647846 | 0.323923 | − | 0.946083i | \(-0.394998\pi\) | ||||
0.323923 | + | 0.946083i | \(0.394998\pi\) | |||||||
\(102\) | −9.23598 | −0.00896567 | ||||||||
\(103\) | −110.500 | −0.105707 | −0.0528537 | − | 0.998602i | \(-0.516832\pi\) | ||||
−0.0528537 | + | 0.998602i | \(0.516832\pi\) | |||||||
\(104\) | −2755.20 | −2.59779 | ||||||||
\(105\) | −121.120 | −0.112573 | ||||||||
\(106\) | −608.076 | −0.557184 | ||||||||
\(107\) | 1118.03 | 1.01013 | 0.505066 | − | 0.863081i | \(-0.331468\pi\) | ||||
0.505066 | + | 0.863081i | \(0.331468\pi\) | |||||||
\(108\) | 898.888 | 0.800885 | ||||||||
\(109\) | 762.073 | 0.669664 | 0.334832 | − | 0.942278i | \(-0.391320\pi\) | ||||
0.334832 | + | 0.942278i | \(0.391320\pi\) | |||||||
\(110\) | −619.997 | −0.537403 | ||||||||
\(111\) | 177.785 | 0.152024 | ||||||||
\(112\) | 3187.54 | 2.68923 | ||||||||
\(113\) | −1796.37 | −1.49547 | −0.747734 | − | 0.663999i | \(-0.768858\pi\) | ||||
−0.747734 | + | 0.663999i | \(0.768858\pi\) | |||||||
\(114\) | −392.458 | −0.322431 | ||||||||
\(115\) | 904.372 | 0.733332 | ||||||||
\(116\) | 91.5534 | 0.0732804 | ||||||||
\(117\) | −858.563 | −0.678411 | ||||||||
\(118\) | 2459.45 | 1.91873 | ||||||||
\(119\) | −25.1796 | −0.0193967 | ||||||||
\(120\) | 932.903 | 0.709684 | ||||||||
\(121\) | −1277.41 | −0.959737 | ||||||||
\(122\) | 3492.15 | 2.59151 | ||||||||
\(123\) | −16.7737 | −0.0122962 | ||||||||
\(124\) | −1720.77 | −1.24621 | ||||||||
\(125\) | −305.698 | −0.218740 | ||||||||
\(126\) | 1631.49 | 1.15353 | ||||||||
\(127\) | −1633.90 | −1.14161 | −0.570806 | − | 0.821085i | \(-0.693369\pi\) | ||||
−0.570806 | + | 0.821085i | \(0.693369\pi\) | |||||||
\(128\) | −8776.56 | −6.06051 | ||||||||
\(129\) | 397.140 | 0.271056 | ||||||||
\(130\) | −2746.47 | −1.85293 | ||||||||
\(131\) | 1001.88 | 0.668205 | 0.334103 | − | 0.942537i | \(-0.391567\pi\) | ||||
0.334103 | + | 0.942537i | \(0.391567\pi\) | |||||||
\(132\) | −123.054 | −0.0811399 | ||||||||
\(133\) | −1069.94 | −0.697560 | ||||||||
\(134\) | −520.710 | −0.335690 | ||||||||
\(135\) | 587.173 | 0.374340 | ||||||||
\(136\) | 193.940 | 0.122281 | ||||||||
\(137\) | −2812.29 | −1.75380 | −0.876899 | − | 0.480674i | \(-0.840392\pi\) | ||||
−0.876899 | + | 0.480674i | \(0.840392\pi\) | |||||||
\(138\) | 241.367 | 0.148888 | ||||||||
\(139\) | −184.618 | −0.112655 | −0.0563275 | − | 0.998412i | \(-0.517939\pi\) | ||||
−0.0563275 | + | 0.998412i | \(0.517939\pi\) | |||||||
\(140\) | 3881.16 | 2.34299 | ||||||||
\(141\) | −27.7214 | −0.0165572 | ||||||||
\(142\) | −3620.60 | −2.13967 | ||||||||
\(143\) | 237.396 | 0.138825 | ||||||||
\(144\) | −7650.56 | −4.42741 | ||||||||
\(145\) | 59.8047 | 0.0342518 | ||||||||
\(146\) | 4862.39 | 2.75626 | ||||||||
\(147\) | 160.298 | 0.0899400 | ||||||||
\(148\) | −5696.93 | −3.16408 | ||||||||
\(149\) | 1439.33 | 0.791371 | 0.395685 | − | 0.918386i | \(-0.370507\pi\) | ||||
0.395685 | + | 0.918386i | \(0.370507\pi\) | |||||||
\(150\) | 424.179 | 0.230894 | ||||||||
\(151\) | −589.663 | −0.317789 | −0.158894 | − | 0.987296i | \(-0.550793\pi\) | ||||
−0.158894 | + | 0.987296i | \(0.550793\pi\) | |||||||
\(152\) | 8240.96 | 4.39757 | ||||||||
\(153\) | 60.4346 | 0.0319336 | ||||||||
\(154\) | −451.114 | −0.236050 | ||||||||
\(155\) | −1124.04 | −0.582487 | ||||||||
\(156\) | −545.105 | −0.279765 | ||||||||
\(157\) | 1921.12 | 0.976576 | 0.488288 | − | 0.872683i | \(-0.337622\pi\) | ||||
0.488288 | + | 0.872683i | \(0.337622\pi\) | |||||||
\(158\) | −972.682 | −0.489762 | ||||||||
\(159\) | −78.8360 | −0.0393214 | ||||||||
\(160\) | −14169.1 | −7.00102 | ||||||||
\(161\) | 658.027 | 0.322111 | ||||||||
\(162\) | −3836.70 | −1.86074 | ||||||||
\(163\) | −586.067 | −0.281622 | −0.140811 | − | 0.990037i | \(-0.544971\pi\) | ||||
−0.140811 | + | 0.990037i | \(0.544971\pi\) | |||||||
\(164\) | 537.493 | 0.255922 | ||||||||
\(165\) | −80.3815 | −0.0379254 | ||||||||
\(166\) | 3323.05 | 1.55373 | ||||||||
\(167\) | −1104.92 | −0.511983 | −0.255992 | − | 0.966679i | \(-0.582402\pi\) | ||||
−0.255992 | + | 0.966679i | \(0.582402\pi\) | |||||||
\(168\) | 678.787 | 0.311723 | ||||||||
\(169\) | −1145.38 | −0.521339 | ||||||||
\(170\) | 193.325 | 0.0872197 | ||||||||
\(171\) | 2568.01 | 1.14842 | ||||||||
\(172\) | −12725.9 | −5.64151 | ||||||||
\(173\) | −1711.54 | −0.752175 | −0.376087 | − | 0.926584i | \(-0.622731\pi\) | ||||
−0.376087 | + | 0.926584i | \(0.622731\pi\) | |||||||
\(174\) | 15.9613 | 0.00695413 | ||||||||
\(175\) | 1156.42 | 0.499525 | ||||||||
\(176\) | 2115.41 | 0.905993 | ||||||||
\(177\) | 318.863 | 0.135408 | ||||||||
\(178\) | 2697.49 | 1.13587 | ||||||||
\(179\) | 1468.89 | 0.613353 | 0.306676 | − | 0.951814i | \(-0.400783\pi\) | ||||
0.306676 | + | 0.951814i | \(0.400783\pi\) | |||||||
\(180\) | −9315.36 | −3.85737 | ||||||||
\(181\) | 3398.58 | 1.39566 | 0.697830 | − | 0.716263i | \(-0.254149\pi\) | ||||
0.697830 | + | 0.716263i | \(0.254149\pi\) | |||||||
\(182\) | −1998.35 | −0.813887 | ||||||||
\(183\) | 452.751 | 0.182887 | ||||||||
\(184\) | −5068.31 | −2.03066 | ||||||||
\(185\) | −3721.36 | −1.47892 | ||||||||
\(186\) | −299.996 | −0.118262 | ||||||||
\(187\) | −16.7104 | −0.00653468 | ||||||||
\(188\) | 888.299 | 0.344606 | ||||||||
\(189\) | 427.231 | 0.164426 | ||||||||
\(190\) | 8214.84 | 3.13667 | ||||||||
\(191\) | 2733.19 | 1.03543 | 0.517714 | − | 0.855554i | \(-0.326783\pi\) | ||||
0.517714 | + | 0.855554i | \(0.326783\pi\) | |||||||
\(192\) | −2107.23 | −0.792065 | ||||||||
\(193\) | −512.420 | −0.191113 | −0.0955564 | − | 0.995424i | \(-0.530463\pi\) | ||||
−0.0955564 | + | 0.995424i | \(0.530463\pi\) | |||||||
\(194\) | −7521.32 | −2.78350 | ||||||||
\(195\) | −356.075 | −0.130764 | ||||||||
\(196\) | −5136.57 | −1.87193 | ||||||||
\(197\) | 1994.13 | 0.721197 | 0.360598 | − | 0.932721i | \(-0.382572\pi\) | ||||
0.360598 | + | 0.932721i | \(0.382572\pi\) | |||||||
\(198\) | 1082.74 | 0.388621 | ||||||||
\(199\) | 598.848 | 0.213323 | 0.106661 | − | 0.994295i | \(-0.465984\pi\) | ||||
0.106661 | + | 0.994295i | \(0.465984\pi\) | |||||||
\(200\) | −8907.04 | −3.14911 | ||||||||
\(201\) | −67.5092 | −0.0236902 | ||||||||
\(202\) | −3673.59 | −1.27957 | ||||||||
\(203\) | 43.5143 | 0.0150449 | ||||||||
\(204\) | 38.3702 | 0.0131689 | ||||||||
\(205\) | 351.102 | 0.119620 | ||||||||
\(206\) | 617.302 | 0.208784 | ||||||||
\(207\) | −1579.36 | −0.530305 | ||||||||
\(208\) | 9370.85 | 3.12381 | ||||||||
\(209\) | −710.064 | −0.235005 | ||||||||
\(210\) | 676.635 | 0.222344 | ||||||||
\(211\) | 2547.16 | 0.831061 | 0.415530 | − | 0.909579i | \(-0.363596\pi\) | ||||
0.415530 | + | 0.909579i | \(0.363596\pi\) | |||||||
\(212\) | 2526.21 | 0.818399 | ||||||||
\(213\) | −469.404 | −0.151000 | ||||||||
\(214\) | −6245.84 | −1.99512 | ||||||||
\(215\) | −8312.83 | −2.63688 | ||||||||
\(216\) | −3290.65 | −1.03658 | ||||||||
\(217\) | −817.862 | −0.255853 | ||||||||
\(218\) | −4257.29 | −1.32266 | ||||||||
\(219\) | 630.400 | 0.194514 | ||||||||
\(220\) | 2575.73 | 0.789344 | ||||||||
\(221\) | −74.0238 | −0.0225311 | ||||||||
\(222\) | −993.191 | −0.300264 | ||||||||
\(223\) | 1106.21 | 0.332186 | 0.166093 | − | 0.986110i | \(-0.446885\pi\) | ||||
0.166093 | + | 0.986110i | \(0.446885\pi\) | |||||||
\(224\) | −10309.5 | −3.07515 | ||||||||
\(225\) | −2775.57 | −0.822391 | ||||||||
\(226\) | 10035.3 | 2.95372 | ||||||||
\(227\) | 2276.01 | 0.665482 | 0.332741 | − | 0.943018i | \(-0.392027\pi\) | ||||
0.332741 | + | 0.943018i | \(0.392027\pi\) | |||||||
\(228\) | 1630.44 | 0.473590 | ||||||||
\(229\) | −961.568 | −0.277477 | −0.138738 | − | 0.990329i | \(-0.544305\pi\) | ||||
−0.138738 | + | 0.990329i | \(0.544305\pi\) | |||||||
\(230\) | −5052.24 | −1.44841 | ||||||||
\(231\) | −58.4861 | −0.0166585 | ||||||||
\(232\) | −335.159 | −0.0948461 | ||||||||
\(233\) | 1098.43 | 0.308845 | 0.154422 | − | 0.988005i | \(-0.450648\pi\) | ||||
0.154422 | + | 0.988005i | \(0.450648\pi\) | |||||||
\(234\) | 4796.33 | 1.33994 | ||||||||
\(235\) | 580.257 | 0.161071 | ||||||||
\(236\) | −10217.6 | −2.81826 | ||||||||
\(237\) | −126.106 | −0.0345633 | ||||||||
\(238\) | 140.665 | 0.0383106 | ||||||||
\(239\) | 2780.88 | 0.752636 | 0.376318 | − | 0.926490i | \(-0.377190\pi\) | ||||
0.376318 | + | 0.926490i | \(0.377190\pi\) | |||||||
\(240\) | −3172.94 | −0.853386 | ||||||||
\(241\) | −6220.17 | −1.66256 | −0.831279 | − | 0.555855i | \(-0.812391\pi\) | ||||
−0.831279 | + | 0.555855i | \(0.812391\pi\) | |||||||
\(242\) | 7136.20 | 1.89559 | ||||||||
\(243\) | −1543.16 | −0.407380 | ||||||||
\(244\) | −14507.9 | −3.80644 | ||||||||
\(245\) | −3355.32 | −0.874953 | ||||||||
\(246\) | 93.7055 | 0.0242864 | ||||||||
\(247\) | −3145.45 | −0.810284 | ||||||||
\(248\) | 6299.40 | 1.61295 | ||||||||
\(249\) | 430.828 | 0.109649 | ||||||||
\(250\) | 1707.77 | 0.432036 | ||||||||
\(251\) | −3000.28 | −0.754487 | −0.377243 | − | 0.926114i | \(-0.623128\pi\) | ||||
−0.377243 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(252\) | −6777.92 | −1.69432 | ||||||||
\(253\) | 436.699 | 0.108518 | ||||||||
\(254\) | 9127.70 | 2.25481 | ||||||||
\(255\) | 25.0643 | 0.00615523 | ||||||||
\(256\) | 25754.4 | 6.28769 | ||||||||
\(257\) | 7794.92 | 1.89196 | 0.945980 | − | 0.324226i | \(-0.105104\pi\) | ||||
0.945980 | + | 0.324226i | \(0.105104\pi\) | |||||||
\(258\) | −2218.61 | −0.535366 | ||||||||
\(259\) | −2707.69 | −0.649604 | ||||||||
\(260\) | 11410.0 | 2.72161 | ||||||||
\(261\) | −104.441 | −0.0247690 | ||||||||
\(262\) | −5596.98 | −1.31978 | ||||||||
\(263\) | −6760.71 | −1.58511 | −0.792554 | − | 0.609801i | \(-0.791249\pi\) | ||||
−0.792554 | + | 0.609801i | \(0.791249\pi\) | |||||||
\(264\) | 450.476 | 0.105019 | ||||||||
\(265\) | 1650.17 | 0.382526 | ||||||||
\(266\) | 5977.17 | 1.37776 | ||||||||
\(267\) | 349.725 | 0.0801603 | ||||||||
\(268\) | 2163.25 | 0.493066 | ||||||||
\(269\) | 8019.95 | 1.81779 | 0.908894 | − | 0.417026i | \(-0.136928\pi\) | ||||
0.908894 | + | 0.417026i | \(0.136928\pi\) | |||||||
\(270\) | −3280.22 | −0.739363 | ||||||||
\(271\) | −2331.05 | −0.522514 | −0.261257 | − | 0.965269i | \(-0.584137\pi\) | ||||
−0.261257 | + | 0.965269i | \(0.584137\pi\) | |||||||
\(272\) | −659.618 | −0.147041 | ||||||||
\(273\) | −259.082 | −0.0574373 | ||||||||
\(274\) | 15710.8 | 3.46395 | ||||||||
\(275\) | 767.455 | 0.168288 | ||||||||
\(276\) | −1002.74 | −0.218689 | ||||||||
\(277\) | −4742.62 | −1.02872 | −0.514361 | − | 0.857574i | \(-0.671971\pi\) | ||||
−0.514361 | + | 0.857574i | \(0.671971\pi\) | |||||||
\(278\) | 1031.36 | 0.222506 | ||||||||
\(279\) | 1962.99 | 0.421222 | ||||||||
\(280\) | −14208.2 | −3.03251 | ||||||||
\(281\) | 5915.81 | 1.25590 | 0.627950 | − | 0.778254i | \(-0.283894\pi\) | ||||
0.627950 | + | 0.778254i | \(0.283894\pi\) | |||||||
\(282\) | 154.864 | 0.0327023 | ||||||||
\(283\) | −2946.42 | −0.618891 | −0.309446 | − | 0.950917i | \(-0.600143\pi\) | ||||
−0.309446 | + | 0.950917i | \(0.600143\pi\) | |||||||
\(284\) | 15041.5 | 3.14278 | ||||||||
\(285\) | 1065.04 | 0.221360 | ||||||||
\(286\) | −1326.20 | −0.274196 | ||||||||
\(287\) | 255.464 | 0.0525421 | ||||||||
\(288\) | 24744.3 | 5.06275 | ||||||||
\(289\) | −4907.79 | −0.998939 | ||||||||
\(290\) | −334.097 | −0.0676512 | ||||||||
\(291\) | −975.126 | −0.196436 | ||||||||
\(292\) | −20200.4 | −4.04843 | ||||||||
\(293\) | −6799.29 | −1.35570 | −0.677848 | − | 0.735202i | \(-0.737087\pi\) | ||||
−0.677848 | + | 0.735202i | \(0.737087\pi\) | |||||||
\(294\) | −895.500 | −0.177642 | ||||||||
\(295\) | −6674.35 | −1.31727 | ||||||||
\(296\) | 20855.3 | 4.09524 | ||||||||
\(297\) | 283.532 | 0.0553945 | ||||||||
\(298\) | −8040.74 | −1.56305 | ||||||||
\(299\) | 1934.49 | 0.374163 | ||||||||
\(300\) | −1762.22 | −0.339140 | ||||||||
\(301\) | −6048.47 | −1.15823 | ||||||||
\(302\) | 3294.13 | 0.627668 | ||||||||
\(303\) | −476.274 | −0.0903011 | ||||||||
\(304\) | −28028.7 | −5.28802 | ||||||||
\(305\) | −9476.87 | −1.77916 | ||||||||
\(306\) | −337.615 | −0.0630725 | ||||||||
\(307\) | −173.629 | −0.0322786 | −0.0161393 | − | 0.999870i | \(-0.505138\pi\) | ||||
−0.0161393 | + | 0.999870i | \(0.505138\pi\) | |||||||
\(308\) | 1874.12 | 0.346714 | ||||||||
\(309\) | 80.0322 | 0.0147342 | ||||||||
\(310\) | 6279.43 | 1.15048 | ||||||||
\(311\) | −2686.30 | −0.489795 | −0.244897 | − | 0.969549i | \(-0.578754\pi\) | ||||
−0.244897 | + | 0.969549i | \(0.578754\pi\) | |||||||
\(312\) | 1995.52 | 0.362097 | ||||||||
\(313\) | −4188.49 | −0.756381 | −0.378191 | − | 0.925728i | \(-0.623454\pi\) | ||||
−0.378191 | + | 0.925728i | \(0.623454\pi\) | |||||||
\(314\) | −10732.3 | −1.92885 | ||||||||
\(315\) | −4427.48 | −0.791938 | ||||||||
\(316\) | 4040.94 | 0.719368 | ||||||||
\(317\) | −7105.93 | −1.25902 | −0.629509 | − | 0.776993i | \(-0.716744\pi\) | ||||
−0.629509 | + | 0.776993i | \(0.716744\pi\) | |||||||
\(318\) | 440.414 | 0.0776641 | ||||||||
\(319\) | 28.8782 | 0.00506856 | ||||||||
\(320\) | 44108.1 | 7.70536 | ||||||||
\(321\) | −809.762 | −0.140799 | ||||||||
\(322\) | −3676.04 | −0.636205 | ||||||||
\(323\) | 221.409 | 0.0381410 | ||||||||
\(324\) | 15939.3 | 2.73307 | ||||||||
\(325\) | 3399.68 | 0.580247 | ||||||||
\(326\) | 3274.04 | 0.556235 | ||||||||
\(327\) | −551.950 | −0.0933422 | ||||||||
\(328\) | −1967.66 | −0.331237 | ||||||||
\(329\) | 422.199 | 0.0707494 | ||||||||
\(330\) | 449.048 | 0.0749069 | ||||||||
\(331\) | −11278.9 | −1.87295 | −0.936474 | − | 0.350738i | \(-0.885931\pi\) | ||||
−0.936474 | + | 0.350738i | \(0.885931\pi\) | |||||||
\(332\) | −13805.4 | −2.28214 | ||||||||
\(333\) | 6498.84 | 1.06947 | ||||||||
\(334\) | 6172.59 | 1.01122 | ||||||||
\(335\) | 1413.08 | 0.230463 | ||||||||
\(336\) | −2308.65 | −0.374844 | ||||||||
\(337\) | −4755.69 | −0.768722 | −0.384361 | − | 0.923183i | \(-0.625578\pi\) | ||||
−0.384361 | + | 0.923183i | \(0.625578\pi\) | |||||||
\(338\) | 6398.63 | 1.02970 | ||||||||
\(339\) | 1301.06 | 0.208448 | ||||||||
\(340\) | −803.155 | −0.128109 | ||||||||
\(341\) | −542.773 | −0.0861960 | ||||||||
\(342\) | −14346.1 | −2.26827 | ||||||||
\(343\) | −6224.90 | −0.979922 | ||||||||
\(344\) | 46587.0 | 7.30175 | ||||||||
\(345\) | −655.014 | −0.102217 | ||||||||
\(346\) | 9561.47 | 1.48563 | ||||||||
\(347\) | −9116.20 | −1.41033 | −0.705163 | − | 0.709045i | \(-0.749126\pi\) | ||||
−0.705163 | + | 0.709045i | \(0.749126\pi\) | |||||||
\(348\) | −66.3099 | −0.0102143 | ||||||||
\(349\) | −5704.75 | −0.874981 | −0.437491 | − | 0.899223i | \(-0.644133\pi\) | ||||
−0.437491 | + | 0.899223i | \(0.644133\pi\) | |||||||
\(350\) | −6460.28 | −0.986618 | ||||||||
\(351\) | 1255.99 | 0.190997 | ||||||||
\(352\) | −6841.89 | −1.03601 | ||||||||
\(353\) | 4197.75 | 0.632928 | 0.316464 | − | 0.948604i | \(-0.397504\pi\) | ||||
0.316464 | + | 0.948604i | \(0.397504\pi\) | |||||||
\(354\) | −1781.31 | −0.267446 | ||||||||
\(355\) | 9825.44 | 1.46896 | ||||||||
\(356\) | −11206.5 | −1.66838 | ||||||||
\(357\) | 18.2369 | 0.00270364 | ||||||||
\(358\) | −8205.91 | −1.21144 | ||||||||
\(359\) | −1076.79 | −0.158304 | −0.0791518 | − | 0.996863i | \(-0.525221\pi\) | ||||
−0.0791518 | + | 0.996863i | \(0.525221\pi\) | |||||||
\(360\) | 34101.7 | 4.99255 | ||||||||
\(361\) | 2549.21 | 0.371659 | ||||||||
\(362\) | −18986.0 | −2.75659 | ||||||||
\(363\) | 925.196 | 0.133775 | ||||||||
\(364\) | 8301.99 | 1.19545 | ||||||||
\(365\) | −13195.4 | −1.89227 | ||||||||
\(366\) | −2529.28 | −0.361222 | ||||||||
\(367\) | 3001.72 | 0.426944 | 0.213472 | − | 0.976949i | \(-0.431523\pi\) | ||||
0.213472 | + | 0.976949i | \(0.431523\pi\) | |||||||
\(368\) | 17238.1 | 2.44184 | ||||||||
\(369\) | −613.152 | −0.0865025 | ||||||||
\(370\) | 20789.2 | 2.92103 | ||||||||
\(371\) | 1200.68 | 0.168022 | ||||||||
\(372\) | 1246.31 | 0.173705 | ||||||||
\(373\) | −335.052 | −0.0465102 | −0.0232551 | − | 0.999730i | \(-0.507403\pi\) | ||||
−0.0232551 | + | 0.999730i | \(0.507403\pi\) | |||||||
\(374\) | 93.3519 | 0.0129067 | ||||||||
\(375\) | 221.410 | 0.0304894 | ||||||||
\(376\) | −3251.89 | −0.446020 | ||||||||
\(377\) | 127.925 | 0.0174761 | ||||||||
\(378\) | −2386.71 | −0.324760 | ||||||||
\(379\) | 662.384 | 0.0897741 | 0.0448870 | − | 0.998992i | \(-0.485707\pi\) | ||||
0.0448870 | + | 0.998992i | \(0.485707\pi\) | |||||||
\(380\) | −34127.9 | −4.60717 | ||||||||
\(381\) | 1183.39 | 0.159126 | ||||||||
\(382\) | −15268.9 | −2.04509 | ||||||||
\(383\) | 9196.60 | 1.22696 | 0.613478 | − | 0.789712i | \(-0.289770\pi\) | ||||
0.613478 | + | 0.789712i | \(0.289770\pi\) | |||||||
\(384\) | 6356.64 | 0.844755 | ||||||||
\(385\) | 1224.22 | 0.162057 | ||||||||
\(386\) | 2862.61 | 0.377469 | ||||||||
\(387\) | 14517.2 | 1.90685 | ||||||||
\(388\) | 31246.8 | 4.08844 | ||||||||
\(389\) | 10296.4 | 1.34202 | 0.671012 | − | 0.741446i | \(-0.265860\pi\) | ||||
0.671012 | + | 0.741446i | \(0.265860\pi\) | |||||||
\(390\) | 1989.20 | 0.258274 | ||||||||
\(391\) | −136.170 | −0.0176123 | ||||||||
\(392\) | 18804.0 | 2.42282 | ||||||||
\(393\) | −725.638 | −0.0931390 | ||||||||
\(394\) | −11140.1 | −1.42444 | ||||||||
\(395\) | 2639.63 | 0.336238 | ||||||||
\(396\) | −4498.16 | −0.570810 | ||||||||
\(397\) | −11520.5 | −1.45642 | −0.728211 | − | 0.685353i | \(-0.759648\pi\) | ||||
−0.728211 | + | 0.685353i | \(0.759648\pi\) | |||||||
\(398\) | −3345.44 | −0.421336 | ||||||||
\(399\) | 774.930 | 0.0972306 | ||||||||
\(400\) | 30294.2 | 3.78677 | ||||||||
\(401\) | −10747.6 | −1.33843 | −0.669217 | − | 0.743067i | \(-0.733370\pi\) | ||||
−0.669217 | + | 0.743067i | \(0.733370\pi\) | |||||||
\(402\) | 377.137 | 0.0467908 | ||||||||
\(403\) | −2404.38 | −0.297198 | ||||||||
\(404\) | 15261.7 | 1.87944 | ||||||||
\(405\) | 10411.9 | 1.27746 | ||||||||
\(406\) | −243.091 | −0.0297153 | ||||||||
\(407\) | −1796.95 | −0.218849 | ||||||||
\(408\) | −140.466 | −0.0170443 | ||||||||
\(409\) | 14709.3 | 1.77831 | 0.889154 | − | 0.457608i | \(-0.151294\pi\) | ||||
0.889154 | + | 0.457608i | \(0.151294\pi\) | |||||||
\(410\) | −1961.42 | −0.236262 | ||||||||
\(411\) | 2036.87 | 0.244456 | ||||||||
\(412\) | −2564.54 | −0.306664 | ||||||||
\(413\) | −4856.30 | −0.578603 | ||||||||
\(414\) | 8823.04 | 1.04741 | ||||||||
\(415\) | −9017.98 | −1.06669 | ||||||||
\(416\) | −30308.3 | −3.57208 | ||||||||
\(417\) | 133.714 | 0.0157026 | ||||||||
\(418\) | 3966.74 | 0.464162 | ||||||||
\(419\) | 4216.87 | 0.491664 | 0.245832 | − | 0.969312i | \(-0.420939\pi\) | ||||
0.245832 | + | 0.969312i | \(0.420939\pi\) | |||||||
\(420\) | −2811.03 | −0.326581 | ||||||||
\(421\) | −879.771 | −0.101847 | −0.0509233 | − | 0.998703i | \(-0.516216\pi\) | ||||
−0.0509233 | + | 0.998703i | \(0.516216\pi\) | |||||||
\(422\) | −14229.6 | −1.64144 | ||||||||
\(423\) | −1013.34 | −0.116478 | ||||||||
\(424\) | −9247.95 | −1.05925 | ||||||||
\(425\) | −239.305 | −0.0273129 | ||||||||
\(426\) | 2622.31 | 0.298242 | ||||||||
\(427\) | −6895.43 | −0.781483 | ||||||||
\(428\) | 25947.9 | 2.93046 | ||||||||
\(429\) | −171.940 | −0.0193504 | ||||||||
\(430\) | 46439.3 | 5.20814 | ||||||||
\(431\) | 9526.01 | 1.06462 | 0.532310 | − | 0.846549i | \(-0.321324\pi\) | ||||
0.532310 | + | 0.846549i | \(0.321324\pi\) | |||||||
\(432\) | 11192.0 | 1.24647 | ||||||||
\(433\) | 3004.13 | 0.333417 | 0.166708 | − | 0.986006i | \(-0.446686\pi\) | ||||
0.166708 | + | 0.986006i | \(0.446686\pi\) | |||||||
\(434\) | 4568.96 | 0.505339 | ||||||||
\(435\) | −43.3151 | −0.00477425 | ||||||||
\(436\) | 17686.6 | 1.94274 | ||||||||
\(437\) | −5786.18 | −0.633388 | ||||||||
\(438\) | −3521.70 | −0.384186 | ||||||||
\(439\) | −1612.17 | −0.175273 | −0.0876366 | − | 0.996153i | \(-0.527931\pi\) | ||||
−0.0876366 | + | 0.996153i | \(0.527931\pi\) | |||||||
\(440\) | −9429.25 | −1.02164 | ||||||||
\(441\) | 5859.60 | 0.632718 | ||||||||
\(442\) | 413.531 | 0.0445015 | ||||||||
\(443\) | −16859.0 | −1.80812 | −0.904060 | − | 0.427405i | \(-0.859428\pi\) | ||||
−0.904060 | + | 0.427405i | \(0.859428\pi\) | |||||||
\(444\) | 4126.14 | 0.441032 | ||||||||
\(445\) | −7320.34 | −0.779815 | ||||||||
\(446\) | −6179.82 | −0.656105 | ||||||||
\(447\) | −1042.47 | −0.110307 | ||||||||
\(448\) | 32093.3 | 3.38453 | ||||||||
\(449\) | 1449.61 | 0.152364 | 0.0761820 | − | 0.997094i | \(-0.475727\pi\) | ||||
0.0761820 | + | 0.997094i | \(0.475727\pi\) | |||||||
\(450\) | 15505.6 | 1.62431 | ||||||||
\(451\) | 169.539 | 0.0177013 | ||||||||
\(452\) | −41691.0 | −4.33845 | ||||||||
\(453\) | 427.078 | 0.0442955 | ||||||||
\(454\) | −12714.9 | −1.31440 | ||||||||
\(455\) | 5423.04 | 0.558761 | ||||||||
\(456\) | −5968.72 | −0.612963 | ||||||||
\(457\) | 14850.6 | 1.52009 | 0.760044 | − | 0.649872i | \(-0.225178\pi\) | ||||
0.760044 | + | 0.649872i | \(0.225178\pi\) | |||||||
\(458\) | 5371.76 | 0.548048 | ||||||||
\(459\) | −88.4098 | −0.00899045 | ||||||||
\(460\) | 20989.2 | 2.12744 | ||||||||
\(461\) | −2352.85 | −0.237707 | −0.118854 | − | 0.992912i | \(-0.537922\pi\) | ||||
−0.118854 | + | 0.992912i | \(0.537922\pi\) | |||||||
\(462\) | 326.730 | 0.0329023 | ||||||||
\(463\) | −2460.09 | −0.246933 | −0.123467 | − | 0.992349i | \(-0.539401\pi\) | ||||
−0.123467 | + | 0.992349i | \(0.539401\pi\) | |||||||
\(464\) | 1139.93 | 0.114051 | ||||||||
\(465\) | 814.117 | 0.0811909 | ||||||||
\(466\) | −6136.36 | −0.610003 | ||||||||
\(467\) | −11846.1 | −1.17381 | −0.586907 | − | 0.809654i | \(-0.699655\pi\) | ||||
−0.586907 | + | 0.809654i | \(0.699655\pi\) | |||||||
\(468\) | −19926.0 | −1.96812 | ||||||||
\(469\) | 1028.17 | 0.101229 | ||||||||
\(470\) | −3241.58 | −0.318134 | ||||||||
\(471\) | −1391.42 | −0.136122 | ||||||||
\(472\) | 37404.6 | 3.64764 | ||||||||
\(473\) | −4014.06 | −0.390204 | ||||||||
\(474\) | 704.489 | 0.0682663 | ||||||||
\(475\) | −10168.6 | −0.982250 | ||||||||
\(476\) | −584.381 | −0.0562711 | ||||||||
\(477\) | −2881.80 | −0.276622 | ||||||||
\(478\) | −15535.3 | −1.48654 | ||||||||
\(479\) | −11954.2 | −1.14030 | −0.570148 | − | 0.821542i | \(-0.693114\pi\) | ||||
−0.570148 | + | 0.821542i | \(0.693114\pi\) | |||||||
\(480\) | 10262.3 | 0.975849 | ||||||||
\(481\) | −7960.16 | −0.754578 | ||||||||
\(482\) | 34748.8 | 3.28374 | ||||||||
\(483\) | −476.593 | −0.0448980 | ||||||||
\(484\) | −29646.8 | −2.78426 | ||||||||
\(485\) | 20411.1 | 1.91097 | ||||||||
\(486\) | 8620.78 | 0.804622 | ||||||||
\(487\) | 4535.96 | 0.422062 | 0.211031 | − | 0.977479i | \(-0.432318\pi\) | ||||
0.211031 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(488\) | 53110.5 | 4.92664 | ||||||||
\(489\) | 424.474 | 0.0392543 | ||||||||
\(490\) | 18744.4 | 1.72813 | ||||||||
\(491\) | 17766.8 | 1.63300 | 0.816501 | − | 0.577343i | \(-0.195911\pi\) | ||||
0.816501 | + | 0.577343i | \(0.195911\pi\) | |||||||
\(492\) | −389.293 | −0.0356721 | ||||||||
\(493\) | −9.00470 | −0.000822619 0 | ||||||||
\(494\) | 17571.9 | 1.60040 | ||||||||
\(495\) | −2938.30 | −0.266801 | ||||||||
\(496\) | −21425.2 | −1.93956 | ||||||||
\(497\) | 7149.06 | 0.645229 | ||||||||
\(498\) | −2406.81 | −0.216569 | ||||||||
\(499\) | 9734.49 | 0.873298 | 0.436649 | − | 0.899632i | \(-0.356165\pi\) | ||||
0.436649 | + | 0.899632i | \(0.356165\pi\) | |||||||
\(500\) | −7094.81 | −0.634579 | ||||||||
\(501\) | 800.265 | 0.0713637 | ||||||||
\(502\) | 16761.0 | 1.49020 | ||||||||
\(503\) | 14697.7 | 1.30286 | 0.651429 | − | 0.758710i | \(-0.274170\pi\) | ||||
0.651429 | + | 0.758710i | \(0.274170\pi\) | |||||||
\(504\) | 24812.6 | 2.19294 | ||||||||
\(505\) | 9969.25 | 0.878467 | ||||||||
\(506\) | −2439.60 | −0.214335 | ||||||||
\(507\) | 829.571 | 0.0726678 | ||||||||
\(508\) | −37920.4 | −3.31190 | ||||||||
\(509\) | −16450.2 | −1.43250 | −0.716249 | − | 0.697845i | \(-0.754143\pi\) | ||||
−0.716249 | + | 0.697845i | \(0.754143\pi\) | |||||||
\(510\) | −140.020 | −0.0121573 | ||||||||
\(511\) | −9601.04 | −0.831164 | ||||||||
\(512\) | −73663.4 | −6.35839 | ||||||||
\(513\) | −3756.74 | −0.323322 | ||||||||
\(514\) | −43546.0 | −3.73683 | ||||||||
\(515\) | −1675.21 | −0.143337 | ||||||||
\(516\) | 9217.04 | 0.786352 | ||||||||
\(517\) | 280.192 | 0.0238352 | ||||||||
\(518\) | 15126.4 | 1.28304 | ||||||||
\(519\) | 1239.63 | 0.104843 | ||||||||
\(520\) | −41769.8 | −3.52255 | ||||||||
\(521\) | −13924.5 | −1.17091 | −0.585456 | − | 0.810704i | \(-0.699085\pi\) | ||||
−0.585456 | + | 0.810704i | \(0.699085\pi\) | |||||||
\(522\) | 583.454 | 0.0489216 | ||||||||
\(523\) | −13436.0 | −1.12336 | −0.561679 | − | 0.827355i | \(-0.689845\pi\) | ||||
−0.561679 | + | 0.827355i | \(0.689845\pi\) | |||||||
\(524\) | 23252.2 | 1.93851 | ||||||||
\(525\) | −837.564 | −0.0696272 | ||||||||
\(526\) | 37768.5 | 3.13077 | ||||||||
\(527\) | 169.246 | 0.0139895 | ||||||||
\(528\) | −1532.14 | −0.126283 | ||||||||
\(529\) | −8608.42 | −0.707522 | ||||||||
\(530\) | −9218.63 | −0.755532 | ||||||||
\(531\) | 11655.8 | 0.952580 | ||||||||
\(532\) | −24831.7 | −2.02367 | ||||||||
\(533\) | 751.024 | 0.0610328 | ||||||||
\(534\) | −1953.72 | −0.158326 | ||||||||
\(535\) | 16949.7 | 1.36972 | ||||||||
\(536\) | −7919.25 | −0.638170 | ||||||||
\(537\) | −1063.88 | −0.0854933 | ||||||||
\(538\) | −44803.2 | −3.59034 | ||||||||
\(539\) | −1620.20 | −0.129475 | ||||||||
\(540\) | 13627.4 | 1.08598 | ||||||||
\(541\) | 1658.07 | 0.131767 | 0.0658834 | − | 0.997827i | \(-0.479013\pi\) | ||||
0.0658834 | + | 0.997827i | \(0.479013\pi\) | |||||||
\(542\) | 13022.3 | 1.03202 | ||||||||
\(543\) | −2461.51 | −0.194537 | ||||||||
\(544\) | 2133.41 | 0.168142 | ||||||||
\(545\) | 11553.3 | 0.908051 | ||||||||
\(546\) | 1447.35 | 0.113445 | ||||||||
\(547\) | −11736.3 | −0.917379 | −0.458689 | − | 0.888597i | \(-0.651681\pi\) | ||||
−0.458689 | + | 0.888597i | \(0.651681\pi\) | |||||||
\(548\) | −65269.2 | −5.08789 | ||||||||
\(549\) | 16550.0 | 1.28659 | ||||||||
\(550\) | −4287.36 | −0.332388 | ||||||||
\(551\) | −382.631 | −0.0295837 | ||||||||
\(552\) | 3670.85 | 0.283046 | ||||||||
\(553\) | 1920.61 | 0.147690 | ||||||||
\(554\) | 26494.4 | 2.03184 | ||||||||
\(555\) | 2695.29 | 0.206141 | ||||||||
\(556\) | −4284.70 | −0.326820 | ||||||||
\(557\) | −25325.4 | −1.92652 | −0.963262 | − | 0.268564i | \(-0.913451\pi\) | ||||
−0.963262 | + | 0.268564i | \(0.913451\pi\) | |||||||
\(558\) | −10966.2 | −0.831962 | ||||||||
\(559\) | −17781.5 | −1.34540 | ||||||||
\(560\) | 48324.2 | 3.64655 | ||||||||
\(561\) | 12.1029 | 0.000910847 0 | ||||||||
\(562\) | −33048.5 | −2.48054 | ||||||||
\(563\) | −20888.9 | −1.56370 | −0.781851 | − | 0.623466i | \(-0.785724\pi\) | ||||
−0.781851 | + | 0.623466i | \(0.785724\pi\) | |||||||
\(564\) | −643.373 | −0.0480335 | ||||||||
\(565\) | −27233.5 | −2.02783 | ||||||||
\(566\) | 16460.0 | 1.22238 | ||||||||
\(567\) | 7575.76 | 0.561114 | ||||||||
\(568\) | −55064.0 | −4.06767 | ||||||||
\(569\) | 145.182 | 0.0106966 | 0.00534829 | − | 0.999986i | \(-0.498298\pi\) | ||||
0.00534829 | + | 0.999986i | \(0.498298\pi\) | |||||||
\(570\) | −5949.80 | −0.437210 | ||||||||
\(571\) | −3058.43 | −0.224153 | −0.112076 | − | 0.993700i | \(-0.535750\pi\) | ||||
−0.112076 | + | 0.993700i | \(0.535750\pi\) | |||||||
\(572\) | 5509.61 | 0.402742 | ||||||||
\(573\) | −1979.58 | −0.144325 | ||||||||
\(574\) | −1427.14 | −0.103777 | ||||||||
\(575\) | 6253.85 | 0.453571 | ||||||||
\(576\) | −77028.7 | −5.57210 | ||||||||
\(577\) | −9011.91 | −0.650209 | −0.325105 | − | 0.945678i | \(-0.605400\pi\) | ||||
−0.325105 | + | 0.945678i | \(0.605400\pi\) | |||||||
\(578\) | 27417.2 | 1.97302 | ||||||||
\(579\) | 371.133 | 0.0266386 | ||||||||
\(580\) | 1387.98 | 0.0993668 | ||||||||
\(581\) | −6561.55 | −0.468535 | ||||||||
\(582\) | 5447.50 | 0.387983 | ||||||||
\(583\) | 796.828 | 0.0566059 | ||||||||
\(584\) | 73949.8 | 5.23984 | ||||||||
\(585\) | −13016.1 | −0.919913 | ||||||||
\(586\) | 37984.0 | 2.67765 | ||||||||
\(587\) | 21558.6 | 1.51587 | 0.757937 | − | 0.652328i | \(-0.226208\pi\) | ||||
0.757937 | + | 0.652328i | \(0.226208\pi\) | |||||||
\(588\) | 3720.29 | 0.260922 | ||||||||
\(589\) | 7191.65 | 0.503101 | ||||||||
\(590\) | 37286.0 | 2.60176 | ||||||||
\(591\) | −1444.30 | −0.100525 | ||||||||
\(592\) | −70932.1 | −4.92448 | ||||||||
\(593\) | −20569.7 | −1.42444 | −0.712221 | − | 0.701955i | \(-0.752311\pi\) | ||||
−0.712221 | + | 0.701955i | \(0.752311\pi\) | |||||||
\(594\) | −1583.94 | −0.109410 | ||||||||
\(595\) | −381.730 | −0.0263015 | ||||||||
\(596\) | 33404.7 | 2.29582 | ||||||||
\(597\) | −433.730 | −0.0297344 | ||||||||
\(598\) | −10807.0 | −0.739014 | ||||||||
\(599\) | 17853.3 | 1.21780 | 0.608902 | − | 0.793245i | \(-0.291610\pi\) | ||||
0.608902 | + | 0.793245i | \(0.291610\pi\) | |||||||
\(600\) | 6451.15 | 0.438945 | ||||||||
\(601\) | −15952.6 | −1.08273 | −0.541363 | − | 0.840789i | \(-0.682092\pi\) | ||||
−0.541363 | + | 0.840789i | \(0.682092\pi\) | |||||||
\(602\) | 33789.5 | 2.28764 | ||||||||
\(603\) | −2467.76 | −0.166658 | ||||||||
\(604\) | −13685.2 | −0.921926 | ||||||||
\(605\) | −19366.0 | −1.30138 | ||||||||
\(606\) | 2660.69 | 0.178355 | ||||||||
\(607\) | 23868.7 | 1.59605 | 0.798025 | − | 0.602624i | \(-0.205878\pi\) | ||||
0.798025 | + | 0.602624i | \(0.205878\pi\) | |||||||
\(608\) | 90653.8 | 6.04687 | ||||||||
\(609\) | −31.5163 | −0.00209705 | ||||||||
\(610\) | 52942.2 | 3.51404 | ||||||||
\(611\) | 1241.20 | 0.0821824 | ||||||||
\(612\) | 1402.60 | 0.0926417 | ||||||||
\(613\) | −22253.3 | −1.46624 | −0.733118 | − | 0.680102i | \(-0.761936\pi\) | ||||
−0.733118 | + | 0.680102i | \(0.761936\pi\) | |||||||
\(614\) | 969.971 | 0.0637538 | ||||||||
\(615\) | −254.295 | −0.0166734 | ||||||||
\(616\) | −6860.78 | −0.448748 | ||||||||
\(617\) | 21418.9 | 1.39756 | 0.698779 | − | 0.715338i | \(-0.253727\pi\) | ||||
0.698779 | + | 0.715338i | \(0.253727\pi\) | |||||||
\(618\) | −447.097 | −0.0291017 | ||||||||
\(619\) | 2419.44 | 0.157101 | 0.0785504 | − | 0.996910i | \(-0.474971\pi\) | ||||
0.0785504 | + | 0.996910i | \(0.474971\pi\) | |||||||
\(620\) | −26087.4 | −1.68983 | ||||||||
\(621\) | 2310.45 | 0.149300 | ||||||||
\(622\) | 15006.9 | 0.967400 | ||||||||
\(623\) | −5326.33 | −0.342528 | ||||||||
\(624\) | −6787.07 | −0.435417 | ||||||||
\(625\) | −17738.9 | −1.13529 | ||||||||
\(626\) | 23398.8 | 1.49394 | ||||||||
\(627\) | 514.281 | 0.0327566 | ||||||||
\(628\) | 44586.5 | 2.83311 | ||||||||
\(629\) | 560.319 | 0.0355189 | ||||||||
\(630\) | 24734.0 | 1.56417 | ||||||||
\(631\) | 188.414 | 0.0118869 | 0.00594346 | − | 0.999982i | \(-0.498108\pi\) | ||||
0.00594346 | + | 0.999982i | \(0.498108\pi\) | |||||||
\(632\) | −14793.1 | −0.931071 | ||||||||
\(633\) | −1844.84 | −0.115839 | ||||||||
\(634\) | 39697.0 | 2.48670 | ||||||||
\(635\) | −24770.4 | −1.54801 | ||||||||
\(636\) | −1829.67 | −0.114074 | ||||||||
\(637\) | −7177.19 | −0.446422 | ||||||||
\(638\) | −161.327 | −0.0100110 | ||||||||
\(639\) | −17158.8 | −1.06227 | ||||||||
\(640\) | −133056. | −8.21794 | ||||||||
\(641\) | 17778.3 | 1.09548 | 0.547739 | − | 0.836649i | \(-0.315489\pi\) | ||||
0.547739 | + | 0.836649i | \(0.315489\pi\) | |||||||
\(642\) | 4523.70 | 0.278094 | ||||||||
\(643\) | 27731.8 | 1.70083 | 0.850417 | − | 0.526110i | \(-0.176350\pi\) | ||||
0.850417 | + | 0.526110i | \(0.176350\pi\) | |||||||
\(644\) | 15271.9 | 0.934465 | ||||||||
\(645\) | 6020.77 | 0.367547 | ||||||||
\(646\) | −1236.89 | −0.0753328 | ||||||||
\(647\) | −30302.7 | −1.84130 | −0.920652 | − | 0.390384i | \(-0.872342\pi\) | ||||
−0.920652 | + | 0.390384i | \(0.872342\pi\) | |||||||
\(648\) | −58350.6 | −3.53739 | ||||||||
\(649\) | −3222.88 | −0.194929 | ||||||||
\(650\) | −18992.2 | −1.14605 | ||||||||
\(651\) | 592.357 | 0.0356625 | ||||||||
\(652\) | −13601.8 | −0.817004 | ||||||||
\(653\) | −9928.49 | −0.594995 | −0.297498 | − | 0.954723i | \(-0.596152\pi\) | ||||
−0.297498 | + | 0.954723i | \(0.596152\pi\) | |||||||
\(654\) | 3083.45 | 0.184361 | ||||||||
\(655\) | 15188.9 | 0.906074 | ||||||||
\(656\) | 6692.30 | 0.398308 | ||||||||
\(657\) | 23043.9 | 1.36838 | ||||||||
\(658\) | −2358.60 | −0.139738 | ||||||||
\(659\) | −18881.2 | −1.11610 | −0.558048 | − | 0.829809i | \(-0.688449\pi\) | ||||
−0.558048 | + | 0.829809i | \(0.688449\pi\) | |||||||
\(660\) | −1865.54 | −0.110024 | ||||||||
\(661\) | −405.203 | −0.0238435 | −0.0119218 | − | 0.999929i | \(-0.503795\pi\) | ||||
−0.0119218 | + | 0.999929i | \(0.503795\pi\) | |||||||
\(662\) | 63009.2 | 3.69928 | ||||||||
\(663\) | 53.6136 | 0.00314054 | ||||||||
\(664\) | 50538.8 | 2.95375 | ||||||||
\(665\) | −16220.6 | −0.945878 | ||||||||
\(666\) | −36305.5 | −2.11233 | ||||||||
\(667\) | 235.323 | 0.0136608 | ||||||||
\(668\) | −25643.6 | −1.48530 | ||||||||
\(669\) | −801.203 | −0.0463024 | ||||||||
\(670\) | −7894.14 | −0.455190 | ||||||||
\(671\) | −4576.15 | −0.263279 | ||||||||
\(672\) | 7466.92 | 0.428635 | ||||||||
\(673\) | 6752.02 | 0.386733 | 0.193366 | − | 0.981127i | \(-0.438059\pi\) | ||||
0.193366 | + | 0.981127i | \(0.438059\pi\) | |||||||
\(674\) | 26567.5 | 1.51831 | ||||||||
\(675\) | 4060.38 | 0.231532 | ||||||||
\(676\) | −26582.6 | −1.51244 | ||||||||
\(677\) | −16372.7 | −0.929475 | −0.464737 | − | 0.885449i | \(-0.653851\pi\) | ||||
−0.464737 | + | 0.885449i | \(0.653851\pi\) | |||||||
\(678\) | −7268.33 | −0.411709 | ||||||||
\(679\) | 14851.2 | 0.839379 | ||||||||
\(680\) | 2940.19 | 0.165811 | ||||||||
\(681\) | −1648.46 | −0.0927593 | ||||||||
\(682\) | 3032.18 | 0.170247 | ||||||||
\(683\) | 23177.3 | 1.29847 | 0.649234 | − | 0.760589i | \(-0.275090\pi\) | ||||
0.649234 | + | 0.760589i | \(0.275090\pi\) | |||||||
\(684\) | 59599.7 | 3.33166 | ||||||||
\(685\) | −42635.3 | −2.37812 | ||||||||
\(686\) | 34775.2 | 1.93546 | ||||||||
\(687\) | 696.440 | 0.0386766 | ||||||||
\(688\) | −158449. | −8.78026 | ||||||||
\(689\) | 3529.80 | 0.195174 | ||||||||
\(690\) | 3659.21 | 0.201889 | ||||||||
\(691\) | 23872.3 | 1.31425 | 0.657123 | − | 0.753784i | \(-0.271773\pi\) | ||||
0.657123 | + | 0.753784i | \(0.271773\pi\) | |||||||
\(692\) | −39722.4 | −2.18211 | ||||||||
\(693\) | −2137.92 | −0.117190 | ||||||||
\(694\) | 50927.3 | 2.78555 | ||||||||
\(695\) | −2798.86 | −0.152758 | ||||||||
\(696\) | 242.747 | 0.0132203 | ||||||||
\(697\) | −52.8649 | −0.00287289 | ||||||||
\(698\) | 31869.4 | 1.72819 | ||||||||
\(699\) | −795.568 | −0.0430489 | ||||||||
\(700\) | 26838.8 | 1.44916 | ||||||||
\(701\) | −26245.0 | −1.41407 | −0.707033 | − | 0.707180i | \(-0.749967\pi\) | ||||
−0.707033 | + | 0.707180i | \(0.749967\pi\) | |||||||
\(702\) | −7016.55 | −0.377240 | ||||||||
\(703\) | 23809.3 | 1.27736 | ||||||||
\(704\) | 21298.7 | 1.14023 | ||||||||
\(705\) | −420.265 | −0.0224512 | ||||||||
\(706\) | −23450.6 | −1.25010 | ||||||||
\(707\) | 7253.69 | 0.385860 | ||||||||
\(708\) | 7400.34 | 0.392828 | ||||||||
\(709\) | −24596.6 | −1.30288 | −0.651441 | − | 0.758699i | \(-0.725835\pi\) | ||||
−0.651441 | + | 0.758699i | \(0.725835\pi\) | |||||||
\(710\) | −54889.4 | −2.90136 | ||||||||
\(711\) | −4609.75 | −0.243149 | ||||||||
\(712\) | 41024.9 | 2.15937 | ||||||||
\(713\) | −4422.96 | −0.232316 | ||||||||
\(714\) | −101.880 | −0.00534000 | ||||||||
\(715\) | 3599.00 | 0.188245 | ||||||||
\(716\) | 34090.9 | 1.77938 | ||||||||
\(717\) | −2014.12 | −0.104908 | ||||||||
\(718\) | 6015.46 | 0.312667 | ||||||||
\(719\) | 14032.1 | 0.727829 | 0.363915 | − | 0.931432i | \(-0.381440\pi\) | ||||
0.363915 | + | 0.931432i | \(0.381440\pi\) | |||||||
\(720\) | −115985. | −6.00348 | ||||||||
\(721\) | −1218.90 | −0.0629598 | ||||||||
\(722\) | −14241.0 | −0.734068 | ||||||||
\(723\) | 4505.12 | 0.231739 | ||||||||
\(724\) | 78876.1 | 4.04891 | ||||||||
\(725\) | 413.557 | 0.0211850 | ||||||||
\(726\) | −5168.57 | −0.264220 | ||||||||
\(727\) | −23451.3 | −1.19637 | −0.598185 | − | 0.801358i | \(-0.704111\pi\) | ||||
−0.598185 | + | 0.801358i | \(0.704111\pi\) | |||||||
\(728\) | −30392.0 | −1.54725 | ||||||||
\(729\) | −17425.5 | −0.885308 | ||||||||
\(730\) | 73715.4 | 3.73744 | ||||||||
\(731\) | 1251.65 | 0.0633296 | ||||||||
\(732\) | 10507.7 | 0.530568 | ||||||||
\(733\) | 2929.56 | 0.147620 | 0.0738101 | − | 0.997272i | \(-0.476484\pi\) | ||||
0.0738101 | + | 0.997272i | \(0.476484\pi\) | |||||||
\(734\) | −16769.0 | −0.843263 | ||||||||
\(735\) | 2430.17 | 0.121957 | ||||||||
\(736\) | −55753.3 | −2.79225 | ||||||||
\(737\) | 682.344 | 0.0341037 | ||||||||
\(738\) | 3425.35 | 0.170852 | ||||||||
\(739\) | 33904.0 | 1.68766 | 0.843830 | − | 0.536611i | \(-0.180296\pi\) | ||||
0.843830 | + | 0.536611i | \(0.180296\pi\) | |||||||
\(740\) | −86367.3 | −4.29044 | ||||||||
\(741\) | 2278.17 | 0.112943 | ||||||||
\(742\) | −6707.54 | −0.331862 | ||||||||
\(743\) | −2777.21 | −0.137128 | −0.0685639 | − | 0.997647i | \(-0.521842\pi\) | ||||
−0.0685639 | + | 0.997647i | \(0.521842\pi\) | |||||||
\(744\) | −4562.50 | −0.224824 | ||||||||
\(745\) | 21820.7 | 1.07308 | ||||||||
\(746\) | 1871.75 | 0.0918629 | ||||||||
\(747\) | 15748.7 | 0.771370 | ||||||||
\(748\) | −387.824 | −0.0189575 | ||||||||
\(749\) | 12332.7 | 0.601640 | ||||||||
\(750\) | −1236.90 | −0.0602201 | ||||||||
\(751\) | 8652.39 | 0.420413 | 0.210207 | − | 0.977657i | \(-0.432586\pi\) | ||||
0.210207 | + | 0.977657i | \(0.432586\pi\) | |||||||
\(752\) | 11060.2 | 0.536333 | ||||||||
\(753\) | 2173.03 | 0.105165 | ||||||||
\(754\) | −714.649 | −0.0345172 | ||||||||
\(755\) | −8939.48 | −0.430915 | ||||||||
\(756\) | 9915.42 | 0.477011 | ||||||||
\(757\) | 6552.70 | 0.314613 | 0.157306 | − | 0.987550i | \(-0.449719\pi\) | ||||
0.157306 | + | 0.987550i | \(0.449719\pi\) | |||||||
\(758\) | −3700.38 | −0.177314 | ||||||||
\(759\) | −316.290 | −0.0151260 | ||||||||
\(760\) | 124936. | 5.96302 | ||||||||
\(761\) | 9849.58 | 0.469181 | 0.234591 | − | 0.972094i | \(-0.424625\pi\) | ||||
0.234591 | + | 0.972094i | \(0.424625\pi\) | |||||||
\(762\) | −6610.96 | −0.314291 | ||||||||
\(763\) | 8406.24 | 0.398855 | ||||||||
\(764\) | 63433.4 | 3.00385 | ||||||||
\(765\) | 916.208 | 0.0433014 | ||||||||
\(766\) | −51376.5 | −2.42338 | ||||||||
\(767\) | −14276.8 | −0.672104 | ||||||||
\(768\) | −18653.3 | −0.876421 | ||||||||
\(769\) | 14425.2 | 0.676444 | 0.338222 | − | 0.941066i | \(-0.390175\pi\) | ||||
0.338222 | + | 0.941066i | \(0.390175\pi\) | |||||||
\(770\) | −6839.03 | −0.320080 | ||||||||
\(771\) | −5645.66 | −0.263714 | ||||||||
\(772\) | −11892.5 | −0.554431 | ||||||||
\(773\) | −1783.91 | −0.0830047 | −0.0415024 | − | 0.999138i | \(-0.513214\pi\) | ||||
−0.0415024 | + | 0.999138i | \(0.513214\pi\) | |||||||
\(774\) | −81099.8 | −3.76624 | ||||||||
\(775\) | −7772.91 | −0.360273 | ||||||||
\(776\) | −114388. | −5.29163 | ||||||||
\(777\) | 1961.11 | 0.0905462 | ||||||||
\(778\) | −57520.4 | −2.65065 | ||||||||
\(779\) | −2246.36 | −0.103317 | ||||||||
\(780\) | −8263.98 | −0.379356 | ||||||||
\(781\) | 4744.46 | 0.217376 | ||||||||
\(782\) | 760.708 | 0.0347863 | ||||||||
\(783\) | 152.786 | 0.00697335 | ||||||||
\(784\) | −63955.1 | −2.91341 | ||||||||
\(785\) | 29124.9 | 1.32422 | ||||||||
\(786\) | 4053.75 | 0.183960 | ||||||||
\(787\) | −8086.97 | −0.366289 | −0.183144 | − | 0.983086i | \(-0.558628\pi\) | ||||
−0.183144 | + | 0.983086i | \(0.558628\pi\) | |||||||
\(788\) | 46280.8 | 2.09224 | ||||||||
\(789\) | 4896.62 | 0.220943 | ||||||||
\(790\) | −14746.2 | −0.664108 | ||||||||
\(791\) | −19815.3 | −0.890708 | ||||||||
\(792\) | 16466.9 | 0.738794 | ||||||||
\(793\) | −20271.5 | −0.907769 | ||||||||
\(794\) | 64359.1 | 2.87660 | ||||||||
\(795\) | −1195.18 | −0.0533190 | ||||||||
\(796\) | 13898.4 | 0.618864 | ||||||||
\(797\) | 29465.6 | 1.30957 | 0.654783 | − | 0.755817i | \(-0.272760\pi\) | ||||
0.654783 | + | 0.755817i | \(0.272760\pi\) | |||||||
\(798\) | −4329.11 | −0.192041 | ||||||||
\(799\) | −87.3683 | −0.00386842 | ||||||||
\(800\) | −97980.9 | −4.33018 | ||||||||
\(801\) | 12784.0 | 0.563919 | ||||||||
\(802\) | 60041.3 | 2.64356 | ||||||||
\(803\) | −6371.72 | −0.280016 | ||||||||
\(804\) | −1566.79 | −0.0687269 | ||||||||
\(805\) | 9975.91 | 0.436776 | ||||||||
\(806\) | 13432.0 | 0.587000 | ||||||||
\(807\) | −5808.65 | −0.253376 | ||||||||
\(808\) | −55869.9 | −2.43255 | ||||||||
\(809\) | 31904.0 | 1.38651 | 0.693255 | − | 0.720693i | \(-0.256176\pi\) | ||||
0.693255 | + | 0.720693i | \(0.256176\pi\) | |||||||
\(810\) | −58165.6 | −2.52312 | ||||||||
\(811\) | 35204.4 | 1.52428 | 0.762141 | − | 0.647412i | \(-0.224148\pi\) | ||||
0.762141 | + | 0.647412i | \(0.224148\pi\) | |||||||
\(812\) | 1009.90 | 0.0436462 | ||||||||
\(813\) | 1688.32 | 0.0728315 | ||||||||
\(814\) | 10038.6 | 0.432252 | ||||||||
\(815\) | −8884.98 | −0.381874 | ||||||||
\(816\) | 477.745 | 0.0204956 | ||||||||
\(817\) | 53185.5 | 2.27751 | ||||||||
\(818\) | −82172.9 | −3.51236 | ||||||||
\(819\) | −9470.60 | −0.404065 | ||||||||
\(820\) | 8148.58 | 0.347025 | ||||||||
\(821\) | −3407.61 | −0.144855 | −0.0724277 | − | 0.997374i | \(-0.523075\pi\) | ||||
−0.0724277 | + | 0.997374i | \(0.523075\pi\) | |||||||
\(822\) | −11378.9 | −0.482829 | ||||||||
\(823\) | 2013.98 | 0.0853012 | 0.0426506 | − | 0.999090i | \(-0.486420\pi\) | ||||
0.0426506 | + | 0.999090i | \(0.486420\pi\) | |||||||
\(824\) | 9388.27 | 0.396913 | ||||||||
\(825\) | −555.848 | −0.0234572 | ||||||||
\(826\) | 27129.6 | 1.14281 | ||||||||
\(827\) | 41526.9 | 1.74611 | 0.873054 | − | 0.487624i | \(-0.162136\pi\) | ||||
0.873054 | + | 0.487624i | \(0.162136\pi\) | |||||||
\(828\) | −36654.7 | −1.53845 | ||||||||
\(829\) | 40843.2 | 1.71115 | 0.855575 | − | 0.517679i | \(-0.173204\pi\) | ||||
0.855575 | + | 0.517679i | \(0.173204\pi\) | |||||||
\(830\) | 50378.6 | 2.10683 | ||||||||
\(831\) | 3434.96 | 0.143390 | ||||||||
\(832\) | 94349.3 | 3.93146 | ||||||||
\(833\) | 505.205 | 0.0210136 | ||||||||
\(834\) | −746.987 | −0.0310144 | ||||||||
\(835\) | −16750.9 | −0.694240 | ||||||||
\(836\) | −16479.5 | −0.681767 | ||||||||
\(837\) | −2871.66 | −0.118589 | ||||||||
\(838\) | −23557.4 | −0.971092 | ||||||||
\(839\) | 45143.4 | 1.85760 | 0.928798 | − | 0.370586i | \(-0.120843\pi\) | ||||
0.928798 | + | 0.370586i | \(0.120843\pi\) | |||||||
\(840\) | 10290.6 | 0.422691 | ||||||||
\(841\) | −24373.4 | −0.999362 | ||||||||
\(842\) | 4914.81 | 0.201158 | ||||||||
\(843\) | −4284.67 | −0.175056 | ||||||||
\(844\) | 59115.9 | 2.41096 | ||||||||
\(845\) | −17364.4 | −0.706926 | ||||||||
\(846\) | 5660.97 | 0.230057 | ||||||||
\(847\) | −14090.8 | −0.571624 | ||||||||
\(848\) | 31453.7 | 1.27373 | ||||||||
\(849\) | 2134.02 | 0.0862653 | ||||||||
\(850\) | 1336.87 | 0.0539461 | ||||||||
\(851\) | −14643.0 | −0.589844 | ||||||||
\(852\) | −10894.2 | −0.438062 | ||||||||
\(853\) | −25960.3 | −1.04204 | −0.521021 | − | 0.853544i | \(-0.674449\pi\) | ||||
−0.521021 | + | 0.853544i | \(0.674449\pi\) | |||||||
\(854\) | 38521.1 | 1.54352 | ||||||||
\(855\) | 38931.9 | 1.55724 | ||||||||
\(856\) | −94990.1 | −3.79287 | ||||||||
\(857\) | 2624.50 | 0.104610 | 0.0523052 | − | 0.998631i | \(-0.483343\pi\) | ||||
0.0523052 | + | 0.998631i | \(0.483343\pi\) | |||||||
\(858\) | 960.535 | 0.0382192 | ||||||||
\(859\) | 26954.2 | 1.07062 | 0.535312 | − | 0.844654i | \(-0.320194\pi\) | ||||
0.535312 | + | 0.844654i | \(0.320194\pi\) | |||||||
\(860\) | −192929. | −7.64978 | ||||||||
\(861\) | −185.026 | −0.00732368 | ||||||||
\(862\) | −53216.7 | −2.10275 | ||||||||
\(863\) | −17268.2 | −0.681132 | −0.340566 | − | 0.940221i | \(-0.610619\pi\) | ||||
−0.340566 | + | 0.940221i | \(0.610619\pi\) | |||||||
\(864\) | −36198.5 | −1.42534 | ||||||||
\(865\) | −25947.6 | −1.01993 | ||||||||
\(866\) | −16782.5 | −0.658535 | ||||||||
\(867\) | 3554.59 | 0.139239 | ||||||||
\(868\) | −18981.4 | −0.742247 | ||||||||
\(869\) | 1274.61 | 0.0497563 | ||||||||
\(870\) | 241.978 | 0.00942968 | ||||||||
\(871\) | 3022.65 | 0.117588 | ||||||||
\(872\) | −64747.2 | −2.51447 | ||||||||
\(873\) | −35645.1 | −1.38191 | ||||||||
\(874\) | 32324.3 | 1.25101 | ||||||||
\(875\) | −3372.08 | −0.130283 | ||||||||
\(876\) | 14630.7 | 0.564297 | ||||||||
\(877\) | −23724.1 | −0.913461 | −0.456731 | − | 0.889605i | \(-0.650980\pi\) | ||||
−0.456731 | + | 0.889605i | \(0.650980\pi\) | |||||||
\(878\) | 9006.35 | 0.346184 | ||||||||
\(879\) | 4924.56 | 0.188966 | ||||||||
\(880\) | 32070.3 | 1.22851 | ||||||||
\(881\) | 17218.2 | 0.658452 | 0.329226 | − | 0.944251i | \(-0.393212\pi\) | ||||
0.329226 | + | 0.944251i | \(0.393212\pi\) | |||||||
\(882\) | −32734.4 | −1.24969 | ||||||||
\(883\) | 38239.7 | 1.45738 | 0.728691 | − | 0.684842i | \(-0.240129\pi\) | ||||
0.728691 | + | 0.684842i | \(0.240129\pi\) | |||||||
\(884\) | −1717.99 | −0.0653644 | ||||||||
\(885\) | 4834.07 | 0.183611 | ||||||||
\(886\) | 94182.4 | 3.57124 | ||||||||
\(887\) | −6196.78 | −0.234575 | −0.117287 | − | 0.993098i | \(-0.537420\pi\) | ||||
−0.117287 | + | 0.993098i | \(0.537420\pi\) | |||||||
\(888\) | −15105.0 | −0.570823 | ||||||||
\(889\) | −18023.1 | −0.679950 | ||||||||
\(890\) | 40894.8 | 1.54022 | ||||||||
\(891\) | 5027.64 | 0.189037 | ||||||||
\(892\) | 25673.6 | 0.963695 | ||||||||
\(893\) | −3712.49 | −0.139119 | ||||||||
\(894\) | 5823.71 | 0.217868 | ||||||||
\(895\) | 22268.9 | 0.831695 | ||||||||
\(896\) | −96812.1 | −3.60967 | ||||||||
\(897\) | −1401.11 | −0.0521533 | ||||||||
\(898\) | −8098.20 | −0.300936 | ||||||||
\(899\) | −292.484 | −0.0108508 | ||||||||
\(900\) | −64416.9 | −2.38581 | ||||||||
\(901\) | −248.464 | −0.00918706 | ||||||||
\(902\) | −947.121 | −0.0349620 | ||||||||
\(903\) | 4380.75 | 0.161442 | ||||||||
\(904\) | 152623. | 5.61522 | ||||||||
\(905\) | 51523.6 | 1.89249 | ||||||||
\(906\) | −2385.85 | −0.0874886 | ||||||||
\(907\) | 14426.5 | 0.528142 | 0.264071 | − | 0.964503i | \(-0.414935\pi\) | ||||
0.264071 | + | 0.964503i | \(0.414935\pi\) | |||||||
\(908\) | 52823.0 | 1.93061 | ||||||||
\(909\) | −17409.9 | −0.635259 | ||||||||
\(910\) | −30295.6 | −1.10362 | ||||||||
\(911\) | −46318.1 | −1.68451 | −0.842254 | − | 0.539080i | \(-0.818772\pi\) | ||||
−0.842254 | + | 0.539080i | \(0.818772\pi\) | |||||||
\(912\) | 20300.5 | 0.737080 | ||||||||
\(913\) | −4354.56 | −0.157848 | ||||||||
\(914\) | −82962.1 | −3.00234 | ||||||||
\(915\) | 6863.86 | 0.247991 | ||||||||
\(916\) | −22316.6 | −0.804980 | ||||||||
\(917\) | 11051.5 | 0.397986 | ||||||||
\(918\) | 493.898 | 0.0177571 | ||||||||
\(919\) | −20705.8 | −0.743222 | −0.371611 | − | 0.928389i | \(-0.621194\pi\) | ||||
−0.371611 | + | 0.928389i | \(0.621194\pi\) | |||||||
\(920\) | −76837.2 | −2.75353 | ||||||||
\(921\) | 125.755 | 0.00449921 | ||||||||
\(922\) | 13144.1 | 0.469498 | ||||||||
\(923\) | 21017.1 | 0.749497 | ||||||||
\(924\) | −1357.38 | −0.0483273 | ||||||||
\(925\) | −25733.7 | −0.914722 | ||||||||
\(926\) | 13743.2 | 0.487721 | ||||||||
\(927\) | 2925.53 | 0.103654 | ||||||||
\(928\) | −3686.88 | −0.130418 | ||||||||
\(929\) | −26235.4 | −0.926539 | −0.463270 | − | 0.886217i | \(-0.653324\pi\) | ||||
−0.463270 | + | 0.886217i | \(0.653324\pi\) | |||||||
\(930\) | −4548.03 | −0.160361 | ||||||||
\(931\) | 21467.4 | 0.755708 | ||||||||
\(932\) | 25493.1 | 0.895979 | ||||||||
\(933\) | 1945.62 | 0.0682709 | ||||||||
\(934\) | 66177.6 | 2.31841 | ||||||||
\(935\) | −253.335 | −0.00886090 | ||||||||
\(936\) | 72945.2 | 2.54732 | ||||||||
\(937\) | −53053.4 | −1.84971 | −0.924856 | − | 0.380317i | \(-0.875815\pi\) | ||||
−0.924856 | + | 0.380317i | \(0.875815\pi\) | |||||||
\(938\) | −5743.83 | −0.199939 | ||||||||
\(939\) | 3033.62 | 0.105430 | ||||||||
\(940\) | 13466.9 | 0.467279 | ||||||||
\(941\) | −24113.0 | −0.835347 | −0.417674 | − | 0.908597i | \(-0.637154\pi\) | ||||
−0.417674 | + | 0.908597i | \(0.637154\pi\) | |||||||
\(942\) | 7773.12 | 0.268856 | ||||||||
\(943\) | 1381.54 | 0.0477085 | ||||||||
\(944\) | −127219. | −4.38624 | ||||||||
\(945\) | 6476.97 | 0.222959 | ||||||||
\(946\) | 22424.4 | 0.770698 | ||||||||
\(947\) | 143.674 | 0.00493009 | 0.00246504 | − | 0.999997i | \(-0.499215\pi\) | ||||
0.00246504 | + | 0.999997i | \(0.499215\pi\) | |||||||
\(948\) | −2926.75 | −0.100270 | ||||||||
\(949\) | −28225.5 | −0.965478 | ||||||||
\(950\) | 56806.7 | 1.94005 | ||||||||
\(951\) | 5146.64 | 0.175490 | ||||||||
\(952\) | 2139.30 | 0.0728311 | ||||||||
\(953\) | 1173.03 | 0.0398721 | 0.0199360 | − | 0.999801i | \(-0.493654\pi\) | ||||
0.0199360 | + | 0.999801i | \(0.493654\pi\) | |||||||
\(954\) | 16099.1 | 0.546359 | ||||||||
\(955\) | 41436.1 | 1.40402 | ||||||||
\(956\) | 64540.2 | 2.18345 | ||||||||
\(957\) | −20.9158 | −0.000706490 0 | ||||||||
\(958\) | 66781.7 | 2.25221 | ||||||||
\(959\) | −31021.7 | −1.04457 | ||||||||
\(960\) | −31946.4 | −1.07403 | ||||||||
\(961\) | −24293.7 | −0.815471 | ||||||||
\(962\) | 44469.1 | 1.49038 | ||||||||
\(963\) | −29600.3 | −0.990506 | ||||||||
\(964\) | −144361. | −4.82320 | ||||||||
\(965\) | −7768.45 | −0.259145 | ||||||||
\(966\) | 2662.47 | 0.0886785 | ||||||||
\(967\) | 26131.5 | 0.869008 | 0.434504 | − | 0.900670i | \(-0.356924\pi\) | ||||
0.434504 | + | 0.900670i | \(0.356924\pi\) | |||||||
\(968\) | 108531. | 3.60364 | ||||||||
\(969\) | −160.361 | −0.00531635 | ||||||||
\(970\) | −114026. | −3.77438 | ||||||||
\(971\) | 10548.4 | 0.348623 | 0.174312 | − | 0.984691i | \(-0.444230\pi\) | ||||
0.174312 | + | 0.984691i | \(0.444230\pi\) | |||||||
\(972\) | −35814.4 | −1.18184 | ||||||||
\(973\) | −2036.47 | −0.0670979 | ||||||||
\(974\) | −25340.0 | −0.833619 | ||||||||
\(975\) | −2462.30 | −0.0808788 | ||||||||
\(976\) | −180637. | −5.92423 | ||||||||
\(977\) | −2527.24 | −0.0827569 | −0.0413785 | − | 0.999144i | \(-0.513175\pi\) | ||||
−0.0413785 | + | 0.999144i | \(0.513175\pi\) | |||||||
\(978\) | −2371.31 | −0.0775317 | ||||||||
\(979\) | −3534.81 | −0.115396 | ||||||||
\(980\) | −77872.1 | −2.53830 | ||||||||
\(981\) | −20176.2 | −0.656653 | ||||||||
\(982\) | −99253.5 | −3.22536 | ||||||||
\(983\) | 983.000 | 0.0318950 | ||||||||
\(984\) | 1425.12 | 0.0461700 | ||||||||
\(985\) | 30231.7 | 0.977930 | ||||||||
\(986\) | 50.3044 | 0.00162477 | ||||||||
\(987\) | −305.788 | −0.00986154 | ||||||||
\(988\) | −73001.3 | −2.35069 | ||||||||
\(989\) | −32709.8 | −1.05168 | ||||||||
\(990\) | 16414.7 | 0.526962 | ||||||||
\(991\) | 25213.6 | 0.808209 | 0.404104 | − | 0.914713i | \(-0.367583\pi\) | ||||
0.404104 | + | 0.914713i | \(0.367583\pi\) | |||||||
\(992\) | 69295.9 | 2.21789 | ||||||||
\(993\) | 8169.04 | 0.261064 | ||||||||
\(994\) | −39937.9 | −1.27440 | ||||||||
\(995\) | 9078.73 | 0.289261 | ||||||||
\(996\) | 9998.90 | 0.318100 | ||||||||
\(997\) | 33632.7 | 1.06836 | 0.534181 | − | 0.845370i | \(-0.320620\pi\) | ||||
0.534181 | + | 0.845370i | \(0.320620\pi\) | |||||||
\(998\) | −54381.4 | −1.72486 | ||||||||
\(999\) | −9507.15 | −0.301094 |
(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 | 983.4.a.a.1.1 | ✓ | 109 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
983.4.a.a.1.1 | ✓ | 109 | 1.1 | even | 1 | trivial |