Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.48 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.33984 | 1.88792 | 0.943960 | − | 0.330061i | \(-0.107069\pi\) | ||||
0.943960 | + | 0.330061i | \(0.107069\pi\) | |||||||
\(3\) | 6.59560 | 1.26932 | 0.634662 | − | 0.772790i | \(-0.281139\pi\) | ||||
0.634662 | + | 0.772790i | \(0.281139\pi\) | |||||||
\(4\) | 20.5139 | 2.56424 | ||||||||
\(5\) | −12.0752 | −1.08004 | −0.540021 | − | 0.841651i | \(-0.681584\pi\) | ||||
−0.540021 | + | 0.841651i | \(0.681584\pi\) | |||||||
\(6\) | 35.2195 | 2.39638 | ||||||||
\(7\) | −18.2315 | −0.984406 | −0.492203 | − | 0.870480i | \(-0.663808\pi\) | ||||
−0.492203 | + | 0.870480i | \(0.663808\pi\) | |||||||
\(8\) | 66.8223 | 2.95315 | ||||||||
\(9\) | 16.5020 | 0.611184 | ||||||||
\(10\) | −64.4799 | −2.03903 | ||||||||
\(11\) | −44.5541 | −1.22123 | −0.610616 | − | 0.791927i | \(-0.709078\pi\) | ||||
−0.610616 | + | 0.791927i | \(0.709078\pi\) | |||||||
\(12\) | 135.302 | 3.25485 | ||||||||
\(13\) | −45.4579 | −0.969827 | −0.484914 | − | 0.874562i | \(-0.661149\pi\) | ||||
−0.484914 | + | 0.874562i | \(0.661149\pi\) | |||||||
\(14\) | −97.3531 | −1.85848 | ||||||||
\(15\) | −79.6435 | −1.37092 | ||||||||
\(16\) | 192.709 | 3.01108 | ||||||||
\(17\) | −98.4784 | −1.40497 | −0.702486 | − | 0.711698i | \(-0.747927\pi\) | ||||
−0.702486 | + | 0.711698i | \(0.747927\pi\) | |||||||
\(18\) | 88.1179 | 1.15387 | ||||||||
\(19\) | −86.0301 | −1.03877 | −0.519386 | − | 0.854540i | \(-0.673839\pi\) | ||||
−0.519386 | + | 0.854540i | \(0.673839\pi\) | |||||||
\(20\) | −247.710 | −2.76949 | ||||||||
\(21\) | −120.247 | −1.24953 | ||||||||
\(22\) | −237.912 | −2.30559 | ||||||||
\(23\) | 142.930 | 1.29578 | 0.647889 | − | 0.761734i | \(-0.275652\pi\) | ||||
0.647889 | + | 0.761734i | \(0.275652\pi\) | |||||||
\(24\) | 440.733 | 3.74851 | ||||||||
\(25\) | 20.8116 | 0.166493 | ||||||||
\(26\) | −242.738 | −1.83096 | ||||||||
\(27\) | −69.2408 | −0.493534 | ||||||||
\(28\) | −373.998 | −2.52425 | ||||||||
\(29\) | 162.790 | 1.04239 | 0.521196 | − | 0.853437i | \(-0.325486\pi\) | ||||
0.521196 | + | 0.853437i | \(0.325486\pi\) | |||||||
\(30\) | −425.284 | −2.58819 | ||||||||
\(31\) | 68.1625 | 0.394914 | 0.197457 | − | 0.980312i | \(-0.436732\pi\) | ||||
0.197457 | + | 0.980312i | \(0.436732\pi\) | |||||||
\(32\) | 494.458 | 2.73152 | ||||||||
\(33\) | −293.861 | −1.55014 | ||||||||
\(34\) | −525.859 | −2.65247 | ||||||||
\(35\) | 220.149 | 1.06320 | ||||||||
\(36\) | 338.520 | 1.56722 | ||||||||
\(37\) | −13.6258 | −0.0605425 | −0.0302712 | − | 0.999542i | \(-0.509637\pi\) | ||||
−0.0302712 | + | 0.999542i | \(0.509637\pi\) | |||||||
\(38\) | −459.387 | −1.96112 | ||||||||
\(39\) | −299.822 | −1.23103 | ||||||||
\(40\) | −806.895 | −3.18953 | ||||||||
\(41\) | 17.3417 | 0.0660564 | 0.0330282 | − | 0.999454i | \(-0.489485\pi\) | ||||
0.0330282 | + | 0.999454i | \(0.489485\pi\) | |||||||
\(42\) | −642.102 | −2.35901 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −913.978 | −3.13153 | ||||||||
\(45\) | −199.265 | −0.660105 | ||||||||
\(46\) | 763.222 | 2.44633 | ||||||||
\(47\) | 409.667 | 1.27141 | 0.635704 | − | 0.771933i | \(-0.280710\pi\) | ||||
0.635704 | + | 0.771933i | \(0.280710\pi\) | |||||||
\(48\) | 1271.03 | 3.82204 | ||||||||
\(49\) | −10.6139 | −0.0309442 | ||||||||
\(50\) | 111.131 | 0.314325 | ||||||||
\(51\) | −649.524 | −1.78336 | ||||||||
\(52\) | −932.519 | −2.48687 | ||||||||
\(53\) | −161.737 | −0.419175 | −0.209588 | − | 0.977790i | \(-0.567212\pi\) | ||||
−0.209588 | + | 0.977790i | \(0.567212\pi\) | |||||||
\(54\) | −369.735 | −0.931751 | ||||||||
\(55\) | 538.001 | 1.31898 | ||||||||
\(56\) | −1218.27 | −2.90710 | ||||||||
\(57\) | −567.420 | −1.31854 | ||||||||
\(58\) | 869.274 | 1.96795 | ||||||||
\(59\) | −400.387 | −0.883491 | −0.441746 | − | 0.897140i | \(-0.645641\pi\) | ||||
−0.441746 | + | 0.897140i | \(0.645641\pi\) | |||||||
\(60\) | −1633.80 | −3.51538 | ||||||||
\(61\) | −706.565 | −1.48306 | −0.741528 | − | 0.670922i | \(-0.765898\pi\) | ||||
−0.741528 | + | 0.670922i | \(0.765898\pi\) | |||||||
\(62\) | 363.977 | 0.745566 | ||||||||
\(63\) | −300.855 | −0.601653 | ||||||||
\(64\) | 1098.65 | 2.14581 | ||||||||
\(65\) | 548.916 | 1.04746 | ||||||||
\(66\) | −1569.17 | −2.92654 | ||||||||
\(67\) | 334.035 | 0.609088 | 0.304544 | − | 0.952498i | \(-0.401496\pi\) | ||||
0.304544 | + | 0.952498i | \(0.401496\pi\) | |||||||
\(68\) | −2020.18 | −3.60268 | ||||||||
\(69\) | 942.708 | 1.64476 | ||||||||
\(70\) | 1175.56 | 2.00724 | ||||||||
\(71\) | 480.962 | 0.803940 | 0.401970 | − | 0.915653i | \(-0.368326\pi\) | ||||
0.401970 | + | 0.915653i | \(0.368326\pi\) | |||||||
\(72\) | 1102.70 | 1.80492 | ||||||||
\(73\) | −1151.86 | −1.84678 | −0.923390 | − | 0.383863i | \(-0.874593\pi\) | ||||
−0.923390 | + | 0.383863i | \(0.874593\pi\) | |||||||
\(74\) | −72.7597 | −0.114299 | ||||||||
\(75\) | 137.265 | 0.211333 | ||||||||
\(76\) | −1764.81 | −2.66366 | ||||||||
\(77\) | 812.286 | 1.20219 | ||||||||
\(78\) | −1601.00 | −2.32408 | ||||||||
\(79\) | −250.741 | −0.357096 | −0.178548 | − | 0.983931i | \(-0.557140\pi\) | ||||
−0.178548 | + | 0.983931i | \(0.557140\pi\) | |||||||
\(80\) | −2327.01 | −3.25209 | ||||||||
\(81\) | −902.238 | −1.23764 | ||||||||
\(82\) | 92.6018 | 0.124709 | ||||||||
\(83\) | 351.657 | 0.465052 | 0.232526 | − | 0.972590i | \(-0.425301\pi\) | ||||
0.232526 | + | 0.972590i | \(0.425301\pi\) | |||||||
\(84\) | −2466.74 | −3.20409 | ||||||||
\(85\) | 1189.15 | 1.51743 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1073.70 | 1.32313 | ||||||||
\(88\) | −2977.20 | −3.60649 | ||||||||
\(89\) | −117.413 | −0.139840 | −0.0699202 | − | 0.997553i | \(-0.522274\pi\) | ||||
−0.0699202 | + | 0.997553i | \(0.522274\pi\) | |||||||
\(90\) | −1064.05 | −1.24622 | ||||||||
\(91\) | 828.764 | 0.954704 | ||||||||
\(92\) | 2932.05 | 3.32269 | ||||||||
\(93\) | 449.573 | 0.501274 | ||||||||
\(94\) | 2187.56 | 2.40031 | ||||||||
\(95\) | 1038.83 | 1.12192 | ||||||||
\(96\) | 3261.25 | 3.46718 | ||||||||
\(97\) | −609.540 | −0.638035 | −0.319018 | − | 0.947749i | \(-0.603353\pi\) | ||||
−0.319018 | + | 0.947749i | \(0.603353\pi\) | |||||||
\(98\) | −56.6763 | −0.0584201 | ||||||||
\(99\) | −735.230 | −0.746398 | ||||||||
\(100\) | 426.927 | 0.426927 | ||||||||
\(101\) | 641.822 | 0.632314 | 0.316157 | − | 0.948707i | \(-0.397607\pi\) | ||||
0.316157 | + | 0.948707i | \(0.397607\pi\) | |||||||
\(102\) | −3468.36 | −3.36685 | ||||||||
\(103\) | 277.249 | 0.265225 | 0.132613 | − | 0.991168i | \(-0.457663\pi\) | ||||
0.132613 | + | 0.991168i | \(0.457663\pi\) | |||||||
\(104\) | −3037.60 | −2.86405 | ||||||||
\(105\) | 1452.02 | 1.34955 | ||||||||
\(106\) | −863.650 | −0.791369 | ||||||||
\(107\) | 797.093 | 0.720167 | 0.360084 | − | 0.932920i | \(-0.382748\pi\) | ||||
0.360084 | + | 0.932920i | \(0.382748\pi\) | |||||||
\(108\) | −1420.40 | −1.26554 | ||||||||
\(109\) | 673.160 | 0.591532 | 0.295766 | − | 0.955260i | \(-0.404425\pi\) | ||||
0.295766 | + | 0.955260i | \(0.404425\pi\) | |||||||
\(110\) | 2872.84 | 2.49013 | ||||||||
\(111\) | −89.8705 | −0.0768480 | ||||||||
\(112\) | −3513.37 | −2.96413 | ||||||||
\(113\) | 1233.31 | 1.02673 | 0.513363 | − | 0.858172i | \(-0.328400\pi\) | ||||
0.513363 | + | 0.858172i | \(0.328400\pi\) | |||||||
\(114\) | −3029.93 | −2.48929 | ||||||||
\(115\) | −1725.91 | −1.39950 | ||||||||
\(116\) | 3339.46 | 2.67294 | ||||||||
\(117\) | −750.145 | −0.592743 | ||||||||
\(118\) | −2138.00 | −1.66796 | ||||||||
\(119\) | 1795.40 | 1.38306 | ||||||||
\(120\) | −5321.96 | −4.04855 | ||||||||
\(121\) | 654.064 | 0.491408 | ||||||||
\(122\) | −3772.94 | −2.79989 | ||||||||
\(123\) | 114.379 | 0.0838470 | ||||||||
\(124\) | 1398.28 | 1.01265 | ||||||||
\(125\) | 1258.10 | 0.900224 | ||||||||
\(126\) | −1606.52 | −1.13587 | ||||||||
\(127\) | 70.5831 | 0.0493168 | 0.0246584 | − | 0.999696i | \(-0.492150\pi\) | ||||
0.0246584 | + | 0.999696i | \(0.492150\pi\) | |||||||
\(128\) | 1910.97 | 1.31959 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2931.12 | 1.97751 | ||||||||
\(131\) | 276.822 | 0.184626 | 0.0923130 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923130 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(132\) | −6028.23 | −3.97493 | ||||||||
\(133\) | 1568.45 | 1.02257 | ||||||||
\(134\) | 1783.69 | 1.14991 | ||||||||
\(135\) | 836.100 | 0.533037 | ||||||||
\(136\) | −6580.55 | −4.14910 | ||||||||
\(137\) | −548.908 | −0.342309 | −0.171155 | − | 0.985244i | \(-0.554750\pi\) | ||||
−0.171155 | + | 0.985244i | \(0.554750\pi\) | |||||||
\(138\) | 5033.91 | 3.10518 | ||||||||
\(139\) | −1429.65 | −0.872385 | −0.436192 | − | 0.899853i | \(-0.643673\pi\) | ||||
−0.436192 | + | 0.899853i | \(0.643673\pi\) | |||||||
\(140\) | 4516.12 | 2.72630 | ||||||||
\(141\) | 2702.00 | 1.61383 | ||||||||
\(142\) | 2568.26 | 1.51777 | ||||||||
\(143\) | 2025.33 | 1.18438 | ||||||||
\(144\) | 3180.08 | 1.84032 | ||||||||
\(145\) | −1965.73 | −1.12583 | ||||||||
\(146\) | −6150.75 | −3.48657 | ||||||||
\(147\) | −70.0047 | −0.0392782 | ||||||||
\(148\) | −279.519 | −0.155245 | ||||||||
\(149\) | −1636.22 | −0.899624 | −0.449812 | − | 0.893123i | \(-0.648509\pi\) | ||||
−0.449812 | + | 0.893123i | \(0.648509\pi\) | |||||||
\(150\) | 732.973 | 0.398980 | ||||||||
\(151\) | 2732.46 | 1.47261 | 0.736305 | − | 0.676650i | \(-0.236569\pi\) | ||||
0.736305 | + | 0.676650i | \(0.236569\pi\) | |||||||
\(152\) | −5748.72 | −3.06765 | ||||||||
\(153\) | −1625.09 | −0.858696 | ||||||||
\(154\) | 4337.48 | 2.26964 | ||||||||
\(155\) | −823.079 | −0.426525 | ||||||||
\(156\) | −6150.53 | −3.15664 | ||||||||
\(157\) | −2181.13 | −1.10875 | −0.554374 | − | 0.832268i | \(-0.687042\pi\) | ||||
−0.554374 | + | 0.832268i | \(0.687042\pi\) | |||||||
\(158\) | −1338.92 | −0.674169 | ||||||||
\(159\) | −1066.75 | −0.532069 | ||||||||
\(160\) | −5970.70 | −2.95016 | ||||||||
\(161\) | −2605.82 | −1.27557 | ||||||||
\(162\) | −4817.81 | −2.33656 | ||||||||
\(163\) | 3651.49 | 1.75464 | 0.877320 | − | 0.479905i | \(-0.159329\pi\) | ||||
0.877320 | + | 0.479905i | \(0.159329\pi\) | |||||||
\(164\) | 355.745 | 0.169384 | ||||||||
\(165\) | 3548.44 | 1.67422 | ||||||||
\(166\) | 1877.79 | 0.877981 | ||||||||
\(167\) | 2247.21 | 1.04128 | 0.520641 | − | 0.853776i | \(-0.325693\pi\) | ||||
0.520641 | + | 0.853776i | \(0.325693\pi\) | |||||||
\(168\) | −8035.21 | −3.69006 | ||||||||
\(169\) | −130.578 | −0.0594347 | ||||||||
\(170\) | 6349.88 | 2.86478 | ||||||||
\(171\) | −1419.67 | −0.634880 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1431.95 | −0.629302 | −0.314651 | − | 0.949207i | \(-0.601887\pi\) | ||||
−0.314651 | + | 0.949207i | \(0.601887\pi\) | |||||||
\(174\) | 5733.38 | 2.49797 | ||||||||
\(175\) | −379.425 | −0.163896 | ||||||||
\(176\) | −8585.97 | −3.67723 | ||||||||
\(177\) | −2640.79 | −1.12144 | ||||||||
\(178\) | −626.969 | −0.264007 | ||||||||
\(179\) | 3963.35 | 1.65494 | 0.827472 | − | 0.561507i | \(-0.189778\pi\) | ||||
0.827472 | + | 0.561507i | \(0.189778\pi\) | |||||||
\(180\) | −4087.71 | −1.69267 | ||||||||
\(181\) | −1046.09 | −0.429588 | −0.214794 | − | 0.976659i | \(-0.568908\pi\) | ||||
−0.214794 | + | 0.976659i | \(0.568908\pi\) | |||||||
\(182\) | 4425.47 | 1.80240 | ||||||||
\(183\) | −4660.22 | −1.88248 | ||||||||
\(184\) | 9550.89 | 3.82664 | ||||||||
\(185\) | 164.535 | 0.0653885 | ||||||||
\(186\) | 2400.65 | 0.946366 | ||||||||
\(187\) | 4387.61 | 1.71580 | ||||||||
\(188\) | 8403.88 | 3.26019 | ||||||||
\(189\) | 1262.36 | 0.485838 | ||||||||
\(190\) | 5547.21 | 2.11809 | ||||||||
\(191\) | 791.007 | 0.299661 | 0.149831 | − | 0.988712i | \(-0.452127\pi\) | ||||
0.149831 | + | 0.988712i | \(0.452127\pi\) | |||||||
\(192\) | 7246.28 | 2.72372 | ||||||||
\(193\) | −315.336 | −0.117608 | −0.0588042 | − | 0.998270i | \(-0.518729\pi\) | ||||
−0.0588042 | + | 0.998270i | \(0.518729\pi\) | |||||||
\(194\) | −3254.85 | −1.20456 | ||||||||
\(195\) | 3620.43 | 1.32956 | ||||||||
\(196\) | −217.732 | −0.0793482 | ||||||||
\(197\) | −5234.95 | −1.89327 | −0.946637 | − | 0.322301i | \(-0.895544\pi\) | ||||
−0.946637 | + | 0.322301i | \(0.895544\pi\) | |||||||
\(198\) | −3926.01 | −1.40914 | ||||||||
\(199\) | −1299.62 | −0.462955 | −0.231477 | − | 0.972840i | \(-0.574356\pi\) | ||||
−0.231477 | + | 0.972840i | \(0.574356\pi\) | |||||||
\(200\) | 1390.68 | 0.491679 | ||||||||
\(201\) | 2203.16 | 0.773130 | ||||||||
\(202\) | 3427.23 | 1.19376 | ||||||||
\(203\) | −2967.90 | −1.02614 | ||||||||
\(204\) | −13324.3 | −4.57297 | ||||||||
\(205\) | −209.405 | −0.0713438 | ||||||||
\(206\) | 1480.47 | 0.500724 | ||||||||
\(207\) | 2358.62 | 0.791959 | ||||||||
\(208\) | −8760.15 | −2.92023 | ||||||||
\(209\) | 3832.99 | 1.26858 | ||||||||
\(210\) | 7753.54 | 2.54784 | ||||||||
\(211\) | −5760.12 | −1.87935 | −0.939676 | − | 0.342065i | \(-0.888874\pi\) | ||||
−0.939676 | + | 0.342065i | \(0.888874\pi\) | |||||||
\(212\) | −3317.86 | −1.07486 | ||||||||
\(213\) | 3172.24 | 1.02046 | ||||||||
\(214\) | 4256.35 | 1.35962 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4626.83 | −1.45748 | ||||||||
\(217\) | −1242.70 | −0.388756 | ||||||||
\(218\) | 3594.57 | 1.11677 | ||||||||
\(219\) | −7597.21 | −2.34416 | ||||||||
\(220\) | 11036.5 | 3.38219 | ||||||||
\(221\) | 4476.62 | 1.36258 | ||||||||
\(222\) | −479.894 | −0.145083 | ||||||||
\(223\) | −3460.12 | −1.03904 | −0.519522 | − | 0.854457i | \(-0.673890\pi\) | ||||
−0.519522 | + | 0.854457i | \(0.673890\pi\) | |||||||
\(224\) | −9014.69 | −2.68892 | ||||||||
\(225\) | 343.432 | 0.101758 | ||||||||
\(226\) | 6585.68 | 1.93837 | ||||||||
\(227\) | −6727.15 | −1.96695 | −0.983473 | − | 0.181057i | \(-0.942048\pi\) | ||||
−0.983473 | + | 0.181057i | \(0.942048\pi\) | |||||||
\(228\) | −11640.0 | −3.38104 | ||||||||
\(229\) | 3081.40 | 0.889190 | 0.444595 | − | 0.895732i | \(-0.353348\pi\) | ||||
0.444595 | + | 0.895732i | \(0.353348\pi\) | |||||||
\(230\) | −9216.10 | −2.64214 | ||||||||
\(231\) | 5357.51 | 1.52597 | ||||||||
\(232\) | 10878.0 | 3.07835 | ||||||||
\(233\) | −5100.84 | −1.43419 | −0.717097 | − | 0.696973i | \(-0.754530\pi\) | ||||
−0.717097 | + | 0.696973i | \(0.754530\pi\) | |||||||
\(234\) | −4005.66 | −1.11905 | ||||||||
\(235\) | −4946.84 | −1.37317 | ||||||||
\(236\) | −8213.51 | −2.26548 | ||||||||
\(237\) | −1653.79 | −0.453271 | ||||||||
\(238\) | 9587.18 | 2.61111 | ||||||||
\(239\) | −6634.06 | −1.79549 | −0.897744 | − | 0.440517i | \(-0.854795\pi\) | ||||
−0.897744 | + | 0.440517i | \(0.854795\pi\) | |||||||
\(240\) | −15348.0 | −4.12796 | ||||||||
\(241\) | 1508.12 | 0.403097 | 0.201548 | − | 0.979479i | \(-0.435403\pi\) | ||||
0.201548 | + | 0.979479i | \(0.435403\pi\) | |||||||
\(242\) | 3492.60 | 0.927739 | ||||||||
\(243\) | −4081.30 | −1.07743 | ||||||||
\(244\) | −14494.4 | −3.80291 | ||||||||
\(245\) | 128.165 | 0.0334210 | ||||||||
\(246\) | 610.764 | 0.158296 | ||||||||
\(247\) | 3910.75 | 1.00743 | ||||||||
\(248\) | 4554.77 | 1.16624 | ||||||||
\(249\) | 2319.39 | 0.590302 | ||||||||
\(250\) | 6718.06 | 1.69955 | ||||||||
\(251\) | 1448.36 | 0.364223 | 0.182111 | − | 0.983278i | \(-0.441707\pi\) | ||||
0.182111 | + | 0.983278i | \(0.441707\pi\) | |||||||
\(252\) | −6171.71 | −1.54278 | ||||||||
\(253\) | −6368.10 | −1.58245 | ||||||||
\(254\) | 376.903 | 0.0931062 | ||||||||
\(255\) | 7843.16 | 1.92611 | ||||||||
\(256\) | 1415.06 | 0.345474 | ||||||||
\(257\) | 4186.81 | 1.01621 | 0.508105 | − | 0.861295i | \(-0.330346\pi\) | ||||
0.508105 | + | 0.861295i | \(0.330346\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 248.419 | 0.0595984 | ||||||||
\(260\) | 11260.4 | 2.68592 | ||||||||
\(261\) | 2686.36 | 0.637094 | ||||||||
\(262\) | 1478.18 | 0.348559 | ||||||||
\(263\) | 1305.78 | 0.306152 | 0.153076 | − | 0.988214i | \(-0.451082\pi\) | ||||
0.153076 | + | 0.988214i | \(0.451082\pi\) | |||||||
\(264\) | −19636.4 | −4.57780 | ||||||||
\(265\) | 1953.01 | 0.452727 | ||||||||
\(266\) | 8375.29 | 1.93053 | ||||||||
\(267\) | −774.412 | −0.177503 | ||||||||
\(268\) | 6852.36 | 1.56185 | ||||||||
\(269\) | −1244.74 | −0.282131 | −0.141066 | − | 0.990000i | \(-0.545053\pi\) | ||||
−0.141066 | + | 0.990000i | \(0.545053\pi\) | |||||||
\(270\) | 4464.64 | 1.00633 | ||||||||
\(271\) | 1989.22 | 0.445891 | 0.222945 | − | 0.974831i | \(-0.428433\pi\) | ||||
0.222945 | + | 0.974831i | \(0.428433\pi\) | |||||||
\(272\) | −18977.7 | −4.23048 | ||||||||
\(273\) | 5466.20 | 1.21183 | ||||||||
\(274\) | −2931.08 | −0.646253 | ||||||||
\(275\) | −927.240 | −0.203326 | ||||||||
\(276\) | 19338.6 | 4.21756 | ||||||||
\(277\) | 1174.72 | 0.254809 | 0.127404 | − | 0.991851i | \(-0.459335\pi\) | ||||
0.127404 | + | 0.991851i | \(0.459335\pi\) | |||||||
\(278\) | −7634.11 | −1.64699 | ||||||||
\(279\) | 1124.82 | 0.241365 | ||||||||
\(280\) | 14710.9 | 3.13980 | ||||||||
\(281\) | −1511.73 | −0.320934 | −0.160467 | − | 0.987041i | \(-0.551300\pi\) | ||||
−0.160467 | + | 0.987041i | \(0.551300\pi\) | |||||||
\(282\) | 14428.3 | 3.04678 | ||||||||
\(283\) | 5919.78 | 1.24344 | 0.621722 | − | 0.783238i | \(-0.286434\pi\) | ||||
0.621722 | + | 0.783238i | \(0.286434\pi\) | |||||||
\(284\) | 9866.41 | 2.06149 | ||||||||
\(285\) | 6851.74 | 1.42408 | ||||||||
\(286\) | 10815.0 | 2.23602 | ||||||||
\(287\) | −316.164 | −0.0650264 | ||||||||
\(288\) | 8159.52 | 1.66946 | ||||||||
\(289\) | 4784.99 | 0.973945 | ||||||||
\(290\) | −10496.7 | −2.12547 | ||||||||
\(291\) | −4020.28 | −0.809873 | ||||||||
\(292\) | −23629.1 | −4.73558 | ||||||||
\(293\) | −5612.12 | −1.11899 | −0.559494 | − | 0.828834i | \(-0.689005\pi\) | ||||
−0.559494 | + | 0.828834i | \(0.689005\pi\) | |||||||
\(294\) | −373.814 | −0.0741540 | ||||||||
\(295\) | 4834.77 | 0.954208 | ||||||||
\(296\) | −910.508 | −0.178791 | ||||||||
\(297\) | 3084.96 | 0.602719 | ||||||||
\(298\) | −8737.13 | −1.69842 | ||||||||
\(299\) | −6497.29 | −1.25668 | ||||||||
\(300\) | 2815.84 | 0.541908 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 14590.9 | 2.78017 | ||||||||
\(303\) | 4233.20 | 0.802611 | ||||||||
\(304\) | −16578.8 | −3.12782 | ||||||||
\(305\) | 8531.94 | 1.60176 | ||||||||
\(306\) | −8677.71 | −1.62115 | ||||||||
\(307\) | −5016.73 | −0.932638 | −0.466319 | − | 0.884617i | \(-0.654420\pi\) | ||||
−0.466319 | + | 0.884617i | \(0.654420\pi\) | |||||||
\(308\) | 16663.1 | 3.08270 | ||||||||
\(309\) | 1828.63 | 0.336657 | ||||||||
\(310\) | −4395.11 | −0.805244 | ||||||||
\(311\) | 1101.33 | 0.200806 | 0.100403 | − | 0.994947i | \(-0.467987\pi\) | ||||
0.100403 | + | 0.994947i | \(0.467987\pi\) | |||||||
\(312\) | −20034.8 | −3.63541 | ||||||||
\(313\) | −6986.81 | −1.26172 | −0.630859 | − | 0.775898i | \(-0.717297\pi\) | ||||
−0.630859 | + | 0.775898i | \(0.717297\pi\) | |||||||
\(314\) | −11646.9 | −2.09323 | ||||||||
\(315\) | 3632.90 | 0.649811 | ||||||||
\(316\) | −5143.68 | −0.915680 | ||||||||
\(317\) | 8578.02 | 1.51984 | 0.759920 | − | 0.650016i | \(-0.225238\pi\) | ||||
0.759920 | + | 0.650016i | \(0.225238\pi\) | |||||||
\(318\) | −5696.29 | −1.00450 | ||||||||
\(319\) | −7252.96 | −1.27300 | ||||||||
\(320\) | −13266.5 | −2.31756 | ||||||||
\(321\) | 5257.31 | 0.914125 | ||||||||
\(322\) | −13914.7 | −2.40818 | ||||||||
\(323\) | 8472.10 | 1.45944 | ||||||||
\(324\) | −18508.4 | −3.17360 | ||||||||
\(325\) | −946.051 | −0.161469 | ||||||||
\(326\) | 19498.4 | 3.31262 | ||||||||
\(327\) | 4439.90 | 0.750846 | ||||||||
\(328\) | 1158.81 | 0.195075 | ||||||||
\(329\) | −7468.84 | −1.25158 | ||||||||
\(330\) | 18948.1 | 3.16079 | ||||||||
\(331\) | −1403.92 | −0.233130 | −0.116565 | − | 0.993183i | \(-0.537188\pi\) | ||||
−0.116565 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(332\) | 7213.86 | 1.19251 | ||||||||
\(333\) | −224.853 | −0.0370026 | ||||||||
\(334\) | 11999.7 | 1.96586 | ||||||||
\(335\) | −4033.56 | −0.657841 | ||||||||
\(336\) | −23172.8 | −3.76244 | ||||||||
\(337\) | −9324.11 | −1.50717 | −0.753585 | − | 0.657350i | \(-0.771677\pi\) | ||||
−0.753585 | + | 0.657350i | \(0.771677\pi\) | |||||||
\(338\) | −697.267 | −0.112208 | ||||||||
\(339\) | 8134.42 | 1.30325 | ||||||||
\(340\) | 24394.1 | 3.89105 | ||||||||
\(341\) | −3036.92 | −0.482282 | ||||||||
\(342\) | −7580.79 | −1.19860 | ||||||||
\(343\) | 6446.90 | 1.01487 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11383.4 | −1.77641 | ||||||||
\(346\) | −7646.39 | −1.18807 | ||||||||
\(347\) | 8069.15 | 1.24834 | 0.624171 | − | 0.781287i | \(-0.285437\pi\) | ||||
0.624171 | + | 0.781287i | \(0.285437\pi\) | |||||||
\(348\) | 22025.8 | 3.39283 | ||||||||
\(349\) | 1789.13 | 0.274412 | 0.137206 | − | 0.990543i | \(-0.456188\pi\) | ||||
0.137206 | + | 0.990543i | \(0.456188\pi\) | |||||||
\(350\) | −2026.07 | −0.309423 | ||||||||
\(351\) | 3147.54 | 0.478642 | ||||||||
\(352\) | −22030.1 | −3.33582 | ||||||||
\(353\) | 10988.6 | 1.65683 | 0.828416 | − | 0.560113i | \(-0.189242\pi\) | ||||
0.828416 | + | 0.560113i | \(0.189242\pi\) | |||||||
\(354\) | −14101.4 | −2.11718 | ||||||||
\(355\) | −5807.74 | −0.868289 | ||||||||
\(356\) | −2408.61 | −0.358584 | ||||||||
\(357\) | 11841.8 | 1.75556 | ||||||||
\(358\) | 21163.7 | 3.12440 | ||||||||
\(359\) | −7248.69 | −1.06566 | −0.532829 | − | 0.846223i | \(-0.678871\pi\) | ||||
−0.532829 | + | 0.846223i | \(0.678871\pi\) | |||||||
\(360\) | −13315.4 | −1.94939 | ||||||||
\(361\) | 542.172 | 0.0790453 | ||||||||
\(362\) | −5585.96 | −0.811027 | ||||||||
\(363\) | 4313.95 | 0.623756 | ||||||||
\(364\) | 17001.2 | 2.44809 | ||||||||
\(365\) | 13909.0 | 1.99460 | ||||||||
\(366\) | −24884.8 | −3.55397 | ||||||||
\(367\) | −6760.61 | −0.961583 | −0.480791 | − | 0.876835i | \(-0.659651\pi\) | ||||
−0.480791 | + | 0.876835i | \(0.659651\pi\) | |||||||
\(368\) | 27543.9 | 3.90169 | ||||||||
\(369\) | 286.172 | 0.0403726 | ||||||||
\(370\) | 878.592 | 0.123448 | ||||||||
\(371\) | 2948.70 | 0.412639 | ||||||||
\(372\) | 9222.49 | 1.28539 | ||||||||
\(373\) | 2767.85 | 0.384220 | 0.192110 | − | 0.981373i | \(-0.438467\pi\) | ||||
0.192110 | + | 0.981373i | \(0.438467\pi\) | |||||||
\(374\) | 23429.1 | 3.23928 | ||||||||
\(375\) | 8297.93 | 1.14268 | ||||||||
\(376\) | 27374.9 | 3.75466 | ||||||||
\(377\) | −7400.10 | −1.01094 | ||||||||
\(378\) | 6740.81 | 0.917222 | ||||||||
\(379\) | 9178.35 | 1.24396 | 0.621979 | − | 0.783034i | \(-0.286329\pi\) | ||||
0.621979 | + | 0.783034i | \(0.286329\pi\) | |||||||
\(380\) | 21310.5 | 2.87686 | ||||||||
\(381\) | 465.538 | 0.0625990 | ||||||||
\(382\) | 4223.85 | 0.565736 | ||||||||
\(383\) | 6592.70 | 0.879559 | 0.439780 | − | 0.898106i | \(-0.355057\pi\) | ||||
0.439780 | + | 0.898106i | \(0.355057\pi\) | |||||||
\(384\) | 12604.0 | 1.67499 | ||||||||
\(385\) | −9808.55 | −1.29842 | ||||||||
\(386\) | −1683.85 | −0.222035 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12504.0 | −1.63607 | ||||||||
\(389\) | −12393.0 | −1.61530 | −0.807648 | − | 0.589665i | \(-0.799260\pi\) | ||||
−0.807648 | + | 0.589665i | \(0.799260\pi\) | |||||||
\(390\) | 19332.5 | 2.51010 | ||||||||
\(391\) | −14075.5 | −1.82053 | ||||||||
\(392\) | −709.242 | −0.0913829 | ||||||||
\(393\) | 1825.81 | 0.234350 | ||||||||
\(394\) | −27953.8 | −3.57435 | ||||||||
\(395\) | 3027.76 | 0.385679 | ||||||||
\(396\) | −15082.4 | −1.91394 | ||||||||
\(397\) | −5802.01 | −0.733488 | −0.366744 | − | 0.930322i | \(-0.619527\pi\) | ||||
−0.366744 | + | 0.930322i | \(0.619527\pi\) | |||||||
\(398\) | −6939.79 | −0.874021 | ||||||||
\(399\) | 10344.9 | 1.29798 | ||||||||
\(400\) | 4010.58 | 0.501322 | ||||||||
\(401\) | −11595.0 | −1.44396 | −0.721980 | − | 0.691914i | \(-0.756768\pi\) | ||||
−0.721980 | + | 0.691914i | \(0.756768\pi\) | |||||||
\(402\) | 11764.5 | 1.45961 | ||||||||
\(403\) | −3098.53 | −0.382999 | ||||||||
\(404\) | 13166.3 | 1.62140 | ||||||||
\(405\) | 10894.7 | 1.33670 | ||||||||
\(406\) | −15848.1 | −1.93726 | ||||||||
\(407\) | 607.086 | 0.0739364 | ||||||||
\(408\) | −43402.7 | −5.26655 | ||||||||
\(409\) | 6410.71 | 0.775035 | 0.387517 | − | 0.921862i | \(-0.373333\pi\) | ||||
0.387517 | + | 0.921862i | \(0.373333\pi\) | |||||||
\(410\) | −1118.19 | −0.134691 | ||||||||
\(411\) | −3620.38 | −0.434502 | ||||||||
\(412\) | 5687.47 | 0.680100 | ||||||||
\(413\) | 7299.64 | 0.869714 | ||||||||
\(414\) | 12594.7 | 1.49515 | ||||||||
\(415\) | −4246.34 | −0.502277 | ||||||||
\(416\) | −22477.0 | −2.64910 | ||||||||
\(417\) | −9429.42 | −1.10734 | ||||||||
\(418\) | 20467.6 | 2.39498 | ||||||||
\(419\) | 12824.3 | 1.49524 | 0.747620 | − | 0.664127i | \(-0.231196\pi\) | ||||
0.747620 | + | 0.664127i | \(0.231196\pi\) | |||||||
\(420\) | 29786.6 | 3.46056 | ||||||||
\(421\) | 1184.03 | 0.137069 | 0.0685347 | − | 0.997649i | \(-0.478168\pi\) | ||||
0.0685347 | + | 0.997649i | \(0.478168\pi\) | |||||||
\(422\) | −30758.2 | −3.54807 | ||||||||
\(423\) | 6760.32 | 0.777064 | ||||||||
\(424\) | −10807.6 | −1.23789 | ||||||||
\(425\) | −2049.49 | −0.233917 | ||||||||
\(426\) | 16939.2 | 1.92655 | ||||||||
\(427\) | 12881.7 | 1.45993 | ||||||||
\(428\) | 16351.5 | 1.84668 | ||||||||
\(429\) | 13358.3 | 1.50337 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5668.01 | −0.633453 | −0.316726 | − | 0.948517i | \(-0.602584\pi\) | ||||
−0.316726 | + | 0.948517i | \(0.602584\pi\) | |||||||
\(432\) | −13343.3 | −1.48607 | ||||||||
\(433\) | −6623.04 | −0.735064 | −0.367532 | − | 0.930011i | \(-0.619797\pi\) | ||||
−0.367532 | + | 0.930011i | \(0.619797\pi\) | |||||||
\(434\) | −6635.83 | −0.733940 | ||||||||
\(435\) | −12965.2 | −1.42904 | ||||||||
\(436\) | 13809.1 | 1.51683 | ||||||||
\(437\) | −12296.3 | −1.34602 | ||||||||
\(438\) | −40567.9 | −4.42559 | ||||||||
\(439\) | −5719.79 | −0.621847 | −0.310923 | − | 0.950435i | \(-0.600638\pi\) | ||||
−0.310923 | + | 0.950435i | \(0.600638\pi\) | |||||||
\(440\) | 35950.5 | 3.89516 | ||||||||
\(441\) | −175.149 | −0.0189126 | ||||||||
\(442\) | 23904.4 | 2.57244 | ||||||||
\(443\) | 9082.79 | 0.974123 | 0.487061 | − | 0.873368i | \(-0.338069\pi\) | ||||
0.487061 | + | 0.873368i | \(0.338069\pi\) | |||||||
\(444\) | −1843.59 | −0.197057 | ||||||||
\(445\) | 1417.80 | 0.151034 | ||||||||
\(446\) | −18476.5 | −1.96163 | ||||||||
\(447\) | −10791.8 | −1.14191 | ||||||||
\(448\) | −20030.0 | −2.11235 | ||||||||
\(449\) | −4971.70 | −0.522559 | −0.261279 | − | 0.965263i | \(-0.584144\pi\) | ||||
−0.261279 | + | 0.965263i | \(0.584144\pi\) | |||||||
\(450\) | 1833.87 | 0.192110 | ||||||||
\(451\) | −772.642 | −0.0806702 | ||||||||
\(452\) | 25300.0 | 2.63277 | ||||||||
\(453\) | 18022.2 | 1.86922 | ||||||||
\(454\) | −35921.9 | −3.71343 | ||||||||
\(455\) | −10007.5 | −1.03112 | ||||||||
\(456\) | −37916.3 | −3.89384 | ||||||||
\(457\) | 12938.0 | 1.32432 | 0.662158 | − | 0.749365i | \(-0.269641\pi\) | ||||
0.662158 | + | 0.749365i | \(0.269641\pi\) | |||||||
\(458\) | 16454.2 | 1.67872 | ||||||||
\(459\) | 6818.73 | 0.693401 | ||||||||
\(460\) | −35405.2 | −3.58864 | ||||||||
\(461\) | −10910.1 | −1.10224 | −0.551121 | − | 0.834425i | \(-0.685800\pi\) | ||||
−0.551121 | + | 0.834425i | \(0.685800\pi\) | |||||||
\(462\) | 28608.3 | 2.88090 | ||||||||
\(463\) | −5850.83 | −0.587281 | −0.293641 | − | 0.955916i | \(-0.594867\pi\) | ||||
−0.293641 | + | 0.955916i | \(0.594867\pi\) | |||||||
\(464\) | 31371.1 | 3.13873 | ||||||||
\(465\) | −5428.70 | −0.541398 | ||||||||
\(466\) | −27237.7 | −2.70764 | ||||||||
\(467\) | −16089.6 | −1.59430 | −0.797149 | − | 0.603782i | \(-0.793660\pi\) | ||||
−0.797149 | + | 0.603782i | \(0.793660\pi\) | |||||||
\(468\) | −15388.4 | −1.51993 | ||||||||
\(469\) | −6089.95 | −0.599590 | ||||||||
\(470\) | −26415.3 | −2.59244 | ||||||||
\(471\) | −14385.9 | −1.40736 | ||||||||
\(472\) | −26754.8 | −2.60909 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −8830.98 | −0.855739 | ||||||||
\(475\) | −1790.42 | −0.172948 | ||||||||
\(476\) | 36830.8 | 3.54650 | ||||||||
\(477\) | −2668.98 | −0.256193 | ||||||||
\(478\) | −35424.8 | −3.38974 | ||||||||
\(479\) | −5637.28 | −0.537732 | −0.268866 | − | 0.963178i | \(-0.586649\pi\) | ||||
−0.268866 | + | 0.963178i | \(0.586649\pi\) | |||||||
\(480\) | −39380.4 | −3.74471 | ||||||||
\(481\) | 619.401 | 0.0587157 | ||||||||
\(482\) | 8053.10 | 0.761014 | ||||||||
\(483\) | −17186.9 | −1.61912 | ||||||||
\(484\) | 13417.4 | 1.26009 | ||||||||
\(485\) | 7360.34 | 0.689105 | ||||||||
\(486\) | −21793.5 | −2.03410 | ||||||||
\(487\) | −15208.3 | −1.41510 | −0.707548 | − | 0.706665i | \(-0.750199\pi\) | ||||
−0.707548 | + | 0.706665i | \(0.750199\pi\) | |||||||
\(488\) | −47214.3 | −4.37969 | ||||||||
\(489\) | 24083.7 | 2.22721 | ||||||||
\(490\) | 684.380 | 0.0630962 | ||||||||
\(491\) | 10064.5 | 0.925059 | 0.462530 | − | 0.886604i | \(-0.346942\pi\) | ||||
0.462530 | + | 0.886604i | \(0.346942\pi\) | |||||||
\(492\) | 2346.35 | 0.215004 | ||||||||
\(493\) | −16031.3 | −1.46453 | ||||||||
\(494\) | 20882.8 | 1.90194 | ||||||||
\(495\) | 8878.08 | 0.806141 | ||||||||
\(496\) | 13135.5 | 1.18912 | ||||||||
\(497\) | −8768.64 | −0.791403 | ||||||||
\(498\) | 12385.2 | 1.11444 | ||||||||
\(499\) | −179.798 | −0.0161300 | −0.00806501 | − | 0.999967i | \(-0.502567\pi\) | ||||
−0.00806501 | + | 0.999967i | \(0.502567\pi\) | |||||||
\(500\) | 25808.6 | 2.30839 | ||||||||
\(501\) | 14821.7 | 1.32172 | ||||||||
\(502\) | 7734.03 | 0.687623 | ||||||||
\(503\) | 4805.81 | 0.426005 | 0.213002 | − | 0.977052i | \(-0.431676\pi\) | ||||
0.213002 | + | 0.977052i | \(0.431676\pi\) | |||||||
\(504\) | −20103.8 | −1.77678 | ||||||||
\(505\) | −7750.16 | −0.682926 | ||||||||
\(506\) | −34004.6 | −2.98753 | ||||||||
\(507\) | −861.241 | −0.0754420 | ||||||||
\(508\) | 1447.94 | 0.126460 | ||||||||
\(509\) | 18265.8 | 1.59060 | 0.795302 | − | 0.606213i | \(-0.207312\pi\) | ||||
0.795302 | + | 0.606213i | \(0.207312\pi\) | |||||||
\(510\) | 41881.3 | 3.63634 | ||||||||
\(511\) | 21000.1 | 1.81798 | ||||||||
\(512\) | −7731.58 | −0.667364 | ||||||||
\(513\) | 5956.79 | 0.512668 | ||||||||
\(514\) | 22356.9 | 1.91852 | ||||||||
\(515\) | −3347.85 | −0.286455 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18252.3 | −1.55268 | ||||||||
\(518\) | 1326.52 | 0.112517 | ||||||||
\(519\) | −9444.58 | −0.798788 | ||||||||
\(520\) | 36679.8 | 3.09330 | ||||||||
\(521\) | −10272.0 | −0.863772 | −0.431886 | − | 0.901928i | \(-0.642152\pi\) | ||||
−0.431886 | + | 0.901928i | \(0.642152\pi\) | |||||||
\(522\) | 14344.7 | 1.20278 | ||||||||
\(523\) | 3569.87 | 0.298470 | 0.149235 | − | 0.988802i | \(-0.452319\pi\) | ||||
0.149235 | + | 0.988802i | \(0.452319\pi\) | |||||||
\(524\) | 5678.69 | 0.473425 | ||||||||
\(525\) | −2502.54 | −0.208038 | ||||||||
\(526\) | 6972.68 | 0.577991 | ||||||||
\(527\) | −6712.53 | −0.554843 | ||||||||
\(528\) | −56629.7 | −4.66759 | ||||||||
\(529\) | 8261.91 | 0.679043 | ||||||||
\(530\) | 10428.8 | 0.854712 | ||||||||
\(531\) | −6607.18 | −0.539976 | ||||||||
\(532\) | 32175.1 | 2.62212 | ||||||||
\(533\) | −788.316 | −0.0640633 | ||||||||
\(534\) | −4135.24 | −0.335111 | ||||||||
\(535\) | −9625.09 | −0.777811 | ||||||||
\(536\) | 22321.0 | 1.79873 | ||||||||
\(537\) | 26140.7 | 2.10066 | ||||||||
\(538\) | −6646.73 | −0.532641 | ||||||||
\(539\) | 472.890 | 0.0377900 | ||||||||
\(540\) | 17151.7 | 1.36683 | ||||||||
\(541\) | 23215.7 | 1.84496 | 0.922478 | − | 0.386050i | \(-0.126161\pi\) | ||||
0.922478 | + | 0.386050i | \(0.126161\pi\) | |||||||
\(542\) | 10622.1 | 0.841806 | ||||||||
\(543\) | −6899.60 | −0.545286 | ||||||||
\(544\) | −48693.4 | −3.83771 | ||||||||
\(545\) | −8128.57 | −0.638880 | ||||||||
\(546\) | 29188.6 | 2.28784 | ||||||||
\(547\) | −5631.22 | −0.440171 | −0.220086 | − | 0.975481i | \(-0.570634\pi\) | ||||
−0.220086 | + | 0.975481i | \(0.570634\pi\) | |||||||
\(548\) | −11260.3 | −0.877763 | ||||||||
\(549\) | −11659.7 | −0.906419 | ||||||||
\(550\) | −4951.32 | −0.383863 | ||||||||
\(551\) | −14004.9 | −1.08281 | ||||||||
\(552\) | 62993.9 | 4.85724 | ||||||||
\(553\) | 4571.38 | 0.351528 | ||||||||
\(554\) | 6272.81 | 0.481058 | ||||||||
\(555\) | 1085.21 | 0.0829992 | ||||||||
\(556\) | −29327.7 | −2.23700 | ||||||||
\(557\) | −23630.2 | −1.79756 | −0.898782 | − | 0.438397i | \(-0.855547\pi\) | ||||
−0.898782 | + | 0.438397i | \(0.855547\pi\) | |||||||
\(558\) | 6006.34 | 0.455678 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 42424.8 | 3.20138 | ||||||||
\(561\) | 28938.9 | 2.17790 | ||||||||
\(562\) | −8072.42 | −0.605898 | ||||||||
\(563\) | −10592.6 | −0.792942 | −0.396471 | − | 0.918047i | \(-0.629765\pi\) | ||||
−0.396471 | + | 0.918047i | \(0.629765\pi\) | |||||||
\(564\) | 55428.6 | 4.13824 | ||||||||
\(565\) | −14892.5 | −1.10891 | ||||||||
\(566\) | 31610.7 | 2.34752 | ||||||||
\(567\) | 16449.1 | 1.21834 | ||||||||
\(568\) | 32139.0 | 2.37416 | ||||||||
\(569\) | 5540.16 | 0.408182 | 0.204091 | − | 0.978952i | \(-0.434576\pi\) | ||||
0.204091 | + | 0.978952i | \(0.434576\pi\) | |||||||
\(570\) | 36587.2 | 2.68854 | ||||||||
\(571\) | 4608.09 | 0.337728 | 0.168864 | − | 0.985639i | \(-0.445990\pi\) | ||||
0.168864 | + | 0.985639i | \(0.445990\pi\) | |||||||
\(572\) | 41547.5 | 3.03704 | ||||||||
\(573\) | 5217.17 | 0.380367 | ||||||||
\(574\) | −1688.27 | −0.122765 | ||||||||
\(575\) | 2974.59 | 0.215738 | ||||||||
\(576\) | 18129.9 | 1.31148 | ||||||||
\(577\) | −6911.91 | −0.498694 | −0.249347 | − | 0.968414i | \(-0.580216\pi\) | ||||
−0.249347 | + | 0.968414i | \(0.580216\pi\) | |||||||
\(578\) | 25551.1 | 1.83873 | ||||||||
\(579\) | −2079.83 | −0.149283 | ||||||||
\(580\) | −40324.8 | −2.88689 | ||||||||
\(581\) | −6411.22 | −0.457801 | ||||||||
\(582\) | −21467.7 | −1.52898 | ||||||||
\(583\) | 7206.04 | 0.511910 | ||||||||
\(584\) | −76969.9 | −5.45383 | ||||||||
\(585\) | 9058.19 | 0.640188 | ||||||||
\(586\) | −29967.8 | −2.11256 | ||||||||
\(587\) | 2894.60 | 0.203531 | 0.101766 | − | 0.994808i | \(-0.467551\pi\) | ||||
0.101766 | + | 0.994808i | \(0.467551\pi\) | |||||||
\(588\) | −1436.07 | −0.100719 | ||||||||
\(589\) | −5864.02 | −0.410226 | ||||||||
\(590\) | 25816.9 | 1.80147 | ||||||||
\(591\) | −34527.7 | −2.40318 | ||||||||
\(592\) | −2625.82 | −0.182298 | ||||||||
\(593\) | 284.980 | 0.0197348 | 0.00986738 | − | 0.999951i | \(-0.496859\pi\) | ||||
0.00986738 | + | 0.999951i | \(0.496859\pi\) | |||||||
\(594\) | 16473.2 | 1.13788 | ||||||||
\(595\) | −21680.0 | −1.49377 | ||||||||
\(596\) | −33565.2 | −2.30685 | ||||||||
\(597\) | −8571.81 | −0.587639 | ||||||||
\(598\) | −34694.5 | −2.37251 | ||||||||
\(599\) | −17636.8 | −1.20304 | −0.601521 | − | 0.798857i | \(-0.705438\pi\) | ||||
−0.601521 | + | 0.798857i | \(0.705438\pi\) | |||||||
\(600\) | 9172.35 | 0.624099 | ||||||||
\(601\) | 8368.50 | 0.567984 | 0.283992 | − | 0.958827i | \(-0.408341\pi\) | ||||
0.283992 | + | 0.958827i | \(0.408341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5512.23 | 0.372265 | ||||||||
\(604\) | 56053.3 | 3.77612 | ||||||||
\(605\) | −7897.99 | −0.530742 | ||||||||
\(606\) | 22604.6 | 1.51527 | ||||||||
\(607\) | −17771.6 | −1.18835 | −0.594175 | − | 0.804336i | \(-0.702521\pi\) | ||||
−0.594175 | + | 0.804336i | \(0.702521\pi\) | |||||||
\(608\) | −42538.2 | −2.83742 | ||||||||
\(609\) | −19575.1 | −1.30250 | ||||||||
\(610\) | 45559.2 | 3.02400 | ||||||||
\(611\) | −18622.6 | −1.23305 | ||||||||
\(612\) | −33336.9 | −2.20190 | ||||||||
\(613\) | −15578.5 | −1.02645 | −0.513223 | − | 0.858255i | \(-0.671549\pi\) | ||||
−0.513223 | + | 0.858255i | \(0.671549\pi\) | |||||||
\(614\) | −26788.5 | −1.76074 | ||||||||
\(615\) | −1381.15 | −0.0905584 | ||||||||
\(616\) | 54278.8 | 3.55025 | ||||||||
\(617\) | 17840.6 | 1.16407 | 0.582037 | − | 0.813162i | \(-0.302256\pi\) | ||||
0.582037 | + | 0.813162i | \(0.302256\pi\) | |||||||
\(618\) | 9764.58 | 0.635581 | ||||||||
\(619\) | −9101.50 | −0.590986 | −0.295493 | − | 0.955345i | \(-0.595484\pi\) | ||||
−0.295493 | + | 0.955345i | \(0.595484\pi\) | |||||||
\(620\) | −16884.6 | −1.09371 | ||||||||
\(621\) | −9896.58 | −0.639510 | ||||||||
\(622\) | 5880.94 | 0.379106 | ||||||||
\(623\) | 2140.62 | 0.137660 | ||||||||
\(624\) | −57778.5 | −3.70672 | ||||||||
\(625\) | −17793.3 | −1.13877 | ||||||||
\(626\) | −37308.4 | −2.38202 | ||||||||
\(627\) | 25280.9 | 1.61024 | ||||||||
\(628\) | −44743.6 | −2.84309 | ||||||||
\(629\) | 1341.85 | 0.0850604 | ||||||||
\(630\) | 19399.1 | 1.22679 | ||||||||
\(631\) | 25799.9 | 1.62770 | 0.813850 | − | 0.581075i | \(-0.197368\pi\) | ||||
0.813850 | + | 0.581075i | \(0.197368\pi\) | |||||||
\(632\) | −16755.1 | −1.05456 | ||||||||
\(633\) | −37991.5 | −2.38551 | ||||||||
\(634\) | 45805.3 | 2.86934 | ||||||||
\(635\) | −852.308 | −0.0532643 | ||||||||
\(636\) | −21883.3 | −1.36435 | ||||||||
\(637\) | 482.484 | 0.0300105 | ||||||||
\(638\) | −38729.7 | −2.40333 | ||||||||
\(639\) | 7936.82 | 0.491355 | ||||||||
\(640\) | −23075.5 | −1.42521 | ||||||||
\(641\) | 17234.5 | 1.06197 | 0.530984 | − | 0.847382i | \(-0.321822\pi\) | ||||
0.530984 | + | 0.847382i | \(0.321822\pi\) | |||||||
\(642\) | 28073.2 | 1.72579 | ||||||||
\(643\) | 1598.30 | 0.0980263 | 0.0490131 | − | 0.998798i | \(-0.484392\pi\) | ||||
0.0490131 | + | 0.998798i | \(0.484392\pi\) | |||||||
\(644\) | −53455.5 | −3.27087 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 45239.7 | 2.75531 | ||||||||
\(647\) | −15691.0 | −0.953443 | −0.476722 | − | 0.879054i | \(-0.658175\pi\) | ||||
−0.476722 | + | 0.879054i | \(0.658175\pi\) | |||||||
\(648\) | −60289.6 | −3.65494 | ||||||||
\(649\) | 17838.9 | 1.07895 | ||||||||
\(650\) | −5051.76 | −0.304841 | ||||||||
\(651\) | −8196.37 | −0.493458 | ||||||||
\(652\) | 74906.2 | 4.49932 | ||||||||
\(653\) | 27692.4 | 1.65955 | 0.829776 | − | 0.558097i | \(-0.188468\pi\) | ||||
0.829776 | + | 0.558097i | \(0.188468\pi\) | |||||||
\(654\) | 23708.3 | 1.41754 | ||||||||
\(655\) | −3342.69 | −0.199404 | ||||||||
\(656\) | 3341.90 | 0.198901 | ||||||||
\(657\) | −19007.9 | −1.12872 | ||||||||
\(658\) | −39882.4 | −2.36288 | ||||||||
\(659\) | −7256.63 | −0.428950 | −0.214475 | − | 0.976729i | \(-0.568804\pi\) | ||||
−0.214475 | + | 0.976729i | \(0.568804\pi\) | |||||||
\(660\) | 72792.4 | 4.29309 | ||||||||
\(661\) | 9023.69 | 0.530985 | 0.265492 | − | 0.964113i | \(-0.414465\pi\) | ||||
0.265492 | + | 0.964113i | \(0.414465\pi\) | |||||||
\(662\) | −7496.69 | −0.440131 | ||||||||
\(663\) | 29526.0 | 1.72956 | ||||||||
\(664\) | 23498.5 | 1.37337 | ||||||||
\(665\) | −18939.5 | −1.10442 | ||||||||
\(666\) | −1200.68 | −0.0698579 | ||||||||
\(667\) | 23267.6 | 1.35071 | ||||||||
\(668\) | 46099.0 | 2.67010 | ||||||||
\(669\) | −22821.6 | −1.31888 | ||||||||
\(670\) | −21538.5 | −1.24195 | ||||||||
\(671\) | 31480.3 | 1.81115 | ||||||||
\(672\) | −59457.3 | −3.41312 | ||||||||
\(673\) | −7238.86 | −0.414617 | −0.207309 | − | 0.978276i | \(-0.566470\pi\) | ||||
−0.207309 | + | 0.978276i | \(0.566470\pi\) | |||||||
\(674\) | −49789.3 | −2.84542 | ||||||||
\(675\) | −1441.01 | −0.0821697 | ||||||||
\(676\) | −2678.67 | −0.152405 | ||||||||
\(677\) | −16437.0 | −0.933122 | −0.466561 | − | 0.884489i | \(-0.654507\pi\) | ||||
−0.466561 | + | 0.884489i | \(0.654507\pi\) | |||||||
\(678\) | 43436.5 | 2.46043 | ||||||||
\(679\) | 11112.8 | 0.628086 | ||||||||
\(680\) | 79461.7 | 4.48120 | ||||||||
\(681\) | −44369.6 | −2.49669 | ||||||||
\(682\) | −16216.7 | −0.910510 | ||||||||
\(683\) | −16644.8 | −0.932498 | −0.466249 | − | 0.884654i | \(-0.654395\pi\) | ||||
−0.466249 | + | 0.884654i | \(0.654395\pi\) | |||||||
\(684\) | −29122.9 | −1.62798 | ||||||||
\(685\) | 6628.20 | 0.369709 | ||||||||
\(686\) | 34425.4 | 1.91599 | ||||||||
\(687\) | 20323.7 | 1.12867 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7352.23 | 0.406528 | ||||||||
\(690\) | −60785.7 | −3.35373 | ||||||||
\(691\) | 20899.8 | 1.15060 | 0.575301 | − | 0.817942i | \(-0.304885\pi\) | ||||
0.575301 | + | 0.817942i | \(0.304885\pi\) | |||||||
\(692\) | −29374.9 | −1.61368 | ||||||||
\(693\) | 13404.3 | 0.734758 | ||||||||
\(694\) | 43088.0 | 2.35677 | ||||||||
\(695\) | 17263.4 | 0.942213 | ||||||||
\(696\) | 71747.0 | 3.90742 | ||||||||
\(697\) | −1707.78 | −0.0928074 | ||||||||
\(698\) | 9553.65 | 0.518067 | ||||||||
\(699\) | −33643.1 | −1.82046 | ||||||||
\(700\) | −7783.50 | −0.420269 | ||||||||
\(701\) | −31205.4 | −1.68133 | −0.840664 | − | 0.541557i | \(-0.817835\pi\) | ||||
−0.840664 | + | 0.541557i | \(0.817835\pi\) | |||||||
\(702\) | 16807.4 | 0.903638 | ||||||||
\(703\) | 1172.23 | 0.0628898 | ||||||||
\(704\) | −48949.5 | −2.62053 | ||||||||
\(705\) | −32627.4 | −1.74300 | ||||||||
\(706\) | 58677.2 | 3.12797 | ||||||||
\(707\) | −11701.4 | −0.622454 | ||||||||
\(708\) | −54173.0 | −2.87563 | ||||||||
\(709\) | 17422.0 | 0.922845 | 0.461422 | − | 0.887181i | \(-0.347339\pi\) | ||||
0.461422 | + | 0.887181i | \(0.347339\pi\) | |||||||
\(710\) | −31012.4 | −1.63926 | ||||||||
\(711\) | −4137.73 | −0.218252 | ||||||||
\(712\) | −7845.83 | −0.412970 | ||||||||
\(713\) | 9742.45 | 0.511722 | ||||||||
\(714\) | 63233.2 | 3.31435 | ||||||||
\(715\) | −24456.4 | −1.27919 | ||||||||
\(716\) | 81303.8 | 4.24367 | ||||||||
\(717\) | −43755.6 | −2.27906 | ||||||||
\(718\) | −38706.9 | −2.01188 | ||||||||
\(719\) | −9699.27 | −0.503090 | −0.251545 | − | 0.967846i | \(-0.580939\pi\) | ||||
−0.251545 | + | 0.967846i | \(0.580939\pi\) | |||||||
\(720\) | −38400.2 | −1.98763 | ||||||||
\(721\) | −5054.66 | −0.261089 | ||||||||
\(722\) | 2895.11 | 0.149231 | ||||||||
\(723\) | 9946.94 | 0.511661 | ||||||||
\(724\) | −21459.4 | −1.10157 | ||||||||
\(725\) | 3387.92 | 0.173551 | ||||||||
\(726\) | 23035.8 | 1.17760 | ||||||||
\(727\) | −13700.6 | −0.698939 | −0.349470 | − | 0.936948i | \(-0.613638\pi\) | ||||
−0.349470 | + | 0.936948i | \(0.613638\pi\) | |||||||
\(728\) | 55379.9 | 2.81939 | ||||||||
\(729\) | −2558.21 | −0.129970 | ||||||||
\(730\) | 74271.8 | 3.76565 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −95599.3 | −4.82712 | ||||||||
\(733\) | 25874.9 | 1.30384 | 0.651918 | − | 0.758289i | \(-0.273965\pi\) | ||||
0.651918 | + | 0.758289i | \(0.273965\pi\) | |||||||
\(734\) | −36100.6 | −1.81539 | ||||||||
\(735\) | 845.325 | 0.0424221 | ||||||||
\(736\) | 70672.7 | 3.53944 | ||||||||
\(737\) | −14882.6 | −0.743837 | ||||||||
\(738\) | 1528.11 | 0.0762203 | ||||||||
\(739\) | 9153.21 | 0.455624 | 0.227812 | − | 0.973705i | \(-0.426843\pi\) | ||||
0.227812 | + | 0.973705i | \(0.426843\pi\) | |||||||
\(740\) | 3375.26 | 0.167672 | ||||||||
\(741\) | 25793.7 | 1.27875 | ||||||||
\(742\) | 15745.6 | 0.779028 | ||||||||
\(743\) | 19565.2 | 0.966052 | 0.483026 | − | 0.875606i | \(-0.339538\pi\) | ||||
0.483026 | + | 0.875606i | \(0.339538\pi\) | |||||||
\(744\) | 30041.5 | 1.48034 | ||||||||
\(745\) | 19757.7 | 0.971632 | ||||||||
\(746\) | 14779.9 | 0.725376 | ||||||||
\(747\) | 5803.03 | 0.284233 | ||||||||
\(748\) | 90007.0 | 4.39971 | ||||||||
\(749\) | −14532.2 | −0.708937 | ||||||||
\(750\) | 44309.6 | 2.15728 | ||||||||
\(751\) | 24252.8 | 1.17842 | 0.589212 | − | 0.807978i | \(-0.299438\pi\) | ||||
0.589212 | + | 0.807978i | \(0.299438\pi\) | |||||||
\(752\) | 78946.6 | 3.82831 | ||||||||
\(753\) | 9552.83 | 0.462317 | ||||||||
\(754\) | −39515.4 | −1.90857 | ||||||||
\(755\) | −32995.1 | −1.59048 | ||||||||
\(756\) | 25896.0 | 1.24580 | ||||||||
\(757\) | −38026.1 | −1.82573 | −0.912867 | − | 0.408257i | \(-0.866137\pi\) | ||||
−0.912867 | + | 0.408257i | \(0.866137\pi\) | |||||||
\(758\) | 49011.0 | 2.34849 | ||||||||
\(759\) | −42001.5 | −2.00864 | ||||||||
\(760\) | 69417.3 | 3.31320 | ||||||||
\(761\) | 7521.42 | 0.358280 | 0.179140 | − | 0.983824i | \(-0.442668\pi\) | ||||
0.179140 | + | 0.983824i | \(0.442668\pi\) | |||||||
\(762\) | 2485.90 | 0.118182 | ||||||||
\(763\) | −12272.7 | −0.582308 | ||||||||
\(764\) | 16226.6 | 0.768403 | ||||||||
\(765\) | 19623.3 | 0.927428 | ||||||||
\(766\) | 35204.0 | 1.66054 | ||||||||
\(767\) | 18200.8 | 0.856834 | ||||||||
\(768\) | 9333.17 | 0.438518 | ||||||||
\(769\) | 21632.7 | 1.01443 | 0.507213 | − | 0.861821i | \(-0.330676\pi\) | ||||
0.507213 | + | 0.861821i | \(0.330676\pi\) | |||||||
\(770\) | −52376.1 | −2.45130 | ||||||||
\(771\) | 27614.5 | 1.28990 | ||||||||
\(772\) | −6468.78 | −0.301576 | ||||||||
\(773\) | −4537.97 | −0.211151 | −0.105575 | − | 0.994411i | \(-0.533668\pi\) | ||||
−0.105575 | + | 0.994411i | \(0.533668\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1418.57 | 0.0657503 | ||||||||
\(776\) | −40730.8 | −1.88422 | ||||||||
\(777\) | 1638.47 | 0.0756497 | ||||||||
\(778\) | −66176.7 | −3.04955 | ||||||||
\(779\) | −1491.90 | −0.0686175 | ||||||||
\(780\) | 74269.1 | 3.40931 | ||||||||
\(781\) | −21428.8 | −0.981797 | ||||||||
\(782\) | −75160.9 | −3.43702 | ||||||||
\(783\) | −11271.7 | −0.514456 | ||||||||
\(784\) | −2045.39 | −0.0931754 | ||||||||
\(785\) | 26337.7 | 1.19749 | ||||||||
\(786\) | 9749.51 | 0.442434 | ||||||||
\(787\) | 33633.9 | 1.52340 | 0.761702 | − | 0.647928i | \(-0.224364\pi\) | ||||
0.761702 | + | 0.647928i | \(0.224364\pi\) | |||||||
\(788\) | −107389. | −4.85481 | ||||||||
\(789\) | 8612.43 | 0.388607 | ||||||||
\(790\) | 16167.8 | 0.728131 | ||||||||
\(791\) | −22485.0 | −1.01072 | ||||||||
\(792\) | −49129.7 | −2.20423 | ||||||||
\(793\) | 32119.0 | 1.43831 | ||||||||
\(794\) | −30981.8 | −1.38477 | ||||||||
\(795\) | 12881.3 | 0.574657 | ||||||||
\(796\) | −26660.4 | −1.18713 | ||||||||
\(797\) | −15416.5 | −0.685172 | −0.342586 | − | 0.939487i | \(-0.611303\pi\) | ||||
−0.342586 | + | 0.939487i | \(0.611303\pi\) | |||||||
\(798\) | 55240.1 | 2.45047 | ||||||||
\(799\) | −40343.4 | −1.78629 | ||||||||
\(800\) | 10290.4 | 0.454778 | ||||||||
\(801\) | −1937.55 | −0.0854682 | ||||||||
\(802\) | −61915.6 | −2.72608 | ||||||||
\(803\) | 51320.0 | 2.25535 | ||||||||
\(804\) | 45195.5 | 1.98249 | ||||||||
\(805\) | 31465.9 | 1.37767 | ||||||||
\(806\) | −16545.6 | −0.723071 | ||||||||
\(807\) | −8209.83 | −0.358116 | ||||||||
\(808\) | 42888.0 | 1.86732 | ||||||||
\(809\) | 16077.3 | 0.698698 | 0.349349 | − | 0.936993i | \(-0.386403\pi\) | ||||
0.349349 | + | 0.936993i | \(0.386403\pi\) | |||||||
\(810\) | 58176.2 | 2.52359 | ||||||||
\(811\) | 34451.1 | 1.49167 | 0.745833 | − | 0.666133i | \(-0.232052\pi\) | ||||
0.745833 | + | 0.666133i | \(0.232052\pi\) | |||||||
\(812\) | −60883.3 | −2.63126 | ||||||||
\(813\) | 13120.1 | 0.565980 | ||||||||
\(814\) | 3241.74 | 0.139586 | ||||||||
\(815\) | −44092.6 | −1.89509 | ||||||||
\(816\) | −125169. | −5.36985 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 34232.2 | 1.46320 | ||||||||
\(819\) | 13676.2 | 0.583500 | ||||||||
\(820\) | −4295.71 | −0.182942 | ||||||||
\(821\) | −21764.4 | −0.925194 | −0.462597 | − | 0.886569i | \(-0.653082\pi\) | ||||
−0.462597 | + | 0.886569i | \(0.653082\pi\) | |||||||
\(822\) | −19332.3 | −0.820304 | ||||||||
\(823\) | 30308.2 | 1.28369 | 0.641845 | − | 0.766834i | \(-0.278169\pi\) | ||||
0.641845 | + | 0.766834i | \(0.278169\pi\) | |||||||
\(824\) | 18526.4 | 0.783251 | ||||||||
\(825\) | −6115.71 | −0.258087 | ||||||||
\(826\) | 38978.9 | 1.64195 | ||||||||
\(827\) | 17936.3 | 0.754179 | 0.377089 | − | 0.926177i | \(-0.376925\pi\) | ||||
0.377089 | + | 0.926177i | \(0.376925\pi\) | |||||||
\(828\) | 48384.5 | 2.03077 | ||||||||
\(829\) | 19426.9 | 0.813900 | 0.406950 | − | 0.913450i | \(-0.366592\pi\) | ||||
0.406950 | + | 0.913450i | \(0.366592\pi\) | |||||||
\(830\) | −22674.8 | −0.948257 | ||||||||
\(831\) | 7747.98 | 0.323435 | ||||||||
\(832\) | −49942.5 | −2.08106 | ||||||||
\(833\) | 1045.23 | 0.0434757 | ||||||||
\(834\) | −50351.6 | −2.09057 | ||||||||
\(835\) | −27135.6 | −1.12463 | ||||||||
\(836\) | 78629.6 | 3.25294 | ||||||||
\(837\) | −4719.63 | −0.194904 | ||||||||
\(838\) | 68479.5 | 2.82289 | ||||||||
\(839\) | 33848.2 | 1.39281 | 0.696407 | − | 0.717648i | \(-0.254781\pi\) | ||||
0.696407 | + | 0.717648i | \(0.254781\pi\) | |||||||
\(840\) | 97027.1 | 3.98542 | ||||||||
\(841\) | 2111.65 | 0.0865821 | ||||||||
\(842\) | 6322.55 | 0.258776 | ||||||||
\(843\) | −9970.80 | −0.407370 | ||||||||
\(844\) | −118163. | −4.81911 | ||||||||
\(845\) | 1576.76 | 0.0641921 | ||||||||
\(846\) | 36099.0 | 1.46703 | ||||||||
\(847\) | −11924.5 | −0.483745 | ||||||||
\(848\) | −31168.2 | −1.26217 | ||||||||
\(849\) | 39044.5 | 1.57833 | ||||||||
\(850\) | −10944.0 | −0.441617 | ||||||||
\(851\) | −1947.54 | −0.0784496 | ||||||||
\(852\) | 65074.9 | 2.61670 | ||||||||
\(853\) | 41193.8 | 1.65352 | 0.826759 | − | 0.562557i | \(-0.190182\pi\) | ||||
0.826759 | + | 0.562557i | \(0.190182\pi\) | |||||||
\(854\) | 68786.3 | 2.75623 | ||||||||
\(855\) | 17142.8 | 0.685698 | ||||||||
\(856\) | 53263.6 | 2.12676 | ||||||||
\(857\) | −44688.6 | −1.78125 | −0.890625 | − | 0.454738i | \(-0.849733\pi\) | ||||
−0.890625 | + | 0.454738i | \(0.849733\pi\) | |||||||
\(858\) | 71331.2 | 2.83824 | ||||||||
\(859\) | −41271.3 | −1.63930 | −0.819650 | − | 0.572865i | \(-0.805832\pi\) | ||||
−0.819650 | + | 0.572865i | \(0.805832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2085.29 | −0.0825395 | ||||||||
\(862\) | −30266.2 | −1.19591 | ||||||||
\(863\) | −13944.1 | −0.550014 | −0.275007 | − | 0.961442i | \(-0.588680\pi\) | ||||
−0.275007 | + | 0.961442i | \(0.588680\pi\) | |||||||
\(864\) | −34236.7 | −1.34810 | ||||||||
\(865\) | 17291.2 | 0.679673 | ||||||||
\(866\) | −35366.0 | −1.38774 | ||||||||
\(867\) | 31559.9 | 1.23625 | ||||||||
\(868\) | −25492.7 | −0.996864 | ||||||||
\(869\) | 11171.5 | 0.436097 | ||||||||
\(870\) | −69232.0 | −2.69791 | ||||||||
\(871\) | −15184.5 | −0.590710 | ||||||||
\(872\) | 44982.1 | 1.74689 | ||||||||
\(873\) | −10058.6 | −0.389957 | ||||||||
\(874\) | −65660.0 | −2.54117 | ||||||||
\(875\) | −22937.0 | −0.886186 | ||||||||
\(876\) | −155848. | −6.01099 | ||||||||
\(877\) | −1539.42 | −0.0592731 | −0.0296366 | − | 0.999561i | \(-0.509435\pi\) | ||||
−0.0296366 | + | 0.999561i | \(0.509435\pi\) | |||||||
\(878\) | −30542.8 | −1.17400 | ||||||||
\(879\) | −37015.3 | −1.42036 | ||||||||
\(880\) | 103678. | 3.97156 | ||||||||
\(881\) | −30429.5 | −1.16367 | −0.581837 | − | 0.813306i | \(-0.697666\pi\) | ||||
−0.581837 | + | 0.813306i | \(0.697666\pi\) | |||||||
\(882\) | −935.270 | −0.0357054 | ||||||||
\(883\) | 41762.4 | 1.59164 | 0.795819 | − | 0.605535i | \(-0.207041\pi\) | ||||
0.795819 | + | 0.605535i | \(0.207041\pi\) | |||||||
\(884\) | 91833.0 | 3.49398 | ||||||||
\(885\) | 31888.2 | 1.21120 | ||||||||
\(886\) | 48500.6 | 1.83906 | ||||||||
\(887\) | 34349.7 | 1.30028 | 0.650140 | − | 0.759814i | \(-0.274710\pi\) | ||||
0.650140 | + | 0.759814i | \(0.274710\pi\) | |||||||
\(888\) | −6005.35 | −0.226944 | ||||||||
\(889\) | −1286.83 | −0.0485478 | ||||||||
\(890\) | 7570.80 | 0.285139 | ||||||||
\(891\) | 40198.4 | 1.51144 | ||||||||
\(892\) | −70980.6 | −2.66436 | ||||||||
\(893\) | −35243.7 | −1.32070 | ||||||||
\(894\) | −57626.6 | −2.15584 | ||||||||
\(895\) | −47858.5 | −1.78741 | ||||||||
\(896\) | −34839.8 | −1.29901 | ||||||||
\(897\) | −42853.5 | −1.59514 | ||||||||
\(898\) | −26548.1 | −0.986548 | ||||||||
\(899\) | 11096.2 | 0.411656 | ||||||||
\(900\) | 7045.13 | 0.260931 | ||||||||
\(901\) | 15927.6 | 0.588929 | ||||||||
\(902\) | −4125.78 | −0.152299 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 82412.5 | 3.03208 | ||||||||
\(905\) | 12631.8 | 0.463973 | ||||||||
\(906\) | 96235.6 | 3.52893 | ||||||||
\(907\) | 1799.82 | 0.0658897 | 0.0329449 | − | 0.999457i | \(-0.489511\pi\) | ||||
0.0329449 | + | 0.999457i | \(0.489511\pi\) | |||||||
\(908\) | −138000. | −5.04372 | ||||||||
\(909\) | 10591.3 | 0.386460 | ||||||||
\(910\) | −53438.6 | −1.94667 | ||||||||
\(911\) | −16614.8 | −0.604250 | −0.302125 | − | 0.953268i | \(-0.597696\pi\) | ||||
−0.302125 | + | 0.953268i | \(0.597696\pi\) | |||||||
\(912\) | −109347. | −3.97022 | ||||||||
\(913\) | −15667.7 | −0.567937 | ||||||||
\(914\) | 69086.6 | 2.50020 | ||||||||
\(915\) | 56273.3 | 2.03316 | ||||||||
\(916\) | 63211.5 | 2.28010 | ||||||||
\(917\) | −5046.86 | −0.181747 | ||||||||
\(918\) | 36410.9 | 1.30908 | ||||||||
\(919\) | −27368.9 | −0.982389 | −0.491194 | − | 0.871050i | \(-0.663440\pi\) | ||||
−0.491194 | + | 0.871050i | \(0.663440\pi\) | |||||||
\(920\) | −115329. | −4.13293 | ||||||||
\(921\) | −33088.3 | −1.18382 | ||||||||
\(922\) | −58258.2 | −2.08094 | ||||||||
\(923\) | −21863.5 | −0.779683 | ||||||||
\(924\) | 109904. | 3.91294 | ||||||||
\(925\) | −283.575 | −0.0100799 | ||||||||
\(926\) | −31242.5 | −1.10874 | ||||||||
\(927\) | 4575.16 | 0.162101 | ||||||||
\(928\) | 80492.9 | 2.84731 | ||||||||
\(929\) | −33945.3 | −1.19883 | −0.599413 | − | 0.800440i | \(-0.704599\pi\) | ||||
−0.599413 | + | 0.800440i | \(0.704599\pi\) | |||||||
\(930\) | −28988.4 | −1.02212 | ||||||||
\(931\) | 913.110 | 0.0321439 | ||||||||
\(932\) | −104638. | −3.67762 | ||||||||
\(933\) | 7263.95 | 0.254889 | ||||||||
\(934\) | −85915.8 | −3.00991 | ||||||||
\(935\) | −52981.5 | −1.85313 | ||||||||
\(936\) | −50126.4 | −1.75046 | ||||||||
\(937\) | −27.3495 | −0.000953542 0 | −0.000476771 | − | 1.00000i | \(-0.500152\pi\) | ||||
−0.000476771 | 1.00000i | \(0.500152\pi\) | ||||||||
\(938\) | −32519.3 | −1.13198 | ||||||||
\(939\) | −46082.2 | −1.60153 | ||||||||
\(940\) | −101479. | −3.52115 | ||||||||
\(941\) | −30082.0 | −1.04213 | −0.521066 | − | 0.853517i | \(-0.674465\pi\) | ||||
−0.521066 | + | 0.853517i | \(0.674465\pi\) | |||||||
\(942\) | −76818.3 | −2.65698 | ||||||||
\(943\) | 2478.64 | 0.0855945 | ||||||||
\(944\) | −77158.3 | −2.66026 | ||||||||
\(945\) | −15243.3 | −0.524725 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9281.65 | −0.318493 | −0.159247 | − | 0.987239i | \(-0.550907\pi\) | ||||
−0.159247 | + | 0.987239i | \(0.550907\pi\) | |||||||
\(948\) | −33925.7 | −1.16229 | ||||||||
\(949\) | 52361.1 | 1.79106 | ||||||||
\(950\) | −9560.57 | −0.326511 | ||||||||
\(951\) | 56577.2 | 1.92917 | ||||||||
\(952\) | 119973. | 4.08440 | ||||||||
\(953\) | −32201.2 | −1.09454 | −0.547271 | − | 0.836956i | \(-0.684333\pi\) | ||||
−0.547271 | + | 0.836956i | \(0.684333\pi\) | |||||||
\(954\) | −14251.9 | −0.483672 | ||||||||
\(955\) | −9551.61 | −0.323647 | ||||||||
\(956\) | −136091. | −4.60406 | ||||||||
\(957\) | −47837.7 | −1.61585 | ||||||||
\(958\) | −30102.2 | −1.01520 | ||||||||
\(959\) | 10007.4 | 0.336972 | ||||||||
\(960\) | −87500.6 | −2.94174 | ||||||||
\(961\) | −25144.9 | −0.844043 | ||||||||
\(962\) | 3307.51 | 0.110851 | ||||||||
\(963\) | 13153.6 | 0.440155 | ||||||||
\(964\) | 30937.4 | 1.03364 | ||||||||
\(965\) | 3807.76 | 0.127022 | ||||||||
\(966\) | −91775.5 | −3.05676 | ||||||||
\(967\) | −45786.9 | −1.52266 | −0.761328 | − | 0.648367i | \(-0.775452\pi\) | ||||
−0.761328 | + | 0.648367i | \(0.775452\pi\) | |||||||
\(968\) | 43706.1 | 1.45120 | ||||||||
\(969\) | 55878.6 | 1.85251 | ||||||||
\(970\) | 39303.1 | 1.30097 | ||||||||
\(971\) | 13807.1 | 0.456326 | 0.228163 | − | 0.973623i | \(-0.426728\pi\) | ||||
0.228163 | + | 0.973623i | \(0.426728\pi\) | |||||||
\(972\) | −83723.4 | −2.76279 | ||||||||
\(973\) | 26064.6 | 0.858781 | ||||||||
\(974\) | −81209.7 | −2.67159 | ||||||||
\(975\) | −6239.78 | −0.204957 | ||||||||
\(976\) | −136161. | −4.46560 | ||||||||
\(977\) | −19774.4 | −0.647532 | −0.323766 | − | 0.946137i | \(-0.604949\pi\) | ||||
−0.323766 | + | 0.946137i | \(0.604949\pi\) | |||||||
\(978\) | 128603. | 4.20479 | ||||||||
\(979\) | 5231.24 | 0.170778 | ||||||||
\(980\) | 2629.16 | 0.0856995 | ||||||||
\(981\) | 11108.5 | 0.361535 | ||||||||
\(982\) | 53742.8 | 1.74644 | ||||||||
\(983\) | 51283.2 | 1.66397 | 0.831984 | − | 0.554800i | \(-0.187205\pi\) | ||||
0.831984 | + | 0.554800i | \(0.187205\pi\) | |||||||
\(984\) | 7643.05 | 0.247613 | ||||||||
\(985\) | 63213.4 | 2.04482 | ||||||||
\(986\) | −85604.7 | −2.76492 | ||||||||
\(987\) | −49261.5 | −1.58866 | ||||||||
\(988\) | 80224.7 | 2.58329 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 47407.5 | 1.52193 | ||||||||
\(991\) | 19490.1 | 0.624746 | 0.312373 | − | 0.949960i | \(-0.398876\pi\) | ||||
0.312373 | + | 0.949960i | \(0.398876\pi\) | |||||||
\(992\) | 33703.5 | 1.07872 | ||||||||
\(993\) | −9259.67 | −0.295918 | ||||||||
\(994\) | −46823.2 | −1.49411 | ||||||||
\(995\) | 15693.3 | 0.500011 | ||||||||
\(996\) | 47579.7 | 1.51368 | ||||||||
\(997\) | −6503.90 | −0.206600 | −0.103300 | − | 0.994650i | \(-0.532940\pi\) | ||||
−0.103300 | + | 0.994650i | \(0.532940\pi\) | |||||||
\(998\) | −960.095 | −0.0304522 | ||||||||
\(999\) | 943.463 | 0.0298797 |
(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 | 1849.4.a.j.1.48 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.3 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.3 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.48 | yes | 50 | 1.1 | even | 1 | trivial |