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 | 1.16 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.04766 | −1.07751 | −0.538755 | − | 0.842462i | \(-0.681105\pi\) | ||||
−0.538755 | + | 0.842462i | \(0.681105\pi\) | |||||||
\(3\) | −1.42990 | −0.275184 | −0.137592 | − | 0.990489i | \(-0.543936\pi\) | ||||
−0.137592 | + | 0.990489i | \(0.543936\pi\) | |||||||
\(4\) | 1.28824 | 0.161029 | ||||||||
\(5\) | 10.9474 | 0.979161 | 0.489581 | − | 0.871958i | \(-0.337150\pi\) | ||||
0.489581 | + | 0.871958i | \(0.337150\pi\) | |||||||
\(6\) | 4.35784 | 0.296514 | ||||||||
\(7\) | 8.62569 | 0.465743 | 0.232872 | − | 0.972507i | \(-0.425188\pi\) | ||||
0.232872 | + | 0.972507i | \(0.425188\pi\) | |||||||
\(8\) | 20.4552 | 0.904000 | ||||||||
\(9\) | −24.9554 | −0.924274 | ||||||||
\(10\) | −33.3638 | −1.05506 | ||||||||
\(11\) | 42.2441 | 1.15792 | 0.578958 | − | 0.815358i | \(-0.303460\pi\) | ||||
0.578958 | + | 0.815358i | \(0.303460\pi\) | |||||||
\(12\) | −1.84205 | −0.0443127 | ||||||||
\(13\) | 78.4327 | 1.67333 | 0.836666 | − | 0.547713i | \(-0.184501\pi\) | ||||
0.836666 | + | 0.547713i | \(0.184501\pi\) | |||||||
\(14\) | −26.2882 | −0.501843 | ||||||||
\(15\) | −15.6536 | −0.269450 | ||||||||
\(16\) | −72.6463 | −1.13510 | ||||||||
\(17\) | 75.8963 | 1.08280 | 0.541398 | − | 0.840766i | \(-0.317895\pi\) | ||||
0.541398 | + | 0.840766i | \(0.317895\pi\) | |||||||
\(18\) | 76.0556 | 0.995915 | ||||||||
\(19\) | −107.684 | −1.30023 | −0.650117 | − | 0.759834i | \(-0.725280\pi\) | ||||
−0.650117 | + | 0.759834i | \(0.725280\pi\) | |||||||
\(20\) | 14.1028 | 0.157674 | ||||||||
\(21\) | −12.3339 | −0.128165 | ||||||||
\(22\) | −128.746 | −1.24767 | ||||||||
\(23\) | −27.7883 | −0.251924 | −0.125962 | − | 0.992035i | \(-0.540202\pi\) | ||||
−0.125962 | + | 0.992035i | \(0.540202\pi\) | |||||||
\(24\) | −29.2488 | −0.248766 | ||||||||
\(25\) | −5.15536 | −0.0412428 | ||||||||
\(26\) | −239.036 | −1.80303 | ||||||||
\(27\) | 74.2909 | 0.529529 | ||||||||
\(28\) | 11.1119 | 0.0749984 | ||||||||
\(29\) | −12.6364 | −0.0809143 | −0.0404572 | − | 0.999181i | \(-0.512881\pi\) | ||||
−0.0404572 | + | 0.999181i | \(0.512881\pi\) | |||||||
\(30\) | 47.7069 | 0.290335 | ||||||||
\(31\) | −188.821 | −1.09397 | −0.546987 | − | 0.837141i | \(-0.684225\pi\) | ||||
−0.546987 | + | 0.837141i | \(0.684225\pi\) | |||||||
\(32\) | 57.7599 | 0.319082 | ||||||||
\(33\) | −60.4047 | −0.318640 | ||||||||
\(34\) | −231.306 | −1.16673 | ||||||||
\(35\) | 94.4285 | 0.456038 | ||||||||
\(36\) | −32.1484 | −0.148835 | ||||||||
\(37\) | −84.0627 | −0.373509 | −0.186754 | − | 0.982407i | \(-0.559797\pi\) | ||||
−0.186754 | + | 0.982407i | \(0.559797\pi\) | |||||||
\(38\) | 328.185 | 1.40102 | ||||||||
\(39\) | −112.151 | −0.460474 | ||||||||
\(40\) | 223.930 | 0.885162 | ||||||||
\(41\) | −215.325 | −0.820197 | −0.410099 | − | 0.912041i | \(-0.634506\pi\) | ||||
−0.410099 | + | 0.912041i | \(0.634506\pi\) | |||||||
\(42\) | 37.5894 | 0.138099 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 54.4203 | 0.186458 | ||||||||
\(45\) | −273.196 | −0.905013 | ||||||||
\(46\) | 84.6893 | 0.271451 | ||||||||
\(47\) | −598.204 | −1.85653 | −0.928266 | − | 0.371916i | \(-0.878701\pi\) | ||||
−0.928266 | + | 0.371916i | \(0.878701\pi\) | |||||||
\(48\) | 103.877 | 0.312361 | ||||||||
\(49\) | −268.598 | −0.783083 | ||||||||
\(50\) | 15.7118 | 0.0444396 | ||||||||
\(51\) | −108.524 | −0.297968 | ||||||||
\(52\) | 101.040 | 0.269456 | ||||||||
\(53\) | 368.465 | 0.954955 | 0.477477 | − | 0.878644i | \(-0.341551\pi\) | ||||
0.477477 | + | 0.878644i | \(0.341551\pi\) | |||||||
\(54\) | −226.413 | −0.570574 | ||||||||
\(55\) | 462.461 | 1.13379 | ||||||||
\(56\) | 176.440 | 0.421032 | ||||||||
\(57\) | 153.977 | 0.357804 | ||||||||
\(58\) | 38.5114 | 0.0871860 | ||||||||
\(59\) | −62.2843 | −0.137436 | −0.0687180 | − | 0.997636i | \(-0.521891\pi\) | ||||
−0.0687180 | + | 0.997636i | \(0.521891\pi\) | |||||||
\(60\) | −20.1655 | −0.0433893 | ||||||||
\(61\) | −186.541 | −0.391543 | −0.195772 | − | 0.980649i | \(-0.562721\pi\) | ||||
−0.195772 | + | 0.980649i | \(0.562721\pi\) | |||||||
\(62\) | 575.462 | 1.17877 | ||||||||
\(63\) | −215.257 | −0.430474 | ||||||||
\(64\) | 405.138 | 0.791285 | ||||||||
\(65\) | 858.631 | 1.63846 | ||||||||
\(66\) | 184.093 | 0.343338 | ||||||||
\(67\) | −717.716 | −1.30870 | −0.654350 | − | 0.756192i | \(-0.727058\pi\) | ||||
−0.654350 | + | 0.756192i | \(0.727058\pi\) | |||||||
\(68\) | 97.7723 | 0.174362 | ||||||||
\(69\) | 39.7344 | 0.0693256 | ||||||||
\(70\) | −287.786 | −0.491386 | ||||||||
\(71\) | 474.895 | 0.793798 | 0.396899 | − | 0.917862i | \(-0.370086\pi\) | ||||
0.396899 | + | 0.917862i | \(0.370086\pi\) | |||||||
\(72\) | −510.467 | −0.835543 | ||||||||
\(73\) | −1229.76 | −1.97168 | −0.985842 | − | 0.167678i | \(-0.946373\pi\) | ||||
−0.985842 | + | 0.167678i | \(0.946373\pi\) | |||||||
\(74\) | 256.195 | 0.402460 | ||||||||
\(75\) | 7.37163 | 0.0113494 | ||||||||
\(76\) | −138.723 | −0.209376 | ||||||||
\(77\) | 364.384 | 0.539291 | ||||||||
\(78\) | 341.798 | 0.496166 | ||||||||
\(79\) | −1134.35 | −1.61549 | −0.807747 | − | 0.589529i | \(-0.799313\pi\) | ||||
−0.807747 | + | 0.589529i | \(0.799313\pi\) | |||||||
\(80\) | −795.285 | −1.11145 | ||||||||
\(81\) | 567.567 | 0.778556 | ||||||||
\(82\) | 656.237 | 0.883771 | ||||||||
\(83\) | −632.780 | −0.836826 | −0.418413 | − | 0.908257i | \(-0.637414\pi\) | ||||
−0.418413 | + | 0.908257i | \(0.637414\pi\) | |||||||
\(84\) | −15.8889 | −0.0206384 | ||||||||
\(85\) | 830.864 | 1.06023 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.0687 | 0.0222663 | ||||||||
\(88\) | 864.110 | 1.04676 | ||||||||
\(89\) | 6.66926 | 0.00794315 | 0.00397158 | − | 0.999992i | \(-0.498736\pi\) | ||||
0.00397158 | + | 0.999992i | \(0.498736\pi\) | |||||||
\(90\) | 832.607 | 0.975162 | ||||||||
\(91\) | 676.536 | 0.779344 | ||||||||
\(92\) | −35.7979 | −0.0405672 | ||||||||
\(93\) | 269.994 | 0.301044 | ||||||||
\(94\) | 1823.12 | 2.00043 | ||||||||
\(95\) | −1178.86 | −1.27314 | ||||||||
\(96\) | −82.5908 | −0.0878061 | ||||||||
\(97\) | −1024.36 | −1.07224 | −0.536122 | − | 0.844140i | \(-0.680111\pi\) | ||||
−0.536122 | + | 0.844140i | \(0.680111\pi\) | |||||||
\(98\) | 818.594 | 0.843781 | ||||||||
\(99\) | −1054.22 | −1.07023 | ||||||||
\(100\) | −6.64131 | −0.00664131 | ||||||||
\(101\) | 1296.35 | 1.27714 | 0.638572 | − | 0.769562i | \(-0.279526\pi\) | ||||
0.638572 | + | 0.769562i | \(0.279526\pi\) | |||||||
\(102\) | 330.744 | 0.321064 | ||||||||
\(103\) | 30.1268 | 0.0288202 | 0.0144101 | − | 0.999896i | \(-0.495413\pi\) | ||||
0.0144101 | + | 0.999896i | \(0.495413\pi\) | |||||||
\(104\) | 1604.36 | 1.51269 | ||||||||
\(105\) | −135.023 | −0.125494 | ||||||||
\(106\) | −1122.96 | −1.02897 | ||||||||
\(107\) | −1362.61 | −1.23111 | −0.615554 | − | 0.788095i | \(-0.711068\pi\) | ||||
−0.615554 | + | 0.788095i | \(0.711068\pi\) | |||||||
\(108\) | 95.7042 | 0.0852698 | ||||||||
\(109\) | −397.621 | −0.349406 | −0.174703 | − | 0.984621i | \(-0.555896\pi\) | ||||
−0.174703 | + | 0.984621i | \(0.555896\pi\) | |||||||
\(110\) | −1409.42 | −1.22167 | ||||||||
\(111\) | 120.201 | 0.102784 | ||||||||
\(112\) | −626.624 | −0.528665 | ||||||||
\(113\) | 348.680 | 0.290275 | 0.145137 | − | 0.989412i | \(-0.453638\pi\) | ||||
0.145137 | + | 0.989412i | \(0.453638\pi\) | |||||||
\(114\) | −469.271 | −0.385537 | ||||||||
\(115\) | −304.208 | −0.246675 | ||||||||
\(116\) | −16.2786 | −0.0130296 | ||||||||
\(117\) | −1957.32 | −1.54662 | ||||||||
\(118\) | 189.821 | 0.148089 | ||||||||
\(119\) | 654.657 | 0.504305 | ||||||||
\(120\) | −320.197 | −0.243582 | ||||||||
\(121\) | 453.562 | 0.340768 | ||||||||
\(122\) | 568.514 | 0.421892 | ||||||||
\(123\) | 307.893 | 0.225705 | ||||||||
\(124\) | −243.246 | −0.176162 | ||||||||
\(125\) | −1424.86 | −1.01954 | ||||||||
\(126\) | 656.031 | 0.463841 | ||||||||
\(127\) | 296.445 | 0.207128 | 0.103564 | − | 0.994623i | \(-0.466975\pi\) | ||||
0.103564 | + | 0.994623i | \(0.466975\pi\) | |||||||
\(128\) | −1696.80 | −1.17170 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2616.82 | −1.76546 | ||||||||
\(131\) | 1527.08 | 1.01848 | 0.509241 | − | 0.860624i | \(-0.329926\pi\) | ||||
0.509241 | + | 0.860624i | \(0.329926\pi\) | |||||||
\(132\) | −77.8155 | −0.0513104 | ||||||||
\(133\) | −928.850 | −0.605575 | ||||||||
\(134\) | 2187.35 | 1.41014 | ||||||||
\(135\) | 813.289 | 0.518495 | ||||||||
\(136\) | 1552.47 | 0.978848 | ||||||||
\(137\) | 1851.19 | 1.15444 | 0.577220 | − | 0.816589i | \(-0.304138\pi\) | ||||
0.577220 | + | 0.816589i | \(0.304138\pi\) | |||||||
\(138\) | −121.097 | −0.0746990 | ||||||||
\(139\) | −624.022 | −0.380783 | −0.190392 | − | 0.981708i | \(-0.560976\pi\) | ||||
−0.190392 | + | 0.981708i | \(0.560976\pi\) | |||||||
\(140\) | 121.646 | 0.0734355 | ||||||||
\(141\) | 855.371 | 0.510888 | ||||||||
\(142\) | −1447.32 | −0.855326 | ||||||||
\(143\) | 3313.32 | 1.93758 | ||||||||
\(144\) | 1812.92 | 1.04914 | ||||||||
\(145\) | −138.335 | −0.0792282 | ||||||||
\(146\) | 3747.90 | 2.12451 | ||||||||
\(147\) | 384.067 | 0.215492 | ||||||||
\(148\) | −108.293 | −0.0601459 | ||||||||
\(149\) | 2279.84 | 1.25350 | 0.626750 | − | 0.779220i | \(-0.284385\pi\) | ||||
0.626750 | + | 0.779220i | \(0.284385\pi\) | |||||||
\(150\) | −22.4662 | −0.0122291 | ||||||||
\(151\) | 2948.04 | 1.58880 | 0.794398 | − | 0.607398i | \(-0.207787\pi\) | ||||
0.794398 | + | 0.607398i | \(0.207787\pi\) | |||||||
\(152\) | −2202.70 | −1.17541 | ||||||||
\(153\) | −1894.02 | −1.00080 | ||||||||
\(154\) | −1110.52 | −0.581092 | ||||||||
\(155\) | −2067.09 | −1.07118 | ||||||||
\(156\) | −144.477 | −0.0741499 | ||||||||
\(157\) | 1507.11 | 0.766115 | 0.383058 | − | 0.923724i | \(-0.374871\pi\) | ||||
0.383058 | + | 0.923724i | \(0.374871\pi\) | |||||||
\(158\) | 3457.11 | 1.74071 | ||||||||
\(159\) | −526.868 | −0.262788 | ||||||||
\(160\) | 632.319 | 0.312432 | ||||||||
\(161\) | −239.693 | −0.117332 | ||||||||
\(162\) | −1729.75 | −0.838902 | ||||||||
\(163\) | −2880.27 | −1.38405 | −0.692026 | − | 0.721873i | \(-0.743281\pi\) | ||||
−0.692026 | + | 0.721873i | \(0.743281\pi\) | |||||||
\(164\) | −277.389 | −0.132076 | ||||||||
\(165\) | −661.272 | −0.312000 | ||||||||
\(166\) | 1928.50 | 0.901689 | ||||||||
\(167\) | 2282.83 | 1.05779 | 0.528895 | − | 0.848688i | \(-0.322607\pi\) | ||||
0.528895 | + | 0.848688i | \(0.322607\pi\) | |||||||
\(168\) | −252.291 | −0.115861 | ||||||||
\(169\) | 3954.69 | 1.80004 | ||||||||
\(170\) | −2532.19 | −1.14241 | ||||||||
\(171\) | 2687.30 | 1.20177 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1889.09 | −0.830201 | −0.415100 | − | 0.909776i | \(-0.636254\pi\) | ||||
−0.415100 | + | 0.909776i | \(0.636254\pi\) | |||||||
\(174\) | −55.0673 | −0.0239922 | ||||||||
\(175\) | −44.4685 | −0.0192086 | ||||||||
\(176\) | −3068.88 | −1.31435 | ||||||||
\(177\) | 89.0602 | 0.0378202 | ||||||||
\(178\) | −20.3257 | −0.00855883 | ||||||||
\(179\) | −1064.35 | −0.444433 | −0.222216 | − | 0.974997i | \(-0.571329\pi\) | ||||
−0.222216 | + | 0.974997i | \(0.571329\pi\) | |||||||
\(180\) | −351.940 | −0.145734 | ||||||||
\(181\) | 1113.89 | 0.457429 | 0.228715 | − | 0.973494i | \(-0.426548\pi\) | ||||
0.228715 | + | 0.973494i | \(0.426548\pi\) | |||||||
\(182\) | −2061.85 | −0.839751 | ||||||||
\(183\) | 266.735 | 0.107746 | ||||||||
\(184\) | −568.415 | −0.227740 | ||||||||
\(185\) | −920.264 | −0.365725 | ||||||||
\(186\) | −822.851 | −0.324378 | ||||||||
\(187\) | 3206.17 | 1.25379 | ||||||||
\(188\) | −770.628 | −0.298956 | ||||||||
\(189\) | 640.810 | 0.246625 | ||||||||
\(190\) | 3592.76 | 1.37182 | ||||||||
\(191\) | −600.424 | −0.227461 | −0.113731 | − | 0.993512i | \(-0.536280\pi\) | ||||
−0.113731 | + | 0.993512i | \(0.536280\pi\) | |||||||
\(192\) | −579.306 | −0.217749 | ||||||||
\(193\) | −4418.79 | −1.64804 | −0.824019 | − | 0.566562i | \(-0.808273\pi\) | ||||
−0.824019 | + | 0.566562i | \(0.808273\pi\) | |||||||
\(194\) | 3121.89 | 1.15535 | ||||||||
\(195\) | −1227.76 | −0.450879 | ||||||||
\(196\) | −346.017 | −0.126099 | ||||||||
\(197\) | 2202.16 | 0.796434 | 0.398217 | − | 0.917291i | \(-0.369629\pi\) | ||||
0.398217 | + | 0.917291i | \(0.369629\pi\) | |||||||
\(198\) | 3212.90 | 1.15319 | ||||||||
\(199\) | −2962.08 | −1.05516 | −0.527579 | − | 0.849506i | \(-0.676900\pi\) | ||||
−0.527579 | + | 0.849506i | \(0.676900\pi\) | |||||||
\(200\) | −105.454 | −0.0372835 | ||||||||
\(201\) | 1026.26 | 0.360133 | ||||||||
\(202\) | −3950.83 | −1.37614 | ||||||||
\(203\) | −108.997 | −0.0376853 | ||||||||
\(204\) | −139.804 | −0.0479817 | ||||||||
\(205\) | −2357.24 | −0.803106 | ||||||||
\(206\) | −91.8163 | −0.0310541 | ||||||||
\(207\) | 693.468 | 0.232847 | ||||||||
\(208\) | −5697.85 | −1.89940 | ||||||||
\(209\) | −4549.02 | −1.50556 | ||||||||
\(210\) | 411.505 | 0.135221 | ||||||||
\(211\) | 3121.62 | 1.01849 | 0.509244 | − | 0.860622i | \(-0.329925\pi\) | ||||
0.509244 | + | 0.860622i | \(0.329925\pi\) | |||||||
\(212\) | 474.670 | 0.153776 | ||||||||
\(213\) | −679.051 | −0.218440 | ||||||||
\(214\) | 4152.77 | 1.32653 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1519.63 | 0.478694 | ||||||||
\(217\) | −1628.71 | −0.509511 | ||||||||
\(218\) | 1211.82 | 0.376488 | ||||||||
\(219\) | 1758.44 | 0.542576 | ||||||||
\(220\) | 595.759 | 0.182573 | ||||||||
\(221\) | 5952.75 | 1.81188 | ||||||||
\(222\) | −366.332 | −0.110750 | ||||||||
\(223\) | −1921.29 | −0.576946 | −0.288473 | − | 0.957488i | \(-0.593148\pi\) | ||||
−0.288473 | + | 0.957488i | \(0.593148\pi\) | |||||||
\(224\) | 498.219 | 0.148610 | ||||||||
\(225\) | 128.654 | 0.0381197 | ||||||||
\(226\) | −1062.66 | −0.312774 | ||||||||
\(227\) | −548.261 | −0.160306 | −0.0801528 | − | 0.996783i | \(-0.525541\pi\) | ||||
−0.0801528 | + | 0.996783i | \(0.525541\pi\) | |||||||
\(228\) | 198.359 | 0.0576169 | ||||||||
\(229\) | 2286.66 | 0.659854 | 0.329927 | − | 0.944006i | \(-0.392976\pi\) | ||||
0.329927 | + | 0.944006i | \(0.392976\pi\) | |||||||
\(230\) | 927.124 | 0.265795 | ||||||||
\(231\) | −521.032 | −0.148404 | ||||||||
\(232\) | −258.479 | −0.0731465 | ||||||||
\(233\) | 4993.15 | 1.40392 | 0.701958 | − | 0.712218i | \(-0.252309\pi\) | ||||
0.701958 | + | 0.712218i | \(0.252309\pi\) | |||||||
\(234\) | 5965.25 | 1.66650 | ||||||||
\(235\) | −6548.75 | −1.81785 | ||||||||
\(236\) | −80.2368 | −0.0221312 | ||||||||
\(237\) | 1622.00 | 0.444558 | ||||||||
\(238\) | −1995.17 | −0.543394 | ||||||||
\(239\) | −3806.31 | −1.03017 | −0.515083 | − | 0.857140i | \(-0.672239\pi\) | ||||
−0.515083 | + | 0.857140i | \(0.672239\pi\) | |||||||
\(240\) | 1137.18 | 0.305852 | ||||||||
\(241\) | −6268.95 | −1.67559 | −0.837797 | − | 0.545981i | \(-0.816157\pi\) | ||||
−0.837797 | + | 0.545981i | \(0.816157\pi\) | |||||||
\(242\) | −1382.30 | −0.367181 | ||||||||
\(243\) | −2817.42 | −0.743775 | ||||||||
\(244\) | −240.309 | −0.0630500 | ||||||||
\(245\) | −2940.43 | −0.766765 | ||||||||
\(246\) | −938.352 | −0.243200 | ||||||||
\(247\) | −8445.96 | −2.17572 | ||||||||
\(248\) | −3862.36 | −0.988953 | ||||||||
\(249\) | 904.810 | 0.230281 | ||||||||
\(250\) | 4342.48 | 1.09857 | ||||||||
\(251\) | 938.494 | 0.236005 | 0.118002 | − | 0.993013i | \(-0.462351\pi\) | ||||
0.118002 | + | 0.993013i | \(0.462351\pi\) | |||||||
\(252\) | −277.302 | −0.0693190 | ||||||||
\(253\) | −1173.89 | −0.291707 | ||||||||
\(254\) | −903.464 | −0.223183 | ||||||||
\(255\) | −1188.05 | −0.291759 | ||||||||
\(256\) | 1930.17 | 0.471234 | ||||||||
\(257\) | −7223.21 | −1.75320 | −0.876598 | − | 0.481223i | \(-0.840193\pi\) | ||||
−0.876598 | + | 0.481223i | \(0.840193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −725.098 | −0.173959 | ||||||||
\(260\) | 1106.12 | 0.263841 | ||||||||
\(261\) | 315.346 | 0.0747870 | ||||||||
\(262\) | −4654.01 | −1.09743 | ||||||||
\(263\) | 6840.18 | 1.60374 | 0.801870 | − | 0.597498i | \(-0.203838\pi\) | ||||
0.801870 | + | 0.597498i | \(0.203838\pi\) | |||||||
\(264\) | −1235.59 | −0.288050 | ||||||||
\(265\) | 4033.72 | 0.935055 | ||||||||
\(266\) | 2830.82 | 0.652514 | ||||||||
\(267\) | −9.53637 | −0.00218583 | ||||||||
\(268\) | −924.587 | −0.210739 | ||||||||
\(269\) | −3969.81 | −0.899790 | −0.449895 | − | 0.893081i | \(-0.648539\pi\) | ||||
−0.449895 | + | 0.893081i | \(0.648539\pi\) | |||||||
\(270\) | −2478.63 | −0.558684 | ||||||||
\(271\) | −7439.71 | −1.66764 | −0.833820 | − | 0.552037i | \(-0.813851\pi\) | ||||
−0.833820 | + | 0.552037i | \(0.813851\pi\) | |||||||
\(272\) | −5513.59 | −1.22908 | ||||||||
\(273\) | −967.378 | −0.214463 | ||||||||
\(274\) | −5641.81 | −1.24392 | ||||||||
\(275\) | −217.783 | −0.0477557 | ||||||||
\(276\) | 51.1873 | 0.0111635 | ||||||||
\(277\) | −627.394 | −0.136088 | −0.0680442 | − | 0.997682i | \(-0.521676\pi\) | ||||
−0.0680442 | + | 0.997682i | \(0.521676\pi\) | |||||||
\(278\) | 1901.81 | 0.410298 | ||||||||
\(279\) | 4712.10 | 1.01113 | ||||||||
\(280\) | 1931.55 | 0.412258 | ||||||||
\(281\) | 8656.81 | 1.83780 | 0.918900 | − | 0.394489i | \(-0.129079\pi\) | ||||
0.918900 | + | 0.394489i | \(0.129079\pi\) | |||||||
\(282\) | −2606.88 | −0.550487 | ||||||||
\(283\) | −5735.35 | −1.20470 | −0.602352 | − | 0.798231i | \(-0.705769\pi\) | ||||
−0.602352 | + | 0.798231i | \(0.705769\pi\) | |||||||
\(284\) | 611.776 | 0.127825 | ||||||||
\(285\) | 1685.65 | 0.350347 | ||||||||
\(286\) | −10097.9 | −2.08776 | ||||||||
\(287\) | −1857.32 | −0.382001 | ||||||||
\(288\) | −1441.42 | −0.294919 | ||||||||
\(289\) | 847.243 | 0.172449 | ||||||||
\(290\) | 421.598 | 0.0853692 | ||||||||
\(291\) | 1464.73 | 0.295064 | ||||||||
\(292\) | −1584.22 | −0.317499 | ||||||||
\(293\) | −2132.59 | −0.425212 | −0.212606 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212606 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(294\) | −1170.51 | −0.232195 | ||||||||
\(295\) | −681.848 | −0.134572 | ||||||||
\(296\) | −1719.52 | −0.337652 | ||||||||
\(297\) | 3138.35 | 0.613150 | ||||||||
\(298\) | −6948.17 | −1.35066 | ||||||||
\(299\) | −2179.51 | −0.421553 | ||||||||
\(300\) | 9.49640 | 0.00182758 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −8984.63 | −1.71194 | ||||||||
\(303\) | −1853.65 | −0.351449 | ||||||||
\(304\) | 7822.86 | 1.47589 | ||||||||
\(305\) | −2042.13 | −0.383384 | ||||||||
\(306\) | 5772.33 | 1.07837 | ||||||||
\(307\) | −2974.73 | −0.553020 | −0.276510 | − | 0.961011i | \(-0.589178\pi\) | ||||
−0.276510 | + | 0.961011i | \(0.589178\pi\) | |||||||
\(308\) | 469.413 | 0.0868418 | ||||||||
\(309\) | −43.0783 | −0.00793087 | ||||||||
\(310\) | 6299.78 | 1.15421 | ||||||||
\(311\) | −8271.14 | −1.50808 | −0.754040 | − | 0.656828i | \(-0.771898\pi\) | ||||
−0.754040 | + | 0.656828i | \(0.771898\pi\) | |||||||
\(312\) | −2294.07 | −0.416269 | ||||||||
\(313\) | 4256.50 | 0.768664 | 0.384332 | − | 0.923195i | \(-0.374432\pi\) | ||||
0.384332 | + | 0.923195i | \(0.374432\pi\) | |||||||
\(314\) | −4593.15 | −0.825498 | ||||||||
\(315\) | −2356.50 | −0.421504 | ||||||||
\(316\) | −1461.31 | −0.260142 | ||||||||
\(317\) | −5331.95 | −0.944708 | −0.472354 | − | 0.881409i | \(-0.656596\pi\) | ||||
−0.472354 | + | 0.881409i | \(0.656596\pi\) | |||||||
\(318\) | 1605.71 | 0.283157 | ||||||||
\(319\) | −533.812 | −0.0936919 | ||||||||
\(320\) | 4435.19 | 0.774796 | ||||||||
\(321\) | 1948.39 | 0.338781 | ||||||||
\(322\) | 730.503 | 0.126427 | ||||||||
\(323\) | −8172.83 | −1.40789 | ||||||||
\(324\) | 731.160 | 0.125370 | ||||||||
\(325\) | −404.349 | −0.0690130 | ||||||||
\(326\) | 8778.09 | 1.49133 | ||||||||
\(327\) | 568.558 | 0.0961509 | ||||||||
\(328\) | −4404.51 | −0.741458 | ||||||||
\(329\) | −5159.92 | −0.864668 | ||||||||
\(330\) | 2015.33 | 0.336183 | ||||||||
\(331\) | 4689.05 | 0.778650 | 0.389325 | − | 0.921100i | \(-0.372708\pi\) | ||||
0.389325 | + | 0.921100i | \(0.372708\pi\) | |||||||
\(332\) | −815.169 | −0.134754 | ||||||||
\(333\) | 2097.82 | 0.345224 | ||||||||
\(334\) | −6957.29 | −1.13978 | ||||||||
\(335\) | −7857.09 | −1.28143 | ||||||||
\(336\) | 896.009 | 0.145480 | ||||||||
\(337\) | 11172.1 | 1.80588 | 0.902938 | − | 0.429770i | \(-0.141405\pi\) | ||||
0.902938 | + | 0.429770i | \(0.141405\pi\) | |||||||
\(338\) | −12052.6 | −1.93957 | ||||||||
\(339\) | −498.576 | −0.0798789 | ||||||||
\(340\) | 1070.35 | 0.170729 | ||||||||
\(341\) | −7976.56 | −1.26673 | ||||||||
\(342\) | −8189.98 | −1.29492 | ||||||||
\(343\) | −5275.45 | −0.830459 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 434.987 | 0.0678809 | ||||||||
\(346\) | 5757.30 | 0.894550 | ||||||||
\(347\) | 7176.25 | 1.11020 | 0.555102 | − | 0.831782i | \(-0.312679\pi\) | ||||
0.555102 | + | 0.831782i | \(0.312679\pi\) | |||||||
\(348\) | 23.2768 | 0.00358553 | ||||||||
\(349\) | −8305.35 | −1.27385 | −0.636927 | − | 0.770924i | \(-0.719795\pi\) | ||||
−0.636927 | + | 0.770924i | \(0.719795\pi\) | |||||||
\(350\) | 135.525 | 0.0206975 | ||||||||
\(351\) | 5826.84 | 0.886079 | ||||||||
\(352\) | 2440.02 | 0.369469 | ||||||||
\(353\) | 5746.60 | 0.866461 | 0.433231 | − | 0.901283i | \(-0.357374\pi\) | ||||
0.433231 | + | 0.901283i | \(0.357374\pi\) | |||||||
\(354\) | −271.425 | −0.0407516 | ||||||||
\(355\) | 5198.84 | 0.777256 | ||||||||
\(356\) | 8.59158 | 0.00127908 | ||||||||
\(357\) | −936.093 | −0.138777 | ||||||||
\(358\) | 3243.78 | 0.478881 | ||||||||
\(359\) | 1277.28 | 0.187778 | 0.0938891 | − | 0.995583i | \(-0.470070\pi\) | ||||
0.0938891 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(360\) | −5588.27 | −0.818132 | ||||||||
\(361\) | 4736.88 | 0.690608 | ||||||||
\(362\) | −3394.75 | −0.492885 | ||||||||
\(363\) | −648.548 | −0.0937739 | ||||||||
\(364\) | 871.538 | 0.125497 | ||||||||
\(365\) | −13462.7 | −1.93060 | ||||||||
\(366\) | −812.917 | −0.116098 | ||||||||
\(367\) | −3186.62 | −0.453243 | −0.226622 | − | 0.973983i | \(-0.572768\pi\) | ||||
−0.226622 | + | 0.973983i | \(0.572768\pi\) | |||||||
\(368\) | 2018.72 | 0.285959 | ||||||||
\(369\) | 5373.52 | 0.758087 | ||||||||
\(370\) | 2804.65 | 0.394073 | ||||||||
\(371\) | 3178.27 | 0.444764 | ||||||||
\(372\) | 347.816 | 0.0484770 | ||||||||
\(373\) | 10717.8 | 1.48779 | 0.743894 | − | 0.668298i | \(-0.232977\pi\) | ||||
0.743894 | + | 0.668298i | \(0.232977\pi\) | |||||||
\(374\) | −9771.31 | −1.35097 | ||||||||
\(375\) | 2037.40 | 0.280562 | ||||||||
\(376\) | −12236.4 | −1.67831 | ||||||||
\(377\) | −991.105 | −0.135397 | ||||||||
\(378\) | −1952.97 | −0.265741 | ||||||||
\(379\) | 1001.31 | 0.135709 | 0.0678544 | − | 0.997695i | \(-0.478385\pi\) | ||||
0.0678544 | + | 0.997695i | \(0.478385\pi\) | |||||||
\(380\) | −1518.65 | −0.205013 | ||||||||
\(381\) | −423.886 | −0.0569983 | ||||||||
\(382\) | 1829.89 | 0.245092 | ||||||||
\(383\) | −2126.29 | −0.283677 | −0.141838 | − | 0.989890i | \(-0.545301\pi\) | ||||
−0.141838 | + | 0.989890i | \(0.545301\pi\) | |||||||
\(384\) | 2426.25 | 0.322433 | ||||||||
\(385\) | 3989.04 | 0.528053 | ||||||||
\(386\) | 13467.0 | 1.77578 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1319.61 | −0.172663 | ||||||||
\(389\) | −11830.9 | −1.54203 | −0.771014 | − | 0.636819i | \(-0.780250\pi\) | ||||
−0.771014 | + | 0.636819i | \(0.780250\pi\) | |||||||
\(390\) | 3741.78 | 0.485827 | ||||||||
\(391\) | −2109.03 | −0.272783 | ||||||||
\(392\) | −5494.21 | −0.707907 | ||||||||
\(393\) | −2183.56 | −0.280270 | ||||||||
\(394\) | −6711.44 | −0.858166 | ||||||||
\(395\) | −12418.1 | −1.58183 | ||||||||
\(396\) | −1358.08 | −0.172339 | ||||||||
\(397\) | −4635.30 | −0.585992 | −0.292996 | − | 0.956114i | \(-0.594652\pi\) | ||||
−0.292996 | + | 0.956114i | \(0.594652\pi\) | |||||||
\(398\) | 9027.43 | 1.13694 | ||||||||
\(399\) | 1328.16 | 0.166645 | ||||||||
\(400\) | 374.518 | 0.0468147 | ||||||||
\(401\) | −12934.8 | −1.61081 | −0.805406 | − | 0.592724i | \(-0.798052\pi\) | ||||
−0.805406 | + | 0.592724i | \(0.798052\pi\) | |||||||
\(402\) | −3127.69 | −0.388048 | ||||||||
\(403\) | −14809.7 | −1.83058 | ||||||||
\(404\) | 1670.00 | 0.205658 | ||||||||
\(405\) | 6213.36 | 0.762332 | ||||||||
\(406\) | 332.187 | 0.0406063 | ||||||||
\(407\) | −3551.15 | −0.432491 | ||||||||
\(408\) | −2219.88 | −0.269363 | ||||||||
\(409\) | 1367.64 | 0.165343 | 0.0826717 | − | 0.996577i | \(-0.473655\pi\) | ||||
0.0826717 | + | 0.996577i | \(0.473655\pi\) | |||||||
\(410\) | 7184.06 | 0.865355 | ||||||||
\(411\) | −2647.02 | −0.317683 | ||||||||
\(412\) | 38.8104 | 0.00464091 | ||||||||
\(413\) | −537.245 | −0.0640099 | ||||||||
\(414\) | −2113.45 | −0.250895 | ||||||||
\(415\) | −6927.26 | −0.819388 | ||||||||
\(416\) | 4530.27 | 0.533930 | ||||||||
\(417\) | 892.288 | 0.104785 | ||||||||
\(418\) | 13863.9 | 1.62226 | ||||||||
\(419\) | −11334.8 | −1.32158 | −0.660790 | − | 0.750571i | \(-0.729779\pi\) | ||||
−0.660790 | + | 0.750571i | \(0.729779\pi\) | |||||||
\(420\) | −173.942 | −0.0202083 | ||||||||
\(421\) | 16468.4 | 1.90646 | 0.953231 | − | 0.302242i | \(-0.0977350\pi\) | ||||
0.953231 | + | 0.302242i | \(0.0977350\pi\) | |||||||
\(422\) | −9513.63 | −1.09743 | ||||||||
\(423\) | 14928.4 | 1.71594 | ||||||||
\(424\) | 7537.03 | 0.863279 | ||||||||
\(425\) | −391.272 | −0.0446576 | ||||||||
\(426\) | 2069.52 | 0.235372 | ||||||||
\(427\) | −1609.05 | −0.182359 | ||||||||
\(428\) | −1755.36 | −0.198245 | ||||||||
\(429\) | −4737.71 | −0.533190 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10893.5 | 1.21745 | 0.608726 | − | 0.793380i | \(-0.291681\pi\) | ||||
0.608726 | + | 0.793380i | \(0.291681\pi\) | |||||||
\(432\) | −5396.96 | −0.601068 | ||||||||
\(433\) | −7492.45 | −0.831557 | −0.415779 | − | 0.909466i | \(-0.636491\pi\) | ||||
−0.415779 | + | 0.909466i | \(0.636491\pi\) | |||||||
\(434\) | 4963.75 | 0.549004 | ||||||||
\(435\) | 197.805 | 0.0218023 | ||||||||
\(436\) | −512.230 | −0.0562646 | ||||||||
\(437\) | 2992.36 | 0.327561 | ||||||||
\(438\) | −5359.12 | −0.584631 | ||||||||
\(439\) | 4521.53 | 0.491574 | 0.245787 | − | 0.969324i | \(-0.420954\pi\) | ||||
0.245787 | + | 0.969324i | \(0.420954\pi\) | |||||||
\(440\) | 9459.72 | 1.02494 | ||||||||
\(441\) | 6702.96 | 0.723783 | ||||||||
\(442\) | −18142.0 | −1.95232 | ||||||||
\(443\) | −8805.39 | −0.944372 | −0.472186 | − | 0.881499i | \(-0.656535\pi\) | ||||
−0.472186 | + | 0.881499i | \(0.656535\pi\) | |||||||
\(444\) | 154.847 | 0.0165512 | ||||||||
\(445\) | 73.0108 | 0.00777763 | ||||||||
\(446\) | 5855.43 | 0.621665 | ||||||||
\(447\) | −3259.94 | −0.344943 | ||||||||
\(448\) | 3494.59 | 0.368536 | ||||||||
\(449\) | 10437.9 | 1.09709 | 0.548545 | − | 0.836121i | \(-0.315182\pi\) | ||||
0.548545 | + | 0.836121i | \(0.315182\pi\) | |||||||
\(450\) | −392.094 | −0.0410744 | ||||||||
\(451\) | −9096.20 | −0.949719 | ||||||||
\(452\) | 449.181 | 0.0467427 | ||||||||
\(453\) | −4215.40 | −0.437211 | ||||||||
\(454\) | 1670.91 | 0.172731 | ||||||||
\(455\) | 7406.28 | 0.763103 | ||||||||
\(456\) | 3149.64 | 0.323454 | ||||||||
\(457\) | −3984.75 | −0.407875 | −0.203938 | − | 0.978984i | \(-0.565374\pi\) | ||||
−0.203938 | + | 0.978984i | \(0.565374\pi\) | |||||||
\(458\) | −6968.96 | −0.711000 | ||||||||
\(459\) | 5638.40 | 0.573373 | ||||||||
\(460\) | −391.892 | −0.0397219 | ||||||||
\(461\) | −5737.15 | −0.579622 | −0.289811 | − | 0.957084i | \(-0.593592\pi\) | ||||
−0.289811 | + | 0.957084i | \(0.593592\pi\) | |||||||
\(462\) | 1587.93 | 0.159907 | ||||||||
\(463\) | 1479.27 | 0.148483 | 0.0742415 | − | 0.997240i | \(-0.476346\pi\) | ||||
0.0742415 | + | 0.997240i | \(0.476346\pi\) | |||||||
\(464\) | 917.986 | 0.0918457 | ||||||||
\(465\) | 2955.73 | 0.294771 | ||||||||
\(466\) | −15217.4 | −1.51273 | ||||||||
\(467\) | 7229.61 | 0.716373 | 0.358187 | − | 0.933650i | \(-0.383395\pi\) | ||||
0.358187 | + | 0.933650i | \(0.383395\pi\) | |||||||
\(468\) | −2521.49 | −0.249051 | ||||||||
\(469\) | −6190.79 | −0.609518 | ||||||||
\(470\) | 19958.4 | 1.95875 | ||||||||
\(471\) | −2155.01 | −0.210823 | ||||||||
\(472\) | −1274.04 | −0.124242 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −4943.31 | −0.479016 | ||||||||
\(475\) | 555.150 | 0.0536254 | ||||||||
\(476\) | 843.353 | 0.0812080 | ||||||||
\(477\) | −9195.20 | −0.882640 | ||||||||
\(478\) | 11600.3 | 1.11002 | ||||||||
\(479\) | 11043.4 | 1.05342 | 0.526708 | − | 0.850046i | \(-0.323426\pi\) | ||||
0.526708 | + | 0.850046i | \(0.323426\pi\) | |||||||
\(480\) | −904.151 | −0.0859764 | ||||||||
\(481\) | −6593.27 | −0.625004 | ||||||||
\(482\) | 19105.6 | 1.80547 | ||||||||
\(483\) | 342.737 | 0.0322879 | ||||||||
\(484\) | 584.295 | 0.0548737 | ||||||||
\(485\) | −11214.0 | −1.04990 | ||||||||
\(486\) | 8586.53 | 0.801426 | ||||||||
\(487\) | 4969.09 | 0.462364 | 0.231182 | − | 0.972911i | \(-0.425741\pi\) | ||||
0.231182 | + | 0.972911i | \(0.425741\pi\) | |||||||
\(488\) | −3815.73 | −0.353955 | ||||||||
\(489\) | 4118.50 | 0.380869 | ||||||||
\(490\) | 8961.44 | 0.826197 | ||||||||
\(491\) | 7549.09 | 0.693861 | 0.346931 | − | 0.937891i | \(-0.387224\pi\) | ||||
0.346931 | + | 0.937891i | \(0.387224\pi\) | |||||||
\(492\) | 396.638 | 0.0363452 | ||||||||
\(493\) | −959.053 | −0.0876138 | ||||||||
\(494\) | 25740.4 | 2.34437 | ||||||||
\(495\) | −11540.9 | −1.04793 | ||||||||
\(496\) | 13717.1 | 1.24177 | ||||||||
\(497\) | 4096.29 | 0.369706 | ||||||||
\(498\) | −2757.55 | −0.248130 | ||||||||
\(499\) | 2644.30 | 0.237225 | 0.118612 | − | 0.992941i | \(-0.462155\pi\) | ||||
0.118612 | + | 0.992941i | \(0.462155\pi\) | |||||||
\(500\) | −1835.55 | −0.164177 | ||||||||
\(501\) | −3264.22 | −0.291087 | ||||||||
\(502\) | −2860.21 | −0.254298 | ||||||||
\(503\) | 18851.7 | 1.67109 | 0.835544 | − | 0.549424i | \(-0.185153\pi\) | ||||
0.835544 | + | 0.549424i | \(0.185153\pi\) | |||||||
\(504\) | −4403.13 | −0.389149 | ||||||||
\(505\) | 14191.6 | 1.25053 | ||||||||
\(506\) | 3577.62 | 0.314318 | ||||||||
\(507\) | −5654.81 | −0.495343 | ||||||||
\(508\) | 381.891 | 0.0333537 | ||||||||
\(509\) | −7646.38 | −0.665855 | −0.332927 | − | 0.942952i | \(-0.608036\pi\) | ||||
−0.332927 | + | 0.942952i | \(0.608036\pi\) | |||||||
\(510\) | 3620.77 | 0.314374 | ||||||||
\(511\) | −10607.6 | −0.918298 | ||||||||
\(512\) | 7691.90 | 0.663940 | ||||||||
\(513\) | −7999.96 | −0.688512 | ||||||||
\(514\) | 22013.9 | 1.88909 | ||||||||
\(515\) | 329.809 | 0.0282197 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25270.6 | −2.14971 | ||||||||
\(518\) | 2209.85 | 0.187443 | ||||||||
\(519\) | 2701.20 | 0.228458 | ||||||||
\(520\) | 17563.5 | 1.48117 | ||||||||
\(521\) | −15427.5 | −1.29729 | −0.648646 | − | 0.761090i | \(-0.724664\pi\) | ||||
−0.648646 | + | 0.761090i | \(0.724664\pi\) | |||||||
\(522\) | −961.066 | −0.0805838 | ||||||||
\(523\) | −14469.9 | −1.20980 | −0.604899 | − | 0.796302i | \(-0.706786\pi\) | ||||
−0.604899 | + | 0.796302i | \(0.706786\pi\) | |||||||
\(524\) | 1967.23 | 0.164006 | ||||||||
\(525\) | 63.5854 | 0.00528589 | ||||||||
\(526\) | −20846.6 | −1.72805 | ||||||||
\(527\) | −14330.8 | −1.18455 | ||||||||
\(528\) | 4388.18 | 0.361688 | ||||||||
\(529\) | −11394.8 | −0.936534 | ||||||||
\(530\) | −12293.4 | −1.00753 | ||||||||
\(531\) | 1554.33 | 0.127028 | ||||||||
\(532\) | −1196.58 | −0.0975154 | ||||||||
\(533\) | −16888.5 | −1.37246 | ||||||||
\(534\) | 29.0636 | 0.00235525 | ||||||||
\(535\) | −14917.0 | −1.20545 | ||||||||
\(536\) | −14681.0 | −1.18306 | ||||||||
\(537\) | 1521.92 | 0.122301 | ||||||||
\(538\) | 12098.6 | 0.969534 | ||||||||
\(539\) | −11346.7 | −0.906744 | ||||||||
\(540\) | 1047.71 | 0.0834929 | ||||||||
\(541\) | −2852.57 | −0.226694 | −0.113347 | − | 0.993555i | \(-0.536157\pi\) | ||||
−0.113347 | + | 0.993555i | \(0.536157\pi\) | |||||||
\(542\) | 22673.7 | 1.79690 | ||||||||
\(543\) | −1592.75 | −0.125877 | ||||||||
\(544\) | 4383.76 | 0.345501 | ||||||||
\(545\) | −4352.90 | −0.342125 | ||||||||
\(546\) | 2948.24 | 0.231086 | ||||||||
\(547\) | 1910.22 | 0.149315 | 0.0746574 | − | 0.997209i | \(-0.476214\pi\) | ||||
0.0746574 | + | 0.997209i | \(0.476214\pi\) | |||||||
\(548\) | 2384.77 | 0.185899 | ||||||||
\(549\) | 4655.21 | 0.361893 | ||||||||
\(550\) | 663.730 | 0.0514573 | ||||||||
\(551\) | 1360.74 | 0.105208 | ||||||||
\(552\) | 812.775 | 0.0626703 | ||||||||
\(553\) | −9784.53 | −0.752406 | ||||||||
\(554\) | 1912.09 | 0.146637 | ||||||||
\(555\) | 1315.88 | 0.100642 | ||||||||
\(556\) | −803.888 | −0.0613173 | ||||||||
\(557\) | −1503.15 | −0.114345 | −0.0571726 | − | 0.998364i | \(-0.518209\pi\) | ||||
−0.0571726 | + | 0.998364i | \(0.518209\pi\) | |||||||
\(558\) | −14360.9 | −1.08951 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −6859.88 | −0.517648 | ||||||||
\(561\) | −4584.49 | −0.345022 | ||||||||
\(562\) | −26383.0 | −1.98025 | ||||||||
\(563\) | −7608.15 | −0.569530 | −0.284765 | − | 0.958597i | \(-0.591916\pi\) | ||||
−0.284765 | + | 0.958597i | \(0.591916\pi\) | |||||||
\(564\) | 1101.92 | 0.0822680 | ||||||||
\(565\) | 3817.12 | 0.284226 | ||||||||
\(566\) | 17479.4 | 1.29808 | ||||||||
\(567\) | 4895.66 | 0.362607 | ||||||||
\(568\) | 9714.06 | 0.717593 | ||||||||
\(569\) | 5914.01 | 0.435726 | 0.217863 | − | 0.975979i | \(-0.430091\pi\) | ||||
0.217863 | + | 0.975979i | \(0.430091\pi\) | |||||||
\(570\) | −5137.28 | −0.377503 | ||||||||
\(571\) | −7673.35 | −0.562381 | −0.281191 | − | 0.959652i | \(-0.590729\pi\) | ||||
−0.281191 | + | 0.959652i | \(0.590729\pi\) | |||||||
\(572\) | 4268.34 | 0.312007 | ||||||||
\(573\) | 858.545 | 0.0625938 | ||||||||
\(574\) | 5660.49 | 0.411611 | ||||||||
\(575\) | 143.259 | 0.0103901 | ||||||||
\(576\) | −10110.4 | −0.731364 | ||||||||
\(577\) | −14776.8 | −1.06615 | −0.533074 | − | 0.846069i | \(-0.678963\pi\) | ||||
−0.533074 | + | 0.846069i | \(0.678963\pi\) | |||||||
\(578\) | −2582.11 | −0.185816 | ||||||||
\(579\) | 6318.42 | 0.453514 | ||||||||
\(580\) | −178.208 | −0.0127581 | ||||||||
\(581\) | −5458.16 | −0.389746 | ||||||||
\(582\) | −4463.99 | −0.317935 | ||||||||
\(583\) | 15565.5 | 1.10576 | ||||||||
\(584\) | −25155.0 | −1.78240 | ||||||||
\(585\) | −21427.5 | −1.51439 | ||||||||
\(586\) | 6499.41 | 0.458171 | ||||||||
\(587\) | 7695.08 | 0.541073 | 0.270537 | − | 0.962710i | \(-0.412799\pi\) | ||||
0.270537 | + | 0.962710i | \(0.412799\pi\) | |||||||
\(588\) | 494.769 | 0.0347006 | ||||||||
\(589\) | 20333.0 | 1.42242 | ||||||||
\(590\) | 2078.04 | 0.145003 | ||||||||
\(591\) | −3148.87 | −0.219166 | ||||||||
\(592\) | 6106.85 | 0.423969 | ||||||||
\(593\) | 20083.7 | 1.39079 | 0.695395 | − | 0.718628i | \(-0.255229\pi\) | ||||
0.695395 | + | 0.718628i | \(0.255229\pi\) | |||||||
\(594\) | −9564.63 | −0.660676 | ||||||||
\(595\) | 7166.77 | 0.493796 | ||||||||
\(596\) | 2936.97 | 0.201851 | ||||||||
\(597\) | 4235.48 | 0.290363 | ||||||||
\(598\) | 6642.41 | 0.454228 | ||||||||
\(599\) | −15219.6 | −1.03815 | −0.519077 | − | 0.854727i | \(-0.673724\pi\) | ||||
−0.519077 | + | 0.854727i | \(0.673724\pi\) | |||||||
\(600\) | 150.788 | 0.0102598 | ||||||||
\(601\) | −2102.90 | −0.142727 | −0.0713636 | − | 0.997450i | \(-0.522735\pi\) | ||||
−0.0713636 | + | 0.997450i | \(0.522735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17910.9 | 1.20960 | ||||||||
\(604\) | 3797.77 | 0.255843 | ||||||||
\(605\) | 4965.31 | 0.333667 | ||||||||
\(606\) | 5649.28 | 0.378691 | ||||||||
\(607\) | −11150.6 | −0.745617 | −0.372808 | − | 0.927908i | \(-0.621605\pi\) | ||||
−0.372808 | + | 0.927908i | \(0.621605\pi\) | |||||||
\(608\) | −6219.83 | −0.414881 | ||||||||
\(609\) | 155.855 | 0.0103704 | ||||||||
\(610\) | 6223.73 | 0.413101 | ||||||||
\(611\) | −46918.8 | −3.10660 | ||||||||
\(612\) | −2439.95 | −0.161158 | ||||||||
\(613\) | 6496.14 | 0.428021 | 0.214010 | − | 0.976831i | \(-0.431347\pi\) | ||||
0.214010 | + | 0.976831i | \(0.431347\pi\) | |||||||
\(614\) | 9065.98 | 0.595885 | ||||||||
\(615\) | 3370.61 | 0.221002 | ||||||||
\(616\) | 7453.54 | 0.487519 | ||||||||
\(617\) | −5614.43 | −0.366335 | −0.183167 | − | 0.983082i | \(-0.558635\pi\) | ||||
−0.183167 | + | 0.983082i | \(0.558635\pi\) | |||||||
\(618\) | 131.288 | 0.00854559 | ||||||||
\(619\) | 4482.99 | 0.291093 | 0.145546 | − | 0.989351i | \(-0.453506\pi\) | ||||
0.145546 | + | 0.989351i | \(0.453506\pi\) | |||||||
\(620\) | −2662.90 | −0.172491 | ||||||||
\(621\) | −2064.42 | −0.133401 | ||||||||
\(622\) | 25207.6 | 1.62497 | ||||||||
\(623\) | 57.5270 | 0.00369947 | ||||||||
\(624\) | 8147.35 | 0.522684 | ||||||||
\(625\) | −14954.0 | −0.957056 | ||||||||
\(626\) | −12972.4 | −0.828243 | ||||||||
\(627\) | 6504.63 | 0.414306 | ||||||||
\(628\) | 1941.51 | 0.123367 | ||||||||
\(629\) | −6380.04 | −0.404434 | ||||||||
\(630\) | 7181.81 | 0.454175 | ||||||||
\(631\) | 22320.4 | 1.40818 | 0.704088 | − | 0.710112i | \(-0.251356\pi\) | ||||
0.704088 | + | 0.710112i | \(0.251356\pi\) | |||||||
\(632\) | −23203.3 | −1.46041 | ||||||||
\(633\) | −4463.59 | −0.280272 | ||||||||
\(634\) | 16250.0 | 1.01793 | ||||||||
\(635\) | 3245.29 | 0.202812 | ||||||||
\(636\) | −678.730 | −0.0423167 | ||||||||
\(637\) | −21066.8 | −1.31036 | ||||||||
\(638\) | 1626.88 | 0.100954 | ||||||||
\(639\) | −11851.2 | −0.733686 | ||||||||
\(640\) | −18575.5 | −1.14728 | ||||||||
\(641\) | −6797.76 | −0.418869 | −0.209435 | − | 0.977823i | \(-0.567162\pi\) | ||||
−0.209435 | + | 0.977823i | \(0.567162\pi\) | |||||||
\(642\) | −5938.04 | −0.365040 | ||||||||
\(643\) | −6933.22 | −0.425225 | −0.212612 | − | 0.977137i | \(-0.568197\pi\) | ||||
−0.212612 | + | 0.977137i | \(0.568197\pi\) | |||||||
\(644\) | −308.781 | −0.0188939 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24908.0 | 1.51702 | ||||||||
\(647\) | 14748.6 | 0.896180 | 0.448090 | − | 0.893989i | \(-0.352104\pi\) | ||||
0.448090 | + | 0.893989i | \(0.352104\pi\) | |||||||
\(648\) | 11609.7 | 0.703814 | ||||||||
\(649\) | −2631.14 | −0.159139 | ||||||||
\(650\) | 1232.32 | 0.0743623 | ||||||||
\(651\) | 2328.89 | 0.140209 | ||||||||
\(652\) | −3710.47 | −0.222873 | ||||||||
\(653\) | 10205.7 | 0.611605 | 0.305803 | − | 0.952095i | \(-0.401075\pi\) | ||||
0.305803 | + | 0.952095i | \(0.401075\pi\) | |||||||
\(654\) | −1732.77 | −0.103604 | ||||||||
\(655\) | 16717.4 | 0.997259 | ||||||||
\(656\) | 15642.6 | 0.931005 | ||||||||
\(657\) | 30689.2 | 1.82238 | ||||||||
\(658\) | 15725.7 | 0.931689 | ||||||||
\(659\) | 25166.3 | 1.48762 | 0.743809 | − | 0.668392i | \(-0.233017\pi\) | ||||
0.743809 | + | 0.668392i | \(0.233017\pi\) | |||||||
\(660\) | −851.874 | −0.0502412 | ||||||||
\(661\) | 18594.5 | 1.09416 | 0.547080 | − | 0.837080i | \(-0.315739\pi\) | ||||
0.547080 | + | 0.837080i | \(0.315739\pi\) | |||||||
\(662\) | −14290.6 | −0.839004 | ||||||||
\(663\) | −8511.83 | −0.498600 | ||||||||
\(664\) | −12943.6 | −0.756491 | ||||||||
\(665\) | −10168.5 | −0.592956 | ||||||||
\(666\) | −6393.43 | −0.371983 | ||||||||
\(667\) | 351.143 | 0.0203843 | ||||||||
\(668\) | 2940.82 | 0.170335 | ||||||||
\(669\) | 2747.24 | 0.158766 | ||||||||
\(670\) | 23945.7 | 1.38075 | ||||||||
\(671\) | −7880.26 | −0.453374 | ||||||||
\(672\) | −712.402 | −0.0408951 | ||||||||
\(673\) | 25367.1 | 1.45294 | 0.726471 | − | 0.687197i | \(-0.241159\pi\) | ||||
0.726471 | + | 0.687197i | \(0.241159\pi\) | |||||||
\(674\) | −34048.6 | −1.94585 | ||||||||
\(675\) | −382.996 | −0.0218393 | ||||||||
\(676\) | 5094.58 | 0.289860 | ||||||||
\(677\) | −8839.77 | −0.501831 | −0.250916 | − | 0.968009i | \(-0.580732\pi\) | ||||
−0.250916 | + | 0.968009i | \(0.580732\pi\) | |||||||
\(678\) | 1519.49 | 0.0860704 | ||||||||
\(679\) | −8835.78 | −0.499391 | ||||||||
\(680\) | 16995.5 | 0.958450 | ||||||||
\(681\) | 783.957 | 0.0441135 | ||||||||
\(682\) | 24309.8 | 1.36492 | ||||||||
\(683\) | 11252.9 | 0.630426 | 0.315213 | − | 0.949021i | \(-0.397924\pi\) | ||||
0.315213 | + | 0.949021i | \(0.397924\pi\) | |||||||
\(684\) | 3461.88 | 0.193521 | ||||||||
\(685\) | 20265.7 | 1.13038 | ||||||||
\(686\) | 16077.8 | 0.894828 | ||||||||
\(687\) | −3269.69 | −0.181581 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28899.7 | 1.59796 | ||||||||
\(690\) | −1325.69 | −0.0731424 | ||||||||
\(691\) | −19933.8 | −1.09742 | −0.548711 | − | 0.836012i | \(-0.684881\pi\) | ||||
−0.548711 | + | 0.836012i | \(0.684881\pi\) | |||||||
\(692\) | −2433.59 | −0.133687 | ||||||||
\(693\) | −9093.35 | −0.498453 | ||||||||
\(694\) | −21870.8 | −1.19626 | ||||||||
\(695\) | −6831.40 | −0.372848 | ||||||||
\(696\) | 369.599 | 0.0201287 | ||||||||
\(697\) | −16342.4 | −0.888107 | ||||||||
\(698\) | 25311.9 | 1.37259 | ||||||||
\(699\) | −7139.70 | −0.386335 | ||||||||
\(700\) | −57.2859 | −0.00309315 | ||||||||
\(701\) | 13753.9 | 0.741052 | 0.370526 | − | 0.928822i | \(-0.379177\pi\) | ||||
0.370526 | + | 0.928822i | \(0.379177\pi\) | |||||||
\(702\) | −17758.2 | −0.954760 | ||||||||
\(703\) | 9052.22 | 0.485649 | ||||||||
\(704\) | 17114.7 | 0.916241 | ||||||||
\(705\) | 9364.05 | 0.500242 | ||||||||
\(706\) | −17513.7 | −0.933621 | ||||||||
\(707\) | 11181.9 | 0.594821 | ||||||||
\(708\) | 114.730 | 0.00609016 | ||||||||
\(709\) | −22572.7 | −1.19568 | −0.597840 | − | 0.801616i | \(-0.703974\pi\) | ||||
−0.597840 | + | 0.801616i | \(0.703974\pi\) | |||||||
\(710\) | −15844.3 | −0.837502 | ||||||||
\(711\) | 28308.1 | 1.49316 | ||||||||
\(712\) | 136.421 | 0.00718061 | ||||||||
\(713\) | 5247.01 | 0.275599 | ||||||||
\(714\) | 2852.89 | 0.149533 | ||||||||
\(715\) | 36272.1 | 1.89720 | ||||||||
\(716\) | −1371.14 | −0.0715667 | ||||||||
\(717\) | 5442.63 | 0.283485 | ||||||||
\(718\) | −3892.72 | −0.202333 | ||||||||
\(719\) | −12405.4 | −0.643456 | −0.321728 | − | 0.946832i | \(-0.604264\pi\) | ||||
−0.321728 | + | 0.946832i | \(0.604264\pi\) | |||||||
\(720\) | 19846.7 | 1.02728 | ||||||||
\(721\) | 259.865 | 0.0134228 | ||||||||
\(722\) | −14436.4 | −0.744138 | ||||||||
\(723\) | 8963.95 | 0.461097 | ||||||||
\(724\) | 1434.95 | 0.0736595 | ||||||||
\(725\) | 65.1450 | 0.00333714 | ||||||||
\(726\) | 1976.55 | 0.101042 | ||||||||
\(727\) | −20179.9 | −1.02948 | −0.514740 | − | 0.857346i | \(-0.672112\pi\) | ||||
−0.514740 | + | 0.857346i | \(0.672112\pi\) | |||||||
\(728\) | 13838.7 | 0.704526 | ||||||||
\(729\) | −11295.7 | −0.573881 | ||||||||
\(730\) | 41029.6 | 2.08024 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 343.617 | 0.0173504 | ||||||||
\(733\) | 36311.8 | 1.82975 | 0.914875 | − | 0.403736i | \(-0.132289\pi\) | ||||
0.914875 | + | 0.403736i | \(0.132289\pi\) | |||||||
\(734\) | 9711.74 | 0.488374 | ||||||||
\(735\) | 4204.52 | 0.211001 | ||||||||
\(736\) | −1605.05 | −0.0803844 | ||||||||
\(737\) | −30319.2 | −1.51536 | ||||||||
\(738\) | −16376.7 | −0.816847 | ||||||||
\(739\) | 6848.62 | 0.340907 | 0.170454 | − | 0.985366i | \(-0.445477\pi\) | ||||
0.170454 | + | 0.985366i | \(0.445477\pi\) | |||||||
\(740\) | −1185.52 | −0.0588925 | ||||||||
\(741\) | 12076.9 | 0.598724 | ||||||||
\(742\) | −9686.28 | −0.479238 | ||||||||
\(743\) | 10685.7 | 0.527616 | 0.263808 | − | 0.964575i | \(-0.415022\pi\) | ||||
0.263808 | + | 0.964575i | \(0.415022\pi\) | |||||||
\(744\) | 5522.78 | 0.272144 | ||||||||
\(745\) | 24958.2 | 1.22738 | ||||||||
\(746\) | −32664.1 | −1.60311 | ||||||||
\(747\) | 15791.3 | 0.773457 | ||||||||
\(748\) | 4130.30 | 0.201897 | ||||||||
\(749\) | −11753.4 | −0.573380 | ||||||||
\(750\) | −6209.31 | −0.302309 | ||||||||
\(751\) | 17077.6 | 0.829786 | 0.414893 | − | 0.909870i | \(-0.363819\pi\) | ||||
0.414893 | + | 0.909870i | \(0.363819\pi\) | |||||||
\(752\) | 43457.3 | 2.10735 | ||||||||
\(753\) | −1341.95 | −0.0649447 | ||||||||
\(754\) | 3020.55 | 0.145891 | ||||||||
\(755\) | 32273.3 | 1.55569 | ||||||||
\(756\) | 825.514 | 0.0397138 | ||||||||
\(757\) | −13129.5 | −0.630381 | −0.315190 | − | 0.949028i | \(-0.602068\pi\) | ||||
−0.315190 | + | 0.949028i | \(0.602068\pi\) | |||||||
\(758\) | −3051.64 | −0.146228 | ||||||||
\(759\) | 1678.54 | 0.0802731 | ||||||||
\(760\) | −24113.7 | −1.15092 | ||||||||
\(761\) | 3098.58 | 0.147600 | 0.0737999 | − | 0.997273i | \(-0.476487\pi\) | ||||
0.0737999 | + | 0.997273i | \(0.476487\pi\) | |||||||
\(762\) | 1291.86 | 0.0614163 | ||||||||
\(763\) | −3429.76 | −0.162733 | ||||||||
\(764\) | −773.487 | −0.0366280 | ||||||||
\(765\) | −20734.5 | −0.979946 | ||||||||
\(766\) | 6480.20 | 0.305665 | ||||||||
\(767\) | −4885.13 | −0.229976 | ||||||||
\(768\) | −2759.95 | −0.129676 | ||||||||
\(769\) | 38020.8 | 1.78292 | 0.891460 | − | 0.453099i | \(-0.149682\pi\) | ||||
0.891460 | + | 0.453099i | \(0.149682\pi\) | |||||||
\(770\) | −12157.3 | −0.568983 | ||||||||
\(771\) | 10328.5 | 0.482451 | ||||||||
\(772\) | −5692.44 | −0.265383 | ||||||||
\(773\) | 703.368 | 0.0327275 | 0.0163638 | − | 0.999866i | \(-0.494791\pi\) | ||||
0.0163638 | + | 0.999866i | \(0.494791\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 973.438 | 0.0451186 | ||||||||
\(776\) | −20953.4 | −0.969309 | ||||||||
\(777\) | 1036.82 | 0.0478708 | ||||||||
\(778\) | 36056.5 | 1.66155 | ||||||||
\(779\) | 23187.1 | 1.06645 | ||||||||
\(780\) | −1581.64 | −0.0726048 | ||||||||
\(781\) | 20061.5 | 0.919151 | ||||||||
\(782\) | 6427.60 | 0.293927 | ||||||||
\(783\) | −938.767 | −0.0428465 | ||||||||
\(784\) | 19512.6 | 0.888877 | ||||||||
\(785\) | 16498.8 | 0.750151 | ||||||||
\(786\) | 6654.76 | 0.301994 | ||||||||
\(787\) | 24681.7 | 1.11792 | 0.558962 | − | 0.829193i | \(-0.311200\pi\) | ||||
0.558962 | + | 0.829193i | \(0.311200\pi\) | |||||||
\(788\) | 2836.90 | 0.128249 | ||||||||
\(789\) | −9780.77 | −0.441324 | ||||||||
\(790\) | 37846.2 | 1.70444 | ||||||||
\(791\) | 3007.60 | 0.135193 | ||||||||
\(792\) | −21564.2 | −0.967488 | ||||||||
\(793\) | −14630.9 | −0.655183 | ||||||||
\(794\) | 14126.8 | 0.631413 | ||||||||
\(795\) | −5767.81 | −0.257312 | ||||||||
\(796\) | −3815.86 | −0.169912 | ||||||||
\(797\) | −23603.5 | −1.04903 | −0.524516 | − | 0.851401i | \(-0.675754\pi\) | ||||
−0.524516 | + | 0.851401i | \(0.675754\pi\) | |||||||
\(798\) | −4047.78 | −0.179561 | ||||||||
\(799\) | −45401.5 | −2.01025 | ||||||||
\(800\) | −297.773 | −0.0131598 | ||||||||
\(801\) | −166.434 | −0.00734165 | ||||||||
\(802\) | 39421.0 | 1.73567 | ||||||||
\(803\) | −51950.2 | −2.28304 | ||||||||
\(804\) | 1322.06 | 0.0579921 | ||||||||
\(805\) | −2624.01 | −0.114887 | ||||||||
\(806\) | 45135.0 | 1.97247 | ||||||||
\(807\) | 5676.42 | 0.247608 | ||||||||
\(808\) | 26517.0 | 1.15454 | ||||||||
\(809\) | 22689.9 | 0.986075 | 0.493038 | − | 0.870008i | \(-0.335887\pi\) | ||||
0.493038 | + | 0.870008i | \(0.335887\pi\) | |||||||
\(810\) | −18936.2 | −0.821421 | ||||||||
\(811\) | 22849.7 | 0.989347 | 0.494674 | − | 0.869079i | \(-0.335288\pi\) | ||||
0.494674 | + | 0.869079i | \(0.335288\pi\) | |||||||
\(812\) | −140.414 | −0.00606844 | ||||||||
\(813\) | 10638.0 | 0.458908 | ||||||||
\(814\) | 10822.7 | 0.466014 | ||||||||
\(815\) | −31531.4 | −1.35521 | ||||||||
\(816\) | 7883.86 | 0.338224 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −4168.10 | −0.178159 | ||||||||
\(819\) | −16883.2 | −0.720327 | ||||||||
\(820\) | −3036.68 | −0.129324 | ||||||||
\(821\) | −12956.1 | −0.550758 | −0.275379 | − | 0.961336i | \(-0.588803\pi\) | ||||
−0.275379 | + | 0.961336i | \(0.588803\pi\) | |||||||
\(822\) | 8067.22 | 0.342307 | ||||||||
\(823\) | 41910.8 | 1.77511 | 0.887557 | − | 0.460699i | \(-0.152401\pi\) | ||||
0.887557 | + | 0.460699i | \(0.152401\pi\) | |||||||
\(824\) | 616.250 | 0.0260535 | ||||||||
\(825\) | 311.408 | 0.0131416 | ||||||||
\(826\) | 1637.34 | 0.0689713 | ||||||||
\(827\) | 11697.3 | 0.491846 | 0.245923 | − | 0.969289i | \(-0.420909\pi\) | ||||
0.245923 | + | 0.969289i | \(0.420909\pi\) | |||||||
\(828\) | 893.350 | 0.0374952 | ||||||||
\(829\) | 8944.81 | 0.374748 | 0.187374 | − | 0.982289i | \(-0.440002\pi\) | ||||
0.187374 | + | 0.982289i | \(0.440002\pi\) | |||||||
\(830\) | 21112.0 | 0.882899 | ||||||||
\(831\) | 897.110 | 0.0374493 | ||||||||
\(832\) | 31776.1 | 1.32408 | ||||||||
\(833\) | −20385.5 | −0.847920 | ||||||||
\(834\) | −2719.39 | −0.112907 | ||||||||
\(835\) | 24991.0 | 1.03575 | ||||||||
\(836\) | −5860.21 | −0.242440 | ||||||||
\(837\) | −14027.7 | −0.579292 | ||||||||
\(838\) | 34544.7 | 1.42402 | ||||||||
\(839\) | 8980.83 | 0.369550 | 0.184775 | − | 0.982781i | \(-0.440844\pi\) | ||||
0.184775 | + | 0.982781i | \(0.440844\pi\) | |||||||
\(840\) | −2761.92 | −0.113447 | ||||||||
\(841\) | −24229.3 | −0.993453 | ||||||||
\(842\) | −50190.1 | −2.05423 | ||||||||
\(843\) | −12378.4 | −0.505733 | ||||||||
\(844\) | 4021.38 | 0.164007 | ||||||||
\(845\) | 43293.5 | 1.76253 | ||||||||
\(846\) | −45496.7 | −1.84895 | ||||||||
\(847\) | 3912.29 | 0.158710 | ||||||||
\(848\) | −26767.7 | −1.08397 | ||||||||
\(849\) | 8200.96 | 0.331515 | ||||||||
\(850\) | 1192.47 | 0.0481191 | ||||||||
\(851\) | 2335.96 | 0.0940959 | ||||||||
\(852\) | −874.778 | −0.0351753 | ||||||||
\(853\) | 28833.8 | 1.15739 | 0.578694 | − | 0.815545i | \(-0.303563\pi\) | ||||
0.578694 | + | 0.815545i | \(0.303563\pi\) | |||||||
\(854\) | 4903.83 | 0.196493 | ||||||||
\(855\) | 29418.8 | 1.17673 | ||||||||
\(856\) | −27872.4 | −1.11292 | ||||||||
\(857\) | −42317.7 | −1.68675 | −0.843375 | − | 0.537325i | \(-0.819435\pi\) | ||||
−0.843375 | + | 0.537325i | \(0.819435\pi\) | |||||||
\(858\) | 14438.9 | 0.574518 | ||||||||
\(859\) | −46572.9 | −1.84988 | −0.924939 | − | 0.380115i | \(-0.875884\pi\) | ||||
−0.924939 | + | 0.380115i | \(0.875884\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2655.78 | 0.105121 | ||||||||
\(862\) | −33199.7 | −1.31182 | ||||||||
\(863\) | −10911.3 | −0.430388 | −0.215194 | − | 0.976571i | \(-0.569038\pi\) | ||||
−0.215194 | + | 0.976571i | \(0.569038\pi\) | |||||||
\(864\) | 4291.04 | 0.168963 | ||||||||
\(865\) | −20680.5 | −0.812901 | ||||||||
\(866\) | 22834.4 | 0.896012 | ||||||||
\(867\) | −1211.47 | −0.0474552 | ||||||||
\(868\) | −2098.16 | −0.0820463 | ||||||||
\(869\) | −47919.5 | −1.87061 | ||||||||
\(870\) | −602.842 | −0.0234922 | ||||||||
\(871\) | −56292.4 | −2.18989 | ||||||||
\(872\) | −8133.42 | −0.315863 | ||||||||
\(873\) | 25563.2 | 0.991047 | ||||||||
\(874\) | −9119.70 | −0.352950 | ||||||||
\(875\) | −12290.4 | −0.474846 | ||||||||
\(876\) | 2265.28 | 0.0873707 | ||||||||
\(877\) | −12978.3 | −0.499710 | −0.249855 | − | 0.968283i | \(-0.580383\pi\) | ||||
−0.249855 | + | 0.968283i | \(0.580383\pi\) | |||||||
\(878\) | −13780.1 | −0.529676 | ||||||||
\(879\) | 3049.39 | 0.117012 | ||||||||
\(880\) | −33596.1 | −1.28696 | ||||||||
\(881\) | 16494.3 | 0.630768 | 0.315384 | − | 0.948964i | \(-0.397867\pi\) | ||||
0.315384 | + | 0.948964i | \(0.397867\pi\) | |||||||
\(882\) | −20428.3 | −0.779884 | ||||||||
\(883\) | −27803.5 | −1.05964 | −0.529821 | − | 0.848110i | \(-0.677741\pi\) | ||||
−0.529821 | + | 0.848110i | \(0.677741\pi\) | |||||||
\(884\) | 7668.55 | 0.291766 | ||||||||
\(885\) | 974.973 | 0.0370321 | ||||||||
\(886\) | 26835.9 | 1.01757 | ||||||||
\(887\) | 26424.1 | 1.00026 | 0.500132 | − | 0.865949i | \(-0.333285\pi\) | ||||
0.500132 | + | 0.865949i | \(0.333285\pi\) | |||||||
\(888\) | 2458.73 | 0.0929164 | ||||||||
\(889\) | 2557.04 | 0.0964684 | ||||||||
\(890\) | −222.512 | −0.00838048 | ||||||||
\(891\) | 23976.4 | 0.901502 | ||||||||
\(892\) | −2475.07 | −0.0929053 | ||||||||
\(893\) | 64417.1 | 2.41393 | ||||||||
\(894\) | 9935.18 | 0.371680 | ||||||||
\(895\) | −11651.8 | −0.435171 | ||||||||
\(896\) | −14636.1 | −0.545711 | ||||||||
\(897\) | 3116.48 | 0.116005 | ||||||||
\(898\) | −31811.1 | −1.18213 | ||||||||
\(899\) | 2386.01 | 0.0885182 | ||||||||
\(900\) | 165.737 | 0.00613839 | ||||||||
\(901\) | 27965.1 | 1.03402 | ||||||||
\(902\) | 27722.1 | 1.02333 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7132.30 | 0.262408 | ||||||||
\(905\) | 12194.1 | 0.447897 | ||||||||
\(906\) | 12847.1 | 0.471100 | ||||||||
\(907\) | 12059.4 | 0.441484 | 0.220742 | − | 0.975332i | \(-0.429152\pi\) | ||||
0.220742 | + | 0.975332i | \(0.429152\pi\) | |||||||
\(908\) | −706.289 | −0.0258139 | ||||||||
\(909\) | −32350.9 | −1.18043 | ||||||||
\(910\) | −22571.8 | −0.822252 | ||||||||
\(911\) | −11271.8 | −0.409937 | −0.204969 | − | 0.978769i | \(-0.565709\pi\) | ||||
−0.204969 | + | 0.978769i | \(0.565709\pi\) | |||||||
\(912\) | −11185.9 | −0.406142 | ||||||||
\(913\) | −26731.2 | −0.968974 | ||||||||
\(914\) | 12144.2 | 0.439490 | ||||||||
\(915\) | 2920.04 | 0.105501 | ||||||||
\(916\) | 2945.75 | 0.106256 | ||||||||
\(917\) | 13172.1 | 0.474351 | ||||||||
\(918\) | −17183.9 | −0.617815 | ||||||||
\(919\) | 48925.3 | 1.75614 | 0.878072 | − | 0.478529i | \(-0.158830\pi\) | ||||
0.878072 | + | 0.478529i | \(0.158830\pi\) | |||||||
\(920\) | −6222.64 | −0.222994 | ||||||||
\(921\) | 4253.57 | 0.152182 | ||||||||
\(922\) | 17484.9 | 0.624549 | ||||||||
\(923\) | 37247.3 | 1.32829 | ||||||||
\(924\) | −671.212 | −0.0238975 | ||||||||
\(925\) | 433.373 | 0.0154046 | ||||||||
\(926\) | −4508.32 | −0.159992 | ||||||||
\(927\) | −751.827 | −0.0266378 | ||||||||
\(928\) | −729.876 | −0.0258183 | ||||||||
\(929\) | −13417.4 | −0.473854 | −0.236927 | − | 0.971527i | \(-0.576140\pi\) | ||||
−0.236927 | + | 0.971527i | \(0.576140\pi\) | |||||||
\(930\) | −9008.05 | −0.317619 | ||||||||
\(931\) | 28923.7 | 1.01819 | ||||||||
\(932\) | 6432.36 | 0.226072 | ||||||||
\(933\) | 11826.9 | 0.415000 | ||||||||
\(934\) | −22033.4 | −0.771900 | ||||||||
\(935\) | 35099.1 | 1.22766 | ||||||||
\(936\) | −40037.3 | −1.39814 | ||||||||
\(937\) | −16627.3 | −0.579713 | −0.289856 | − | 0.957070i | \(-0.593608\pi\) | ||||
−0.289856 | + | 0.957070i | \(0.593608\pi\) | |||||||
\(938\) | 18867.4 | 0.656763 | ||||||||
\(939\) | −6086.36 | −0.211524 | ||||||||
\(940\) | −8436.34 | −0.292727 | ||||||||
\(941\) | 2488.17 | 0.0861976 | 0.0430988 | − | 0.999071i | \(-0.486277\pi\) | ||||
0.0430988 | + | 0.999071i | \(0.486277\pi\) | |||||||
\(942\) | 6567.73 | 0.227164 | ||||||||
\(943\) | 5983.51 | 0.206628 | ||||||||
\(944\) | 4524.72 | 0.156003 | ||||||||
\(945\) | 7015.18 | 0.241485 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20531.0 | 0.704507 | 0.352254 | − | 0.935905i | \(-0.385415\pi\) | ||||
0.352254 | + | 0.935905i | \(0.385415\pi\) | |||||||
\(948\) | 2089.52 | 0.0715870 | ||||||||
\(949\) | −96453.7 | −3.29928 | ||||||||
\(950\) | −1691.91 | −0.0577819 | ||||||||
\(951\) | 7624.15 | 0.259969 | ||||||||
\(952\) | 13391.1 | 0.455892 | ||||||||
\(953\) | −34038.9 | −1.15701 | −0.578504 | − | 0.815680i | \(-0.696363\pi\) | ||||
−0.578504 | + | 0.815680i | \(0.696363\pi\) | |||||||
\(954\) | 28023.8 | 0.951054 | ||||||||
\(955\) | −6573.05 | −0.222722 | ||||||||
\(956\) | −4903.42 | −0.165887 | ||||||||
\(957\) | 763.296 | 0.0257825 | ||||||||
\(958\) | −33656.6 | −1.13507 | ||||||||
\(959\) | 15967.8 | 0.537672 | ||||||||
\(960\) | −6341.87 | −0.213211 | ||||||||
\(961\) | 5862.28 | 0.196780 | ||||||||
\(962\) | 20094.0 | 0.673449 | ||||||||
\(963\) | 34004.5 | 1.13788 | ||||||||
\(964\) | −8075.88 | −0.269820 | ||||||||
\(965\) | −48374.1 | −1.61370 | ||||||||
\(966\) | −1044.55 | −0.0347906 | ||||||||
\(967\) | −28484.3 | −0.947254 | −0.473627 | − | 0.880726i | \(-0.657055\pi\) | ||||
−0.473627 | + | 0.880726i | \(0.657055\pi\) | |||||||
\(968\) | 9277.70 | 0.308054 | ||||||||
\(969\) | 11686.3 | 0.387429 | ||||||||
\(970\) | 34176.5 | 1.13128 | ||||||||
\(971\) | 15621.7 | 0.516295 | 0.258148 | − | 0.966105i | \(-0.416888\pi\) | ||||
0.258148 | + | 0.966105i | \(0.416888\pi\) | |||||||
\(972\) | −3629.50 | −0.119770 | ||||||||
\(973\) | −5382.62 | −0.177347 | ||||||||
\(974\) | −15144.1 | −0.498202 | ||||||||
\(975\) | 578.177 | 0.0189913 | ||||||||
\(976\) | 13551.5 | 0.444441 | ||||||||
\(977\) | −10336.9 | −0.338491 | −0.169245 | − | 0.985574i | \(-0.554133\pi\) | ||||
−0.169245 | + | 0.985574i | \(0.554133\pi\) | |||||||
\(978\) | −12551.8 | −0.410390 | ||||||||
\(979\) | 281.737 | 0.00919750 | ||||||||
\(980\) | −3787.97 | −0.123472 | ||||||||
\(981\) | 9922.80 | 0.322947 | ||||||||
\(982\) | −23007.1 | −0.747643 | ||||||||
\(983\) | −19360.5 | −0.628182 | −0.314091 | − | 0.949393i | \(-0.601700\pi\) | ||||
−0.314091 | + | 0.949393i | \(0.601700\pi\) | |||||||
\(984\) | 6298.00 | 0.204037 | ||||||||
\(985\) | 24107.8 | 0.779838 | ||||||||
\(986\) | 2922.87 | 0.0944048 | ||||||||
\(987\) | 7378.16 | 0.237943 | ||||||||
\(988\) | −10880.4 | −0.350356 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 35172.7 | 1.12915 | ||||||||
\(991\) | 32122.8 | 1.02968 | 0.514840 | − | 0.857286i | \(-0.327851\pi\) | ||||
0.514840 | + | 0.857286i | \(0.327851\pi\) | |||||||
\(992\) | −10906.3 | −0.349067 | ||||||||
\(993\) | −6704.86 | −0.214272 | ||||||||
\(994\) | −12484.1 | −0.398362 | ||||||||
\(995\) | −32427.0 | −1.03317 | ||||||||
\(996\) | 1165.61 | 0.0370821 | ||||||||
\(997\) | −2315.90 | −0.0735661 | −0.0367831 | − | 0.999323i | \(-0.511711\pi\) | ||||
−0.0367831 | + | 0.999323i | \(0.511711\pi\) | |||||||
\(998\) | −8058.93 | −0.255612 | ||||||||
\(999\) | −6245.09 | −0.197784 |
(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.i.1.16 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.35 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.16 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.35 | yes | 50 | 43.42 | odd | 2 |