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 | 1.49 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.20801 | 1.84131 | 0.920655 | − | 0.390377i | \(-0.127655\pi\) | ||||
0.920655 | + | 0.390377i | \(0.127655\pi\) | |||||||
\(3\) | 5.00842 | 0.963871 | 0.481936 | − | 0.876207i | \(-0.339934\pi\) | ||||
0.481936 | + | 0.876207i | \(0.339934\pi\) | |||||||
\(4\) | 19.1234 | 2.39042 | ||||||||
\(5\) | −13.8519 | −1.23895 | −0.619476 | − | 0.785015i | \(-0.712655\pi\) | ||||
−0.619476 | + | 0.785015i | \(0.712655\pi\) | |||||||
\(6\) | 26.0839 | 1.77479 | ||||||||
\(7\) | −26.6225 | −1.43748 | −0.718740 | − | 0.695279i | \(-0.755281\pi\) | ||||
−0.718740 | + | 0.695279i | \(0.755281\pi\) | |||||||
\(8\) | 57.9307 | 2.56020 | ||||||||
\(9\) | −1.91570 | −0.0709519 | ||||||||
\(10\) | −72.1409 | −2.28130 | ||||||||
\(11\) | 47.0765 | 1.29037 | 0.645187 | − | 0.764025i | \(-0.276780\pi\) | ||||
0.645187 | + | 0.764025i | \(0.276780\pi\) | |||||||
\(12\) | 95.7780 | 2.30406 | ||||||||
\(13\) | −60.3088 | −1.28667 | −0.643333 | − | 0.765587i | \(-0.722449\pi\) | ||||
−0.643333 | + | 0.765587i | \(0.722449\pi\) | |||||||
\(14\) | −138.650 | −2.64685 | ||||||||
\(15\) | −69.3762 | −1.19419 | ||||||||
\(16\) | 148.717 | 2.32370 | ||||||||
\(17\) | 69.2105 | 0.987413 | 0.493706 | − | 0.869629i | \(-0.335642\pi\) | ||||
0.493706 | + | 0.869629i | \(0.335642\pi\) | |||||||
\(18\) | −9.97699 | −0.130644 | ||||||||
\(19\) | −9.96884 | −0.120369 | −0.0601845 | − | 0.998187i | \(-0.519169\pi\) | ||||
−0.0601845 | + | 0.998187i | \(0.519169\pi\) | |||||||
\(20\) | −264.895 | −2.96162 | ||||||||
\(21\) | −133.337 | −1.38555 | ||||||||
\(22\) | 245.175 | 2.37598 | ||||||||
\(23\) | −26.9731 | −0.244534 | −0.122267 | − | 0.992497i | \(-0.539016\pi\) | ||||
−0.122267 | + | 0.992497i | \(0.539016\pi\) | |||||||
\(24\) | 290.142 | 2.46770 | ||||||||
\(25\) | 66.8755 | 0.535004 | ||||||||
\(26\) | −314.089 | −2.36915 | ||||||||
\(27\) | −144.822 | −1.03226 | ||||||||
\(28\) | −509.112 | −3.43619 | ||||||||
\(29\) | −158.022 | −1.01186 | −0.505930 | − | 0.862574i | \(-0.668851\pi\) | ||||
−0.505930 | + | 0.862574i | \(0.668851\pi\) | |||||||
\(30\) | −361.312 | −2.19888 | ||||||||
\(31\) | −129.716 | −0.751537 | −0.375769 | − | 0.926713i | \(-0.622621\pi\) | ||||
−0.375769 | + | 0.926713i | \(0.622621\pi\) | |||||||
\(32\) | 311.073 | 1.71845 | ||||||||
\(33\) | 235.779 | 1.24375 | ||||||||
\(34\) | 360.449 | 1.81813 | ||||||||
\(35\) | 368.773 | 1.78097 | ||||||||
\(36\) | −36.6347 | −0.169605 | ||||||||
\(37\) | −59.9333 | −0.266296 | −0.133148 | − | 0.991096i | \(-0.542509\pi\) | ||||
−0.133148 | + | 0.991096i | \(0.542509\pi\) | |||||||
\(38\) | −51.9178 | −0.221636 | ||||||||
\(39\) | −302.052 | −1.24018 | ||||||||
\(40\) | −802.451 | −3.17197 | ||||||||
\(41\) | −415.611 | −1.58311 | −0.791554 | − | 0.611099i | \(-0.790728\pi\) | ||||
−0.791554 | + | 0.611099i | \(0.790728\pi\) | |||||||
\(42\) | −694.419 | −2.55122 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 900.263 | 3.08454 | ||||||||
\(45\) | 26.5361 | 0.0879061 | ||||||||
\(46\) | −140.476 | −0.450263 | ||||||||
\(47\) | −398.299 | −1.23612 | −0.618062 | − | 0.786129i | \(-0.712082\pi\) | ||||
−0.618062 | + | 0.786129i | \(0.712082\pi\) | |||||||
\(48\) | 744.836 | 2.23975 | ||||||||
\(49\) | 365.758 | 1.06635 | ||||||||
\(50\) | 348.289 | 0.985109 | ||||||||
\(51\) | 346.636 | 0.951739 | ||||||||
\(52\) | −1153.31 | −3.07567 | ||||||||
\(53\) | −280.790 | −0.727725 | −0.363863 | − | 0.931453i | \(-0.618542\pi\) | ||||
−0.363863 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(54\) | −754.235 | −1.90071 | ||||||||
\(55\) | −652.100 | −1.59871 | ||||||||
\(56\) | −1542.26 | −3.68024 | ||||||||
\(57\) | −49.9282 | −0.116020 | ||||||||
\(58\) | −822.981 | −1.86315 | ||||||||
\(59\) | 143.280 | 0.316159 | 0.158080 | − | 0.987426i | \(-0.449470\pi\) | ||||
0.158080 | + | 0.987426i | \(0.449470\pi\) | |||||||
\(60\) | −1326.71 | −2.85462 | ||||||||
\(61\) | 791.993 | 1.66237 | 0.831183 | − | 0.555999i | \(-0.187664\pi\) | ||||
0.831183 | + | 0.555999i | \(0.187664\pi\) | |||||||
\(62\) | −675.562 | −1.38381 | ||||||||
\(63\) | 51.0008 | 0.101992 | ||||||||
\(64\) | 430.337 | 0.840502 | ||||||||
\(65\) | 835.392 | 1.59412 | ||||||||
\(66\) | 1227.94 | 2.29014 | ||||||||
\(67\) | −635.977 | −1.15966 | −0.579828 | − | 0.814739i | \(-0.696880\pi\) | ||||
−0.579828 | + | 0.814739i | \(0.696880\pi\) | |||||||
\(68\) | 1323.54 | 2.36033 | ||||||||
\(69\) | −135.093 | −0.235699 | ||||||||
\(70\) | 1920.57 | 3.27932 | ||||||||
\(71\) | 707.876 | 1.18323 | 0.591615 | − | 0.806220i | \(-0.298490\pi\) | ||||
0.591615 | + | 0.806220i | \(0.298490\pi\) | |||||||
\(72\) | −110.978 | −0.181651 | ||||||||
\(73\) | −168.798 | −0.270634 | −0.135317 | − | 0.990802i | \(-0.543205\pi\) | ||||
−0.135317 | + | 0.990802i | \(0.543205\pi\) | |||||||
\(74\) | −312.133 | −0.490334 | ||||||||
\(75\) | 334.941 | 0.515675 | ||||||||
\(76\) | −190.638 | −0.287733 | ||||||||
\(77\) | −1253.30 | −1.85489 | ||||||||
\(78\) | −1573.09 | −2.28356 | ||||||||
\(79\) | −631.664 | −0.899591 | −0.449796 | − | 0.893131i | \(-0.648503\pi\) | ||||
−0.449796 | + | 0.893131i | \(0.648503\pi\) | |||||||
\(80\) | −2060.01 | −2.87895 | ||||||||
\(81\) | −673.606 | −0.924014 | ||||||||
\(82\) | −2164.50 | −2.91499 | ||||||||
\(83\) | 516.463 | 0.683002 | 0.341501 | − | 0.939881i | \(-0.389065\pi\) | ||||
0.341501 | + | 0.939881i | \(0.389065\pi\) | |||||||
\(84\) | −2549.85 | −3.31204 | ||||||||
\(85\) | −958.698 | −1.22336 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −791.441 | −0.975303 | ||||||||
\(88\) | 2727.18 | 3.30361 | ||||||||
\(89\) | 1272.00 | 1.51496 | 0.757481 | − | 0.652857i | \(-0.226430\pi\) | ||||
0.757481 | + | 0.652857i | \(0.226430\pi\) | |||||||
\(90\) | 138.200 | 0.161862 | ||||||||
\(91\) | 1605.57 | 1.84956 | ||||||||
\(92\) | −515.817 | −0.584540 | ||||||||
\(93\) | −649.672 | −0.724385 | ||||||||
\(94\) | −2074.34 | −2.27609 | ||||||||
\(95\) | 138.088 | 0.149131 | ||||||||
\(96\) | 1557.98 | 1.65637 | ||||||||
\(97\) | −298.811 | −0.312780 | −0.156390 | − | 0.987695i | \(-0.549986\pi\) | ||||
−0.156390 | + | 0.987695i | \(0.549986\pi\) | |||||||
\(98\) | 1904.87 | 1.96348 | ||||||||
\(99\) | −90.1846 | −0.0915545 | ||||||||
\(100\) | 1278.89 | 1.27889 | ||||||||
\(101\) | −842.187 | −0.829711 | −0.414855 | − | 0.909887i | \(-0.636168\pi\) | ||||
−0.414855 | + | 0.909887i | \(0.636168\pi\) | |||||||
\(102\) | 1805.28 | 1.75245 | ||||||||
\(103\) | 330.701 | 0.316359 | 0.158179 | − | 0.987410i | \(-0.449438\pi\) | ||||
0.158179 | + | 0.987410i | \(0.449438\pi\) | |||||||
\(104\) | −3493.73 | −3.29412 | ||||||||
\(105\) | 1846.97 | 1.71663 | ||||||||
\(106\) | −1462.36 | −1.33997 | ||||||||
\(107\) | −691.923 | −0.625147 | −0.312573 | − | 0.949894i | \(-0.601191\pi\) | ||||
−0.312573 | + | 0.949894i | \(0.601191\pi\) | |||||||
\(108\) | −2769.49 | −2.46754 | ||||||||
\(109\) | −1114.65 | −0.979483 | −0.489742 | − | 0.871868i | \(-0.662909\pi\) | ||||
−0.489742 | + | 0.871868i | \(0.662909\pi\) | |||||||
\(110\) | −3396.15 | −2.94373 | ||||||||
\(111\) | −300.171 | −0.256675 | ||||||||
\(112\) | −3959.21 | −3.34027 | ||||||||
\(113\) | 1732.15 | 1.44201 | 0.721005 | − | 0.692929i | \(-0.243680\pi\) | ||||
0.721005 | + | 0.692929i | \(0.243680\pi\) | |||||||
\(114\) | −260.027 | −0.213629 | ||||||||
\(115\) | 373.629 | 0.302966 | ||||||||
\(116\) | −3021.92 | −2.41877 | ||||||||
\(117\) | 115.534 | 0.0912913 | ||||||||
\(118\) | 746.201 | 0.582148 | ||||||||
\(119\) | −1842.56 | −1.41939 | ||||||||
\(120\) | −4019.02 | −3.05737 | ||||||||
\(121\) | 885.201 | 0.665064 | ||||||||
\(122\) | 4124.71 | 3.06093 | ||||||||
\(123\) | −2081.55 | −1.52591 | ||||||||
\(124\) | −2480.61 | −1.79649 | ||||||||
\(125\) | 805.135 | 0.576108 | ||||||||
\(126\) | 265.613 | 0.187799 | ||||||||
\(127\) | 2426.06 | 1.69510 | 0.847550 | − | 0.530715i | \(-0.178077\pi\) | ||||
0.847550 | + | 0.530715i | \(0.178077\pi\) | |||||||
\(128\) | −247.383 | −0.170826 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4350.73 | 2.93527 | ||||||||
\(131\) | 260.318 | 0.173619 | 0.0868094 | − | 0.996225i | \(-0.472333\pi\) | ||||
0.0868094 | + | 0.996225i | \(0.472333\pi\) | |||||||
\(132\) | 4508.90 | 2.97310 | ||||||||
\(133\) | 265.396 | 0.173028 | ||||||||
\(134\) | −3312.18 | −2.13529 | ||||||||
\(135\) | 2006.06 | 1.27892 | ||||||||
\(136\) | 4009.42 | 2.52797 | ||||||||
\(137\) | 209.330 | 0.130542 | 0.0652711 | − | 0.997868i | \(-0.479209\pi\) | ||||
0.0652711 | + | 0.997868i | \(0.479209\pi\) | |||||||
\(138\) | −703.565 | −0.433996 | ||||||||
\(139\) | 253.533 | 0.154708 | 0.0773540 | − | 0.997004i | \(-0.475353\pi\) | ||||
0.0773540 | + | 0.997004i | \(0.475353\pi\) | |||||||
\(140\) | 7052.18 | 4.25727 | ||||||||
\(141\) | −1994.85 | −1.19146 | ||||||||
\(142\) | 3686.62 | 2.17869 | ||||||||
\(143\) | −2839.13 | −1.66028 | ||||||||
\(144\) | −284.897 | −0.164871 | ||||||||
\(145\) | 2188.91 | 1.25365 | ||||||||
\(146\) | −879.100 | −0.498321 | ||||||||
\(147\) | 1831.87 | 1.02782 | ||||||||
\(148\) | −1146.13 | −0.636561 | ||||||||
\(149\) | 2506.92 | 1.37836 | 0.689178 | − | 0.724592i | \(-0.257972\pi\) | ||||
0.689178 | + | 0.724592i | \(0.257972\pi\) | |||||||
\(150\) | 1744.38 | 0.949518 | ||||||||
\(151\) | −1804.46 | −0.972482 | −0.486241 | − | 0.873825i | \(-0.661632\pi\) | ||||
−0.486241 | + | 0.873825i | \(0.661632\pi\) | |||||||
\(152\) | −577.502 | −0.308168 | ||||||||
\(153\) | −132.587 | −0.0700588 | ||||||||
\(154\) | −6527.18 | −3.41542 | ||||||||
\(155\) | 1796.81 | 0.931120 | ||||||||
\(156\) | −5776.25 | −2.96455 | ||||||||
\(157\) | −676.565 | −0.343922 | −0.171961 | − | 0.985104i | \(-0.555010\pi\) | ||||
−0.171961 | + | 0.985104i | \(0.555010\pi\) | |||||||
\(158\) | −3289.71 | −1.65643 | ||||||||
\(159\) | −1406.31 | −0.701433 | ||||||||
\(160\) | −4308.95 | −2.12908 | ||||||||
\(161\) | 718.092 | 0.351513 | ||||||||
\(162\) | −3508.15 | −1.70140 | ||||||||
\(163\) | 509.421 | 0.244791 | 0.122396 | − | 0.992481i | \(-0.460942\pi\) | ||||
0.122396 | + | 0.992481i | \(0.460942\pi\) | |||||||
\(164\) | −7947.88 | −3.78430 | ||||||||
\(165\) | −3265.99 | −1.54095 | ||||||||
\(166\) | 2689.74 | 1.25762 | ||||||||
\(167\) | −1635.97 | −0.758057 | −0.379028 | − | 0.925385i | \(-0.623742\pi\) | ||||
−0.379028 | + | 0.925385i | \(0.623742\pi\) | |||||||
\(168\) | −7724.29 | −3.54727 | ||||||||
\(169\) | 1440.15 | 0.655507 | ||||||||
\(170\) | −4992.91 | −2.25258 | ||||||||
\(171\) | 19.0973 | 0.00854040 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −336.002 | −0.147663 | −0.0738317 | − | 0.997271i | \(-0.523523\pi\) | ||||
−0.0738317 | + | 0.997271i | \(0.523523\pi\) | |||||||
\(174\) | −4121.83 | −1.79584 | ||||||||
\(175\) | −1780.39 | −0.769058 | ||||||||
\(176\) | 7001.07 | 2.99844 | ||||||||
\(177\) | 717.604 | 0.304737 | ||||||||
\(178\) | 6624.59 | 2.78952 | ||||||||
\(179\) | 885.817 | 0.369883 | 0.184941 | − | 0.982750i | \(-0.440790\pi\) | ||||
0.184941 | + | 0.982750i | \(0.440790\pi\) | |||||||
\(180\) | 507.461 | 0.210133 | ||||||||
\(181\) | −3866.02 | −1.58762 | −0.793808 | − | 0.608168i | \(-0.791905\pi\) | ||||
−0.793808 | + | 0.608168i | \(0.791905\pi\) | |||||||
\(182\) | 8361.83 | 3.40561 | ||||||||
\(183\) | 3966.64 | 1.60231 | ||||||||
\(184\) | −1562.57 | −0.626056 | ||||||||
\(185\) | 830.190 | 0.329929 | ||||||||
\(186\) | −3383.50 | −1.33382 | ||||||||
\(187\) | 3258.19 | 1.27413 | ||||||||
\(188\) | −7616.82 | −2.95486 | ||||||||
\(189\) | 3855.53 | 1.48385 | ||||||||
\(190\) | 719.162 | 0.274597 | ||||||||
\(191\) | −3601.46 | −1.36436 | −0.682180 | − | 0.731184i | \(-0.738968\pi\) | ||||
−0.682180 | + | 0.731184i | \(0.738968\pi\) | |||||||
\(192\) | 2155.31 | 0.810136 | ||||||||
\(193\) | −907.399 | −0.338425 | −0.169213 | − | 0.985580i | \(-0.554122\pi\) | ||||
−0.169213 | + | 0.985580i | \(0.554122\pi\) | |||||||
\(194\) | −1556.21 | −0.575926 | ||||||||
\(195\) | 4184.00 | 1.53652 | ||||||||
\(196\) | 6994.52 | 2.54902 | ||||||||
\(197\) | 3133.94 | 1.13342 | 0.566711 | − | 0.823917i | \(-0.308216\pi\) | ||||
0.566711 | + | 0.823917i | \(0.308216\pi\) | |||||||
\(198\) | −469.682 | −0.168580 | ||||||||
\(199\) | −702.456 | −0.250230 | −0.125115 | − | 0.992142i | \(-0.539930\pi\) | ||||
−0.125115 | + | 0.992142i | \(0.539930\pi\) | |||||||
\(200\) | 3874.15 | 1.36972 | ||||||||
\(201\) | −3185.24 | −1.11776 | ||||||||
\(202\) | −4386.12 | −1.52775 | ||||||||
\(203\) | 4206.94 | 1.45453 | ||||||||
\(204\) | 6628.85 | 2.27506 | ||||||||
\(205\) | 5757.00 | 1.96140 | ||||||||
\(206\) | 1722.30 | 0.582515 | ||||||||
\(207\) | 51.6724 | 0.0173502 | ||||||||
\(208\) | −8968.93 | −2.98982 | ||||||||
\(209\) | −469.299 | −0.155321 | ||||||||
\(210\) | 9619.04 | 3.16084 | ||||||||
\(211\) | 2634.32 | 0.859497 | 0.429749 | − | 0.902949i | \(-0.358602\pi\) | ||||
0.429749 | + | 0.902949i | \(0.358602\pi\) | |||||||
\(212\) | −5369.65 | −1.73957 | ||||||||
\(213\) | 3545.34 | 1.14048 | ||||||||
\(214\) | −3603.54 | −1.15109 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8389.65 | −2.64279 | ||||||||
\(217\) | 3453.36 | 1.08032 | ||||||||
\(218\) | −5805.09 | −1.80353 | ||||||||
\(219\) | −845.410 | −0.260856 | ||||||||
\(220\) | −12470.4 | −3.82160 | ||||||||
\(221\) | −4174.00 | −1.27047 | ||||||||
\(222\) | −1563.29 | −0.472619 | ||||||||
\(223\) | −5852.83 | −1.75755 | −0.878776 | − | 0.477234i | \(-0.841639\pi\) | ||||
−0.878776 | + | 0.477234i | \(0.841639\pi\) | |||||||
\(224\) | −8281.54 | −2.47024 | ||||||||
\(225\) | −128.114 | −0.0379596 | ||||||||
\(226\) | 9021.07 | 2.65519 | ||||||||
\(227\) | 2690.65 | 0.786718 | 0.393359 | − | 0.919385i | \(-0.371313\pi\) | ||||
0.393359 | + | 0.919385i | \(0.371313\pi\) | |||||||
\(228\) | −954.796 | −0.277337 | ||||||||
\(229\) | 909.642 | 0.262493 | 0.131246 | − | 0.991350i | \(-0.458102\pi\) | ||||
0.131246 | + | 0.991350i | \(0.458102\pi\) | |||||||
\(230\) | 1945.87 | 0.557855 | ||||||||
\(231\) | −6277.03 | −1.78787 | ||||||||
\(232\) | −9154.33 | −2.59057 | ||||||||
\(233\) | 2711.93 | 0.762509 | 0.381255 | − | 0.924470i | \(-0.375492\pi\) | ||||
0.381255 | + | 0.924470i | \(0.375492\pi\) | |||||||
\(234\) | 601.700 | 0.168096 | ||||||||
\(235\) | 5517.20 | 1.53150 | ||||||||
\(236\) | 2739.99 | 0.755755 | ||||||||
\(237\) | −3163.64 | −0.867090 | ||||||||
\(238\) | −9596.06 | −2.61353 | ||||||||
\(239\) | 2199.65 | 0.595329 | 0.297665 | − | 0.954671i | \(-0.403792\pi\) | ||||
0.297665 | + | 0.954671i | \(0.403792\pi\) | |||||||
\(240\) | −10317.4 | −2.77494 | ||||||||
\(241\) | −2700.40 | −0.721776 | −0.360888 | − | 0.932609i | \(-0.617526\pi\) | ||||
−0.360888 | + | 0.932609i | \(0.617526\pi\) | |||||||
\(242\) | 4610.14 | 1.22459 | ||||||||
\(243\) | 536.491 | 0.141629 | ||||||||
\(244\) | 15145.6 | 3.97376 | ||||||||
\(245\) | −5066.44 | −1.32116 | ||||||||
\(246\) | −10840.8 | −2.80968 | ||||||||
\(247\) | 601.209 | 0.154874 | ||||||||
\(248\) | −7514.53 | −1.92409 | ||||||||
\(249\) | 2586.66 | 0.658326 | ||||||||
\(250\) | 4193.15 | 1.06079 | ||||||||
\(251\) | −5537.81 | −1.39260 | −0.696302 | − | 0.717749i | \(-0.745173\pi\) | ||||
−0.696302 | + | 0.717749i | \(0.745173\pi\) | |||||||
\(252\) | 975.307 | 0.243804 | ||||||||
\(253\) | −1269.80 | −0.315540 | ||||||||
\(254\) | 12634.9 | 3.12121 | ||||||||
\(255\) | −4801.57 | −1.17916 | ||||||||
\(256\) | −4731.07 | −1.15505 | ||||||||
\(257\) | 468.256 | 0.113654 | 0.0568268 | − | 0.998384i | \(-0.481902\pi\) | ||||
0.0568268 | + | 0.998384i | \(0.481902\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1595.57 | 0.382796 | ||||||||
\(260\) | 15975.5 | 3.81062 | ||||||||
\(261\) | 302.723 | 0.0717934 | ||||||||
\(262\) | 1355.74 | 0.319686 | ||||||||
\(263\) | 6435.62 | 1.50889 | 0.754443 | − | 0.656365i | \(-0.227907\pi\) | ||||
0.754443 | + | 0.656365i | \(0.227907\pi\) | |||||||
\(264\) | 13658.9 | 3.18426 | ||||||||
\(265\) | 3889.47 | 0.901617 | ||||||||
\(266\) | 1382.18 | 0.318598 | ||||||||
\(267\) | 6370.71 | 1.46023 | ||||||||
\(268\) | −12162.0 | −2.77207 | ||||||||
\(269\) | −882.896 | −0.200116 | −0.100058 | − | 0.994982i | \(-0.531903\pi\) | ||||
−0.100058 | + | 0.994982i | \(0.531903\pi\) | |||||||
\(270\) | 10447.6 | 2.35489 | ||||||||
\(271\) | 6424.80 | 1.44014 | 0.720071 | − | 0.693900i | \(-0.244109\pi\) | ||||
0.720071 | + | 0.693900i | \(0.244109\pi\) | |||||||
\(272\) | 10292.8 | 2.29445 | ||||||||
\(273\) | 8041.38 | 1.78273 | ||||||||
\(274\) | 1090.19 | 0.240369 | ||||||||
\(275\) | 3148.27 | 0.690356 | ||||||||
\(276\) | −2583.43 | −0.563421 | ||||||||
\(277\) | −1236.99 | −0.268315 | −0.134158 | − | 0.990960i | \(-0.542833\pi\) | ||||
−0.134158 | + | 0.990960i | \(0.542833\pi\) | |||||||
\(278\) | 1320.41 | 0.284866 | ||||||||
\(279\) | 248.497 | 0.0533230 | ||||||||
\(280\) | 21363.3 | 4.55964 | ||||||||
\(281\) | 1461.25 | 0.310217 | 0.155109 | − | 0.987897i | \(-0.450427\pi\) | ||||
0.155109 | + | 0.987897i | \(0.450427\pi\) | |||||||
\(282\) | −10389.2 | −2.19386 | ||||||||
\(283\) | 1698.07 | 0.356678 | 0.178339 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178339 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(284\) | 13537.0 | 2.82842 | ||||||||
\(285\) | 691.601 | 0.143743 | ||||||||
\(286\) | −14786.2 | −3.05709 | ||||||||
\(287\) | 11064.6 | 2.27569 | ||||||||
\(288\) | −595.923 | −0.121927 | ||||||||
\(289\) | −122.902 | −0.0250158 | ||||||||
\(290\) | 11399.9 | 2.30835 | ||||||||
\(291\) | −1496.57 | −0.301480 | ||||||||
\(292\) | −3227.98 | −0.646929 | ||||||||
\(293\) | 3559.87 | 0.709795 | 0.354897 | − | 0.934905i | \(-0.384516\pi\) | ||||
0.354897 | + | 0.934905i | \(0.384516\pi\) | |||||||
\(294\) | 9540.39 | 1.89254 | ||||||||
\(295\) | −1984.70 | −0.391707 | ||||||||
\(296\) | −3471.98 | −0.681772 | ||||||||
\(297\) | −6817.72 | −1.33200 | ||||||||
\(298\) | 13056.1 | 2.53798 | ||||||||
\(299\) | 1626.72 | 0.314634 | ||||||||
\(300\) | 6405.21 | 1.23268 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9397.64 | −1.79064 | ||||||||
\(303\) | −4218.03 | −0.799734 | ||||||||
\(304\) | −1482.53 | −0.279701 | ||||||||
\(305\) | −10970.6 | −2.05959 | ||||||||
\(306\) | −690.513 | −0.129000 | ||||||||
\(307\) | −5590.48 | −1.03930 | −0.519651 | − | 0.854379i | \(-0.673938\pi\) | ||||
−0.519651 | + | 0.854379i | \(0.673938\pi\) | |||||||
\(308\) | −23967.2 | −4.43396 | ||||||||
\(309\) | 1656.29 | 0.304929 | ||||||||
\(310\) | 9357.83 | 1.71448 | ||||||||
\(311\) | 2708.95 | 0.493924 | 0.246962 | − | 0.969025i | \(-0.420568\pi\) | ||||
0.246962 | + | 0.969025i | \(0.420568\pi\) | |||||||
\(312\) | −17498.1 | −3.17511 | ||||||||
\(313\) | −6730.92 | −1.21551 | −0.607754 | − | 0.794125i | \(-0.707929\pi\) | ||||
−0.607754 | + | 0.794125i | \(0.707929\pi\) | |||||||
\(314\) | −3523.56 | −0.633267 | ||||||||
\(315\) | −706.458 | −0.126363 | ||||||||
\(316\) | −12079.5 | −2.15040 | ||||||||
\(317\) | 5984.74 | 1.06037 | 0.530184 | − | 0.847883i | \(-0.322123\pi\) | ||||
0.530184 | + | 0.847883i | \(0.322123\pi\) | |||||||
\(318\) | −7324.10 | −1.29156 | ||||||||
\(319\) | −7439.13 | −1.30568 | ||||||||
\(320\) | −5960.99 | −1.04134 | ||||||||
\(321\) | −3465.44 | −0.602561 | ||||||||
\(322\) | 3739.83 | 0.647244 | ||||||||
\(323\) | −689.949 | −0.118854 | ||||||||
\(324\) | −12881.6 | −2.20878 | ||||||||
\(325\) | −4033.18 | −0.688372 | ||||||||
\(326\) | 2653.07 | 0.450737 | ||||||||
\(327\) | −5582.62 | −0.944096 | ||||||||
\(328\) | −24076.6 | −4.05308 | ||||||||
\(329\) | 10603.7 | 1.77690 | ||||||||
\(330\) | −17009.3 | −2.83737 | ||||||||
\(331\) | 2114.28 | 0.351092 | 0.175546 | − | 0.984471i | \(-0.443831\pi\) | ||||
0.175546 | + | 0.984471i | \(0.443831\pi\) | |||||||
\(332\) | 9876.51 | 1.63266 | ||||||||
\(333\) | 114.814 | 0.0188942 | ||||||||
\(334\) | −8520.17 | −1.39582 | ||||||||
\(335\) | 8809.51 | 1.43676 | ||||||||
\(336\) | −19829.4 | −3.21959 | ||||||||
\(337\) | 10476.9 | 1.69351 | 0.846756 | − | 0.531982i | \(-0.178552\pi\) | ||||
0.846756 | + | 0.531982i | \(0.178552\pi\) | |||||||
\(338\) | 7500.32 | 1.20699 | ||||||||
\(339\) | 8675.35 | 1.38991 | ||||||||
\(340\) | −18333.6 | −2.92434 | ||||||||
\(341\) | −6106.58 | −0.969764 | ||||||||
\(342\) | 99.4591 | 0.0157255 | ||||||||
\(343\) | −605.864 | −0.0953749 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1871.29 | 0.292021 | ||||||||
\(346\) | −1749.90 | −0.271894 | ||||||||
\(347\) | 11253.4 | 1.74096 | 0.870482 | − | 0.492199i | \(-0.163807\pi\) | ||||
0.870482 | + | 0.492199i | \(0.163807\pi\) | |||||||
\(348\) | −15135.0 | −2.33139 | ||||||||
\(349\) | −1170.22 | −0.179486 | −0.0897428 | − | 0.995965i | \(-0.528604\pi\) | ||||
−0.0897428 | + | 0.995965i | \(0.528604\pi\) | |||||||
\(350\) | −9272.31 | −1.41607 | ||||||||
\(351\) | 8734.04 | 1.32817 | ||||||||
\(352\) | 14644.2 | 2.21744 | ||||||||
\(353\) | −804.464 | −0.121295 | −0.0606477 | − | 0.998159i | \(-0.519317\pi\) | ||||
−0.0606477 | + | 0.998159i | \(0.519317\pi\) | |||||||
\(354\) | 3737.29 | 0.561115 | ||||||||
\(355\) | −9805.43 | −1.46597 | ||||||||
\(356\) | 24324.9 | 3.62140 | ||||||||
\(357\) | −9228.31 | −1.36811 | ||||||||
\(358\) | 4613.34 | 0.681069 | ||||||||
\(359\) | 9746.71 | 1.43290 | 0.716451 | − | 0.697638i | \(-0.245765\pi\) | ||||
0.716451 | + | 0.697638i | \(0.245765\pi\) | |||||||
\(360\) | 1537.26 | 0.225057 | ||||||||
\(361\) | −6759.62 | −0.985511 | ||||||||
\(362\) | −20134.3 | −2.92329 | ||||||||
\(363\) | 4433.46 | 0.641037 | ||||||||
\(364\) | 30703.9 | 4.42122 | ||||||||
\(365\) | 2338.17 | 0.335303 | ||||||||
\(366\) | 20658.3 | 2.95034 | ||||||||
\(367\) | −3663.53 | −0.521075 | −0.260538 | − | 0.965464i | \(-0.583900\pi\) | ||||
−0.260538 | + | 0.965464i | \(0.583900\pi\) | |||||||
\(368\) | −4011.36 | −0.568224 | ||||||||
\(369\) | 796.186 | 0.112325 | ||||||||
\(370\) | 4323.64 | 0.607501 | ||||||||
\(371\) | 7475.32 | 1.04609 | ||||||||
\(372\) | −12423.9 | −1.73159 | ||||||||
\(373\) | −13468.9 | −1.86969 | −0.934846 | − | 0.355053i | \(-0.884463\pi\) | ||||
−0.934846 | + | 0.355053i | \(0.884463\pi\) | |||||||
\(374\) | 16968.7 | 2.34607 | ||||||||
\(375\) | 4032.46 | 0.555294 | ||||||||
\(376\) | −23073.7 | −3.16472 | ||||||||
\(377\) | 9530.12 | 1.30193 | ||||||||
\(378\) | 20079.6 | 2.73223 | ||||||||
\(379\) | 2326.69 | 0.315341 | 0.157670 | − | 0.987492i | \(-0.449602\pi\) | ||||
0.157670 | + | 0.987492i | \(0.449602\pi\) | |||||||
\(380\) | 2640.70 | 0.356487 | ||||||||
\(381\) | 12150.7 | 1.63386 | ||||||||
\(382\) | −18756.5 | −2.51221 | ||||||||
\(383\) | 1329.44 | 0.177366 | 0.0886831 | − | 0.996060i | \(-0.471734\pi\) | ||||
0.0886831 | + | 0.996060i | \(0.471734\pi\) | |||||||
\(384\) | −1239.00 | −0.164655 | ||||||||
\(385\) | 17360.5 | 2.29812 | ||||||||
\(386\) | −4725.75 | −0.623145 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5714.28 | −0.747677 | ||||||||
\(389\) | 10163.9 | 1.32475 | 0.662375 | − | 0.749172i | \(-0.269549\pi\) | ||||
0.662375 | + | 0.749172i | \(0.269549\pi\) | |||||||
\(390\) | 21790.3 | 2.82922 | ||||||||
\(391\) | −1866.82 | −0.241456 | ||||||||
\(392\) | 21188.6 | 2.73007 | ||||||||
\(393\) | 1303.78 | 0.167346 | ||||||||
\(394\) | 16321.6 | 2.08698 | ||||||||
\(395\) | 8749.75 | 1.11455 | ||||||||
\(396\) | −1724.63 | −0.218854 | ||||||||
\(397\) | −13306.5 | −1.68221 | −0.841103 | − | 0.540875i | \(-0.818093\pi\) | ||||
−0.841103 | + | 0.540875i | \(0.818093\pi\) | |||||||
\(398\) | −3658.40 | −0.460751 | ||||||||
\(399\) | 1329.21 | 0.166777 | ||||||||
\(400\) | 9945.51 | 1.24319 | ||||||||
\(401\) | 15275.3 | 1.90228 | 0.951140 | − | 0.308759i | \(-0.0999137\pi\) | ||||
0.951140 | + | 0.308759i | \(0.0999137\pi\) | |||||||
\(402\) | −16588.8 | −2.05814 | ||||||||
\(403\) | 7823.01 | 0.966977 | ||||||||
\(404\) | −16105.5 | −1.98336 | ||||||||
\(405\) | 9330.74 | 1.14481 | ||||||||
\(406\) | 21909.8 | 2.67824 | ||||||||
\(407\) | −2821.45 | −0.343622 | ||||||||
\(408\) | 20080.8 | 2.43664 | ||||||||
\(409\) | −16043.3 | −1.93958 | −0.969792 | − | 0.243931i | \(-0.921563\pi\) | ||||
−0.969792 | + | 0.243931i | \(0.921563\pi\) | |||||||
\(410\) | 29982.5 | 3.61154 | ||||||||
\(411\) | 1048.41 | 0.125826 | ||||||||
\(412\) | 6324.13 | 0.756232 | ||||||||
\(413\) | −3814.46 | −0.454473 | ||||||||
\(414\) | 269.111 | 0.0319470 | ||||||||
\(415\) | −7154.00 | −0.846207 | ||||||||
\(416\) | −18760.4 | −2.21107 | ||||||||
\(417\) | 1269.80 | 0.149119 | ||||||||
\(418\) | −2444.11 | −0.285994 | ||||||||
\(419\) | −8887.02 | −1.03618 | −0.518090 | − | 0.855326i | \(-0.673357\pi\) | ||||
−0.518090 | + | 0.855326i | \(0.673357\pi\) | |||||||
\(420\) | 35320.3 | 4.10346 | ||||||||
\(421\) | −600.862 | −0.0695587 | −0.0347794 | − | 0.999395i | \(-0.511073\pi\) | ||||
−0.0347794 | + | 0.999395i | \(0.511073\pi\) | |||||||
\(422\) | 13719.6 | 1.58260 | ||||||||
\(423\) | 763.021 | 0.0877053 | ||||||||
\(424\) | −16266.3 | −1.86312 | ||||||||
\(425\) | 4628.49 | 0.528270 | ||||||||
\(426\) | 18464.2 | 2.09998 | ||||||||
\(427\) | −21084.8 | −2.38962 | ||||||||
\(428\) | −13231.9 | −1.49436 | ||||||||
\(429\) | −14219.6 | −1.60030 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16834.7 | −1.88143 | −0.940717 | − | 0.339193i | \(-0.889846\pi\) | ||||
−0.940717 | + | 0.339193i | \(0.889846\pi\) | |||||||
\(432\) | −21537.5 | −2.39866 | ||||||||
\(433\) | 1169.19 | 0.129764 | 0.0648820 | − | 0.997893i | \(-0.479333\pi\) | ||||
0.0648820 | + | 0.997893i | \(0.479333\pi\) | |||||||
\(434\) | 17985.1 | 1.98920 | ||||||||
\(435\) | 10963.0 | 1.20836 | ||||||||
\(436\) | −21315.8 | −2.34138 | ||||||||
\(437\) | 268.891 | 0.0294343 | ||||||||
\(438\) | −4402.91 | −0.480317 | ||||||||
\(439\) | 404.634 | 0.0439912 | 0.0219956 | − | 0.999758i | \(-0.492998\pi\) | ||||
0.0219956 | + | 0.999758i | \(0.492998\pi\) | |||||||
\(440\) | −37776.6 | −4.09302 | ||||||||
\(441\) | −700.682 | −0.0756595 | ||||||||
\(442\) | −21738.3 | −2.33933 | ||||||||
\(443\) | 8522.87 | 0.914071 | 0.457036 | − | 0.889448i | \(-0.348911\pi\) | ||||
0.457036 | + | 0.889448i | \(0.348911\pi\) | |||||||
\(444\) | −5740.29 | −0.613563 | ||||||||
\(445\) | −17619.6 | −1.87697 | ||||||||
\(446\) | −30481.6 | −3.23620 | ||||||||
\(447\) | 12555.7 | 1.32856 | ||||||||
\(448\) | −11456.6 | −1.20820 | ||||||||
\(449\) | −2477.35 | −0.260386 | −0.130193 | − | 0.991489i | \(-0.541560\pi\) | ||||
−0.130193 | + | 0.991489i | \(0.541560\pi\) | |||||||
\(450\) | −667.217 | −0.0698954 | ||||||||
\(451\) | −19565.5 | −2.04280 | ||||||||
\(452\) | 33124.6 | 3.44702 | ||||||||
\(453\) | −9037.49 | −0.937347 | ||||||||
\(454\) | 14013.0 | 1.44859 | ||||||||
\(455\) | −22240.2 | −2.29151 | ||||||||
\(456\) | −2892.37 | −0.297035 | ||||||||
\(457\) | −4605.88 | −0.471453 | −0.235727 | − | 0.971819i | \(-0.575747\pi\) | ||||
−0.235727 | + | 0.971819i | \(0.575747\pi\) | |||||||
\(458\) | 4737.42 | 0.483330 | ||||||||
\(459\) | −10023.2 | −1.01927 | ||||||||
\(460\) | 7145.06 | 0.724218 | ||||||||
\(461\) | −11285.7 | −1.14019 | −0.570093 | − | 0.821580i | \(-0.693093\pi\) | ||||
−0.570093 | + | 0.821580i | \(0.693093\pi\) | |||||||
\(462\) | −32690.9 | −3.29203 | ||||||||
\(463\) | −508.870 | −0.0510782 | −0.0255391 | − | 0.999674i | \(-0.508130\pi\) | ||||
−0.0255391 | + | 0.999674i | \(0.508130\pi\) | |||||||
\(464\) | −23500.5 | −2.35126 | ||||||||
\(465\) | 8999.20 | 0.897480 | ||||||||
\(466\) | 14123.8 | 1.40402 | ||||||||
\(467\) | 568.788 | 0.0563606 | 0.0281803 | − | 0.999603i | \(-0.491029\pi\) | ||||
0.0281803 | + | 0.999603i | \(0.491029\pi\) | |||||||
\(468\) | 2209.39 | 0.218225 | ||||||||
\(469\) | 16931.3 | 1.66698 | ||||||||
\(470\) | 28733.6 | 2.81997 | ||||||||
\(471\) | −3388.52 | −0.331497 | ||||||||
\(472\) | 8300.29 | 0.809431 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −16476.3 | −1.59658 | ||||||||
\(475\) | −666.672 | −0.0643979 | ||||||||
\(476\) | −35235.9 | −3.39293 | ||||||||
\(477\) | 537.909 | 0.0516335 | ||||||||
\(478\) | 11455.8 | 1.09619 | ||||||||
\(479\) | −3278.52 | −0.312734 | −0.156367 | − | 0.987699i | \(-0.549978\pi\) | ||||
−0.156367 | + | 0.987699i | \(0.549978\pi\) | |||||||
\(480\) | −21581.1 | −2.05216 | ||||||||
\(481\) | 3614.50 | 0.342634 | ||||||||
\(482\) | −14063.7 | −1.32901 | ||||||||
\(483\) | 3596.51 | 0.338813 | ||||||||
\(484\) | 16928.0 | 1.58979 | ||||||||
\(485\) | 4139.11 | 0.387520 | ||||||||
\(486\) | 2794.05 | 0.260783 | ||||||||
\(487\) | 3439.30 | 0.320020 | 0.160010 | − | 0.987115i | \(-0.448847\pi\) | ||||
0.160010 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(488\) | 45880.7 | 4.25599 | ||||||||
\(489\) | 2551.40 | 0.235947 | ||||||||
\(490\) | −26386.1 | −2.43266 | ||||||||
\(491\) | −3116.14 | −0.286414 | −0.143207 | − | 0.989693i | \(-0.545741\pi\) | ||||
−0.143207 | + | 0.989693i | \(0.545741\pi\) | |||||||
\(492\) | −39806.3 | −3.64758 | ||||||||
\(493\) | −10936.8 | −0.999124 | ||||||||
\(494\) | 3131.10 | 0.285172 | ||||||||
\(495\) | 1249.23 | 0.113432 | ||||||||
\(496\) | −19290.9 | −1.74635 | ||||||||
\(497\) | −18845.4 | −1.70087 | ||||||||
\(498\) | 13471.4 | 1.21218 | ||||||||
\(499\) | −16962.6 | −1.52175 | −0.760874 | − | 0.648899i | \(-0.775230\pi\) | ||||
−0.760874 | + | 0.648899i | \(0.775230\pi\) | |||||||
\(500\) | 15396.9 | 1.37714 | ||||||||
\(501\) | −8193.65 | −0.730669 | ||||||||
\(502\) | −28841.0 | −2.56422 | ||||||||
\(503\) | −17725.1 | −1.57122 | −0.785610 | − | 0.618722i | \(-0.787651\pi\) | ||||
−0.785610 | + | 0.618722i | \(0.787651\pi\) | |||||||
\(504\) | 2954.51 | 0.261120 | ||||||||
\(505\) | 11665.9 | 1.02797 | ||||||||
\(506\) | −6613.14 | −0.581008 | ||||||||
\(507\) | 7212.88 | 0.631825 | ||||||||
\(508\) | 46394.4 | 4.05201 | ||||||||
\(509\) | 3044.24 | 0.265095 | 0.132548 | − | 0.991177i | \(-0.457684\pi\) | ||||
0.132548 | + | 0.991177i | \(0.457684\pi\) | |||||||
\(510\) | −25006.6 | −2.17120 | ||||||||
\(511\) | 4493.82 | 0.389031 | ||||||||
\(512\) | −22660.4 | −1.95597 | ||||||||
\(513\) | 1443.71 | 0.124252 | ||||||||
\(514\) | 2438.68 | 0.209272 | ||||||||
\(515\) | −4580.85 | −0.391954 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18750.5 | −1.59506 | ||||||||
\(518\) | 8309.76 | 0.704846 | ||||||||
\(519\) | −1682.84 | −0.142329 | ||||||||
\(520\) | 48394.9 | 4.08126 | ||||||||
\(521\) | −12593.9 | −1.05902 | −0.529509 | − | 0.848304i | \(-0.677624\pi\) | ||||
−0.529509 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(522\) | 1576.59 | 0.132194 | ||||||||
\(523\) | −15100.1 | −1.26249 | −0.631243 | − | 0.775585i | \(-0.717455\pi\) | ||||
−0.631243 | + | 0.775585i | \(0.717455\pi\) | |||||||
\(524\) | 4978.16 | 0.415023 | ||||||||
\(525\) | −8916.97 | −0.741273 | ||||||||
\(526\) | 33516.8 | 2.77833 | ||||||||
\(527\) | −8977.71 | −0.742078 | ||||||||
\(528\) | 35064.3 | 2.89011 | ||||||||
\(529\) | −11439.5 | −0.940203 | ||||||||
\(530\) | 20256.4 | 1.66016 | ||||||||
\(531\) | −274.481 | −0.0224321 | ||||||||
\(532\) | 5075.26 | 0.413610 | ||||||||
\(533\) | 25065.0 | 2.03693 | ||||||||
\(534\) | 33178.7 | 2.68873 | ||||||||
\(535\) | 9584.45 | 0.774527 | ||||||||
\(536\) | −36842.6 | −2.96895 | ||||||||
\(537\) | 4436.54 | 0.356520 | ||||||||
\(538\) | −4598.13 | −0.368475 | ||||||||
\(539\) | 17218.6 | 1.37599 | ||||||||
\(540\) | 38362.7 | 3.05716 | ||||||||
\(541\) | −11318.5 | −0.899485 | −0.449743 | − | 0.893158i | \(-0.648484\pi\) | ||||
−0.449743 | + | 0.893158i | \(0.648484\pi\) | |||||||
\(542\) | 33460.4 | 2.65175 | ||||||||
\(543\) | −19362.6 | −1.53026 | ||||||||
\(544\) | 21529.5 | 1.69682 | ||||||||
\(545\) | 15440.0 | 1.21353 | ||||||||
\(546\) | 41879.6 | 3.28257 | ||||||||
\(547\) | −4299.81 | −0.336100 | −0.168050 | − | 0.985778i | \(-0.553747\pi\) | ||||
−0.168050 | + | 0.985778i | \(0.553747\pi\) | |||||||
\(548\) | 4003.10 | 0.312051 | ||||||||
\(549\) | −1517.22 | −0.117948 | ||||||||
\(550\) | 16396.2 | 1.27116 | ||||||||
\(551\) | 1575.30 | 0.121797 | ||||||||
\(552\) | −7826.02 | −0.603438 | ||||||||
\(553\) | 16816.5 | 1.29314 | ||||||||
\(554\) | −6442.24 | −0.494052 | ||||||||
\(555\) | 4157.94 | 0.318009 | ||||||||
\(556\) | 4848.42 | 0.369818 | ||||||||
\(557\) | −8356.80 | −0.635707 | −0.317854 | − | 0.948140i | \(-0.602962\pi\) | ||||
−0.317854 | + | 0.948140i | \(0.602962\pi\) | |||||||
\(558\) | 1294.17 | 0.0981842 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 54842.7 | 4.13844 | ||||||||
\(561\) | 16318.4 | 1.22810 | ||||||||
\(562\) | 7610.22 | 0.571206 | ||||||||
\(563\) | −17758.8 | −1.32938 | −0.664692 | − | 0.747118i | \(-0.731437\pi\) | ||||
−0.664692 | + | 0.747118i | \(0.731437\pi\) | |||||||
\(564\) | −38148.2 | −2.84810 | ||||||||
\(565\) | −23993.6 | −1.78658 | ||||||||
\(566\) | 8843.57 | 0.656754 | ||||||||
\(567\) | 17933.1 | 1.32825 | ||||||||
\(568\) | 41007.7 | 3.02931 | ||||||||
\(569\) | −6954.03 | −0.512352 | −0.256176 | − | 0.966630i | \(-0.582463\pi\) | ||||
−0.256176 | + | 0.966630i | \(0.582463\pi\) | |||||||
\(570\) | 3601.87 | 0.264676 | ||||||||
\(571\) | −20289.4 | −1.48701 | −0.743505 | − | 0.668730i | \(-0.766838\pi\) | ||||
−0.743505 | + | 0.668730i | \(0.766838\pi\) | |||||||
\(572\) | −54293.8 | −3.96877 | ||||||||
\(573\) | −18037.6 | −1.31507 | ||||||||
\(574\) | 57624.5 | 4.19025 | ||||||||
\(575\) | −1803.84 | −0.130827 | ||||||||
\(576\) | −824.397 | −0.0596352 | ||||||||
\(577\) | 5613.49 | 0.405013 | 0.202507 | − | 0.979281i | \(-0.435091\pi\) | ||||
0.202507 | + | 0.979281i | \(0.435091\pi\) | |||||||
\(578\) | −640.078 | −0.0460618 | ||||||||
\(579\) | −4544.64 | −0.326198 | ||||||||
\(580\) | 41859.3 | 2.99675 | ||||||||
\(581\) | −13749.5 | −0.981801 | ||||||||
\(582\) | −7794.17 | −0.555118 | ||||||||
\(583\) | −13218.6 | −0.939037 | ||||||||
\(584\) | −9778.57 | −0.692877 | ||||||||
\(585\) | −1600.36 | −0.113106 | ||||||||
\(586\) | 18539.8 | 1.30695 | ||||||||
\(587\) | 8010.42 | 0.563246 | 0.281623 | − | 0.959525i | \(-0.409127\pi\) | ||||
0.281623 | + | 0.959525i | \(0.409127\pi\) | |||||||
\(588\) | 35031.5 | 2.45693 | ||||||||
\(589\) | 1293.12 | 0.0904617 | ||||||||
\(590\) | −10336.3 | −0.721253 | ||||||||
\(591\) | 15696.1 | 1.09247 | ||||||||
\(592\) | −8913.08 | −0.618793 | ||||||||
\(593\) | 6472.49 | 0.448218 | 0.224109 | − | 0.974564i | \(-0.428053\pi\) | ||||
0.224109 | + | 0.974564i | \(0.428053\pi\) | |||||||
\(594\) | −35506.8 | −2.45263 | ||||||||
\(595\) | 25522.9 | 1.75855 | ||||||||
\(596\) | 47940.8 | 3.29485 | ||||||||
\(597\) | −3518.20 | −0.241190 | ||||||||
\(598\) | 8471.96 | 0.579338 | ||||||||
\(599\) | −25455.3 | −1.73635 | −0.868176 | − | 0.496257i | \(-0.834708\pi\) | ||||
−0.868176 | + | 0.496257i | \(0.834708\pi\) | |||||||
\(600\) | 19403.4 | 1.32023 | ||||||||
\(601\) | 13600.1 | 0.923064 | 0.461532 | − | 0.887124i | \(-0.347300\pi\) | ||||
0.461532 | + | 0.887124i | \(0.347300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1218.34 | 0.0822799 | ||||||||
\(604\) | −34507.4 | −2.32464 | ||||||||
\(605\) | −12261.7 | −0.823983 | ||||||||
\(606\) | −21967.5 | −1.47256 | ||||||||
\(607\) | 8144.66 | 0.544616 | 0.272308 | − | 0.962210i | \(-0.412213\pi\) | ||||
0.272308 | + | 0.962210i | \(0.412213\pi\) | |||||||
\(608\) | −3101.04 | −0.206848 | ||||||||
\(609\) | 21070.1 | 1.40198 | ||||||||
\(610\) | −57135.1 | −3.79235 | ||||||||
\(611\) | 24020.9 | 1.59048 | ||||||||
\(612\) | −2535.51 | −0.167470 | ||||||||
\(613\) | 21750.5 | 1.43311 | 0.716554 | − | 0.697531i | \(-0.245718\pi\) | ||||
0.716554 | + | 0.697531i | \(0.245718\pi\) | |||||||
\(614\) | −29115.3 | −1.91368 | ||||||||
\(615\) | 28833.5 | 1.89053 | ||||||||
\(616\) | −72604.3 | −4.74888 | ||||||||
\(617\) | 11659.4 | 0.760758 | 0.380379 | − | 0.924831i | \(-0.375793\pi\) | ||||
0.380379 | + | 0.924831i | \(0.375793\pi\) | |||||||
\(618\) | 8625.99 | 0.561469 | ||||||||
\(619\) | 17054.3 | 1.10738 | 0.553692 | − | 0.832722i | \(-0.313219\pi\) | ||||
0.553692 | + | 0.832722i | \(0.313219\pi\) | |||||||
\(620\) | 34361.2 | 2.22577 | ||||||||
\(621\) | 3906.30 | 0.252423 | ||||||||
\(622\) | 14108.2 | 0.909467 | ||||||||
\(623\) | −33863.8 | −2.17773 | ||||||||
\(624\) | −44920.2 | −2.88180 | ||||||||
\(625\) | −19512.1 | −1.24877 | ||||||||
\(626\) | −35054.7 | −2.23813 | ||||||||
\(627\) | −2350.45 | −0.149709 | ||||||||
\(628\) | −12938.2 | −0.822119 | ||||||||
\(629\) | −4148.01 | −0.262944 | ||||||||
\(630\) | −3679.24 | −0.232674 | ||||||||
\(631\) | 15049.7 | 0.949475 | 0.474737 | − | 0.880128i | \(-0.342543\pi\) | ||||
0.474737 | + | 0.880128i | \(0.342543\pi\) | |||||||
\(632\) | −36592.7 | −2.30313 | ||||||||
\(633\) | 13193.8 | 0.828445 | ||||||||
\(634\) | 31168.6 | 1.95247 | ||||||||
\(635\) | −33605.5 | −2.10015 | ||||||||
\(636\) | −26893.5 | −1.67672 | ||||||||
\(637\) | −22058.4 | −1.37203 | ||||||||
\(638\) | −38743.1 | −2.40416 | ||||||||
\(639\) | −1356.08 | −0.0839525 | ||||||||
\(640\) | 3426.73 | 0.211646 | ||||||||
\(641\) | −22558.3 | −1.39002 | −0.695008 | − | 0.719002i | \(-0.744599\pi\) | ||||
−0.695008 | + | 0.719002i | \(0.744599\pi\) | |||||||
\(642\) | −18048.1 | −1.10950 | ||||||||
\(643\) | 16170.3 | 0.991748 | 0.495874 | − | 0.868395i | \(-0.334848\pi\) | ||||
0.495874 | + | 0.868395i | \(0.334848\pi\) | |||||||
\(644\) | 13732.3 | 0.840265 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3593.26 | −0.218847 | ||||||||
\(647\) | 16223.2 | 0.985778 | 0.492889 | − | 0.870092i | \(-0.335941\pi\) | ||||
0.492889 | + | 0.870092i | \(0.335941\pi\) | |||||||
\(648\) | −39022.5 | −2.36566 | ||||||||
\(649\) | 6745.10 | 0.407964 | ||||||||
\(650\) | −21004.9 | −1.26751 | ||||||||
\(651\) | 17295.9 | 1.04129 | ||||||||
\(652\) | 9741.86 | 0.585155 | ||||||||
\(653\) | −6142.50 | −0.368108 | −0.184054 | − | 0.982916i | \(-0.558922\pi\) | ||||
−0.184054 | + | 0.982916i | \(0.558922\pi\) | |||||||
\(654\) | −29074.3 | −1.73837 | ||||||||
\(655\) | −3605.90 | −0.215106 | ||||||||
\(656\) | −61808.3 | −3.67867 | ||||||||
\(657\) | 323.366 | 0.0192020 | ||||||||
\(658\) | 55224.2 | 3.27183 | ||||||||
\(659\) | −14009.5 | −0.828123 | −0.414061 | − | 0.910249i | \(-0.635890\pi\) | ||||
−0.414061 | + | 0.910249i | \(0.635890\pi\) | |||||||
\(660\) | −62456.9 | −3.68353 | ||||||||
\(661\) | −26667.6 | −1.56921 | −0.784605 | − | 0.619996i | \(-0.787134\pi\) | ||||
−0.784605 | + | 0.619996i | \(0.787134\pi\) | |||||||
\(662\) | 11011.2 | 0.646470 | ||||||||
\(663\) | −20905.2 | −1.22457 | ||||||||
\(664\) | 29919.0 | 1.74862 | ||||||||
\(665\) | −3676.24 | −0.214373 | ||||||||
\(666\) | 597.954 | 0.0347901 | ||||||||
\(667\) | 4262.35 | 0.247434 | ||||||||
\(668\) | −31285.4 | −1.81208 | ||||||||
\(669\) | −29313.4 | −1.69405 | ||||||||
\(670\) | 45880.0 | 2.64552 | ||||||||
\(671\) | 37284.3 | 2.14507 | ||||||||
\(672\) | −41477.4 | −2.38099 | ||||||||
\(673\) | −26390.1 | −1.51153 | −0.755767 | − | 0.654841i | \(-0.772736\pi\) | ||||
−0.755767 | + | 0.654841i | \(0.772736\pi\) | |||||||
\(674\) | 54563.8 | 3.11828 | ||||||||
\(675\) | −9685.05 | −0.552264 | ||||||||
\(676\) | 27540.5 | 1.56694 | ||||||||
\(677\) | −10340.1 | −0.587006 | −0.293503 | − | 0.955958i | \(-0.594821\pi\) | ||||
−0.293503 | + | 0.955958i | \(0.594821\pi\) | |||||||
\(678\) | 45181.3 | 2.55926 | ||||||||
\(679\) | 7955.10 | 0.449615 | ||||||||
\(680\) | −55538.1 | −3.13204 | ||||||||
\(681\) | 13475.9 | 0.758295 | ||||||||
\(682\) | −31803.1 | −1.78564 | ||||||||
\(683\) | 3929.56 | 0.220147 | 0.110074 | − | 0.993923i | \(-0.464891\pi\) | ||||
0.110074 | + | 0.993923i | \(0.464891\pi\) | |||||||
\(684\) | 365.205 | 0.0204152 | ||||||||
\(685\) | −2899.62 | −0.161736 | ||||||||
\(686\) | −3155.35 | −0.175615 | ||||||||
\(687\) | 4555.87 | 0.253009 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16934.1 | 0.936339 | ||||||||
\(690\) | 9745.72 | 0.537700 | ||||||||
\(691\) | 2660.45 | 0.146466 | 0.0732332 | − | 0.997315i | \(-0.476668\pi\) | ||||
0.0732332 | + | 0.997315i | \(0.476668\pi\) | |||||||
\(692\) | −6425.50 | −0.352978 | ||||||||
\(693\) | 2400.94 | 0.131608 | ||||||||
\(694\) | 58607.9 | 3.20566 | ||||||||
\(695\) | −3511.92 | −0.191676 | ||||||||
\(696\) | −45848.8 | −2.49697 | ||||||||
\(697\) | −28764.6 | −1.56318 | ||||||||
\(698\) | −6094.52 | −0.330489 | ||||||||
\(699\) | 13582.5 | 0.734961 | ||||||||
\(700\) | −34047.2 | −1.83837 | ||||||||
\(701\) | 27310.9 | 1.47150 | 0.735749 | − | 0.677255i | \(-0.236830\pi\) | ||||
0.735749 | + | 0.677255i | \(0.236830\pi\) | |||||||
\(702\) | 45487.0 | 2.44558 | ||||||||
\(703\) | 597.465 | 0.0320538 | ||||||||
\(704\) | 20258.8 | 1.08456 | ||||||||
\(705\) | 27632.5 | 1.47617 | ||||||||
\(706\) | −4189.66 | −0.223342 | ||||||||
\(707\) | 22421.1 | 1.19269 | ||||||||
\(708\) | 13723.0 | 0.728450 | ||||||||
\(709\) | 2281.77 | 0.120866 | 0.0604328 | − | 0.998172i | \(-0.480752\pi\) | ||||
0.0604328 | + | 0.998172i | \(0.480752\pi\) | |||||||
\(710\) | −51066.8 | −2.69930 | ||||||||
\(711\) | 1210.08 | 0.0638277 | ||||||||
\(712\) | 73687.8 | 3.87861 | ||||||||
\(713\) | 3498.84 | 0.183777 | ||||||||
\(714\) | −48061.1 | −2.51911 | ||||||||
\(715\) | 39327.4 | 2.05701 | ||||||||
\(716\) | 16939.8 | 0.884177 | ||||||||
\(717\) | 11016.8 | 0.573821 | ||||||||
\(718\) | 50761.0 | 2.63842 | ||||||||
\(719\) | −7427.41 | −0.385251 | −0.192626 | − | 0.981272i | \(-0.561700\pi\) | ||||
−0.192626 | + | 0.981272i | \(0.561700\pi\) | |||||||
\(720\) | 3946.37 | 0.204267 | ||||||||
\(721\) | −8804.10 | −0.454760 | ||||||||
\(722\) | −35204.2 | −1.81463 | ||||||||
\(723\) | −13524.7 | −0.695699 | ||||||||
\(724\) | −73931.3 | −3.79508 | ||||||||
\(725\) | −10567.8 | −0.541350 | ||||||||
\(726\) | 23089.5 | 1.18035 | ||||||||
\(727\) | −31960.7 | −1.63048 | −0.815240 | − | 0.579124i | \(-0.803395\pi\) | ||||
−0.815240 | + | 0.579124i | \(0.803395\pi\) | |||||||
\(728\) | 93011.9 | 4.73523 | ||||||||
\(729\) | 20874.3 | 1.06053 | ||||||||
\(730\) | 12177.2 | 0.617396 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 75855.5 | 3.83019 | ||||||||
\(733\) | −3379.50 | −0.170293 | −0.0851463 | − | 0.996368i | \(-0.527136\pi\) | ||||
−0.0851463 | + | 0.996368i | \(0.527136\pi\) | |||||||
\(734\) | −19079.7 | −0.959462 | ||||||||
\(735\) | −25374.9 | −1.27342 | ||||||||
\(736\) | −8390.61 | −0.420220 | ||||||||
\(737\) | −29939.6 | −1.49639 | ||||||||
\(738\) | 4146.54 | 0.206824 | ||||||||
\(739\) | 32194.7 | 1.60257 | 0.801285 | − | 0.598283i | \(-0.204150\pi\) | ||||
0.801285 | + | 0.598283i | \(0.204150\pi\) | |||||||
\(740\) | 15876.0 | 0.788669 | ||||||||
\(741\) | 3011.11 | 0.149279 | ||||||||
\(742\) | 38931.6 | 1.92618 | ||||||||
\(743\) | 8237.10 | 0.406716 | 0.203358 | − | 0.979104i | \(-0.434815\pi\) | ||||
0.203358 | + | 0.979104i | \(0.434815\pi\) | |||||||
\(744\) | −37636.0 | −1.85457 | ||||||||
\(745\) | −34725.6 | −1.70772 | ||||||||
\(746\) | −70146.4 | −3.44268 | ||||||||
\(747\) | −989.388 | −0.0484603 | ||||||||
\(748\) | 62307.7 | 3.04571 | ||||||||
\(749\) | 18420.7 | 0.898636 | ||||||||
\(750\) | 21001.1 | 1.02247 | ||||||||
\(751\) | 33321.1 | 1.61904 | 0.809522 | − | 0.587089i | \(-0.199726\pi\) | ||||
0.809522 | + | 0.587089i | \(0.199726\pi\) | |||||||
\(752\) | −59233.7 | −2.87238 | ||||||||
\(753\) | −27735.7 | −1.34229 | ||||||||
\(754\) | 49633.0 | 2.39725 | ||||||||
\(755\) | 24995.2 | 1.20486 | ||||||||
\(756\) | 73730.7 | 3.54704 | ||||||||
\(757\) | −40005.7 | −1.92078 | −0.960391 | − | 0.278656i | \(-0.910111\pi\) | ||||
−0.960391 | + | 0.278656i | \(0.910111\pi\) | |||||||
\(758\) | 12117.4 | 0.580640 | ||||||||
\(759\) | −6359.70 | −0.304140 | ||||||||
\(760\) | 7999.51 | 0.381806 | ||||||||
\(761\) | 1344.71 | 0.0640549 | 0.0320274 | − | 0.999487i | \(-0.489804\pi\) | ||||
0.0320274 | + | 0.999487i | \(0.489804\pi\) | |||||||
\(762\) | 63281.1 | 3.00844 | ||||||||
\(763\) | 29674.6 | 1.40799 | ||||||||
\(764\) | −68872.1 | −3.26140 | ||||||||
\(765\) | 1836.58 | 0.0867996 | ||||||||
\(766\) | 6923.74 | 0.326586 | ||||||||
\(767\) | −8641.02 | −0.406791 | ||||||||
\(768\) | −23695.2 | −1.11332 | ||||||||
\(769\) | −41407.9 | −1.94175 | −0.970875 | − | 0.239586i | \(-0.922988\pi\) | ||||
−0.970875 | + | 0.239586i | \(0.922988\pi\) | |||||||
\(770\) | 90413.9 | 4.23155 | ||||||||
\(771\) | 2345.22 | 0.109547 | ||||||||
\(772\) | −17352.5 | −0.808979 | ||||||||
\(773\) | −10328.8 | −0.480598 | −0.240299 | − | 0.970699i | \(-0.577245\pi\) | ||||
−0.240299 | + | 0.970699i | \(0.577245\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8674.82 | −0.402076 | ||||||||
\(776\) | −17310.4 | −0.800780 | ||||||||
\(777\) | 7991.30 | 0.368966 | ||||||||
\(778\) | 52933.5 | 2.43928 | ||||||||
\(779\) | 4143.16 | 0.190557 | ||||||||
\(780\) | 80012.2 | 3.67294 | ||||||||
\(781\) | 33324.3 | 1.52681 | ||||||||
\(782\) | −9722.44 | −0.444596 | ||||||||
\(783\) | 22885.1 | 1.04450 | ||||||||
\(784\) | 54394.3 | 2.47787 | ||||||||
\(785\) | 9371.72 | 0.426103 | ||||||||
\(786\) | 6790.11 | 0.308136 | ||||||||
\(787\) | −35833.2 | −1.62302 | −0.811509 | − | 0.584341i | \(-0.801353\pi\) | ||||
−0.811509 | + | 0.584341i | \(0.801353\pi\) | |||||||
\(788\) | 59931.5 | 2.70936 | ||||||||
\(789\) | 32232.3 | 1.45437 | ||||||||
\(790\) | 45568.8 | 2.05223 | ||||||||
\(791\) | −46114.2 | −2.07286 | ||||||||
\(792\) | −5224.46 | −0.234398 | ||||||||
\(793\) | −47764.2 | −2.13891 | ||||||||
\(794\) | −69300.6 | −3.09746 | ||||||||
\(795\) | 19480.1 | 0.869043 | ||||||||
\(796\) | −13433.3 | −0.598156 | ||||||||
\(797\) | 9312.94 | 0.413904 | 0.206952 | − | 0.978351i | \(-0.433646\pi\) | ||||
0.206952 | + | 0.978351i | \(0.433646\pi\) | |||||||
\(798\) | 6922.56 | 0.307088 | ||||||||
\(799\) | −27566.5 | −1.22056 | ||||||||
\(800\) | 20803.2 | 0.919379 | ||||||||
\(801\) | −2436.77 | −0.107489 | ||||||||
\(802\) | 79554.2 | 3.50269 | ||||||||
\(803\) | −7946.41 | −0.349219 | ||||||||
\(804\) | −60912.6 | −2.67192 | ||||||||
\(805\) | −9946.95 | −0.435508 | ||||||||
\(806\) | 40742.3 | 1.78050 | ||||||||
\(807\) | −4421.92 | −0.192886 | ||||||||
\(808\) | −48788.5 | −2.12422 | ||||||||
\(809\) | 29114.8 | 1.26529 | 0.632646 | − | 0.774441i | \(-0.281969\pi\) | ||||
0.632646 | + | 0.774441i | \(0.281969\pi\) | |||||||
\(810\) | 48594.6 | 2.10795 | ||||||||
\(811\) | 41592.3 | 1.80087 | 0.900434 | − | 0.434993i | \(-0.143249\pi\) | ||||
0.900434 | + | 0.434993i | \(0.143249\pi\) | |||||||
\(812\) | 80451.0 | 3.47694 | ||||||||
\(813\) | 32178.1 | 1.38811 | ||||||||
\(814\) | −14694.1 | −0.632714 | ||||||||
\(815\) | −7056.46 | −0.303285 | ||||||||
\(816\) | 51550.5 | 2.21156 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −83553.7 | −3.57138 | ||||||||
\(819\) | −3075.79 | −0.131229 | ||||||||
\(820\) | 110093. | 4.68857 | ||||||||
\(821\) | −39650.4 | −1.68551 | −0.842757 | − | 0.538294i | \(-0.819069\pi\) | ||||
−0.842757 | + | 0.538294i | \(0.819069\pi\) | |||||||
\(822\) | 5460.15 | 0.231684 | ||||||||
\(823\) | −18879.4 | −0.799629 | −0.399815 | − | 0.916596i | \(-0.630925\pi\) | ||||
−0.399815 | + | 0.916596i | \(0.630925\pi\) | |||||||
\(824\) | 19157.8 | 0.809942 | ||||||||
\(825\) | 15767.9 | 0.665414 | ||||||||
\(826\) | −19865.8 | −0.836825 | ||||||||
\(827\) | 19740.1 | 0.830024 | 0.415012 | − | 0.909816i | \(-0.363777\pi\) | ||||
0.415012 | + | 0.909816i | \(0.363777\pi\) | |||||||
\(828\) | 988.152 | 0.0414742 | ||||||||
\(829\) | 26241.2 | 1.09939 | 0.549695 | − | 0.835365i | \(-0.314744\pi\) | ||||
0.549695 | + | 0.835365i | \(0.314744\pi\) | |||||||
\(830\) | −37258.1 | −1.55813 | ||||||||
\(831\) | −6195.35 | −0.258621 | ||||||||
\(832\) | −25953.1 | −1.08144 | ||||||||
\(833\) | 25314.3 | 1.05293 | ||||||||
\(834\) | 6613.15 | 0.274574 | ||||||||
\(835\) | 22661.4 | 0.939197 | ||||||||
\(836\) | −8974.58 | −0.371283 | ||||||||
\(837\) | 18785.7 | 0.775782 | ||||||||
\(838\) | −46283.7 | −1.90793 | ||||||||
\(839\) | 9598.19 | 0.394954 | 0.197477 | − | 0.980308i | \(-0.436725\pi\) | ||||
0.197477 | + | 0.980308i | \(0.436725\pi\) | |||||||
\(840\) | 106996. | 4.39491 | ||||||||
\(841\) | 581.966 | 0.0238618 | ||||||||
\(842\) | −3129.30 | −0.128079 | ||||||||
\(843\) | 7318.57 | 0.299009 | ||||||||
\(844\) | 50377.1 | 2.05456 | ||||||||
\(845\) | −19948.8 | −0.812143 | ||||||||
\(846\) | 3973.82 | 0.161493 | ||||||||
\(847\) | −23566.3 | −0.956017 | ||||||||
\(848\) | −41758.1 | −1.69101 | ||||||||
\(849\) | 8504.65 | 0.343791 | ||||||||
\(850\) | 24105.2 | 0.972709 | ||||||||
\(851\) | 1616.59 | 0.0651186 | ||||||||
\(852\) | 67798.9 | 2.72623 | ||||||||
\(853\) | −13278.1 | −0.532981 | −0.266490 | − | 0.963838i | \(-0.585864\pi\) | ||||
−0.266490 | + | 0.963838i | \(0.585864\pi\) | |||||||
\(854\) | −109810. | −4.40003 | ||||||||
\(855\) | −264.534 | −0.0105812 | ||||||||
\(856\) | −40083.6 | −1.60050 | ||||||||
\(857\) | −18835.6 | −0.750773 | −0.375386 | − | 0.926868i | \(-0.622490\pi\) | ||||
−0.375386 | + | 0.926868i | \(0.622490\pi\) | |||||||
\(858\) | −74055.6 | −2.94664 | ||||||||
\(859\) | 8470.49 | 0.336449 | 0.168224 | − | 0.985749i | \(-0.446197\pi\) | ||||
0.168224 | + | 0.985749i | \(0.446197\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 55416.2 | 2.19347 | ||||||||
\(862\) | −87675.2 | −3.46430 | ||||||||
\(863\) | 14654.0 | 0.578017 | 0.289008 | − | 0.957327i | \(-0.406674\pi\) | ||||
0.289008 | + | 0.957327i | \(0.406674\pi\) | |||||||
\(864\) | −45050.2 | −1.77389 | ||||||||
\(865\) | 4654.27 | 0.182948 | ||||||||
\(866\) | 6089.17 | 0.238936 | ||||||||
\(867\) | −615.548 | −0.0241120 | ||||||||
\(868\) | 66040.0 | 2.58242 | ||||||||
\(869\) | −29736.5 | −1.16081 | ||||||||
\(870\) | 57095.3 | 2.22496 | ||||||||
\(871\) | 38355.0 | 1.49209 | ||||||||
\(872\) | −64572.2 | −2.50767 | ||||||||
\(873\) | 572.433 | 0.0221924 | ||||||||
\(874\) | 1400.39 | 0.0541977 | ||||||||
\(875\) | −21434.7 | −0.828143 | ||||||||
\(876\) | −16167.1 | −0.623557 | ||||||||
\(877\) | 31034.9 | 1.19495 | 0.597477 | − | 0.801886i | \(-0.296170\pi\) | ||||
0.597477 | + | 0.801886i | \(0.296170\pi\) | |||||||
\(878\) | 2107.34 | 0.0810015 | ||||||||
\(879\) | 17829.3 | 0.684151 | ||||||||
\(880\) | −96978.2 | −3.71493 | ||||||||
\(881\) | −2331.10 | −0.0891449 | −0.0445725 | − | 0.999006i | \(-0.514193\pi\) | ||||
−0.0445725 | + | 0.999006i | \(0.514193\pi\) | |||||||
\(882\) | −3649.16 | −0.139313 | ||||||||
\(883\) | 38070.6 | 1.45094 | 0.725469 | − | 0.688255i | \(-0.241623\pi\) | ||||
0.725469 | + | 0.688255i | \(0.241623\pi\) | |||||||
\(884\) | −79821.1 | −3.03696 | ||||||||
\(885\) | −9940.20 | −0.377555 | ||||||||
\(886\) | 44387.2 | 1.68309 | ||||||||
\(887\) | −19683.4 | −0.745102 | −0.372551 | − | 0.928012i | \(-0.621517\pi\) | ||||
−0.372551 | + | 0.928012i | \(0.621517\pi\) | |||||||
\(888\) | −17389.1 | −0.657141 | ||||||||
\(889\) | −64587.7 | −2.43667 | ||||||||
\(890\) | −91763.2 | −3.45608 | ||||||||
\(891\) | −31711.0 | −1.19232 | ||||||||
\(892\) | −111926. | −4.20129 | ||||||||
\(893\) | 3970.58 | 0.148791 | ||||||||
\(894\) | 65390.3 | 2.44629 | ||||||||
\(895\) | −12270.3 | −0.458268 | ||||||||
\(896\) | 6585.95 | 0.245559 | ||||||||
\(897\) | 8147.28 | 0.303266 | ||||||||
\(898\) | −12902.1 | −0.479451 | ||||||||
\(899\) | 20498.0 | 0.760451 | ||||||||
\(900\) | −2449.97 | −0.0907394 | ||||||||
\(901\) | −19433.6 | −0.718565 | ||||||||
\(902\) | −101897. | −3.76143 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 100345. | 3.69184 | ||||||||
\(905\) | 53551.7 | 1.96698 | ||||||||
\(906\) | −47067.4 | −1.72595 | ||||||||
\(907\) | −3322.49 | −0.121633 | −0.0608167 | − | 0.998149i | \(-0.519371\pi\) | ||||
−0.0608167 | + | 0.998149i | \(0.519371\pi\) | |||||||
\(908\) | 51454.4 | 1.88059 | ||||||||
\(909\) | 1613.38 | 0.0588695 | ||||||||
\(910\) | −115827. | −4.21938 | ||||||||
\(911\) | −36251.9 | −1.31842 | −0.659209 | − | 0.751959i | \(-0.729109\pi\) | ||||
−0.659209 | + | 0.751959i | \(0.729109\pi\) | |||||||
\(912\) | −7425.16 | −0.269596 | ||||||||
\(913\) | 24313.3 | 0.881327 | ||||||||
\(914\) | −23987.5 | −0.868092 | ||||||||
\(915\) | −54945.5 | −1.98518 | ||||||||
\(916\) | 17395.4 | 0.627468 | ||||||||
\(917\) | −6930.31 | −0.249574 | ||||||||
\(918\) | −52201.0 | −1.87679 | ||||||||
\(919\) | 20127.9 | 0.722477 | 0.361239 | − | 0.932473i | \(-0.382354\pi\) | ||||
0.361239 | + | 0.932473i | \(0.382354\pi\) | |||||||
\(920\) | 21644.6 | 0.775654 | ||||||||
\(921\) | −27999.5 | −1.00175 | ||||||||
\(922\) | −58775.9 | −2.09944 | ||||||||
\(923\) | −42691.1 | −1.52242 | ||||||||
\(924\) | −120038. | −4.27377 | ||||||||
\(925\) | −4008.07 | −0.142470 | ||||||||
\(926\) | −2650.20 | −0.0940508 | ||||||||
\(927\) | −633.525 | −0.0224463 | ||||||||
\(928\) | −49156.4 | −1.73883 | ||||||||
\(929\) | 39220.1 | 1.38511 | 0.692557 | − | 0.721364i | \(-0.256484\pi\) | ||||
0.692557 | + | 0.721364i | \(0.256484\pi\) | |||||||
\(930\) | 46867.9 | 1.65254 | ||||||||
\(931\) | −3646.18 | −0.128355 | ||||||||
\(932\) | 51861.4 | 1.82272 | ||||||||
\(933\) | 13567.5 | 0.476079 | ||||||||
\(934\) | 2962.26 | 0.103777 | ||||||||
\(935\) | −45132.2 | −1.57859 | ||||||||
\(936\) | 6692.94 | 0.233724 | ||||||||
\(937\) | −12798.4 | −0.446218 | −0.223109 | − | 0.974794i | \(-0.571621\pi\) | ||||
−0.223109 | + | 0.974794i | \(0.571621\pi\) | |||||||
\(938\) | 88178.5 | 3.06943 | ||||||||
\(939\) | −33711.3 | −1.17159 | ||||||||
\(940\) | 105507. | 3.66093 | ||||||||
\(941\) | −45827.7 | −1.58761 | −0.793805 | − | 0.608172i | \(-0.791903\pi\) | ||||
−0.793805 | + | 0.608172i | \(0.791903\pi\) | |||||||
\(942\) | −17647.5 | −0.610388 | ||||||||
\(943\) | 11210.3 | 0.387124 | ||||||||
\(944\) | 21308.1 | 0.734659 | ||||||||
\(945\) | −53406.4 | −1.83842 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8956.69 | 0.307342 | 0.153671 | − | 0.988122i | \(-0.450890\pi\) | ||||
0.153671 | + | 0.988122i | \(0.450890\pi\) | |||||||
\(948\) | −60499.5 | −2.07271 | ||||||||
\(949\) | 10180.0 | 0.348215 | ||||||||
\(950\) | −3472.03 | −0.118576 | ||||||||
\(951\) | 29974.1 | 1.02206 | ||||||||
\(952\) | −106741. | −3.63391 | ||||||||
\(953\) | 32038.7 | 1.08902 | 0.544510 | − | 0.838754i | \(-0.316715\pi\) | ||||
0.544510 | + | 0.838754i | \(0.316715\pi\) | |||||||
\(954\) | 2801.44 | 0.0950732 | ||||||||
\(955\) | 49887.2 | 1.69038 | ||||||||
\(956\) | 42064.8 | 1.42309 | ||||||||
\(957\) | −37258.3 | −1.25851 | ||||||||
\(958\) | −17074.6 | −0.575840 | ||||||||
\(959\) | −5572.89 | −0.187652 | ||||||||
\(960\) | −29855.2 | −1.00372 | ||||||||
\(961\) | −12964.8 | −0.435191 | ||||||||
\(962\) | 18824.4 | 0.630896 | ||||||||
\(963\) | 1325.52 | 0.0443553 | ||||||||
\(964\) | −51640.8 | −1.72535 | ||||||||
\(965\) | 12569.2 | 0.419293 | ||||||||
\(966\) | 18730.7 | 0.623860 | ||||||||
\(967\) | −33896.0 | −1.12722 | −0.563610 | − | 0.826041i | \(-0.690588\pi\) | ||||
−0.563610 | + | 0.826041i | \(0.690588\pi\) | |||||||
\(968\) | 51280.3 | 1.70270 | ||||||||
\(969\) | −3455.56 | −0.114560 | ||||||||
\(970\) | 21556.5 | 0.713545 | ||||||||
\(971\) | −37446.8 | −1.23762 | −0.618808 | − | 0.785542i | \(-0.712384\pi\) | ||||
−0.618808 | + | 0.785542i | \(0.712384\pi\) | |||||||
\(972\) | 10259.5 | 0.338554 | ||||||||
\(973\) | −6749.69 | −0.222390 | ||||||||
\(974\) | 17911.9 | 0.589256 | ||||||||
\(975\) | −20199.9 | −0.663502 | ||||||||
\(976\) | 117783. | 3.86284 | ||||||||
\(977\) | 23276.6 | 0.762214 | 0.381107 | − | 0.924531i | \(-0.375543\pi\) | ||||
0.381107 | + | 0.924531i | \(0.375543\pi\) | |||||||
\(978\) | 13287.7 | 0.434452 | ||||||||
\(979\) | 59881.3 | 1.95487 | ||||||||
\(980\) | −96887.5 | −3.15812 | ||||||||
\(981\) | 2135.33 | 0.0694962 | ||||||||
\(982\) | −16228.9 | −0.527377 | ||||||||
\(983\) | −20647.7 | −0.669947 | −0.334974 | − | 0.942228i | \(-0.608727\pi\) | ||||
−0.334974 | + | 0.942228i | \(0.608727\pi\) | |||||||
\(984\) | −120586. | −3.90664 | ||||||||
\(985\) | −43411.1 | −1.40426 | ||||||||
\(986\) | −56958.9 | −1.83970 | ||||||||
\(987\) | 53107.8 | 1.71271 | ||||||||
\(988\) | 11497.1 | 0.370216 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 6506.00 | 0.208863 | ||||||||
\(991\) | 20706.8 | 0.663745 | 0.331873 | − | 0.943324i | \(-0.392320\pi\) | ||||
0.331873 | + | 0.943324i | \(0.392320\pi\) | |||||||
\(992\) | −40351.1 | −1.29148 | ||||||||
\(993\) | 10589.2 | 0.338408 | ||||||||
\(994\) | −98147.2 | −3.13183 | ||||||||
\(995\) | 9730.36 | 0.310023 | ||||||||
\(996\) | 49465.7 | 1.57368 | ||||||||
\(997\) | −55958.1 | −1.77754 | −0.888771 | − | 0.458351i | \(-0.848440\pi\) | ||||
−0.888771 | + | 0.458351i | \(0.848440\pi\) | |||||||
\(998\) | −88341.7 | −2.80201 | ||||||||
\(999\) | 8679.66 | 0.274887 |
(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.1.49 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.2 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.49 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.2 | yes | 50 | 43.42 | odd | 2 |