Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2009,4,Mod(1,2009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2009.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2009 = 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2009.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: | \(118.534837202\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 2009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.08931 | −1.44579 | −0.722894 | − | 0.690959i | \(-0.757189\pi\) | ||||
−0.722894 | + | 0.690959i | \(0.757189\pi\) | |||||||
\(3\) | −7.07895 | −1.36234 | −0.681172 | − | 0.732123i | \(-0.738529\pi\) | ||||
−0.681172 | + | 0.732123i | \(0.738529\pi\) | |||||||
\(4\) | 8.72244 | 1.09030 | ||||||||
\(5\) | −1.42150 | −0.127143 | −0.0635716 | − | 0.997977i | \(-0.520249\pi\) | ||||
−0.0635716 | + | 0.997977i | \(0.520249\pi\) | |||||||
\(6\) | 28.9480 | 1.96966 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.95427 | −0.130562 | ||||||||
\(9\) | 23.1115 | 0.855982 | ||||||||
\(10\) | 5.81297 | 0.183822 | ||||||||
\(11\) | −0.443165 | −0.0121472 | −0.00607360 | − | 0.999982i | \(-0.501933\pi\) | ||||
−0.00607360 | + | 0.999982i | \(0.501933\pi\) | |||||||
\(12\) | −61.7457 | −1.48537 | ||||||||
\(13\) | −64.4823 | −1.37571 | −0.687853 | − | 0.725850i | \(-0.741447\pi\) | ||||
−0.687853 | + | 0.725850i | \(0.741447\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.0628 | 0.173213 | ||||||||
\(16\) | −57.6986 | −0.901540 | ||||||||
\(17\) | 92.0664 | 1.31349 | 0.656747 | − | 0.754111i | \(-0.271932\pi\) | ||||
0.656747 | + | 0.754111i | \(0.271932\pi\) | |||||||
\(18\) | −94.5101 | −1.23757 | ||||||||
\(19\) | −110.432 | −1.33341 | −0.666705 | − | 0.745321i | \(-0.732296\pi\) | ||||
−0.666705 | + | 0.745321i | \(0.732296\pi\) | |||||||
\(20\) | −12.3990 | −0.138625 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.81224 | 0.0175623 | ||||||||
\(23\) | 46.8679 | 0.424897 | 0.212449 | − | 0.977172i | \(-0.431856\pi\) | ||||
0.212449 | + | 0.977172i | \(0.431856\pi\) | |||||||
\(24\) | 20.9131 | 0.177870 | ||||||||
\(25\) | −122.979 | −0.983835 | ||||||||
\(26\) | 263.688 | 1.98898 | ||||||||
\(27\) | 27.5264 | 0.196202 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −84.6016 | −0.541728 | −0.270864 | − | 0.962618i | \(-0.587309\pi\) | ||||
−0.270864 | + | 0.962618i | \(0.587309\pi\) | |||||||
\(30\) | −41.1497 | −0.250429 | ||||||||
\(31\) | 22.6404 | 0.131172 | 0.0655861 | − | 0.997847i | \(-0.479108\pi\) | ||||
0.0655861 | + | 0.997847i | \(0.479108\pi\) | |||||||
\(32\) | 259.581 | 1.43400 | ||||||||
\(33\) | 3.13714 | 0.0165487 | ||||||||
\(34\) | −376.488 | −1.89903 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 201.589 | 0.933281 | ||||||||
\(37\) | −416.907 | −1.85241 | −0.926205 | − | 0.377021i | \(-0.876948\pi\) | ||||
−0.926205 | + | 0.377021i | \(0.876948\pi\) | |||||||
\(38\) | 451.590 | 1.92783 | ||||||||
\(39\) | 456.467 | 1.87418 | ||||||||
\(40\) | 4.19951 | 0.0166000 | ||||||||
\(41\) | −41.0000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −423.747 | −1.50281 | −0.751405 | − | 0.659842i | \(-0.770623\pi\) | ||||
−0.751405 | + | 0.659842i | \(0.770623\pi\) | |||||||
\(44\) | −3.86548 | −0.0132442 | ||||||||
\(45\) | −32.8531 | −0.108832 | ||||||||
\(46\) | −191.657 | −0.614312 | ||||||||
\(47\) | 598.465 | 1.85734 | 0.928672 | − | 0.370903i | \(-0.120952\pi\) | ||||
0.928672 | + | 0.370903i | \(0.120952\pi\) | |||||||
\(48\) | 408.445 | 1.22821 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 502.900 | 1.42242 | ||||||||
\(51\) | −651.733 | −1.78943 | ||||||||
\(52\) | −562.443 | −1.49994 | ||||||||
\(53\) | 386.740 | 1.00232 | 0.501159 | − | 0.865355i | \(-0.332907\pi\) | ||||
0.501159 | + | 0.865355i | \(0.332907\pi\) | |||||||
\(54\) | −112.564 | −0.283667 | ||||||||
\(55\) | 0.629961 | 0.00154443 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 781.742 | 1.81656 | ||||||||
\(58\) | 345.962 | 0.783225 | ||||||||
\(59\) | −335.463 | −0.740230 | −0.370115 | − | 0.928986i | \(-0.620682\pi\) | ||||
−0.370115 | + | 0.928986i | \(0.620682\pi\) | |||||||
\(60\) | 87.7718 | 0.188855 | ||||||||
\(61\) | 607.222 | 1.27454 | 0.637268 | − | 0.770642i | \(-0.280064\pi\) | ||||
0.637268 | + | 0.770642i | \(0.280064\pi\) | |||||||
\(62\) | −92.5836 | −0.189647 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −599.920 | −1.17172 | ||||||||
\(65\) | 91.6619 | 0.174912 | ||||||||
\(66\) | −12.8287 | −0.0239259 | ||||||||
\(67\) | 898.110 | 1.63764 | 0.818818 | − | 0.574054i | \(-0.194630\pi\) | ||||
0.818818 | + | 0.574054i | \(0.194630\pi\) | |||||||
\(68\) | 803.044 | 1.43211 | ||||||||
\(69\) | −331.776 | −0.578856 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −33.8041 | −0.0565044 | −0.0282522 | − | 0.999601i | \(-0.508994\pi\) | ||||
−0.0282522 | + | 0.999601i | \(0.508994\pi\) | |||||||
\(72\) | −68.2777 | −0.111758 | ||||||||
\(73\) | 376.733 | 0.604017 | 0.302008 | − | 0.953305i | \(-0.402343\pi\) | ||||
0.302008 | + | 0.953305i | \(0.402343\pi\) | |||||||
\(74\) | 1704.86 | 2.67819 | ||||||||
\(75\) | 870.564 | 1.34032 | ||||||||
\(76\) | −963.235 | −1.45382 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1866.63 | −2.70968 | ||||||||
\(79\) | −1369.36 | −1.95019 | −0.975093 | − | 0.221797i | \(-0.928808\pi\) | ||||
−0.975093 | + | 0.221797i | \(0.928808\pi\) | |||||||
\(80\) | 82.0188 | 0.114625 | ||||||||
\(81\) | −818.869 | −1.12328 | ||||||||
\(82\) | 167.662 | 0.225794 | ||||||||
\(83\) | −986.916 | −1.30516 | −0.652579 | − | 0.757721i | \(-0.726313\pi\) | ||||
−0.652579 | + | 0.757721i | \(0.726313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −130.873 | −0.167002 | ||||||||
\(86\) | 1732.83 | 2.17274 | ||||||||
\(87\) | 598.890 | 0.738021 | ||||||||
\(88\) | 1.30923 | 0.00158596 | ||||||||
\(89\) | −36.7885 | −0.0438154 | −0.0219077 | − | 0.999760i | \(-0.506974\pi\) | ||||
−0.0219077 | + | 0.999760i | \(0.506974\pi\) | |||||||
\(90\) | 134.347 | 0.157349 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 408.803 | 0.463268 | ||||||||
\(93\) | −160.270 | −0.178702 | ||||||||
\(94\) | −2447.31 | −2.68533 | ||||||||
\(95\) | 156.979 | 0.169534 | ||||||||
\(96\) | −1837.56 | −1.95360 | ||||||||
\(97\) | −464.373 | −0.486081 | −0.243041 | − | 0.970016i | \(-0.578145\pi\) | ||||
−0.243041 | + | 0.970016i | \(0.578145\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.2422 | −0.0103978 | ||||||||
\(100\) | −1072.68 | −1.07268 | ||||||||
\(101\) | 597.970 | 0.589111 | 0.294556 | − | 0.955634i | \(-0.404828\pi\) | ||||
0.294556 | + | 0.955634i | \(0.404828\pi\) | |||||||
\(102\) | 2665.14 | 2.58714 | ||||||||
\(103\) | −1623.12 | −1.55273 | −0.776363 | − | 0.630287i | \(-0.782937\pi\) | ||||
−0.776363 | + | 0.630287i | \(0.782937\pi\) | |||||||
\(104\) | 190.498 | 0.179614 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1581.50 | −1.44914 | ||||||||
\(107\) | −1456.63 | −1.31605 | −0.658026 | − | 0.752995i | \(-0.728608\pi\) | ||||
−0.658026 | + | 0.752995i | \(0.728608\pi\) | |||||||
\(108\) | 240.097 | 0.213920 | ||||||||
\(109\) | 194.605 | 0.171007 | 0.0855035 | − | 0.996338i | \(-0.472750\pi\) | ||||
0.0855035 | + | 0.996338i | \(0.472750\pi\) | |||||||
\(110\) | −2.57610 | −0.00223293 | ||||||||
\(111\) | 2951.27 | 2.52362 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −873.093 | −0.726846 | −0.363423 | − | 0.931624i | \(-0.618392\pi\) | ||||
−0.363423 | + | 0.931624i | \(0.618392\pi\) | |||||||
\(114\) | −3196.78 | −2.62637 | ||||||||
\(115\) | −66.6230 | −0.0540228 | ||||||||
\(116\) | −737.932 | −0.590649 | ||||||||
\(117\) | −1490.28 | −1.17758 | ||||||||
\(118\) | 1371.81 | 1.07022 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −29.7281 | −0.0226150 | ||||||||
\(121\) | −1330.80 | −0.999852 | ||||||||
\(122\) | −2483.12 | −1.84271 | ||||||||
\(123\) | 290.237 | 0.212762 | ||||||||
\(124\) | 197.480 | 0.143018 | ||||||||
\(125\) | 352.504 | 0.252231 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −428.426 | −0.299344 | −0.149672 | − | 0.988736i | \(-0.547822\pi\) | ||||
−0.149672 | + | 0.988736i | \(0.547822\pi\) | |||||||
\(128\) | 376.605 | 0.260059 | ||||||||
\(129\) | 2999.68 | 2.04734 | ||||||||
\(130\) | −374.834 | −0.252885 | ||||||||
\(131\) | −1121.62 | −0.748064 | −0.374032 | − | 0.927416i | \(-0.622025\pi\) | ||||
−0.374032 | + | 0.927416i | \(0.622025\pi\) | |||||||
\(132\) | 27.3635 | 0.0180431 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3672.65 | −2.36767 | ||||||||
\(135\) | −39.1289 | −0.0249458 | ||||||||
\(136\) | −271.989 | −0.171492 | ||||||||
\(137\) | −360.664 | −0.224917 | −0.112458 | − | 0.993656i | \(-0.535872\pi\) | ||||
−0.112458 | + | 0.993656i | \(0.535872\pi\) | |||||||
\(138\) | 1356.73 | 0.836904 | ||||||||
\(139\) | 1791.36 | 1.09310 | 0.546552 | − | 0.837425i | \(-0.315940\pi\) | ||||
0.546552 | + | 0.837425i | \(0.315940\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4236.50 | −2.53034 | ||||||||
\(142\) | 138.236 | 0.0816934 | ||||||||
\(143\) | 28.5763 | 0.0167110 | ||||||||
\(144\) | −1333.50 | −0.771702 | ||||||||
\(145\) | 120.262 | 0.0688771 | ||||||||
\(146\) | −1540.58 | −0.873280 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3636.45 | −2.01969 | ||||||||
\(149\) | −1358.92 | −0.747160 | −0.373580 | − | 0.927598i | \(-0.621870\pi\) | ||||
−0.373580 | + | 0.927598i | \(0.621870\pi\) | |||||||
\(150\) | −3560.01 | −1.93782 | ||||||||
\(151\) | 11.3793 | 0.00613269 | 0.00306634 | − | 0.999995i | \(-0.499024\pi\) | ||||
0.00306634 | + | 0.999995i | \(0.499024\pi\) | |||||||
\(152\) | 326.246 | 0.174092 | ||||||||
\(153\) | 2127.79 | 1.12433 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −32.1835 | −0.0166777 | ||||||||
\(156\) | 3981.50 | 2.04343 | ||||||||
\(157\) | −1448.58 | −0.736367 | −0.368184 | − | 0.929753i | \(-0.620020\pi\) | ||||
−0.368184 | + | 0.929753i | \(0.620020\pi\) | |||||||
\(158\) | 5599.72 | 2.81956 | ||||||||
\(159\) | −2737.71 | −1.36550 | ||||||||
\(160\) | −368.996 | −0.182323 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 3348.61 | 1.62402 | ||||||||
\(163\) | −3623.55 | −1.74122 | −0.870609 | − | 0.491975i | \(-0.836275\pi\) | ||||
−0.870609 | + | 0.491975i | \(0.836275\pi\) | |||||||
\(164\) | −357.620 | −0.170277 | ||||||||
\(165\) | −4.45946 | −0.00210405 | ||||||||
\(166\) | 4035.80 | 1.88698 | ||||||||
\(167\) | −2324.38 | −1.07704 | −0.538520 | − | 0.842613i | \(-0.681016\pi\) | ||||
−0.538520 | + | 0.842613i | \(0.681016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1960.97 | 0.892566 | ||||||||
\(170\) | 535.179 | 0.241449 | ||||||||
\(171\) | −2552.25 | −1.14138 | ||||||||
\(172\) | −3696.11 | −1.63852 | ||||||||
\(173\) | −1631.00 | −0.716777 | −0.358388 | − | 0.933573i | \(-0.616674\pi\) | ||||
−0.358388 | + | 0.933573i | \(0.616674\pi\) | |||||||
\(174\) | −2449.05 | −1.06702 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 25.5700 | 0.0109512 | ||||||||
\(177\) | 2374.73 | 1.00845 | ||||||||
\(178\) | 150.439 | 0.0633478 | ||||||||
\(179\) | −726.863 | −0.303510 | −0.151755 | − | 0.988418i | \(-0.548492\pi\) | ||||
−0.151755 | + | 0.988418i | \(0.548492\pi\) | |||||||
\(180\) | −286.559 | −0.118660 | ||||||||
\(181\) | 2095.37 | 0.860485 | 0.430243 | − | 0.902713i | \(-0.358428\pi\) | ||||
0.430243 | + | 0.902713i | \(0.358428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4298.49 | −1.73636 | ||||||||
\(184\) | −138.461 | −0.0554753 | ||||||||
\(185\) | 592.636 | 0.235521 | ||||||||
\(186\) | 655.395 | 0.258365 | ||||||||
\(187\) | −40.8006 | −0.0159553 | ||||||||
\(188\) | 5220.08 | 2.02507 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −641.937 | −0.245111 | ||||||||
\(191\) | 4021.22 | 1.52338 | 0.761688 | − | 0.647943i | \(-0.224371\pi\) | ||||
0.761688 | + | 0.647943i | \(0.224371\pi\) | |||||||
\(192\) | 4246.80 | 1.59628 | ||||||||
\(193\) | −1840.45 | −0.686418 | −0.343209 | − | 0.939259i | \(-0.611514\pi\) | ||||
−0.343209 | + | 0.939259i | \(0.611514\pi\) | |||||||
\(194\) | 1898.96 | 0.702771 | ||||||||
\(195\) | −648.870 | −0.238290 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 773.389 | 0.279704 | 0.139852 | − | 0.990172i | \(-0.455337\pi\) | ||||
0.139852 | + | 0.990172i | \(0.455337\pi\) | |||||||
\(198\) | 41.8836 | 0.0150330 | ||||||||
\(199\) | 318.267 | 0.113374 | 0.0566868 | − | 0.998392i | \(-0.481946\pi\) | ||||
0.0566868 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(200\) | 363.314 | 0.128451 | ||||||||
\(201\) | −6357.67 | −2.23102 | ||||||||
\(202\) | −2445.28 | −0.851730 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −5684.70 | −1.95102 | ||||||||
\(205\) | 58.2817 | 0.0198564 | ||||||||
\(206\) | 6637.43 | 2.24491 | ||||||||
\(207\) | 1083.19 | 0.363705 | ||||||||
\(208\) | 3720.54 | 1.24025 | ||||||||
\(209\) | 48.9395 | 0.0161972 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3115.90 | 1.01662 | 0.508312 | − | 0.861173i | \(-0.330270\pi\) | ||||
0.508312 | + | 0.861173i | \(0.330270\pi\) | |||||||
\(212\) | 3373.32 | 1.09283 | ||||||||
\(213\) | 239.298 | 0.0769785 | ||||||||
\(214\) | 5956.60 | 1.90273 | ||||||||
\(215\) | 602.358 | 0.191072 | ||||||||
\(216\) | −81.3204 | −0.0256165 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −795.799 | −0.247240 | ||||||||
\(219\) | −2666.87 | −0.822878 | ||||||||
\(220\) | 5.49480 | 0.00168390 | ||||||||
\(221\) | −5936.65 | −1.80698 | ||||||||
\(222\) | −12068.6 | −3.64862 | ||||||||
\(223\) | −5895.18 | −1.77027 | −0.885135 | − | 0.465334i | \(-0.845934\pi\) | ||||
−0.885135 | + | 0.465334i | \(0.845934\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2842.24 | −0.842145 | ||||||||
\(226\) | 3570.34 | 1.05087 | ||||||||
\(227\) | −5516.68 | −1.61302 | −0.806509 | − | 0.591222i | \(-0.798646\pi\) | ||||
−0.806509 | + | 0.591222i | \(0.798646\pi\) | |||||||
\(228\) | 6818.69 | 1.98061 | ||||||||
\(229\) | −1940.65 | −0.560009 | −0.280004 | − | 0.959999i | \(-0.590336\pi\) | ||||
−0.280004 | + | 0.959999i | \(0.590336\pi\) | |||||||
\(230\) | 272.442 | 0.0781056 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 249.936 | 0.0707290 | ||||||||
\(233\) | −5371.80 | −1.51038 | −0.755189 | − | 0.655507i | \(-0.772455\pi\) | ||||
−0.755189 | + | 0.655507i | \(0.772455\pi\) | |||||||
\(234\) | 6094.23 | 1.70253 | ||||||||
\(235\) | −850.721 | −0.236149 | ||||||||
\(236\) | −2926.06 | −0.807077 | ||||||||
\(237\) | 9693.61 | 2.65682 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −686.208 | −0.185720 | −0.0928601 | − | 0.995679i | \(-0.529601\pi\) | ||||
−0.0928601 | + | 0.995679i | \(0.529601\pi\) | |||||||
\(240\) | −580.607 | −0.156158 | ||||||||
\(241\) | 3181.94 | 0.850485 | 0.425242 | − | 0.905079i | \(-0.360189\pi\) | ||||
0.425242 | + | 0.905079i | \(0.360189\pi\) | |||||||
\(242\) | 5442.07 | 1.44558 | ||||||||
\(243\) | 5053.52 | 1.33409 | ||||||||
\(244\) | 5296.45 | 1.38963 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1186.87 | −0.307610 | ||||||||
\(247\) | 7120.90 | 1.83438 | ||||||||
\(248\) | −66.8860 | −0.0171261 | ||||||||
\(249\) | 6986.33 | 1.77807 | ||||||||
\(250\) | −1441.50 | −0.364673 | ||||||||
\(251\) | −2350.99 | −0.591209 | −0.295605 | − | 0.955310i | \(-0.595521\pi\) | ||||
−0.295605 | + | 0.955310i | \(0.595521\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.7702 | −0.00516131 | ||||||||
\(254\) | 1751.97 | 0.432788 | ||||||||
\(255\) | 926.442 | 0.227514 | ||||||||
\(256\) | 3259.30 | 0.795728 | ||||||||
\(257\) | 4564.13 | 1.10779 | 0.553897 | − | 0.832585i | \(-0.313140\pi\) | ||||
0.553897 | + | 0.832585i | \(0.313140\pi\) | |||||||
\(258\) | −12266.6 | −2.96003 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 799.515 | 0.190707 | ||||||||
\(261\) | −1955.27 | −0.463710 | ||||||||
\(262\) | 4586.65 | 1.08154 | ||||||||
\(263\) | −2052.97 | −0.481337 | −0.240668 | − | 0.970607i | \(-0.577367\pi\) | ||||
−0.240668 | + | 0.970607i | \(0.577367\pi\) | |||||||
\(264\) | −9.26797 | −0.00216062 | ||||||||
\(265\) | −549.753 | −0.127438 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 260.424 | 0.0596917 | ||||||||
\(268\) | 7833.71 | 1.78552 | ||||||||
\(269\) | −2667.62 | −0.604638 | −0.302319 | − | 0.953207i | \(-0.597761\pi\) | ||||
−0.302319 | + | 0.953207i | \(0.597761\pi\) | |||||||
\(270\) | 160.010 | 0.0360663 | ||||||||
\(271\) | 4750.66 | 1.06488 | 0.532439 | − | 0.846468i | \(-0.321276\pi\) | ||||
0.532439 | + | 0.846468i | \(0.321276\pi\) | |||||||
\(272\) | −5312.10 | −1.18417 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1474.87 | 0.325182 | ||||||||
\(275\) | 54.5001 | 0.0119508 | ||||||||
\(276\) | −2893.89 | −0.631130 | ||||||||
\(277\) | 742.520 | 0.161060 | 0.0805301 | − | 0.996752i | \(-0.474339\pi\) | ||||
0.0805301 | + | 0.996752i | \(0.474339\pi\) | |||||||
\(278\) | −7325.44 | −1.58040 | ||||||||
\(279\) | 523.254 | 0.112281 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3614.96 | 0.767438 | 0.383719 | − | 0.923450i | \(-0.374643\pi\) | ||||
0.383719 | + | 0.923450i | \(0.374643\pi\) | |||||||
\(282\) | 17324.4 | 3.65834 | ||||||||
\(283\) | −3228.25 | −0.678090 | −0.339045 | − | 0.940770i | \(-0.610104\pi\) | ||||
−0.339045 | + | 0.940770i | \(0.610104\pi\) | |||||||
\(284\) | −294.855 | −0.0616070 | ||||||||
\(285\) | −1111.25 | −0.230964 | ||||||||
\(286\) | −116.857 | −0.0241605 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5999.32 | 1.22748 | ||||||||
\(289\) | 3563.22 | 0.725264 | ||||||||
\(290\) | −491.787 | −0.0995817 | ||||||||
\(291\) | 3287.27 | 0.662210 | ||||||||
\(292\) | 3286.03 | 0.658562 | ||||||||
\(293\) | −3630.04 | −0.723785 | −0.361893 | − | 0.932220i | \(-0.617869\pi\) | ||||
−0.361893 | + | 0.932220i | \(0.617869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 476.862 | 0.0941153 | ||||||||
\(296\) | 1231.66 | 0.241854 | ||||||||
\(297\) | −12.1987 | −0.00238331 | ||||||||
\(298\) | 5557.03 | 1.08023 | ||||||||
\(299\) | −3022.15 | −0.584534 | ||||||||
\(300\) | 7593.44 | 1.46136 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −46.5335 | −0.00886657 | ||||||||
\(303\) | −4233.00 | −0.802572 | ||||||||
\(304\) | 6371.76 | 1.20212 | ||||||||
\(305\) | −863.168 | −0.162049 | ||||||||
\(306\) | −8701.21 | −1.62554 | ||||||||
\(307\) | 639.170 | 0.118825 | 0.0594127 | − | 0.998234i | \(-0.481077\pi\) | ||||
0.0594127 | + | 0.998234i | \(0.481077\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11490.0 | 2.11535 | ||||||||
\(310\) | 131.608 | 0.0241124 | ||||||||
\(311\) | 2883.44 | 0.525740 | 0.262870 | − | 0.964831i | \(-0.415331\pi\) | ||||
0.262870 | + | 0.964831i | \(0.415331\pi\) | |||||||
\(312\) | −1348.53 | −0.244697 | ||||||||
\(313\) | 2679.89 | 0.483951 | 0.241975 | − | 0.970282i | \(-0.422205\pi\) | ||||
0.241975 | + | 0.970282i | \(0.422205\pi\) | |||||||
\(314\) | 5923.71 | 1.06463 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11944.1 | −2.12630 | ||||||||
\(317\) | −6345.80 | −1.12434 | −0.562170 | − | 0.827022i | \(-0.690033\pi\) | ||||
−0.562170 | + | 0.827022i | \(0.690033\pi\) | |||||||
\(318\) | 11195.4 | 1.97423 | ||||||||
\(319\) | 37.4925 | 0.00658049 | ||||||||
\(320\) | 852.789 | 0.148976 | ||||||||
\(321\) | 10311.4 | 1.79292 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10167.1 | −1.75143 | ||||||||
\(324\) | −7142.53 | −1.22471 | ||||||||
\(325\) | 7929.99 | 1.35347 | ||||||||
\(326\) | 14817.8 | 2.51743 | ||||||||
\(327\) | −1377.60 | −0.232970 | ||||||||
\(328\) | 121.125 | 0.0203903 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 18.2361 | 0.00304201 | ||||||||
\(331\) | 5273.78 | 0.875749 | 0.437875 | − | 0.899036i | \(-0.355731\pi\) | ||||
0.437875 | + | 0.899036i | \(0.355731\pi\) | |||||||
\(332\) | −8608.31 | −1.42302 | ||||||||
\(333\) | −9635.36 | −1.58563 | ||||||||
\(334\) | 9505.09 | 1.55717 | ||||||||
\(335\) | −1276.67 | −0.208214 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9269.40 | −1.49833 | −0.749164 | − | 0.662385i | \(-0.769544\pi\) | ||||
−0.749164 | + | 0.662385i | \(0.769544\pi\) | |||||||
\(338\) | −8019.00 | −1.29046 | ||||||||
\(339\) | 6180.58 | 0.990215 | ||||||||
\(340\) | −1141.53 | −0.182083 | ||||||||
\(341\) | −10.0334 | −0.00159338 | ||||||||
\(342\) | 10436.9 | 1.65019 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1251.86 | 0.196209 | ||||||||
\(345\) | 471.621 | 0.0735977 | ||||||||
\(346\) | 6669.65 | 1.03631 | ||||||||
\(347\) | 9018.35 | 1.39519 | 0.697594 | − | 0.716493i | \(-0.254254\pi\) | ||||
0.697594 | + | 0.716493i | \(0.254254\pi\) | |||||||
\(348\) | 5223.79 | 0.804668 | ||||||||
\(349\) | −9339.16 | −1.43242 | −0.716209 | − | 0.697886i | \(-0.754124\pi\) | ||||
−0.716209 | + | 0.697886i | \(0.754124\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1774.96 | −0.269916 | ||||||||
\(352\) | −115.037 | −0.0174191 | ||||||||
\(353\) | 7162.24 | 1.07991 | 0.539954 | − | 0.841694i | \(-0.318441\pi\) | ||||
0.539954 | + | 0.841694i | \(0.318441\pi\) | |||||||
\(354\) | −9710.99 | −1.45800 | ||||||||
\(355\) | 48.0527 | 0.00718415 | ||||||||
\(356\) | −320.885 | −0.0477722 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2972.37 | 0.438811 | ||||||||
\(359\) | 4997.02 | 0.734632 | 0.367316 | − | 0.930096i | \(-0.380277\pi\) | ||||
0.367316 | + | 0.930096i | \(0.380277\pi\) | |||||||
\(360\) | 97.0571 | 0.0142093 | ||||||||
\(361\) | 5336.20 | 0.777985 | ||||||||
\(362\) | −8568.63 | −1.24408 | ||||||||
\(363\) | 9420.69 | 1.36214 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −535.527 | −0.0767966 | ||||||||
\(366\) | 17577.8 | 2.51041 | ||||||||
\(367\) | 9994.87 | 1.42160 | 0.710801 | − | 0.703393i | \(-0.248333\pi\) | ||||
0.710801 | + | 0.703393i | \(0.248333\pi\) | |||||||
\(368\) | −2704.21 | −0.383062 | ||||||||
\(369\) | −947.572 | −0.133682 | ||||||||
\(370\) | −2423.47 | −0.340514 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1397.95 | −0.194839 | ||||||||
\(373\) | −13406.3 | −1.86100 | −0.930500 | − | 0.366293i | \(-0.880627\pi\) | ||||
−0.930500 | + | 0.366293i | \(0.880627\pi\) | |||||||
\(374\) | 166.846 | 0.0230679 | ||||||||
\(375\) | −2495.36 | −0.343626 | ||||||||
\(376\) | −1768.03 | −0.242498 | ||||||||
\(377\) | 5455.31 | 0.745259 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2796.87 | 0.379065 | 0.189533 | − | 0.981874i | \(-0.439303\pi\) | ||||
0.189533 | + | 0.981874i | \(0.439303\pi\) | |||||||
\(380\) | 1369.24 | 0.184844 | ||||||||
\(381\) | 3032.81 | 0.407809 | ||||||||
\(382\) | −16444.0 | −2.20248 | ||||||||
\(383\) | 14364.8 | 1.91646 | 0.958231 | − | 0.285995i | \(-0.0923239\pi\) | ||||
0.958231 | + | 0.285995i | \(0.0923239\pi\) | |||||||
\(384\) | −2665.97 | −0.354289 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7526.18 | 0.992415 | ||||||||
\(387\) | −9793.43 | −1.28638 | ||||||||
\(388\) | −4050.46 | −0.529977 | ||||||||
\(389\) | −14534.0 | −1.89435 | −0.947176 | − | 0.320715i | \(-0.896077\pi\) | ||||
−0.947176 | + | 0.320715i | \(0.896077\pi\) | |||||||
\(390\) | 2653.43 | 0.344517 | ||||||||
\(391\) | 4314.96 | 0.558100 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7939.89 | 1.01912 | ||||||||
\(394\) | −3162.63 | −0.404393 | ||||||||
\(395\) | 1946.55 | 0.247953 | ||||||||
\(396\) | −89.3371 | −0.0113368 | ||||||||
\(397\) | −806.635 | −0.101974 | −0.0509872 | − | 0.998699i | \(-0.516237\pi\) | ||||
−0.0509872 | + | 0.998699i | \(0.516237\pi\) | |||||||
\(398\) | −1301.49 | −0.163914 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7095.73 | 0.886966 | ||||||||
\(401\) | 8355.35 | 1.04051 | 0.520257 | − | 0.854010i | \(-0.325836\pi\) | ||||
0.520257 | + | 0.854010i | \(0.325836\pi\) | |||||||
\(402\) | 25998.5 | 3.22559 | ||||||||
\(403\) | −1459.91 | −0.180454 | ||||||||
\(404\) | 5215.76 | 0.642311 | ||||||||
\(405\) | 1164.03 | 0.142817 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 184.759 | 0.0225016 | ||||||||
\(408\) | 1925.40 | 0.233631 | ||||||||
\(409\) | −12493.6 | −1.51043 | −0.755217 | − | 0.655475i | \(-0.772469\pi\) | ||||
−0.755217 | + | 0.655475i | \(0.772469\pi\) | |||||||
\(410\) | −238.332 | −0.0287082 | ||||||||
\(411\) | 2553.12 | 0.306414 | ||||||||
\(412\) | −14157.6 | −1.69294 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4429.49 | −0.525840 | ||||||||
\(415\) | 1402.91 | 0.165942 | ||||||||
\(416\) | −16738.4 | −1.97276 | ||||||||
\(417\) | −12681.0 | −1.48918 | ||||||||
\(418\) | −200.129 | −0.0234177 | ||||||||
\(419\) | 15197.6 | 1.77196 | 0.885978 | − | 0.463727i | \(-0.153488\pi\) | ||||
0.885978 | + | 0.463727i | \(0.153488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9793.07 | −1.13369 | −0.566847 | − | 0.823823i | \(-0.691837\pi\) | ||||
−0.566847 | + | 0.823823i | \(0.691837\pi\) | |||||||
\(422\) | −12741.9 | −1.46982 | ||||||||
\(423\) | 13831.4 | 1.58985 | ||||||||
\(424\) | −1142.54 | −0.130864 | ||||||||
\(425\) | −11322.3 | −1.29226 | ||||||||
\(426\) | −978.562 | −0.111295 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12705.4 | −1.43490 | ||||||||
\(429\) | −202.290 | −0.0227661 | ||||||||
\(430\) | −2463.23 | −0.276250 | ||||||||
\(431\) | 3305.27 | 0.369395 | 0.184697 | − | 0.982795i | \(-0.440870\pi\) | ||||
0.184697 | + | 0.982795i | \(0.440870\pi\) | |||||||
\(432\) | −1588.23 | −0.176884 | ||||||||
\(433\) | −1573.63 | −0.174651 | −0.0873257 | − | 0.996180i | \(-0.527832\pi\) | ||||
−0.0873257 | + | 0.996180i | \(0.527832\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −851.326 | −0.0938343 | ||||||||
\(436\) | 1697.43 | 0.186450 | ||||||||
\(437\) | −5175.71 | −0.566563 | ||||||||
\(438\) | 10905.7 | 1.18971 | ||||||||
\(439\) | 9839.76 | 1.06976 | 0.534882 | − | 0.844927i | \(-0.320356\pi\) | ||||
0.534882 | + | 0.844927i | \(0.320356\pi\) | |||||||
\(440\) | −1.86108 | −0.000201644 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24276.8 | 2.61251 | ||||||||
\(443\) | 7477.25 | 0.801930 | 0.400965 | − | 0.916093i | \(-0.368675\pi\) | ||||
0.400965 | + | 0.916093i | \(0.368675\pi\) | |||||||
\(444\) | 25742.2 | 2.75151 | ||||||||
\(445\) | 52.2950 | 0.00557084 | ||||||||
\(446\) | 24107.2 | 2.55944 | ||||||||
\(447\) | 9619.70 | 1.01789 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12696.6 | 1.33450 | 0.667250 | − | 0.744834i | \(-0.267471\pi\) | ||||
0.667250 | + | 0.744834i | \(0.267471\pi\) | |||||||
\(450\) | 11622.8 | 1.21756 | ||||||||
\(451\) | 18.1698 | 0.00189707 | ||||||||
\(452\) | −7615.50 | −0.792484 | ||||||||
\(453\) | −80.5536 | −0.00835483 | ||||||||
\(454\) | 22559.4 | 2.33208 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2309.48 | −0.237174 | ||||||||
\(457\) | −1679.52 | −0.171914 | −0.0859569 | − | 0.996299i | \(-0.527395\pi\) | ||||
−0.0859569 | + | 0.996299i | \(0.527395\pi\) | |||||||
\(458\) | 7935.93 | 0.809655 | ||||||||
\(459\) | 2534.25 | 0.257710 | ||||||||
\(460\) | −581.115 | −0.0589013 | ||||||||
\(461\) | 7090.48 | 0.716348 | 0.358174 | − | 0.933655i | \(-0.383399\pi\) | ||||
0.358174 | + | 0.933655i | \(0.383399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5139.68 | −0.515899 | −0.257949 | − | 0.966158i | \(-0.583047\pi\) | ||||
−0.257949 | + | 0.966158i | \(0.583047\pi\) | |||||||
\(464\) | 4881.39 | 0.488390 | ||||||||
\(465\) | 227.825 | 0.0227207 | ||||||||
\(466\) | 21966.9 | 2.18369 | ||||||||
\(467\) | 14308.1 | 1.41778 | 0.708888 | − | 0.705321i | \(-0.249197\pi\) | ||||
0.708888 | + | 0.705321i | \(0.249197\pi\) | |||||||
\(468\) | −12998.9 | −1.28392 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3478.86 | 0.341421 | ||||||||
\(471\) | 10254.5 | 1.00319 | ||||||||
\(472\) | 991.050 | 0.0966457 | ||||||||
\(473\) | 187.790 | 0.0182549 | ||||||||
\(474\) | −39640.1 | −3.84121 | ||||||||
\(475\) | 13580.8 | 1.31186 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8938.15 | 0.857966 | ||||||||
\(478\) | 2806.12 | 0.268512 | ||||||||
\(479\) | −12233.0 | −1.16689 | −0.583447 | − | 0.812151i | \(-0.698296\pi\) | ||||
−0.583447 | + | 0.812151i | \(0.698296\pi\) | |||||||
\(480\) | 2612.11 | 0.248387 | ||||||||
\(481\) | 26883.1 | 2.54837 | ||||||||
\(482\) | −13011.9 | −1.22962 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11607.9 | −1.09014 | ||||||||
\(485\) | 660.108 | 0.0618020 | ||||||||
\(486\) | −20665.4 | −1.92881 | ||||||||
\(487\) | −14271.9 | −1.32797 | −0.663983 | − | 0.747748i | \(-0.731135\pi\) | ||||
−0.663983 | + | 0.747748i | \(0.731135\pi\) | |||||||
\(488\) | −1793.90 | −0.166406 | ||||||||
\(489\) | 25650.9 | 2.37214 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5568.25 | −0.511795 | −0.255898 | − | 0.966704i | \(-0.582371\pi\) | ||||
−0.255898 | + | 0.966704i | \(0.582371\pi\) | |||||||
\(492\) | 2531.57 | 0.231976 | ||||||||
\(493\) | −7788.97 | −0.711557 | ||||||||
\(494\) | −29119.6 | −2.65213 | ||||||||
\(495\) | 14.5594 | 0.00132201 | ||||||||
\(496\) | −1306.32 | −0.118257 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −28569.2 | −2.57072 | ||||||||
\(499\) | 9605.95 | 0.861766 | 0.430883 | − | 0.902408i | \(-0.358202\pi\) | ||||
0.430883 | + | 0.902408i | \(0.358202\pi\) | |||||||
\(500\) | 3074.69 | 0.275009 | ||||||||
\(501\) | 16454.1 | 1.46730 | ||||||||
\(502\) | 9613.94 | 0.854763 | ||||||||
\(503\) | 10790.6 | 0.956521 | 0.478261 | − | 0.878218i | \(-0.341267\pi\) | ||||
0.478261 | + | 0.878218i | \(0.341267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −850.017 | −0.0749015 | ||||||||
\(506\) | 84.9358 | 0.00746217 | ||||||||
\(507\) | −13881.6 | −1.21598 | ||||||||
\(508\) | −3736.92 | −0.326376 | ||||||||
\(509\) | −21164.7 | −1.84305 | −0.921523 | − | 0.388325i | \(-0.873054\pi\) | ||||
−0.921523 | + | 0.388325i | \(0.873054\pi\) | |||||||
\(510\) | −3788.51 | −0.328937 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16341.1 | −1.41051 | ||||||||
\(513\) | −3039.79 | −0.261618 | ||||||||
\(514\) | −18664.1 | −1.60163 | ||||||||
\(515\) | 2307.27 | 0.197419 | ||||||||
\(516\) | 26164.5 | 2.23223 | ||||||||
\(517\) | −265.219 | −0.0225615 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11545.7 | 0.976497 | ||||||||
\(520\) | −270.794 | −0.0228368 | ||||||||
\(521\) | 10417.2 | 0.875982 | 0.437991 | − | 0.898979i | \(-0.355690\pi\) | ||||
0.437991 | + | 0.898979i | \(0.355690\pi\) | |||||||
\(522\) | 7995.71 | 0.670426 | ||||||||
\(523\) | 21337.9 | 1.78402 | 0.892009 | − | 0.452017i | \(-0.149295\pi\) | ||||
0.892009 | + | 0.452017i | \(0.149295\pi\) | |||||||
\(524\) | −9783.26 | −0.815618 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8395.22 | 0.695911 | ||||||||
\(527\) | 2084.42 | 0.172294 | ||||||||
\(528\) | −181.009 | −0.0149193 | ||||||||
\(529\) | −9970.40 | −0.819462 | ||||||||
\(530\) | 2248.11 | 0.184248 | ||||||||
\(531\) | −7753.06 | −0.633624 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2643.77 | 0.214849 | ||||||||
\(534\) | −1064.95 | −0.0863016 | ||||||||
\(535\) | 2070.60 | 0.167327 | ||||||||
\(536\) | −2653.26 | −0.213812 | ||||||||
\(537\) | 5145.43 | 0.413485 | ||||||||
\(538\) | 10908.7 | 0.874178 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −341.299 | −0.0271985 | ||||||||
\(541\) | 1166.74 | 0.0927211 | 0.0463606 | − | 0.998925i | \(-0.485238\pi\) | ||||
0.0463606 | + | 0.998925i | \(0.485238\pi\) | |||||||
\(542\) | −19426.9 | −1.53959 | ||||||||
\(543\) | −14833.0 | −1.17228 | ||||||||
\(544\) | 23898.7 | 1.88355 | ||||||||
\(545\) | −276.632 | −0.0217424 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1415.20 | 0.110621 | 0.0553104 | − | 0.998469i | \(-0.482385\pi\) | ||||
0.0553104 | + | 0.998469i | \(0.482385\pi\) | |||||||
\(548\) | −3145.87 | −0.245228 | ||||||||
\(549\) | 14033.8 | 1.09098 | ||||||||
\(550\) | −222.868 | −0.0172784 | ||||||||
\(551\) | 9342.71 | 0.722347 | ||||||||
\(552\) | 980.156 | 0.0755765 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3036.39 | −0.232859 | ||||||||
\(555\) | −4195.24 | −0.320861 | ||||||||
\(556\) | 15625.1 | 1.19182 | ||||||||
\(557\) | −12608.8 | −0.959157 | −0.479579 | − | 0.877499i | \(-0.659210\pi\) | ||||
−0.479579 | + | 0.877499i | \(0.659210\pi\) | |||||||
\(558\) | −2139.75 | −0.162335 | ||||||||
\(559\) | 27324.2 | 2.06742 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 288.825 | 0.0217366 | ||||||||
\(562\) | −14782.7 | −1.10955 | ||||||||
\(563\) | −2553.01 | −0.191113 | −0.0955565 | − | 0.995424i | \(-0.530463\pi\) | ||||
−0.0955565 | + | 0.995424i | \(0.530463\pi\) | |||||||
\(564\) | −36952.7 | −2.75884 | ||||||||
\(565\) | 1241.11 | 0.0924136 | ||||||||
\(566\) | 13201.3 | 0.980375 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 99.8666 | 0.00737731 | ||||||||
\(569\) | −15993.3 | −1.17834 | −0.589169 | − | 0.808010i | \(-0.700545\pi\) | ||||
−0.589169 | + | 0.808010i | \(0.700545\pi\) | |||||||
\(570\) | 4544.24 | 0.333925 | ||||||||
\(571\) | −20133.8 | −1.47561 | −0.737804 | − | 0.675015i | \(-0.764137\pi\) | ||||
−0.737804 | + | 0.675015i | \(0.764137\pi\) | |||||||
\(572\) | 249.255 | 0.0182201 | ||||||||
\(573\) | −28466.0 | −2.07536 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5763.79 | −0.418029 | ||||||||
\(576\) | −13865.1 | −1.00297 | ||||||||
\(577\) | −84.9551 | −0.00612951 | −0.00306475 | − | 0.999995i | \(-0.500976\pi\) | ||||
−0.00306475 | + | 0.999995i | \(0.500976\pi\) | |||||||
\(578\) | −14571.1 | −1.04858 | ||||||||
\(579\) | 13028.5 | 0.935137 | ||||||||
\(580\) | 1048.97 | 0.0750970 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −13442.7 | −0.957416 | ||||||||
\(583\) | −171.390 | −0.0121754 | ||||||||
\(584\) | −1112.97 | −0.0788614 | ||||||||
\(585\) | 2118.45 | 0.149721 | ||||||||
\(586\) | 14844.3 | 1.04644 | ||||||||
\(587\) | −7667.08 | −0.539104 | −0.269552 | − | 0.962986i | \(-0.586876\pi\) | ||||
−0.269552 | + | 0.962986i | \(0.586876\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2500.22 | −0.174906 | ||||||||
\(590\) | −1950.04 | −0.136071 | ||||||||
\(591\) | −5474.78 | −0.381053 | ||||||||
\(592\) | 24055.0 | 1.67002 | ||||||||
\(593\) | −3719.32 | −0.257562 | −0.128781 | − | 0.991673i | \(-0.541106\pi\) | ||||
−0.128781 | + | 0.991673i | \(0.541106\pi\) | |||||||
\(594\) | 49.8843 | 0.00344576 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11853.1 | −0.814632 | ||||||||
\(597\) | −2253.00 | −0.154454 | ||||||||
\(598\) | 12358.5 | 0.845112 | ||||||||
\(599\) | 9714.86 | 0.662669 | 0.331334 | − | 0.943513i | \(-0.392501\pi\) | ||||
0.331334 | + | 0.943513i | \(0.392501\pi\) | |||||||
\(600\) | −2571.88 | −0.174995 | ||||||||
\(601\) | 11489.3 | 0.779798 | 0.389899 | − | 0.920858i | \(-0.372510\pi\) | ||||
0.389899 | + | 0.920858i | \(0.372510\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20756.7 | 1.40179 | ||||||||
\(604\) | 99.2554 | 0.00668650 | ||||||||
\(605\) | 1891.74 | 0.127124 | ||||||||
\(606\) | 17310.0 | 1.16035 | ||||||||
\(607\) | −17561.7 | −1.17431 | −0.587156 | − | 0.809474i | \(-0.699752\pi\) | ||||
−0.587156 | + | 0.809474i | \(0.699752\pi\) | |||||||
\(608\) | −28666.1 | −1.91211 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3529.76 | 0.234288 | ||||||||
\(611\) | −38590.4 | −2.55516 | ||||||||
\(612\) | 18559.6 | 1.22586 | ||||||||
\(613\) | −12593.5 | −0.829765 | −0.414882 | − | 0.909875i | \(-0.636177\pi\) | ||||
−0.414882 | + | 0.909875i | \(0.636177\pi\) | |||||||
\(614\) | −2613.76 | −0.171796 | ||||||||
\(615\) | −412.573 | −0.0270513 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28778.8 | 1.87778 | 0.938889 | − | 0.344219i | \(-0.111856\pi\) | ||||
0.938889 | + | 0.344219i | \(0.111856\pi\) | |||||||
\(618\) | −46986.1 | −3.05834 | ||||||||
\(619\) | −19154.3 | −1.24374 | −0.621872 | − | 0.783119i | \(-0.713628\pi\) | ||||
−0.621872 | + | 0.783119i | \(0.713628\pi\) | |||||||
\(620\) | −280.718 | −0.0181837 | ||||||||
\(621\) | 1290.10 | 0.0833657 | ||||||||
\(622\) | −11791.3 | −0.760109 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −26337.5 | −1.68965 | ||||||||
\(625\) | 14871.3 | 0.951765 | ||||||||
\(626\) | −10958.9 | −0.699690 | ||||||||
\(627\) | −346.440 | −0.0220662 | ||||||||
\(628\) | −12635.2 | −0.802865 | ||||||||
\(629\) | −38383.2 | −2.43313 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15611.9 | −0.984943 | −0.492472 | − | 0.870328i | \(-0.663906\pi\) | ||||
−0.492472 | + | 0.870328i | \(0.663906\pi\) | |||||||
\(632\) | 4045.45 | 0.254619 | ||||||||
\(633\) | −22057.3 | −1.38499 | ||||||||
\(634\) | 25949.9 | 1.62556 | ||||||||
\(635\) | 609.010 | 0.0380595 | ||||||||
\(636\) | −23879.5 | −1.48881 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −153.318 | −0.00951399 | ||||||||
\(639\) | −781.265 | −0.0483668 | ||||||||
\(640\) | −535.346 | −0.0330647 | ||||||||
\(641\) | −15727.8 | −0.969125 | −0.484563 | − | 0.874757i | \(-0.661021\pi\) | ||||
−0.484563 | + | 0.874757i | \(0.661021\pi\) | |||||||
\(642\) | −42166.5 | −2.59218 | ||||||||
\(643\) | 3262.00 | 0.200063 | 0.100032 | − | 0.994984i | \(-0.468106\pi\) | ||||
0.100032 | + | 0.994984i | \(0.468106\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4264.06 | −0.260306 | ||||||||
\(646\) | 41576.3 | 2.53219 | ||||||||
\(647\) | 10999.7 | 0.668383 | 0.334191 | − | 0.942505i | \(-0.391537\pi\) | ||||
0.334191 | + | 0.942505i | \(0.391537\pi\) | |||||||
\(648\) | 2419.16 | 0.146657 | ||||||||
\(649\) | 148.665 | 0.00899173 | ||||||||
\(650\) | −32428.2 | −1.95683 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −31606.2 | −1.89846 | ||||||||
\(653\) | −4179.66 | −0.250479 | −0.125240 | − | 0.992127i | \(-0.539970\pi\) | ||||
−0.125240 | + | 0.992127i | \(0.539970\pi\) | |||||||
\(654\) | 5633.42 | 0.336826 | ||||||||
\(655\) | 1594.39 | 0.0951113 | ||||||||
\(656\) | 2365.64 | 0.140797 | ||||||||
\(657\) | 8706.86 | 0.517027 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11285.5 | −0.667105 | −0.333552 | − | 0.942732i | \(-0.608247\pi\) | ||||
−0.333552 | + | 0.942732i | \(0.608247\pi\) | |||||||
\(660\) | −38.8974 | −0.00229406 | ||||||||
\(661\) | 9571.75 | 0.563235 | 0.281617 | − | 0.959527i | \(-0.409129\pi\) | ||||
0.281617 | + | 0.959527i | \(0.409129\pi\) | |||||||
\(662\) | −21566.1 | −1.26615 | ||||||||
\(663\) | 42025.3 | 2.46173 | ||||||||
\(664\) | 2915.62 | 0.170404 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 39402.0 | 2.29248 | ||||||||
\(667\) | −3965.10 | −0.230179 | ||||||||
\(668\) | −20274.2 | −1.17430 | ||||||||
\(669\) | 41731.7 | 2.41172 | ||||||||
\(670\) | 5220.68 | 0.301034 | ||||||||
\(671\) | −269.099 | −0.0154821 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3807.87 | 0.218102 | 0.109051 | − | 0.994036i | \(-0.465219\pi\) | ||||
0.109051 | + | 0.994036i | \(0.465219\pi\) | |||||||
\(674\) | 37905.4 | 2.16626 | ||||||||
\(675\) | −3385.18 | −0.193030 | ||||||||
\(676\) | 17104.4 | 0.973169 | ||||||||
\(677\) | −26320.9 | −1.49423 | −0.747117 | − | 0.664693i | \(-0.768562\pi\) | ||||
−0.747117 | + | 0.664693i | \(0.768562\pi\) | |||||||
\(678\) | −25274.3 | −1.43164 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 386.634 | 0.0218040 | ||||||||
\(681\) | 39052.3 | 2.19748 | ||||||||
\(682\) | 41.0298 | 0.00230368 | ||||||||
\(683\) | 27730.3 | 1.55354 | 0.776771 | − | 0.629783i | \(-0.216856\pi\) | ||||
0.776771 | + | 0.629783i | \(0.216856\pi\) | |||||||
\(684\) | −22261.8 | −1.24445 | ||||||||
\(685\) | 512.685 | 0.0285966 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13737.8 | 0.762925 | ||||||||
\(688\) | 24449.6 | 1.35484 | ||||||||
\(689\) | −24937.9 | −1.37889 | ||||||||
\(690\) | −1928.60 | −0.106407 | ||||||||
\(691\) | −22356.5 | −1.23080 | −0.615400 | − | 0.788215i | \(-0.711005\pi\) | ||||
−0.615400 | + | 0.788215i | \(0.711005\pi\) | |||||||
\(692\) | −14226.3 | −0.781505 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −36878.8 | −2.01715 | ||||||||
\(695\) | −2546.43 | −0.138981 | ||||||||
\(696\) | −1769.29 | −0.0963572 | ||||||||
\(697\) | −3774.72 | −0.205133 | ||||||||
\(698\) | 38190.7 | 2.07097 | ||||||||
\(699\) | 38026.7 | 2.05766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24877.9 | 1.34040 | 0.670202 | − | 0.742178i | \(-0.266207\pi\) | ||||
0.670202 | + | 0.742178i | \(0.266207\pi\) | |||||||
\(702\) | 7258.38 | 0.390242 | ||||||||
\(703\) | 46039.9 | 2.47002 | ||||||||
\(704\) | 265.863 | 0.0142331 | ||||||||
\(705\) | 6022.21 | 0.321716 | ||||||||
\(706\) | −29288.6 | −1.56132 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 20713.4 | 1.09952 | ||||||||
\(709\) | −16422.4 | −0.869895 | −0.434948 | − | 0.900456i | \(-0.643233\pi\) | ||||
−0.434948 | + | 0.900456i | \(0.643233\pi\) | |||||||
\(710\) | −196.502 | −0.0103868 | ||||||||
\(711\) | −31647.9 | −1.66932 | ||||||||
\(712\) | 108.683 | 0.00572061 | ||||||||
\(713\) | 1061.11 | 0.0557347 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −40.6213 | −0.00212469 | ||||||||
\(716\) | −6340.02 | −0.330918 | ||||||||
\(717\) | 4857.63 | 0.253015 | ||||||||
\(718\) | −20434.4 | −1.06212 | ||||||||
\(719\) | −503.826 | −0.0261329 | −0.0130664 | − | 0.999915i | \(-0.504159\pi\) | ||||
−0.0130664 | + | 0.999915i | \(0.504159\pi\) | |||||||
\(720\) | 1895.58 | 0.0981167 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −21821.3 | −1.12480 | ||||||||
\(723\) | −22524.8 | −1.15865 | ||||||||
\(724\) | 18276.8 | 0.938191 | ||||||||
\(725\) | 10404.2 | 0.532971 | ||||||||
\(726\) | −38524.1 | −1.96937 | ||||||||
\(727\) | −13609.7 | −0.694301 | −0.347150 | − | 0.937809i | \(-0.612851\pi\) | ||||
−0.347150 | + | 0.937809i | \(0.612851\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13664.1 | −0.694210 | ||||||||
\(730\) | 2189.93 | 0.111032 | ||||||||
\(731\) | −39012.9 | −1.97393 | ||||||||
\(732\) | −37493.3 | −1.89316 | ||||||||
\(733\) | 7638.07 | 0.384882 | 0.192441 | − | 0.981309i | \(-0.438360\pi\) | ||||
0.192441 | + | 0.981309i | \(0.438360\pi\) | |||||||
\(734\) | −40872.1 | −2.05534 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12166.0 | 0.609302 | ||||||||
\(737\) | −398.011 | −0.0198927 | ||||||||
\(738\) | 3874.91 | 0.193276 | ||||||||
\(739\) | −7373.88 | −0.367053 | −0.183527 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183527 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(740\) | 5169.23 | 0.256790 | ||||||||
\(741\) | −50408.5 | −2.49906 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5274.83 | 0.260450 | 0.130225 | − | 0.991484i | \(-0.458430\pi\) | ||||
0.130225 | + | 0.991484i | \(0.458430\pi\) | |||||||
\(744\) | 473.482 | 0.0233316 | ||||||||
\(745\) | 1931.71 | 0.0949963 | ||||||||
\(746\) | 54822.6 | 2.69061 | ||||||||
\(747\) | −22809.1 | −1.11719 | ||||||||
\(748\) | −355.881 | −0.0173961 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10204.3 | 0.496810 | ||||||||
\(751\) | 23106.8 | 1.12274 | 0.561371 | − | 0.827564i | \(-0.310274\pi\) | ||||
0.561371 | + | 0.827564i | \(0.310274\pi\) | |||||||
\(752\) | −34530.6 | −1.67447 | ||||||||
\(753\) | 16642.6 | 0.805430 | ||||||||
\(754\) | −22308.4 | −1.07749 | ||||||||
\(755\) | −16.1758 | −0.000779730 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1680.06 | −0.0806642 | −0.0403321 | − | 0.999186i | \(-0.512842\pi\) | ||||
−0.0403321 | + | 0.999186i | \(0.512842\pi\) | |||||||
\(758\) | −11437.3 | −0.548048 | ||||||||
\(759\) | 147.031 | 0.00703149 | ||||||||
\(760\) | −463.760 | −0.0221347 | ||||||||
\(761\) | 34574.9 | 1.64697 | 0.823483 | − | 0.567341i | \(-0.192028\pi\) | ||||
0.823483 | + | 0.567341i | \(0.192028\pi\) | |||||||
\(762\) | −12402.1 | −0.589606 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 35074.8 | 1.66095 | ||||||||
\(765\) | −3024.67 | −0.142951 | ||||||||
\(766\) | −58741.9 | −2.77080 | ||||||||
\(767\) | 21631.4 | 1.01834 | ||||||||
\(768\) | −23072.4 | −1.08406 | ||||||||
\(769\) | 27231.8 | 1.27699 | 0.638495 | − | 0.769626i | \(-0.279557\pi\) | ||||
0.638495 | + | 0.769626i | \(0.279557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32309.3 | −1.50920 | ||||||||
\(772\) | −16053.2 | −0.748405 | ||||||||
\(773\) | −3917.59 | −0.182284 | −0.0911422 | − | 0.995838i | \(-0.529052\pi\) | ||||
−0.0911422 | + | 0.995838i | \(0.529052\pi\) | |||||||
\(774\) | 40048.4 | 1.85983 | ||||||||
\(775\) | −2784.30 | −0.129052 | ||||||||
\(776\) | 1371.88 | 0.0634636 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 59434.0 | 2.73883 | ||||||||
\(779\) | 4527.71 | 0.208244 | ||||||||
\(780\) | −5659.73 | −0.259809 | ||||||||
\(781\) | 14.9808 | 0.000686371 0 | ||||||||
\(782\) | −17645.2 | −0.806894 | ||||||||
\(783\) | −2328.78 | −0.106288 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2059.17 | 0.0936241 | ||||||||
\(786\) | −32468.7 | −1.47343 | ||||||||
\(787\) | 19805.2 | 0.897052 | 0.448526 | − | 0.893770i | \(-0.351949\pi\) | ||||
0.448526 | + | 0.893770i | \(0.351949\pi\) | |||||||
\(788\) | 6745.84 | 0.304963 | ||||||||
\(789\) | 14532.9 | 0.655746 | ||||||||
\(790\) | −7960.03 | −0.358488 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 30.2583 | 0.00135755 | ||||||||
\(793\) | −39155.0 | −1.75339 | ||||||||
\(794\) | 3298.58 | 0.147434 | ||||||||
\(795\) | 3891.67 | 0.173614 | ||||||||
\(796\) | 2776.06 | 0.123612 | ||||||||
\(797\) | 16785.4 | 0.746007 | 0.373004 | − | 0.927830i | \(-0.378328\pi\) | ||||
0.373004 | + | 0.927830i | \(0.378328\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55098.5 | 2.43961 | ||||||||
\(800\) | −31923.1 | −1.41082 | ||||||||
\(801\) | −850.238 | −0.0375052 | ||||||||
\(802\) | −34167.6 | −1.50436 | ||||||||
\(803\) | −166.955 | −0.00733711 | ||||||||
\(804\) | −55454.4 | −2.43250 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5970.01 | 0.260899 | ||||||||
\(807\) | 18883.9 | 0.823725 | ||||||||
\(808\) | −1766.57 | −0.0769153 | ||||||||
\(809\) | 18468.0 | 0.802594 | 0.401297 | − | 0.915948i | \(-0.368559\pi\) | ||||
0.401297 | + | 0.915948i | \(0.368559\pi\) | |||||||
\(810\) | −4760.06 | −0.206483 | ||||||||
\(811\) | 19533.4 | 0.845757 | 0.422878 | − | 0.906186i | \(-0.361020\pi\) | ||||
0.422878 | + | 0.906186i | \(0.361020\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33629.7 | −1.45073 | ||||||||
\(814\) | −755.535 | −0.0325325 | ||||||||
\(815\) | 5150.90 | 0.221384 | ||||||||
\(816\) | 37604.1 | 1.61324 | ||||||||
\(817\) | 46795.2 | 2.00386 | ||||||||
\(818\) | 51090.1 | 2.18377 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 508.358 | 0.0216496 | ||||||||
\(821\) | 7331.04 | 0.311638 | 0.155819 | − | 0.987786i | \(-0.450198\pi\) | ||||
0.155819 | + | 0.987786i | \(0.450198\pi\) | |||||||
\(822\) | −10440.5 | −0.443010 | ||||||||
\(823\) | 23520.8 | 0.996213 | 0.498106 | − | 0.867116i | \(-0.334029\pi\) | ||||
0.498106 | + | 0.867116i | \(0.334029\pi\) | |||||||
\(824\) | 4795.14 | 0.202726 | ||||||||
\(825\) | −385.804 | −0.0162812 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23518.7 | 0.988908 | 0.494454 | − | 0.869204i | \(-0.335368\pi\) | ||||
0.494454 | + | 0.869204i | \(0.335368\pi\) | |||||||
\(828\) | 9448.05 | 0.396549 | ||||||||
\(829\) | 21805.3 | 0.913544 | 0.456772 | − | 0.889584i | \(-0.349006\pi\) | ||||
0.456772 | + | 0.889584i | \(0.349006\pi\) | |||||||
\(830\) | −5736.91 | −0.239917 | ||||||||
\(831\) | −5256.26 | −0.219420 | ||||||||
\(832\) | 38684.2 | 1.61194 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 51856.4 | 2.15305 | ||||||||
\(835\) | 3304.11 | 0.136938 | ||||||||
\(836\) | 426.872 | 0.0176599 | ||||||||
\(837\) | 623.209 | 0.0257363 | ||||||||
\(838\) | −62147.5 | −2.56187 | ||||||||
\(839\) | 8162.43 | 0.335874 | 0.167937 | − | 0.985798i | \(-0.446289\pi\) | ||||
0.167937 | + | 0.985798i | \(0.446289\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17231.6 | −0.706530 | ||||||||
\(842\) | 40046.9 | 1.63908 | ||||||||
\(843\) | −25590.1 | −1.04552 | ||||||||
\(844\) | 27178.3 | 1.10843 | ||||||||
\(845\) | −2787.52 | −0.113484 | ||||||||
\(846\) | −56561.0 | −2.29859 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −22314.3 | −0.903630 | ||||||||
\(849\) | 22852.6 | 0.923792 | ||||||||
\(850\) | 46300.2 | 1.86833 | ||||||||
\(851\) | −19539.6 | −0.787084 | ||||||||
\(852\) | 2087.26 | 0.0839300 | ||||||||
\(853\) | 40044.5 | 1.60738 | 0.803692 | − | 0.595046i | \(-0.202866\pi\) | ||||
0.803692 | + | 0.595046i | \(0.202866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3628.03 | 0.145118 | ||||||||
\(856\) | 4303.28 | 0.171826 | ||||||||
\(857\) | 2627.05 | 0.104712 | 0.0523560 | − | 0.998628i | \(-0.483327\pi\) | ||||
0.0523560 | + | 0.998628i | \(0.483327\pi\) | |||||||
\(858\) | 827.227 | 0.0329150 | ||||||||
\(859\) | −29663.0 | −1.17822 | −0.589109 | − | 0.808054i | \(-0.700521\pi\) | ||||
−0.589109 | + | 0.808054i | \(0.700521\pi\) | |||||||
\(860\) | 5254.03 | 0.208327 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13516.3 | −0.534067 | ||||||||
\(863\) | 14241.7 | 0.561753 | 0.280876 | − | 0.959744i | \(-0.409375\pi\) | ||||
0.280876 | + | 0.959744i | \(0.409375\pi\) | |||||||
\(864\) | 7145.34 | 0.281353 | ||||||||
\(865\) | 2318.47 | 0.0911333 | ||||||||
\(866\) | 6435.08 | 0.252509 | ||||||||
\(867\) | −25223.9 | −0.988060 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 606.851 | 0.0236893 | ||||||||
\(870\) | 3481.33 | 0.135665 | ||||||||
\(871\) | −57912.2 | −2.25290 | ||||||||
\(872\) | −574.916 | −0.0223270 | ||||||||
\(873\) | −10732.4 | −0.416077 | ||||||||
\(874\) | 21165.1 | 0.819130 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −23261.6 | −0.897188 | ||||||||
\(877\) | 28414.7 | 1.09407 | 0.547034 | − | 0.837110i | \(-0.315757\pi\) | ||||
0.547034 | + | 0.837110i | \(0.315757\pi\) | |||||||
\(878\) | −40237.8 | −1.54665 | ||||||||
\(879\) | 25696.8 | 0.986045 | ||||||||
\(880\) | −36.3478 | −0.00139237 | ||||||||
\(881\) | −5469.81 | −0.209174 | −0.104587 | − | 0.994516i | \(-0.533352\pi\) | ||||
−0.104587 | + | 0.994516i | \(0.533352\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36038.6 | −1.37350 | −0.686748 | − | 0.726896i | \(-0.740962\pi\) | ||||
−0.686748 | + | 0.726896i | \(0.740962\pi\) | |||||||
\(884\) | −51782.1 | −1.97016 | ||||||||
\(885\) | −3375.68 | −0.128217 | ||||||||
\(886\) | −30576.8 | −1.15942 | ||||||||
\(887\) | −30844.0 | −1.16758 | −0.583789 | − | 0.811905i | \(-0.698430\pi\) | ||||
−0.583789 | + | 0.811905i | \(0.698430\pi\) | |||||||
\(888\) | −8718.84 | −0.329488 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −213.850 | −0.00805425 | ||||||||
\(891\) | 362.894 | 0.0136447 | ||||||||
\(892\) | −51420.3 | −1.93013 | ||||||||
\(893\) | −66089.6 | −2.47660 | ||||||||
\(894\) | −39337.9 | −1.47165 | ||||||||
\(895\) | 1033.24 | 0.0385893 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21393.7 | 0.796336 | ||||||||
\(898\) | −51920.4 | −1.92940 | ||||||||
\(899\) | −1915.42 | −0.0710597 | ||||||||
\(900\) | −24791.3 | −0.918194 | ||||||||
\(901\) | 35605.8 | 1.31654 | ||||||||
\(902\) | −74.3017 | −0.00274277 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2579.35 | 0.0948983 | ||||||||
\(905\) | −2978.58 | −0.109405 | ||||||||
\(906\) | 329.409 | 0.0120793 | ||||||||
\(907\) | −19283.6 | −0.705956 | −0.352978 | − | 0.935632i | \(-0.614831\pi\) | ||||
−0.352978 | + | 0.935632i | \(0.614831\pi\) | |||||||
\(908\) | −48118.9 | −1.75868 | ||||||||
\(909\) | 13820.0 | 0.504269 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12302.1 | 0.447406 | 0.223703 | − | 0.974657i | \(-0.428185\pi\) | ||||
0.223703 | + | 0.974657i | \(0.428185\pi\) | |||||||
\(912\) | −45105.4 | −1.63771 | ||||||||
\(913\) | 437.366 | 0.0158540 | ||||||||
\(914\) | 6868.07 | 0.248551 | ||||||||
\(915\) | 6110.32 | 0.220766 | ||||||||
\(916\) | −16927.2 | −0.610580 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −10363.3 | −0.372594 | ||||||||
\(919\) | 32839.7 | 1.17876 | 0.589381 | − | 0.807855i | \(-0.299372\pi\) | ||||
0.589381 | + | 0.807855i | \(0.299372\pi\) | |||||||
\(920\) | 196.822 | 0.00705331 | ||||||||
\(921\) | −4524.65 | −0.161881 | ||||||||
\(922\) | −28995.1 | −1.03569 | ||||||||
\(923\) | 2179.77 | 0.0777334 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 51271.0 | 1.82246 | ||||||||
\(926\) | 21017.7 | 0.745880 | ||||||||
\(927\) | −37512.7 | −1.32910 | ||||||||
\(928\) | −21961.0 | −0.776838 | ||||||||
\(929\) | 39502.9 | 1.39510 | 0.697550 | − | 0.716536i | \(-0.254274\pi\) | ||||
0.697550 | + | 0.716536i | \(0.254274\pi\) | |||||||
\(930\) | −931.647 | −0.0328494 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −46855.2 | −1.64677 | ||||||||
\(933\) | −20411.7 | −0.716239 | ||||||||
\(934\) | −58510.3 | −2.04980 | ||||||||
\(935\) | 57.9982 | 0.00202860 | ||||||||
\(936\) | 4402.70 | 0.153747 | ||||||||
\(937\) | −22914.6 | −0.798918 | −0.399459 | − | 0.916751i | \(-0.630802\pi\) | ||||
−0.399459 | + | 0.916751i | \(0.630802\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −18970.8 | −0.659307 | ||||||||
\(940\) | −7420.36 | −0.257474 | ||||||||
\(941\) | −15688.6 | −0.543502 | −0.271751 | − | 0.962368i | \(-0.587603\pi\) | ||||
−0.271751 | + | 0.962368i | \(0.587603\pi\) | |||||||
\(942\) | −41933.6 | −1.45039 | ||||||||
\(943\) | −1921.59 | −0.0663578 | ||||||||
\(944\) | 19355.7 | 0.667347 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −767.930 | −0.0263928 | ||||||||
\(947\) | −16605.2 | −0.569797 | −0.284898 | − | 0.958558i | \(-0.591960\pi\) | ||||
−0.284898 | + | 0.958558i | \(0.591960\pi\) | |||||||
\(948\) | 84551.9 | 2.89675 | ||||||||
\(949\) | −24292.6 | −0.830949 | ||||||||
\(950\) | −55536.2 | −1.89667 | ||||||||
\(951\) | 44921.6 | 1.53174 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28512.6 | 0.969163 | 0.484582 | − | 0.874746i | \(-0.338972\pi\) | ||||
0.484582 | + | 0.874746i | \(0.338972\pi\) | |||||||
\(954\) | −36550.8 | −1.24044 | ||||||||
\(955\) | −5716.18 | −0.193687 | ||||||||
\(956\) | −5985.41 | −0.202492 | ||||||||
\(957\) | −265.407 | −0.00896489 | ||||||||
\(958\) | 50024.7 | 1.68708 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −6036.85 | −0.202957 | ||||||||
\(961\) | −29278.4 | −0.982794 | ||||||||
\(962\) | −109933. | −3.68440 | ||||||||
\(963\) | −33664.9 | −1.12652 | ||||||||
\(964\) | 27754.3 | 0.927288 | ||||||||
\(965\) | 2616.21 | 0.0872734 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24286.3 | 0.807646 | 0.403823 | − | 0.914837i | \(-0.367681\pi\) | ||||
0.403823 | + | 0.914837i | \(0.367681\pi\) | |||||||
\(968\) | 3931.56 | 0.130542 | ||||||||
\(969\) | 71972.1 | 2.38605 | ||||||||
\(970\) | −2699.38 | −0.0893526 | ||||||||
\(971\) | −24151.0 | −0.798191 | −0.399095 | − | 0.916909i | \(-0.630676\pi\) | ||||
−0.399095 | + | 0.916909i | \(0.630676\pi\) | |||||||
\(972\) | 44079.0 | 1.45456 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 58362.0 | 1.91996 | ||||||||
\(975\) | −56136.0 | −1.84389 | ||||||||
\(976\) | −35035.8 | −1.14905 | ||||||||
\(977\) | 46579.9 | 1.52531 | 0.762653 | − | 0.646808i | \(-0.223896\pi\) | ||||
0.762653 | + | 0.646808i | \(0.223896\pi\) | |||||||
\(978\) | −104895. | −3.42961 | ||||||||
\(979\) | 16.3034 | 0.000532235 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4497.61 | 0.146379 | ||||||||
\(982\) | 22770.3 | 0.739948 | ||||||||
\(983\) | 12068.2 | 0.391573 | 0.195786 | − | 0.980647i | \(-0.437274\pi\) | ||||
0.195786 | + | 0.980647i | \(0.437274\pi\) | |||||||
\(984\) | −857.439 | −0.0277786 | ||||||||
\(985\) | −1099.38 | −0.0355625 | ||||||||
\(986\) | 31851.5 | 1.02876 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 62111.6 | 2.00003 | ||||||||
\(989\) | −19860.1 | −0.638540 | ||||||||
\(990\) | −59.5377 | −0.00191134 | ||||||||
\(991\) | −1736.75 | −0.0556708 | −0.0278354 | − | 0.999613i | \(-0.508861\pi\) | ||||
−0.0278354 | + | 0.999613i | \(0.508861\pi\) | |||||||
\(992\) | 5877.03 | 0.188101 | ||||||||
\(993\) | −37332.8 | −1.19307 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −452.418 | −0.0144147 | ||||||||
\(996\) | 60937.8 | 1.93864 | ||||||||
\(997\) | 8120.26 | 0.257945 | 0.128973 | − | 0.991648i | \(-0.458832\pi\) | ||||
0.128973 | + | 0.991648i | \(0.458832\pi\) | |||||||
\(998\) | −39281.7 | −1.24593 | ||||||||
\(999\) | −11476.0 | −0.363446 |
(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 | 2009.4.a.o.1.10 | yes | 60 | |
7.6 | odd | 2 | 2009.4.a.n.1.10 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2009.4.a.n.1.10 | ✓ | 60 | 7.6 | odd | 2 | ||
2009.4.a.o.1.10 | yes | 60 | 1.1 | even | 1 | trivial |