Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(1,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, 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("128.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.92820 | 0.948433 | 0.474217 | − | 0.880408i | \(-0.342731\pi\) | ||||
0.474217 | + | 0.880408i | \(0.342731\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.8564 | 1.41824 | 0.709120 | − | 0.705088i | \(-0.249092\pi\) | ||||
0.709120 | + | 0.705088i | \(0.249092\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.8564 | 0.964155 | 0.482078 | − | 0.876128i | \(-0.339882\pi\) | ||||
0.482078 | + | 0.876128i | \(0.339882\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.71281 | −0.100475 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −52.9282 | −1.45077 | −0.725384 | − | 0.688344i | \(-0.758338\pi\) | ||||
−0.725384 | + | 0.688344i | \(0.758338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.43078 | 0.179868 | 0.0899338 | − | 0.995948i | \(-0.471334\pi\) | ||||
0.0899338 | + | 0.995948i | \(0.471334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 78.1436 | 1.34511 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 129.138 | 1.84239 | 0.921196 | − | 0.389098i | \(-0.127213\pi\) | ||||
0.921196 | + | 0.389098i | \(0.127213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.4974 | −0.609732 | −0.304866 | − | 0.952395i | \(-0.598612\pi\) | ||||
−0.304866 | + | 0.952395i | \(0.598612\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 88.0000 | 0.914437 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −128.708 | −1.16684 | −0.583422 | − | 0.812169i | \(-0.698287\pi\) | ||||
−0.583422 | + | 0.812169i | \(0.698287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 126.426 | 1.01141 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −146.431 | −1.04373 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 111.282 | 0.712571 | 0.356285 | − | 0.934377i | \(-0.384043\pi\) | ||||
0.356285 | + | 0.934377i | \(0.384043\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 302.851 | 1.75464 | 0.877318 | − | 0.479910i | \(-0.159331\pi\) | ||||
0.877318 | + | 0.479910i | \(0.159331\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −260.841 | −1.37596 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 283.138 | 1.36740 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −182.995 | −0.813086 | −0.406543 | − | 0.913632i | \(-0.633266\pi\) | ||||
−0.406543 | + | 0.913632i | \(0.633266\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 41.5486 | 0.170592 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −94.5744 | −0.360245 | −0.180122 | − | 0.983644i | \(-0.557649\pi\) | ||||
−0.180122 | + | 0.983644i | \(0.557649\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −184.641 | −0.654825 | −0.327413 | − | 0.944881i | \(-0.606177\pi\) | ||||
−0.327413 | + | 0.944881i | \(0.606177\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −43.0155 | −0.142497 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −296.841 | −0.921249 | −0.460624 | − | 0.887595i | \(-0.652375\pi\) | ||||
−0.460624 | + | 0.887595i | \(0.652375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.1487 | −0.0704045 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 636.420 | 1.74739 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −102.995 | −0.266933 | −0.133466 | − | 0.991053i | \(-0.542611\pi\) | ||||
−0.133466 | + | 0.991053i | \(0.542611\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −839.251 | −2.05754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −248.862 | −0.578290 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 93.3693 | 0.206028 | 0.103014 | − | 0.994680i | \(-0.467151\pi\) | ||||
0.103014 | + | 0.994680i | \(0.467151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −338.974 | −0.711495 | −0.355748 | − | 0.934582i | \(-0.615774\pi\) | ||||
−0.355748 | + | 0.934582i | \(0.615774\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −48.4411 | −0.0968731 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 133.682 | 0.255095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −489.041 | −0.891729 | −0.445865 | − | 0.895100i | \(-0.647104\pi\) | ||||
−0.445865 | + | 0.895100i | \(0.647104\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −634.297 | −1.10667 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 86.9845 | 0.145397 | 0.0726983 | − | 0.997354i | \(-0.476839\pi\) | ||||
0.0726983 | + | 0.997354i | \(0.476839\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −154.267 | −0.247336 | −0.123668 | − | 0.992324i | \(-0.539466\pi\) | ||||
−0.123668 | + | 0.992324i | \(0.539466\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 623.051 | 0.959250 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −945.108 | −1.39877 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 449.415 | 0.640040 | 0.320020 | − | 0.947411i | \(-0.396310\pi\) | ||||
0.320020 | + | 0.947411i | \(0.396310\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −648.395 | −0.889430 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −383.933 | −0.507737 | −0.253868 | − | 0.967239i | \(-0.581703\pi\) | ||||
−0.253868 | + | 0.967239i | \(0.581703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2047.67 | 2.61295 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 548.420 | 0.675826 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −517.672 | −0.616551 | −0.308276 | − | 0.951297i | \(-0.599752\pi\) | ||||
−0.308276 | + | 0.951297i | \(0.599752\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 150.543 | 0.173420 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1492.51 | 1.66415 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −800.708 | −0.864746 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1739.39 | 1.82071 | 0.910355 | − | 0.413829i | \(-0.135809\pi\) | ||||
0.910355 | + | 0.413829i | \(0.135809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 143.584 | 0.145765 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1158.99 | −1.14182 | −0.570912 | − | 0.821011i | \(-0.693410\pi\) | ||||
−0.570912 | + | 0.821011i | \(0.693410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1635.01 | 1.56410 | 0.782048 | − | 0.623218i | \(-0.214175\pi\) | ||||
0.782048 | + | 0.623218i | \(0.214175\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1395.36 | 1.29689 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −282.589 | −0.255317 | −0.127659 | − | 0.991818i | \(-0.540746\pi\) | ||||
−0.127659 | + | 0.991818i | \(0.540746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1004.98 | 0.883120 | 0.441560 | − | 0.897232i | \(-0.354425\pi\) | ||||
0.441560 | + | 0.897232i | \(0.354425\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −901.836 | −0.771157 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −567.108 | −0.472115 | −0.236057 | − | 0.971739i | \(-0.575855\pi\) | ||||
−0.236057 | + | 0.971739i | \(0.575855\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2040.84 | −1.65486 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22.8711 | −0.0180721 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2305.95 | 1.77635 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1470.39 | 1.10473 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −466.082 | −0.341668 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 22.6053 | 0.0161750 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 496.616 | 0.346988 | 0.173494 | − | 0.984835i | \(-0.444494\pi\) | ||||
0.173494 | + | 0.984835i | \(0.444494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −909.948 | −0.621058 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1658.72 | −1.10628 | −0.553142 | − | 0.833087i | \(-0.686571\pi\) | ||||
−0.553142 | + | 0.833087i | \(0.686571\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −901.703 | −0.587876 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2321.87 | −1.48025 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −432.872 | −0.269947 | −0.134974 | − | 0.990849i | \(-0.543095\pi\) | ||||
−0.134974 | + | 0.990849i | \(0.543095\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 146.148 | 0.0891809 | 0.0445904 | − | 0.999005i | \(-0.485802\pi\) | ||||
0.0445904 | + | 0.999005i | \(0.485802\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1462.89 | −0.873743 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −446.226 | −0.260946 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1764.53 | 1.01060 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −119.010 | −0.0667740 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3556.29 | 1.95532 | 0.977659 | − | 0.210198i | \(-0.0674108\pi\) | ||||
0.977659 | + | 0.210198i | \(0.0674108\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1320.32 | 0.711562 | 0.355781 | − | 0.934569i | \(-0.384215\pi\) | ||||
0.355781 | + | 0.934569i | \(0.384215\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −350.328 | −0.185114 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4802.13 | 2.48849 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2040.43 | 1.03722 | 0.518612 | − | 0.855010i | \(-0.326449\pi\) | ||||
0.518612 | + | 0.855010i | \(0.326449\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −507.580 | −0.253168 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2298.26 | −1.12502 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2392.21 | 1.14952 | 0.574762 | − | 0.818321i | \(-0.305095\pi\) | ||||
0.574762 | + | 0.818321i | \(0.305095\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4136.00 | −1.95144 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2068.34 | −0.958400 | −0.479200 | − | 0.877706i | \(-0.659073\pi\) | ||||
−0.479200 | + | 0.877706i | \(0.659073\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2125.92 | −0.967648 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 136.990 | 0.0612625 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2441.87 | −1.07313 | −0.536566 | − | 0.843859i | \(-0.680279\pi\) | ||||
−0.536566 | + | 0.843859i | \(0.680279\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2257.51 | 0.975152 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 460.143 | 0.195404 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2430.84 | 1.01502 | 0.507512 | − | 0.861645i | \(-0.330565\pi\) | ||||
0.507512 | + | 0.861645i | \(0.330565\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1928.96 | 0.792148 | 0.396074 | − | 0.918219i | \(-0.370372\pi\) | ||||
0.396074 | + | 0.918219i | \(0.370372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1670.53 | −0.674806 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2901.64 | −1.15315 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6835.07 | −2.67288 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2614.73 | −1.00631 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4087.34 | −1.54843 | −0.774214 | − | 0.632924i | \(-0.781855\pi\) | ||||
−0.774214 | + | 0.632924i | \(0.781855\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1156.52 | −0.431339 | −0.215669 | − | 0.976466i | \(-0.569193\pi\) | ||||
−0.215669 | + | 0.976466i | \(0.569193\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 658.811 | 0.241941 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2658.44 | −0.961452 | −0.480726 | − | 0.876871i | \(-0.659627\pi\) | ||||
−0.480726 | + | 0.876871i | \(0.659627\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 742.369 | 0.264448 | 0.132224 | − | 0.991220i | \(-0.457788\pi\) | ||||
0.132224 | + | 0.991220i | \(0.457788\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2410.09 | −0.845745 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1987.10 | 0.687029 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1499.61 | −0.510914 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 349.160 | 0.117238 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2672.74 | 0.884580 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3838.30 | 1.25232 | 0.626160 | − | 0.779694i | \(-0.284626\pi\) | ||||
0.626160 | + | 0.779694i | \(0.284626\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 428.677 | 0.137899 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2927.74 | −0.928700 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5407.84 | 1.69174 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −760.257 | −0.234582 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1088.74 | 0.331387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3418.34 | 1.02650 | 0.513249 | − | 0.858240i | \(-0.328442\pi\) | ||||
0.513249 | + | 0.858240i | \(0.328442\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −342.969 | −0.101620 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −515.729 | −0.150793 | −0.0753967 | − | 0.997154i | \(-0.524022\pi\) | ||||
−0.0753967 | + | 0.997154i | \(0.524022\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1595.26 | 0.460340 | 0.230170 | − | 0.973150i | \(-0.426072\pi\) | ||||
0.230170 | + | 0.973150i | \(0.426072\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4657.68 | −1.32664 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5251.27 | 1.47649 | 0.738245 | − | 0.674533i | \(-0.235655\pi\) | ||||
0.738245 | + | 0.674533i | \(0.235655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4706.83 | −1.30655 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2214.81 | 0.607035 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2029.27 | 0.549216 | 0.274608 | − | 0.961556i | \(-0.411452\pi\) | ||||
0.274608 | + | 0.961556i | \(0.411452\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4615.72 | −1.23371 | −0.616856 | − | 0.787076i | \(-0.711594\pi\) | ||||
−0.616856 | + | 0.787076i | \(0.711594\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 758.210 | 0.200161 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −382.912 | −0.0998505 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −425.733 | −0.109671 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1892.10 | −0.481554 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2702.52 | 0.679607 | 0.339804 | − | 0.940496i | \(-0.389639\pi\) | ||||
0.339804 | + | 0.940496i | \(0.389639\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6812.27 | 1.69282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10091.3 | 2.47821 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 991.785 | 0.240723 | 0.120362 | − | 0.992730i | \(-0.461595\pi\) | ||||
0.120362 | + | 0.992730i | \(0.461595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3267.63 | −0.783941 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −301.887 | −0.0715952 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7430.74 | 1.74220 | 0.871101 | − | 0.491105i | \(-0.163407\pi\) | ||||
0.871101 | + | 0.491105i | \(0.163407\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1633.13 | −0.378575 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2551.19 | −0.584758 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3281.50 | 0.743778 | 0.371889 | − | 0.928277i | \(-0.378710\pi\) | ||||
0.371889 | + | 0.928277i | \(0.378710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 221.518 | 0.0496542 | 0.0248271 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248271 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 741.909 | 0.164477 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6691.48 | −1.46731 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1106.28 | 0.239963 | 0.119982 | − | 0.992776i | \(-0.461716\pi\) | ||||
0.119982 | + | 0.992776i | \(0.461716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −821.579 | −0.176296 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2372.52 | −0.503676 | −0.251838 | − | 0.967769i | \(-0.581035\pi\) | ||||
−0.251838 | + | 0.967769i | \(0.581035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2549.89 | −0.535602 | −0.267801 | − | 0.963474i | \(-0.586297\pi\) | ||||
−0.267801 | + | 0.963474i | \(0.586297\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3946.05 | −0.820154 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1688.76 | −0.347332 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11763.7 | 2.39441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8572.09 | 1.72682 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 130.319 | 0.0259840 | 0.0129920 | − | 0.999916i | \(-0.495864\pi\) | ||||
0.0129920 | + | 0.999916i | \(0.495864\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1480.50 | 0.292197 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7750.32 | 1.51421 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1085.11 | −0.209877 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3297.03 | −0.631353 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5711.76 | −1.08294 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5374.91 | −1.00907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 62.1182 | 0.0115481 | 0.00577406 | − | 0.999983i | \(-0.498162\pi\) | ||||
0.00577406 | + | 0.999983i | \(0.498162\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8057.64 | 1.48344 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 593.837 | 0.108275 | 0.0541373 | − | 0.998533i | \(-0.482759\pi\) | ||||
0.0541373 | + | 0.998533i | \(0.482759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3669.69 | 0.662694 | 0.331347 | − | 0.943509i | \(-0.392497\pi\) | ||||
0.331347 | + | 0.943509i | \(0.392497\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −768.102 | −0.137389 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 374.339 | 0.0663249 | 0.0331625 | − | 0.999450i | \(-0.489442\pi\) | ||||
0.0331625 | + | 0.999450i | \(0.489442\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5889.96 | −1.03378 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1392.66 | −0.242151 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6521.16 | −1.12337 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1065.87 | 0.181919 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4952.77 | 0.837580 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5300.51 | −0.888227 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5871.13 | 0.974945 | 0.487472 | − | 0.873138i | \(-0.337919\pi\) | ||||
0.487472 | + | 0.873138i | \(0.337919\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 496.431 | 0.0816944 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7754.43 | −1.26469 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1047.83 | 0.169373 | 0.0846865 | − | 0.996408i | \(-0.473011\pi\) | ||||
0.0846865 | + | 0.996408i | \(0.473011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2794.82 | −0.447769 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16029.4 | −2.54557 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6555.96 | −1.03204 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10057.7 | −1.56953 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3921.88 | 0.606737 | 0.303368 | − | 0.952873i | \(-0.401889\pi\) | ||||
0.303368 | + | 0.952873i | \(0.401889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11604.9 | −1.77993 | −0.889966 | − | 0.456027i | \(-0.849272\pi\) | ||||
−0.889966 | + | 0.456027i | \(0.849272\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1234.53 | −0.187733 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1530.22 | −0.230724 | −0.115362 | − | 0.993324i | \(-0.536803\pi\) | ||||
−0.115362 | + | 0.993324i | \(0.536803\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1379.26 | 0.206207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11364.2 | 1.68475 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10764.0 | 1.58246 | 0.791231 | − | 0.611518i | \(-0.209441\pi\) | ||||
0.791231 | + | 0.611518i | \(0.209441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4309.01 | −0.628227 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7246.40 | 1.04776 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2446.11 | −0.350782 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10713.0 | 1.52374 | 0.761869 | − | 0.647731i | \(-0.224282\pi\) | ||||
0.761869 | + | 0.647731i | \(0.224282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 256.563 | 0.0361954 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1839.12 | −0.257365 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9186.32 | −1.27520 | −0.637600 | − | 0.770368i | \(-0.720073\pi\) | ||||
−0.637600 | + | 0.770368i | \(0.720073\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 111.404 | 0.0153409 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 938.194 | 0.128168 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14201.0 | 1.92468 | 0.962342 | − | 0.271842i | \(-0.0876327\pi\) | ||||
0.962342 | + | 0.271842i | \(0.0876327\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2447.42 | 0.329095 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9691.24 | −1.29295 | −0.646474 | − | 0.762936i | \(-0.723757\pi\) | ||||
−0.646474 | + | 0.762936i | \(0.723757\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14986.0 | −1.98379 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 500.897 | 0.0657933 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6358.79 | 0.828801 | 0.414400 | − | 0.910095i | \(-0.363991\pi\) | ||||
0.414400 | + | 0.910095i | \(0.363991\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −16621.1 | −2.14978 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8174.52 | −1.04924 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7126.11 | 0.907731 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13034.2 | 1.64778 | 0.823888 | − | 0.566752i | \(-0.191800\pi\) | ||||
0.823888 | + | 0.566752i | \(0.191800\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4443.77 | −0.557561 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6705.06 | 0.834999 | 0.417499 | − | 0.908677i | \(-0.362907\pi\) | ||||
0.417499 | + | 0.908677i | \(0.362907\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2553.27 | 0.315602 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10281.2 | −1.26143 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9685.59 | 1.17960 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10967.8 | 1.32598 | 0.662988 | − | 0.748630i | \(-0.269288\pi\) | ||||
0.662988 | + | 0.748630i | \(0.269288\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2133.28 | −0.256027 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1667.24 | 0.198643 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6087.80 | −0.720093 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 720.249 | 0.0845821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13686.0 | −1.59571 | −0.797856 | − | 0.602849i | \(-0.794032\pi\) | ||||
−0.797856 | + | 0.602849i | \(0.794032\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8552.92 | −0.990128 | −0.495064 | − | 0.868857i | \(-0.664855\pi\) | ||||
−0.495064 | + | 0.868857i | \(0.664855\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 805.274 | 0.0925621 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16326.4 | 1.86340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6052.86 | −0.685992 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2199.09 | −0.247490 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12187.6 | −1.36208 | −0.681039 | − | 0.732247i | \(-0.738472\pi\) | ||||
−0.681039 | + | 0.732247i | \(0.738472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8906.35 | −0.988480 | −0.494240 | − | 0.869326i | \(-0.664554\pi\) | ||||
−0.494240 | + | 0.869326i | \(0.664554\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8695.98 | 0.958483 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6499.41 | 0.711462 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4655.21 | 0.506107 | 0.253054 | − | 0.967452i | \(-0.418565\pi\) | ||||
0.253054 | + | 0.967452i | \(0.418565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 65.5110 | 0.00707386 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10008.8 | −1.07343 | −0.536716 | − | 0.843763i | \(-0.680335\pi\) | ||||
−0.536716 | + | 0.843763i | \(0.680335\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8208.41 | −0.874418 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17526.1 | 1.85449 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3373.71 | −0.354600 | −0.177300 | − | 0.984157i | \(-0.556736\pi\) | ||||
−0.177300 | + | 0.984157i | \(0.556736\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5005.65 | 0.522632 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6506.79 | 0.674869 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2387.08 | 0.245952 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13600.4 | −1.39212 | −0.696060 | − | 0.717984i | \(-0.745065\pi\) | ||||
−0.696060 | + | 0.717984i | \(0.745065\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18909.8 | −1.92295 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3559.45 | −0.359609 | −0.179805 | − | 0.983702i | \(-0.557547\pi\) | ||||
−0.179805 | + | 0.983702i | \(0.557547\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8019.14 | 0.804926 | 0.402463 | − | 0.915436i | \(-0.368154\pi\) | ||||
0.402463 | + | 0.915436i | \(0.368154\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 23665.9 | 2.36017 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2066.14 | 0.204731 | 0.102365 | − | 0.994747i | \(-0.467359\pi\) | ||||
0.102365 | + | 0.994747i | \(0.467359\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8732.51 | −0.859765 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10055.7 | 0.983737 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9772.72 | 0.950000 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6384.17 | −0.616686 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 279.406 | 0.0268199 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3679.26 | 0.350960 | 0.175480 | − | 0.984483i | \(-0.443852\pi\) | ||||
0.175480 | + | 0.984483i | \(0.443852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1542.79 | −0.146248 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11326.3 | −1.06700 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27580.5 | 2.58220 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10884.4 | −1.01277 | −0.506386 | − | 0.862307i | \(-0.669019\pi\) | ||||
−0.506386 | + | 0.862307i | \(0.669019\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11789.3 | 1.09025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14548.9 | 1.33723 | 0.668616 | − | 0.743608i | \(-0.266887\pi\) | ||||
0.668616 | + | 0.743608i | \(0.266887\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14370.8 | 1.31284 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2276.73 | 0.206730 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1553.23 | 0.140185 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8461.92 | −0.759134 | −0.379567 | − | 0.925164i | \(-0.623927\pi\) | ||||
−0.379567 | + | 0.925164i | \(0.623927\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10193.2 | −0.908978 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 983.702 | 0.0871990 | 0.0435995 | − | 0.999049i | \(-0.486117\pi\) | ||||
0.0435995 | + | 0.999049i | \(0.486117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18377.5 | −1.61938 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10477.0 | −0.917749 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14472.5 | 1.26028 | 0.630140 | − | 0.776481i | \(-0.282997\pi\) | ||||
0.630140 | + | 0.776481i | \(0.282997\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2754.65 | −0.238470 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7394.38 | 0.636393 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25925.3 | 2.21826 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15711.3 | 1.33652 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12034.0 | −1.01779 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10761.8 | −0.904959 | −0.452480 | − | 0.891775i | \(-0.649460\pi\) | ||||
−0.452480 | + | 0.891775i | \(0.649460\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1516.67 | 0.126806 | 0.0634029 | − | 0.997988i | \(-0.479805\pi\) | ||||
0.0634029 | + | 0.997988i | \(0.479805\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11125.5 | 0.924866 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39109.7 | 3.23273 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4398.66 | 0.361524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −253.293 | −0.0207006 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −797.336 | −0.0647963 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4480.85 | −0.362101 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11979.7 | 0.962682 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1278.15 | 0.102141 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22541.9 | −1.79141 | −0.895704 | − | 0.444652i | \(-0.853327\pi\) | ||||
−0.895704 | + | 0.444652i | \(0.853327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9506.33 | 0.751299 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15935.4 | 1.25248 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10202.0 | 0.797448 | 0.398724 | − | 0.917071i | \(-0.369453\pi\) | ||||
0.398724 | + | 0.917071i | \(0.369453\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 919.574 | 0.0714872 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5619.46 | −0.434477 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8024.94 | 0.617098 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14299.9 | −1.09369 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7139.06 | −0.543073 | −0.271536 | − | 0.962428i | \(-0.587532\pi\) | ||||
−0.271536 | + | 0.962428i | \(0.587532\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1556.67 | −0.117782 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33684.6 | −2.53505 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19558.0 | −1.46407 | −0.732034 | − | 0.681268i | \(-0.761429\pi\) | ||||
−0.732034 | + | 0.681268i | \(0.761429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8992.29 | −0.669572 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11578.0 | −0.857549 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5835.86 | −0.429969 | −0.214984 | − | 0.976617i | \(-0.568970\pi\) | ||||
−0.214984 | + | 0.976617i | \(0.568970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9820.65 | 0.719757 | 0.359879 | − | 0.932999i | \(-0.382818\pi\) | ||||
0.359879 | + | 0.932999i | \(0.382818\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20143.3 | −1.46858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16271.9 | −1.18015 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 451.231 | 0.0325563 | 0.0162782 | − | 0.999868i | \(-0.494818\pi\) | ||||
0.0162782 | + | 0.999868i | \(0.494818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5699.58 | −0.409096 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6855.67 | −0.489537 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5451.33 | 0.387257 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −362.654 | −0.0256306 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −24775.7 | −1.74208 | −0.871042 | − | 0.491209i | \(-0.836555\pi\) | ||||
−0.871042 | + | 0.491209i | \(0.836555\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15293.2 | −1.06986 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13101.3 | −0.911873 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4207.64 | −0.291378 | −0.145689 | − | 0.989330i | \(-0.546540\pi\) | ||||
−0.145689 | + | 0.989330i | \(0.546540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36564.1 | 2.51929 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3658.54 | 0.250811 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1916.32 | −0.130715 | −0.0653577 | − | 0.997862i | \(-0.520819\pi\) | ||||
−0.0653577 | + | 0.997862i | \(0.520819\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19361.1 | −1.31407 | −0.657034 | − | 0.753861i | \(-0.728189\pi\) | ||||
−0.657034 | + | 0.753861i | \(0.728189\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1326.68 | 0.0895961 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23315.2 | 1.56677 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6097.02 | −0.407694 | −0.203847 | − | 0.979003i | \(-0.565345\pi\) | ||||
−0.203847 | + | 0.979003i | \(0.565345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9792.82 | 0.651601 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2502.60 | −0.165703 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13837.7 | −0.911743 | −0.455872 | − | 0.890046i | \(-0.650672\pi\) | ||||
−0.455872 | + | 0.890046i | \(0.650672\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7390.38 | −0.484567 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11959.1 | 0.780318 | 0.390159 | − | 0.920747i | \(-0.372420\pi\) | ||||
0.390159 | + | 0.920747i | \(0.372420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8385.02 | 0.544463 | 0.272231 | − | 0.962232i | \(-0.412238\pi\) | ||||
0.272231 | + | 0.962232i | \(0.412238\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18846.8 | 1.21787 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9243.75 | −0.594451 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15444.8 | −0.988465 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13171.8 | 0.838965 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23631.7 | −1.49802 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13592.1 | −0.857513 | −0.428757 | − | 0.903420i | \(-0.641048\pi\) | ||||
−0.428757 | + | 0.903420i | \(0.641048\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18915.9 | 1.18774 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7874.54 | 0.492113 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −203.593 | −0.0126635 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −235.973 | −0.0146087 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18123.4 | −1.11674 | −0.558371 | − | 0.829591i | \(-0.688573\pi\) | ||||
−0.558371 | + | 0.829591i | \(0.688573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25042.1 | 1.53587 | 0.767935 | − | 0.640528i | \(-0.221284\pi\) | ||||
0.767935 | + | 0.640528i | \(0.221284\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14428.5 | −0.880809 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6022.08 | 0.365923 | 0.182962 | − | 0.983120i | \(-0.441432\pi\) | ||||
0.182962 | + | 0.983120i | \(0.441432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4941.87 | −0.298899 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26650.9 | 1.60450 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14093.8 | −0.844617 | −0.422308 | − | 0.906452i | \(-0.638780\pi\) | ||||
−0.422308 | + | 0.906452i | \(0.638780\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26301.4 | −1.56898 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 418.496 | 0.0248510 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17240.7 | −1.01912 | −0.509562 | − | 0.860434i | \(-0.670193\pi\) | ||||
−0.509562 | + | 0.860434i | \(0.670193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20209.5 | 1.18920 | 0.594598 | − | 0.804023i | \(-0.297311\pi\) | ||||
0.594598 | + | 0.804023i | \(0.297311\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5365.52 | 0.314298 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14297.8 | −0.833749 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14322.8 | −0.831459 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16846.3 | 0.973564 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17941.3 | 1.03221 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6838.55 | 0.391689 | 0.195845 | − | 0.980635i | \(-0.437255\pi\) | ||||
0.195845 | + | 0.980635i | \(0.437255\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18512.6 | −1.05563 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −187.425 | −0.0106401 | −0.00532003 | − | 0.999986i | \(-0.501693\pi\) | ||||
−0.00532003 | + | 0.999986i | \(0.501693\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31059.3 | 1.75545 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2541.62 | −0.143018 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23476.0 | 1.31520 | 0.657601 | − | 0.753367i | \(-0.271571\pi\) | ||||
0.657601 | + | 0.753367i | \(0.271571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6863.79 | −0.382850 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7861.77 | 0.436602 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −868.327 | −0.0480125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6309.92 | −0.347382 | −0.173691 | − | 0.984800i | \(-0.555569\pi\) | ||||
−0.173691 | + | 0.984800i | \(0.555569\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2563.90 | 0.140540 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2317.39 | 0.126480 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12213.2 | −0.663712 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25879.3 | 1.40035 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24920.4 | −1.34270 | −0.671348 | − | 0.741142i | \(-0.734284\pi\) | ||||
−0.671348 | + | 0.741142i | \(0.734284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9240.77 | 0.495764 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23196.2 | −1.23918 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20695.5 | −1.10090 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14478.9 | 0.766949 | 0.383474 | − | 0.923551i | \(-0.374727\pi\) | ||||
0.383474 | + | 0.923551i | \(0.374727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1219.18 | −0.0643077 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38979.3 | −2.04738 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7075.54 | −0.370084 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10000.7 | 0.520895 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6411.30 | −0.332547 | −0.166273 | − | 0.986080i | \(-0.553173\pi\) | ||||
−0.166273 | + | 0.986080i | \(0.553173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 29195.3 | 1.50803 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −22747.2 | −1.17009 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14068.9 | 0.720698 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20626.3 | −1.05225 | −0.526126 | − | 0.850407i | \(-0.676356\pi\) | ||||
−0.526126 | + | 0.850407i | \(0.676356\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21243.3 | 1.07927 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23844.3 | −1.20645 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5732.29 | 0.288850 | 0.144425 | − | 0.989516i | \(-0.453867\pi\) | ||||
0.144425 | + | 0.989516i | \(0.453867\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1887.07 | −0.0947015 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25884.1 | 1.29369 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36336.0 | −1.80872 | −0.904359 | − | 0.426773i | \(-0.859650\pi\) | ||||
−0.904359 | + | 0.426773i | \(0.859650\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2098.10 | −0.104016 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4363.83 | 0.215469 | 0.107734 | − | 0.994180i | \(-0.465640\pi\) | ||||
0.107734 | + | 0.994180i | \(0.465640\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 56389.9 | 2.77311 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1041.54 | 0.0510146 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5046.03 | −0.246166 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16162.7 | −0.785334 | −0.392667 | − | 0.919681i | \(-0.628448\pi\) | ||||
−0.392667 | + | 0.919681i | \(0.628448\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13318.6 | 0.644562 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20935.5 | 1.00917 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4411.92 | 0.211828 | 0.105914 | − | 0.994375i | \(-0.466223\pi\) | ||||
0.105914 | + | 0.994375i | \(0.466223\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33572.2 | 1.60553 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28281.8 | 1.34719 | 0.673597 | − | 0.739099i | \(-0.264749\pi\) | ||||
0.673597 | + | 0.739099i | \(0.264749\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17945.4 | 0.851465 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5554.95 | −0.262535 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 787.176 | 0.0370577 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15016.8 | −0.704186 | −0.352093 | − | 0.935965i | \(-0.614530\pi\) | ||||
−0.352093 | + | 0.935965i | \(0.614530\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4887.72 | 0.228310 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8674.11 | 0.403604 | 0.201802 | − | 0.979426i | \(-0.435320\pi\) | ||||
0.201802 | + | 0.979426i | \(0.435320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38288.2 | 1.77465 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16103.5 | −0.743515 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4775.76 | 0.219653 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4603.94 | −0.210937 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16295.1 | −0.743729 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32353.9 | 1.47103 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23660.2 | −1.07166 | −0.535829 | − | 0.844327i | \(-0.680001\pi\) | ||||
−0.535829 | + | 0.844327i | \(0.680001\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36620.2 | 1.65236 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10126.5 | −0.455192 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2857.82 | −0.127975 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8048.39 | −0.359053 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35432.5 | 1.57476 | 0.787380 | − | 0.616468i | \(-0.211437\pi\) | ||||
0.787380 | + | 0.616468i | \(0.211437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −38333.6 | −1.69730 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1404.35 | 0.0619477 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8165.05 | 0.358827 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36442.1 | −1.59555 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16171.9 | 0.705424 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14005.5 | −0.608664 | −0.304332 | − | 0.952566i | \(-0.598433\pi\) | ||||
−0.304332 | + | 0.952566i | \(0.598433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22580.8 | −0.977706 | −0.488853 | − | 0.872366i | \(-0.662584\pi\) | ||||
−0.488853 | + | 0.872366i | \(0.662584\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1091.69 | 0.0470937 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37931.8 | 1.63030 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9323.90 | 0.399268 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −408.396 | −0.0174243 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21308.9 | 0.905827 | 0.452914 | − | 0.891554i | \(-0.350385\pi\) | ||||
0.452914 | + | 0.891554i | \(0.350385\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13571.4 | 0.574810 | 0.287405 | − | 0.957809i | \(-0.407207\pi\) | ||||
0.287405 | + | 0.957809i | \(0.407207\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −32977.0 | −1.39165 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19295.2 | −0.811318 | −0.405659 | − | 0.914025i | \(-0.632958\pi\) | ||||
−0.405659 | + | 0.914025i | \(0.632958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28752.7 | 1.20461 | 0.602306 | − | 0.798265i | \(-0.294249\pi\) | ||||
0.602306 | + | 0.798265i | \(0.294249\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5451.96 | 0.227589 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3118.53 | −0.129713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32796.4 | −1.35924 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −44346.7 | −1.83136 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −566.927 | −0.0233284 | −0.0116642 | − | 0.999932i | \(-0.503713\pi\) | ||||
−0.0116642 | + | 0.999932i | \(0.503713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12005.3 | −0.492243 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11692.3 | −0.477703 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −33709.5 | −1.37236 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26256.0 | 1.06513 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12566.4 | −0.507983 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23552.8 | 0.948744 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34698.1 | 1.39278 | 0.696389 | − | 0.717665i | \(-0.254789\pi\) | ||||
0.696389 | + | 0.717665i | \(0.254789\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2172.17 | 0.0868850 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37362.0 | 1.48922 | 0.744610 | − | 0.667500i | \(-0.232636\pi\) | ||||
0.744610 | + | 0.667500i | \(0.232636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29572.2 | 1.17461 | 0.587305 | − | 0.809366i | \(-0.300189\pi\) | ||||
0.587305 | + | 0.809366i | \(0.300189\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8322.54 | −0.329421 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11636.5 | −0.458994 | −0.229497 | − | 0.973309i | \(-0.573708\pi\) | ||||
−0.229497 | + | 0.973309i | \(0.573708\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38719.2 | −1.52196 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 57974.1 | 2.27094 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23786.7 | −0.928550 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4123.00 | −0.160393 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4718.65 | −0.182935 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 403.649 | 0.0155952 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19878.2 | 0.765380 | 0.382690 | − | 0.923877i | \(-0.374998\pi\) | ||||
0.382690 | + | 0.923877i | \(0.374998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 642.238 | 0.0246441 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36460.3 | −1.39430 | −0.697150 | − | 0.716926i | \(-0.745549\pi\) | ||||
−0.697150 | + | 0.716926i | \(0.745549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28119.9 | −1.07170 | −0.535849 | − | 0.844314i | \(-0.680009\pi\) | ||||
−0.535849 | + | 0.844314i | \(0.680009\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7296.21 | 0.277129 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41888.4 | −1.58565 | −0.792826 | − | 0.609448i | \(-0.791391\pi\) | ||||
−0.792826 | + | 0.609448i | \(0.791391\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8867.77 | 0.334551 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 34318.4 | 1.29036 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14989.7 | 0.561715 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38544.3 | 1.43955 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5347.62 | −0.199055 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33701.9 | 1.25030 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13300.6 | −0.491795 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16248.4 | −0.598796 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30586.4 | 1.12346 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12575.3 | 0.460371 | 0.230185 | − | 0.973147i | \(-0.426067\pi\) | ||||
0.230185 | + | 0.973147i | \(0.426067\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3144.14 | 0.114724 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39814.7 | −1.44799 | −0.723995 | − | 0.689805i | \(-0.757696\pi\) | ||||
−0.723995 | + | 0.689805i | \(0.757696\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20320.9 | 0.736609 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −26488.7 | −0.957036 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29618.8 | −1.06663 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8987.93 | 0.322616 | 0.161308 | − | 0.986904i | \(-0.448429\pi\) | ||||
0.161308 | + | 0.986904i | \(0.448429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 306.131 | 0.0109526 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 733.348 | 0.0261521 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23135.2 | −0.822359 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4435.46 | −0.157152 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 234.252 | 0.00827293 | 0.00413647 | − | 0.999991i | \(-0.498683\pi\) | ||||
0.00413647 | + | 0.999991i | \(0.498683\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1219.45 | 0.0429279 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2926.55 | 0.102691 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −108380. | −3.79079 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17624.6 | 0.614483 | 0.307241 | − | 0.951632i | \(-0.400594\pi\) | ||||
0.307241 | + | 0.951632i | \(0.400594\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18085.0 | 0.628521 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30532.1 | −1.05772 | −0.528861 | − | 0.848708i | \(-0.677381\pi\) | ||||
−0.528861 | + | 0.848708i | \(0.677381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12172.4 | 0.420349 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −41460.2 | −1.42720 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42092.8 | 1.44438 | 0.722192 | − | 0.691692i | \(-0.243135\pi\) | ||||
0.722192 | + | 0.691692i | \(0.243135\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1300.59 | −0.0444877 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1844.82 | 0.0629048 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48641.0 | −1.65334 | −0.826672 | − | 0.562683i | \(-0.809769\pi\) | ||||
−0.826672 | + | 0.562683i | \(0.809769\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −64810.6 | −2.19604 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29026.9 | −0.980467 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7729.54 | −0.260271 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61927.9 | 2.07874 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 766.612 | 0.0256529 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18338.3 | −0.611742 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53000.5 | −1.76254 | −0.881272 | − | 0.472609i | \(-0.843312\pi\) | ||||
−0.881272 | + | 0.472609i | \(0.843312\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32137.6 | −1.06544 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26286.3 | −0.868761 | −0.434381 | − | 0.900729i | \(-0.643033\pi\) | ||||
−0.434381 | + | 0.900729i | \(0.643033\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2609.68 | 0.0859842 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5252.81 | 0.172538 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30508.0 | −0.999014 | −0.499507 | − | 0.866310i | \(-0.666486\pi\) | ||||
−0.499507 | + | 0.866310i | \(0.666486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27399.4 | 0.894473 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2726.34 | −0.0887311 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37044.3 | 1.20196 | 0.600982 | − | 0.799263i | \(-0.294776\pi\) | ||||
0.600982 | + | 0.799263i | \(0.294776\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −42153.3 | −1.36357 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −26122.0 | −0.842424 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23764.7 | 0.764079 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47803.5 | 1.53232 | 0.766160 | − | 0.642650i | \(-0.222165\pi\) | ||||
0.766160 | + | 0.642650i | \(0.222165\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28934.1 | 0.924670 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11771.3 | 0.375051 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13478.1 | −0.428140 | −0.214070 | − | 0.976818i | \(-0.568672\pi\) | ||||
−0.214070 | + | 0.976818i | \(0.568672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26796.1 | 0.848639 |
(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 | 128.4.a.f.1.2 | yes | 2 | |
3.2 | odd | 2 | 1152.4.a.r.1.1 | 2 | |||
4.3 | odd | 2 | 128.4.a.h.1.1 | yes | 2 | ||
8.3 | odd | 2 | 128.4.a.e.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 128.4.a.g.1.1 | yes | 2 | ||
12.11 | even | 2 | 1152.4.a.q.1.1 | 2 | |||
16.3 | odd | 4 | 256.4.b.i.129.2 | 4 | |||
16.5 | even | 4 | 256.4.b.h.129.2 | 4 | |||
16.11 | odd | 4 | 256.4.b.i.129.3 | 4 | |||
16.13 | even | 4 | 256.4.b.h.129.3 | 4 | |||
24.5 | odd | 2 | 1152.4.a.t.1.2 | 2 | |||
24.11 | even | 2 | 1152.4.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
128.4.a.e.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
128.4.a.f.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
128.4.a.g.1.1 | yes | 2 | 8.5 | even | 2 | ||
128.4.a.h.1.1 | yes | 2 | 4.3 | odd | 2 | ||
256.4.b.h.129.2 | 4 | 16.5 | even | 4 | |||
256.4.b.h.129.3 | 4 | 16.13 | even | 4 | |||
256.4.b.i.129.2 | 4 | 16.3 | odd | 4 | |||
256.4.b.i.129.3 | 4 | 16.11 | odd | 4 | |||
1152.4.a.q.1.1 | 2 | 12.11 | even | 2 | |||
1152.4.a.r.1.1 | 2 | 3.2 | odd | 2 | |||
1152.4.a.s.1.2 | 2 | 24.11 | even | 2 | |||
1152.4.a.t.1.2 | 2 | 24.5 | odd | 2 |