Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,4,Mod(1,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, 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("1150.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.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: | \(67.8521965066\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - x^{4} - 38x^{3} + 38x^{2} + 202x + 101 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-5.76842\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 1.80744 | 0.347842 | 0.173921 | − | 0.984760i | \(-0.444356\pi\) | ||||
0.173921 | + | 0.984760i | \(0.444356\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.61488 | −0.245961 | ||||||||
\(7\) | 9.19471 | 0.496468 | 0.248234 | − | 0.968700i | \(-0.420150\pi\) | ||||
0.248234 | + | 0.968700i | \(0.420150\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −23.7332 | −0.879006 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43.1821 | 1.18363 | 0.591814 | − | 0.806075i | \(-0.298412\pi\) | ||||
0.591814 | + | 0.806075i | \(0.298412\pi\) | |||||||
\(12\) | 7.22976 | 0.173921 | ||||||||
\(13\) | 25.6824 | 0.547924 | 0.273962 | − | 0.961741i | \(-0.411666\pi\) | ||||
0.273962 | + | 0.961741i | \(0.411666\pi\) | |||||||
\(14\) | −18.3894 | −0.351056 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 22.9669 | 0.327665 | 0.163832 | − | 0.986488i | \(-0.447614\pi\) | ||||
0.163832 | + | 0.986488i | \(0.447614\pi\) | |||||||
\(18\) | 47.4663 | 0.621551 | ||||||||
\(19\) | 101.823 | 1.22946 | 0.614732 | − | 0.788736i | \(-0.289264\pi\) | ||||
0.614732 | + | 0.788736i | \(0.289264\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.6189 | 0.172692 | ||||||||
\(22\) | −86.3643 | −0.836951 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −14.4595 | −0.122981 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −51.3647 | −0.387440 | ||||||||
\(27\) | −91.6972 | −0.653597 | ||||||||
\(28\) | 36.7788 | 0.248234 | ||||||||
\(29\) | −146.682 | −0.939250 | −0.469625 | − | 0.882866i | \(-0.655611\pi\) | ||||
−0.469625 | + | 0.882866i | \(0.655611\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 23.9712 | 0.138882 | 0.0694412 | − | 0.997586i | \(-0.477878\pi\) | ||||
0.0694412 | + | 0.997586i | \(0.477878\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 78.0491 | 0.411715 | ||||||||
\(34\) | −45.9339 | −0.231694 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −94.9326 | −0.439503 | ||||||||
\(37\) | 294.572 | 1.30885 | 0.654423 | − | 0.756129i | \(-0.272912\pi\) | ||||
0.654423 | + | 0.756129i | \(0.272912\pi\) | |||||||
\(38\) | −203.646 | −0.869362 | ||||||||
\(39\) | 46.4193 | 0.190591 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −127.823 | −0.486891 | −0.243445 | − | 0.969915i | \(-0.578278\pi\) | ||||
−0.243445 | + | 0.969915i | \(0.578278\pi\) | |||||||
\(42\) | −33.2378 | −0.122112 | ||||||||
\(43\) | −502.072 | −1.78059 | −0.890293 | − | 0.455388i | \(-0.849501\pi\) | ||||
−0.890293 | + | 0.455388i | \(0.849501\pi\) | |||||||
\(44\) | 172.729 | 0.591814 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 607.879 | 1.88656 | 0.943279 | − | 0.332002i | \(-0.107724\pi\) | ||||
0.943279 | + | 0.332002i | \(0.107724\pi\) | |||||||
\(48\) | 28.9190 | 0.0869605 | ||||||||
\(49\) | −258.457 | −0.753520 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 41.5114 | 0.113976 | ||||||||
\(52\) | 102.729 | 0.273962 | ||||||||
\(53\) | 674.254 | 1.74747 | 0.873735 | − | 0.486401i | \(-0.161691\pi\) | ||||
0.873735 | + | 0.486401i | \(0.161691\pi\) | |||||||
\(54\) | 183.394 | 0.462163 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −73.5577 | −0.175528 | ||||||||
\(57\) | 184.039 | 0.427659 | ||||||||
\(58\) | 293.365 | 0.664150 | ||||||||
\(59\) | 14.8056 | 0.0326700 | 0.0163350 | − | 0.999867i | \(-0.494800\pi\) | ||||
0.0163350 | + | 0.999867i | \(0.494800\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −478.549 | −1.00446 | −0.502229 | − | 0.864735i | \(-0.667487\pi\) | ||||
−0.502229 | + | 0.864735i | \(0.667487\pi\) | |||||||
\(62\) | −47.9424 | −0.0982047 | ||||||||
\(63\) | −218.220 | −0.436398 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −156.098 | −0.291127 | ||||||||
\(67\) | 458.422 | 0.835898 | 0.417949 | − | 0.908471i | \(-0.362749\pi\) | ||||
0.417949 | + | 0.908471i | \(0.362749\pi\) | |||||||
\(68\) | 91.8678 | 0.163832 | ||||||||
\(69\) | −41.5711 | −0.0725301 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1012.83 | 1.69296 | 0.846481 | − | 0.532419i | \(-0.178717\pi\) | ||||
0.846481 | + | 0.532419i | \(0.178717\pi\) | |||||||
\(72\) | 189.865 | 0.310776 | ||||||||
\(73\) | −750.521 | −1.20331 | −0.601657 | − | 0.798755i | \(-0.705492\pi\) | ||||
−0.601657 | + | 0.798755i | \(0.705492\pi\) | |||||||
\(74\) | −589.144 | −0.925494 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 407.292 | 0.614732 | ||||||||
\(77\) | 397.047 | 0.587633 | ||||||||
\(78\) | −92.8387 | −0.134768 | ||||||||
\(79\) | −641.648 | −0.913811 | −0.456905 | − | 0.889515i | \(-0.651042\pi\) | ||||
−0.456905 | + | 0.889515i | \(0.651042\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 475.058 | 0.651657 | ||||||||
\(82\) | 255.645 | 0.344284 | ||||||||
\(83\) | 900.187 | 1.19046 | 0.595231 | − | 0.803554i | \(-0.297060\pi\) | ||||
0.595231 | + | 0.803554i | \(0.297060\pi\) | |||||||
\(84\) | 66.4756 | 0.0863462 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1004.14 | 1.25906 | ||||||||
\(87\) | −265.120 | −0.326711 | ||||||||
\(88\) | −345.457 | −0.418476 | ||||||||
\(89\) | −923.770 | −1.10022 | −0.550109 | − | 0.835093i | \(-0.685414\pi\) | ||||
−0.550109 | + | 0.835093i | \(0.685414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 236.142 | 0.272026 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 43.3265 | 0.0483091 | ||||||||
\(94\) | −1215.76 | −1.33400 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −57.8381 | −0.0614904 | ||||||||
\(97\) | 168.230 | 0.176095 | 0.0880473 | − | 0.996116i | \(-0.471937\pi\) | ||||
0.0880473 | + | 0.996116i | \(0.471937\pi\) | |||||||
\(98\) | 516.915 | 0.532819 | ||||||||
\(99\) | −1024.85 | −1.04042 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −633.410 | −0.624026 | −0.312013 | − | 0.950078i | \(-0.601003\pi\) | ||||
−0.312013 | + | 0.950078i | \(0.601003\pi\) | |||||||
\(102\) | −83.0228 | −0.0805929 | ||||||||
\(103\) | 1300.63 | 1.24422 | 0.622111 | − | 0.782929i | \(-0.286275\pi\) | ||||
0.622111 | + | 0.782929i | \(0.286275\pi\) | |||||||
\(104\) | −205.459 | −0.193720 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1348.51 | −1.23565 | ||||||||
\(107\) | −495.620 | −0.447789 | −0.223894 | − | 0.974613i | \(-0.571877\pi\) | ||||
−0.223894 | + | 0.974613i | \(0.571877\pi\) | |||||||
\(108\) | −366.789 | −0.326799 | ||||||||
\(109\) | −198.210 | −0.174175 | −0.0870874 | − | 0.996201i | \(-0.527756\pi\) | ||||
−0.0870874 | + | 0.996201i | \(0.527756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 532.421 | 0.455272 | ||||||||
\(112\) | 147.115 | 0.124117 | ||||||||
\(113\) | 868.555 | 0.723069 | 0.361534 | − | 0.932359i | \(-0.382253\pi\) | ||||
0.361534 | + | 0.932359i | \(0.382253\pi\) | |||||||
\(114\) | −368.078 | −0.302401 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −586.730 | −0.469625 | ||||||||
\(117\) | −609.524 | −0.481628 | ||||||||
\(118\) | −29.6113 | −0.0231012 | ||||||||
\(119\) | 211.174 | 0.162675 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 533.696 | 0.400974 | ||||||||
\(122\) | 957.098 | 0.710259 | ||||||||
\(123\) | −231.032 | −0.169361 | ||||||||
\(124\) | 95.8848 | 0.0694412 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 436.439 | 0.308580 | ||||||||
\(127\) | 2152.32 | 1.50384 | 0.751918 | − | 0.659257i | \(-0.229129\pi\) | ||||
0.751918 | + | 0.659257i | \(0.229129\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −907.464 | −0.619363 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1726.29 | 1.15135 | 0.575673 | − | 0.817680i | \(-0.304740\pi\) | ||||
0.575673 | + | 0.817680i | \(0.304740\pi\) | |||||||
\(132\) | 312.196 | 0.205858 | ||||||||
\(133\) | 936.233 | 0.610389 | ||||||||
\(134\) | −916.844 | −0.591069 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −183.736 | −0.115847 | ||||||||
\(137\) | −1771.09 | −1.10448 | −0.552242 | − | 0.833684i | \(-0.686227\pi\) | ||||
−0.552242 | + | 0.833684i | \(0.686227\pi\) | |||||||
\(138\) | 83.1423 | 0.0512865 | ||||||||
\(139\) | 2789.08 | 1.70192 | 0.850959 | − | 0.525232i | \(-0.176021\pi\) | ||||
0.850959 | + | 0.525232i | \(0.176021\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1098.70 | 0.656224 | ||||||||
\(142\) | −2025.65 | −1.19710 | ||||||||
\(143\) | 1109.02 | 0.648537 | ||||||||
\(144\) | −379.731 | −0.219751 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1501.04 | 0.850871 | ||||||||
\(147\) | −467.146 | −0.262106 | ||||||||
\(148\) | 1178.29 | 0.654423 | ||||||||
\(149\) | −2190.05 | −1.20413 | −0.602067 | − | 0.798445i | \(-0.705656\pi\) | ||||
−0.602067 | + | 0.798445i | \(0.705656\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1569.59 | −0.845902 | −0.422951 | − | 0.906153i | \(-0.639006\pi\) | ||||
−0.422951 | + | 0.906153i | \(0.639006\pi\) | |||||||
\(152\) | −814.584 | −0.434681 | ||||||||
\(153\) | −545.078 | −0.288019 | ||||||||
\(154\) | −794.094 | −0.415519 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 185.677 | 0.0952954 | ||||||||
\(157\) | 2633.86 | 1.33888 | 0.669442 | − | 0.742864i | \(-0.266533\pi\) | ||||
0.669442 | + | 0.742864i | \(0.266533\pi\) | |||||||
\(158\) | 1283.30 | 0.646162 | ||||||||
\(159\) | 1218.67 | 0.607844 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −211.478 | −0.103521 | ||||||||
\(162\) | −950.116 | −0.460791 | ||||||||
\(163\) | −287.657 | −0.138227 | −0.0691135 | − | 0.997609i | \(-0.522017\pi\) | ||||
−0.0691135 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(164\) | −511.290 | −0.243445 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1800.37 | −0.841784 | ||||||||
\(167\) | 1295.54 | 0.600310 | 0.300155 | − | 0.953890i | \(-0.402962\pi\) | ||||
0.300155 | + | 0.953890i | \(0.402962\pi\) | |||||||
\(168\) | −132.951 | −0.0610560 | ||||||||
\(169\) | −1537.42 | −0.699780 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2416.58 | −1.08071 | ||||||||
\(172\) | −2008.29 | −0.890293 | ||||||||
\(173\) | −1313.46 | −0.577230 | −0.288615 | − | 0.957445i | \(-0.593195\pi\) | ||||
−0.288615 | + | 0.957445i | \(0.593195\pi\) | |||||||
\(174\) | 530.240 | 0.231019 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 690.914 | 0.295907 | ||||||||
\(177\) | 26.7603 | 0.0113640 | ||||||||
\(178\) | 1847.54 | 0.777972 | ||||||||
\(179\) | 1916.37 | 0.800204 | 0.400102 | − | 0.916471i | \(-0.368975\pi\) | ||||
0.400102 | + | 0.916471i | \(0.368975\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4443.32 | 1.82469 | 0.912345 | − | 0.409421i | \(-0.134269\pi\) | ||||
0.912345 | + | 0.409421i | \(0.134269\pi\) | |||||||
\(182\) | −472.284 | −0.192352 | ||||||||
\(183\) | −864.949 | −0.349393 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −86.6530 | −0.0341597 | ||||||||
\(187\) | 991.762 | 0.387833 | ||||||||
\(188\) | 2431.51 | 0.943279 | ||||||||
\(189\) | −843.129 | −0.324490 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1903.54 | 0.721129 | 0.360564 | − | 0.932734i | \(-0.382584\pi\) | ||||
0.360564 | + | 0.932734i | \(0.382584\pi\) | |||||||
\(192\) | 115.676 | 0.0434803 | ||||||||
\(193\) | 3417.60 | 1.27463 | 0.637317 | − | 0.770602i | \(-0.280044\pi\) | ||||
0.637317 | + | 0.770602i | \(0.280044\pi\) | |||||||
\(194\) | −336.460 | −0.124518 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1033.83 | −0.376760 | ||||||||
\(197\) | 1609.57 | 0.582117 | 0.291059 | − | 0.956705i | \(-0.405993\pi\) | ||||
0.291059 | + | 0.956705i | \(0.405993\pi\) | |||||||
\(198\) | 2049.70 | 0.735685 | ||||||||
\(199\) | −4518.91 | −1.60973 | −0.804866 | − | 0.593456i | \(-0.797763\pi\) | ||||
−0.804866 | + | 0.593456i | \(0.797763\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 828.570 | 0.290760 | ||||||||
\(202\) | 1266.82 | 0.441253 | ||||||||
\(203\) | −1348.70 | −0.466307 | ||||||||
\(204\) | 166.046 | 0.0569878 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2601.26 | −0.879798 | ||||||||
\(207\) | 545.863 | 0.183285 | ||||||||
\(208\) | 410.918 | 0.136981 | ||||||||
\(209\) | 4396.94 | 1.45523 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5408.64 | 1.76467 | 0.882337 | − | 0.470618i | \(-0.155969\pi\) | ||||
0.882337 | + | 0.470618i | \(0.155969\pi\) | |||||||
\(212\) | 2697.02 | 0.873735 | ||||||||
\(213\) | 1830.62 | 0.588883 | ||||||||
\(214\) | 991.240 | 0.316634 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 733.577 | 0.231082 | ||||||||
\(217\) | 220.408 | 0.0689506 | ||||||||
\(218\) | 396.420 | 0.123160 | ||||||||
\(219\) | −1356.52 | −0.418563 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 589.846 | 0.179535 | ||||||||
\(222\) | −1064.84 | −0.321926 | ||||||||
\(223\) | 5812.74 | 1.74552 | 0.872758 | − | 0.488154i | \(-0.162329\pi\) | ||||
0.872758 | + | 0.488154i | \(0.162329\pi\) | |||||||
\(224\) | −294.231 | −0.0877639 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1737.11 | −0.511287 | ||||||||
\(227\) | 2033.30 | 0.594514 | 0.297257 | − | 0.954798i | \(-0.403928\pi\) | ||||
0.297257 | + | 0.954798i | \(0.403928\pi\) | |||||||
\(228\) | 736.156 | 0.213830 | ||||||||
\(229\) | −435.903 | −0.125787 | −0.0628936 | − | 0.998020i | \(-0.520033\pi\) | ||||
−0.0628936 | + | 0.998020i | \(0.520033\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 717.639 | 0.204403 | ||||||||
\(232\) | 1173.46 | 0.332075 | ||||||||
\(233\) | −1582.05 | −0.444822 | −0.222411 | − | 0.974953i | \(-0.571393\pi\) | ||||
−0.222411 | + | 0.974953i | \(0.571393\pi\) | |||||||
\(234\) | 1219.05 | 0.340562 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 59.2226 | 0.0163350 | ||||||||
\(237\) | −1159.74 | −0.317862 | ||||||||
\(238\) | −422.349 | −0.115029 | ||||||||
\(239\) | −1732.60 | −0.468923 | −0.234461 | − | 0.972125i | \(-0.575333\pi\) | ||||
−0.234461 | + | 0.972125i | \(0.575333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4441.73 | −1.18721 | −0.593604 | − | 0.804757i | \(-0.702296\pi\) | ||||
−0.593604 | + | 0.804757i | \(0.702296\pi\) | |||||||
\(242\) | −1067.39 | −0.283531 | ||||||||
\(243\) | 3334.46 | 0.880271 | ||||||||
\(244\) | −1914.20 | −0.502229 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 462.063 | 0.119756 | ||||||||
\(247\) | 2615.06 | 0.673652 | ||||||||
\(248\) | −191.770 | −0.0491023 | ||||||||
\(249\) | 1627.03 | 0.414093 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4714.54 | 1.18557 | 0.592787 | − | 0.805359i | \(-0.298028\pi\) | ||||
0.592787 | + | 0.805359i | \(0.298028\pi\) | |||||||
\(252\) | −872.878 | −0.218199 | ||||||||
\(253\) | −993.189 | −0.246803 | ||||||||
\(254\) | −4304.63 | −1.06337 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4229.41 | 1.02655 | 0.513275 | − | 0.858224i | \(-0.328432\pi\) | ||||
0.513275 | + | 0.858224i | \(0.328432\pi\) | |||||||
\(258\) | 1814.93 | 0.437956 | ||||||||
\(259\) | 2708.50 | 0.649800 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3481.24 | 0.825606 | ||||||||
\(262\) | −3452.57 | −0.814125 | ||||||||
\(263\) | 4848.80 | 1.13684 | 0.568422 | − | 0.822737i | \(-0.307554\pi\) | ||||
0.568422 | + | 0.822737i | \(0.307554\pi\) | |||||||
\(264\) | −624.393 | −0.145563 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1872.47 | −0.431610 | ||||||||
\(267\) | −1669.66 | −0.382702 | ||||||||
\(268\) | 1833.69 | 0.417949 | ||||||||
\(269\) | 4603.64 | 1.04345 | 0.521726 | − | 0.853113i | \(-0.325288\pi\) | ||||
0.521726 | + | 0.853113i | \(0.325288\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1521.31 | −0.341008 | −0.170504 | − | 0.985357i | \(-0.554540\pi\) | ||||
−0.170504 | + | 0.985357i | \(0.554540\pi\) | |||||||
\(272\) | 367.471 | 0.0819162 | ||||||||
\(273\) | 426.812 | 0.0946222 | ||||||||
\(274\) | 3542.18 | 0.780988 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −166.285 | −0.0362650 | ||||||||
\(277\) | −3293.74 | −0.714446 | −0.357223 | − | 0.934019i | \(-0.616276\pi\) | ||||
−0.357223 | + | 0.934019i | \(0.616276\pi\) | |||||||
\(278\) | −5578.16 | −1.20344 | ||||||||
\(279\) | −568.912 | −0.122078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8857.86 | 1.88048 | 0.940242 | − | 0.340508i | \(-0.110599\pi\) | ||||
0.940242 | + | 0.340508i | \(0.110599\pi\) | |||||||
\(282\) | −2197.41 | −0.464020 | ||||||||
\(283\) | −5470.44 | −1.14906 | −0.574530 | − | 0.818483i | \(-0.694815\pi\) | ||||
−0.574530 | + | 0.818483i | \(0.694815\pi\) | |||||||
\(284\) | 4051.30 | 0.846481 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2218.04 | −0.458585 | ||||||||
\(287\) | −1175.29 | −0.241726 | ||||||||
\(288\) | 759.461 | 0.155388 | ||||||||
\(289\) | −4385.52 | −0.892636 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 304.066 | 0.0612531 | ||||||||
\(292\) | −3002.09 | −0.601657 | ||||||||
\(293\) | 629.599 | 0.125534 | 0.0627672 | − | 0.998028i | \(-0.480007\pi\) | ||||
0.0627672 | + | 0.998028i | \(0.480007\pi\) | |||||||
\(294\) | 934.292 | 0.185337 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2356.57 | −0.462747 | ||||||||
\(297\) | −3959.68 | −0.773616 | ||||||||
\(298\) | 4380.10 | 0.851452 | ||||||||
\(299\) | −590.694 | −0.114250 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4616.40 | −0.884004 | ||||||||
\(302\) | 3139.17 | 0.598143 | ||||||||
\(303\) | −1144.85 | −0.217062 | ||||||||
\(304\) | 1629.17 | 0.307366 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1090.16 | 0.203660 | ||||||||
\(307\) | −791.929 | −0.147224 | −0.0736120 | − | 0.997287i | \(-0.523453\pi\) | ||||
−0.0736120 | + | 0.997287i | \(0.523453\pi\) | |||||||
\(308\) | 1588.19 | 0.293816 | ||||||||
\(309\) | 2350.81 | 0.432793 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2109.26 | 0.384582 | 0.192291 | − | 0.981338i | \(-0.438408\pi\) | ||||
0.192291 | + | 0.981338i | \(0.438408\pi\) | |||||||
\(312\) | −371.355 | −0.0673840 | ||||||||
\(313\) | −207.600 | −0.0374896 | −0.0187448 | − | 0.999824i | \(-0.505967\pi\) | ||||
−0.0187448 | + | 0.999824i | \(0.505967\pi\) | |||||||
\(314\) | −5267.72 | −0.946734 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2566.59 | −0.456905 | ||||||||
\(317\) | −4013.96 | −0.711188 | −0.355594 | − | 0.934640i | \(-0.615721\pi\) | ||||
−0.355594 | + | 0.934640i | \(0.615721\pi\) | |||||||
\(318\) | −2437.35 | −0.429811 | ||||||||
\(319\) | −6334.06 | −1.11172 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −895.803 | −0.155760 | ||||||||
\(322\) | 422.957 | 0.0732002 | ||||||||
\(323\) | 2338.56 | 0.402852 | ||||||||
\(324\) | 1900.23 | 0.325829 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 575.313 | 0.0977413 | ||||||||
\(327\) | −358.252 | −0.0605853 | ||||||||
\(328\) | 1022.58 | 0.172142 | ||||||||
\(329\) | 5589.27 | 0.936615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1196.79 | 0.198736 | 0.0993678 | − | 0.995051i | \(-0.468318\pi\) | ||||
0.0993678 | + | 0.995051i | \(0.468318\pi\) | |||||||
\(332\) | 3600.75 | 0.595231 | ||||||||
\(333\) | −6991.12 | −1.15048 | ||||||||
\(334\) | −2591.08 | −0.424484 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 265.902 | 0.0431731 | ||||||||
\(337\) | 3245.42 | 0.524597 | 0.262299 | − | 0.964987i | \(-0.415519\pi\) | ||||
0.262299 | + | 0.964987i | \(0.415519\pi\) | |||||||
\(338\) | 3074.83 | 0.494819 | ||||||||
\(339\) | 1569.86 | 0.251514 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1035.13 | 0.164385 | ||||||||
\(342\) | 4833.16 | 0.764174 | ||||||||
\(343\) | −5530.23 | −0.870566 | ||||||||
\(344\) | 4016.57 | 0.629532 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2626.93 | 0.408163 | ||||||||
\(347\) | 10510.0 | 1.62596 | 0.812981 | − | 0.582290i | \(-0.197843\pi\) | ||||
0.812981 | + | 0.582290i | \(0.197843\pi\) | |||||||
\(348\) | −1060.48 | −0.163355 | ||||||||
\(349\) | 6150.02 | 0.943276 | 0.471638 | − | 0.881792i | \(-0.343663\pi\) | ||||
0.471638 | + | 0.881792i | \(0.343663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2355.00 | −0.358121 | ||||||||
\(352\) | −1381.83 | −0.209238 | ||||||||
\(353\) | 1123.35 | 0.169376 | 0.0846882 | − | 0.996408i | \(-0.473011\pi\) | ||||
0.0846882 | + | 0.996408i | \(0.473011\pi\) | |||||||
\(354\) | −53.5206 | −0.00803556 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3695.08 | −0.550109 | ||||||||
\(357\) | 381.685 | 0.0565852 | ||||||||
\(358\) | −3832.75 | −0.565829 | ||||||||
\(359\) | 2209.46 | 0.324821 | 0.162411 | − | 0.986723i | \(-0.448073\pi\) | ||||
0.162411 | + | 0.986723i | \(0.448073\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3508.93 | 0.511581 | ||||||||
\(362\) | −8886.63 | −1.29025 | ||||||||
\(363\) | 964.624 | 0.139476 | ||||||||
\(364\) | 944.568 | 0.136013 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1729.90 | 0.247058 | ||||||||
\(367\) | −9017.63 | −1.28261 | −0.641303 | − | 0.767287i | \(-0.721606\pi\) | ||||
−0.641303 | + | 0.767287i | \(0.721606\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 3033.63 | 0.427980 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6199.57 | 0.867563 | ||||||||
\(372\) | 173.306 | 0.0241546 | ||||||||
\(373\) | 2000.52 | 0.277702 | 0.138851 | − | 0.990313i | \(-0.455659\pi\) | ||||
0.138851 | + | 0.990313i | \(0.455659\pi\) | |||||||
\(374\) | −1983.52 | −0.274239 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4863.03 | −0.666999 | ||||||||
\(377\) | −3767.15 | −0.514637 | ||||||||
\(378\) | 1686.26 | 0.229449 | ||||||||
\(379\) | 5404.84 | 0.732528 | 0.366264 | − | 0.930511i | \(-0.380637\pi\) | ||||
0.366264 | + | 0.930511i | \(0.380637\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3890.18 | 0.523097 | ||||||||
\(382\) | −3807.09 | −0.509915 | ||||||||
\(383\) | −9355.83 | −1.24820 | −0.624100 | − | 0.781345i | \(-0.714534\pi\) | ||||
−0.624100 | + | 0.781345i | \(0.714534\pi\) | |||||||
\(384\) | −231.352 | −0.0307452 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6835.20 | −0.901302 | ||||||||
\(387\) | 11915.7 | 1.56515 | ||||||||
\(388\) | 672.920 | 0.0880473 | ||||||||
\(389\) | 7771.25 | 1.01290 | 0.506450 | − | 0.862269i | \(-0.330958\pi\) | ||||
0.506450 | + | 0.862269i | \(0.330958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −528.240 | −0.0683229 | ||||||||
\(392\) | 2067.66 | 0.266409 | ||||||||
\(393\) | 3120.16 | 0.400487 | ||||||||
\(394\) | −3219.14 | −0.411619 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4099.39 | −0.520208 | ||||||||
\(397\) | −2509.29 | −0.317223 | −0.158612 | − | 0.987341i | \(-0.550702\pi\) | ||||
−0.158612 | + | 0.987341i | \(0.550702\pi\) | |||||||
\(398\) | 9037.81 | 1.13825 | ||||||||
\(399\) | 1692.19 | 0.212319 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1502.71 | 0.187136 | 0.0935681 | − | 0.995613i | \(-0.470173\pi\) | ||||
0.0935681 | + | 0.995613i | \(0.470173\pi\) | |||||||
\(402\) | −1657.14 | −0.205599 | ||||||||
\(403\) | 615.637 | 0.0760969 | ||||||||
\(404\) | −2533.64 | −0.312013 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2697.41 | 0.329729 | ||||||||
\(407\) | 12720.2 | 1.54919 | ||||||||
\(408\) | −332.091 | −0.0402965 | ||||||||
\(409\) | 6281.54 | 0.759419 | 0.379709 | − | 0.925106i | \(-0.376024\pi\) | ||||
0.379709 | + | 0.925106i | \(0.376024\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3201.14 | −0.384186 | ||||||||
\(412\) | 5202.52 | 0.622111 | ||||||||
\(413\) | 136.134 | 0.0162196 | ||||||||
\(414\) | −1091.73 | −0.129602 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −821.836 | −0.0968601 | ||||||||
\(417\) | 5041.09 | 0.591999 | ||||||||
\(418\) | −8793.87 | −1.02900 | ||||||||
\(419\) | −5437.48 | −0.633982 | −0.316991 | − | 0.948429i | \(-0.602672\pi\) | ||||
−0.316991 | + | 0.948429i | \(0.602672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8424.12 | 0.975217 | 0.487608 | − | 0.873062i | \(-0.337869\pi\) | ||||
0.487608 | + | 0.873062i | \(0.337869\pi\) | |||||||
\(422\) | −10817.3 | −1.24781 | ||||||||
\(423\) | −14426.9 | −1.65830 | ||||||||
\(424\) | −5394.03 | −0.617824 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3661.24 | −0.416403 | ||||||||
\(427\) | −4400.12 | −0.498681 | ||||||||
\(428\) | −1982.48 | −0.223894 | ||||||||
\(429\) | 2004.49 | 0.225589 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2280.19 | −0.254832 | −0.127416 | − | 0.991849i | \(-0.540668\pi\) | ||||
−0.127416 | + | 0.991849i | \(0.540668\pi\) | |||||||
\(432\) | −1467.15 | −0.163399 | ||||||||
\(433\) | −9676.90 | −1.07400 | −0.537000 | − | 0.843582i | \(-0.680443\pi\) | ||||
−0.537000 | + | 0.843582i | \(0.680443\pi\) | |||||||
\(434\) | −440.816 | −0.0487554 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −792.839 | −0.0870874 | ||||||||
\(437\) | −2341.93 | −0.256361 | ||||||||
\(438\) | 2713.04 | 0.295969 | ||||||||
\(439\) | −10267.6 | −1.11628 | −0.558138 | − | 0.829748i | \(-0.688484\pi\) | ||||
−0.558138 | + | 0.829748i | \(0.688484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6134.01 | 0.662348 | ||||||||
\(442\) | −1179.69 | −0.126951 | ||||||||
\(443\) | 2947.70 | 0.316139 | 0.158069 | − | 0.987428i | \(-0.449473\pi\) | ||||
0.158069 | + | 0.987428i | \(0.449473\pi\) | |||||||
\(444\) | 2129.68 | 0.227636 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11625.5 | −1.23427 | ||||||||
\(447\) | −3958.39 | −0.418849 | ||||||||
\(448\) | 588.462 | 0.0620585 | ||||||||
\(449\) | −14322.2 | −1.50536 | −0.752682 | − | 0.658385i | \(-0.771240\pi\) | ||||
−0.752682 | + | 0.658385i | \(0.771240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5519.65 | −0.576297 | ||||||||
\(452\) | 3474.22 | 0.361534 | ||||||||
\(453\) | −2836.94 | −0.294240 | ||||||||
\(454\) | −4066.59 | −0.420385 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1472.31 | −0.151200 | ||||||||
\(457\) | −13404.4 | −1.37206 | −0.686029 | − | 0.727574i | \(-0.740648\pi\) | ||||
−0.686029 | + | 0.727574i | \(0.740648\pi\) | |||||||
\(458\) | 871.805 | 0.0889449 | ||||||||
\(459\) | −2106.00 | −0.214161 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16928.6 | −1.71029 | −0.855144 | − | 0.518390i | \(-0.826532\pi\) | ||||
−0.855144 | + | 0.518390i | \(0.826532\pi\) | |||||||
\(462\) | −1435.28 | −0.144535 | ||||||||
\(463\) | −13109.3 | −1.31585 | −0.657925 | − | 0.753083i | \(-0.728566\pi\) | ||||
−0.657925 | + | 0.753083i | \(0.728566\pi\) | |||||||
\(464\) | −2346.92 | −0.234812 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3164.10 | 0.314537 | ||||||||
\(467\) | 4676.02 | 0.463341 | 0.231671 | − | 0.972794i | \(-0.425581\pi\) | ||||
0.231671 | + | 0.972794i | \(0.425581\pi\) | |||||||
\(468\) | −2438.09 | −0.240814 | ||||||||
\(469\) | 4215.06 | 0.414996 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4760.54 | 0.465720 | ||||||||
\(472\) | −118.445 | −0.0115506 | ||||||||
\(473\) | −21680.5 | −2.10755 | ||||||||
\(474\) | 2319.48 | 0.224762 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 844.698 | 0.0813375 | ||||||||
\(477\) | −16002.2 | −1.53604 | ||||||||
\(478\) | 3465.20 | 0.331579 | ||||||||
\(479\) | −13518.0 | −1.28947 | −0.644734 | − | 0.764407i | \(-0.723032\pi\) | ||||
−0.644734 | + | 0.764407i | \(0.723032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7565.30 | 0.717148 | ||||||||
\(482\) | 8883.47 | 0.839483 | ||||||||
\(483\) | −382.234 | −0.0360088 | ||||||||
\(484\) | 2134.79 | 0.200487 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6668.92 | −0.622446 | ||||||||
\(487\) | −14914.7 | −1.38778 | −0.693889 | − | 0.720082i | \(-0.744104\pi\) | ||||
−0.693889 | + | 0.720082i | \(0.744104\pi\) | |||||||
\(488\) | 3828.39 | 0.355129 | ||||||||
\(489\) | −519.922 | −0.0480812 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3706.99 | −0.340722 | −0.170361 | − | 0.985382i | \(-0.554493\pi\) | ||||
−0.170361 | + | 0.985382i | \(0.554493\pi\) | |||||||
\(492\) | −924.126 | −0.0846806 | ||||||||
\(493\) | −3368.85 | −0.307759 | ||||||||
\(494\) | −5230.11 | −0.476344 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 383.539 | 0.0347206 | ||||||||
\(497\) | 9312.64 | 0.840501 | ||||||||
\(498\) | −3254.07 | −0.292808 | ||||||||
\(499\) | 13037.0 | 1.16957 | 0.584784 | − | 0.811189i | \(-0.301179\pi\) | ||||
0.584784 | + | 0.811189i | \(0.301179\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2341.61 | 0.208813 | ||||||||
\(502\) | −9429.08 | −0.838328 | ||||||||
\(503\) | −2976.34 | −0.263834 | −0.131917 | − | 0.991261i | \(-0.542113\pi\) | ||||
−0.131917 | + | 0.991261i | \(0.542113\pi\) | |||||||
\(504\) | 1745.76 | 0.154290 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1986.38 | 0.174516 | ||||||||
\(507\) | −2778.79 | −0.243413 | ||||||||
\(508\) | 8609.26 | 0.751918 | ||||||||
\(509\) | 20818.7 | 1.81292 | 0.906458 | − | 0.422297i | \(-0.138776\pi\) | ||||
0.906458 | + | 0.422297i | \(0.138776\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6900.83 | −0.597406 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −9336.88 | −0.803574 | ||||||||
\(514\) | −8458.82 | −0.725881 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3629.86 | −0.309681 | ||||||||
\(517\) | 26249.5 | 2.23298 | ||||||||
\(518\) | −5417.00 | −0.459478 | ||||||||
\(519\) | −2374.01 | −0.200785 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10439.5 | −0.877855 | −0.438927 | − | 0.898522i | \(-0.644641\pi\) | ||||
−0.438927 | + | 0.898522i | \(0.644641\pi\) | |||||||
\(522\) | −6962.48 | −0.583792 | ||||||||
\(523\) | −22364.9 | −1.86988 | −0.934942 | − | 0.354801i | \(-0.884549\pi\) | ||||
−0.934942 | + | 0.354801i | \(0.884549\pi\) | |||||||
\(524\) | 6905.15 | 0.575673 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9697.60 | −0.803870 | ||||||||
\(527\) | 550.545 | 0.0455069 | ||||||||
\(528\) | 1248.79 | 0.102929 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −351.385 | −0.0287171 | ||||||||
\(532\) | 3744.93 | 0.305194 | ||||||||
\(533\) | −3282.78 | −0.266779 | ||||||||
\(534\) | 3339.32 | 0.270611 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3667.38 | −0.295535 | ||||||||
\(537\) | 3463.73 | 0.278344 | ||||||||
\(538\) | −9207.27 | −0.737832 | ||||||||
\(539\) | −11160.7 | −0.891887 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22462.5 | −1.78510 | −0.892550 | − | 0.450949i | \(-0.851086\pi\) | ||||
−0.892550 | + | 0.450949i | \(0.851086\pi\) | |||||||
\(542\) | 3042.63 | 0.241129 | ||||||||
\(543\) | 8031.03 | 0.634704 | ||||||||
\(544\) | −734.942 | −0.0579235 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −853.625 | −0.0669080 | ||||||||
\(547\) | −4367.35 | −0.341379 | −0.170690 | − | 0.985325i | \(-0.554600\pi\) | ||||
−0.170690 | + | 0.985325i | \(0.554600\pi\) | |||||||
\(548\) | −7084.35 | −0.552242 | ||||||||
\(549\) | 11357.5 | 0.882924 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14935.7 | −1.15477 | ||||||||
\(552\) | 332.569 | 0.0256433 | ||||||||
\(553\) | −5899.77 | −0.453677 | ||||||||
\(554\) | 6587.47 | 0.505189 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11156.3 | 0.850959 | ||||||||
\(557\) | 13805.9 | 1.05022 | 0.525110 | − | 0.851034i | \(-0.324024\pi\) | ||||
0.525110 | + | 0.851034i | \(0.324024\pi\) | |||||||
\(558\) | 1137.82 | 0.0863225 | ||||||||
\(559\) | −12894.4 | −0.975625 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1792.55 | 0.134905 | ||||||||
\(562\) | −17715.7 | −1.32970 | ||||||||
\(563\) | −8149.77 | −0.610075 | −0.305037 | − | 0.952340i | \(-0.598669\pi\) | ||||
−0.305037 | + | 0.952340i | \(0.598669\pi\) | |||||||
\(564\) | 4394.82 | 0.328112 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10940.9 | 0.812508 | ||||||||
\(567\) | 4368.02 | 0.323527 | ||||||||
\(568\) | −8102.60 | −0.598552 | ||||||||
\(569\) | −11539.9 | −0.850226 | −0.425113 | − | 0.905140i | \(-0.639766\pi\) | ||||
−0.425113 | + | 0.905140i | \(0.639766\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2436.53 | −0.178573 | −0.0892867 | − | 0.996006i | \(-0.528459\pi\) | ||||
−0.0892867 | + | 0.996006i | \(0.528459\pi\) | |||||||
\(572\) | 4436.08 | 0.324269 | ||||||||
\(573\) | 3440.54 | 0.250839 | ||||||||
\(574\) | 2350.58 | 0.170926 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1518.92 | −0.109876 | ||||||||
\(577\) | 6965.59 | 0.502567 | 0.251284 | − | 0.967913i | \(-0.419147\pi\) | ||||
0.251284 | + | 0.967913i | \(0.419147\pi\) | |||||||
\(578\) | 8771.04 | 0.631189 | ||||||||
\(579\) | 6177.11 | 0.443371 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8276.96 | 0.591026 | ||||||||
\(582\) | −608.132 | −0.0433125 | ||||||||
\(583\) | 29115.7 | 2.06835 | ||||||||
\(584\) | 6004.17 | 0.425435 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1259.20 | −0.0887662 | ||||||||
\(587\) | −3080.79 | −0.216623 | −0.108311 | − | 0.994117i | \(-0.534544\pi\) | ||||
−0.108311 | + | 0.994117i | \(0.534544\pi\) | |||||||
\(588\) | −1868.58 | −0.131053 | ||||||||
\(589\) | 2440.82 | 0.170751 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2909.20 | 0.202485 | ||||||||
\(592\) | 4713.15 | 0.327211 | ||||||||
\(593\) | 13741.0 | 0.951563 | 0.475782 | − | 0.879564i | \(-0.342165\pi\) | ||||
0.475782 | + | 0.879564i | \(0.342165\pi\) | |||||||
\(594\) | 7919.36 | 0.547029 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8760.21 | −0.602067 | ||||||||
\(597\) | −8167.65 | −0.559933 | ||||||||
\(598\) | 1181.39 | 0.0807869 | ||||||||
\(599\) | 24131.0 | 1.64602 | 0.823011 | − | 0.568026i | \(-0.192293\pi\) | ||||
0.823011 | + | 0.568026i | \(0.192293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18108.3 | −1.22904 | −0.614520 | − | 0.788901i | \(-0.710650\pi\) | ||||
−0.614520 | + | 0.788901i | \(0.710650\pi\) | |||||||
\(602\) | 9232.81 | 0.625085 | ||||||||
\(603\) | −10879.8 | −0.734759 | ||||||||
\(604\) | −6278.35 | −0.422951 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2289.70 | 0.153486 | ||||||||
\(607\) | −10257.1 | −0.685873 | −0.342936 | − | 0.939359i | \(-0.611422\pi\) | ||||
−0.342936 | + | 0.939359i | \(0.611422\pi\) | |||||||
\(608\) | −3258.34 | −0.217340 | ||||||||
\(609\) | −2437.70 | −0.162201 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15611.8 | 1.03369 | ||||||||
\(612\) | −2180.31 | −0.144010 | ||||||||
\(613\) | 2710.49 | 0.178590 | 0.0892951 | − | 0.996005i | \(-0.471539\pi\) | ||||
0.0892951 | + | 0.996005i | \(0.471539\pi\) | |||||||
\(614\) | 1583.86 | 0.104103 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3176.38 | −0.207760 | ||||||||
\(617\) | −20517.7 | −1.33875 | −0.669377 | − | 0.742923i | \(-0.733439\pi\) | ||||
−0.669377 | + | 0.742923i | \(0.733439\pi\) | |||||||
\(618\) | −4701.62 | −0.306031 | ||||||||
\(619\) | −5220.67 | −0.338992 | −0.169496 | − | 0.985531i | \(-0.554214\pi\) | ||||
−0.169496 | + | 0.985531i | \(0.554214\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2109.03 | 0.136284 | ||||||||
\(622\) | −4218.52 | −0.271941 | ||||||||
\(623\) | −8493.80 | −0.546223 | ||||||||
\(624\) | 742.710 | 0.0476477 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 415.200 | 0.0265092 | ||||||||
\(627\) | 7947.20 | 0.506189 | ||||||||
\(628\) | 10535.4 | 0.669442 | ||||||||
\(629\) | 6765.41 | 0.428863 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19100.5 | −1.20504 | −0.602520 | − | 0.798103i | \(-0.705837\pi\) | ||||
−0.602520 | + | 0.798103i | \(0.705837\pi\) | |||||||
\(632\) | 5133.18 | 0.323081 | ||||||||
\(633\) | 9775.80 | 0.613828 | ||||||||
\(634\) | 8027.93 | 0.502886 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4874.70 | 0.303922 | ||||||||
\(637\) | −6637.79 | −0.412871 | ||||||||
\(638\) | 12668.1 | 0.786106 | ||||||||
\(639\) | −24037.5 | −1.48812 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15088.0 | 0.929701 | 0.464851 | − | 0.885389i | \(-0.346108\pi\) | ||||
0.464851 | + | 0.885389i | \(0.346108\pi\) | |||||||
\(642\) | 1791.61 | 0.110139 | ||||||||
\(643\) | −1568.01 | −0.0961687 | −0.0480843 | − | 0.998843i | \(-0.515312\pi\) | ||||
−0.0480843 | + | 0.998843i | \(0.515312\pi\) | |||||||
\(644\) | −845.913 | −0.0517603 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4677.13 | −0.284859 | ||||||||
\(647\) | 15035.4 | 0.913603 | 0.456801 | − | 0.889569i | \(-0.348995\pi\) | ||||
0.456801 | + | 0.889569i | \(0.348995\pi\) | |||||||
\(648\) | −3800.47 | −0.230396 | ||||||||
\(649\) | 639.339 | 0.0386691 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 398.375 | 0.0239839 | ||||||||
\(652\) | −1150.63 | −0.0691135 | ||||||||
\(653\) | 22403.7 | 1.34261 | 0.671307 | − | 0.741180i | \(-0.265733\pi\) | ||||
0.671307 | + | 0.741180i | \(0.265733\pi\) | |||||||
\(654\) | 716.505 | 0.0428403 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2045.16 | −0.121723 | ||||||||
\(657\) | 17812.2 | 1.05772 | ||||||||
\(658\) | −11178.5 | −0.662287 | ||||||||
\(659\) | 890.918 | 0.0526635 | 0.0263317 | − | 0.999653i | \(-0.491617\pi\) | ||||
0.0263317 | + | 0.999653i | \(0.491617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28636.0 | −1.68504 | −0.842519 | − | 0.538667i | \(-0.818928\pi\) | ||||
−0.842519 | + | 0.538667i | \(0.818928\pi\) | |||||||
\(662\) | −2393.58 | −0.140527 | ||||||||
\(663\) | 1066.11 | 0.0624499 | ||||||||
\(664\) | −7201.50 | −0.420892 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13982.2 | 0.813515 | ||||||||
\(667\) | 3373.70 | 0.195847 | ||||||||
\(668\) | 5182.16 | 0.300155 | ||||||||
\(669\) | 10506.2 | 0.607164 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20664.8 | −1.18890 | ||||||||
\(672\) | −531.805 | −0.0305280 | ||||||||
\(673\) | −15056.8 | −0.862405 | −0.431203 | − | 0.902255i | \(-0.641911\pi\) | ||||
−0.431203 | + | 0.902255i | \(0.641911\pi\) | |||||||
\(674\) | −6490.84 | −0.370946 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6149.66 | −0.349890 | ||||||||
\(677\) | 1612.72 | 0.0915539 | 0.0457770 | − | 0.998952i | \(-0.485424\pi\) | ||||
0.0457770 | + | 0.998952i | \(0.485424\pi\) | |||||||
\(678\) | −3139.72 | −0.177847 | ||||||||
\(679\) | 1546.83 | 0.0874253 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3675.06 | 0.206797 | ||||||||
\(682\) | −2070.25 | −0.116238 | ||||||||
\(683\) | −20264.3 | −1.13527 | −0.567637 | − | 0.823279i | \(-0.692142\pi\) | ||||
−0.567637 | + | 0.823279i | \(0.692142\pi\) | |||||||
\(684\) | −9666.33 | −0.540353 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 11060.5 | 0.615583 | ||||||||
\(687\) | −787.868 | −0.0437540 | ||||||||
\(688\) | −8033.15 | −0.445147 | ||||||||
\(689\) | 17316.4 | 0.957481 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7628.56 | −0.419977 | −0.209988 | − | 0.977704i | \(-0.567343\pi\) | ||||
−0.209988 | + | 0.977704i | \(0.567343\pi\) | |||||||
\(692\) | −5253.85 | −0.288615 | ||||||||
\(693\) | −9423.19 | −0.516533 | ||||||||
\(694\) | −21020.1 | −1.14973 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2120.96 | 0.115510 | ||||||||
\(697\) | −2935.69 | −0.159537 | ||||||||
\(698\) | −12300.0 | −0.666997 | ||||||||
\(699\) | −2859.46 | −0.154728 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18206.5 | 0.980953 | 0.490477 | − | 0.871454i | \(-0.336823\pi\) | ||||
0.490477 | + | 0.871454i | \(0.336823\pi\) | |||||||
\(702\) | 4710.00 | 0.253230 | ||||||||
\(703\) | 29994.2 | 1.60918 | ||||||||
\(704\) | 2763.66 | 0.147953 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2246.70 | −0.119767 | ||||||||
\(707\) | −5824.02 | −0.309809 | ||||||||
\(708\) | 107.041 | 0.00568200 | ||||||||
\(709\) | 14793.4 | 0.783607 | 0.391804 | − | 0.920049i | \(-0.371851\pi\) | ||||
0.391804 | + | 0.920049i | \(0.371851\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15228.3 | 0.803245 | ||||||||
\(712\) | 7390.16 | 0.388986 | ||||||||
\(713\) | −551.337 | −0.0289590 | ||||||||
\(714\) | −763.370 | −0.0400118 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7665.49 | 0.400102 | ||||||||
\(717\) | −3131.57 | −0.163111 | ||||||||
\(718\) | −4418.92 | −0.229683 | ||||||||
\(719\) | 32215.9 | 1.67100 | 0.835500 | − | 0.549490i | \(-0.185178\pi\) | ||||
0.835500 | + | 0.549490i | \(0.185178\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11958.9 | 0.617716 | ||||||||
\(722\) | −7017.86 | −0.361742 | ||||||||
\(723\) | −8028.17 | −0.412961 | ||||||||
\(724\) | 17773.3 | 0.912345 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1929.25 | −0.0986242 | ||||||||
\(727\) | 1853.37 | 0.0945497 | 0.0472748 | − | 0.998882i | \(-0.484946\pi\) | ||||
0.0472748 | + | 0.998882i | \(0.484946\pi\) | |||||||
\(728\) | −1889.14 | −0.0961759 | ||||||||
\(729\) | −6799.73 | −0.345462 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11531.1 | −0.583436 | ||||||||
\(732\) | −3459.80 | −0.174696 | ||||||||
\(733\) | 6958.47 | 0.350637 | 0.175319 | − | 0.984512i | \(-0.443904\pi\) | ||||
0.175319 | + | 0.984512i | \(0.443904\pi\) | |||||||
\(734\) | 18035.3 | 0.906940 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 19795.6 | 0.989392 | ||||||||
\(738\) | −6067.26 | −0.302628 | ||||||||
\(739\) | 6469.54 | 0.322038 | 0.161019 | − | 0.986951i | \(-0.448522\pi\) | ||||
0.161019 | + | 0.986951i | \(0.448522\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4726.56 | 0.234325 | ||||||||
\(742\) | −12399.1 | −0.613460 | ||||||||
\(743\) | 6992.55 | 0.345265 | 0.172632 | − | 0.984986i | \(-0.444773\pi\) | ||||
0.172632 | + | 0.984986i | \(0.444773\pi\) | |||||||
\(744\) | −346.612 | −0.0170799 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4001.04 | −0.196365 | ||||||||
\(747\) | −21364.3 | −1.04642 | ||||||||
\(748\) | 3967.05 | 0.193917 | ||||||||
\(749\) | −4557.08 | −0.222313 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24595.2 | 1.19506 | 0.597531 | − | 0.801846i | \(-0.296148\pi\) | ||||
0.597531 | + | 0.801846i | \(0.296148\pi\) | |||||||
\(752\) | 9726.06 | 0.471639 | ||||||||
\(753\) | 8521.25 | 0.412393 | ||||||||
\(754\) | 7534.30 | 0.363903 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3372.52 | −0.162245 | ||||||||
\(757\) | −35778.4 | −1.71782 | −0.858909 | − | 0.512128i | \(-0.828857\pi\) | ||||
−0.858909 | + | 0.512128i | \(0.828857\pi\) | |||||||
\(758\) | −10809.7 | −0.517975 | ||||||||
\(759\) | −1795.13 | −0.0858486 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39181.2 | −1.86638 | −0.933191 | − | 0.359380i | \(-0.882988\pi\) | ||||
−0.933191 | + | 0.359380i | \(0.882988\pi\) | |||||||
\(762\) | −7780.37 | −0.369886 | ||||||||
\(763\) | −1822.48 | −0.0864722 | ||||||||
\(764\) | 7614.18 | 0.360564 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18711.7 | 0.882610 | ||||||||
\(767\) | 380.244 | 0.0179007 | ||||||||
\(768\) | 462.705 | 0.0217401 | ||||||||
\(769\) | 9455.39 | 0.443394 | 0.221697 | − | 0.975116i | \(-0.428840\pi\) | ||||
0.221697 | + | 0.975116i | \(0.428840\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7644.41 | 0.357077 | ||||||||
\(772\) | 13670.4 | 0.637317 | ||||||||
\(773\) | 5683.75 | 0.264464 | 0.132232 | − | 0.991219i | \(-0.457786\pi\) | ||||
0.132232 | + | 0.991219i | \(0.457786\pi\) | |||||||
\(774\) | −23831.5 | −1.10673 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1345.84 | −0.0622588 | ||||||||
\(777\) | 4895.46 | 0.226028 | ||||||||
\(778\) | −15542.5 | −0.716228 | ||||||||
\(779\) | −13015.3 | −0.598615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43736.0 | 2.00384 | ||||||||
\(782\) | 1056.48 | 0.0483116 | ||||||||
\(783\) | 13450.4 | 0.613891 | ||||||||
\(784\) | −4135.32 | −0.188380 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6240.32 | −0.283187 | ||||||||
\(787\) | 18500.7 | 0.837966 | 0.418983 | − | 0.907994i | \(-0.362387\pi\) | ||||
0.418983 | + | 0.907994i | \(0.362387\pi\) | |||||||
\(788\) | 6438.28 | 0.291059 | ||||||||
\(789\) | 8763.91 | 0.395442 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7986.11 | 0.358980 | ||||||||
\(792\) | 8198.79 | 0.367842 | ||||||||
\(793\) | −12290.3 | −0.550366 | ||||||||
\(794\) | 5018.58 | 0.224311 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18075.6 | −0.804866 | ||||||||
\(797\) | −30464.4 | −1.35396 | −0.676979 | − | 0.736002i | \(-0.736711\pi\) | ||||
−0.676979 | + | 0.736002i | \(0.736711\pi\) | |||||||
\(798\) | −3384.37 | −0.150132 | ||||||||
\(799\) | 13961.1 | 0.618159 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21924.0 | 0.967099 | ||||||||
\(802\) | −3005.42 | −0.132325 | ||||||||
\(803\) | −32409.1 | −1.42427 | ||||||||
\(804\) | 3314.28 | 0.145380 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1231.27 | −0.0538087 | ||||||||
\(807\) | 8320.80 | 0.362957 | ||||||||
\(808\) | 5067.28 | 0.220626 | ||||||||
\(809\) | −20168.5 | −0.876500 | −0.438250 | − | 0.898853i | \(-0.644401\pi\) | ||||
−0.438250 | + | 0.898853i | \(0.644401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3472.00 | 0.150331 | 0.0751655 | − | 0.997171i | \(-0.476051\pi\) | ||||
0.0751655 | + | 0.997171i | \(0.476051\pi\) | |||||||
\(812\) | −5394.81 | −0.233154 | ||||||||
\(813\) | −2749.68 | −0.118617 | ||||||||
\(814\) | −25440.5 | −1.09544 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 664.182 | 0.0284939 | ||||||||
\(817\) | −51122.5 | −2.18917 | ||||||||
\(818\) | −12563.1 | −0.536990 | ||||||||
\(819\) | −5604.39 | −0.239113 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7377.27 | 0.313603 | 0.156802 | − | 0.987630i | \(-0.449882\pi\) | ||||
0.156802 | + | 0.987630i | \(0.449882\pi\) | |||||||
\(822\) | 6402.27 | 0.271660 | ||||||||
\(823\) | 19960.3 | 0.845411 | 0.422705 | − | 0.906267i | \(-0.361081\pi\) | ||||
0.422705 | + | 0.906267i | \(0.361081\pi\) | |||||||
\(824\) | −10405.0 | −0.439899 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −272.267 | −0.0114690 | ||||||||
\(827\) | 3105.37 | 0.130574 | 0.0652868 | − | 0.997867i | \(-0.479204\pi\) | ||||
0.0652868 | + | 0.997867i | \(0.479204\pi\) | |||||||
\(828\) | 2183.45 | 0.0916427 | ||||||||
\(829\) | −10780.3 | −0.451646 | −0.225823 | − | 0.974168i | \(-0.572507\pi\) | ||||
−0.225823 | + | 0.974168i | \(0.572507\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5953.23 | −0.248514 | ||||||||
\(832\) | 1643.67 | 0.0684905 | ||||||||
\(833\) | −5935.98 | −0.246902 | ||||||||
\(834\) | −10082.2 | −0.418606 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17587.7 | 0.727613 | ||||||||
\(837\) | −2198.09 | −0.0907731 | ||||||||
\(838\) | 10875.0 | 0.448293 | ||||||||
\(839\) | 2884.27 | 0.118684 | 0.0593422 | − | 0.998238i | \(-0.481100\pi\) | ||||
0.0593422 | + | 0.998238i | \(0.481100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2873.26 | −0.117810 | ||||||||
\(842\) | −16848.2 | −0.689582 | ||||||||
\(843\) | 16010.1 | 0.654111 | ||||||||
\(844\) | 21634.6 | 0.882337 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 28853.8 | 1.17259 | ||||||||
\(847\) | 4907.18 | 0.199071 | ||||||||
\(848\) | 10788.1 | 0.436868 | ||||||||
\(849\) | −9887.50 | −0.399691 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6775.15 | −0.272913 | ||||||||
\(852\) | 7322.49 | 0.294442 | ||||||||
\(853\) | 13694.1 | 0.549681 | 0.274841 | − | 0.961490i | \(-0.411375\pi\) | ||||
0.274841 | + | 0.961490i | \(0.411375\pi\) | |||||||
\(854\) | 8800.24 | 0.352621 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3964.96 | 0.158317 | ||||||||
\(857\) | 31610.2 | 1.25996 | 0.629978 | − | 0.776613i | \(-0.283064\pi\) | ||||
0.629978 | + | 0.776613i | \(0.283064\pi\) | |||||||
\(858\) | −4008.97 | −0.159515 | ||||||||
\(859\) | −20316.3 | −0.806964 | −0.403482 | − | 0.914988i | \(-0.632200\pi\) | ||||
−0.403482 | + | 0.914988i | \(0.632200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2124.27 | −0.0840823 | ||||||||
\(862\) | 4560.37 | 0.180194 | ||||||||
\(863\) | 9902.42 | 0.390593 | 0.195297 | − | 0.980744i | \(-0.437433\pi\) | ||||
0.195297 | + | 0.980744i | \(0.437433\pi\) | |||||||
\(864\) | 2934.31 | 0.115541 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19353.8 | 0.759433 | ||||||||
\(867\) | −7926.56 | −0.310496 | ||||||||
\(868\) | 881.633 | 0.0344753 | ||||||||
\(869\) | −27707.7 | −1.08161 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11773.4 | 0.458008 | ||||||||
\(872\) | 1585.68 | 0.0615801 | ||||||||
\(873\) | −3992.63 | −0.154788 | ||||||||
\(874\) | 4683.86 | 0.181275 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5426.09 | −0.209281 | ||||||||
\(877\) | 11027.7 | 0.424606 | 0.212303 | − | 0.977204i | \(-0.431904\pi\) | ||||
0.212303 | + | 0.977204i | \(0.431904\pi\) | |||||||
\(878\) | 20535.2 | 0.789326 | ||||||||
\(879\) | 1137.96 | 0.0436661 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27892.8 | −1.06667 | −0.533333 | − | 0.845906i | \(-0.679061\pi\) | ||||
−0.533333 | + | 0.845906i | \(0.679061\pi\) | |||||||
\(882\) | −12268.0 | −0.468351 | ||||||||
\(883\) | 1618.76 | 0.0616937 | 0.0308468 | − | 0.999524i | \(-0.490180\pi\) | ||||
0.0308468 | + | 0.999524i | \(0.490180\pi\) | |||||||
\(884\) | 2359.38 | 0.0897677 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5895.40 | −0.223544 | ||||||||
\(887\) | −9518.69 | −0.360323 | −0.180161 | − | 0.983637i | \(-0.557662\pi\) | ||||
−0.180161 | + | 0.983637i | \(0.557662\pi\) | |||||||
\(888\) | −4259.37 | −0.160963 | ||||||||
\(889\) | 19789.9 | 0.746606 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 20514.0 | 0.771319 | ||||||||
\(892\) | 23251.0 | 0.872758 | ||||||||
\(893\) | 61896.0 | 2.31945 | ||||||||
\(894\) | 7916.78 | 0.296171 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1176.92 | −0.0438820 | ||||||||
\(897\) | −1067.64 | −0.0397409 | ||||||||
\(898\) | 28644.5 | 1.06445 | ||||||||
\(899\) | −3516.15 | −0.130445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15485.6 | 0.572585 | ||||||||
\(902\) | 11039.3 | 0.407504 | ||||||||
\(903\) | −8343.87 | −0.307494 | ||||||||
\(904\) | −6948.44 | −0.255643 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5673.87 | 0.208059 | ||||||||
\(907\) | 9580.94 | 0.350750 | 0.175375 | − | 0.984502i | \(-0.443886\pi\) | ||||
0.175375 | + | 0.984502i | \(0.443886\pi\) | |||||||
\(908\) | 8133.18 | 0.297257 | ||||||||
\(909\) | 15032.8 | 0.548522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18016.6 | −0.655232 | −0.327616 | − | 0.944811i | \(-0.606245\pi\) | ||||
−0.327616 | + | 0.944811i | \(0.606245\pi\) | |||||||
\(912\) | 2944.62 | 0.106915 | ||||||||
\(913\) | 38872.0 | 1.40906 | ||||||||
\(914\) | 26808.8 | 0.970192 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1743.61 | −0.0628936 | ||||||||
\(917\) | 15872.7 | 0.571606 | ||||||||
\(918\) | 4212.01 | 0.151435 | ||||||||
\(919\) | −36712.5 | −1.31777 | −0.658887 | − | 0.752242i | \(-0.728973\pi\) | ||||
−0.658887 | + | 0.752242i | \(0.728973\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1431.36 | −0.0512107 | ||||||||
\(922\) | 33857.2 | 1.20936 | ||||||||
\(923\) | 26011.8 | 0.927614 | ||||||||
\(924\) | 2870.56 | 0.102202 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26218.5 | 0.930447 | ||||||||
\(927\) | −30868.1 | −1.09368 | ||||||||
\(928\) | 4693.84 | 0.166037 | ||||||||
\(929\) | 4117.08 | 0.145400 | 0.0727002 | − | 0.997354i | \(-0.476838\pi\) | ||||
0.0727002 | + | 0.997354i | \(0.476838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26316.9 | −0.926425 | ||||||||
\(932\) | −6328.20 | −0.222411 | ||||||||
\(933\) | 3812.36 | 0.133774 | ||||||||
\(934\) | −9352.04 | −0.327632 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4876.19 | 0.170281 | ||||||||
\(937\) | −11540.5 | −0.402362 | −0.201181 | − | 0.979554i | \(-0.564478\pi\) | ||||
−0.201181 | + | 0.979554i | \(0.564478\pi\) | |||||||
\(938\) | −8430.12 | −0.293447 | ||||||||
\(939\) | −375.225 | −0.0130405 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8600.43 | −0.297945 | −0.148972 | − | 0.988841i | \(-0.547597\pi\) | ||||
−0.148972 | + | 0.988841i | \(0.547597\pi\) | |||||||
\(942\) | −9521.08 | −0.329314 | ||||||||
\(943\) | 2939.92 | 0.101524 | ||||||||
\(944\) | 236.890 | 0.00816750 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 43361.0 | 1.49026 | ||||||||
\(947\) | 48782.8 | 1.67395 | 0.836974 | − | 0.547243i | \(-0.184323\pi\) | ||||
0.836974 | + | 0.547243i | \(0.184323\pi\) | |||||||
\(948\) | −4638.96 | −0.158931 | ||||||||
\(949\) | −19275.2 | −0.659324 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7255.00 | −0.247381 | ||||||||
\(952\) | −1689.40 | −0.0575143 | ||||||||
\(953\) | 42550.4 | 1.44632 | 0.723160 | − | 0.690681i | \(-0.242689\pi\) | ||||
0.723160 | + | 0.690681i | \(0.242689\pi\) | |||||||
\(954\) | 32004.4 | 1.08614 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6930.40 | −0.234461 | ||||||||
\(957\) | −11448.4 | −0.386704 | ||||||||
\(958\) | 27036.1 | 0.911791 | ||||||||
\(959\) | −16284.6 | −0.548341 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29216.4 | −0.980712 | ||||||||
\(962\) | −15130.6 | −0.507100 | ||||||||
\(963\) | 11762.6 | 0.393609 | ||||||||
\(964\) | −17766.9 | −0.593604 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 764.469 | 0.0254621 | ||||||||
\(967\) | −25119.6 | −0.835360 | −0.417680 | − | 0.908594i | \(-0.637157\pi\) | ||||
−0.417680 | + | 0.908594i | \(0.637157\pi\) | |||||||
\(968\) | −4269.57 | −0.141766 | ||||||||
\(969\) | 4226.82 | 0.140129 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11624.9 | 0.384204 | 0.192102 | − | 0.981375i | \(-0.438470\pi\) | ||||
0.192102 | + | 0.981375i | \(0.438470\pi\) | |||||||
\(972\) | 13337.8 | 0.440136 | ||||||||
\(973\) | 25644.8 | 0.844947 | ||||||||
\(974\) | 29829.3 | 0.981308 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7656.78 | −0.251114 | ||||||||
\(977\) | −15427.4 | −0.505187 | −0.252593 | − | 0.967573i | \(-0.581283\pi\) | ||||
−0.252593 | + | 0.967573i | \(0.581283\pi\) | |||||||
\(978\) | 1039.84 | 0.0339985 | ||||||||
\(979\) | −39890.4 | −1.30225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4704.14 | 0.153101 | ||||||||
\(982\) | 7413.99 | 0.240927 | ||||||||
\(983\) | −42012.4 | −1.36316 | −0.681580 | − | 0.731744i | \(-0.738707\pi\) | ||||
−0.681580 | + | 0.731744i | \(0.738707\pi\) | |||||||
\(984\) | 1848.25 | 0.0598782 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6737.70 | 0.217619 | ||||||||
\(987\) | 10102.3 | 0.325794 | ||||||||
\(988\) | 10460.2 | 0.336826 | ||||||||
\(989\) | 11547.6 | 0.371278 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30889.0 | 0.990132 | 0.495066 | − | 0.868855i | \(-0.335144\pi\) | ||||
0.495066 | + | 0.868855i | \(0.335144\pi\) | |||||||
\(992\) | −767.078 | −0.0245512 | ||||||||
\(993\) | 2163.13 | 0.0691286 | ||||||||
\(994\) | −18625.3 | −0.594324 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6508.14 | 0.207046 | ||||||||
\(997\) | 10011.2 | 0.318011 | 0.159005 | − | 0.987278i | \(-0.449171\pi\) | ||||
0.159005 | + | 0.987278i | \(0.449171\pi\) | |||||||
\(998\) | −26073.9 | −0.827009 | ||||||||
\(999\) | −27011.4 | −0.855458 |
(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 | 1150.4.a.s.1.3 | ✓ | 5 | |
5.2 | odd | 4 | 1150.4.b.p.599.3 | 10 | |||
5.3 | odd | 4 | 1150.4.b.p.599.8 | 10 | |||
5.4 | even | 2 | 1150.4.a.t.1.3 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1150.4.a.s.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1150.4.a.t.1.3 | yes | 5 | 5.4 | even | 2 | ||
1150.4.b.p.599.3 | 10 | 5.2 | odd | 4 | |||
1150.4.b.p.599.8 | 10 | 5.3 | odd | 4 |