Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 672) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.31662\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.6332 | −0.951067 | −0.475533 | − | 0.879698i | \(-0.657745\pi\) | ||||
−0.475533 | + | 0.879698i | \(0.657745\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 68.4327 | 1.87575 | 0.937875 | − | 0.346973i | \(-0.112791\pi\) | ||||
0.937875 | + | 0.346973i | \(0.112791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.0660 | −0.492104 | −0.246052 | − | 0.969257i | \(-0.579133\pi\) | ||||
−0.246052 | + | 0.969257i | \(0.579133\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 31.8997 | 0.549099 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −62.2322 | −0.887855 | −0.443928 | − | 0.896063i | \(-0.646415\pi\) | ||||
−0.443928 | + | 0.896063i | \(0.646415\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 53.2665 | 0.643167 | 0.321583 | − | 0.946881i | \(-0.395785\pi\) | ||||
0.321583 | + | 0.946881i | \(0.395785\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −89.8997 | −0.815017 | −0.407509 | − | 0.913201i | \(-0.633602\pi\) | ||||
−0.407509 | + | 0.913201i | \(0.633602\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.9340 | −0.0954720 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 43.2665 | 0.277048 | 0.138524 | − | 0.990359i | \(-0.455764\pi\) | ||||
0.138524 | + | 0.990359i | \(0.455764\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −102.734 | −0.595209 | −0.297605 | − | 0.954689i | \(-0.596188\pi\) | ||||
−0.297605 | + | 0.954689i | \(0.596188\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −205.298 | −1.08296 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 74.4327 | 0.359469 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 302.264 | 1.34302 | 0.671512 | − | 0.740994i | \(-0.265645\pi\) | ||||
0.671512 | + | 0.740994i | \(0.265645\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 69.1980 | 0.284117 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 73.4302 | 0.279704 | 0.139852 | − | 0.990172i | \(-0.455337\pi\) | ||||
0.139852 | + | 0.990172i | \(0.455337\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −377.330 | −1.33819 | −0.669096 | − | 0.743176i | \(-0.733319\pi\) | ||||
−0.669096 | + | 0.743176i | \(0.733319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −95.6992 | −0.317022 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −487.662 | −1.51347 | −0.756733 | − | 0.653724i | \(-0.773206\pi\) | ||||
−0.756733 | + | 0.653724i | \(0.773206\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 186.697 | 0.512603 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −467.594 | −1.21187 | −0.605934 | − | 0.795515i | \(-0.707200\pi\) | ||||
−0.605934 | + | 0.795515i | \(0.707200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −727.662 | −1.78396 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −159.799 | −0.371333 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −432.327 | −0.953970 | −0.476985 | − | 0.878911i | \(-0.658270\pi\) | ||||
−0.476985 | + | 0.878911i | \(0.658270\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 70.4645 | 0.147903 | 0.0739513 | − | 0.997262i | \(-0.476439\pi\) | ||||
0.0739513 | + | 0.997262i | \(0.476439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 245.266 | 0.468024 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 475.799 | 0.867584 | 0.433792 | − | 0.901013i | \(-0.357175\pi\) | ||||
0.433792 | + | 0.901013i | \(0.357175\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 269.699 | 0.470550 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 680.824 | 1.13801 | 0.569006 | − | 0.822333i | \(-0.307328\pi\) | ||||
0.569006 | + | 0.822333i | \(0.307328\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 604.069 | 0.968505 | 0.484253 | − | 0.874928i | \(-0.339092\pi\) | ||||
0.484253 | + | 0.874928i | \(0.339092\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 35.8020 | 0.0551208 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −479.029 | −0.708967 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −329.140 | −0.468748 | −0.234374 | − | 0.972147i | \(-0.575304\pi\) | ||||
−0.234374 | + | 0.972147i | \(0.575304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 834.670 | 1.10382 | 0.551909 | − | 0.833904i | \(-0.313899\pi\) | ||||
0.551909 | + | 0.833904i | \(0.313899\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 661.731 | 0.844409 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −129.799 | −0.159954 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −947.890 | −1.12895 | −0.564473 | − | 0.825452i | \(-0.690920\pi\) | ||||
−0.564473 | + | 0.825452i | \(0.690920\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 161.462 | 0.185998 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 308.201 | 0.343644 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −566.396 | −0.611695 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 661.272 | 0.692185 | 0.346093 | − | 0.938200i | \(-0.387508\pi\) | ||||
0.346093 | + | 0.938200i | \(0.387508\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 615.895 | 0.625250 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 745.293 | 0.734252 | 0.367126 | − | 0.930171i | \(-0.380342\pi\) | ||||
0.367126 | + | 0.930171i | \(0.380342\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −863.261 | −0.825822 | −0.412911 | − | 0.910771i | \(-0.635488\pi\) | ||||
−0.412911 | + | 0.910771i | \(0.635488\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −223.298 | −0.207540 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1198.42 | 1.08276 | 0.541380 | − | 0.840778i | \(-0.317902\pi\) | ||||
0.541380 | + | 0.840778i | \(0.317902\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 84.1320 | 0.0739301 | 0.0369651 | − | 0.999317i | \(-0.488231\pi\) | ||||
0.0369651 | + | 0.999317i | \(0.488231\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −906.792 | −0.775395 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2030.12 | 1.69006 | 0.845032 | − | 0.534715i | \(-0.179581\pi\) | ||||
0.845032 | + | 0.534715i | \(0.179581\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 955.926 | 0.775136 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −207.594 | −0.164035 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 435.626 | 0.335578 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3352.04 | 2.51844 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −220.291 | −0.161487 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1456.05 | 1.04187 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1363.12 | −0.952423 | −0.476212 | − | 0.879331i | \(-0.657990\pi\) | ||||
−0.476212 | + | 0.879331i | \(0.657990\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1131.99 | 0.772606 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1115.20 | 0.743781 | 0.371890 | − | 0.928277i | \(-0.378710\pi\) | ||||
0.371890 | + | 0.928277i | \(0.378710\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −372.865 | −0.243094 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 287.098 | 0.183033 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 361.536 | 0.225460 | 0.112730 | − | 0.993626i | \(-0.464040\pi\) | ||||
0.112730 | + | 0.993626i | \(0.464040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 426.543 | 0.260280 | 0.130140 | − | 0.991496i | \(-0.458457\pi\) | ||||
0.130140 | + | 0.991496i | \(0.458457\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1462.99 | 0.873800 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1578.47 | −0.923065 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −460.063 | −0.263491 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2861.46 | 1.57329 | 0.786645 | − | 0.617406i | \(-0.211816\pi\) | ||||
0.786645 | + | 0.617406i | \(0.211816\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 816.127 | 0.439838 | 0.219919 | − | 0.975518i | \(-0.429421\pi\) | ||||
0.219919 | + | 0.975518i | \(0.429421\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −560.090 | −0.295952 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1092.39 | 0.566084 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3243.63 | −1.64885 | −0.824426 | − | 0.565970i | \(-0.808502\pi\) | ||||
−0.824426 | + | 0.565970i | \(0.808502\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1402.78 | 0.699672 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 629.298 | 0.308048 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3363.76 | −1.61638 | −0.808190 | − | 0.588922i | \(-0.799553\pi\) | ||||
−0.808190 | + | 0.588922i | \(0.799553\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2182.99 | 1.02997 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1352.59 | −0.626747 | −0.313373 | − | 0.949630i | \(-0.601459\pi\) | ||||
−0.313373 | + | 0.949630i | \(0.601459\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1664.96 | −0.757833 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 479.398 | 0.214389 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3491.30 | 1.53433 | 0.767163 | − | 0.641452i | \(-0.221668\pi\) | ||||
0.767163 | + | 0.641452i | \(0.221668\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 83.5380 | 0.0360850 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1296.98 | 0.550775 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2547.82 | 1.06387 | 0.531936 | − | 0.846785i | \(-0.321465\pi\) | ||||
0.531936 | + | 0.846785i | \(0.321465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 358.254 | 0.147120 | 0.0735602 | − | 0.997291i | \(-0.476564\pi\) | ||||
0.0735602 | + | 0.997291i | \(0.476564\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −211.393 | −0.0853916 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3214.05 | −1.27731 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4258.72 | −1.66539 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2139.78 | 0.810622 | 0.405311 | − | 0.914179i | \(-0.367163\pi\) | ||||
0.405311 | + | 0.914179i | \(0.367163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2183.47 | 0.814349 | 0.407175 | − | 0.913350i | \(-0.366514\pi\) | ||||
0.407175 | + | 0.913350i | \(0.366514\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −735.799 | −0.270214 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1536.25 | 0.555600 | 0.277800 | − | 0.960639i | \(-0.410395\pi\) | ||||
0.277800 | + | 0.960639i | \(0.410395\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3413.15 | −1.21584 | −0.607920 | − | 0.793999i | \(-0.707996\pi\) | ||||
−0.607920 | + | 0.793999i | \(0.707996\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1427.40 | −0.500900 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −302.865 | −0.104714 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −780.802 | −0.266017 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −809.098 | −0.271672 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3645.17 | 1.20642 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2045.57 | 0.667408 | 0.333704 | − | 0.942678i | \(-0.391701\pi\) | ||||
0.333704 | + | 0.942678i | \(0.391701\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2042.47 | −0.657032 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4012.24 | 1.27271 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 719.135 | 0.224968 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1812.21 | −0.559167 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1435.45 | 0.436917 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4769.00 | 1.43209 | 0.716044 | − | 0.698055i | \(-0.245951\pi\) | ||||
0.716044 | + | 0.698055i | \(0.245951\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −107.406 | −0.0318240 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3817.49 | −1.11619 | −0.558096 | − | 0.829776i | \(-0.688468\pi\) | ||||
−0.558096 | + | 0.829776i | \(0.688468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −288.289 | −0.0831907 | −0.0415954 | − | 0.999135i | \(-0.513244\pi\) | ||||
−0.0415954 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1437.09 | 0.409322 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.15461 | 0.00257398 | 0.00128699 | − | 0.999999i | \(-0.499590\pi\) | ||||
0.00128699 | + | 0.999999i | \(0.499590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5185.44 | 1.43941 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 987.419 | 0.270632 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6630.35 | 1.79449 | 0.897243 | − | 0.441538i | \(-0.145567\pi\) | ||||
0.897243 | + | 0.441538i | \(0.145567\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6727.26 | 1.79809 | 0.899047 | − | 0.437852i | \(-0.144261\pi\) | ||||
0.899047 | + | 0.437852i | \(0.144261\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −521.029 | −0.135867 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1228.64 | −0.316505 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2504.01 | −0.637290 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 877.794 | 0.220741 | 0.110370 | − | 0.993891i | \(-0.464796\pi\) | ||||
0.110370 | + | 0.993891i | \(0.464796\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6152.09 | −1.52877 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1985.19 | −0.487520 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6332.65 | −1.53704 | −0.768521 | − | 0.639824i | \(-0.779007\pi\) | ||||
−0.768521 | + | 0.639824i | \(0.779007\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2115.85 | −0.507615 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 389.398 | 0.0923493 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3614.23 | 0.847387 | 0.423694 | − | 0.905806i | \(-0.360733\pi\) | ||||
0.423694 | + | 0.905806i | \(0.360733\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4972.04 | 1.15257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2843.67 | 0.651797 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7114.90 | 1.61265 | 0.806326 | − | 0.591472i | \(-0.201453\pi\) | ||||
0.806326 | + | 0.591472i | \(0.201453\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −547.378 | −0.122697 | −0.0613485 | − | 0.998116i | \(-0.519540\pi\) | ||||
−0.0613485 | + | 0.998116i | \(0.519540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −484.386 | −0.107386 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −816.677 | −0.179082 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5726.12 | 1.24205 | 0.621027 | − | 0.783789i | \(-0.286716\pi\) | ||||
0.621027 | + | 0.783789i | \(0.286716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −924.602 | −0.198403 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 237.378 | 0.0503943 | 0.0251972 | − | 0.999683i | \(-0.491979\pi\) | ||||
0.0251972 | + | 0.999683i | \(0.491979\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3179.66 | −0.667885 | −0.333942 | − | 0.942594i | \(-0.608379\pi\) | ||||
−0.333942 | + | 0.942594i | \(0.608379\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1699.19 | 0.353162 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −514.012 | −0.105718 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1040.15 | −0.211713 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1983.81 | −0.399633 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7757.59 | −1.54677 | −0.773384 | − | 0.633937i | \(-0.781438\pi\) | ||||
−0.773384 | + | 0.633937i | \(0.781438\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4597.05 | 0.907289 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1847.68 | −0.360988 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2073.63 | 0.401073 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2641.31 | 0.505789 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2235.88 | −0.423921 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −749.266 | −0.140665 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8587.01 | 1.59637 | 0.798187 | − | 0.602410i | \(-0.205793\pi\) | ||||
0.798187 | + | 0.602410i | \(0.205793\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2589.78 | 0.476789 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3889.43 | 0.709163 | 0.354581 | − | 0.935025i | \(-0.384623\pi\) | ||||
0.354581 | + | 0.935025i | \(0.384623\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8408.84 | 1.51852 | 0.759259 | − | 0.650789i | \(-0.225562\pi\) | ||||
0.759259 | + | 0.650789i | \(0.225562\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 669.895 | 0.119823 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5651.73 | 1.00137 | 0.500683 | − | 0.865631i | \(-0.333082\pi\) | ||||
0.500683 | + | 0.865631i | \(0.333082\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2960.85 | 0.519672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3595.25 | −0.625132 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3314.89 | −0.571039 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 275.270 | 0.0469822 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −252.396 | −0.0426836 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3413.64 | 0.572036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7993.33 | −1.32735 | −0.663675 | − | 0.748021i | \(-0.731004\pi\) | ||||
−0.663675 | + | 0.748021i | \(0.731004\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2720.38 | 0.447675 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5059.29 | −0.825131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8193.32 | 1.32439 | 0.662194 | − | 0.749332i | \(-0.269625\pi\) | ||||
0.662194 | + | 0.749332i | \(0.269625\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6090.35 | −0.975759 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7030.34 | −1.11646 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2867.78 | −0.447525 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8551.14 | −1.32291 | −0.661454 | − | 0.749986i | \(-0.730060\pi\) | ||||
−0.661454 | + | 0.749986i | \(0.730060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5411.94 | −0.830070 | −0.415035 | − | 0.909805i | \(-0.636231\pi\) | ||||
−0.415035 | + | 0.909805i | \(0.636231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 622.782 | 0.0947055 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11454.0 | 1.72701 | 0.863505 | − | 0.504340i | \(-0.168264\pi\) | ||||
0.863505 | + | 0.504340i | \(0.168264\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7239.37 | −1.08233 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1306.88 | −0.193746 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −268.349 | −0.0394511 | −0.0197255 | − | 0.999805i | \(-0.506279\pi\) | ||||
−0.0197255 | + | 0.999805i | \(0.506279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4021.68 | −0.586336 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10056.1 | −1.45402 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6423.21 | −0.921113 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5471.90 | 0.778286 | 0.389143 | − | 0.921177i | \(-0.372771\pi\) | ||||
0.389143 | + | 0.921177i | \(0.372771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 660.872 | 0.0932348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3273.16 | 0.458043 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6921.68 | −0.960833 | −0.480417 | − | 0.877040i | \(-0.659515\pi\) | ||||
−0.480417 | + | 0.877040i | \(0.659515\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4368.16 | −0.601522 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −997.985 | −0.136336 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11178.3 | −1.51502 | −0.757508 | − | 0.652826i | \(-0.773583\pi\) | ||||
−0.757508 | + | 0.652826i | \(0.773583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4089.37 | 0.549882 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13507.1 | −1.80204 | −0.901020 | − | 0.433779i | \(-0.857180\pi\) | ||||
−0.901020 | + | 0.433779i | \(0.857180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5093.64 | 0.674275 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3395.97 | −0.446064 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12818.4 | 1.67075 | 0.835373 | − | 0.549684i | \(-0.185252\pi\) | ||||
0.835373 | + | 0.549684i | \(0.185252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5594.66 | 0.723617 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3345.59 | −0.429422 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3499.82 | 0.445811 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7832.26 | 0.990151 | 0.495076 | − | 0.868850i | \(-0.335140\pi\) | ||||
0.495076 | + | 0.868850i | \(0.335140\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1118.60 | 0.140351 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7603.91 | −0.946936 | −0.473468 | − | 0.880811i | \(-0.656998\pi\) | ||||
−0.473468 | + | 0.880811i | \(0.656998\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2369.65 | 0.292905 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −861.293 | −0.105674 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20684.8 | 2.51918 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4190.24 | 0.506587 | 0.253293 | − | 0.967389i | \(-0.418486\pi\) | ||||
0.253293 | + | 0.967389i | \(0.418486\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1084.61 | −0.130170 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3026.29 | 0.360567 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8875.25 | −1.04981 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1279.63 | −0.150273 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8650.38 | 1.00859 | 0.504294 | − | 0.863532i | \(-0.331753\pi\) | ||||
0.504294 | + | 0.863532i | \(0.331753\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11932.8 | −1.38140 | −0.690698 | − | 0.723143i | \(-0.742697\pi\) | ||||
−0.690698 | + | 0.723143i | \(0.742697\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4388.96 | −0.504489 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 742.680 | 0.0847653 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −493.251 | −0.0559019 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4735.41 | 0.532932 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7617.80 | 0.851361 | 0.425680 | − | 0.904874i | \(-0.360035\pi\) | ||||
0.425680 | + | 0.904874i | \(0.360035\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 289.679 | 0.0321504 | 0.0160752 | − | 0.999871i | \(-0.494883\pi\) | ||||
0.0160752 | + | 0.999871i | \(0.494883\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1380.19 | 0.152127 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4788.64 | −0.524192 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −320.401 | −0.0348335 | −0.0174167 | − | 0.999848i | \(-0.505544\pi\) | ||||
−0.0174167 | + | 0.999848i | \(0.505544\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4874.58 | 0.522795 | 0.261398 | − | 0.965231i | \(-0.415817\pi\) | ||||
0.261398 | + | 0.965231i | \(0.415817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10079.1 | 1.07370 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8584.39 | −0.908339 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −599.497 | −0.0630112 | −0.0315056 | − | 0.999504i | \(-0.510030\pi\) | ||||
−0.0315056 | + | 0.999504i | \(0.510030\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5025.03 | 0.524655 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2448.38 | −0.253940 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1716.87 | −0.176896 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15202.5 | −1.55611 | −0.778056 | − | 0.628195i | \(-0.783794\pi\) | ||||
−0.778056 | + | 0.628195i | \(0.783794\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1680.27 | 0.170868 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7069.98 | 0.714278 | 0.357139 | − | 0.934051i | \(-0.383752\pi\) | ||||
0.357139 | + | 0.934051i | \(0.383752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12087.1 | −1.21325 | −0.606624 | − | 0.794989i | \(-0.707477\pi\) | ||||
−0.606624 | + | 0.794989i | \(0.707477\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3277.17 | −0.326829 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2346.52 | 0.232514 | 0.116257 | − | 0.993219i | \(-0.462910\pi\) | ||||
0.116257 | + | 0.993219i | \(0.462910\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3330.60 | −0.327916 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9730.88 | 0.951965 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25821.7 | −2.51011 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −635.683 | −0.0614045 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4208.35 | −0.403956 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6961.37 | 0.664036 | 0.332018 | − | 0.943273i | \(-0.392271\pi\) | ||||
0.332018 | + | 0.943273i | \(0.392271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6972.02 | −0.660908 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1887.89 | −0.177851 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7031.47 | −0.658314 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2005.69 | −0.186626 | −0.0933128 | − | 0.995637i | \(-0.529746\pi\) | ||||
−0.0933128 | + | 0.995637i | \(0.529746\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10091.3 | 0.933218 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16154.0 | 1.48476 | 0.742382 | − | 0.669977i | \(-0.233696\pi\) | ||||
0.742382 | + | 0.669977i | \(0.233696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2692.57 | −0.245978 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6548.96 | −0.594654 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4765.77 | −0.430128 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1601.46 | 0.143669 | 0.0718347 | − | 0.997417i | \(-0.477115\pi\) | ||||
0.0718347 | + | 0.997417i | \(0.477115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4057.77 | 0.361852 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6982.59 | −0.618963 | −0.309481 | − | 0.950905i | \(-0.600155\pi\) | ||||
−0.309481 | + | 0.950905i | \(0.600155\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7924.89 | −0.698323 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4994.88 | 0.437535 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3691.65 | −0.321472 | −0.160736 | − | 0.986997i | \(-0.551387\pi\) | ||||
−0.160736 | + | 0.986997i | \(0.551387\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4228.48 | −0.366061 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1438.20 | −0.123778 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9179.27 | 0.785412 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33372.1 | −2.83888 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10473.9 | −0.885844 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7809.75 | 0.656721 | 0.328360 | − | 0.944553i | \(-0.393504\pi\) | ||||
0.328360 | + | 0.944553i | \(0.393504\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10258.3 | −0.857677 | −0.428838 | − | 0.903381i | \(-0.641077\pi\) | ||||
−0.428838 | + | 0.903381i | \(0.641077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −250.614 | −0.0208337 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6393.34 | 0.528459 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4085.04 | −0.335747 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3890.95 | −0.317990 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1693.74 | −0.137644 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12743.1 | −1.02978 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7643.46 | −0.614227 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3353.20 | 0.267964 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8734.64 | 0.694144 | 0.347072 | − | 0.937839i | \(-0.387176\pi\) | ||||
0.347072 | + | 0.937839i | \(0.387176\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1074.76 | −0.0849400 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −894.596 | −0.0703125 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22581.7 | 1.76512 | 0.882561 | − | 0.470197i | \(-0.155817\pi\) | ||||
0.882561 | + | 0.470197i | \(0.155817\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 634.180 | 0.0493008 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2304.65 | 0.178188 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2303.98 | 0.177170 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 9642.15 | 0.737453 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17694.2 | 1.34601 | 0.673003 | − | 0.739640i | \(-0.265004\pi\) | ||||
0.673003 | + | 0.739640i | \(0.265004\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8703.49 | 0.658530 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12776.2 | 0.961516 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3648.96 | 0.273153 | 0.136577 | − | 0.990630i | \(-0.456390\pi\) | ||||
0.136577 | + | 0.990630i | \(0.456390\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21586.7 | −1.60736 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8165.45 | 0.601605 | 0.300803 | − | 0.953686i | \(-0.402745\pi\) | ||||
0.300803 | + | 0.953686i | \(0.402745\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9544.36 | 0.699508 | 0.349754 | − | 0.936842i | \(-0.386265\pi\) | ||||
0.349754 | + | 0.936842i | \(0.386265\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6419.33 | −0.468013 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1072.86 | 0.0778113 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9915.88 | 0.715431 | 0.357715 | − | 0.933831i | \(-0.383556\pi\) | ||||
0.357715 | + | 0.933831i | \(0.383556\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6550.40 | −0.470165 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5842.69 | −0.417204 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31998.7 | −2.27316 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2207.40 | 0.156008 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12548.4 | −0.882328 | −0.441164 | − | 0.897426i | \(-0.645434\pi\) | ||||
−0.441164 | + | 0.897426i | \(0.645434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5472.25 | −0.382819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4608.75 | −0.320776 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14944.8 | −1.03493 | −0.517463 | − | 0.855706i | \(-0.673123\pi\) | ||||
−0.517463 | + | 0.855706i | \(0.673123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4632.12 | −0.319157 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10239.5 | 0.701965 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1446.20 | 0.0986478 | 0.0493239 | − | 0.998783i | \(-0.484293\pi\) | ||||
0.0493239 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8561.02 | −0.581050 | −0.290525 | − | 0.956867i | \(-0.593830\pi\) | ||||
−0.290525 | + | 0.956867i | \(0.593830\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4282.20 | 0.289195 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35643.1 | −2.39520 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 705.590 | 0.0471813 | 0.0235906 | − | 0.999722i | \(-0.492490\pi\) | ||||
0.0235906 | + | 0.999722i | \(0.492490\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 908.596 | 0.0604568 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11248.4 | 0.744783 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9680.02 | 0.637801 | 0.318901 | − | 0.947788i | \(-0.396686\pi\) | ||||
0.318901 | + | 0.947788i | \(0.396686\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2342.41 | 0.153585 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19754.3 | −1.28894 | −0.644471 | − | 0.764629i | \(-0.722922\pi\) | ||||
−0.644471 | + | 0.764629i | \(0.722922\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11766.6 | 0.764041 | 0.382020 | − | 0.924154i | \(-0.375228\pi\) | ||||
0.382020 | + | 0.924154i | \(0.375228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2427.29 | 0.156850 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6635.23 | 0.426701 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13990.8 | −0.895413 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10935.5 | −0.696527 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18810.6 | −1.19241 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2830.92 | −0.178601 | −0.0893005 | − | 0.996005i | \(-0.528463\pi\) | ||||
−0.0893005 | + | 0.996005i | \(0.528463\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6136.72 | −0.385328 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14494.4 | 0.905818 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1130.23 | −0.0703006 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6127.41 | 0.379338 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20128.9 | −1.24032 | −0.620159 | − | 0.784476i | \(-0.712932\pi\) | ||||
−0.620159 | + | 0.784476i | \(0.712932\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25860.4 | −1.58606 | −0.793029 | − | 0.609183i | \(-0.791497\pi\) | ||||
−0.793029 | + | 0.609183i | \(0.791497\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12036.7 | −0.734800 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10812.4 | 0.657000 | 0.328500 | − | 0.944504i | \(-0.393457\pi\) | ||||
0.328500 | + | 0.944504i | \(0.393457\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29585.4 | −1.78941 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2157.40 | −0.129885 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16162.9 | 0.968610 | 0.484305 | − | 0.874899i | \(-0.339073\pi\) | ||||
0.484305 | + | 0.874899i | \(0.339073\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11858.2 | −0.707385 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5436.62 | 0.322835 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23949.7 | 1.41570 | 0.707852 | − | 0.706361i | \(-0.249664\pi\) | ||||
0.707852 | + | 0.706361i | \(0.249664\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5942.54 | 0.349679 | 0.174840 | − | 0.984597i | \(-0.444059\pi\) | ||||
0.174840 | + | 0.984597i | \(0.444059\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4306.35 | −0.252254 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3964.77 | 0.231199 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3889.65 | −0.225799 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14307.0 | −0.826816 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4822.08 | 0.277428 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19802.4 | 1.13422 | 0.567108 | − | 0.823643i | \(-0.308062\pi\) | ||||
0.567108 | + | 0.823643i | \(0.308062\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 322.218 | 0.0183736 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2528.24 | 0.143528 | 0.0717639 | − | 0.997422i | \(-0.477137\pi\) | ||||
0.0717639 | + | 0.997422i | \(0.477137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4628.90 | −0.261621 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11452.5 | 0.644434 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21934.9 | 1.22887 | 0.614434 | − | 0.788968i | \(-0.289384\pi\) | ||||
0.614434 | + | 0.788968i | \(0.289384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3844.30 | −0.214428 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 864.867 | 0.0480302 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10785.5 | 0.596365 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11360.7 | −0.625444 | −0.312722 | − | 0.949845i | \(-0.601241\pi\) | ||||
−0.312722 | + | 0.949845i | \(0.601241\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4311.26 | −0.236322 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4535.54 | −0.247544 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4569.73 | −0.248337 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.4638 | −0.00148609 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2020.57 | −0.108867 | −0.0544335 | − | 0.998517i | \(-0.517335\pi\) | ||||
−0.0544335 | + | 0.998517i | \(0.517335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16100.5 | 0.863789 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15556.3 | −0.831042 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5217.05 | −0.277521 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21569.3 | −1.14253 | −0.571265 | − | 0.820766i | \(-0.693547\pi\) | ||||
−0.571265 | + | 0.820766i | \(0.693547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2962.26 | −0.156249 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9235.72 | 0.485106 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16784.3 | 0.877896 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19891.1 | −1.03605 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11383.4 | −0.590442 | −0.295221 | − | 0.955429i | \(-0.595393\pi\) | ||||
−0.295221 | + | 0.955429i | \(0.595393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6042.83 | 0.312131 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20181.8 | −1.03813 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −516.343 | −0.0264503 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22056.2 | −1.12520 | −0.562600 | − | 0.826730i | \(-0.690199\pi\) | ||||
−0.562600 | + | 0.826730i | \(0.690199\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23482.1 | 1.18812 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29711.0 | 1.49713 | 0.748567 | − | 0.663059i | \(-0.230742\pi\) | ||||
0.748567 | + | 0.663059i | \(0.230742\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1563.09 | 0.0784427 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32560.3 | 1.62737 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27088.3 | −1.34839 | −0.674195 | − | 0.738554i | \(-0.735509\pi\) | ||||
−0.674195 | + | 0.738554i | \(0.735509\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3685.93 | 0.182734 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8755.28 | 0.432301 | 0.216151 | − | 0.976360i | \(-0.430650\pi\) | ||||
0.216151 | + | 0.976360i | \(0.430650\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30426.6 | −1.49630 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 7512.03 | 0.367940 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8388.92 | −0.409245 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23256.5 | 1.13001 | 0.565007 | − | 0.825086i | \(-0.308874\pi\) | ||||
0.565007 | + | 0.825086i | \(0.308874\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2633.38 | −0.127445 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8678.08 | −0.418315 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14819.9 | 0.711544 | 0.355772 | − | 0.934573i | \(-0.384218\pi\) | ||||
0.355772 | + | 0.934573i | \(0.384218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 18456.3 | 0.882635 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19782.1 | −0.942316 | −0.471158 | − | 0.882049i | \(-0.656164\pi\) | ||||
−0.471158 | + | 0.882049i | \(0.656164\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −588.924 | −0.0279430 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5955.58 | 0.281470 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9972.06 | 0.469453 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29944.9 | 1.40421 | 0.702107 | − | 0.712071i | \(-0.252243\pi\) | ||||
0.702107 | + | 0.712071i | \(0.252243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18998.0 | 0.887412 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30341.6 | −1.41179 | −0.705894 | − | 0.708317i | \(-0.749455\pi\) | ||||
−0.705894 | + | 0.708317i | \(0.749455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1226.02 | 0.0568258 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6347.54 | 0.293072 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3911.37 | 0.179897 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46590.6 | 2.13463 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1168.20 | −0.0533179 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 34490.3 | 1.56817 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15196.6 | 0.688309 | 0.344154 | − | 0.938913i | \(-0.388166\pi\) | ||||
0.344154 | + | 0.938913i | \(0.388166\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10842.7 | −0.489239 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14210.8 | −0.638784 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1625.33 | −0.0727835 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14916.1 | −0.665435 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4576.99 | 0.203419 | 0.101710 | − | 0.994814i | \(-0.467569\pi\) | ||||
0.101710 | + | 0.994814i | \(0.467569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30348.3 | 1.34374 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8531.01 | −0.376315 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41338.1 | 1.81667 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6691.49 | −0.292974 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21344.7 | −0.931065 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21624.5 | −0.939775 | −0.469887 | − | 0.882726i | \(-0.655705\pi\) | ||||
−0.469887 | + | 0.882726i | \(0.655705\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7916.86 | −0.342785 | −0.171392 | − | 0.985203i | \(-0.554827\pi\) | ||||
−0.171392 | + | 0.985203i | \(0.554827\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1642.14 | 0.0708391 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35767.7 | 1.53729 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −20099.0 | −0.860681 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1453.16 | 0.0619993 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3640.19 | 0.154742 | 0.0773712 | − | 0.997002i | \(-0.475347\pi\) | ||||
0.0773712 | + | 0.997002i | \(0.475347\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24397.0 | −1.03333 | −0.516663 | − | 0.856189i | \(-0.672826\pi\) | ||||
−0.516663 | + | 0.856189i | \(0.672826\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2450.03 | 0.103393 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −21546.0 | −0.905959 | −0.452979 | − | 0.891521i | \(-0.649639\pi\) | ||||
−0.452979 | + | 0.891521i | \(0.649639\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9899.71 | 0.414754 | 0.207377 | − | 0.978261i | \(-0.433507\pi\) | ||||
0.207377 | + | 0.978261i | \(0.433507\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17178.4 | −0.717100 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3049.38 | −0.126836 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14382.4 | 0.596078 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2773.80 | 0.114548 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15138.9 | 0.622948 | 0.311474 | − | 0.950255i | \(-0.399177\pi\) | ||||
0.311474 | + | 0.950255i | \(0.399177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22517.0 | −0.923244 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −712.135 | −0.0290952 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17703.9 | 0.720750 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23464.3 | −0.951880 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9538.99 | 0.385603 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27173.5 | −1.09459 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35656.2 | 1.43124 | 0.715618 | − | 0.698492i | \(-0.246145\pi\) | ||||
0.715618 | + | 0.698492i | \(0.246145\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5097.56 | −0.203898 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1951.71 | 0.0777938 | 0.0388969 | − | 0.999243i | \(-0.487616\pi\) | ||||
0.0388969 | + | 0.999243i | \(0.487616\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41249.5 | −1.63843 | −0.819217 | − | 0.573483i | \(-0.805592\pi\) | ||||
−0.819217 | + | 0.573483i | \(0.805592\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1542.03 | 0.0610365 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7354.01 | −0.290074 | −0.145037 | − | 0.989426i | \(-0.546330\pi\) | ||||
−0.145037 | + | 0.989426i | \(0.546330\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37123.8 | −1.45925 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3120.44 | 0.122233 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22523.9 | −0.879254 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10974.8 | −0.426942 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5951.44 | 0.230728 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10192.4 | −0.393789 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31367.3 | 1.20775 | 0.603875 | − | 0.797079i | \(-0.293623\pi\) | ||||
0.603875 | + | 0.797079i | \(0.293623\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23272.8 | 0.893027 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44120.3 | 1.68723 | 0.843615 | − | 0.536948i | \(-0.180423\pi\) | ||||
0.843615 | + | 0.536948i | \(0.180423\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48261.2 | −1.83932 | −0.919659 | − | 0.392719i | \(-0.871535\pi\) | ||||
−0.919659 | + | 0.392719i | \(0.871535\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13791.1 | −0.523824 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11769.9 | 0.445541 | 0.222770 | − | 0.974871i | \(-0.428490\pi\) | ||||
0.222770 | + | 0.974871i | \(0.428490\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9541.87 | 0.359982 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5543.05 | 0.208417 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25976.1 | −0.973411 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27091.6 | −1.01181 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6220.88 | −0.231560 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4444.92 | −0.164901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29099.4 | 1.07596 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7923.93 | −0.292018 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3809.40 | −0.139921 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11072.5 | 0.405355 | 0.202678 | − | 0.979246i | \(-0.435036\pi\) | ||||
0.202678 | + | 0.979246i | \(0.435036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6707.64 | 0.244751 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7014.73 | 0.255114 | 0.127557 | − | 0.991831i | \(-0.459286\pi\) | ||||
0.127557 | + | 0.991831i | \(0.459286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 57118.8 | 2.07049 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2247.80 | 0.0812131 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7806.39 | −0.281123 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10087.5 | −0.362086 | −0.181043 | − | 0.983475i | \(-0.557947\pi\) | ||||
−0.181043 | + | 0.983475i | \(0.557947\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25761.0 | −0.921667 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15703.9 | −0.560021 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3607.22 | −0.128221 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7769.35 | −0.275274 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3648.41 | 0.128849 | 0.0644243 | − | 0.997923i | \(-0.479479\pi\) | ||||
0.0644243 | + | 0.997923i | \(0.479479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2610.06 | 0.0918810 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11668.3 | −0.409435 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 45284.1 | 1.58390 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38160.4 | −1.33047 | −0.665233 | − | 0.746636i | \(-0.731668\pi\) | ||||
−0.665233 | + | 0.746636i | \(0.731668\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25226.5 | −0.876716 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14259.1 | 0.493978 | 0.246989 | − | 0.969018i | \(-0.420559\pi\) | ||||
0.246989 | + | 0.969018i | \(0.420559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6601.36 | −0.227964 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2009.68 | −0.0691799 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25268.1 | −0.867058 | −0.433529 | − | 0.901140i | \(-0.642732\pi\) | ||||
−0.433529 | + | 0.901140i | \(0.642732\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13933.4 | −0.476606 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16955.2 | −0.578139 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2129.49 | −0.0723831 | −0.0361916 | − | 0.999345i | \(-0.511523\pi\) | ||||
−0.0361916 | + | 0.999345i | \(0.511523\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22752.8 | −0.770956 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8882.54 | −0.300033 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2530.75 | −0.0852160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19236.8 | −0.645726 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10785.8 | 0.360920 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23217.3 | −0.774500 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 56049.1 | 1.86393 | 0.931963 | − | 0.362554i | \(-0.118095\pi\) | ||||
0.931963 | + | 0.362554i | \(0.118095\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9944.68 | 0.329690 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55037.1 | −1.81898 | −0.909488 | − | 0.415730i | \(-0.863526\pi\) | ||||
−0.909488 | + | 0.415730i | \(0.863526\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2985.80 | −0.0983766 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −825.809 | −0.0271252 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41094.1 | 1.34567 | 0.672833 | − | 0.739794i | \(-0.265077\pi\) | ||||
0.672833 | + | 0.739794i | \(0.265077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64866.7 | −2.11762 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 757.188 | 0.0246434 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 60115.9 | 1.95056 | 0.975279 | − | 0.220975i | \(-0.0709241\pi\) | ||||
0.975279 | + | 0.220975i | \(0.0709241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16335.3 | −0.528413 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10240.9 | −0.330265 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33921.9 | 1.09065 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13233.5 | 0.424194 | 0.212097 | − | 0.977249i | \(-0.431971\pi\) | ||||
0.212097 | + | 0.977249i | \(0.431971\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23980.0 | 0.766346 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36292.9 | 1.15634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24562.9 | −0.780256 | −0.390128 | − | 0.920761i | \(-0.627569\pi\) | ||||
−0.390128 | + | 0.920761i | \(0.627569\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8161.13 | −0.258465 |
(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 | 1344.4.a.bf.1.1 | 2 | ||
4.3 | odd | 2 | 1344.4.a.bn.1.1 | 2 | |||
8.3 | odd | 2 | 672.4.a.g.1.2 | ✓ | 2 | ||
8.5 | even | 2 | 672.4.a.l.1.2 | yes | 2 | ||
24.5 | odd | 2 | 2016.4.a.k.1.1 | 2 | |||
24.11 | even | 2 | 2016.4.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.a.g.1.2 | ✓ | 2 | 8.3 | odd | 2 | ||
672.4.a.l.1.2 | yes | 2 | 8.5 | even | 2 | ||
1344.4.a.bf.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.bn.1.1 | 2 | 4.3 | odd | 2 | |||
2016.4.a.k.1.1 | 2 | 24.5 | odd | 2 | |||
2016.4.a.l.1.1 | 2 | 24.11 | even | 2 |