Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2304,4,Mod(1,2304)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2304, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2304.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2304 = 2^{8} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2304.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: | \(135.940400653\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 384) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2304.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.4222 | 0.932190 | 0.466095 | − | 0.884735i | \(-0.345660\pi\) | ||||
0.466095 | + | 0.884735i | \(0.345660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.42221 | 0.346766 | 0.173383 | − | 0.984854i | \(-0.444530\pi\) | ||||
0.173383 | + | 0.984854i | \(0.444530\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −61.6888 | −1.69090 | −0.845449 | − | 0.534056i | \(-0.820667\pi\) | ||||
−0.845449 | + | 0.534056i | \(0.820667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −64.8444 | −1.38343 | −0.691716 | − | 0.722170i | \(-0.743145\pi\) | ||||
−0.691716 | + | 0.722170i | \(0.743145\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 75.6888 | 1.07984 | 0.539919 | − | 0.841717i | \(-0.318455\pi\) | ||||
0.539919 | + | 0.841717i | \(0.318455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.3112 | −0.124502 | −0.0622512 | − | 0.998061i | \(-0.519828\pi\) | ||||
−0.0622512 | + | 0.998061i | \(0.519828\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 156.844 | 1.42193 | 0.710963 | − | 0.703229i | \(-0.248259\pi\) | ||||
0.710963 | + | 0.703229i | \(0.248259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −16.3776 | −0.131021 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −53.7998 | −0.344496 | −0.172248 | − | 0.985054i | \(-0.555103\pi\) | ||||
−0.172248 | + | 0.985054i | \(0.555103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 227.489 | 1.31801 | 0.659003 | − | 0.752141i | \(-0.270979\pi\) | ||||
0.659003 | + | 0.752141i | \(0.270979\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 66.9335 | 0.323252 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.3112 | −0.0458148 | −0.0229074 | − | 0.999738i | \(-0.507292\pi\) | ||||
−0.0229074 | + | 0.999738i | \(0.507292\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70.4441 | −0.268330 | −0.134165 | − | 0.990959i | \(-0.542835\pi\) | ||||
−0.134165 | + | 0.990959i | \(0.542835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 298.311 | 1.05795 | 0.528977 | − | 0.848636i | \(-0.322576\pi\) | ||||
0.528977 | + | 0.848636i | \(0.322576\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 89.9109 | 0.279039 | 0.139520 | − | 0.990219i | \(-0.455444\pi\) | ||||
0.139520 | + | 0.990219i | \(0.455444\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −301.755 | −0.879753 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 388.333 | 1.00645 | 0.503223 | − | 0.864157i | \(-0.332147\pi\) | ||||
0.503223 | + | 0.864157i | \(0.332147\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −642.934 | −1.57624 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −324.000 | −0.714936 | −0.357468 | − | 0.933925i | \(-0.616360\pi\) | ||||
−0.357468 | + | 0.933925i | \(0.616360\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −324.000 | −0.680065 | −0.340032 | − | 0.940414i | \(-0.610438\pi\) | ||||
−0.340032 | + | 0.940414i | \(0.610438\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −675.822 | −1.28962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −920.266 | −1.67804 | −0.839018 | − | 0.544104i | \(-0.816870\pi\) | ||||
−0.839018 | + | 0.544104i | \(0.816870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 995.156 | 1.66343 | 0.831713 | − | 0.555206i | \(-0.187361\pi\) | ||||
0.831713 | + | 0.555206i | \(0.187361\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −362.266 | −0.580822 | −0.290411 | − | 0.956902i | \(-0.593792\pi\) | ||||
−0.290411 | + | 0.956902i | \(0.593792\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −396.178 | −0.586347 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1098.91 | −1.56503 | −0.782513 | − | 0.622634i | \(-0.786062\pi\) | ||||
−0.782513 | + | 0.622634i | \(0.786062\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 791.822 | 1.04715 | 0.523577 | − | 0.851979i | \(-0.324597\pi\) | ||||
0.523577 | + | 0.851979i | \(0.324597\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 788.844 | 1.00661 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −150.622 | −0.179393 | −0.0896963 | − | 0.995969i | \(-0.528590\pi\) | ||||
−0.0896963 | + | 0.995969i | \(0.528590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −416.444 | −0.479728 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −107.465 | −0.116060 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1879.15 | −1.96700 | −0.983501 | − | 0.180903i | \(-0.942098\pi\) | ||||
−0.983501 | + | 0.180903i | \(0.942098\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1722.51 | −1.69699 | −0.848496 | − | 0.529202i | \(-0.822491\pi\) | ||||
−0.848496 | + | 0.529202i | \(0.822491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1908.82 | −1.82604 | −0.913018 | − | 0.407919i | \(-0.866255\pi\) | ||||
−0.913018 | + | 0.407919i | \(0.866255\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −128.622 | −0.116209 | −0.0581046 | − | 0.998310i | \(-0.518506\pi\) | ||||
−0.0581046 | + | 0.998310i | \(0.518506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −758.267 | −0.666320 | −0.333160 | − | 0.942870i | \(-0.608115\pi\) | ||||
−0.333160 | + | 0.942870i | \(0.608115\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −921.643 | −0.767265 | −0.383632 | − | 0.923486i | \(-0.625327\pi\) | ||||
−0.383632 | + | 0.923486i | \(0.625327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1634.66 | 1.32551 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 486.089 | 0.374451 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2474.51 | 1.85914 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1473.47 | −1.05433 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1647.22 | −1.15092 | −0.575462 | − | 0.817828i | \(-0.695178\pi\) | ||||
−0.575462 | + | 0.817828i | \(0.695178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2000.27 | −1.33408 | −0.667038 | − | 0.745023i | \(-0.732438\pi\) | ||||
−0.667038 | + | 0.745023i | \(0.732438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −66.2205 | −0.0431733 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2574.71 | 1.60564 | 0.802819 | − | 0.596223i | \(-0.203333\pi\) | ||||
0.802819 | + | 0.596223i | \(0.203333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1331.29 | 0.812362 | 0.406181 | − | 0.913793i | \(-0.366860\pi\) | ||||
0.406181 | + | 0.913793i | \(0.366860\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4000.18 | 2.33924 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −560.713 | −0.321136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 552.377 | 0.303708 | 0.151854 | − | 0.988403i | \(-0.451476\pi\) | ||||
0.151854 | + | 0.988403i | \(0.451476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1307.13 | 0.704456 | 0.352228 | − | 0.935914i | \(-0.385424\pi\) | ||||
0.352228 | + | 0.935914i | \(0.385424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2370.93 | 1.22863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3527.11 | −1.79295 | −0.896477 | − | 0.443089i | \(-0.853882\pi\) | ||||
−0.896477 | + | 0.443089i | \(0.853882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1007.29 | 0.493077 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 926.045 | 0.444991 | 0.222495 | − | 0.974934i | \(-0.428580\pi\) | ||||
0.222495 | + | 0.974934i | \(0.428580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1393.33 | −0.645624 | −0.322812 | − | 0.946463i | \(-0.604628\pi\) | ||||
−0.322812 | + | 0.946463i | \(0.604628\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2007.80 | 0.913881 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3311.71 | −1.45540 | −0.727701 | − | 0.685894i | \(-0.759411\pi\) | ||||
−0.727701 | + | 0.685894i | \(0.759411\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −105.181 | −0.0454337 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 323.287 | 0.134992 | 0.0674961 | − | 0.997720i | \(-0.478499\pi\) | ||||
0.0674961 | + | 0.997720i | \(0.478499\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3066.80 | 1.25941 | 0.629705 | − | 0.776834i | \(-0.283176\pi\) | ||||
0.629705 | + | 0.776834i | \(0.283176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −107.465 | −0.0427081 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4669.15 | −1.82589 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1856.44 | 0.703286 | 0.351643 | − | 0.936134i | \(-0.385623\pi\) | ||||
0.351643 | + | 0.936134i | \(0.385623\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3008.84 | 1.12218 | 0.561091 | − | 0.827754i | \(-0.310382\pi\) | ||||
0.561091 | + | 0.827754i | \(0.310382\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 909.309 | 0.328861 | 0.164430 | − | 0.986389i | \(-0.447421\pi\) | ||||
0.164430 | + | 0.986389i | \(0.447421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2780.24 | 0.990383 | 0.495191 | − | 0.868784i | \(-0.335098\pi\) | ||||
0.495191 | + | 0.868784i | \(0.335098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −345.514 | −0.119460 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −734.183 | −0.250134 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 636.085 | 0.210521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −385.511 | −0.125780 | −0.0628901 | − | 0.998020i | \(-0.520032\pi\) | ||||
−0.0628901 | + | 0.998020i | \(0.520032\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3109.06 | 0.986215 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1460.98 | 0.457040 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4908.00 | −1.49388 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −601.975 | −0.180768 | −0.0903839 | − | 0.995907i | \(-0.528809\pi\) | ||||
−0.0903839 | + | 0.995907i | \(0.528809\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −185.779 | −0.0543199 | −0.0271600 | − | 0.999631i | \(-0.508646\pi\) | ||||
−0.0271600 | + | 0.999631i | \(0.508646\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1237.11 | −0.356989 | −0.178495 | − | 0.983941i | \(-0.557123\pi\) | ||||
−0.178495 | + | 0.983941i | \(0.557123\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 217.378 | 0.0611197 | 0.0305598 | − | 0.999533i | \(-0.490271\pi\) | ||||
0.0305598 | + | 0.999533i | \(0.490271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 937.070 | 0.260118 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6055.99 | −1.63904 | −0.819518 | − | 0.573053i | \(-0.805759\pi\) | ||||
−0.819518 | + | 0.573053i | \(0.805759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6815.69 | −1.82173 | −0.910865 | − | 0.412705i | \(-0.864584\pi\) | ||||
−0.910865 | + | 0.412705i | \(0.864584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3144.96 | −0.820097 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 668.622 | 0.172241 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2448.53 | 0.615738 | 0.307869 | − | 0.951429i | \(-0.400384\pi\) | ||||
0.307869 | + | 0.951429i | \(0.400384\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9675.55 | −2.40433 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2949.55 | −0.715907 | −0.357953 | − | 0.933739i | \(-0.616525\pi\) | ||||
−0.357953 | + | 0.933739i | \(0.616525\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −66.2205 | −0.0158870 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4831.64 | −1.13282 | −0.566410 | − | 0.824124i | \(-0.691668\pi\) | ||||
−0.566410 | + | 0.824124i | \(0.691668\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4047.29 | 0.938199 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1093.84 | 0.247928 | 0.123964 | − | 0.992287i | \(-0.460439\pi\) | ||||
0.123964 | + | 0.992287i | \(0.460439\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3079.80 | 0.690349 | 0.345175 | − | 0.938539i | \(-0.387820\pi\) | ||||
0.345175 | + | 0.938539i | \(0.387820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1010.32 | 0.221543 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5600.75 | −1.21486 | −0.607430 | − | 0.794373i | \(-0.707800\pi\) | ||||
−0.607430 | + | 0.794373i | \(0.707800\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −203.426 | −0.0431864 | −0.0215932 | − | 0.999767i | \(-0.506874\pi\) | ||||
−0.0215932 | + | 0.999767i | \(0.506874\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2214.84 | 0.465225 | 0.232612 | − | 0.972570i | \(-0.425273\pi\) | ||||
0.232612 | + | 0.972570i | \(0.425273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −452.406 | −0.0930478 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 815.798 | 0.166049 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5812.37 | −1.15892 | −0.579458 | − | 0.815002i | \(-0.696736\pi\) | ||||
−0.579458 | + | 0.815002i | \(0.696736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3376.79 | −0.666456 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10170.5 | −1.96714 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1915.82 | 0.366863 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3376.79 | −0.633950 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7337.33 | −1.36405 | −0.682025 | − | 0.731329i | \(-0.738901\pi\) | ||||
−0.682025 | + | 0.731329i | \(0.738901\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6575.91 | −1.19899 | −0.599494 | − | 0.800379i | \(-0.704632\pi\) | ||||
−0.599494 | + | 0.800379i | \(0.704632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1556.67 | −0.281113 | −0.140556 | − | 0.990073i | \(-0.544889\pi\) | ||||
−0.140556 | + | 0.990073i | \(0.544889\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9457.27 | −1.67562 | −0.837812 | − | 0.545959i | \(-0.816166\pi\) | ||||
−0.837812 | + | 0.545959i | \(0.816166\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3318.85 | 0.582507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −780.441 | −0.134442 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1062.00 | 0.181259 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 577.426 | 0.0967615 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10907.6 | 1.81129 | 0.905647 | − | 0.424032i | \(-0.139386\pi\) | ||||
0.905647 | + | 0.424032i | \(0.139386\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9591.20 | −1.56425 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4256.22 | 0.687986 | 0.343993 | − | 0.938972i | \(-0.388220\pi\) | ||||
0.343993 | + | 0.938972i | \(0.388220\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14033.5 | −2.22861 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4140.75 | −0.651835 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4217.07 | 0.652403 | 0.326202 | − | 0.945300i | \(-0.394231\pi\) | ||||
0.326202 | + | 0.945300i | \(0.394231\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2986.57 | 0.458073 | 0.229037 | − | 0.973418i | \(-0.426442\pi\) | ||||
0.229037 | + | 0.973418i | \(0.426442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8231.42 | 1.24112 | 0.620558 | − | 0.784160i | \(-0.286906\pi\) | ||||
0.620558 | + | 0.784160i | \(0.286906\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10371.7 | 1.55063 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5857.19 | 0.861088 | 0.430544 | − | 0.902569i | \(-0.358322\pi\) | ||||
0.430544 | + | 0.902569i | \(0.358322\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6752.68 | −0.984499 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3775.61 | −0.541437 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10715.7 | 1.52412 | 0.762061 | − | 0.647505i | \(-0.224188\pi\) | ||||
0.762061 | + | 0.647505i | \(0.224188\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2493.95 | 0.349002 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1817.52 | −0.252299 | −0.126149 | − | 0.992011i | \(-0.540262\pi\) | ||||
−0.126149 | + | 0.992011i | \(0.540262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3488.62 | 0.476586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9789.68 | −1.32681 | −0.663407 | − | 0.748259i | \(-0.730890\pi\) | ||||
−0.663407 | + | 0.748259i | \(0.730890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11502.3 | −1.53457 | −0.767285 | − | 0.641306i | \(-0.778393\pi\) | ||||
−0.767285 | + | 0.641306i | \(0.778393\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4129.05 | −0.546587 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.06261 | 0.000790197 0 | 0.000395098 | − | 1.00000i | \(-0.499874\pi\) | ||||
0.000395098 | 1.00000i | \(0.499874\pi\) | ||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11871.4 | 1.53545 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11453.1 | −1.45890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5982.31 | 0.756281 | 0.378141 | − | 0.925748i | \(-0.376564\pi\) | ||||
0.378141 | + | 0.925748i | \(0.376564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10443.6 | −1.30057 | −0.650284 | − | 0.759691i | \(-0.725350\pi\) | ||||
−0.650284 | + | 0.759691i | \(0.725350\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14751.4 | −1.82337 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 636.085 | 0.0774682 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8141.01 | −0.984223 | −0.492112 | − | 0.870532i | \(-0.663775\pi\) | ||||
−0.492112 | + | 0.870532i | \(0.663775\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2080.79 | −0.247916 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8252.53 | 0.976146 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8716.96 | 1.01635 | 0.508176 | − | 0.861253i | \(-0.330320\pi\) | ||||
0.508176 | + | 0.861253i | \(0.330320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13437.5 | −1.55560 | −0.777798 | − | 0.628514i | \(-0.783663\pi\) | ||||
−0.777798 | + | 0.628514i | \(0.783663\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1239.60 | −0.141482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2080.79 | −0.235824 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7343.86 | 0.820745 | 0.410373 | − | 0.911918i | \(-0.365399\pi\) | ||||
0.410373 | + | 0.911918i | \(0.365399\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4490.80 | 0.498416 | 0.249208 | − | 0.968450i | \(-0.419830\pi\) | ||||
0.249208 | + | 0.968450i | \(0.419830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1617.25 | −0.177033 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9437.93 | 1.02608 | 0.513038 | − | 0.858366i | \(-0.328520\pi\) | ||||
0.513038 | + | 0.858366i | \(0.328520\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12668.3 | 1.35866 | 0.679331 | − | 0.733832i | \(-0.262270\pi\) | ||||
0.679331 | + | 0.733832i | \(0.262270\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1569.82 | −0.167228 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13052.0 | 1.37186 | 0.685929 | − | 0.727669i | \(-0.259396\pi\) | ||||
0.685929 | + | 0.727669i | \(0.259396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4345.61 | 0.453718 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4340.27 | −0.447197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1313.64 | −0.134463 | −0.0672316 | − | 0.997737i | \(-0.521417\pi\) | ||||
−0.0672316 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −627.883 | −0.0634347 | −0.0317174 | − | 0.999497i | \(-0.510098\pi\) | ||||
−0.0317174 | + | 0.999497i | \(0.510098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7315.03 | −0.734251 | −0.367126 | − | 0.930171i | \(-0.619658\pi\) | ||||
−0.367126 | + | 0.930171i | \(0.619658\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 759.997 | 0.0753072 | 0.0376536 | − | 0.999291i | \(-0.488012\pi\) | ||||
0.0376536 | + | 0.999291i | \(0.488012\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5910.14 | −0.581886 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18402.5 | −1.78889 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 168.873 | 0.0163125 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7403.51 | 0.706211 | 0.353106 | − | 0.935583i | \(-0.385126\pi\) | ||||
0.353106 | + | 0.935583i | \(0.385126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 668.622 | 0.0633816 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19584.9 | −1.83362 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3488.11 | 0.324561 | 0.162281 | − | 0.986745i | \(-0.448115\pi\) | ||||
0.162281 | + | 0.986745i | \(0.448115\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6575.73 | 0.604396 | 0.302198 | − | 0.953245i | \(-0.402280\pi\) | ||||
0.302198 | + | 0.953245i | \(0.402280\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4072.05 | −0.372000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6391.09 | 0.576820 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5187.82 | 0.465408 | 0.232704 | − | 0.972548i | \(-0.425243\pi\) | ||||
0.232704 | + | 0.972548i | \(0.425243\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7248.38 | −0.642524 | −0.321262 | − | 0.946990i | \(-0.604107\pi\) | ||||
−0.321262 | + | 0.946990i | \(0.604107\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17952.4 | −1.58192 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6613.44 | −0.575905 | −0.287952 | − | 0.957645i | \(-0.592974\pi\) | ||||
−0.287952 | + | 0.957645i | \(0.592974\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2326.55 | −0.201410 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19894.1 | −1.70221 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5546.50 | −0.471827 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20761.3 | −1.74581 | −0.872906 | − | 0.487888i | \(-0.837767\pi\) | ||||
−0.872906 | + | 0.487888i | \(0.837767\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13494.2 | 1.12822 | 0.564112 | − | 0.825698i | \(-0.309219\pi\) | ||||
0.564112 | + | 0.825698i | \(0.309219\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17218.3 | 1.42323 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12433.2 | 1.02188 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4567.91 | 0.371216 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1340.53 | −0.108329 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18614.9 | 1.48757 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2708.58 | 0.215251 | 0.107626 | − | 0.994191i | \(-0.465675\pi\) | ||||
0.107626 | + | 0.994191i | \(0.465675\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7902.82 | −0.621137 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15783.5 | 1.23373 | 0.616866 | − | 0.787068i | \(-0.288402\pi\) | ||||
0.616866 | + | 0.787068i | \(0.288402\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 554.740 | 0.0428906 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7057.43 | −0.542699 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1892.77 | −0.143984 | −0.0719922 | − | 0.997405i | \(-0.522936\pi\) | ||||
−0.0719922 | + | 0.997405i | \(0.522936\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19343.8 | −1.46361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3876.26 | −0.290169 | −0.145084 | − | 0.989419i | \(-0.546345\pi\) | ||||
−0.145084 | + | 0.989419i | \(0.546345\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9605.56 | −0.715237 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14900.9 | 1.09785 | 0.548927 | − | 0.835870i | \(-0.315037\pi\) | ||||
0.548927 | + | 0.835870i | \(0.315037\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24926.0 | −1.82683 | −0.913414 | − | 0.407032i | \(-0.866564\pi\) | ||||
−0.913414 | + | 0.407032i | \(0.866564\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2568.74 | −0.186302 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21022.4 | 1.51677 | 0.758384 | − | 0.651808i | \(-0.225989\pi\) | ||||
0.758384 | + | 0.651808i | \(0.225989\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5085.24 | 0.363118 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23955.8 | −1.70180 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13847.0 | −0.973641 | −0.486821 | − | 0.873502i | \(-0.661843\pi\) | ||||
−0.486821 | + | 0.873502i | \(0.661843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2345.68 | −0.164095 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4113.01 | 0.284825 | 0.142413 | − | 0.989807i | \(-0.454514\pi\) | ||||
0.142413 | + | 0.989807i | \(0.454514\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5066.12 | 0.349060 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4863.60 | 0.331755 | 0.165878 | − | 0.986146i | \(-0.446954\pi\) | ||||
0.165878 | + | 0.986146i | \(0.446954\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6827.76 | 0.463411 | 0.231706 | − | 0.972786i | \(-0.425569\pi\) | ||||
0.231706 | + | 0.972786i | \(0.425569\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25789.9 | 1.73307 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18178.3 | −1.21554 | −0.607770 | − | 0.794113i | \(-0.707936\pi\) | ||||
−0.607770 | + | 0.794113i | \(0.707936\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5830.22 | −0.386032 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15687.2 | −1.03360 | −0.516802 | − | 0.856105i | \(-0.672878\pi\) | ||||
−0.516802 | + | 0.856105i | \(0.672878\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16420.2 | 1.07140 | 0.535700 | − | 0.844409i | \(-0.320048\pi\) | ||||
0.535700 | + | 0.844409i | \(0.320048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5517.78 | −0.358285 | −0.179142 | − | 0.983823i | \(-0.557332\pi\) | ||||
−0.179142 | + | 0.983823i | \(0.557332\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −967.328 | −0.0622073 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13309.6 | −0.851812 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −780.441 | −0.0494725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1559.17 | −0.0983670 | −0.0491835 | − | 0.998790i | \(-0.515662\pi\) | ||||
−0.0491835 | + | 0.998790i | \(0.515662\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17167.7 | −1.07288 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19567.1 | 1.21708 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15188.6 | 0.935900 | 0.467950 | − | 0.883755i | \(-0.344993\pi\) | ||||
0.467950 | + | 0.883755i | \(0.344993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16666.6 | −1.02219 | −0.511095 | − | 0.859524i | \(-0.670760\pi\) | ||||
−0.511095 | + | 0.859524i | \(0.670760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3038.27 | 0.184616 | 0.0923081 | − | 0.995730i | \(-0.470576\pi\) | ||||
0.0923081 | + | 0.995730i | \(0.470576\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19987.2 | 1.20888 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9078.99 | −0.544086 | −0.272043 | − | 0.962285i | \(-0.587699\pi\) | ||||
−0.272043 | + | 0.962285i | \(0.587699\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20847.2 | −1.24361 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16892.0 | 0.998511 | 0.499255 | − | 0.866455i | \(-0.333607\pi\) | ||||
0.499255 | + | 0.866455i | \(0.333607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5064.16 | −0.297992 | −0.148996 | − | 0.988838i | \(-0.547604\pi\) | ||||
−0.148996 | + | 0.988838i | \(0.547604\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −690.164 | −0.0402457 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8438.21 | −0.489848 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19987.2 | 1.14992 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28625.9 | 1.63959 | 0.819797 | − | 0.572654i | \(-0.194086\pi\) | ||||
0.819797 | + | 0.572654i | \(0.194086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16061.2 | −0.911791 | −0.455895 | − | 0.890033i | \(-0.650681\pi\) | ||||
−0.455895 | + | 0.890033i | \(0.650681\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12068.3 | −0.682090 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7868.09 | −0.440796 | −0.220398 | − | 0.975410i | \(-0.570736\pi\) | ||||
−0.220398 | + | 0.975410i | \(0.570736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26834.2 | 1.49676 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25181.2 | −1.39235 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16886.2 | 0.929641 | 0.464820 | − | 0.885405i | \(-0.346119\pi\) | ||||
0.464820 | + | 0.885405i | \(0.346119\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13874.9 | 0.757276 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5331.83 | −0.289753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18293.6 | 0.985647 | 0.492824 | − | 0.870129i | \(-0.335965\pi\) | ||||
0.492824 | + | 0.870129i | \(0.335965\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 106.320 | 0.00570406 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11062.3 | −0.588460 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21555.6 | 1.14180 | 0.570900 | − | 0.821019i | \(-0.306594\pi\) | ||||
0.570900 | + | 0.821019i | \(0.306594\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35680.3 | 1.87411 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41690.6 | 2.18062 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9059.31 | −0.469896 | −0.234948 | − | 0.972008i | \(-0.575492\pi\) | ||||
−0.234948 | + | 0.972008i | \(0.575492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12258.8 | −0.633208 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 881.115 | 0.0451362 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7074.83 | −0.360923 | −0.180462 | − | 0.983582i | \(-0.557759\pi\) | ||||
−0.180462 | + | 0.983582i | \(0.557759\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22578.8 | 1.14242 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17095.9 | 0.861459 | 0.430730 | − | 0.902481i | \(-0.358256\pi\) | ||||
0.430730 | + | 0.902481i | \(0.358256\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 56770.1 | 2.83739 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28157.4 | −1.40161 | −0.700803 | − | 0.713355i | \(-0.747175\pi\) | ||||
−0.700803 | + | 0.713355i | \(0.747175\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34033.2 | 1.68043 | 0.840214 | − | 0.542255i | \(-0.182429\pi\) | ||||
0.840214 | + | 0.542255i | \(0.182429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5756.99 | 0.283114 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −826.039 | −0.0402975 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34356.8 | 1.66937 | 0.834685 | − | 0.550728i | \(-0.185650\pi\) | ||||
0.834685 | + | 0.550728i | \(0.185650\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 13623.2 | 0.656687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29464.6 | 1.41467 | 0.707337 | − | 0.706876i | \(-0.249896\pi\) | ||||
0.707337 | + | 0.706876i | \(0.249896\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27284.5 | −1.29969 | −0.649843 | − | 0.760069i | \(-0.725165\pi\) | ||||
−0.649843 | + | 0.760069i | \(0.725165\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4869.75 | −0.231057 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21009.6 | 0.989064 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2320.13 | 0.108798 | 0.0543992 | − | 0.998519i | \(-0.482676\pi\) | ||||
0.0543992 | + | 0.998519i | \(0.482676\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4217.83 | 0.196254 | 0.0981272 | − | 0.995174i | \(-0.468715\pi\) | ||||
0.0981272 | + | 0.995174i | \(0.468715\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3725.73 | −0.172687 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 726.362 | 0.0334077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −61390.0 | −2.81268 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36760.3 | −1.67138 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11436.3 | −0.517991 | −0.258995 | − | 0.965879i | \(-0.583391\pi\) | ||||
−0.258995 | + | 0.965879i | \(0.583391\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5918.98 | −0.266062 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21009.6 | 0.940823 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14102.3 | −0.626761 | −0.313381 | − | 0.949628i | \(-0.601462\pi\) | ||||
−0.313381 | + | 0.949628i | \(0.601462\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6805.25 | 0.301317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22347.8 | 0.982111 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10498.2 | 0.459641 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18791.3 | −0.816647 | −0.408323 | − | 0.912837i | \(-0.633886\pi\) | ||||
−0.408323 | + | 0.912837i | \(0.633886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14452.6 | −0.625771 | −0.312886 | − | 0.949791i | \(-0.601296\pi\) | ||||
−0.312886 | + | 0.949791i | \(0.601296\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9651.43 | 0.414816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3075.94 | −0.131718 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27786.1 | 1.18117 | 0.590585 | − | 0.806975i | \(-0.298897\pi\) | ||||
0.590585 | + | 0.806975i | \(0.298897\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39205.8 | −1.66055 | −0.830273 | − | 0.557357i | \(-0.811815\pi\) | ||||
−0.830273 | + | 0.557357i | \(0.811815\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5929.15 | −0.249307 | −0.124653 | − | 0.992200i | \(-0.539782\pi\) | ||||
−0.124653 | + | 0.992200i | \(0.539782\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1269.44 | 0.0531840 | 0.0265920 | − | 0.999646i | \(-0.491535\pi\) | ||||
0.0265920 | + | 0.999646i | \(0.491535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22839.5 | −0.949990 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14521.6 | −0.601845 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17884.1 | 0.735910 | 0.367955 | − | 0.929844i | \(-0.380058\pi\) | ||||
0.367955 | + | 0.929844i | \(0.380058\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21494.6 | −0.881323 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 20925.7 | 0.851911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15891.8 | 0.644686 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1617.25 | −0.0651453 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16083.4 | −0.645585 | −0.322793 | − | 0.946470i | \(-0.604622\pi\) | ||||
−0.322793 | + | 0.946470i | \(0.604622\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17203.6 | −0.685722 | −0.342861 | − | 0.939386i | \(-0.611396\pi\) | ||||
−0.342861 | + | 0.939386i | \(0.611396\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24427.5 | 0.970264 | 0.485132 | − | 0.874441i | \(-0.338772\pi\) | ||||
0.485132 | + | 0.874441i | \(0.338772\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46584.1 | −1.83747 | −0.918737 | − | 0.394870i | \(-0.870790\pi\) | ||||
−0.918737 | + | 0.394870i | \(0.870790\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34515.3 | −1.35671 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 67790.5 | 2.64630 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 59674.1 | 2.32145 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9462.91 | −0.365605 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7402.05 | 0.285005 | 0.142503 | − | 0.989794i | \(-0.454485\pi\) | ||||
0.142503 | + | 0.989794i | \(0.454485\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12044.7 | −0.460608 | −0.230304 | − | 0.973119i | \(-0.573972\pi\) | ||||
−0.230304 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7150.02 | 0.272500 | 0.136250 | − | 0.990674i | \(-0.456495\pi\) | ||||
0.136250 | + | 0.990674i | \(0.456495\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21897.6 | 0.828916 | 0.414458 | − | 0.910068i | \(-0.363971\pi\) | ||||
0.414458 | + | 0.910068i | \(0.363971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10578.8 | −0.399102 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −927.087 | −0.0347411 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3369.36 | 0.125838 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12238.9 | −0.454047 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29392.5 | 1.08680 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31962.8 | 1.17401 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −800.885 | −0.0293197 | −0.0146598 | − | 0.999893i | \(-0.504667\pi\) | ||||
−0.0146598 | + | 0.999893i | \(0.504667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26742.9 | −0.972593 | −0.486296 | − | 0.873794i | \(-0.661652\pi\) | ||||
−0.486296 | + | 0.873794i | \(0.661652\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48846.5 | −1.77063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12846.1 | −0.462613 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3744.72 | 0.134414 | 0.0672072 | − | 0.997739i | \(-0.478591\pi\) | ||||
0.0672072 | + | 0.997739i | \(0.478591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −64530.3 | −2.30124 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 168.873 | 0.00600271 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25667.3 | 0.906477 | 0.453238 | − | 0.891389i | \(-0.350269\pi\) | ||||
0.453238 | + | 0.891389i | \(0.350269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3111.45 | 0.109531 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −48662.9 | −1.70208 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17978.7 | 0.626829 | 0.313414 | − | 0.949616i | \(-0.398527\pi\) | ||||
0.313414 | + | 0.949616i | \(0.398527\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8120.01 | 0.281302 | 0.140651 | − | 0.990059i | \(-0.455081\pi\) | ||||
0.140651 | + | 0.990059i | \(0.455081\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11048.8 | −0.381545 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7930.95 | −0.272145 | −0.136072 | − | 0.990699i | \(-0.543448\pi\) | ||||
−0.136072 | + | 0.990699i | \(0.543448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23490.9 | 0.803527 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29833.3 | −1.01406 | −0.507028 | − | 0.861930i | \(-0.669256\pi\) | ||||
−0.507028 | + | 0.861930i | \(0.669256\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19348.2 | 0.655596 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16535.3 | 0.556781 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21960.1 | 0.737139 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31358.7 | 1.04609 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7650.56 | −0.254421 | −0.127211 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127211 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5634.51 | 0.186220 | 0.0931102 | − | 0.995656i | \(-0.470319\pi\) | ||||
0.0931102 | + | 0.995656i | \(0.470319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8549.80 | 0.281700 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43983.5 | −1.44028 | −0.720142 | − | 0.693827i | \(-0.755923\pi\) | ||||
−0.720142 | + | 0.693827i | \(0.755923\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9291.72 | 0.303335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7759.30 | −0.251763 | −0.125882 | − | 0.992045i | \(-0.540176\pi\) | ||||
−0.125882 | + | 0.992045i | \(0.540176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9477.00 | 0.306561 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 46788.4 | 1.50433 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10114.8 | −0.324226 | −0.162113 | − | 0.986772i | \(-0.551831\pi\) | ||||
−0.162113 | + | 0.986772i | \(0.551831\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28976.3 | 0.923225 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43842.2 | 1.39267 | 0.696337 | − | 0.717715i | \(-0.254812\pi\) | ||||
0.696337 | + | 0.717715i | \(0.254812\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2304.4.a.s.1.2 | 2 | ||
3.2 | odd | 2 | 768.4.a.p.1.1 | 2 | |||
4.3 | odd | 2 | 2304.4.a.t.1.2 | 2 | |||
8.3 | odd | 2 | 2304.4.a.bq.1.1 | 2 | |||
8.5 | even | 2 | 2304.4.a.bp.1.1 | 2 | |||
12.11 | even | 2 | 768.4.a.j.1.1 | 2 | |||
16.3 | odd | 4 | 1152.4.d.i.577.2 | 4 | |||
16.5 | even | 4 | 1152.4.d.o.577.3 | 4 | |||
16.11 | odd | 4 | 1152.4.d.i.577.3 | 4 | |||
16.13 | even | 4 | 1152.4.d.o.577.2 | 4 | |||
24.5 | odd | 2 | 768.4.a.e.1.2 | 2 | |||
24.11 | even | 2 | 768.4.a.k.1.2 | 2 | |||
48.5 | odd | 4 | 384.4.d.e.193.1 | yes | 4 | ||
48.11 | even | 4 | 384.4.d.c.193.3 | yes | 4 | ||
48.29 | odd | 4 | 384.4.d.e.193.4 | yes | 4 | ||
48.35 | even | 4 | 384.4.d.c.193.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.4.d.c.193.2 | ✓ | 4 | 48.35 | even | 4 | ||
384.4.d.c.193.3 | yes | 4 | 48.11 | even | 4 | ||
384.4.d.e.193.1 | yes | 4 | 48.5 | odd | 4 | ||
384.4.d.e.193.4 | yes | 4 | 48.29 | odd | 4 | ||
768.4.a.e.1.2 | 2 | 24.5 | odd | 2 | |||
768.4.a.j.1.1 | 2 | 12.11 | even | 2 | |||
768.4.a.k.1.2 | 2 | 24.11 | even | 2 | |||
768.4.a.p.1.1 | 2 | 3.2 | odd | 2 | |||
1152.4.d.i.577.2 | 4 | 16.3 | odd | 4 | |||
1152.4.d.i.577.3 | 4 | 16.11 | odd | 4 | |||
1152.4.d.o.577.2 | 4 | 16.13 | even | 4 | |||
1152.4.d.o.577.3 | 4 | 16.5 | even | 4 | |||
2304.4.a.s.1.2 | 2 | 1.1 | even | 1 | trivial | ||
2304.4.a.t.1.2 | 2 | 4.3 | odd | 2 | |||
2304.4.a.bp.1.1 | 2 | 8.5 | even | 2 | |||
2304.4.a.bq.1.1 | 2 | 8.3 | odd | 2 |