Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [928,4,Mod(1,928)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(928, 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("928.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 928 = 2^{5} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 928.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: | \(54.7537724853\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 138x^{7} + 394x^{6} + 5872x^{5} - 10822x^{4} - 85158x^{3} + 30654x^{2} + 439999x + 396802 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-7.63776\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 928.1 |
$q$-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 | ||||||||
\(3\) | −7.63776 | −1.46989 | −0.734943 | − | 0.678128i | \(-0.762791\pi\) | ||||
−0.734943 | + | 0.678128i | \(0.762791\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.65015 | −0.684250 | −0.342125 | − | 0.939654i | \(-0.611147\pi\) | ||||
−0.342125 | + | 0.939654i | \(0.611147\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.64550 | 0.304829 | 0.152414 | − | 0.988317i | \(-0.451295\pi\) | ||||
0.152414 | + | 0.988317i | \(0.451295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 31.3353 | 1.16057 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 64.9460 | 1.78018 | 0.890089 | − | 0.455787i | \(-0.150642\pi\) | ||||
0.890089 | + | 0.455787i | \(0.150642\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 54.0253 | 1.15261 | 0.576304 | − | 0.817235i | \(-0.304494\pi\) | ||||
0.576304 | + | 0.817235i | \(0.304494\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 58.4300 | 1.00577 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −20.0898 | −0.286618 | −0.143309 | − | 0.989678i | \(-0.545774\pi\) | ||||
−0.143309 | + | 0.989678i | \(0.545774\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −52.3646 | −0.632277 | −0.316139 | − | 0.948713i | \(-0.602386\pi\) | ||||
−0.316139 | + | 0.948713i | \(0.602386\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −43.1190 | −0.448064 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −132.044 | −1.19709 | −0.598547 | − | 0.801088i | \(-0.704255\pi\) | ||||
−0.598547 | + | 0.801088i | \(0.704255\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −66.4752 | −0.531802 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −33.1122 | −0.236016 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 135.023 | 0.782284 | 0.391142 | − | 0.920330i | \(-0.372080\pi\) | ||||
0.391142 | + | 0.920330i | \(0.372080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −496.042 | −2.61666 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −43.1889 | −0.208579 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −137.761 | −0.612101 | −0.306050 | − | 0.952015i | \(-0.599008\pi\) | ||||
−0.306050 | + | 0.952015i | \(0.599008\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −412.632 | −1.69420 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −229.496 | −0.874176 | −0.437088 | − | 0.899419i | \(-0.643990\pi\) | ||||
−0.437088 | + | 0.899419i | \(0.643990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 46.2145 | 0.163899 | 0.0819493 | − | 0.996637i | \(-0.473885\pi\) | ||||
0.0819493 | + | 0.996637i | \(0.473885\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −239.720 | −0.794118 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 327.225 | 1.01555 | 0.507773 | − | 0.861491i | \(-0.330469\pi\) | ||||
0.507773 | + | 0.861491i | \(0.330469\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −311.128 | −0.907080 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 153.441 | 0.421295 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 32.9249 | 0.0853318 | 0.0426659 | − | 0.999089i | \(-0.486415\pi\) | ||||
0.0426659 | + | 0.999089i | \(0.486415\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −496.846 | −1.21809 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 399.948 | 0.929376 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 378.832 | 0.835929 | 0.417964 | − | 0.908463i | \(-0.362744\pi\) | ||||
0.417964 | + | 0.908463i | \(0.362744\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −18.5312 | −0.0388964 | −0.0194482 | − | 0.999811i | \(-0.506191\pi\) | ||||
−0.0194482 | + | 0.999811i | \(0.506191\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 176.904 | 0.353774 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −413.301 | −0.788673 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 998.295 | 1.82032 | 0.910158 | − | 0.414261i | \(-0.135960\pi\) | ||||
0.910158 | + | 0.414261i | \(0.135960\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1008.52 | 1.75959 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 570.499 | 0.953602 | 0.476801 | − | 0.879011i | \(-0.341796\pi\) | ||||
0.476801 | + | 0.879011i | \(0.341796\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −224.392 | −0.359768 | −0.179884 | − | 0.983688i | \(-0.557572\pi\) | ||||
−0.179884 | + | 0.983688i | \(0.557572\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 507.722 | 0.781689 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 366.653 | 0.542649 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −430.785 | −0.613507 | −0.306754 | − | 0.951789i | \(-0.599243\pi\) | ||||
−0.306754 | + | 0.951789i | \(0.599243\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −593.151 | −0.813650 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1390.04 | 1.83828 | 0.919138 | − | 0.393935i | \(-0.128886\pi\) | ||||
0.919138 | + | 0.393935i | \(0.128886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 153.690 | 0.196118 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 221.495 | 0.272951 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −131.569 | −0.156700 | −0.0783501 | − | 0.996926i | \(-0.524965\pi\) | ||||
−0.0783501 | + | 0.996926i | \(0.524965\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 305.000 | 0.351348 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1031.27 | −1.14987 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 400.597 | 0.432636 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 837.766 | 0.876930 | 0.438465 | − | 0.898748i | \(-0.355522\pi\) | ||||
0.438465 | + | 0.898748i | \(0.355522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2035.10 | 2.06602 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1595.03 | −1.57140 | −0.785702 | − | 0.618605i | \(-0.787698\pi\) | ||||
−0.785702 | + | 0.618605i | \(0.787698\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1565.54 | −1.49765 | −0.748824 | − | 0.662769i | \(-0.769381\pi\) | ||||
−0.748824 | + | 0.662769i | \(0.769381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 329.867 | 0.306587 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1243.19 | −1.12321 | −0.561604 | − | 0.827406i | \(-0.689816\pi\) | ||||
−0.561604 | + | 0.827406i | \(0.689816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1158.97 | 1.01843 | 0.509217 | − | 0.860638i | \(-0.329935\pi\) | ||||
0.509217 | + | 0.860638i | \(0.329935\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1052.18 | 0.899719 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −341.404 | −0.284217 | −0.142109 | − | 0.989851i | \(-0.545388\pi\) | ||||
−0.142109 | + | 0.989851i | \(0.545388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1010.16 | 0.819111 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1692.90 | 1.33768 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −113.417 | −0.0873692 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2886.98 | 2.16903 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1752.83 | 1.28494 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1464.81 | 1.04814 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −258.090 | −0.180329 | −0.0901644 | − | 0.995927i | \(-0.528739\pi\) | ||||
−0.0901644 | + | 0.995927i | \(0.528739\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −352.975 | −0.240912 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −728.188 | −0.485665 | −0.242832 | − | 0.970068i | \(-0.578077\pi\) | ||||
−0.242832 | + | 0.970068i | \(0.578077\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −295.625 | −0.192736 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 253.313 | 0.161494 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 82.1655 | 0.0512400 | 0.0256200 | − | 0.999672i | \(-0.491844\pi\) | ||||
0.0256200 | + | 0.999672i | \(0.491844\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −593.000 | −0.361853 | −0.180927 | − | 0.983497i | \(-0.557910\pi\) | ||||
−0.180927 | + | 0.983497i | \(0.557910\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2499.27 | −1.49274 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3508.73 | 2.05185 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 221.854 | 0.127062 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2376.32 | 1.33330 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 728.700 | 0.400654 | 0.200327 | − | 0.979729i | \(-0.435800\pi\) | ||||
0.200327 | + | 0.979729i | \(0.435800\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1203.47 | −0.648590 | −0.324295 | − | 0.945956i | \(-0.605127\pi\) | ||||
−0.324295 | + | 0.945956i | \(0.605127\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −629.521 | −0.332639 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1032.94 | −0.535278 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2704.74 | 1.37492 | 0.687458 | − | 0.726224i | \(-0.258727\pi\) | ||||
0.687458 | + | 0.726224i | \(0.258727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −251.473 | −0.125428 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −745.457 | −0.364908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1310.50 | −0.629732 | −0.314866 | − | 0.949136i | \(-0.601960\pi\) | ||||
−0.314866 | + | 0.949136i | \(0.601960\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3794.79 | 1.79045 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2891.17 | 1.33967 | 0.669837 | − | 0.742508i | \(-0.266364\pi\) | ||||
0.669837 | + | 0.742508i | \(0.266364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 721.730 | 0.328507 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1640.86 | −0.733800 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2915.04 | 1.28108 | 0.640539 | − | 0.767925i | \(-0.278711\pi\) | ||||
0.640539 | + | 0.767925i | \(0.278711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −375.286 | −0.162108 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2893.43 | −1.22872 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2414.92 | −1.00838 | −0.504188 | − | 0.863594i | \(-0.668208\pi\) | ||||
−0.504188 | + | 0.863594i | \(0.668208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 100.467 | 0.0412576 | 0.0206288 | − | 0.999787i | \(-0.493433\pi\) | ||||
0.0206288 | + | 0.999787i | \(0.493433\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 141.537 | 0.0571733 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1053.89 | 0.418830 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1304.75 | −0.510230 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −186.935 | −0.0719445 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4186.06 | 1.58583 | 0.792914 | − | 0.609334i | \(-0.208563\pi\) | ||||
0.792914 | + | 0.609334i | \(0.208563\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2681.27 | 1.00001 | 0.500006 | − | 0.866022i | \(-0.333331\pi\) | ||||
0.500006 | + | 0.866022i | \(0.333331\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3156.69 | 1.15926 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2684.48 | 0.970869 | 0.485435 | − | 0.874273i | \(-0.338661\pi\) | ||||
0.485435 | + | 0.874273i | \(0.338661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3671.70 | 1.30794 | 0.653970 | − | 0.756520i | \(-0.273102\pi\) | ||||
0.653970 | + | 0.756520i | \(0.273102\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7624.74 | −2.67566 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −163.720 | −0.0566052 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1755.68 | 0.598155 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4137.65 | −1.38931 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3400.87 | −1.12557 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4641.03 | 1.51423 | 0.757113 | − | 0.653284i | \(-0.226609\pi\) | ||||
0.757113 | + | 0.653284i | \(0.226609\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4357.33 | −1.40169 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −353.547 | −0.112148 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 762.272 | 0.238462 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1713.85 | 0.528819 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1085.36 | −0.330358 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1275.71 | 0.383086 | 0.191543 | − | 0.981484i | \(-0.438651\pi\) | ||||
0.191543 | + | 0.981484i | \(0.438651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2083.02 | −0.617192 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 876.500 | 0.256279 | 0.128140 | − | 0.991756i | \(-0.459099\pi\) | ||||
0.128140 | + | 0.991756i | \(0.459099\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1083.31 | −0.312606 | −0.156303 | − | 0.987709i | \(-0.549958\pi\) | ||||
−0.156303 | + | 0.987709i | \(0.549958\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2800.41 | −0.797633 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5786.21 | 1.62690 | 0.813448 | − | 0.581637i | \(-0.197588\pi\) | ||||
0.813448 | + | 0.581637i | \(0.197588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2503.32 | −0.694888 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3290.23 | 0.901786 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1971.04 | −0.533456 | −0.266728 | − | 0.963772i | \(-0.585943\pi\) | ||||
−0.266728 | + | 0.963772i | \(0.585943\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4272.70 | −1.14203 | −0.571014 | − | 0.820941i | \(-0.693450\pi\) | ||||
−0.571014 | + | 0.820941i | \(0.693450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5424.37 | 1.43199 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2380.18 | 0.620669 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2829.01 | −0.728768 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10616.8 | −2.70206 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2804.44 | 0.705238 | 0.352619 | − | 0.935767i | \(-0.385291\pi\) | ||||
0.352619 | + | 0.935767i | \(0.385291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8575.75 | −2.13104 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1173.85 | −0.288271 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3591.88 | 0.871811 | 0.435906 | − | 0.899992i | \(-0.356428\pi\) | ||||
0.435906 | + | 0.899992i | \(0.356428\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −777.729 | −0.186586 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −908.724 | −0.215512 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4143.91 | 0.971576 | 0.485788 | − | 0.874077i | \(-0.338533\pi\) | ||||
0.485788 | + | 0.874077i | \(0.338533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −251.880 | −0.0583883 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1004.89 | 0.230331 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4024.31 | 0.912143 | 0.456072 | − | 0.889943i | \(-0.349256\pi\) | ||||
0.456072 | + | 0.889943i | \(0.349256\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6233.96 | 1.39737 | 0.698683 | − | 0.715431i | \(-0.253770\pi\) | ||||
0.698683 | + | 0.715431i | \(0.253770\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2329.52 | −0.516442 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4317.30 | −0.946702 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −435.106 | −0.0943789 | −0.0471895 | − | 0.998886i | \(-0.515026\pi\) | ||||
−0.0471895 | + | 0.998886i | \(0.515026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4230.98 | 0.907893 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3805.46 | −0.807882 | −0.403941 | − | 0.914785i | \(-0.632360\pi\) | ||||
−0.403941 | + | 0.914785i | \(0.632360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −239.164 | −0.0502361 | −0.0251180 | − | 0.999684i | \(-0.507996\pi\) | ||||
−0.0251180 | + | 0.999684i | \(0.507996\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3059.66 | −0.635926 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1295.62 | −0.266474 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4509.40 | −0.917850 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6398.65 | −1.28899 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 719.126 | 0.143385 | 0.0716925 | − | 0.997427i | \(-0.477160\pi\) | ||||
0.0716925 | + | 0.997427i | \(0.477160\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2898.12 | −0.571984 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2150.50 | −0.420151 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7133.73 | −1.37978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 260.904 | 0.0499610 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12182.5 | 2.30979 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 141.767 | 0.0266148 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9702.09 | −1.80367 | −0.901836 | − | 0.432078i | \(-0.857780\pi\) | ||||
−0.901836 | + | 0.432078i | \(0.857780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11957.2 | 2.20137 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3369.02 | 0.614275 | 0.307137 | − | 0.951665i | \(-0.400629\pi\) | ||||
0.307137 | + | 0.951665i | \(0.400629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5269.30 | −0.951561 | −0.475781 | − | 0.879564i | \(-0.657834\pi\) | ||||
−0.475781 | + | 0.879564i | \(0.657834\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1353.34 | −0.242070 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7664.88 | −1.35805 | −0.679026 | − | 0.734114i | \(-0.737598\pi\) | ||||
−0.679026 | + | 0.734114i | \(0.737598\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1883.43 | −0.330571 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9495.15 | 1.65099 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1052.00 | 0.181222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3591.34 | −0.612960 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8851.94 | −1.49698 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1847.35 | 0.309568 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6587.05 | −1.09383 | −0.546914 | − | 0.837189i | \(-0.684198\pi\) | ||||
−0.546914 | + | 0.837189i | \(0.684198\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4316.78 | −0.710385 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7637.11 | −1.24555 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11419.9 | 1.84595 | 0.922973 | − | 0.384865i | \(-0.125752\pi\) | ||||
0.922973 | + | 0.384865i | \(0.125752\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2607.56 | 0.417767 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8769.19 | 1.39260 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3692.88 | −0.581332 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7715.35 | −1.20400 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2175.03 | −0.336488 | −0.168244 | − | 0.985745i | \(-0.553810\pi\) | ||||
−0.168244 | + | 0.985745i | \(0.553810\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5659.99 | 0.868115 | 0.434058 | − | 0.900885i | \(-0.357081\pi\) | ||||
0.434058 | + | 0.900885i | \(0.357081\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1788.89 | −0.272034 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2506.30 | −0.377895 | −0.188948 | − | 0.981987i | \(-0.560508\pi\) | ||||
−0.188948 | + | 0.981987i | \(0.560508\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4364.40 | −0.652502 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 866.253 | 0.128423 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4848.73 | 0.712831 | 0.356415 | − | 0.934328i | \(-0.383999\pi\) | ||||
0.356415 | + | 0.934328i | \(0.383999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4116.95 | −0.600226 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22050.1 | −3.18823 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1716.63 | 0.246171 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9034.96 | 1.28507 | 0.642535 | − | 0.766256i | \(-0.277883\pi\) | ||||
0.642535 | + | 0.766256i | \(0.277883\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7191.32 | −1.01454 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 185.878 | 0.0260116 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4060.90 | 0.563715 | 0.281857 | − | 0.959456i | \(-0.409050\pi\) | ||||
0.281857 | + | 0.959456i | \(0.409050\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11187.9 | −1.54064 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1566.73 | −0.214034 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6094.76 | 0.826034 | 0.413017 | − | 0.910723i | \(-0.364475\pi\) | ||||
0.413017 | + | 0.910723i | \(0.364475\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1971.23 | 0.265063 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4602.40 | 0.614025 | 0.307013 | − | 0.951705i | \(-0.400671\pi\) | ||||
0.307013 | + | 0.951705i | \(0.400671\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2804.95 | −0.371308 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1448.15 | 0.190215 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9393.43 | 1.22433 | 0.612167 | − | 0.790729i | \(-0.290298\pi\) | ||||
0.612167 | + | 0.790729i | \(0.290298\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2652.75 | 0.343108 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5561.72 | 0.713872 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3295.57 | 0.419792 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13398.1 | 1.69378 | 0.846889 | − | 0.531769i | \(-0.178473\pi\) | ||||
0.846889 | + | 0.531769i | \(0.178473\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2257.91 | 0.283300 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12917.9 | −1.60870 | −0.804348 | − | 0.594159i | \(-0.797485\pi\) | ||||
−0.804348 | + | 0.594159i | \(0.797485\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7294.64 | 0.901667 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4537.69 | 0.556740 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8947.01 | −1.08965 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5221.70 | −0.631288 | −0.315644 | − | 0.948878i | \(-0.602220\pi\) | ||||
−0.315644 | + | 0.948878i | \(0.602220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −627.560 | −0.0753169 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2138.70 | 0.254815 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10634.0 | −1.25784 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4529.19 | 0.531883 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6246.54 | −0.728314 | −0.364157 | − | 0.931338i | \(-0.618643\pi\) | ||||
−0.364157 | + | 0.931338i | \(0.618643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 583.420 | 0.0675396 | 0.0337698 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337698 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10253.7 | 1.17861 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1335.48 | 0.152424 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −104.618 | −0.0118567 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −26798.8 | −3.01599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4845.37 | 0.541516 | 0.270758 | − | 0.962647i | \(-0.412726\pi\) | ||||
0.270758 | + | 0.962647i | \(0.412726\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2159.85 | 0.239714 | 0.119857 | − | 0.992791i | \(-0.461756\pi\) | ||||
0.119857 | + | 0.992791i | \(0.461756\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1694.47 | −0.186767 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6914.45 | 0.756895 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17016.0 | −1.84995 | −0.924976 | − | 0.380026i | \(-0.875915\pi\) | ||||
−0.924976 | + | 0.380026i | \(0.875915\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9749.31 | −1.05273 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3676.92 | −0.394347 | −0.197173 | − | 0.980369i | \(-0.563176\pi\) | ||||
−0.197173 | + | 0.980369i | \(0.563176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1006.52 | 0.107222 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5565.63 | −0.588916 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11074.1 | 1.16396 | 0.581979 | − | 0.813204i | \(-0.302279\pi\) | ||||
0.581979 | + | 0.813204i | \(0.302279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14904.8 | −1.55619 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9191.82 | 0.953354 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2333.29 | −0.240410 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1146.80 | −0.117386 | −0.0586928 | − | 0.998276i | \(-0.518693\pi\) | ||||
−0.0586928 | + | 0.998276i | \(0.518693\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 665.217 | 0.0676464 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15788.0 | 1.59505 | 0.797526 | − | 0.603284i | \(-0.206142\pi\) | ||||
0.797526 | + | 0.603284i | \(0.206142\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2709.43 | −0.271961 | −0.135981 | − | 0.990711i | \(-0.543418\pi\) | ||||
−0.135981 | + | 0.990711i | \(0.543418\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7889.37 | 0.786798 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16216.0 | 1.60682 | 0.803411 | − | 0.595425i | \(-0.203016\pi\) | ||||
0.803411 | + | 0.595425i | \(0.203016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5635.88 | 0.554884 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20658.2 | −2.02097 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3001.44 | 0.291769 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3480.95 | 0.336246 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1031.71 | 0.0990333 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12106.9 | 1.15487 | 0.577433 | − | 0.816438i | \(-0.304055\pi\) | ||||
0.577433 | + | 0.816438i | \(0.304055\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7442.56 | −0.705513 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5693.62 | 0.536374 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6409.03 | −0.600039 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14106.0 | −1.31253 | −0.656267 | − | 0.754529i | \(-0.727865\pi\) | ||||
−0.656267 | + | 0.754529i | \(0.727865\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10009.3 | 0.925635 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16587.4 | 1.52460 | 0.762299 | − | 0.647225i | \(-0.224070\pi\) | ||||
0.762299 | + | 0.647225i | \(0.224070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 582.605 | 0.0532235 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15568.8 | −1.41367 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3220.75 | 0.290685 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5294.94 | 0.475018 | 0.237509 | − | 0.971385i | \(-0.423669\pi\) | ||||
0.237509 | + | 0.971385i | \(0.423669\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −22082.1 | −1.96917 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5856.03 | −0.519101 | −0.259550 | − | 0.965730i | \(-0.583574\pi\) | ||||
−0.259550 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12202.2 | 1.07523 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5512.40 | −0.482868 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3680.23 | 0.320478 | 0.160239 | − | 0.987078i | \(-0.448773\pi\) | ||||
0.160239 | + | 0.987078i | \(0.448773\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1266.81 | −0.109668 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1733.91 | 0.149228 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11976.6 | 1.02477 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21252.0 | 1.80785 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22264.4 | −1.88304 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15679.1 | 1.31845 | 0.659227 | − | 0.751944i | \(-0.270884\pi\) | ||||
0.659227 | + | 0.751944i | \(0.270884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17311.4 | −1.44737 | −0.723686 | − | 0.690130i | \(-0.757553\pi\) | ||||
−0.723686 | + | 0.690130i | \(0.757553\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2866.35 | 0.238281 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2712.58 | −0.224216 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5268.72 | 0.433034 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11870.8 | 0.970152 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12398.6 | −1.00758 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9510.55 | 0.768555 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18444.6 | 1.48220 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −20206.5 | −1.61476 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7300.99 | 0.580211 | 0.290105 | − | 0.956995i | \(-0.406310\pi\) | ||||
0.290105 | + | 0.956995i | \(0.406310\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −767.340 | −0.0606441 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8866.30 | −0.696863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12610.1 | 0.985684 | 0.492842 | − | 0.870119i | \(-0.335958\pi\) | ||||
0.492842 | + | 0.870119i | \(0.335958\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −580.682 | −0.0451419 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1518.57 | 0.117411 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2432.00 | −0.187015 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8049.36 | −0.615633 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2845.32 | −0.216446 | −0.108223 | − | 0.994127i | \(-0.534516\pi\) | ||||
−0.108223 | + | 0.994127i | \(0.534516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2496.75 | 0.188911 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9965.39 | 0.749981 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3877.50 | 0.290261 | 0.145131 | − | 0.989412i | \(-0.453640\pi\) | ||||
0.145131 | + | 0.989412i | \(0.453640\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2611.79 | 0.194476 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3348.64 | −0.248024 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22052.8 | −1.62478 | −0.812391 | − | 0.583113i | \(-0.801835\pi\) | ||||
−0.812391 | + | 0.583113i | \(0.801835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3017.56 | 0.221158 | 0.110579 | − | 0.993867i | \(-0.464730\pi\) | ||||
0.110579 | + | 0.993867i | \(0.464730\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31972.1 | −2.33099 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8777.68 | 0.636617 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9766.04 | 0.704620 | 0.352310 | − | 0.935883i | \(-0.385396\pi\) | ||||
0.352310 | + | 0.935883i | \(0.385396\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −20478.9 | −1.46990 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7847.49 | 0.560359 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2138.34 | 0.151906 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12950.9 | −0.915308 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20684.2 | 1.45439 | 0.727195 | − | 0.686431i | \(-0.240824\pi\) | ||||
0.727195 | + | 0.686431i | \(0.240824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7070.41 | −0.494620 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20503.4 | −1.42707 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20556.7 | 1.42354 | 0.711772 | − | 0.702410i | \(-0.247893\pi\) | ||||
0.711772 | + | 0.702410i | \(0.247893\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 867.658 | 0.0597824 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28043.6 | −1.92252 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11055.7 | 0.754131 | 0.377066 | − | 0.926186i | \(-0.376933\pi\) | ||||
0.377066 | + | 0.926186i | \(0.376933\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8326.30 | −0.565119 | −0.282560 | − | 0.959250i | \(-0.591184\pi\) | ||||
−0.282560 | + | 0.959250i | \(0.591184\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31281.9 | 2.11260 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22085.8 | −1.48416 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22922.1 | 1.53275 | 0.766374 | − | 0.642395i | \(-0.222059\pi\) | ||||
0.766374 | + | 0.642395i | \(0.222059\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1250.45 | 0.0832033 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17678.4 | 1.17053 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8197.48 | −0.540119 | −0.270060 | − | 0.962844i | \(-0.587043\pi\) | ||||
−0.270060 | + | 0.962844i | \(0.587043\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −13409.4 | −0.879220 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27147.0 | −1.77131 | −0.885656 | − | 0.464343i | \(-0.846291\pi\) | ||||
−0.885656 | + | 0.464343i | \(0.846291\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 472.406 | 0.0306747 | 0.0153373 | − | 0.999882i | \(-0.495118\pi\) | ||||
0.0153373 | + | 0.999882i | \(0.495118\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4372.27 | 0.282534 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −742.775 | −0.0477667 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2896.64 | −0.185385 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25975.0 | 1.65445 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2767.59 | 0.175439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2414.00 | 0.152297 | 0.0761487 | − | 0.997096i | \(-0.475738\pi\) | ||||
0.0761487 | + | 0.997096i | \(0.475738\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −35447.1 | −2.22574 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1974.42 | 0.123390 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16808.8 | −1.04551 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17876.8 | 1.10672 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10379.6 | −0.639575 | −0.319788 | − | 0.947489i | \(-0.603612\pi\) | ||||
−0.319788 | + | 0.947489i | \(0.603612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19509.5 | −1.19655 | −0.598275 | − | 0.801291i | \(-0.704147\pi\) | ||||
−0.598275 | + | 0.801291i | \(0.704147\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2700.31 | 0.164844 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15125.8 | 0.919096 | 0.459548 | − | 0.888153i | \(-0.348011\pi\) | ||||
0.459548 | + | 0.888153i | \(0.348011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24603.7 | 1.48810 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5822.04 | −0.350513 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22790.8 | −1.36581 | −0.682905 | − | 0.730507i | \(-0.739284\pi\) | ||||
−0.682905 | + | 0.730507i | \(0.739284\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5570.75 | 0.332316 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −7031.39 | −0.417535 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13542.4 | −0.800514 | −0.400257 | − | 0.916403i | \(-0.631079\pi\) | ||||
−0.400257 | + | 0.916403i | \(0.631079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23999.0 | −1.41218 | −0.706092 | − | 0.708120i | \(-0.749544\pi\) | ||||
−0.706092 | + | 0.708120i | \(0.749544\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8289.70 | 0.485589 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2261.57 | 0.131880 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3829.29 | 0.222295 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9743.59 | −0.563092 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1203.53 | −0.0692425 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34631.5 | 1.98357 | 0.991787 | − | 0.127901i | \(-0.0408240\pi\) | ||||
0.991787 | + | 0.127901i | \(0.0408240\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2201.14 | 0.125514 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5200.08 | 0.295207 | 0.147604 | − | 0.989047i | \(-0.452844\pi\) | ||||
0.147604 | + | 0.989047i | \(0.452844\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4729.61 | 0.267313 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6694.50 | −0.376701 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11690.2 | −0.654926 | −0.327463 | − | 0.944864i | \(-0.606194\pi\) | ||||
−0.327463 | + | 0.944864i | \(0.606194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −628.578 | −0.0350609 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8274.03 | 0.459496 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1778.78 | 0.0983542 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13188.4 | 0.726064 | 0.363032 | − | 0.931777i | \(-0.381742\pi\) | ||||
0.363032 | + | 0.931777i | \(0.381742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11489.2 | 0.629781 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4536.54 | 0.247598 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4610.53 | 0.250554 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −44193.6 | −2.39135 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19761.3 | −1.06473 | −0.532364 | − | 0.846516i | \(-0.678696\pi\) | ||||
−0.532364 | + | 0.846516i | \(0.678696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7213.79 | 0.387017 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19119.8 | 1.02141 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9004.77 | −0.479009 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16955.0 | −0.898106 | −0.449053 | − | 0.893505i | \(-0.648239\pi\) | ||||
−0.449053 | + | 0.893505i | \(0.648239\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13498.8 | −0.712017 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17829.0 | −0.936467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26842.3 | −1.40398 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15054.3 | 0.784120 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8924.11 | −0.462884 | −0.231442 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231442 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8838.29 | −0.456526 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32633.8 | 1.67865 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1927.78 | 0.0987531 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14644.9 | −0.747112 | −0.373556 | − | 0.927608i | \(-0.621862\pi\) | ||||
−0.373556 | + | 0.927608i | \(0.621862\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25415.0 | −1.29121 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −928.440 | −0.0469762 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31105.6 | 1.56741 | 0.783704 | − | 0.621134i | \(-0.213328\pi\) | ||||
0.783704 | + | 0.621134i | \(0.213328\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −18179.2 | −0.912313 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 64835.3 | 3.24049 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29071.3 | −1.44710 | −0.723549 | − | 0.690273i | \(-0.757490\pi\) | ||||
−0.723549 | + | 0.690273i | \(0.757490\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21607.3 | 1.07121 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8095.53 | −0.399726 | −0.199863 | − | 0.979824i | \(-0.564050\pi\) | ||||
−0.199863 | + | 0.979824i | \(0.564050\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5574.66 | −0.274147 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 43557.4 | 2.13344 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7018.41 | −0.342386 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6109.17 | 0.296840 | 0.148420 | − | 0.988924i | \(-0.452581\pi\) | ||||
0.148420 | + | 0.988924i | \(0.452581\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21419.6 | −1.03662 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9206.73 | 0.443798 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17269.3 | 0.829146 | 0.414573 | − | 0.910016i | \(-0.363931\pi\) | ||||
0.414573 | + | 0.910016i | \(0.363931\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 65499.5 | 3.13239 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39975.0 | 1.90420 | 0.952098 | − | 0.305792i | \(-0.0989212\pi\) | ||||
0.952098 | + | 0.305792i | \(0.0989212\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6542.97 | 0.310448 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4815.93 | 0.227608 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20466.5 | 0.963499 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29413.2 | −1.37928 | −0.689640 | − | 0.724152i | \(-0.742231\pi\) | ||||
−0.689640 | + | 0.724152i | \(0.742231\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27433.9 | −1.28146 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29797.9 | 1.38649 | 0.693245 | − | 0.720702i | \(-0.256180\pi\) | ||||
0.693245 | + | 0.720702i | \(0.256180\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8975.67 | −0.416020 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5940.11 | 0.274260 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12017.5 | 0.552721 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 37051.6 | 1.69758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 960.253 | 0.0438271 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20691.7 | −0.940786 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29580.7 | 1.33982 | 0.669910 | − | 0.742443i | \(-0.266333\pi\) | ||||
0.669910 | + | 0.742443i | \(0.266333\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31650.2 | −1.42811 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1927.40 | −0.0866375 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1001.15 | −0.0448323 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1923.80 | 0.0858242 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35669.3 | 1.58528 | 0.792642 | − | 0.609688i | \(-0.208705\pi\) | ||||
0.792642 | + | 0.609688i | \(0.208705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6573.90 | −0.291073 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4122.77 | −0.181861 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14573.4 | −0.640451 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5702.86 | 0.249689 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30736.7 | −1.34075 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27538.1 | −1.19677 | −0.598386 | − | 0.801208i | \(-0.704191\pi\) | ||||
−0.598386 | + | 0.801208i | \(0.704191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −428.113 | −0.0185365 | −0.00926824 | − | 0.999957i | \(-0.502950\pi\) | ||||
−0.00926824 | + | 0.999957i | \(0.502950\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −47613.5 | −2.05397 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10025.5 | 0.430894 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2420.00 | −0.103629 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 9557.27 | 0.407763 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22381.3 | −0.951415 | −0.475707 | − | 0.879604i | \(-0.657808\pi\) | ||||
−0.475707 | + | 0.879604i | \(0.657808\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4884.52 | −0.206882 | −0.103441 | − | 0.994636i | \(-0.532985\pi\) | ||||
−0.103441 | + | 0.994636i | \(0.532985\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 32974.5 | 1.39154 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20727.9 | 0.871558 | 0.435779 | − | 0.900054i | \(-0.356473\pi\) | ||||
0.435779 | + | 0.900054i | \(0.356473\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7720.98 | −0.323475 | −0.161738 | − | 0.986834i | \(-0.551710\pi\) | ||||
−0.161738 | + | 0.986834i | \(0.551710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3323.23 | 0.138726 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6250.51 | 0.259985 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22117.9 | −0.916671 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4470.90 | −0.184632 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39526.8 | 1.62648 | 0.813239 | − | 0.581929i | \(-0.197702\pi\) | ||||
0.813239 | + | 0.581929i | \(0.197702\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29065.2 | 1.18749 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5521.34 | −0.224781 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16298.5 | 0.661183 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1826.67 | 0.0738414 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18190.5 | 0.732742 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6398.26 | −0.256826 | −0.128413 | − | 0.991721i | \(-0.540988\pi\) | ||||
−0.128413 | + | 0.991721i | \(0.540988\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12552.8 | 0.502103 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18780.2 | 0.748563 | 0.374282 | − | 0.927315i | \(-0.377889\pi\) | ||||
0.374282 | + | 0.927315i | \(0.377889\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18787.8 | 0.746253 | 0.373127 | − | 0.927780i | \(-0.378286\pi\) | ||||
0.373127 | + | 0.927780i | \(0.378286\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9895.62 | 0.391686 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28372.1 | −1.11912 | −0.559559 | − | 0.828791i | \(-0.689029\pi\) | ||||
−0.559559 | + | 0.828791i | \(0.689029\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22300.5 | −0.876578 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34441.7 | 1.34914 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27977.7 | −1.09215 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 53933.2 | 2.09811 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 26251.7 | 1.01774 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8269.61 | 0.319502 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3003.79 | 0.115656 | 0.0578282 | − | 0.998327i | \(-0.481582\pi\) | ||||
0.0578282 | + | 0.998327i | \(0.481582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5492.51 | −0.210760 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28184.2 | 1.07781 | 0.538904 | − | 0.842367i | \(-0.318838\pi\) | ||||
0.538904 | + | 0.842367i | \(0.318838\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12092.6 | −0.460871 | −0.230435 | − | 0.973088i | \(-0.574015\pi\) | ||||
−0.230435 | + | 0.973088i | \(0.574015\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 22135.2 | 0.840752 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41525.1 | 1.57190 | 0.785951 | − | 0.618289i | \(-0.212174\pi\) | ||||
0.785951 | + | 0.618289i | \(0.212174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1457.05 | −0.0549694 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38522.8 | −1.44844 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −17135.0 | −0.642107 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18474.5 | 0.689982 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 54485.7 | 2.02812 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3915.66 | −0.145266 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −661.456 | −0.0244576 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1992.72 | −0.0734370 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −768.585 | −0.0282305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17464.3 | −0.639353 | −0.319676 | − | 0.947527i | \(-0.603574\pi\) | ||||
−0.319676 | + | 0.947527i | \(0.603574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −49980.9 | −1.82372 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8847.73 | 0.321776 | 0.160888 | − | 0.986973i | \(-0.448564\pi\) | ||||
0.160888 | + | 0.986973i | \(0.448564\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 90277.7 | 3.27246 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1082.78 | −0.0391208 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4110.99 | −0.148044 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45221.9 | 1.62321 | 0.811606 | − | 0.584205i | \(-0.198594\pi\) | ||||
0.811606 | + | 0.584205i | \(0.198594\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 74102.2 | 2.65119 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30821.4 | 1.09913 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9157.68 | 0.325516 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −49056.9 | −1.73812 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5013.65 | −0.177064 | −0.0885320 | − | 0.996073i | \(-0.528218\pi\) | ||||
−0.0885320 | + | 0.996073i | \(0.528218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16292.1 | 0.573526 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −25731.7 | −0.902915 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9981.56 | 0.349125 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39065.1 | −1.36201 | −0.681004 | − | 0.732280i | \(-0.738456\pi\) | ||||
−0.681004 | + | 0.732280i | \(0.738456\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 40245.7 | 1.39869 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18526.0 | 0.641796 | 0.320898 | − | 0.947114i | \(-0.396015\pi\) | ||||
0.320898 | + | 0.947114i | \(0.396015\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30303.6 | 1.04647 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1430.08 | 0.0492280 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30773.5 | −1.05597 | −0.527986 | − | 0.849253i | \(-0.677053\pi\) | ||||
−0.527986 | + | 0.849253i | \(0.677053\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12122.8 | −0.414672 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 58542.5 | 1.99618 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32135.7 | −1.09232 | −0.546158 | − | 0.837682i | \(-0.683910\pi\) | ||||
−0.546158 | + | 0.837682i | \(0.683910\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32024.0 | −1.08510 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14385.2 | 0.485902 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 463.866 | 0.0156194 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11559.9 | −0.388032 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38955.6 | −1.30356 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −20512.1 | −0.684258 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10300.8 | 0.342555 | 0.171278 | − | 0.985223i | \(-0.445211\pi\) | ||||
0.171278 | + | 0.985223i | \(0.445211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8034.89 | −0.266375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26187.1 | 0.865485 | 0.432742 | − | 0.901518i | \(-0.357546\pi\) | ||||
0.432742 | + | 0.901518i | \(0.357546\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3347.78 | −0.110303 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 27429.8 | 0.900981 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21578.3 | 0.706604 | 0.353302 | − | 0.935509i | \(-0.385059\pi\) | ||||
0.353302 | + | 0.935509i | \(0.385059\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8544.90 | −0.278954 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36316.7 | 1.18196 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2362.28 | −0.0766481 | −0.0383240 | − | 0.999265i | \(-0.512202\pi\) | ||||
−0.0383240 | + | 0.999265i | \(0.512202\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20536.7 | −0.664317 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14109.6 | −0.455029 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6102.36 | −0.196202 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15492.6 | −0.496609 | −0.248304 | − | 0.968682i | \(-0.579873\pi\) | ||||
−0.248304 | + | 0.968682i | \(0.579873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 50310.3 | 1.60780 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28089.1 | −0.894958 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30991.6 | 0.984467 | 0.492233 | − | 0.870463i | \(-0.336181\pi\) | ||||
0.492233 | + | 0.870463i | \(0.336181\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4561.56 | 0.144466 |
(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 | 928.4.a.e.1.1 | yes | 9 | |
4.3 | odd | 2 | 928.4.a.d.1.9 | ✓ | 9 | ||
8.3 | odd | 2 | 1856.4.a.bg.1.1 | 9 | |||
8.5 | even | 2 | 1856.4.a.bf.1.9 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.d.1.9 | ✓ | 9 | 4.3 | odd | 2 | ||
928.4.a.e.1.1 | yes | 9 | 1.1 | even | 1 | trivial | |
1856.4.a.bf.1.9 | 9 | 8.5 | even | 2 | |||
1856.4.a.bg.1.1 | 9 | 8.3 | odd | 2 |