Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,4,Mod(1,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.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: | \(69.3862461668\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{177}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-6.15207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.30413 | 0.563859 | 0.281929 | − | 0.959435i | \(-0.409026\pi\) | ||||
0.281929 | + | 0.959435i | \(0.409026\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 48.9124 | 1.34069 | 0.670347 | − | 0.742047i | \(-0.266145\pi\) | ||||
0.670347 | + | 0.742047i | \(0.266145\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60827 | 0.0556464 | 0.0278232 | − | 0.999613i | \(-0.491142\pi\) | ||||
0.0278232 | + | 0.999613i | \(0.491142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.9124 | −0.325544 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −136.737 | −1.95080 | −0.975401 | − | 0.220436i | \(-0.929252\pi\) | ||||
−0.975401 | + | 0.220436i | \(0.929252\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45.2165 | −0.545968 | −0.272984 | − | 0.962019i | \(-0.588011\pi\) | ||||
−0.272984 | + | 0.962019i | \(0.588011\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −38.1289 | −0.345671 | −0.172836 | − | 0.984951i | \(-0.555293\pi\) | ||||
−0.172836 | + | 0.984951i | \(0.555293\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −85.2579 | −0.682063 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.7835 | 0.337988 | 0.168994 | − | 0.985617i | \(-0.445948\pi\) | ||||
0.168994 | + | 0.985617i | \(0.445948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.7835 | 0.0856512 | 0.0428256 | − | 0.999083i | \(-0.486364\pi\) | ||||
0.0428256 | + | 0.999083i | \(0.486364\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −146.737 | −0.774051 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 333.908 | 1.48362 | 0.741812 | − | 0.670608i | \(-0.233967\pi\) | ||||
0.741812 | + | 0.670608i | \(0.233967\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.82481 | −0.0321275 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −227.263 | −0.865670 | −0.432835 | − | 0.901473i | \(-0.642487\pi\) | ||||
−0.432835 | + | 0.901473i | \(0.642487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −398.433 | −1.41303 | −0.706517 | − | 0.707696i | \(-0.749735\pi\) | ||||
−0.706517 | + | 0.707696i | \(0.749735\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 56.7372 | 0.187953 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 184.608 | 0.572934 | 0.286467 | − | 0.958090i | \(-0.407519\pi\) | ||||
0.286467 | + | 0.958090i | \(0.407519\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 410.212 | 1.12630 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 359.825 | 0.932561 | 0.466281 | − | 0.884637i | \(-0.345594\pi\) | ||||
0.466281 | + | 0.884637i | \(0.345594\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 308.350 | 0.755963 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 135.650 | 0.315215 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −99.9075 | −0.220455 | −0.110228 | − | 0.993906i | \(-0.535158\pi\) | ||||
−0.110228 | + | 0.993906i | \(0.535158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 674.516 | 1.41579 | 0.707893 | − | 0.706320i | \(-0.249646\pi\) | ||||
0.707893 | + | 0.706320i | \(0.249646\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.4429 | 0.0313767 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −376.959 | −0.687356 | −0.343678 | − | 0.939088i | \(-0.611673\pi\) | ||||
−0.343678 | + | 0.939088i | \(0.611673\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 114.387 | 0.199573 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1187.60 | −1.98511 | −0.992553 | − | 0.121810i | \(-0.961130\pi\) | ||||
−0.992553 | + | 0.121810i | \(0.961130\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 735.825 | 1.17975 | 0.589875 | − | 0.807494i | \(-0.299177\pi\) | ||||
0.589875 | + | 0.807494i | \(0.299177\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 255.774 | 0.393789 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −836.774 | −1.19170 | −0.595851 | − | 0.803095i | \(-0.703185\pi\) | ||||
−0.595851 | + | 0.803095i | \(0.703185\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −293.732 | −0.388450 | −0.194225 | − | 0.980957i | \(-0.562219\pi\) | ||||
−0.194225 | + | 0.980957i | \(0.562219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −862.010 | −1.09998 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −158.350 | −0.195137 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1298.89 | −1.54699 | −0.773496 | − | 0.633801i | \(-0.781494\pi\) | ||||
−0.773496 | + | 0.633801i | \(0.781494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −44.3504 | −0.0494508 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −285.051 | −0.307849 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 201.041 | 0.210440 | 0.105220 | − | 0.994449i | \(-0.466445\pi\) | ||||
0.105220 | + | 0.994449i | \(0.466445\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 440.212 | 0.446898 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1053.51 | 1.03790 | 0.518952 | − | 0.854804i | \(-0.326322\pi\) | ||||
0.518952 | + | 0.854804i | \(0.326322\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1025.73 | −0.981247 | −0.490623 | − | 0.871372i | \(-0.663231\pi\) | ||||
−0.490623 | + | 0.871372i | \(0.663231\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −103.418 | −0.0934377 | −0.0467188 | − | 0.998908i | \(-0.514876\pi\) | ||||
−0.0467188 | + | 0.998908i | \(0.514876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −677.134 | −0.595024 | −0.297512 | − | 0.954718i | \(-0.596157\pi\) | ||||
−0.297512 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1001.72 | −0.856570 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −452.083 | −0.376357 | −0.188179 | − | 0.982135i | \(-0.560258\pi\) | ||||
−0.188179 | + | 0.982135i | \(0.560258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −240.370 | −0.194910 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.4744 | 0.0185488 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1061.42 | 0.797463 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 681.788 | 0.499795 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1325.49 | −0.948446 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1182.88 | −0.826482 | −0.413241 | − | 0.910622i | \(-0.635603\pi\) | ||||
−0.413241 | + | 0.910622i | \(0.635603\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1195.30 | 0.815816 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1257.75 | −0.838857 | −0.419429 | − | 0.907788i | \(-0.637770\pi\) | ||||
−0.419429 | + | 0.907788i | \(0.637770\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −170.212 | −0.108515 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −56.5256 | −0.0352504 | −0.0176252 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176252 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2113.57 | −1.28972 | −0.644858 | − | 0.764303i | \(-0.723083\pi\) | ||||
−0.644858 | + | 0.764303i | \(0.723083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −553.825 | −0.330783 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 127.577 | 0.0746049 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 332.754 | 0.190577 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1794.96 | 0.986904 | 0.493452 | − | 0.869773i | \(-0.335735\pi\) | ||||
0.493452 | + | 0.869773i | \(0.335735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 377.032 | 0.203195 | 0.101597 | − | 0.994826i | \(-0.467605\pi\) | ||||
0.101597 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1230.63 | −0.650268 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 93.1969 | 0.0482952 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 898.701 | 0.456842 | 0.228421 | − | 0.973562i | \(-0.426644\pi\) | ||||
0.228421 | + | 0.973562i | \(0.426644\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1079.47 | −0.538414 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3863.52 | 1.85653 | 0.928264 | − | 0.371922i | \(-0.121301\pi\) | ||||
0.928264 | + | 0.371922i | \(0.121301\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −925.051 | −0.436455 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2861.44 | 1.32590 | 0.662948 | − | 0.748666i | \(-0.269305\pi\) | ||||
0.662948 | + | 0.748666i | \(0.269305\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2190.20 | −0.996903 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −406.949 | −0.181989 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −979.005 | −0.430245 | −0.215122 | − | 0.976587i | \(-0.569015\pi\) | ||||
−0.215122 | + | 0.976587i | \(0.569015\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 299.723 | 0.127280 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1146.27 | −0.478640 | −0.239320 | − | 0.970941i | \(-0.576925\pi\) | ||||
−0.239320 | + | 0.970941i | \(0.576925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3929.33 | −1.61362 | −0.806809 | − | 0.590812i | \(-0.798808\pi\) | ||||
−0.806809 | + | 0.590812i | \(0.798808\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2023.55 | −0.817404 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2105.00 | 0.836554 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6688.15 | −2.61543 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2937.36 | −1.11277 | −0.556386 | − | 0.830924i | \(-0.687813\pi\) | ||||
−0.556386 | + | 0.830924i | \(0.687813\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3533.17 | −1.31774 | −0.658868 | − | 0.752259i | \(-0.728964\pi\) | ||||
−0.658868 | + | 0.752259i | \(0.728964\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −49.3286 | −0.0181154 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 584.856 | 0.211519 | 0.105760 | − | 0.994392i | \(-0.466273\pi\) | ||||
0.105760 | + | 0.994392i | \(0.466273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2158.08 | −0.768756 | −0.384378 | − | 0.923176i | \(-0.625584\pi\) | ||||
−0.384378 | + | 0.923176i | \(0.625584\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1130.88 | 0.396845 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1432.70 | −0.488116 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −343.160 | −0.115224 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2211.65 | −0.731976 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4290.04 | −1.39971 | −0.699855 | − | 0.714285i | \(-0.746752\pi\) | ||||
−0.699855 | + | 0.714285i | \(0.746752\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3562.81 | 1.14610 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2511.78 | −0.796752 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2207.47 | −0.681129 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −356.647 | −0.108555 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2743.78 | 0.823932 | 0.411966 | − | 0.911199i | \(-0.364842\pi\) | ||||
0.411966 | + | 0.911199i | \(0.364842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −767.321 | −0.227354 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1724.79 | 0.504311 | 0.252155 | − | 0.967687i | \(-0.418861\pi\) | ||||
0.252155 | + | 0.967687i | \(0.418861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4201.70 | −1.21247 | −0.606237 | − | 0.795284i | \(-0.707322\pi\) | ||||
−0.606237 | + | 0.795284i | \(0.707322\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1274.94 | 0.358472 | 0.179236 | − | 0.983806i | \(-0.442637\pi\) | ||||
0.179236 | + | 0.983806i | \(0.442637\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1163.80 | 0.323054 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2510.32 | 0.688029 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5967.16 | −1.61499 | −0.807497 | − | 0.589872i | \(-0.799178\pi\) | ||||
−0.807497 | + | 0.589872i | \(0.799178\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4881.64 | −1.30479 | −0.652395 | − | 0.757879i | \(-0.726236\pi\) | ||||
−0.652395 | + | 0.757879i | \(0.726236\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −117.937 | −0.0303812 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 881.197 | 0.224271 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2262.63 | −0.568988 | −0.284494 | − | 0.958678i | \(-0.591826\pi\) | ||||
−0.284494 | + | 0.958678i | \(0.591826\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1864.98 | −0.463439 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2586.03 | 0.635072 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6210.60 | 1.50742 | 0.753709 | − | 0.657209i | \(-0.228263\pi\) | ||||
0.753709 | + | 0.657209i | \(0.228263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 475.051 | 0.112663 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2972.69 | −0.696973 | −0.348486 | − | 0.937314i | \(-0.613304\pi\) | ||||
−0.348486 | + | 0.937314i | \(0.613304\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2268.38 | 0.525833 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3896.68 | 0.893157 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4443.42 | 1.00714 | 0.503569 | − | 0.863955i | \(-0.332020\pi\) | ||||
0.503569 | + | 0.863955i | \(0.332020\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6840.25 | 1.53327 | 0.766634 | − | 0.642084i | \(-0.221930\pi\) | ||||
0.766634 | + | 0.642084i | \(0.221930\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4170.17 | −0.914439 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3228.67 | −0.700332 | −0.350166 | − | 0.936688i | \(-0.613875\pi\) | ||||
−0.350166 | + | 0.936688i | \(0.613875\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 133.051 | 0.0285504 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6453.83 | −1.37012 | −0.685059 | − | 0.728488i | \(-0.740224\pi\) | ||||
−0.685059 | + | 0.728488i | \(0.740224\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3840.72 | −0.806739 | −0.403369 | − | 0.915037i | \(-0.632161\pi\) | ||||
−0.403369 | + | 0.915037i | \(0.632161\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 855.153 | 0.177737 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13784.1 | 2.80563 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −603.124 | −0.121497 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8801.01 | −1.75481 | −0.877407 | − | 0.479747i | \(-0.840728\pi\) | ||||
−0.877407 | + | 0.479747i | \(0.840728\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −629.830 | −0.124306 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1320.63 | −0.258017 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −99.4506 | −0.0192354 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3160.53 | −0.599234 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4252.24 | 0.798303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3926.72 | 0.730000 | 0.365000 | − | 0.931008i | \(-0.381069\pi\) | ||||
0.365000 | + | 0.931008i | \(0.381069\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3077.20 | 0.566523 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6143.13 | 1.12008 | 0.560040 | − | 0.828466i | \(-0.310786\pi\) | ||||
0.560040 | + | 0.828466i | \(0.310786\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3824.19 | −0.690594 | −0.345297 | − | 0.938493i | \(-0.612222\pi\) | ||||
−0.345297 | + | 0.938493i | \(0.612222\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7949.68 | 1.40851 | 0.704257 | − | 0.709946i | \(-0.251280\pi\) | ||||
0.704257 | + | 0.709946i | \(0.251280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2581.77 | 0.453138 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 310.255 | 0.0539463 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6182.78 | 1.06508 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −222.376 | −0.0379544 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2031.40 | 0.343537 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11236.4 | −1.86588 | −0.932940 | − | 0.360032i | \(-0.882766\pi\) | ||||
−0.932940 | + | 0.360032i | \(0.882766\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3005.17 | 0.494541 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2376.40 | −0.387572 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8425.41 | 1.36190 | 0.680951 | − | 0.732329i | \(-0.261567\pi\) | ||||
0.680951 | + | 0.732329i | \(0.261567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1356.25 | 0.217290 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 723.095 | 0.114832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 721.110 | 0.112531 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7177.15 | 1.11034 | 0.555172 | − | 0.831735i | \(-0.312652\pi\) | ||||
0.555172 | + | 0.831735i | \(0.312652\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1549.41 | −0.237644 | −0.118822 | − | 0.992916i | \(-0.537912\pi\) | ||||
−0.118822 | + | 0.992916i | \(0.537912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −70.4233 | −0.0107092 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 566.231 | 0.0853752 | 0.0426876 | − | 0.999088i | \(-0.486408\pi\) | ||||
0.0426876 | + | 0.999088i | \(0.486408\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7486.81 | −1.11932 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3848.19 | 0.565738 | 0.282869 | − | 0.959159i | \(-0.408714\pi\) | ||||
0.282869 | + | 0.959159i | \(0.408714\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4814.46 | −0.701919 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3184.27 | −0.460415 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4638.74 | 0.665213 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12542.2 | −1.78392 | −0.891960 | − | 0.452113i | \(-0.850670\pi\) | ||||
−0.891960 | + | 0.452113i | \(0.850670\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2045.37 | −0.288557 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6345.87 | 0.880903 | 0.440452 | − | 0.897776i | \(-0.354818\pi\) | ||||
0.440452 | + | 0.897776i | \(0.354818\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3976.48 | 0.547586 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 137.673 | 0.0188078 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12200.2 | −1.65351 | −0.826757 | − | 0.562559i | \(-0.809817\pi\) | ||||
−0.826757 | + | 0.562559i | \(0.809817\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3548.63 | 0.477170 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2770.91 | 0.369679 | 0.184839 | − | 0.982769i | \(-0.440824\pi\) | ||||
0.184839 | + | 0.982769i | \(0.440824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3585.90 | −0.471011 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1581.89 | 0.206183 | 0.103091 | − | 0.994672i | \(-0.467127\pi\) | ||||
0.103091 | + | 0.994672i | \(0.467127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5213.65 | 0.674336 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3773.26 | 0.484314 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5275.13 | −0.671951 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14235.9 | 1.79970 | 0.899848 | − | 0.436203i | \(-0.143677\pi\) | ||||
0.899848 | + | 0.436203i | \(0.143677\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9556.18 | −1.19006 | −0.595028 | − | 0.803705i | \(-0.702859\pi\) | ||||
−0.595028 | + | 0.803705i | \(0.702859\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.5592 | 0.00476619 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 510.635 | 0.0626510 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16332.2 | 1.98909 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2858.17 | −0.345544 | −0.172772 | − | 0.984962i | \(-0.555272\pi\) | ||||
−0.172772 | + | 0.984962i | \(0.555272\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 169.577 | 0.0203518 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1851.73 | −0.219031 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6340.70 | 0.744617 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13333.3 | 1.55460 | 0.777299 | − | 0.629132i | \(-0.216589\pi\) | ||||
0.777299 | + | 0.629132i | \(0.216589\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13567.4 | −1.57063 | −0.785314 | − | 0.619098i | \(-0.787499\pi\) | ||||
−0.785314 | + | 0.619098i | \(0.787499\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1661.47 | 0.190978 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11657.9 | 1.33057 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −382.730 | −0.0430732 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14207.3 | 1.58780 | 0.793898 | − | 0.608051i | \(-0.208048\pi\) | ||||
0.793898 | + | 0.608051i | \(0.208048\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10530.6 | 1.16875 | 0.584375 | − | 0.811484i | \(-0.301340\pi\) | ||||
0.584375 | + | 0.811484i | \(0.301340\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −998.262 | −0.110030 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1724.06 | 0.188725 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4038.23 | 0.439030 | 0.219515 | − | 0.975609i | \(-0.429553\pi\) | ||||
0.219515 | + | 0.975609i | \(0.429553\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4574.15 | −0.490574 | −0.245287 | − | 0.969450i | \(-0.578882\pi\) | ||||
−0.245287 | + | 0.969450i | \(0.578882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8188.40 | −0.872286 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5384.88 | −0.569789 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14957.1 | 1.57209 | 0.786044 | − | 0.618171i | \(-0.212126\pi\) | ||||
0.786044 | + | 0.618171i | \(0.212126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11116.0 | −1.16060 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1131.09 | −0.117314 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3027.65 | 0.309907 | 0.154954 | − | 0.987922i | \(-0.450477\pi\) | ||||
0.154954 | + | 0.987922i | \(0.450477\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3691.90 | 0.375432 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10877.7 | 1.09897 | 0.549484 | − | 0.835504i | \(-0.314824\pi\) | ||||
0.549484 | + | 0.835504i | \(0.314824\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4038.28 | −0.405345 | −0.202673 | − | 0.979247i | \(-0.564963\pi\) | ||||
−0.202673 | + | 0.979247i | \(0.564963\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −279.591 | −0.0278833 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8411.80 | −0.833515 | −0.416758 | − | 0.909018i | \(-0.636834\pi\) | ||||
−0.416758 | + | 0.909018i | \(0.636834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2696.10 | −0.263758 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −19488.3 | −1.89445 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3855.07 | 0.372384 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3238.42 | 0.310854 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7172.70 | −0.684194 | −0.342097 | − | 0.939665i | \(-0.611137\pi\) | ||||
−0.342097 | + | 0.939665i | \(0.611137\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 870.921 | 0.0825584 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1267.39 | 0.118658 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5580.52 | −0.519256 | −0.259628 | − | 0.965709i | \(-0.583600\pi\) | ||||
−0.259628 | + | 0.965709i | \(0.583600\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11590.6 | −1.07187 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12489.4 | 1.14794 | 0.573972 | − | 0.818875i | \(-0.305402\pi\) | ||||
0.573972 | + | 0.818875i | \(0.305402\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7217.46 | −0.659347 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2775.15 | 0.251988 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15216.6 | −1.36511 | −0.682556 | − | 0.730834i | \(-0.739131\pi\) | ||||
−0.682556 | + | 0.730834i | \(0.739131\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8584.31 | −0.765506 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1814.89 | 0.160879 | 0.0804393 | − | 0.996760i | \(-0.474368\pi\) | ||||
0.0804393 | + | 0.996760i | \(0.474368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6641.47 | 0.585231 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6570.59 | 0.575562 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4853.68 | 0.422663 | 0.211332 | − | 0.977414i | \(-0.432220\pi\) | ||||
0.211332 | + | 0.977414i | \(0.432220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1220.85 | 0.105072 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6466.35 | −0.553285 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9029.63 | 0.768129 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2937.01 | 0.248402 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9913.18 | 0.833598 | 0.416799 | − | 0.908999i | \(-0.363152\pi\) | ||||
0.416799 | + | 0.908999i | \(0.363152\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4524.29 | 0.378267 | 0.189133 | − | 0.981951i | \(-0.439432\pi\) | ||||
0.189133 | + | 0.981951i | \(0.439432\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2021.45 | −0.167089 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10713.2 | −0.880512 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −899.168 | −0.0734850 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −592.763 | −0.0481715 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −651.963 | −0.0526857 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3438.82 | 0.276343 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3724.94 | 0.296022 | 0.148011 | − | 0.988986i | \(-0.452713\pi\) | ||||
0.148011 | + | 0.988986i | \(0.452713\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11788.0 | 0.931623 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4268.74 | −0.335510 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16121.6 | 1.26016 | 0.630082 | − | 0.776528i | \(-0.283021\pi\) | ||||
0.630082 | + | 0.776528i | \(0.283021\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6070.64 | 0.471928 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2386.69 | −0.184530 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6314.99 | −0.482985 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20451.7 | 1.55577 | 0.777887 | − | 0.628405i | \(-0.216292\pi\) | ||||
0.777887 | + | 0.628405i | \(0.216292\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1039.22 | −0.0786303 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20064.4 | 1.51002 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10046.7 | 0.752078 | 0.376039 | − | 0.926604i | \(-0.377286\pi\) | ||||
0.376039 | + | 0.926604i | \(0.377286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2849.99 | −0.212212 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15356.4 | −1.13141 | −0.565705 | − | 0.824608i | \(-0.691396\pi\) | ||||
−0.565705 | + | 0.824608i | \(0.691396\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19333.6 | −1.41696 | −0.708480 | − | 0.705731i | \(-0.750619\pi\) | ||||
−0.708480 | + | 0.705731i | \(0.750619\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8812.07 | 0.642460 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3250.79 | 0.235769 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26258.8 | −1.89458 | −0.947288 | − | 0.320384i | \(-0.896188\pi\) | ||||
−0.947288 | + | 0.320384i | \(0.896188\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10599.5 | 0.760795 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17599.9 | 1.25028 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 147.986 | 0.0104589 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4868.98 | 0.342358 | 0.171179 | − | 0.985240i | \(-0.445242\pi\) | ||||
0.171179 | + | 0.985240i | \(0.445242\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −668.457 | −0.0467628 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1754.57 | −0.122121 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13647.1 | 0.945055 | 0.472528 | − | 0.881316i | \(-0.343342\pi\) | ||||
0.472528 | + | 0.881316i | \(0.343342\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6474.25 | 0.443841 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7543.11 | 0.514529 | 0.257265 | − | 0.966341i | \(-0.417179\pi\) | ||||
0.257265 | + | 0.966341i | \(0.417179\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19522.4 | 1.32501 | 0.662507 | − | 0.749056i | \(-0.269493\pi\) | ||||
0.662507 | + | 0.749056i | \(0.269493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3392.63 | −0.229119 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6691.36 | 0.449657 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13804.5 | −0.923079 | −0.461539 | − | 0.887120i | \(-0.652703\pi\) | ||||
−0.461539 | + | 0.887120i | \(0.652703\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 481.508 | 0.0318817 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21718.8 | 1.43102 | 0.715508 | − | 0.698605i | \(-0.246195\pi\) | ||||
0.715508 | + | 0.698605i | \(0.246195\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4298.09 | 0.281814 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5183.85 | −0.338240 | −0.169120 | − | 0.985595i | \(-0.554093\pi\) | ||||
−0.169120 | + | 0.985595i | \(0.554093\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22003.7 | −1.42876 | −0.714382 | − | 0.699756i | \(-0.753292\pi\) | ||||
−0.714382 | + | 0.699756i | \(0.753292\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1029.48 | 0.0665244 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2301.14 | 0.147273 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6634.95 | 0.422607 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −45657.6 | −2.89426 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −985.836 | −0.0621957 | −0.0310979 | − | 0.999516i | \(-0.509900\pi\) | ||||
−0.0310979 | + | 0.999516i | \(0.509900\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12870.1 | 0.808123 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7457.01 | −0.466020 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10688.4 | −0.661702 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24282.6 | 1.49626 | 0.748131 | − | 0.663551i | \(-0.230951\pi\) | ||||
0.748131 | + | 0.663551i | \(0.230951\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4743.12 | 0.290903 | 0.145451 | − | 0.989365i | \(-0.453537\pi\) | ||||
0.145451 | + | 0.989365i | \(0.453537\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7535.33 | 0.460005 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29641.1 | −1.80110 | −0.900549 | − | 0.434754i | \(-0.856835\pi\) | ||||
−0.900549 | + | 0.434754i | \(0.856835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4886.72 | −0.295563 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23046.9 | −1.38116 | −0.690578 | − | 0.723258i | \(-0.742644\pi\) | ||||
−0.690578 | + | 0.723258i | \(0.742644\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7929.04 | −0.472997 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6622.42 | 0.393250 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5795.12 | 0.342558 | 0.171279 | − | 0.985223i | \(-0.445210\pi\) | ||||
0.171279 | + | 0.985223i | \(0.445210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2592.59 | −0.152557 | −0.0762784 | − | 0.997087i | \(-0.524304\pi\) | ||||
−0.0762784 | + | 0.997087i | \(0.524304\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1069.94 | 0.0626744 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2012.58 | −0.116833 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8231.33 | −0.475697 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32992.2 | 1.89814 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28156.0 | 1.61268 | 0.806341 | − | 0.591451i | \(-0.201445\pi\) | ||||
0.806341 | + | 0.591451i | \(0.201445\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2301.96 | 0.131263 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −20271.4 | −1.15080 | −0.575402 | − | 0.817871i | \(-0.695154\pi\) | ||||
−0.575402 | + | 0.817871i | \(0.695154\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5174.38 | −0.291164 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13267.0 | −0.743264 | −0.371632 | − | 0.928380i | \(-0.621202\pi\) | ||||
−0.371632 | + | 0.928380i | \(0.621202\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −356.345 | −0.0198763 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12605.1 | 0.700022 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 938.520 | 0.0518937 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15966.3 | 0.878995 | 0.439497 | − | 0.898244i | \(-0.355157\pi\) | ||||
0.439497 | + | 0.898244i | \(0.355157\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −13324.2 | −0.727217 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31075.3 | 1.68875 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3824.82 | −0.206964 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7525.29 | 0.405458 | 0.202729 | − | 0.979235i | \(-0.435019\pi\) | ||||
0.202729 | + | 0.979235i | \(0.435019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15098.1 | −0.810010 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3491.39 | −0.186515 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20033.6 | 1.06118 | 0.530591 | − | 0.847628i | \(-0.321970\pi\) | ||||
0.530591 | + | 0.847628i | \(0.321970\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7530.96 | −0.397234 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −563.678 | −0.0296071 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 804.261 | 0.0420666 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17901.5 | 0.932417 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8081.69 | 0.419188 | 0.209594 | − | 0.977788i | \(-0.432786\pi\) | ||||
0.209594 | + | 0.977788i | \(0.432786\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14644.9 | 0.753321 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4500.21 | −0.230529 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34117.8 | −1.74052 | −0.870262 | − | 0.492590i | \(-0.836050\pi\) | ||||
−0.870262 | + | 0.492590i | \(0.836050\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54480.6 | 2.75655 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20048.0 | −1.01022 | −0.505110 | − | 0.863055i | \(-0.668548\pi\) | ||||
−0.505110 | + | 0.863055i | \(0.668548\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18438.0 | −0.921534 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −407.607 | −0.0202897 | −0.0101448 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101448 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 353.811 | 0.0175406 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −128.374 | −0.00633861 | −0.00316930 | − | 0.999995i | \(-0.501009\pi\) | ||||
−0.00316930 | + | 0.999995i | \(0.501009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11315.7 | 0.556475 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2643.59 | −0.129483 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25076.0 | 1.21842 | 0.609212 | − | 0.793007i | \(-0.291486\pi\) | ||||
0.609212 | + | 0.793007i | \(0.291486\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6787.90 | 0.328506 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2376.86 | 0.114573 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21824.1 | −1.04783 | −0.523916 | − | 0.851770i | \(-0.675530\pi\) | ||||
−0.523916 | + | 0.851770i | \(0.675530\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5594.93 | 0.267567 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38939.2 | 1.85485 | 0.927427 | − | 0.374004i | \(-0.122015\pi\) | ||||
0.927427 | + | 0.374004i | \(0.122015\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7758.09 | −0.366659 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −260.586 | −0.0122675 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3079.42 | −0.144404 | −0.0722021 | − | 0.997390i | \(-0.523003\pi\) | ||||
−0.0722021 | + | 0.997390i | \(0.523003\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18631.8 | −0.870308 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31770.9 | −1.47829 | −0.739146 | − | 0.673545i | \(-0.764771\pi\) | ||||
−0.739146 | + | 0.673545i | \(0.764771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1260.41 | −0.0584195 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10276.0 | 0.472628 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −58088.5 | −2.66142 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1425.15 | −0.0650458 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5665.53 | 0.257594 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6736.02 | −0.305099 | −0.152550 | − | 0.988296i | \(-0.548748\pi\) | ||||
−0.152550 | + | 0.988296i | \(0.548748\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8918.06 | 0.402397 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1759.32 | 0.0787834 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6805.15 | −0.303590 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13445.1 | −0.597552 | −0.298776 | − | 0.954323i | \(-0.596578\pi\) | ||||
−0.298776 | + | 0.954323i | \(0.596578\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25242.8 | −1.11768 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11690.0 | −0.515664 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35991.0 | 1.58169 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13330.3 | −0.581472 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20337.7 | 0.883853 | 0.441927 | − | 0.897051i | \(-0.354295\pi\) | ||||
0.441927 | + | 0.897051i | \(0.354295\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23069.9 | 0.998884 | 0.499442 | − | 0.866347i | \(-0.333538\pi\) | ||||
0.499442 | + | 0.866347i | \(0.333538\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20520.8 | −0.885233 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24356.1 | 1.04682 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18015.8 | 0.771471 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8230.74 | 0.349884 | 0.174942 | − | 0.984579i | \(-0.444026\pi\) | ||||
0.174942 | + | 0.984579i | \(0.444026\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17577.9 | 0.744506 | 0.372253 | − | 0.928131i | \(-0.378585\pi\) | ||||
0.372253 | + | 0.928131i | \(0.378585\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12510.5 | 0.527951 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6440.14 | −0.270793 | −0.135396 | − | 0.990792i | \(-0.543231\pi\) | ||||
−0.135396 | + | 0.990792i | \(0.543231\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5084.23 | −0.213007 | −0.106503 | − | 0.994312i | \(-0.533966\pi\) | ||||
−0.106503 | + | 0.994312i | \(0.533966\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9686.01 | 0.404337 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18038.9 | 0.747618 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −399.153 | −0.0164836 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25150.5 | 1.03491 | 0.517456 | − | 0.855710i | \(-0.326879\pi\) | ||||
0.517456 | + | 0.855710i | \(0.326879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21602.9 | −0.885764 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19361.5 | 0.791038 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13807.3 | −0.562113 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11522.2 | 0.465771 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12731.5 | −0.512846 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6408.37 | 0.257232 | 0.128616 | − | 0.991694i | \(-0.458947\pi\) | ||||
0.128616 | + | 0.991694i | \(0.458947\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2565.46 | −0.102616 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17248.6 | −0.687515 | −0.343758 | − | 0.939058i | \(-0.611700\pi\) | ||||
−0.343758 | + | 0.939058i | \(0.611700\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3159.07 | −0.125479 | −0.0627393 | − | 0.998030i | \(-0.519984\pi\) | ||||
−0.0627393 | + | 0.998030i | \(0.519984\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 41071.9 | 1.62005 | 0.810025 | − | 0.586395i | \(-0.199453\pi\) | ||||
0.810025 | + | 0.586395i | \(0.199453\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6171.78 | −0.242597 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −41352.2 | −1.61983 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −40928.6 | −1.59771 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −983.210 | −0.0382489 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1809.37 | 0.0701466 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1034.90 | −0.0398472 | −0.0199236 | − | 0.999802i | \(-0.506342\pi\) | ||||
−0.0199236 | + | 0.999802i | \(0.506342\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26403.0 | 1.01314 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3109.73 | 0.118921 | 0.0594606 | − | 0.998231i | \(-0.481062\pi\) | ||||
0.0594606 | + | 0.998231i | \(0.481062\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19782.8 | −0.753955 | −0.376978 | − | 0.926222i | \(-0.623037\pi\) | ||||
−0.376978 | + | 0.926222i | \(0.623037\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1889.49 | 0.0717678 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9355.56 | −0.354148 | −0.177074 | − | 0.984198i | \(-0.556663\pi\) | ||||
−0.177074 | + | 0.984198i | \(0.556663\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3961.90 | 0.148966 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8347.35 | −0.312803 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7226.27 | −0.269886 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 298.352 | 0.0111055 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 780.322 | 0.0289491 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −49201.4 | −1.81924 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24771.0 | −0.909853 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16211.9 | 0.593505 | 0.296752 | − | 0.954954i | \(-0.404096\pi\) | ||||
0.296752 | + | 0.954954i | \(0.404096\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9481.60 | 0.345968 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14540.6 | 0.528816 | 0.264408 | − | 0.964411i | \(-0.414823\pi\) | ||||
0.264408 | + | 0.964411i | \(0.414823\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14367.2 | −0.520792 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12756.7 | −0.460901 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37239.2 | −1.33668 | −0.668339 | − | 0.743857i | \(-0.732995\pi\) | ||||
−0.668339 | + | 0.743857i | \(0.732995\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11780.2 | −0.421466 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3097.59 | −0.110464 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28468.2 | −1.01192 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9231.59 | −0.327082 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22062.5 | −0.779167 | −0.389583 | − | 0.920991i | \(-0.627381\pi\) | ||||
−0.389583 | + | 0.920991i | \(0.627381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18429.4 | −0.646678 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −42163.0 | −1.47473 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15597.3 | 0.543800 | 0.271900 | − | 0.962326i | \(-0.412348\pi\) | ||||
0.271900 | + | 0.962326i | \(0.412348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 11472.6 | 0.398715 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15887.1 | 0.550377 | 0.275188 | − | 0.961390i | \(-0.411260\pi\) | ||||
0.275188 | + | 0.961390i | \(0.411260\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8665.29 | 0.299237 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 54754.6 | 1.87887 | 0.939433 | − | 0.342733i | \(-0.111352\pi\) | ||||
0.939433 | + | 0.342733i | \(0.111352\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1919.23 | 0.0656489 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23849.0 | −0.813205 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12091.3 | 0.410992 | 0.205496 | − | 0.978658i | \(-0.434119\pi\) | ||||
0.205496 | + | 0.978658i | \(0.434119\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18517.5 | −0.627447 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7745.30 | −0.261620 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29572.4 | −0.992664 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −930.765 | −0.0311459 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22273.6 | −0.743017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27415.1 | −0.911695 | −0.455848 | − | 0.890058i | \(-0.650664\pi\) | ||||
−0.455848 | + | 0.890058i | \(0.650664\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18548.4 | −0.614921 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −55397.0 | −1.83087 | −0.915435 | − | 0.402466i | \(-0.868153\pi\) | ||||
−0.915435 | + | 0.402466i | \(0.868153\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 667.127 | 0.0219130 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18294.3 | 0.599065 | 0.299532 | − | 0.954086i | \(-0.403169\pi\) | ||||
0.299532 | + | 0.954086i | \(0.403169\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −63532.0 | −2.07405 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6094.20 | −0.198341 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23803.2 | 0.772334 | 0.386167 | − | 0.922429i | \(-0.373799\pi\) | ||||
0.386167 | + | 0.922429i | \(0.373799\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3687.01 | 0.119267 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15191.8 | 0.488445 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13624.5 | −0.436726 | −0.218363 | − | 0.975868i | \(-0.570072\pi\) | ||||
−0.218363 | + | 0.975868i | \(0.570072\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33709.1 | 1.07727 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13604.8 | −0.433470 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46834.4 | 1.48772 | 0.743861 | − | 0.668334i | \(-0.232992\pi\) | ||||
0.743861 | + | 0.668334i | \(0.232992\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9015.50 | −0.285523 |
(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 | 1176.4.a.p.1.2 | 2 | ||
4.3 | odd | 2 | 2352.4.a.bv.1.2 | 2 | |||
7.6 | odd | 2 | 168.4.a.h.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 504.4.a.j.1.2 | 2 | |||
28.27 | even | 2 | 336.4.a.n.1.1 | 2 | |||
56.13 | odd | 2 | 1344.4.a.bd.1.2 | 2 | |||
56.27 | even | 2 | 1344.4.a.bl.1.2 | 2 | |||
84.83 | odd | 2 | 1008.4.a.y.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.h.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
336.4.a.n.1.1 | 2 | 28.27 | even | 2 | |||
504.4.a.j.1.2 | 2 | 21.20 | even | 2 | |||
1008.4.a.y.1.2 | 2 | 84.83 | odd | 2 | |||
1176.4.a.p.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1344.4.a.bd.1.2 | 2 | 56.13 | odd | 2 | |||
1344.4.a.bl.1.2 | 2 | 56.27 | even | 2 | |||
2352.4.a.bv.1.2 | 2 | 4.3 | odd | 2 |