Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,4,Mod(1,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, 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("1296.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.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: | \(76.4664753674\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 9) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1296.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.62772 | −0.413916 | −0.206958 | − | 0.978350i | \(-0.566356\pi\) | ||||
−0.206958 | + | 0.978350i | \(0.566356\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.1168 | −0.654248 | −0.327124 | − | 0.944981i | \(-0.606079\pi\) | ||||
−0.327124 | + | 0.944981i | \(0.606079\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.0217 | 0.274697 | 0.137349 | − | 0.990523i | \(-0.456142\pi\) | ||||
0.137349 | + | 0.990523i | \(0.456142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −48.5842 | −1.03653 | −0.518263 | − | 0.855221i | \(-0.673421\pi\) | ||||
−0.518263 | + | 0.855221i | \(0.673421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −75.3505 | −1.07501 | −0.537506 | − | 0.843260i | \(-0.680633\pi\) | ||||
−0.537506 | + | 0.843260i | \(0.680633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 116.052 | 1.40127 | 0.700633 | − | 0.713522i | \(-0.252901\pi\) | ||||
0.700633 | + | 0.713522i | \(0.252901\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −38.0733 | −0.345167 | −0.172584 | − | 0.984995i | \(-0.555211\pi\) | ||||
−0.172584 | + | 0.984995i | \(0.555211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −103.584 | −0.828674 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.6277 | 0.144892 | 0.0724459 | − | 0.997372i | \(-0.476920\pi\) | ||||
0.0724459 | + | 0.997372i | \(0.476920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −30.1168 | −0.174489 | −0.0872443 | − | 0.996187i | \(-0.527806\pi\) | ||||
−0.0872443 | + | 0.996187i | \(0.527806\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 56.0733 | 0.270804 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 130.103 | 0.578077 | 0.289038 | − | 0.957318i | \(-0.406665\pi\) | ||||
0.289038 | + | 0.957318i | \(0.406665\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −347.484 | −1.32361 | −0.661803 | − | 0.749678i | \(-0.730208\pi\) | ||||
−0.661803 | + | 0.749678i | \(0.730208\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.7663 | −0.0949261 | −0.0474631 | − | 0.998873i | \(-0.515114\pi\) | ||||
−0.0474631 | + | 0.998873i | \(0.515114\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 460.878 | 1.43034 | 0.715169 | − | 0.698951i | \(-0.246350\pi\) | ||||
0.715169 | + | 0.698951i | \(0.246350\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −196.182 | −0.571959 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 438.310 | 1.13597 | 0.567985 | − | 0.823039i | \(-0.307723\pi\) | ||||
0.567985 | + | 0.823039i | \(0.307723\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −46.3778 | −0.113702 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.36974 | 0.0184686 | 0.00923430 | − | 0.999957i | \(-0.497061\pi\) | ||||
0.00923430 | + | 0.999957i | \(0.497061\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −82.0895 | −0.172303 | −0.0861515 | − | 0.996282i | \(-0.527457\pi\) | ||||
−0.0861515 | + | 0.996282i | \(0.527457\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 224.834 | 0.429034 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −683.571 | −1.24644 | −0.623220 | − | 0.782047i | \(-0.714176\pi\) | ||||
−0.623220 | + | 0.782047i | \(0.714176\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1097.61 | 1.83468 | 0.917339 | − | 0.398107i | \(-0.130333\pi\) | ||||
0.917339 | + | 0.398107i | \(0.130333\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 470.464 | 0.754297 | 0.377149 | − | 0.926153i | \(-0.376905\pi\) | ||||
0.377149 | + | 0.926153i | \(0.376905\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −121.432 | −0.179720 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −486.035 | −0.692192 | −0.346096 | − | 0.938199i | \(-0.612493\pi\) | ||||
−0.346096 | + | 0.938199i | \(0.612493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 99.1659 | 0.131143 | 0.0655715 | − | 0.997848i | \(-0.479113\pi\) | ||||
0.0655715 | + | 0.997848i | \(0.479113\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 348.701 | 0.444964 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.80426 | −0.0104859 | −0.00524297 | − | 0.999986i | \(-0.501669\pi\) | ||||
−0.00524297 | + | 0.999986i | \(0.501669\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 588.687 | 0.678145 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −537.054 | −0.580006 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 660.973 | 0.691872 | 0.345936 | − | 0.938258i | \(-0.387561\pi\) | ||||
0.345936 | + | 0.938258i | \(0.387561\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 565.122 | 0.556750 | 0.278375 | − | 0.960472i | \(-0.410204\pi\) | ||||
0.278375 | + | 0.960472i | \(0.410204\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 971.182 | 0.929062 | 0.464531 | − | 0.885557i | \(-0.346223\pi\) | ||||
0.464531 | + | 0.885557i | \(0.346223\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −563.845 | −0.509430 | −0.254715 | − | 0.967016i | \(-0.581982\pi\) | ||||
−0.254715 | + | 0.967016i | \(0.581982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 225.484 | 0.198142 | 0.0990709 | − | 0.995080i | \(-0.468413\pi\) | ||||
0.0990709 | + | 0.995080i | \(0.468413\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 691.063 | 0.575307 | 0.287654 | − | 0.957735i | \(-0.407125\pi\) | ||||
0.287654 | + | 0.957735i | \(0.407125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 176.193 | 0.142870 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 913.011 | 0.703324 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1230.56 | −0.924541 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1057.82 | 0.756917 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 895.897 | 0.625968 | 0.312984 | − | 0.949758i | \(-0.398671\pi\) | ||||
0.312984 | + | 0.949758i | \(0.398671\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1654.86 | 1.10371 | 0.551853 | − | 0.833942i | \(-0.313921\pi\) | ||||
0.551853 | + | 0.833942i | \(0.313921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1406.18 | −0.916776 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2651.09 | 1.65327 | 0.826635 | − | 0.562738i | \(-0.190252\pi\) | ||||
0.826635 | + | 0.562738i | \(0.190252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −634.168 | −0.386975 | −0.193487 | − | 0.981103i | \(-0.561980\pi\) | ||||
−0.193487 | + | 0.981103i | \(0.561980\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −486.899 | −0.284731 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −104.715 | −0.0599730 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3406.32 | 1.87286 | 0.936432 | − | 0.350849i | \(-0.114107\pi\) | ||||
0.936432 | + | 0.350849i | \(0.114107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1750.32 | 0.943303 | 0.471652 | − | 0.881785i | \(-0.343658\pi\) | ||||
0.471652 | + | 0.881785i | \(0.343658\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 139.372 | 0.0722236 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2178.57 | 1.10745 | 0.553723 | − | 0.832701i | \(-0.313207\pi\) | ||||
0.553723 | + | 0.832701i | \(0.313207\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 461.329 | 0.225825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2188.41 | −1.05159 | −0.525797 | − | 0.850610i | \(-0.676233\pi\) | ||||
−0.525797 | + | 0.850610i | \(0.676233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1921.04 | 0.890147 | 0.445074 | − | 0.895494i | \(-0.353178\pi\) | ||||
0.445074 | + | 0.895494i | \(0.353178\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 163.426 | 0.0743862 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3169.83 | −1.39305 | −0.696525 | − | 0.717533i | \(-0.745271\pi\) | ||||
−0.696525 | + | 0.717533i | \(0.745271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1255.11 | 0.542158 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1368.78 | 0.571551 | 0.285776 | − | 0.958297i | \(-0.407749\pi\) | ||||
0.285776 | + | 0.958297i | \(0.407749\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3951.44 | −1.62270 | −0.811350 | − | 0.584561i | \(-0.801267\pi\) | ||||
−0.811350 | + | 0.584561i | \(0.801267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −602.081 | −0.239275 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −755.144 | −0.295303 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2402.59 | −0.910184 | −0.455092 | − | 0.890444i | \(-0.650394\pi\) | ||||
−0.455092 | + | 0.890444i | \(0.650394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1335.07 | −0.497930 | −0.248965 | − | 0.968513i | \(-0.580090\pi\) | ||||
−0.248965 | + | 0.968513i | \(0.580090\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2630.89 | 0.951487 | 0.475743 | − | 0.879584i | \(-0.342179\pi\) | ||||
0.475743 | + | 0.879584i | \(0.342179\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2477.34 | −0.882483 | −0.441241 | − | 0.897388i | \(-0.645462\pi\) | ||||
−0.441241 | + | 0.897388i | \(0.645462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −274.177 | −0.0947952 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1608.06 | 0.547861 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1163.04 | 0.384924 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2784.73 | 0.908572 | 0.454286 | − | 0.890856i | \(-0.349894\pi\) | ||||
0.454286 | + | 0.890856i | \(0.349894\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 123.867 | 0.0392914 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 364.921 | 0.114159 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3660.85 | 1.11428 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 43.0576 | 0.0129298 | 0.00646491 | − | 0.999979i | \(-0.497942\pi\) | ||||
0.00646491 | + | 0.999979i | \(0.497942\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 683.260 | 0.199778 | 0.0998889 | − | 0.994999i | \(-0.468151\pi\) | ||||
0.0998889 | + | 0.994999i | \(0.468151\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4294.31 | 1.23920 | 0.619598 | − | 0.784920i | \(-0.287296\pi\) | ||||
0.619598 | + | 0.784920i | \(0.287296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3466.34 | −0.974625 | −0.487313 | − | 0.873228i | \(-0.662023\pi\) | ||||
−0.487313 | + | 0.873228i | \(0.662023\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2132.81 | −0.592040 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5643.37 | 1.52736 | 0.763681 | − | 0.645594i | \(-0.223390\pi\) | ||||
0.763681 | + | 0.645594i | \(0.223390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6589.43 | 1.76125 | 0.880627 | − | 0.473810i | \(-0.157121\pi\) | ||||
0.880627 | + | 0.473810i | \(0.157121\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 907.876 | 0.236743 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5638.28 | −1.45245 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4135.47 | 1.03996 | 0.519978 | − | 0.854180i | \(-0.325940\pi\) | ||||
0.519978 | + | 0.854180i | \(0.325940\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −381.562 | −0.0948165 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3344.62 | 0.811796 | 0.405898 | − | 0.913918i | \(-0.366959\pi\) | ||||
0.405898 | + | 0.913918i | \(0.366959\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1576.44 | −0.378205 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6521.50 | 1.52902 | 0.764511 | − | 0.644611i | \(-0.222981\pi\) | ||||
0.764511 | + | 0.644611i | \(0.222981\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2028.37 | −0.470196 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2904.99 | 0.658441 | 0.329220 | − | 0.944253i | \(-0.393214\pi\) | ||||
0.329220 | + | 0.944253i | \(0.393214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1335.38 | 0.299331 | 0.149665 | − | 0.988737i | \(-0.452180\pi\) | ||||
0.149665 | + | 0.988737i | \(0.452180\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1038.10 | −0.227635 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8375.64 | −1.81676 | −0.908381 | − | 0.418143i | \(-0.862681\pi\) | ||||
−0.908381 | + | 0.418143i | \(0.862681\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5179.33 | 1.09955 | 0.549774 | − | 0.835313i | \(-0.314714\pi\) | ||||
0.549774 | + | 0.835313i | \(0.314714\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3080.07 | 0.646965 | 0.323482 | − | 0.946234i | \(-0.395146\pi\) | ||||
0.323482 | + | 0.946234i | \(0.395146\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4210.40 | 0.865966 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 764.703 | 0.155649 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3648.89 | −0.727545 | −0.363773 | − | 0.931488i | \(-0.618511\pi\) | ||||
−0.363773 | + | 0.931488i | \(0.618511\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.7328 | −0.00764444 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1849.76 | 0.357775 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 324.323 | 0.0621052 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 379.887 | 0.0713190 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3439.25 | 0.639376 | 0.319688 | − | 0.947523i | \(-0.396422\pi\) | ||||
0.319688 | + | 0.947523i | \(0.396422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7175.33 | 1.30828 | 0.654141 | − | 0.756373i | \(-0.273030\pi\) | ||||
0.654141 | + | 0.756373i | \(0.273030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4857.30 | −0.877159 | −0.438579 | − | 0.898692i | \(-0.644518\pi\) | ||||
−0.438579 | + | 0.898692i | \(0.644518\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7547.93 | −1.33733 | −0.668666 | − | 0.743563i | \(-0.733134\pi\) | ||||
−0.668666 | + | 0.743563i | \(0.733134\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 226.769 | 0.0398014 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8744.55 | −1.50638 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5032.56 | 0.858942 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5584.38 | −0.935796 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3129.72 | 0.519712 | 0.259856 | − | 0.965647i | \(-0.416325\pi\) | ||||
0.259856 | + | 0.965647i | \(0.416325\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3163.37 | 0.515921 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9229.98 | −1.49196 | −0.745978 | − | 0.665971i | \(-0.768017\pi\) | ||||
−0.745978 | + | 0.665971i | \(0.768017\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −301.823 | −0.0479315 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6533.19 | 1.02845 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8104.40 | −1.25379 | −0.626897 | − | 0.779102i | \(-0.715675\pi\) | ||||
−0.626897 | + | 0.779102i | \(0.715675\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3076.42 | 0.471854 | 0.235927 | − | 0.971771i | \(-0.424187\pi\) | ||||
0.235927 | + | 0.971771i | \(0.424187\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6150.08 | 0.927297 | 0.463649 | − | 0.886019i | \(-0.346540\pi\) | ||||
0.463649 | + | 0.886019i | \(0.346540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5079.42 | −0.759402 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3307.94 | 0.486313 | 0.243156 | − | 0.969987i | \(-0.421817\pi\) | ||||
0.243156 | + | 0.969987i | \(0.421817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6608.97 | 0.963548 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2177.18 | −0.312215 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2949.29 | −0.419488 | −0.209744 | − | 0.977756i | \(-0.567263\pi\) | ||||
−0.209744 | + | 0.977756i | \(0.567263\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5310.93 | −0.743207 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1163.58 | 0.161522 | 0.0807612 | − | 0.996733i | \(-0.474265\pi\) | ||||
0.0807612 | + | 0.996733i | \(0.474265\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1099.35 | −0.150184 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4016.67 | 0.544387 | 0.272193 | − | 0.962243i | \(-0.412251\pi\) | ||||
0.272193 | + | 0.962243i | \(0.412251\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10803.3 | −1.44131 | −0.720656 | − | 0.693293i | \(-0.756159\pi\) | ||||
−0.720656 | + | 0.693293i | \(0.756159\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 561.953 | 0.0743890 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2064.59 | −0.269097 | −0.134549 | − | 0.990907i | \(-0.542958\pi\) | ||||
−0.134549 | + | 0.990907i | \(0.542958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2868.85 | 0.371058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2249.23 | 0.286509 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7937.61 | −1.00347 | −0.501735 | − | 0.865022i | \(-0.667305\pi\) | ||||
−0.501735 | + | 0.865022i | \(0.667305\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2578.21 | −0.321071 | −0.160536 | − | 0.987030i | \(-0.551322\pi\) | ||||
−0.160536 | + | 0.987030i | \(0.551322\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1463.20 | 0.180862 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1303.86 | 0.158796 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5845.76 | 0.706734 | 0.353367 | − | 0.935485i | \(-0.385037\pi\) | ||||
0.353367 | + | 0.935485i | \(0.385037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −101.415 | −0.0120830 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −458.912 | −0.0542822 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8741.31 | −1.01919 | −0.509596 | − | 0.860414i | \(-0.670205\pi\) | ||||
−0.509596 | + | 0.860414i | \(0.670205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1056.51 | 0.122307 | 0.0611533 | − | 0.998128i | \(-0.480522\pi\) | ||||
0.0611533 | + | 0.998128i | \(0.480522\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7805.13 | 0.890833 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 994.666 | 0.112729 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9868.64 | 1.10291 | 0.551457 | − | 0.834203i | \(-0.314072\pi\) | ||||
0.551457 | + | 0.834203i | \(0.314072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 477.948 | 0.0530456 | 0.0265228 | − | 0.999648i | \(-0.491557\pi\) | ||||
0.0265228 | + | 0.999648i | \(0.491557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4418.47 | −0.483671 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1052.48 | 0.114424 | 0.0572119 | − | 0.998362i | \(-0.481779\pi\) | ||||
0.0572119 | + | 0.998362i | \(0.481779\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10498.7 | −1.12598 | −0.562989 | − | 0.826464i | \(-0.690349\pi\) | ||||
−0.562989 | + | 0.826464i | \(0.690349\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 40.7436 | 0.00434030 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7329.40 | 0.770369 | 0.385184 | − | 0.922840i | \(-0.374138\pi\) | ||||
0.385184 | + | 0.922840i | \(0.374138\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3482.39 | −0.363591 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2724.28 | −0.280695 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7144.40 | 0.731293 | 0.365646 | − | 0.930754i | \(-0.380848\pi\) | ||||
0.365646 | + | 0.930754i | \(0.380848\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5718.69 | −0.577757 | −0.288878 | − | 0.957366i | \(-0.593282\pi\) | ||||
−0.288878 | + | 0.957366i | \(0.593282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −788.466 | −0.0791428 | −0.0395714 | − | 0.999217i | \(-0.512599\pi\) | ||||
−0.0395714 | + | 0.999217i | \(0.512599\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17068.0 | −1.69125 | −0.845626 | − | 0.533776i | \(-0.820772\pi\) | ||||
−0.845626 | + | 0.533776i | \(0.820772\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8282.72 | 0.815481 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −268.245 | −0.0260760 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12021.1 | −1.16119 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1517.99 | 0.144799 | 0.0723994 | − | 0.997376i | \(-0.476934\pi\) | ||||
0.0723994 | + | 0.997376i | \(0.476934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6320.96 | −0.599191 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3058.80 | −0.286377 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12737.3 | −1.18518 | −0.592591 | − | 0.805503i | \(-0.701895\pi\) | ||||
−0.592591 | + | 0.805503i | \(0.701895\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5647.70 | 0.519098 | 0.259549 | − | 0.965730i | \(-0.416426\pi\) | ||||
0.259549 | + | 0.965730i | \(0.416426\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1705.01 | −0.155760 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13299.6 | −1.20033 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10846.3 | −0.973038 | −0.486519 | − | 0.873670i | \(-0.661734\pi\) | ||||
−0.486519 | + | 0.873670i | \(0.661734\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12345.7 | −1.09437 | −0.547186 | − | 0.837011i | \(-0.684301\pi\) | ||||
−0.547186 | + | 0.837011i | \(0.684301\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2615.23 | −0.230448 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5895.75 | 0.513408 | 0.256704 | − | 0.966490i | \(-0.417364\pi\) | ||||
0.256704 | + | 0.966490i | \(0.417364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5700.54 | −0.493497 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4494.36 | −0.384554 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4618.80 | 0.392910 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5211.51 | −0.438235 | −0.219118 | − | 0.975698i | \(-0.570318\pi\) | ||||
−0.219118 | + | 0.975698i | \(0.570318\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9809.86 | 0.820182 | 0.410091 | − | 0.912045i | \(-0.365497\pi\) | ||||
0.410091 | + | 0.912045i | \(0.365497\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2269.32 | 0.187577 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10717.4 | −0.880860 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16882.2 | 1.37195 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2609.32 | 0.210861 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1966.09 | −0.157116 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8084.25 | 0.642456 | 0.321228 | − | 0.947002i | \(-0.395904\pi\) | ||||
0.321228 | + | 0.947002i | \(0.395904\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1043.48 | −0.0820140 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24067.1 | 1.88123 | 0.940617 | − | 0.339470i | \(-0.110248\pi\) | ||||
0.940617 | + | 0.339470i | \(0.110248\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2625.98 | 0.203032 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5889.21 | 0.452866 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4582.37 | −0.348584 | −0.174292 | − | 0.984694i | \(-0.555764\pi\) | ||||
−0.174292 | + | 0.984694i | \(0.555764\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1300.42 | 0.0983934 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3095.31 | −0.231709 | −0.115854 | − | 0.993266i | \(-0.536961\pi\) | ||||
−0.115854 | + | 0.993266i | \(0.536961\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3198.04 | −0.238129 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20565.1 | −1.51517 | −0.757586 | − | 0.652735i | \(-0.773621\pi\) | ||||
−0.757586 | + | 0.652735i | \(0.773621\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1169.98 | 0.0857483 | 0.0428742 | − | 0.999080i | \(-0.486349\pi\) | ||||
0.0428742 | + | 0.999080i | \(0.486349\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3943.80 | 0.286031 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13073.0 | −0.943214 | −0.471607 | − | 0.881809i | \(-0.656326\pi\) | ||||
−0.471607 | + | 0.881809i | \(0.656326\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1201.58 | −0.0858001 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4392.63 | 0.312048 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14547.8 | −1.02292 | −0.511459 | − | 0.859308i | \(-0.670895\pi\) | ||||
−0.511459 | + | 0.859308i | \(0.670895\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3495.11 | −0.244505 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19018.0 | −1.31699 | −0.658494 | − | 0.752586i | \(-0.728806\pi\) | ||||
−0.658494 | + | 0.752586i | \(0.728806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4225.16 | −0.291117 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11174.4 | 0.762227 | 0.381113 | − | 0.924528i | \(-0.375541\pi\) | ||||
0.381113 | + | 0.924528i | \(0.375541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4588.54 | 0.311432 | 0.155716 | − | 0.987802i | \(-0.450232\pi\) | ||||
0.155716 | + | 0.987802i | \(0.450232\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5694.71 | 0.382682 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11490.0 | 0.768309 | 0.384155 | − | 0.923269i | \(-0.374493\pi\) | ||||
0.384155 | + | 0.923269i | \(0.374493\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22391.4 | −1.48258 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22966.9 | −1.51326 | −0.756628 | − | 0.653846i | \(-0.773154\pi\) | ||||
−0.756628 | + | 0.653846i | \(0.773154\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8496.63 | 0.554394 | 0.277197 | − | 0.960813i | \(-0.410594\pi\) | ||||
0.277197 | + | 0.960813i | \(0.410594\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14339.9 | −0.931129 | −0.465564 | − | 0.885014i | \(-0.654149\pi\) | ||||
−0.465564 | + | 0.885014i | \(0.654149\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 106.680 | 0.00686041 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8052.72 | 0.515374 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9803.34 | −0.621439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17834.3 | −1.12516 | −0.562578 | − | 0.826744i | \(-0.690190\pi\) | ||||
−0.562578 | + | 0.826744i | \(0.690190\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4145.96 | −0.259098 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9531.35 | 0.592851 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26346.0 | −1.62341 | −0.811705 | − | 0.584068i | \(-0.801460\pi\) | ||||
−0.811705 | + | 0.584068i | \(0.801460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21565.1 | 1.32262 | 0.661309 | − | 0.750114i | \(-0.270001\pi\) | ||||
0.661309 | + | 0.750114i | \(0.270001\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4186.32 | 0.254376 | 0.127188 | − | 0.991879i | \(-0.459405\pi\) | ||||
0.127188 | + | 0.991879i | \(0.459405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 83.8794 | 0.00507328 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2805.14 | −0.168107 | −0.0840534 | − | 0.996461i | \(-0.526787\pi\) | ||||
−0.0840534 | + | 0.996461i | \(0.526787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7658.21 | −0.456841 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19072.3 | −1.12739 | −0.563696 | − | 0.825982i | \(-0.690621\pi\) | ||||
−0.563696 | + | 0.825982i | \(0.690621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24513.1 | −1.44243 | −0.721216 | − | 0.692710i | \(-0.756417\pi\) | ||||
−0.721216 | + | 0.692710i | \(0.756417\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6507.40 | 0.379468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −861.513 | −0.0500119 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −822.681 | −0.0473312 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3546.65 | −0.203140 | −0.101570 | − | 0.994828i | \(-0.532387\pi\) | ||||
−0.101570 | + | 0.994828i | \(0.532387\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17875.0 | −1.01476 | −0.507380 | − | 0.861723i | \(-0.669386\pi\) | ||||
−0.507380 | + | 0.861723i | \(0.669386\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8008.90 | −0.452656 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2857.23 | 0.160072 | 0.0800358 | − | 0.996792i | \(-0.474497\pi\) | ||||
0.0800358 | + | 0.996792i | \(0.474497\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12268.5 | −0.684315 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −21294.9 | −1.17746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15627.6 | 0.860349 | 0.430175 | − | 0.902746i | \(-0.358452\pi\) | ||||
0.430175 | + | 0.902746i | \(0.358452\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2934.75 | 0.160175 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26183.1 | 1.42289 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17562.6 | −0.946264 | −0.473132 | − | 0.880992i | \(-0.656877\pi\) | ||||
−0.473132 | + | 0.880992i | \(0.656877\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15098.7 | 0.810039 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6847.50 | −0.364253 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20003.6 | 1.05959 | 0.529795 | − | 0.848126i | \(-0.322269\pi\) | ||||
0.529795 | + | 0.848126i | \(0.322269\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1146.65 | 0.0602277 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2253.23 | 0.117855 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25504.1 | 1.32287 | 0.661435 | − | 0.750002i | \(-0.269948\pi\) | ||||
0.661435 | + | 0.750002i | \(0.269948\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11767.7 | −0.607837 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2343.87 | −0.120068 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23909.8 | 1.21976 | 0.609879 | − | 0.792494i | \(-0.291218\pi\) | ||||
0.609879 | + | 0.792494i | \(0.291218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2016.86 | 0.102047 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8505.54 | −0.428594 | −0.214297 | − | 0.976769i | \(-0.568746\pi\) | ||||
−0.214297 | + | 0.976769i | \(0.568746\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6850.57 | −0.342394 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25802.5 | −1.28438 | −0.642192 | − | 0.766544i | \(-0.721975\pi\) | ||||
−0.642192 | + | 0.766544i | \(0.721975\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27337.6 | 1.34982 | 0.674911 | − | 0.737899i | \(-0.264182\pi\) | ||||
0.674911 | + | 0.737899i | \(0.264182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15763.5 | −0.775208 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6832.02 | 0.333293 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3336.64 | −0.162125 | −0.0810623 | − | 0.996709i | \(-0.525831\pi\) | ||||
−0.0810623 | + | 0.996709i | \(0.525831\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8099.98 | −0.390448 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33149.5 | 1.59160 | 0.795798 | − | 0.605562i | \(-0.207052\pi\) | ||||
0.795798 | + | 0.605562i | \(0.207052\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10996.8 | 0.523831 | 0.261915 | − | 0.965091i | \(-0.415646\pi\) | ||||
0.261915 | + | 0.965091i | \(0.415646\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2732.15 | −0.129634 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −406.637 | −0.0191432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33285.0 | 1.56084 | 0.780420 | − | 0.625255i | \(-0.215005\pi\) | ||||
0.780420 | + | 0.625255i | \(0.215005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7242.46 | 0.336990 | 0.168495 | − | 0.985703i | \(-0.446109\pi\) | ||||
0.168495 | + | 0.985703i | \(0.446109\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3119.63 | 0.144594 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −40326.0 | −1.85472 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11000.0 | 0.503981 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10081.8 | −0.458389 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17414.3 | −0.788758 | −0.394379 | − | 0.918948i | \(-0.629040\pi\) | ||||
−0.394379 | + | 0.918948i | \(0.629040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8373.50 | −0.376394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3988.26 | 0.178597 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29132.9 | −1.29478 | −0.647391 | − | 0.762158i | \(-0.724140\pi\) | ||||
−0.647391 | + | 0.762158i | \(0.724140\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34727.4 | −1.53763 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4714.88 | 0.207203 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2134.90 | −0.0934725 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36440.1 | 1.58364 | 0.791820 | − | 0.610754i | \(-0.209134\pi\) | ||||
0.791820 | + | 0.610754i | \(0.209134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18922.0 | 0.819286 | 0.409643 | − | 0.912246i | \(-0.365653\pi\) | ||||
0.409643 | + | 0.912246i | \(0.365653\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10127.4 | 0.435271 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3106.27 | −0.133017 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17910.7 | 0.761374 | 0.380687 | − | 0.924704i | \(-0.375688\pi\) | ||||
0.380687 | + | 0.924704i | \(0.375688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17524.4 | −0.742240 | −0.371120 | − | 0.928585i | \(-0.621026\pi\) | ||||
−0.371120 | + | 0.928585i | \(0.621026\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17643.9 | −0.741885 | −0.370943 | − | 0.928656i | \(-0.620965\pi\) | ||||
−0.370943 | + | 0.928656i | \(0.620965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45178.6 | 1.89278 | 0.946391 | − | 0.323023i | \(-0.104699\pi\) | ||||
0.946391 | + | 0.323023i | \(0.104699\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14782.4 | 0.614863 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8890.03 | −0.368446 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26776.0 | 1.10180 | 0.550901 | − | 0.834571i | \(-0.314284\pi\) | ||||
0.550901 | + | 0.834571i | \(0.314284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23877.0 | −0.979006 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −756.291 | −0.0307896 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14910.6 | 0.604879 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4953.46 | −0.199533 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7911.75 | −0.317577 | −0.158789 | − | 0.987313i | \(-0.550759\pi\) | ||||
−0.158789 | + | 0.987313i | \(0.550759\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1848.30 | −0.0736717 | −0.0368359 | − | 0.999321i | \(-0.511728\pi\) | ||||
−0.0368359 | + | 0.999321i | \(0.511728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18854.2 | 0.748890 | 0.374445 | − | 0.927249i | \(-0.377833\pi\) | ||||
0.374445 | + | 0.927249i | \(0.377833\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2086.03 | 0.0822821 | 0.0411410 | − | 0.999153i | \(-0.486901\pi\) | ||||
0.0411410 | + | 0.999153i | \(0.486901\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14669.1 | 0.576605 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4870.92 | −0.190143 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33210.7 | 1.29197 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12817.5 | −0.495211 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24777.2 | −0.954010 | −0.477005 | − | 0.878901i | \(-0.658278\pi\) | ||||
−0.477005 | + | 0.878901i | \(0.658278\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3741.26 | −0.143072 | −0.0715359 | − | 0.997438i | \(-0.522790\pi\) | ||||
−0.0715359 | + | 0.997438i | \(0.522790\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14131.6 | −0.538580 | −0.269290 | − | 0.963059i | \(-0.586789\pi\) | ||||
−0.269290 | + | 0.963059i | \(0.586789\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26622.5 | 1.00778 | 0.503888 | − | 0.863769i | \(-0.331903\pi\) | ||||
0.503888 | + | 0.863769i | \(0.331903\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10855.4 | −0.409539 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 53485.6 | 2.00429 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6334.34 | −0.236574 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −681.475 | −0.0252820 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33026.9 | −1.22118 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18286.2 | 0.671661 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −52619.4 | −1.92635 | −0.963174 | − | 0.268878i | \(-0.913347\pi\) | ||||
−0.963174 | + | 0.268878i | \(0.913347\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10180.4 | 0.370245 | 0.185122 | − | 0.982715i | \(-0.440732\pi\) | ||||
0.185122 | + | 0.982715i | \(0.440732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 993.816 | 0.0360246 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20051.6 | −0.722097 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45618.2 | 1.63744 | 0.818718 | − | 0.574195i | \(-0.194685\pi\) | ||||
0.818718 | + | 0.574195i | \(0.194685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −53326.5 | −1.90169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13476.6 | −0.479037 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13200.4 | 0.466190 | 0.233095 | − | 0.972454i | \(-0.425115\pi\) | ||||
0.233095 | + | 0.972454i | \(0.425115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22767.2 | −0.801468 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3494.59 | 0.122230 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13468.1 | −0.469565 | −0.234783 | − | 0.972048i | \(-0.575438\pi\) | ||||
−0.234783 | + | 0.972048i | \(0.575438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13884.1 | −0.480987 | −0.240493 | − | 0.970651i | \(-0.577309\pi\) | ||||
−0.240493 | + | 0.970651i | \(0.577309\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13229.9 | 0.456865 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5276.64 | 0.181064 | 0.0905320 | − | 0.995894i | \(-0.471143\pi\) | ||||
0.0905320 | + | 0.995894i | \(0.471143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22857.1 | −0.781849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26131.4 | 0.888225 | 0.444112 | − | 0.895971i | \(-0.353519\pi\) | ||||
0.444112 | + | 0.895971i | \(0.353519\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11118.5 | 0.376740 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32122.9 | −1.08165 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28884.0 | −0.969554 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6178.33 | 0.206101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3997.53 | 0.132939 | 0.0664695 | − | 0.997788i | \(-0.478827\pi\) | ||||
0.0664695 | + | 0.997788i | \(0.478827\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41785.1 | 1.38100 | 0.690499 | − | 0.723334i | \(-0.257391\pi\) | ||||
0.690499 | + | 0.723334i | \(0.257391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7684.12 | 0.253177 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12245.1 | −0.400978 | −0.200489 | − | 0.979696i | \(-0.564253\pi\) | ||||
−0.200489 | + | 0.979696i | \(0.564253\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −88.2340 | −0.00288046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43783.1 | 1.42061 | 0.710307 | − | 0.703892i | \(-0.248556\pi\) | ||||
0.710307 | + | 0.703892i | \(0.248556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12175.0 | −0.393835 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1019.08 | 0.0327654 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5178.38 | −0.165991 | −0.0829953 | − | 0.996550i | \(-0.526449\pi\) | ||||
−0.0829953 | + | 0.996550i | \(0.526449\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11464.4 | 0.365274 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25720.9 | 0.817041 | 0.408520 | − | 0.912749i | \(-0.366045\pi\) | ||||
0.408520 | + | 0.912749i | \(0.366045\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1296.4.a.i.1.2 | 2 | ||
3.2 | odd | 2 | 1296.4.a.u.1.1 | 2 | |||
4.3 | odd | 2 | 81.4.a.a.1.1 | 2 | |||
9.2 | odd | 6 | 144.4.i.c.49.1 | 4 | |||
9.4 | even | 3 | 432.4.i.c.289.1 | 4 | |||
9.5 | odd | 6 | 144.4.i.c.97.1 | 4 | |||
9.7 | even | 3 | 432.4.i.c.145.1 | 4 | |||
12.11 | even | 2 | 81.4.a.d.1.2 | 2 | |||
20.19 | odd | 2 | 2025.4.a.n.1.2 | 2 | |||
36.7 | odd | 6 | 27.4.c.a.10.2 | 4 | |||
36.11 | even | 6 | 9.4.c.a.4.1 | ✓ | 4 | ||
36.23 | even | 6 | 9.4.c.a.7.1 | yes | 4 | ||
36.31 | odd | 6 | 27.4.c.a.19.2 | 4 | |||
60.59 | even | 2 | 2025.4.a.g.1.1 | 2 | |||
180.23 | odd | 12 | 225.4.k.b.124.4 | 8 | |||
180.47 | odd | 12 | 225.4.k.b.49.4 | 8 | |||
180.59 | even | 6 | 225.4.e.b.151.2 | 4 | |||
180.83 | odd | 12 | 225.4.k.b.49.1 | 8 | |||
180.119 | even | 6 | 225.4.e.b.76.2 | 4 | |||
180.167 | odd | 12 | 225.4.k.b.124.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.4.c.a.4.1 | ✓ | 4 | 36.11 | even | 6 | ||
9.4.c.a.7.1 | yes | 4 | 36.23 | even | 6 | ||
27.4.c.a.10.2 | 4 | 36.7 | odd | 6 | |||
27.4.c.a.19.2 | 4 | 36.31 | odd | 6 | |||
81.4.a.a.1.1 | 2 | 4.3 | odd | 2 | |||
81.4.a.d.1.2 | 2 | 12.11 | even | 2 | |||
144.4.i.c.49.1 | 4 | 9.2 | odd | 6 | |||
144.4.i.c.97.1 | 4 | 9.5 | odd | 6 | |||
225.4.e.b.76.2 | 4 | 180.119 | even | 6 | |||
225.4.e.b.151.2 | 4 | 180.59 | even | 6 | |||
225.4.k.b.49.1 | 8 | 180.83 | odd | 12 | |||
225.4.k.b.49.4 | 8 | 180.47 | odd | 12 | |||
225.4.k.b.124.1 | 8 | 180.167 | odd | 12 | |||
225.4.k.b.124.4 | 8 | 180.23 | odd | 12 | |||
432.4.i.c.145.1 | 4 | 9.7 | even | 3 | |||
432.4.i.c.289.1 | 4 | 9.4 | even | 3 | |||
1296.4.a.i.1.2 | 2 | 1.1 | even | 1 | trivial | ||
1296.4.a.u.1.1 | 2 | 3.2 | odd | 2 | |||
2025.4.a.g.1.1 | 2 | 60.59 | even | 2 | |||
2025.4.a.n.1.2 | 2 | 20.19 | odd | 2 |