Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{58}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(7.61577\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 15.2315 | 1.36235 | 0.681175 | − | 0.732120i | \(-0.261469\pi\) | ||||
0.681175 | + | 0.732120i | \(0.261469\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 30.4631 | 0.963328 | ||||||||
\(11\) | 2.00000 | 0.0548202 | 0.0274101 | − | 0.999624i | \(-0.491274\pi\) | ||||
0.0274101 | + | 0.999624i | \(0.491274\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.4631 | −0.649919 | −0.324959 | − | 0.945728i | \(-0.605351\pi\) | ||||
−0.324959 | + | 0.945728i | \(0.605351\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −45.6946 | −0.651916 | −0.325958 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325958 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 152.315 | 1.83913 | 0.919567 | − | 0.392932i | \(-0.128539\pi\) | ||||
0.919567 | + | 0.392932i | \(0.128539\pi\) | |||||||
\(20\) | 60.9262 | 0.681175 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000 | 0.0387638 | ||||||||
\(23\) | 30.0000 | 0.271975 | 0.135988 | − | 0.990711i | \(-0.456579\pi\) | ||||
0.135988 | + | 0.990711i | \(0.456579\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 107.000 | 0.856000 | ||||||||
\(26\) | −60.9262 | −0.459562 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 212.000 | 1.35750 | 0.678748 | − | 0.734371i | \(-0.262523\pi\) | ||||
0.678748 | + | 0.734371i | \(0.262523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 213.242 | 1.23546 | 0.617731 | − | 0.786389i | \(-0.288052\pi\) | ||||
0.617731 | + | 0.786389i | \(0.288052\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −91.3893 | −0.460974 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 246.000 | 1.09303 | 0.546516 | − | 0.837449i | \(-0.315954\pi\) | ||||
0.546516 | + | 0.837449i | \(0.315954\pi\) | |||||||
\(38\) | 304.631 | 1.30046 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 121.852 | 0.481664 | ||||||||
\(41\) | −319.862 | −1.21839 | −0.609197 | − | 0.793019i | \(-0.708508\pi\) | ||||
−0.609197 | + | 0.793019i | \(0.708508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −284.000 | −1.00720 | −0.503600 | − | 0.863937i | \(-0.667991\pi\) | ||||
−0.503600 | + | 0.863937i | \(0.667991\pi\) | |||||||
\(44\) | 8.00000 | 0.0274101 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 60.0000 | 0.192316 | ||||||||
\(47\) | 60.9262 | 0.189085 | 0.0945425 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945425 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 214.000 | 0.605283 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −121.852 | −0.324959 | ||||||||
\(53\) | 548.000 | 1.42026 | 0.710128 | − | 0.704072i | \(-0.248637\pi\) | ||||
0.710128 | + | 0.704072i | \(0.248637\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30.4631 | 0.0746844 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 424.000 | 0.959895 | ||||||||
\(59\) | −670.188 | −1.47883 | −0.739416 | − | 0.673249i | \(-0.764898\pi\) | ||||
−0.739416 | + | 0.673249i | \(0.764898\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −517.873 | −1.08700 | −0.543498 | − | 0.839410i | \(-0.682901\pi\) | ||||
−0.543498 | + | 0.839410i | \(0.682901\pi\) | |||||||
\(62\) | 426.483 | 0.873604 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −464.000 | −0.885417 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 652.000 | 1.18887 | 0.594436 | − | 0.804143i | \(-0.297375\pi\) | ||||
0.594436 | + | 0.804143i | \(0.297375\pi\) | |||||||
\(68\) | −182.779 | −0.325958 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 770.000 | 1.28707 | 0.643537 | − | 0.765415i | \(-0.277466\pi\) | ||||
0.643537 | + | 0.765415i | \(0.277466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −974.819 | −1.56293 | −0.781465 | − | 0.623949i | \(-0.785527\pi\) | ||||
−0.781465 | + | 0.623949i | \(0.785527\pi\) | |||||||
\(74\) | 492.000 | 0.772890 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 609.262 | 0.919567 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 472.000 | 0.672204 | 0.336102 | − | 0.941826i | \(-0.390891\pi\) | ||||
0.336102 | + | 0.941826i | \(0.390891\pi\) | |||||||
\(80\) | 243.705 | 0.340588 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −639.725 | −0.861534 | ||||||||
\(83\) | 182.779 | 0.241718 | 0.120859 | − | 0.992670i | \(-0.461435\pi\) | ||||
0.120859 | + | 0.992670i | \(0.461435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −696.000 | −0.888139 | ||||||||
\(86\) | −568.000 | −0.712198 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 16.0000 | 0.0193819 | ||||||||
\(89\) | 715.883 | 0.852623 | 0.426311 | − | 0.904577i | \(-0.359813\pi\) | ||||
0.426311 | + | 0.904577i | \(0.359813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 120.000 | 0.135988 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 121.852 | 0.133703 | ||||||||
\(95\) | 2320.00 | 2.50555 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 304.631 | 0.318872 | 0.159436 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159436 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 428.000 | 0.428000 | ||||||||
\(101\) | 1020.51 | 1.00540 | 0.502698 | − | 0.864462i | \(-0.332341\pi\) | ||||
0.502698 | + | 0.864462i | \(0.332341\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −578.799 | −0.553696 | −0.276848 | − | 0.960914i | \(-0.589290\pi\) | ||||
−0.276848 | + | 0.960914i | \(0.589290\pi\) | |||||||
\(104\) | −243.705 | −0.229781 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1096.00 | 1.00427 | ||||||||
\(107\) | −1646.00 | −1.48715 | −0.743574 | − | 0.668654i | \(-0.766871\pi\) | ||||
−0.743574 | + | 0.668654i | \(0.766871\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 982.000 | 0.862922 | 0.431461 | − | 0.902131i | \(-0.357998\pi\) | ||||
0.431461 | + | 0.902131i | \(0.357998\pi\) | |||||||
\(110\) | 60.9262 | 0.0528099 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1288.00 | 1.07226 | 0.536128 | − | 0.844137i | \(-0.319887\pi\) | ||||
0.536128 | + | 0.844137i | \(0.319887\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 456.946 | 0.370526 | ||||||||
\(116\) | 848.000 | 0.678748 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1340.38 | −1.04569 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1327.00 | −0.996995 | ||||||||
\(122\) | −1035.75 | −0.768623 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 852.967 | 0.617731 | ||||||||
\(125\) | −274.168 | −0.196179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1072.00 | −0.749013 | −0.374506 | − | 0.927224i | \(-0.622188\pi\) | ||||
−0.374506 | + | 0.927224i | \(0.622188\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −928.000 | −0.626084 | ||||||||
\(131\) | −2741.68 | −1.82856 | −0.914281 | − | 0.405081i | \(-0.867243\pi\) | ||||
−0.914281 | + | 0.405081i | \(0.867243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1304.00 | 0.840660 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −365.557 | −0.230487 | ||||||||
\(137\) | 2936.00 | 1.83094 | 0.915472 | − | 0.402381i | \(-0.131817\pi\) | ||||
0.915472 | + | 0.402381i | \(0.131817\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 182.779 | 0.111533 | 0.0557665 | − | 0.998444i | \(-0.482240\pi\) | ||||
0.0557665 | + | 0.998444i | \(0.482240\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1540.00 | 0.910098 | ||||||||
\(143\) | −60.9262 | −0.0356287 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3229.09 | 1.84939 | ||||||||
\(146\) | −1949.64 | −1.10516 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 984.000 | 0.546516 | ||||||||
\(149\) | −964.000 | −0.530027 | −0.265013 | − | 0.964245i | \(-0.585376\pi\) | ||||
−0.265013 | + | 0.964245i | \(0.585376\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1688.00 | −0.909718 | −0.454859 | − | 0.890563i | \(-0.650310\pi\) | ||||
−0.454859 | + | 0.890563i | \(0.650310\pi\) | |||||||
\(152\) | 1218.52 | 0.650232 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3248.00 | 1.68313 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3442.33 | 1.74986 | 0.874929 | − | 0.484251i | \(-0.160908\pi\) | ||||
0.874929 | + | 0.484251i | \(0.160908\pi\) | |||||||
\(158\) | 944.000 | 0.475320 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 487.409 | 0.240832 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3324.00 | −1.59727 | −0.798637 | − | 0.601813i | \(-0.794445\pi\) | ||||
−0.798637 | + | 0.601813i | \(0.794445\pi\) | |||||||
\(164\) | −1279.45 | −0.609197 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 365.557 | 0.170920 | ||||||||
\(167\) | 3046.31 | 1.41156 | 0.705780 | − | 0.708431i | \(-0.250597\pi\) | ||||
0.705780 | + | 0.708431i | \(0.250597\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1269.00 | −0.577606 | ||||||||
\(170\) | −1392.00 | −0.628009 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1136.00 | −0.503600 | ||||||||
\(173\) | 3274.78 | 1.43917 | 0.719587 | − | 0.694402i | \(-0.244331\pi\) | ||||
0.719587 | + | 0.694402i | \(0.244331\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 32.0000 | 0.0137051 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1431.77 | 0.602895 | ||||||||
\(179\) | 1254.00 | 0.523622 | 0.261811 | − | 0.965119i | \(-0.415680\pi\) | ||||
0.261811 | + | 0.965119i | \(0.415680\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3076.77 | −1.26351 | −0.631753 | − | 0.775170i | \(-0.717664\pi\) | ||||
−0.631753 | + | 0.775170i | \(0.717664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 240.000 | 0.0961578 | ||||||||
\(185\) | 3746.96 | 1.48909 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −91.3893 | −0.0357382 | ||||||||
\(188\) | 243.705 | 0.0945425 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4640.00 | 1.77169 | ||||||||
\(191\) | 906.000 | 0.343224 | 0.171612 | − | 0.985165i | \(-0.445102\pi\) | ||||
0.171612 | + | 0.985165i | \(0.445102\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 182.000 | 0.0678790 | 0.0339395 | − | 0.999424i | \(-0.489195\pi\) | ||||
0.0339395 | + | 0.999424i | \(0.489195\pi\) | |||||||
\(194\) | 609.262 | 0.225477 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3468.00 | 1.25424 | 0.627119 | − | 0.778924i | \(-0.284234\pi\) | ||||
0.627119 | + | 0.778924i | \(0.284234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3899.28 | −1.38901 | −0.694503 | − | 0.719489i | \(-0.744376\pi\) | ||||
−0.694503 | + | 0.719489i | \(0.744376\pi\) | |||||||
\(200\) | 856.000 | 0.302642 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2041.03 | 0.710922 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4872.00 | −1.65988 | ||||||||
\(206\) | −1157.60 | −0.391523 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −487.409 | −0.162480 | ||||||||
\(209\) | 304.631 | 0.100822 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2620.00 | −0.854826 | −0.427413 | − | 0.904057i | \(-0.640575\pi\) | ||||
−0.427413 | + | 0.904057i | \(0.640575\pi\) | |||||||
\(212\) | 2192.00 | 0.710128 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3292.00 | −1.05157 | ||||||||
\(215\) | −4325.76 | −1.37216 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1964.00 | 0.610178 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 121.852 | 0.0373422 | ||||||||
\(221\) | 1392.00 | 0.423693 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1401.30 | 0.420799 | 0.210399 | − | 0.977616i | \(-0.432524\pi\) | ||||
0.210399 | + | 0.977616i | \(0.432524\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2576.00 | 0.758199 | ||||||||
\(227\) | −3899.28 | −1.14011 | −0.570053 | − | 0.821608i | \(-0.693077\pi\) | ||||
−0.570053 | + | 0.821608i | \(0.693077\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5513.82 | −1.59111 | −0.795553 | − | 0.605883i | \(-0.792820\pi\) | ||||
−0.795553 | + | 0.605883i | \(0.792820\pi\) | |||||||
\(230\) | 913.893 | 0.262001 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1696.00 | 0.479948 | ||||||||
\(233\) | −712.000 | −0.200192 | −0.100096 | − | 0.994978i | \(-0.531915\pi\) | ||||
−0.100096 | + | 0.994978i | \(0.531915\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 928.000 | 0.257600 | ||||||||
\(236\) | −2680.75 | −0.739416 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2586.00 | −0.699893 | −0.349947 | − | 0.936770i | \(-0.613800\pi\) | ||||
−0.349947 | + | 0.936770i | \(0.613800\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2254.27 | −0.602532 | −0.301266 | − | 0.953540i | \(-0.597409\pi\) | ||||
−0.301266 | + | 0.953540i | \(0.597409\pi\) | |||||||
\(242\) | −2654.00 | −0.704982 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2071.49 | −0.543498 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4640.00 | −1.19529 | ||||||||
\(248\) | 1705.93 | 0.436802 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −548.336 | −0.138719 | ||||||||
\(251\) | −4508.54 | −1.13377 | −0.566885 | − | 0.823797i | \(-0.691852\pi\) | ||||
−0.566885 | + | 0.823797i | \(0.691852\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 60.0000 | 0.0149098 | ||||||||
\(254\) | −2144.00 | −0.529632 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4554.23 | 1.10539 | 0.552695 | − | 0.833384i | \(-0.313599\pi\) | ||||
0.552695 | + | 0.833384i | \(0.313599\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1856.00 | −0.442709 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5483.36 | −1.29299 | ||||||||
\(263\) | −2578.00 | −0.604435 | −0.302217 | − | 0.953239i | \(-0.597727\pi\) | ||||
−0.302217 | + | 0.953239i | \(0.597727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8346.89 | 1.93489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2608.00 | 0.594436 | ||||||||
\(269\) | 929.124 | 0.210594 | 0.105297 | − | 0.994441i | \(-0.466421\pi\) | ||||
0.105297 | + | 0.994441i | \(0.466421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1127.13 | −0.252651 | −0.126326 | − | 0.991989i | \(-0.540318\pi\) | ||||
−0.126326 | + | 0.991989i | \(0.540318\pi\) | |||||||
\(272\) | −731.114 | −0.162979 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5872.00 | 1.29467 | ||||||||
\(275\) | 214.000 | 0.0469261 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1510.00 | 0.327535 | 0.163767 | − | 0.986499i | \(-0.447635\pi\) | ||||
0.163767 | + | 0.986499i | \(0.447635\pi\) | |||||||
\(278\) | 365.557 | 0.0788657 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4008.00 | −0.850880 | −0.425440 | − | 0.904987i | \(-0.639881\pi\) | ||||
−0.425440 | + | 0.904987i | \(0.639881\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2406.58 | 0.505500 | 0.252750 | − | 0.967532i | \(-0.418665\pi\) | ||||
0.252750 | + | 0.967532i | \(0.418665\pi\) | |||||||
\(284\) | 3080.00 | 0.643537 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −121.852 | −0.0251933 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2825.00 | −0.575005 | ||||||||
\(290\) | 6458.18 | 1.30771 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3899.28 | −0.781465 | ||||||||
\(293\) | −5254.88 | −1.04776 | −0.523880 | − | 0.851792i | \(-0.675516\pi\) | ||||
−0.523880 | + | 0.851792i | \(0.675516\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10208.0 | −2.01469 | ||||||||
\(296\) | 1968.00 | 0.386445 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1928.00 | −0.374785 | ||||||||
\(299\) | −913.893 | −0.176762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3376.00 | −0.643268 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2437.05 | 0.459784 | ||||||||
\(305\) | −7888.00 | −1.48087 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6366.79 | −1.18362 | −0.591811 | − | 0.806077i | \(-0.701587\pi\) | ||||
−0.591811 | + | 0.806077i | \(0.701587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6496.00 | 1.19015 | ||||||||
\(311\) | −7372.07 | −1.34415 | −0.672077 | − | 0.740482i | \(-0.734597\pi\) | ||||
−0.672077 | + | 0.740482i | \(0.734597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 548.336 | 0.0990216 | 0.0495108 | − | 0.998774i | \(-0.484234\pi\) | ||||
0.0495108 | + | 0.998774i | \(0.484234\pi\) | |||||||
\(314\) | 6884.66 | 1.23734 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1888.00 | 0.336102 | ||||||||
\(317\) | 3780.00 | 0.669735 | 0.334867 | − | 0.942265i | \(-0.391308\pi\) | ||||
0.334867 | + | 0.942265i | \(0.391308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 424.000 | 0.0744183 | ||||||||
\(320\) | 974.819 | 0.170294 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6960.00 | −1.19896 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3259.55 | −0.556330 | ||||||||
\(326\) | −6648.00 | −1.12944 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2558.90 | −0.430767 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6260.00 | 1.03952 | 0.519759 | − | 0.854313i | \(-0.326022\pi\) | ||||
0.519759 | + | 0.854313i | \(0.326022\pi\) | |||||||
\(332\) | 731.114 | 0.120859 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6092.62 | 0.998124 | ||||||||
\(335\) | 9930.97 | 1.61966 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3166.00 | −0.511760 | −0.255880 | − | 0.966709i | \(-0.582365\pi\) | ||||
−0.255880 | + | 0.966709i | \(0.582365\pi\) | |||||||
\(338\) | −2538.00 | −0.408429 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2784.00 | −0.444069 | ||||||||
\(341\) | 426.483 | 0.0677283 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2272.00 | −0.356099 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6549.56 | 1.01765 | ||||||||
\(347\) | −3618.00 | −0.559725 | −0.279862 | − | 0.960040i | \(-0.590289\pi\) | ||||
−0.279862 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4478.07 | −0.686836 | −0.343418 | − | 0.939183i | \(-0.611585\pi\) | ||||
−0.343418 | + | 0.939183i | \(0.611585\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 64.0000 | 0.00969094 | ||||||||
\(353\) | −3701.27 | −0.558069 | −0.279035 | − | 0.960281i | \(-0.590014\pi\) | ||||
−0.279035 | + | 0.960281i | \(0.590014\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11728.3 | 1.75345 | ||||||||
\(356\) | 2863.53 | 0.426311 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2508.00 | 0.370257 | ||||||||
\(359\) | 130.000 | 0.0191118 | 0.00955590 | − | 0.999954i | \(-0.496958\pi\) | ||||
0.00955590 | + | 0.999954i | \(0.496958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16341.0 | 2.38242 | ||||||||
\(362\) | −6153.54 | −0.893434 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14848.0 | −2.12926 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7798.55 | 1.10921 | 0.554606 | − | 0.832113i | \(-0.312869\pi\) | ||||
0.554606 | + | 0.832113i | \(0.312869\pi\) | |||||||
\(368\) | 480.000 | 0.0679938 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7493.92 | 1.05295 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −50.0000 | −0.00694076 | −0.00347038 | − | 0.999994i | \(-0.501105\pi\) | ||||
−0.00347038 | + | 0.999994i | \(0.501105\pi\) | |||||||
\(374\) | −182.779 | −0.0252707 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 487.409 | 0.0668517 | ||||||||
\(377\) | −6458.18 | −0.882263 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4956.00 | −0.671696 | −0.335848 | − | 0.941916i | \(-0.609023\pi\) | ||||
−0.335848 | + | 0.941916i | \(0.609023\pi\) | |||||||
\(380\) | 9280.00 | 1.25277 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1812.00 | 0.242696 | ||||||||
\(383\) | 6762.81 | 0.902254 | 0.451127 | − | 0.892460i | \(-0.351022\pi\) | ||||
0.451127 | + | 0.892460i | \(0.351022\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 364.000 | 0.0479977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1218.52 | 0.159436 | ||||||||
\(389\) | −13140.0 | −1.71266 | −0.856330 | − | 0.516430i | \(-0.827261\pi\) | ||||
−0.856330 | + | 0.516430i | \(0.827261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1370.84 | −0.177305 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6936.00 | 0.886880 | ||||||||
\(395\) | 7189.29 | 0.915778 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3807.89 | 0.481391 | 0.240696 | − | 0.970601i | \(-0.422624\pi\) | ||||
0.240696 | + | 0.970601i | \(0.422624\pi\) | |||||||
\(398\) | −7798.55 | −0.982176 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1712.00 | 0.214000 | ||||||||
\(401\) | 4824.00 | 0.600746 | 0.300373 | − | 0.953822i | \(-0.402889\pi\) | ||||
0.300373 | + | 0.953822i | \(0.402889\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6496.00 | −0.802950 | ||||||||
\(404\) | 4082.05 | 0.502698 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 492.000 | 0.0599202 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5300.58 | 0.640823 | 0.320412 | − | 0.947278i | \(-0.396179\pi\) | ||||
0.320412 | + | 0.947278i | \(0.396179\pi\) | |||||||
\(410\) | −9744.00 | −1.17371 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2315.20 | −0.276848 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2784.00 | 0.329304 | ||||||||
\(416\) | −974.819 | −0.114890 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 609.262 | 0.0712918 | ||||||||
\(419\) | −10540.2 | −1.22894 | −0.614468 | − | 0.788942i | \(-0.710629\pi\) | ||||
−0.614468 | + | 0.788942i | \(0.710629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4458.00 | −0.516080 | −0.258040 | − | 0.966134i | \(-0.583077\pi\) | ||||
−0.258040 | + | 0.966134i | \(0.583077\pi\) | |||||||
\(422\) | −5240.00 | −0.604453 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4384.00 | 0.502136 | ||||||||
\(425\) | −4889.33 | −0.558040 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6584.00 | −0.743574 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8651.52 | −0.970263 | ||||||||
\(431\) | −16214.0 | −1.81207 | −0.906034 | − | 0.423206i | \(-0.860905\pi\) | ||||
−0.906034 | + | 0.423206i | \(0.860905\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3594.64 | −0.398955 | −0.199478 | − | 0.979902i | \(-0.563925\pi\) | ||||
−0.199478 | + | 0.979902i | \(0.563925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3928.00 | 0.431461 | ||||||||
\(437\) | 4569.46 | 0.500199 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8590.59 | −0.933956 | −0.466978 | − | 0.884269i | \(-0.654657\pi\) | ||||
−0.466978 | + | 0.884269i | \(0.654657\pi\) | |||||||
\(440\) | 243.705 | 0.0264049 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2784.00 | 0.299596 | ||||||||
\(443\) | 15006.0 | 1.60938 | 0.804691 | − | 0.593693i | \(-0.202331\pi\) | ||||
0.804691 | + | 0.593693i | \(0.202331\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10904.0 | 1.16157 | ||||||||
\(446\) | 2802.60 | 0.297550 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1824.00 | 0.191715 | 0.0958573 | − | 0.995395i | \(-0.469441\pi\) | ||||
0.0958573 | + | 0.995395i | \(0.469441\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −639.725 | −0.0667926 | ||||||||
\(452\) | 5152.00 | 0.536128 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7798.55 | −0.806177 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −586.000 | −0.0599823 | −0.0299912 | − | 0.999550i | \(-0.509548\pi\) | ||||
−0.0299912 | + | 0.999550i | \(0.509548\pi\) | |||||||
\(458\) | −11027.6 | −1.12508 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1827.79 | 0.185263 | ||||||||
\(461\) | 15399.1 | 1.55576 | 0.777882 | − | 0.628410i | \(-0.216294\pi\) | ||||
0.777882 | + | 0.628410i | \(0.216294\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −88.0000 | −0.00883306 | −0.00441653 | − | 0.999990i | \(-0.501406\pi\) | ||||
−0.00441653 | + | 0.999990i | \(0.501406\pi\) | |||||||
\(464\) | 3392.00 | 0.339374 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1424.00 | −0.141557 | ||||||||
\(467\) | −9748.19 | −0.965937 | −0.482968 | − | 0.875638i | \(-0.660441\pi\) | ||||
−0.482968 | + | 0.875638i | \(0.660441\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1856.00 | 0.182151 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5361.50 | −0.522846 | ||||||||
\(473\) | −568.000 | −0.0552149 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16297.8 | 1.57430 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5172.00 | −0.494899 | ||||||||
\(479\) | 4935.02 | 0.470745 | 0.235373 | − | 0.971905i | \(-0.424369\pi\) | ||||
0.235373 | + | 0.971905i | \(0.424369\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7493.92 | −0.710381 | ||||||||
\(482\) | −4508.54 | −0.426054 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5308.00 | −0.498497 | ||||||||
\(485\) | 4640.00 | 0.434416 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −824.000 | −0.0766715 | −0.0383357 | − | 0.999265i | \(-0.512206\pi\) | ||||
−0.0383357 | + | 0.999265i | \(0.512206\pi\) | |||||||
\(488\) | −4142.98 | −0.384311 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15426.0 | −1.41785 | −0.708926 | − | 0.705283i | \(-0.750820\pi\) | ||||
−0.708926 | + | 0.705283i | \(0.750820\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9687.26 | −0.884974 | ||||||||
\(494\) | −9280.00 | −0.845196 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3411.87 | 0.308866 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5844.00 | 0.524275 | 0.262138 | − | 0.965030i | \(-0.415573\pi\) | ||||
0.262138 | + | 0.965030i | \(0.415573\pi\) | |||||||
\(500\) | −1096.67 | −0.0980893 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9017.08 | −0.801697 | ||||||||
\(503\) | 10174.7 | 0.901921 | 0.450960 | − | 0.892544i | \(-0.351082\pi\) | ||||
0.450960 | + | 0.892544i | \(0.351082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15544.0 | 1.36970 | ||||||||
\(506\) | 120.000 | 0.0105428 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4288.00 | −0.374506 | ||||||||
\(509\) | −11804.4 | −1.02794 | −0.513971 | − | 0.857807i | \(-0.671826\pi\) | ||||
−0.513971 | + | 0.857807i | \(0.671826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9108.46 | 0.781629 | ||||||||
\(515\) | −8816.00 | −0.754329 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 121.852 | 0.0103657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3712.00 | −0.313042 | ||||||||
\(521\) | −1568.85 | −0.131924 | −0.0659621 | − | 0.997822i | \(-0.521012\pi\) | ||||
−0.0659621 | + | 0.997822i | \(0.521012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19130.8 | −1.59949 | −0.799744 | − | 0.600341i | \(-0.795032\pi\) | ||||
−0.799744 | + | 0.600341i | \(0.795032\pi\) | |||||||
\(524\) | −10966.7 | −0.914281 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5156.00 | −0.427400 | ||||||||
\(527\) | −9744.00 | −0.805418 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11267.0 | −0.926029 | ||||||||
\(530\) | 16693.8 | 1.36817 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9744.00 | 0.791856 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25071.1 | −2.02602 | ||||||||
\(536\) | 5216.00 | 0.420330 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1858.25 | 0.148912 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6626.00 | −0.526569 | −0.263285 | − | 0.964718i | \(-0.584806\pi\) | ||||
−0.263285 | + | 0.964718i | \(0.584806\pi\) | |||||||
\(542\) | −2254.27 | −0.178652 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1462.23 | −0.115244 | ||||||||
\(545\) | 14957.4 | 1.17560 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19964.0 | −1.56051 | −0.780255 | − | 0.625462i | \(-0.784911\pi\) | ||||
−0.780255 | + | 0.625462i | \(0.784911\pi\) | |||||||
\(548\) | 11744.0 | 0.915472 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 428.000 | 0.0331818 | ||||||||
\(551\) | 32290.9 | 2.49662 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3020.00 | 0.231602 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 731.114 | 0.0557665 | ||||||||
\(557\) | 6780.00 | 0.515759 | 0.257880 | − | 0.966177i | \(-0.416976\pi\) | ||||
0.257880 | + | 0.966177i | \(0.416976\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8651.52 | 0.654598 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8016.00 | −0.601663 | ||||||||
\(563\) | 18948.0 | 1.41841 | 0.709205 | − | 0.705002i | \(-0.249054\pi\) | ||||
0.709205 | + | 0.705002i | \(0.249054\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19618.2 | 1.46079 | ||||||||
\(566\) | 4813.17 | 0.357443 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6160.00 | 0.455049 | ||||||||
\(569\) | −192.000 | −0.0141460 | −0.00707299 | − | 0.999975i | \(-0.502251\pi\) | ||||
−0.00707299 | + | 0.999975i | \(0.502251\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23028.0 | −1.68773 | −0.843863 | − | 0.536558i | \(-0.819724\pi\) | ||||
−0.843863 | + | 0.536558i | \(0.819724\pi\) | |||||||
\(572\) | −243.705 | −0.0178143 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3210.00 | 0.232811 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10723.0 | 0.773665 | 0.386832 | − | 0.922150i | \(-0.373569\pi\) | ||||
0.386832 | + | 0.922150i | \(0.373569\pi\) | |||||||
\(578\) | −5650.00 | −0.406590 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12916.4 | 0.924694 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1096.00 | 0.0778588 | ||||||||
\(584\) | −7798.55 | −0.552579 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10509.8 | −0.740878 | ||||||||
\(587\) | −19496.4 | −1.37087 | −0.685436 | − | 0.728133i | \(-0.740388\pi\) | ||||
−0.685436 | + | 0.728133i | \(0.740388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32480.0 | 2.27218 | ||||||||
\(590\) | −20416.0 | −1.42460 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3936.00 | 0.273258 | ||||||||
\(593\) | −13388.5 | −0.927152 | −0.463576 | − | 0.886057i | \(-0.653434\pi\) | ||||
−0.463576 | + | 0.886057i | \(0.653434\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3856.00 | −0.265013 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1827.79 | −0.124989 | ||||||||
\(599\) | 18066.0 | 1.23232 | 0.616158 | − | 0.787623i | \(-0.288688\pi\) | ||||
0.616158 | + | 0.787623i | \(0.288688\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19861.9 | −1.34806 | −0.674031 | − | 0.738703i | \(-0.735439\pi\) | ||||
−0.674031 | + | 0.738703i | \(0.735439\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6752.00 | −0.454859 | ||||||||
\(605\) | −20212.3 | −1.35826 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5300.58 | 0.354438 | 0.177219 | − | 0.984171i | \(-0.443290\pi\) | ||||
0.177219 | + | 0.984171i | \(0.443290\pi\) | |||||||
\(608\) | 4874.09 | 0.325116 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15776.0 | −1.04713 | ||||||||
\(611\) | −1856.00 | −0.122890 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15938.0 | 1.05013 | 0.525065 | − | 0.851062i | \(-0.324041\pi\) | ||||
0.525065 | + | 0.851062i | \(0.324041\pi\) | |||||||
\(614\) | −12733.6 | −0.836947 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11696.0 | −0.763149 | −0.381575 | − | 0.924338i | \(-0.624618\pi\) | ||||
−0.381575 | + | 0.924338i | \(0.624618\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13464.7 | 0.874300 | 0.437150 | − | 0.899389i | \(-0.355988\pi\) | ||||
0.437150 | + | 0.899389i | \(0.355988\pi\) | |||||||
\(620\) | 12992.0 | 0.841567 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14744.1 | −0.950460 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17551.0 | −1.12326 | ||||||||
\(626\) | 1096.67 | 0.0700189 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13769.3 | 0.874929 | ||||||||
\(629\) | −11240.9 | −0.712565 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11856.0 | 0.747987 | 0.373994 | − | 0.927431i | \(-0.377988\pi\) | ||||
0.373994 | + | 0.927431i | \(0.377988\pi\) | |||||||
\(632\) | 3776.00 | 0.237660 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7560.00 | 0.473574 | ||||||||
\(635\) | −16328.2 | −1.02042 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 848.000 | 0.0526217 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1949.64 | 0.120416 | ||||||||
\(641\) | 5608.00 | 0.345558 | 0.172779 | − | 0.984961i | \(-0.444725\pi\) | ||||
0.172779 | + | 0.984961i | \(0.444725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25314.8 | −1.55260 | −0.776298 | − | 0.630366i | \(-0.782905\pi\) | ||||
−0.776298 | + | 0.630366i | \(0.782905\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13920.0 | −0.847794 | ||||||||
\(647\) | 5848.91 | 0.355401 | 0.177701 | − | 0.984085i | \(-0.443134\pi\) | ||||
0.177701 | + | 0.984085i | \(0.443134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1340.38 | −0.0810699 | ||||||||
\(650\) | −6519.10 | −0.393385 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13296.0 | −0.798637 | ||||||||
\(653\) | −28636.0 | −1.71610 | −0.858050 | − | 0.513566i | \(-0.828324\pi\) | ||||
−0.858050 | + | 0.513566i | \(0.828324\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41760.0 | −2.49114 | ||||||||
\(656\) | −5117.80 | −0.304598 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 31786.0 | 1.87892 | 0.939459 | − | 0.342662i | \(-0.111328\pi\) | ||||
0.939459 | + | 0.342662i | \(0.111328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9474.02 | 0.557484 | 0.278742 | − | 0.960366i | \(-0.410083\pi\) | ||||
0.278742 | + | 0.960366i | \(0.410083\pi\) | |||||||
\(662\) | 12520.0 | 0.735051 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1462.23 | 0.0854600 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6360.00 | 0.369206 | ||||||||
\(668\) | 12185.2 | 0.705780 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19861.9 | 1.14527 | ||||||||
\(671\) | −1035.75 | −0.0595894 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24986.0 | 1.43111 | 0.715557 | − | 0.698555i | \(-0.246173\pi\) | ||||
0.715557 | + | 0.698555i | \(0.246173\pi\) | |||||||
\(674\) | −6332.00 | −0.361869 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5076.00 | −0.288803 | ||||||||
\(677\) | 45.6946 | 0.00259407 | 0.00129704 | − | 0.999999i | \(-0.499587\pi\) | ||||
0.00129704 | + | 0.999999i | \(0.499587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5568.00 | −0.314004 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 852.967 | 0.0478912 | ||||||||
\(683\) | 30094.0 | 1.68597 | 0.842983 | − | 0.537940i | \(-0.180797\pi\) | ||||
0.842983 | + | 0.537940i | \(0.180797\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44719.8 | 2.49439 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4544.00 | −0.251800 | ||||||||
\(689\) | −16693.8 | −0.923051 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16937.5 | 0.932463 | 0.466232 | − | 0.884663i | \(-0.345611\pi\) | ||||
0.466232 | + | 0.884663i | \(0.345611\pi\) | |||||||
\(692\) | 13099.1 | 0.719587 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7236.00 | −0.395785 | ||||||||
\(695\) | 2784.00 | 0.151947 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14616.0 | 0.794290 | ||||||||
\(698\) | −8956.15 | −0.485667 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7660.00 | 0.412716 | 0.206358 | − | 0.978477i | \(-0.433839\pi\) | ||||
0.206358 | + | 0.978477i | \(0.433839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37469.6 | 2.01023 | ||||||||
\(704\) | 128.000 | 0.00685253 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7402.53 | −0.394615 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10654.0 | 0.564343 | 0.282172 | − | 0.959364i | \(-0.408945\pi\) | ||||
0.282172 | + | 0.959364i | \(0.408945\pi\) | |||||||
\(710\) | 23456.6 | 1.23987 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5727.06 | 0.301448 | ||||||||
\(713\) | 6397.25 | 0.336015 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −928.000 | −0.0485388 | ||||||||
\(716\) | 5016.00 | 0.261811 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 260.000 | 0.0135141 | ||||||||
\(719\) | 37104.0 | 1.92454 | 0.962272 | − | 0.272089i | \(-0.0877144\pi\) | ||||
0.962272 | + | 0.272089i | \(0.0877144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 32682.0 | 1.68462 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12307.1 | −0.631753 | ||||||||
\(725\) | 22684.0 | 1.16202 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17760.0 | −0.906027 | −0.453013 | − | 0.891504i | \(-0.649651\pi\) | ||||
−0.453013 | + | 0.891504i | \(0.649651\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29696.0 | −1.50561 | ||||||||
\(731\) | 12977.3 | 0.656610 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2528.44 | −0.127408 | −0.0637039 | − | 0.997969i | \(-0.520291\pi\) | ||||
−0.0637039 | + | 0.997969i | \(0.520291\pi\) | |||||||
\(734\) | 15597.1 | 0.784332 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 960.000 | 0.0480789 | ||||||||
\(737\) | 1304.00 | 0.0651743 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8156.00 | −0.405986 | −0.202993 | − | 0.979180i | \(-0.565067\pi\) | ||||
−0.202993 | + | 0.979180i | \(0.565067\pi\) | |||||||
\(740\) | 14987.8 | 0.744546 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2910.00 | −0.143684 | −0.0718422 | − | 0.997416i | \(-0.522888\pi\) | ||||
−0.0718422 | + | 0.997416i | \(0.522888\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14683.2 | −0.722082 | ||||||||
\(746\) | −100.000 | −0.00490786 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −365.557 | −0.0178691 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13584.0 | 0.660036 | 0.330018 | − | 0.943975i | \(-0.392945\pi\) | ||||
0.330018 | + | 0.943975i | \(0.392945\pi\) | |||||||
\(752\) | 974.819 | 0.0472713 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12916.4 | −0.623854 | ||||||||
\(755\) | −25710.9 | −1.23936 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19054.0 | 0.914834 | 0.457417 | − | 0.889252i | \(-0.348775\pi\) | ||||
0.457417 | + | 0.889252i | \(0.348775\pi\) | |||||||
\(758\) | −9912.00 | −0.474960 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 18560.0 | 0.885845 | ||||||||
\(761\) | −5011.18 | −0.238706 | −0.119353 | − | 0.992852i | \(-0.538082\pi\) | ||||
−0.119353 | + | 0.992852i | \(0.538082\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3624.00 | 0.171612 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13525.6 | 0.637990 | ||||||||
\(767\) | 20416.0 | 0.961120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21506.9 | −1.00853 | −0.504265 | − | 0.863549i | \(-0.668237\pi\) | ||||
−0.504265 | + | 0.863549i | \(0.668237\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 728.000 | 0.0339395 | ||||||||
\(773\) | −23715.5 | −1.10348 | −0.551739 | − | 0.834017i | \(-0.686035\pi\) | ||||
−0.551739 | + | 0.834017i | \(0.686035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22816.9 | 1.05756 | ||||||||
\(776\) | 2437.05 | 0.112738 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −26280.0 | −1.21103 | ||||||||
\(779\) | −48720.0 | −2.24079 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1540.00 | 0.0705577 | ||||||||
\(782\) | −2741.68 | −0.125374 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52432.0 | 2.38392 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −36982.2 | −1.67506 | −0.837530 | − | 0.546391i | \(-0.816001\pi\) | ||||
−0.837530 | + | 0.546391i | \(0.816001\pi\) | |||||||
\(788\) | 13872.0 | 0.627119 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14378.6 | 0.647553 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15776.0 | 0.706459 | ||||||||
\(794\) | 7615.77 | 0.340395 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15597.1 | −0.694503 | ||||||||
\(797\) | 5346.27 | 0.237609 | 0.118805 | − | 0.992918i | \(-0.462094\pi\) | ||||
0.118805 | + | 0.992918i | \(0.462094\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2784.00 | −0.123268 | ||||||||
\(800\) | 3424.00 | 0.151321 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9648.00 | 0.424791 | ||||||||
\(803\) | −1949.64 | −0.0856802 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12992.0 | −0.567771 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8164.11 | 0.355461 | ||||||||
\(809\) | 19776.0 | 0.859440 | 0.429720 | − | 0.902962i | \(-0.358612\pi\) | ||||
0.429720 | + | 0.902962i | \(0.358612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15962.7 | 0.691153 | 0.345576 | − | 0.938391i | \(-0.387683\pi\) | ||||
0.345576 | + | 0.938391i | \(0.387683\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 984.000 | 0.0423700 | ||||||||
\(815\) | −50629.7 | −2.17605 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43257.6 | −1.85238 | ||||||||
\(818\) | 10601.2 | 0.453130 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19488.0 | −0.829940 | ||||||||
\(821\) | 29972.0 | 1.27409 | 0.637046 | − | 0.770826i | \(-0.280156\pi\) | ||||
0.637046 | + | 0.770826i | \(0.280156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38816.0 | −1.64403 | −0.822017 | − | 0.569462i | \(-0.807151\pi\) | ||||
−0.822017 | + | 0.569462i | \(0.807151\pi\) | |||||||
\(824\) | −4630.39 | −0.195761 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34386.0 | 1.44585 | 0.722925 | − | 0.690926i | \(-0.242797\pi\) | ||||
0.722925 | + | 0.690926i | \(0.242797\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13129.6 | −0.550072 | −0.275036 | − | 0.961434i | \(-0.588690\pi\) | ||||
−0.275036 | + | 0.961434i | \(0.588690\pi\) | |||||||
\(830\) | 5568.00 | 0.232853 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1949.64 | −0.0812398 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46400.0 | 1.92304 | ||||||||
\(836\) | 1218.52 | 0.0504109 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −21080.5 | −0.868989 | ||||||||
\(839\) | 27051.2 | 1.11313 | 0.556563 | − | 0.830806i | \(-0.312120\pi\) | ||||
0.556563 | + | 0.830806i | \(0.312120\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20555.0 | 0.842798 | ||||||||
\(842\) | −8916.00 | −0.364924 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10480.0 | −0.427413 | ||||||||
\(845\) | −19328.8 | −0.786902 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8768.00 | 0.355064 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9778.65 | −0.394594 | ||||||||
\(851\) | 7380.00 | 0.297277 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14774.6 | 0.593051 | 0.296526 | − | 0.955025i | \(-0.404172\pi\) | ||||
0.296526 | + | 0.955025i | \(0.404172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13168.0 | −0.525786 | ||||||||
\(857\) | 19603.0 | 0.781360 | 0.390680 | − | 0.920527i | \(-0.372240\pi\) | ||||
0.390680 | + | 0.920527i | \(0.372240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12520.3 | −0.497309 | −0.248654 | − | 0.968592i | \(-0.579988\pi\) | ||||
−0.248654 | + | 0.968592i | \(0.579988\pi\) | |||||||
\(860\) | −17303.0 | −0.686080 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32428.0 | −1.28132 | ||||||||
\(863\) | 30774.0 | 1.21386 | 0.606929 | − | 0.794756i | \(-0.292401\pi\) | ||||
0.606929 | + | 0.794756i | \(0.292401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49880.0 | 1.96066 | ||||||||
\(866\) | −7189.29 | −0.282104 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 944.000 | 0.0368504 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19861.9 | −0.772671 | ||||||||
\(872\) | 7856.00 | 0.305089 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9138.93 | 0.353694 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16758.0 | −0.645242 | −0.322621 | − | 0.946528i | \(-0.604564\pi\) | ||||
−0.322621 | + | 0.946528i | \(0.604564\pi\) | |||||||
\(878\) | −17181.2 | −0.660406 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 487.409 | 0.0186711 | ||||||||
\(881\) | −25208.2 | −0.964002 | −0.482001 | − | 0.876171i | \(-0.660090\pi\) | ||||
−0.482001 | + | 0.876171i | \(0.660090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5468.00 | −0.208395 | −0.104198 | − | 0.994557i | \(-0.533227\pi\) | ||||
−0.104198 | + | 0.994557i | \(0.533227\pi\) | |||||||
\(884\) | 5568.00 | 0.211846 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30012.0 | 1.13801 | ||||||||
\(887\) | 27051.2 | 1.02400 | 0.512002 | − | 0.858984i | \(-0.328904\pi\) | ||||
0.512002 | + | 0.858984i | \(0.328904\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21808.0 | 0.821355 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5605.21 | 0.210399 | ||||||||
\(893\) | 9280.00 | 0.347753 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19100.4 | 0.713357 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3648.00 | 0.135563 | ||||||||
\(899\) | 45207.2 | 1.67714 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25040.7 | −0.925888 | ||||||||
\(902\) | −1279.45 | −0.0472295 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10304.0 | 0.379099 | ||||||||
\(905\) | −46864.0 | −1.72134 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5876.00 | −0.215115 | −0.107558 | − | 0.994199i | \(-0.534303\pi\) | ||||
−0.107558 | + | 0.994199i | \(0.534303\pi\) | |||||||
\(908\) | −15597.1 | −0.570053 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17962.0 | 0.653247 | 0.326623 | − | 0.945155i | \(-0.394089\pi\) | ||||
0.326623 | + | 0.945155i | \(0.394089\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 365.557 | 0.0132510 | ||||||||
\(914\) | −1172.00 | −0.0424139 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22055.3 | −0.795553 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53424.0 | 1.91762 | 0.958811 | − | 0.284044i | \(-0.0916761\pi\) | ||||
0.958811 | + | 0.284044i | \(0.0916761\pi\) | |||||||
\(920\) | 3655.57 | 0.131001 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30798.2 | 1.10009 | ||||||||
\(923\) | −23456.6 | −0.836493 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26322.0 | 0.935635 | ||||||||
\(926\) | −176.000 | −0.00624592 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6784.00 | 0.239974 | ||||||||
\(929\) | −5986.00 | −0.211404 | −0.105702 | − | 0.994398i | \(-0.533709\pi\) | ||||
−0.105702 | + | 0.994398i | \(0.533709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2848.00 | −0.100096 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19496.4 | −0.683020 | ||||||||
\(935\) | −1392.00 | −0.0486880 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3655.57 | 0.127452 | 0.0637259 | − | 0.997967i | \(-0.479702\pi\) | ||||
0.0637259 | + | 0.997967i | \(0.479702\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3712.00 | 0.128800 | ||||||||
\(941\) | 53142.9 | 1.84103 | 0.920514 | − | 0.390709i | \(-0.127770\pi\) | ||||
0.920514 | + | 0.390709i | \(0.127770\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9595.87 | −0.331373 | ||||||||
\(944\) | −10723.0 | −0.369708 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1136.00 | −0.0390429 | ||||||||
\(947\) | 10202.0 | 0.350074 | 0.175037 | − | 0.984562i | \(-0.443995\pi\) | ||||
0.175037 | + | 0.984562i | \(0.443995\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29696.0 | 1.01578 | ||||||||
\(950\) | 32595.5 | 1.11320 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8856.00 | −0.301022 | −0.150511 | − | 0.988608i | \(-0.548092\pi\) | ||||
−0.150511 | + | 0.988608i | \(0.548092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13799.8 | 0.467592 | ||||||||
\(956\) | −10344.0 | −0.349947 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9870.04 | 0.332867 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15681.0 | 0.526367 | ||||||||
\(962\) | −14987.8 | −0.502315 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9017.08 | −0.301266 | ||||||||
\(965\) | 2772.14 | 0.0924750 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40760.0 | −1.35548 | −0.677742 | − | 0.735300i | \(-0.737041\pi\) | ||||
−0.677742 | + | 0.735300i | \(0.737041\pi\) | |||||||
\(968\) | −10616.0 | −0.352491 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9280.00 | 0.307178 | ||||||||
\(971\) | −46182.0 | −1.52632 | −0.763158 | − | 0.646212i | \(-0.776352\pi\) | ||||
−0.763158 | + | 0.646212i | \(0.776352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1648.00 | −0.0542149 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8285.96 | −0.271749 | ||||||||
\(977\) | 23360.0 | 0.764946 | 0.382473 | − | 0.923967i | \(-0.375072\pi\) | ||||
0.382473 | + | 0.923967i | \(0.375072\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1431.77 | 0.0467410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −30852.0 | −1.00257 | ||||||||
\(983\) | −12550.8 | −0.407231 | −0.203616 | − | 0.979051i | \(-0.565269\pi\) | ||||
−0.203616 | + | 0.979051i | \(0.565269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52823.0 | 1.70871 | ||||||||
\(986\) | −19374.5 | −0.625771 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18560.0 | −0.597644 | ||||||||
\(989\) | −8520.00 | −0.273934 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19480.0 | −0.624422 | −0.312211 | − | 0.950013i | \(-0.601070\pi\) | ||||
−0.312211 | + | 0.950013i | \(0.601070\pi\) | |||||||
\(992\) | 6823.73 | 0.218401 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −59392.0 | −1.89231 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36525.2 | 1.16025 | 0.580123 | − | 0.814529i | \(-0.303004\pi\) | ||||
0.580123 | + | 0.814529i | \(0.303004\pi\) | |||||||
\(998\) | 11688.0 | 0.370719 | ||||||||
\(999\) | 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 | 882.4.a.bf.1.2 | yes | 2 | |
3.2 | odd | 2 | 882.4.a.x.1.1 | ✓ | 2 | ||
7.2 | even | 3 | 882.4.g.bb.361.1 | 4 | |||
7.3 | odd | 6 | 882.4.g.bb.667.2 | 4 | |||
7.4 | even | 3 | 882.4.g.bb.667.1 | 4 | |||
7.5 | odd | 6 | 882.4.g.bb.361.2 | 4 | |||
7.6 | odd | 2 | inner | 882.4.a.bf.1.1 | yes | 2 | |
21.2 | odd | 6 | 882.4.g.bh.361.2 | 4 | |||
21.5 | even | 6 | 882.4.g.bh.361.1 | 4 | |||
21.11 | odd | 6 | 882.4.g.bh.667.2 | 4 | |||
21.17 | even | 6 | 882.4.g.bh.667.1 | 4 | |||
21.20 | even | 2 | 882.4.a.x.1.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.4.a.x.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
882.4.a.x.1.2 | yes | 2 | 21.20 | even | 2 | ||
882.4.a.bf.1.1 | yes | 2 | 7.6 | odd | 2 | inner | |
882.4.a.bf.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
882.4.g.bb.361.1 | 4 | 7.2 | even | 3 | |||
882.4.g.bb.361.2 | 4 | 7.5 | odd | 6 | |||
882.4.g.bb.667.1 | 4 | 7.4 | even | 3 | |||
882.4.g.bb.667.2 | 4 | 7.3 | odd | 6 | |||
882.4.g.bh.361.1 | 4 | 21.5 | even | 6 | |||
882.4.g.bh.361.2 | 4 | 21.2 | odd | 6 | |||
882.4.g.bh.667.1 | 4 | 21.17 | even | 6 | |||
882.4.g.bh.667.2 | 4 | 21.11 | odd | 6 |