Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,4,Mod(1,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.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: | \(70.8022920069\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1200.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.00000 | 0.215980 | 0.107990 | − | 0.994152i | \(-0.465559\pi\) | ||||
0.107990 | + | 0.994152i | \(0.465559\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 28.0000 | 0.767483 | 0.383742 | − | 0.923440i | \(-0.374635\pi\) | ||||
0.383742 | + | 0.923440i | \(0.374635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.0000 | 0.341354 | 0.170677 | − | 0.985327i | \(-0.445405\pi\) | ||||
0.170677 | + | 0.985327i | \(0.445405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −108.000 | −1.54081 | −0.770407 | − | 0.637552i | \(-0.779947\pi\) | ||||
−0.770407 | + | 0.637552i | \(0.779947\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.0000 | −0.386384 | −0.193192 | − | 0.981161i | \(-0.561884\pi\) | ||||
−0.193192 | + | 0.981161i | \(0.561884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.0000 | −0.124696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.0000 | −0.253844 | −0.126922 | − | 0.991913i | \(-0.540510\pi\) | ||||
−0.126922 | + | 0.991913i | \(0.540510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −238.000 | −1.52398 | −0.761991 | − | 0.647587i | \(-0.775778\pi\) | ||||
−0.761991 | + | 0.647587i | \(0.775778\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 180.000 | 1.04287 | 0.521435 | − | 0.853291i | \(-0.325397\pi\) | ||||
0.521435 | + | 0.853291i | \(0.325397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −84.0000 | −0.443107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.0000 | 0.177729 | 0.0888643 | − | 0.996044i | \(-0.471676\pi\) | ||||
0.0888643 | + | 0.996044i | \(0.471676\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −48.0000 | −0.197081 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 422.000 | 1.60745 | 0.803724 | − | 0.595003i | \(-0.202849\pi\) | ||||
0.803724 | + | 0.595003i | \(0.202849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 276.000 | 0.978828 | 0.489414 | − | 0.872052i | \(-0.337211\pi\) | ||||
0.489414 | + | 0.872052i | \(0.337211\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 60.0000 | 0.186211 | 0.0931053 | − | 0.995656i | \(-0.470321\pi\) | ||||
0.0931053 | + | 0.995656i | \(0.470321\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −327.000 | −0.953353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 324.000 | 0.889590 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −220.000 | −0.570176 | −0.285088 | − | 0.958501i | \(-0.592023\pi\) | ||||
−0.285088 | + | 0.958501i | \(0.592023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 96.0000 | 0.223079 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 804.000 | 1.77410 | 0.887050 | − | 0.461674i | \(-0.152751\pi\) | ||||
0.887050 | + | 0.461674i | \(0.152751\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −358.000 | −0.751430 | −0.375715 | − | 0.926735i | \(-0.622603\pi\) | ||||
−0.375715 | + | 0.926735i | \(0.622603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 36.0000 | 0.0719932 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −884.000 | −1.61191 | −0.805954 | − | 0.591979i | \(-0.798347\pi\) | ||||
−0.805954 | + | 0.591979i | \(0.798347\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 84.0000 | 0.146557 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 64.0000 | 0.106978 | 0.0534888 | − | 0.998568i | \(-0.482966\pi\) | ||||
0.0534888 | + | 0.998568i | \(0.482966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 152.000 | 0.243702 | 0.121851 | − | 0.992548i | \(-0.461117\pi\) | ||||
0.121851 | + | 0.992548i | \(0.461117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 112.000 | 0.165761 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 932.000 | 1.32732 | 0.663659 | − | 0.748035i | \(-0.269002\pi\) | ||||
0.663659 | + | 0.748035i | \(0.269002\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1292.00 | −1.70862 | −0.854310 | − | 0.519764i | \(-0.826020\pi\) | ||||
−0.854310 | + | 0.519764i | \(0.826020\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 714.000 | 0.879872 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1146.00 | −1.36490 | −0.682448 | − | 0.730934i | \(-0.739085\pi\) | ||||
−0.682448 | + | 0.730934i | \(0.739085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 64.0000 | 0.0737255 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −540.000 | −0.602101 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −824.000 | −0.862521 | −0.431260 | − | 0.902227i | \(-0.641931\pi\) | ||||
−0.431260 | + | 0.902227i | \(0.641931\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 252.000 | 0.255828 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1290.00 | −1.27089 | −0.635445 | − | 0.772147i | \(-0.719183\pi\) | ||||
−0.635445 | + | 0.772147i | \(0.719183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1604.00 | −1.53444 | −0.767218 | − | 0.641387i | \(-0.778359\pi\) | ||||
−0.767218 | + | 0.641387i | \(0.778359\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 892.000 | 0.805915 | 0.402957 | − | 0.915219i | \(-0.367982\pi\) | ||||
0.402957 | + | 0.915219i | \(0.367982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 966.000 | 0.848863 | 0.424431 | − | 0.905460i | \(-0.360474\pi\) | ||||
0.424431 | + | 0.905460i | \(0.360474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −120.000 | −0.102612 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1124.00 | −0.935726 | −0.467863 | − | 0.883801i | \(-0.654976\pi\) | ||||
−0.467863 | + | 0.883801i | \(0.654976\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 144.000 | 0.113785 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −432.000 | −0.332785 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −547.000 | −0.410969 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1266.00 | −0.928060 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1884.00 | −1.31636 | −0.658181 | − | 0.752860i | \(-0.728674\pi\) | ||||
−0.658181 | + | 0.752860i | \(0.728674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −828.000 | −0.565127 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 588.000 | 0.392166 | 0.196083 | − | 0.980587i | \(-0.437178\pi\) | ||||
0.196083 | + | 0.980587i | \(0.437178\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −128.000 | −0.0834512 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1060.00 | −0.661036 | −0.330518 | − | 0.943800i | \(-0.607223\pi\) | ||||
−0.330518 | + | 0.943800i | \(0.607223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2864.00 | 1.74764 | 0.873818 | − | 0.486254i | \(-0.161637\pi\) | ||||
0.873818 | + | 0.486254i | \(0.161637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −180.000 | −0.107509 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 448.000 | 0.261984 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 981.000 | 0.550418 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 342.000 | 0.188038 | 0.0940192 | − | 0.995570i | \(-0.470028\pi\) | ||||
0.0940192 | + | 0.995570i | \(0.470028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1636.00 | −0.881694 | −0.440847 | − | 0.897582i | \(-0.645322\pi\) | ||||
−0.440847 | + | 0.897582i | \(0.645322\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −972.000 | −0.513605 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2072.00 | 1.05327 | 0.526636 | − | 0.850091i | \(-0.323453\pi\) | ||||
0.526636 | + | 0.850091i | \(0.323453\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 660.000 | 0.329191 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −112.000 | −0.0548251 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 772.000 | 0.370968 | 0.185484 | − | 0.982647i | \(-0.440615\pi\) | ||||
0.185484 | + | 0.982647i | \(0.440615\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1044.00 | −0.483755 | −0.241878 | − | 0.970307i | \(-0.577763\pi\) | ||||
−0.241878 | + | 0.970307i | \(0.577763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1941.00 | −0.883477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −288.000 | −0.128795 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4404.00 | −1.93543 | −0.967717 | − | 0.252041i | \(-0.918898\pi\) | ||||
−0.967717 | + | 0.252041i | \(0.918898\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2412.00 | −1.02428 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3452.00 | −1.44142 | −0.720711 | − | 0.693235i | \(-0.756185\pi\) | ||||
−0.720711 | + | 0.693235i | \(0.756185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 526.000 | 0.216007 | 0.108004 | − | 0.994151i | \(-0.465554\pi\) | ||||
0.108004 | + | 0.994151i | \(0.465554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1074.00 | 0.433838 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3024.00 | −1.18255 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −108.000 | −0.0415653 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −72.0000 | −0.0272761 | −0.0136381 | − | 0.999907i | \(-0.504341\pi\) | ||||
−0.0136381 | + | 0.999907i | \(0.504341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −208.000 | −0.0775760 | −0.0387880 | − | 0.999247i | \(-0.512350\pi\) | ||||
−0.0387880 | + | 0.999247i | \(0.512350\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −372.000 | −0.134538 | −0.0672688 | − | 0.997735i | \(-0.521429\pi\) | ||||
−0.0672688 | + | 0.997735i | \(0.521429\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4348.00 | −1.54885 | −0.774426 | − | 0.632665i | \(-0.781961\pi\) | ||||
−0.774426 | + | 0.632665i | \(0.781961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2652.00 | 0.930635 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −952.000 | −0.329149 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −252.000 | −0.0846145 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −896.000 | −0.296544 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 416.000 | 0.135728 | 0.0678640 | − | 0.997695i | \(-0.478382\pi\) | ||||
0.0678640 | + | 0.997695i | \(0.478382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −192.000 | −0.0617635 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 720.000 | 0.225239 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −456.000 | −0.140701 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1728.00 | −0.525963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5748.00 | −1.72607 | −0.863037 | − | 0.505141i | \(-0.831441\pi\) | ||||
−0.863037 | + | 0.505141i | \(0.831441\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1148.00 | 0.335663 | 0.167831 | − | 0.985816i | \(-0.446324\pi\) | ||||
0.167831 | + | 0.985816i | \(0.446324\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3234.00 | 0.933226 | 0.466613 | − | 0.884462i | \(-0.345474\pi\) | ||||
0.466613 | + | 0.884462i | \(0.345474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −336.000 | −0.0957021 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 228.000 | 0.0641063 | 0.0320532 | − | 0.999486i | \(-0.489795\pi\) | ||||
0.0320532 | + | 0.999486i | \(0.489795\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2796.00 | −0.766328 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4760.00 | −1.28828 | −0.644140 | − | 0.764908i | \(-0.722784\pi\) | ||||
−0.644140 | + | 0.764908i | \(0.722784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3230.00 | 0.863330 | 0.431665 | − | 0.902034i | \(-0.357926\pi\) | ||||
0.431665 | + | 0.902034i | \(0.357926\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −512.000 | −0.131894 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3876.00 | 0.986472 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1708.00 | −0.429514 | −0.214757 | − | 0.976668i | \(-0.568896\pi\) | ||||
−0.214757 | + | 0.976668i | \(0.568896\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −784.000 | −0.194821 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6372.00 | −1.54659 | −0.773297 | − | 0.634044i | \(-0.781394\pi\) | ||||
−0.773297 | + | 0.634044i | \(0.781394\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 160.000 | 0.0383858 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2142.00 | −0.507994 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3036.00 | −0.711817 | −0.355908 | − | 0.934521i | \(-0.615828\pi\) | ||||
−0.355908 | + | 0.934521i | \(0.615828\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3438.00 | 0.788023 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −114.000 | −0.0258390 | −0.0129195 | − | 0.999917i | \(-0.504113\pi\) | ||||
−0.0129195 | + | 0.999917i | \(0.504113\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5236.00 | 1.17367 | 0.586835 | − | 0.809707i | \(-0.300374\pi\) | ||||
0.586835 | + | 0.809707i | \(0.300374\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −192.000 | −0.0425655 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5712.00 | 1.23899 | 0.619496 | − | 0.785000i | \(-0.287337\pi\) | ||||
0.619496 | + | 0.785000i | \(0.287337\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1620.00 | 0.347623 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3222.00 | 0.684016 | 0.342008 | − | 0.939697i | \(-0.388893\pi\) | ||||
0.342008 | + | 0.939697i | \(0.388893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4620.00 | −0.970426 | −0.485213 | − | 0.874396i | \(-0.661258\pi\) | ||||
−0.485213 | + | 0.874396i | \(0.661258\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1688.00 | 0.347176 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6751.00 | 1.37411 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2472.00 | 0.497977 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5404.00 | 1.07749 | 0.538746 | − | 0.842468i | \(-0.318898\pi\) | ||||
0.538746 | + | 0.842468i | \(0.318898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −756.000 | −0.147702 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −448.000 | −0.0866505 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1104.00 | 0.211407 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3870.00 | 0.733748 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9700.00 | −1.80328 | −0.901642 | − | 0.432483i | \(-0.857638\pi\) | ||||
−0.901642 | + | 0.432483i | \(0.857638\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4812.00 | 0.885907 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9672.00 | −1.76350 | −0.881750 | − | 0.471716i | \(-0.843635\pi\) | ||||
−0.881750 | + | 0.471716i | \(0.843635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4048.00 | −0.731011 | −0.365506 | − | 0.930809i | \(-0.619104\pi\) | ||||
−0.365506 | + | 0.930809i | \(0.619104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 84.0000 | 0.0148830 | 0.00744150 | − | 0.999972i | \(-0.497631\pi\) | ||||
0.00744150 | + | 0.999972i | \(0.497631\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6664.00 | −1.16963 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2676.00 | −0.465295 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3456.00 | 0.595347 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2898.00 | −0.490091 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 240.000 | 0.0402177 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5416.00 | −0.899366 | −0.449683 | − | 0.893188i | \(-0.648463\pi\) | ||||
−0.449683 | + | 0.893188i | \(0.648463\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 360.000 | 0.0592429 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8216.00 | 1.32805 | 0.664027 | − | 0.747709i | \(-0.268846\pi\) | ||||
0.664027 | + | 0.747709i | \(0.268846\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3372.00 | 0.540242 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5040.00 | 0.800385 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2680.00 | −0.421885 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3836.00 | 0.593450 | 0.296725 | − | 0.954963i | \(-0.404105\pi\) | ||||
0.296725 | + | 0.954963i | \(0.404105\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2038.00 | −0.312583 | −0.156292 | − | 0.987711i | \(-0.549954\pi\) | ||||
−0.156292 | + | 0.987711i | \(0.549954\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −432.000 | −0.0656936 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5292.00 | −0.797917 | −0.398959 | − | 0.916969i | \(-0.630628\pi\) | ||||
−0.398959 | + | 0.916969i | \(0.630628\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1296.00 | 0.192133 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3896.00 | 0.572766 | 0.286383 | − | 0.958115i | \(-0.407547\pi\) | ||||
0.286383 | + | 0.958115i | \(0.407547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5835.00 | −0.850707 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1641.00 | 0.237273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7652.00 | 1.08837 | 0.544184 | − | 0.838966i | \(-0.316839\pi\) | ||||
0.544184 | + | 0.838966i | \(0.316839\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3798.00 | 0.535816 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −880.000 | −0.123146 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1576.00 | 0.218773 | 0.109386 | − | 0.993999i | \(-0.465111\pi\) | ||||
0.109386 | + | 0.993999i | \(0.465111\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3808.00 | −0.520217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5416.00 | 0.734040 | 0.367020 | − | 0.930213i | \(-0.380378\pi\) | ||||
0.367020 | + | 0.930213i | \(0.380378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5652.00 | 0.760002 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8292.00 | 1.10627 | 0.553135 | − | 0.833092i | \(-0.313431\pi\) | ||||
0.553135 | + | 0.833092i | \(0.313431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2484.00 | 0.326276 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9642.00 | −1.25673 | −0.628366 | − | 0.777918i | \(-0.716276\pi\) | ||||
−0.628366 | + | 0.777918i | \(0.716276\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3024.00 | 0.391126 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1764.00 | −0.226417 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13032.0 | 1.64750 | 0.823750 | − | 0.566954i | \(-0.191878\pi\) | ||||
0.823750 | + | 0.566954i | \(0.191878\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 384.000 | 0.0481806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13358.0 | −1.66351 | −0.831754 | − | 0.555144i | \(-0.812663\pi\) | ||||
−0.831754 | + | 0.555144i | \(0.812663\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2880.00 | 0.355988 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1120.00 | 0.136404 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6410.00 | 0.774949 | 0.387474 | − | 0.921880i | \(-0.373348\pi\) | ||||
0.387474 | + | 0.921880i | \(0.373348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3180.00 | 0.381649 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3216.00 | 0.383170 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8592.00 | −1.00900 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7644.00 | −0.891250 | −0.445625 | − | 0.895220i | \(-0.647019\pi\) | ||||
−0.445625 | + | 0.895220i | \(0.647019\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14674.0 | 1.69873 | 0.849367 | − | 0.527803i | \(-0.176984\pi\) | ||||
0.849367 | + | 0.527803i | \(0.176984\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 540.000 | 0.0620702 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1432.00 | −0.162294 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1344.00 | −0.151256 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9704.00 | 1.08451 | 0.542257 | − | 0.840213i | \(-0.317570\pi\) | ||||
0.542257 | + | 0.840213i | \(0.317570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1296.00 | −0.143838 | −0.0719189 | − | 0.997410i | \(-0.522912\pi\) | ||||
−0.0719189 | + | 0.997410i | \(0.522912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 896.000 | 0.0980812 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15684.0 | 1.70514 | 0.852570 | − | 0.522613i | \(-0.175043\pi\) | ||||
0.852570 | + | 0.522613i | \(0.175043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2943.00 | −0.317784 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5772.00 | −0.619043 | −0.309521 | − | 0.950892i | \(-0.600169\pi\) | ||||
−0.309521 | + | 0.950892i | \(0.600169\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1026.00 | −0.108564 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4782.00 | −0.502620 | −0.251310 | − | 0.967907i | \(-0.580861\pi\) | ||||
−0.251310 | + | 0.967907i | \(0.580861\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11816.0 | 1.23369 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4908.00 | 0.509046 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15000.0 | −1.53538 | −0.767692 | − | 0.640819i | \(-0.778595\pi\) | ||||
−0.767692 | + | 0.640819i | \(0.778595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2916.00 | 0.296530 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3762.00 | −0.380073 | −0.190037 | − | 0.981777i | \(-0.560861\pi\) | ||||
−0.190037 | + | 0.981777i | \(0.560861\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5036.00 | 0.505492 | 0.252746 | − | 0.967533i | \(-0.418666\pi\) | ||||
0.252746 | + | 0.967533i | \(0.418666\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2268.00 | 0.224733 | 0.112367 | − | 0.993667i | \(-0.464157\pi\) | ||||
0.112367 | + | 0.993667i | \(0.464157\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3536.00 | −0.348139 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6216.00 | −0.608106 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7728.00 | 0.751234 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1980.00 | −0.190059 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16208.0 | −1.54606 | −0.773030 | − | 0.634370i | \(-0.781260\pi\) | ||||
−0.773030 | + | 0.634370i | \(0.781260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 640.000 | 0.0606684 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 336.000 | 0.0316533 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11572.0 | 1.07675 | 0.538375 | − | 0.842705i | \(-0.319038\pi\) | ||||
0.538375 | + | 0.842705i | \(0.319038\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2316.00 | −0.214178 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5636.00 | −0.518023 | −0.259011 | − | 0.965874i | \(-0.583397\pi\) | ||||
−0.259011 | + | 0.965874i | \(0.583397\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25704.0 | 2.34817 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 256.000 | 0.0231050 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5560.00 | 0.498797 | 0.249399 | − | 0.968401i | \(-0.419767\pi\) | ||||
0.249399 | + | 0.968401i | \(0.419767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3132.00 | 0.279296 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15172.0 | 1.34490 | 0.672451 | − | 0.740141i | \(-0.265241\pi\) | ||||
0.672451 | + | 0.740141i | \(0.265241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5823.00 | 0.510076 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17342.0 | −1.51016 | −0.755079 | − | 0.655634i | \(-0.772402\pi\) | ||||
−0.755079 | + | 0.655634i | \(0.772402\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 608.000 | 0.0526347 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 864.000 | 0.0743597 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1680.00 | 0.142914 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13212.0 | 1.11742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4886.00 | −0.410863 | −0.205431 | − | 0.978672i | \(-0.565860\pi\) | ||||
−0.205431 | + | 0.978672i | \(0.565860\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18548.0 | 1.55076 | 0.775380 | − | 0.631495i | \(-0.217558\pi\) | ||||
0.775380 | + | 0.631495i | \(0.217558\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19440.0 | −1.60687 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11383.0 | −0.935563 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7236.00 | 0.591367 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6752.00 | 0.548708 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10356.0 | 0.832206 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9156.00 | −0.731682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15770.0 | −1.25324 | −0.626622 | − | 0.779323i | \(-0.715563\pi\) | ||||
−0.626622 | + | 0.779323i | \(0.715563\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1578.00 | −0.124712 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7700.00 | −0.601880 | −0.300940 | − | 0.953643i | \(-0.597300\pi\) | ||||
−0.300940 | + | 0.953643i | \(0.597300\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3222.00 | −0.250477 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7616.00 | 0.588843 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3728.00 | 0.286674 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19236.0 | 1.46330 | 0.731648 | − | 0.681683i | \(-0.238752\pi\) | ||||
0.731648 | + | 0.681683i | \(0.238752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4416.00 | 0.334127 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9072.00 | 0.682745 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8388.00 | 0.627908 | 0.313954 | − | 0.949438i | \(-0.398346\pi\) | ||||
0.313954 | + | 0.949438i | \(0.398346\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 324.000 | 0.0239977 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16758.0 | −1.23468 | −0.617339 | − | 0.786697i | \(-0.711789\pi\) | ||||
−0.617339 | + | 0.786697i | \(0.711789\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8056.00 | −0.590426 | −0.295213 | − | 0.955432i | \(-0.595391\pi\) | ||||
−0.295213 | + | 0.955432i | \(0.595391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 216.000 | 0.0157479 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5728.00 | −0.413275 | −0.206638 | − | 0.978418i | \(-0.566252\pi\) | ||||
−0.206638 | + | 0.978418i | \(0.566252\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 624.000 | 0.0447885 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5168.00 | −0.369027 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6160.00 | −0.437601 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12172.0 | 0.855864 | 0.427932 | − | 0.903811i | \(-0.359242\pi\) | ||||
0.427932 | + | 0.903811i | \(0.359242\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5760.00 | −0.402948 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1116.00 | 0.0776753 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10708.0 | −0.741526 | −0.370763 | − | 0.928728i | \(-0.620904\pi\) | ||||
−0.370763 | + | 0.928728i | \(0.620904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13044.0 | 0.894230 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9416.00 | 0.642283 | 0.321141 | − | 0.947031i | \(-0.395934\pi\) | ||||
0.321141 | + | 0.947031i | \(0.395934\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9270.00 | 0.629170 | 0.314585 | − | 0.949229i | \(-0.398135\pi\) | ||||
0.314585 | + | 0.949229i | \(0.398135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7956.00 | −0.537302 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7996.00 | −0.534675 | −0.267337 | − | 0.963603i | \(-0.586144\pi\) | ||||
−0.267337 | + | 0.963603i | \(0.586144\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2856.00 | 0.190034 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 960.000 | 0.0635637 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 232.000 | 0.0152861 | 0.00764306 | − | 0.999971i | \(-0.497567\pi\) | ||||
0.00764306 | + | 0.999971i | \(0.497567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3740.00 | −0.244030 | −0.122015 | − | 0.992528i | \(-0.538936\pi\) | ||||
−0.122015 | + | 0.992528i | \(0.538936\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26000.0 | 1.68825 | 0.844126 | − | 0.536145i | \(-0.180120\pi\) | ||||
0.844126 | + | 0.536145i | \(0.180120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 756.000 | 0.0488522 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4584.00 | −0.294790 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2688.00 | 0.171210 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4320.00 | −0.273847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11660.0 | −0.735622 | −0.367811 | − | 0.929901i | \(-0.619893\pi\) | ||||
−0.367811 | + | 0.929901i | \(0.619893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1248.00 | −0.0783626 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5232.00 | −0.325431 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 576.000 | 0.0356592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7602.00 | −0.468426 | −0.234213 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234213 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29268.0 | 1.79505 | 0.897525 | − | 0.440963i | \(-0.145363\pi\) | ||||
0.897525 | + | 0.440963i | \(0.145363\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17836.0 | 1.08378 | 0.541890 | − | 0.840449i | \(-0.317709\pi\) | ||||
0.541890 | + | 0.840449i | \(0.317709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22512.0 | 1.36159 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2160.00 | −0.130042 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19188.0 | 1.14990 | 0.574950 | − | 0.818189i | \(-0.305022\pi\) | ||||
0.574950 | + | 0.818189i | \(0.305022\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1368.00 | 0.0812340 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13860.0 | −0.819285 | −0.409643 | − | 0.912246i | \(-0.634347\pi\) | ||||
−0.409643 | + | 0.912246i | \(0.634347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16558.0 | −0.974329 | −0.487165 | − | 0.873310i | \(-0.661969\pi\) | ||||
−0.487165 | + | 0.873310i | \(0.661969\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5184.00 | 0.303665 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6664.00 | 0.386853 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17244.0 | 0.996549 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10024.0 | −0.576710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4640.00 | 0.265764 | 0.132882 | − | 0.991132i | \(-0.457577\pi\) | ||||
0.132882 | + | 0.991132i | \(0.457577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34260.0 | 1.94493 | 0.972466 | − | 0.233045i | \(-0.0748691\pi\) | ||||
0.972466 | + | 0.233045i | \(0.0748691\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3296.00 | −0.186287 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3444.00 | −0.193795 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19420.0 | −1.08797 | −0.543987 | − | 0.839094i | \(-0.683086\pi\) | ||||
−0.543987 | + | 0.839094i | \(0.683086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9702.00 | −0.538798 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3520.00 | −0.194632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4608.00 | −0.253685 | −0.126843 | − | 0.991923i | \(-0.540484\pi\) | ||||
−0.126843 | + | 0.991923i | \(0.540484\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1008.00 | 0.0552536 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45576.0 | −2.47678 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −684.000 | −0.0370118 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2318.00 | −0.124893 | −0.0624463 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624463 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1280.00 | −0.0686716 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5160.00 | −0.274486 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16834.0 | 0.891698 | 0.445849 | − | 0.895108i | \(-0.352902\pi\) | ||||
0.445849 | + | 0.895108i | \(0.352902\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8388.00 | 0.442440 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5040.00 | −0.264726 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14280.0 | 0.743789 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7400.00 | 0.383830 | 0.191915 | − | 0.981412i | \(-0.438530\pi\) | ||||
0.191915 | + | 0.981412i | \(0.438530\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6416.00 | −0.331407 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9690.00 | −0.498444 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20340.0 | 1.03765 | 0.518823 | − | 0.854882i | \(-0.326370\pi\) | ||||
0.518823 | + | 0.854882i | \(0.326370\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29808.0 | −1.50819 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4896.00 | −0.246709 | −0.123355 | − | 0.992363i | \(-0.539365\pi\) | ||||
−0.123355 | + | 0.992363i | \(0.539365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24752.0 | −1.23711 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26040.0 | −1.29621 | −0.648103 | − | 0.761552i | \(-0.724438\pi\) | ||||
−0.648103 | + | 0.761552i | \(0.724438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1536.00 | 0.0761489 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6780.00 | −0.334770 | −0.167385 | − | 0.985892i | \(-0.553532\pi\) | ||||
−0.167385 | + | 0.985892i | \(0.553532\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11628.0 | −0.569540 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3568.00 | 0.174061 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20692.0 | 1.00541 | 0.502704 | − | 0.864458i | \(-0.332338\pi\) | ||||
0.502704 | + | 0.864458i | \(0.332338\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5124.00 | 0.247980 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10816.0 | 0.519305 | 0.259653 | − | 0.965702i | \(-0.416392\pi\) | ||||
0.259653 | + | 0.965702i | \(0.416392\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2352.00 | 0.112480 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13978.0 | 0.665837 | 0.332919 | − | 0.942956i | \(-0.391967\pi\) | ||||
0.332919 | + | 0.942956i | \(0.391967\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3864.00 | 0.183337 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12864.0 | 0.605596 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2926.00 | 0.137210 | 0.0686048 | − | 0.997644i | \(-0.478145\pi\) | ||||
0.0686048 | + | 0.997644i | \(0.478145\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19116.0 | 0.892926 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13916.0 | −0.647508 | −0.323754 | − | 0.946141i | \(-0.604945\pi\) | ||||
−0.323754 | + | 0.946141i | \(0.604945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −480.000 | −0.0221620 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13504.0 | −0.621092 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1792.00 | 0.0821035 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6426.00 | 0.293291 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29996.0 | 1.35863 | 0.679315 | − | 0.733847i | \(-0.262277\pi\) | ||||
0.679315 | + | 0.733847i | \(0.262277\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9108.00 | 0.410968 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4496.00 | −0.202098 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5728.00 | −0.256503 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8940.00 | 0.397329 | 0.198664 | − | 0.980068i | \(-0.436340\pi\) | ||||
0.198664 | + | 0.980068i | \(0.436340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6480.00 | −0.286916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10314.0 | −0.454965 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4256.00 | 0.187037 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 342.000 | 0.0149182 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10698.0 | −0.464922 | −0.232461 | − | 0.972606i | \(-0.574678\pi\) | ||||
−0.232461 | + | 0.972606i | \(0.574678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6408.00 | 0.277454 | 0.138727 | − | 0.990331i | \(-0.455699\pi\) | ||||
0.138727 | + | 0.990331i | \(0.455699\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15708.0 | −0.677618 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8832.00 | −0.378204 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 576.000 | 0.0245752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23130.0 | 0.983243 | 0.491622 | − | 0.870809i | \(-0.336404\pi\) | ||||
0.491622 | + | 0.870809i | \(0.336404\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11852.0 | 0.501986 | 0.250993 | − | 0.967989i | \(-0.419243\pi\) | ||||
0.250993 | + | 0.967989i | \(0.419243\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32628.0 | −1.37193 | −0.685965 | − | 0.727634i | \(-0.740620\pi\) | ||||
−0.685965 | + | 0.727634i | \(0.740620\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36694.0 | 1.53732 | 0.768658 | − | 0.639660i | \(-0.220925\pi\) | ||||
0.768658 | + | 0.639660i | \(0.220925\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17136.0 | −0.715332 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35316.0 | 1.46894 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4860.00 | −0.200700 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1704.00 | 0.0701175 | 0.0350588 | − | 0.999385i | \(-0.488838\pi\) | ||||
0.0350588 | + | 0.999385i | \(0.488838\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32255.0 | 1.32252 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9666.00 | −0.394917 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2188.00 | −0.0887610 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13860.0 | 0.560276 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1120.00 | −0.0451153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31880.0 | −1.27966 | −0.639830 | − | 0.768516i | \(-0.720995\pi\) | ||||
−0.639830 | + | 0.768516i | \(0.720995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7972.00 | 0.317758 | 0.158879 | − | 0.987298i | \(-0.449212\pi\) | ||||
0.158879 | + | 0.987298i | \(0.449212\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6008.00 | 0.238638 | 0.119319 | − | 0.992856i | \(-0.461929\pi\) | ||||
0.119319 | + | 0.992856i | \(0.461929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5064.00 | −0.200442 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1716.00 | 0.0676863 | 0.0338432 | − | 0.999427i | \(-0.489225\pi\) | ||||
0.0338432 | + | 0.999427i | \(0.489225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −20253.0 | −0.793342 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26096.0 | 1.01870 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14144.0 | −0.550231 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7416.00 | −0.287507 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9032.00 | 0.347764 | 0.173882 | − | 0.984767i | \(-0.444369\pi\) | ||||
0.173882 | + | 0.984767i | \(0.444369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16212.0 | −0.622090 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27838.0 | 1.06457 | 0.532285 | − | 0.846565i | \(-0.321334\pi\) | ||||
0.532285 | + | 0.846565i | \(0.321334\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4316.00 | −0.164490 | −0.0822452 | − | 0.996612i | \(-0.526209\pi\) | ||||
−0.0822452 | + | 0.996612i | \(0.526209\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43524.0 | −1.64757 | −0.823784 | − | 0.566904i | \(-0.808141\pi\) | ||||
−0.823784 | + | 0.566904i | \(0.808141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7536.00 | −0.284307 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2268.00 | 0.0852759 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1920.00 | −0.0719489 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1344.00 | 0.0500277 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −42840.0 | −1.58931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23760.0 | 0.878535 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3312.00 | −0.122056 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10556.0 | 0.386446 | 0.193223 | − | 0.981155i | \(-0.438106\pi\) | ||||
0.193223 | + | 0.981155i | \(0.438106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11610.0 | −0.423630 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47472.0 | 1.72647 | 0.863237 | − | 0.504799i | \(-0.168433\pi\) | ||||
0.863237 | + | 0.504799i | \(0.168433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36176.0 | −1.31134 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2352.00 | 0.0847000 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11964.0 | −0.429441 | −0.214720 | − | 0.976676i | \(-0.568884\pi\) | ||||
−0.214720 | + | 0.976676i | \(0.568884\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29100.0 | 1.04113 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1024.00 | 0.0365172 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14436.0 | −0.511478 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15214.0 | −0.537304 | −0.268652 | − | 0.963237i | \(-0.586578\pi\) | ||||
−0.268652 | + | 0.963237i | \(0.586578\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10464.0 | 0.368361 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29016.0 | 1.01816 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39712.0 | −1.38456 | −0.692281 | − | 0.721628i | \(-0.743394\pi\) | ||||
−0.692281 | + | 0.721628i | \(0.743394\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12144.0 | 0.422049 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36034.0 | −1.24833 | −0.624163 | − | 0.781294i | \(-0.714560\pi\) | ||||
−0.624163 | + | 0.781294i | \(0.714560\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11816.0 | −0.408040 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2532.00 | −0.0868838 | −0.0434419 | − | 0.999056i | \(-0.513832\pi\) | ||||
−0.0434419 | + | 0.999056i | \(0.513832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2432.00 | 0.0831887 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −252.000 | −0.00859270 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55284.0 | −1.87914 | −0.939572 | − | 0.342351i | \(-0.888777\pi\) | ||||
−0.939572 | + | 0.342351i | \(0.888777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19992.0 | 0.675287 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4240.00 | −0.142770 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2609.00 | 0.0875768 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8028.00 | 0.268638 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4372.00 | 0.145392 | 0.0726960 | − | 0.997354i | \(-0.476840\pi\) | ||||
0.0726960 | + | 0.997354i | \(0.476840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10368.0 | −0.343724 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24300.0 | −0.803114 | −0.401557 | − | 0.915834i | \(-0.631531\pi\) | ||||
−0.401557 | + | 0.915834i | \(0.631531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11456.0 | 0.377454 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46204.0 | −1.51300 | −0.756498 | − | 0.653996i | \(-0.773091\pi\) | ||||
−0.756498 | + | 0.653996i | \(0.773091\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32088.0 | −1.04754 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8694.00 | 0.282954 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25468.0 | −0.826351 | −0.413176 | − | 0.910651i | \(-0.635580\pi\) | ||||
−0.413176 | + | 0.910651i | \(0.635580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −720.000 | −0.0232197 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7728.00 | −0.248469 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11668.0 | −0.374012 | −0.187006 | − | 0.982359i | \(-0.559878\pi\) | ||||
−0.187006 | + | 0.982359i | \(0.559878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16248.0 | 0.519249 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7224.00 | 0.229475 | 0.114737 | − | 0.993396i | \(-0.463397\pi\) | ||||
0.114737 | + | 0.993396i | \(0.463397\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1080.00 | −0.0342039 |
(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 | 1200.4.a.l.1.1 | 1 | ||
4.3 | odd | 2 | 600.4.a.k.1.1 | 1 | |||
5.2 | odd | 4 | 240.4.f.e.49.2 | 2 | |||
5.3 | odd | 4 | 240.4.f.e.49.1 | 2 | |||
5.4 | even | 2 | 1200.4.a.z.1.1 | 1 | |||
12.11 | even | 2 | 1800.4.a.o.1.1 | 1 | |||
15.2 | even | 4 | 720.4.f.b.289.2 | 2 | |||
15.8 | even | 4 | 720.4.f.b.289.1 | 2 | |||
20.3 | even | 4 | 120.4.f.c.49.2 | yes | 2 | ||
20.7 | even | 4 | 120.4.f.c.49.1 | ✓ | 2 | ||
20.19 | odd | 2 | 600.4.a.f.1.1 | 1 | |||
40.3 | even | 4 | 960.4.f.b.769.1 | 2 | |||
40.13 | odd | 4 | 960.4.f.a.769.2 | 2 | |||
40.27 | even | 4 | 960.4.f.b.769.2 | 2 | |||
40.37 | odd | 4 | 960.4.f.a.769.1 | 2 | |||
60.23 | odd | 4 | 360.4.f.a.289.1 | 2 | |||
60.47 | odd | 4 | 360.4.f.a.289.2 | 2 | |||
60.59 | even | 2 | 1800.4.a.u.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.4.f.c.49.1 | ✓ | 2 | 20.7 | even | 4 | ||
120.4.f.c.49.2 | yes | 2 | 20.3 | even | 4 | ||
240.4.f.e.49.1 | 2 | 5.3 | odd | 4 | |||
240.4.f.e.49.2 | 2 | 5.2 | odd | 4 | |||
360.4.f.a.289.1 | 2 | 60.23 | odd | 4 | |||
360.4.f.a.289.2 | 2 | 60.47 | odd | 4 | |||
600.4.a.f.1.1 | 1 | 20.19 | odd | 2 | |||
600.4.a.k.1.1 | 1 | 4.3 | odd | 2 | |||
720.4.f.b.289.1 | 2 | 15.8 | even | 4 | |||
720.4.f.b.289.2 | 2 | 15.2 | even | 4 | |||
960.4.f.a.769.1 | 2 | 40.37 | odd | 4 | |||
960.4.f.a.769.2 | 2 | 40.13 | odd | 4 | |||
960.4.f.b.769.1 | 2 | 40.3 | even | 4 | |||
960.4.f.b.769.2 | 2 | 40.27 | even | 4 | |||
1200.4.a.l.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1200.4.a.z.1.1 | 1 | 5.4 | even | 2 | |||
1800.4.a.o.1.1 | 1 | 12.11 | even | 2 | |||
1800.4.a.u.1.1 | 1 | 60.59 | even | 2 |