Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1872,4,Mod(1,1872)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1872, 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("1872.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1872.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: | \(110.451575531\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 234) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1872.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | 0.178885 | 0.0894427 | − | 0.995992i | \(-0.471491\pi\) | ||||
0.0894427 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 26.0000 | 1.40387 | 0.701934 | − | 0.712242i | \(-0.252320\pi\) | ||||
0.701934 | + | 0.712242i | \(0.252320\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −52.0000 | −1.42533 | −0.712663 | − | 0.701506i | \(-0.752511\pi\) | ||||
−0.712663 | + | 0.701506i | \(0.752511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 48.0000 | 0.684806 | 0.342403 | − | 0.939553i | \(-0.388759\pi\) | ||||
0.342403 | + | 0.939553i | \(0.388759\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.0000 | −0.217341 | −0.108671 | − | 0.994078i | \(-0.534659\pi\) | ||||
−0.108671 | + | 0.994078i | \(0.534659\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 52.0000 | 0.471424 | 0.235712 | − | 0.971823i | \(-0.424258\pi\) | ||||
0.235712 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −121.000 | −0.968000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 224.000 | 1.43434 | 0.717168 | − | 0.696900i | \(-0.245438\pi\) | ||||
0.717168 | + | 0.696900i | \(0.245438\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −310.000 | −1.79605 | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 52.0000 | 0.251132 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −18.0000 | −0.0799779 | −0.0399889 | − | 0.999200i | \(-0.512732\pi\) | ||||
−0.0399889 | + | 0.999200i | \(0.512732\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 330.000 | 1.25701 | 0.628504 | − | 0.777806i | \(-0.283668\pi\) | ||||
0.628504 | + | 0.777806i | \(0.283668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −328.000 | −1.16324 | −0.581622 | − | 0.813459i | \(-0.697582\pi\) | ||||
−0.581622 | + | 0.813459i | \(0.697582\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −616.000 | −1.91176 | −0.955881 | − | 0.293753i | \(-0.905096\pi\) | ||||
−0.955881 | + | 0.293753i | \(0.905096\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 333.000 | 0.970845 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −324.000 | −0.839714 | −0.419857 | − | 0.907590i | \(-0.637920\pi\) | ||||
−0.419857 | + | 0.907590i | \(0.637920\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −104.000 | −0.254970 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −188.000 | −0.414839 | −0.207420 | − | 0.978252i | \(-0.566507\pi\) | ||||
−0.207420 | + | 0.978252i | \(0.566507\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −110.000 | −0.230886 | −0.115443 | − | 0.993314i | \(-0.536829\pi\) | ||||
−0.115443 | + | 0.993314i | \(0.536829\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −26.0000 | −0.0496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −118.000 | −0.215164 | −0.107582 | − | 0.994196i | \(-0.534311\pi\) | ||||
−0.107582 | + | 0.994196i | \(0.534311\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 656.000 | 1.09652 | 0.548260 | − | 0.836308i | \(-0.315291\pi\) | ||||
0.548260 | + | 0.836308i | \(0.315291\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −178.000 | −0.285388 | −0.142694 | − | 0.989767i | \(-0.545576\pi\) | ||||
−0.142694 | + | 0.989767i | \(0.545576\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1352.00 | −2.00097 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −836.000 | −1.19060 | −0.595300 | − | 0.803504i | \(-0.702967\pi\) | ||||
−0.595300 | + | 0.803504i | \(0.702967\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −60.0000 | −0.0793477 | −0.0396738 | − | 0.999213i | \(-0.512632\pi\) | ||||
−0.0396738 | + | 0.999213i | \(0.512632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 96.0000 | 0.122502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 870.000 | 1.03618 | 0.518089 | − | 0.855327i | \(-0.326644\pi\) | ||||
0.518089 | + | 0.855327i | \(0.326644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −338.000 | −0.389363 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.0000 | −0.0388792 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1238.00 | 1.29587 | 0.647937 | − | 0.761694i | \(-0.275632\pi\) | ||||
0.647937 | + | 0.761694i | \(0.275632\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −920.000 | −0.906371 | −0.453185 | − | 0.891416i | \(-0.649712\pi\) | ||||
−0.453185 | + | 0.891416i | \(0.649712\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 836.000 | 0.799743 | 0.399871 | − | 0.916571i | \(-0.369055\pi\) | ||||
0.399871 | + | 0.916571i | \(0.369055\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −260.000 | −0.234908 | −0.117454 | − | 0.993078i | \(-0.537473\pi\) | ||||
−0.117454 | + | 0.993078i | \(0.537473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2078.00 | −1.82602 | −0.913011 | − | 0.407936i | \(-0.866249\pi\) | ||||
−0.913011 | + | 0.407936i | \(0.866249\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1156.00 | −0.962366 | −0.481183 | − | 0.876620i | \(-0.659793\pi\) | ||||
−0.481183 | + | 0.876620i | \(0.659793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 104.000 | 0.0843309 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1248.00 | 0.961378 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1373.00 | 1.03156 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −492.000 | −0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 752.000 | 0.525427 | 0.262713 | − | 0.964874i | \(-0.415383\pi\) | ||||
0.262713 | + | 0.964874i | \(0.415383\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1972.00 | 1.31522 | 0.657612 | − | 0.753356i | \(-0.271566\pi\) | ||||
0.657612 | + | 0.753356i | \(0.271566\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −468.000 | −0.305118 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 258.000 | 0.160894 | 0.0804468 | − | 0.996759i | \(-0.474365\pi\) | ||||
0.0804468 | + | 0.996759i | \(0.474365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1468.00 | −0.895785 | −0.447893 | − | 0.894087i | \(-0.647825\pi\) | ||||
−0.447893 | + | 0.894087i | \(0.647825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 676.000 | 0.395314 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 448.000 | 0.256582 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3414.00 | 1.87709 | 0.938543 | − | 0.345163i | \(-0.112176\pi\) | ||||
0.938543 | + | 0.345163i | \(0.112176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2214.00 | 1.19320 | 0.596599 | − | 0.802540i | \(-0.296518\pi\) | ||||
0.596599 | + | 0.802540i | \(0.296518\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −620.000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2230.00 | −1.13359 | −0.566794 | − | 0.823859i | \(-0.691817\pi\) | ||||
−0.566794 | + | 0.823859i | \(0.691817\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1352.00 | 0.661817 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1118.00 | −0.537230 | −0.268615 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268615 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 288.000 | 0.133450 | 0.0667249 | − | 0.997771i | \(-0.478745\pi\) | ||||
0.0667249 | + | 0.997771i | \(0.478745\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −328.000 | −0.144147 | −0.0720733 | − | 0.997399i | \(-0.522962\pi\) | ||||
−0.0720733 | + | 0.997399i | \(0.522962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3146.00 | −1.35894 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2820.00 | −1.17752 | −0.588762 | − | 0.808307i | \(-0.700384\pi\) | ||||
−0.588762 | + | 0.808307i | \(0.700384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2250.00 | −0.923984 | −0.461992 | − | 0.886884i | \(-0.652865\pi\) | ||||
−0.461992 | + | 0.886884i | \(0.652865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −36.0000 | −0.0143069 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2496.00 | −0.976073 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3604.00 | −1.36532 | −0.682660 | − | 0.730736i | \(-0.739177\pi\) | ||||
−0.682660 | + | 0.730736i | \(0.739177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1198.00 | −0.446808 | −0.223404 | − | 0.974726i | \(-0.571717\pi\) | ||||
−0.223404 | + | 0.974726i | \(0.571717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1026.00 | 0.371063 | 0.185532 | − | 0.982638i | \(-0.440599\pi\) | ||||
0.185532 | + | 0.982638i | \(0.440599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2528.00 | −0.900528 | −0.450264 | − | 0.892895i | \(-0.648670\pi\) | ||||
−0.450264 | + | 0.892895i | \(0.648670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5824.00 | 2.01362 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 660.000 | 0.224860 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 936.000 | 0.309782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3160.00 | 1.03101 | 0.515506 | − | 0.856886i | \(-0.327604\pi\) | ||||
0.515506 | + | 0.856886i | \(0.327604\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −656.000 | −0.208088 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8060.00 | −2.52142 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −624.000 | −0.189931 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2670.00 | −0.801778 | −0.400889 | − | 0.916127i | \(-0.631299\pi\) | ||||
−0.400889 | + | 0.916127i | \(0.631299\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5220.00 | −1.52627 | −0.763136 | − | 0.646238i | \(-0.776341\pi\) | ||||
−0.763136 | + | 0.646238i | \(0.776341\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6246.00 | −1.80239 | −0.901195 | − | 0.433414i | \(-0.857309\pi\) | ||||
−0.901195 | + | 0.433414i | \(0.857309\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2860.00 | 0.804141 | 0.402070 | − | 0.915609i | \(-0.368291\pi\) | ||||
0.402070 | + | 0.915609i | \(0.368291\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1232.00 | −0.341986 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7176.00 | −1.94216 | −0.971081 | − | 0.238749i | \(-0.923263\pi\) | ||||
−0.971081 | + | 0.238749i | \(0.923263\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2922.00 | −0.781006 | −0.390503 | − | 0.920602i | \(-0.627699\pi\) | ||||
−0.390503 | + | 0.920602i | \(0.627699\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 666.000 | 0.173670 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 234.000 | 0.0602796 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1440.00 | 0.362119 | 0.181060 | − | 0.983472i | \(-0.442047\pi\) | ||||
0.181060 | + | 0.983472i | \(0.442047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2704.00 | −0.671933 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3852.00 | −0.934946 | −0.467473 | − | 0.884007i | \(-0.654836\pi\) | ||||
−0.467473 | + | 0.884007i | \(0.654836\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −468.000 | −0.112278 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7008.00 | −1.64309 | −0.821543 | − | 0.570146i | \(-0.806887\pi\) | ||||
−0.821543 | + | 0.570146i | \(0.806887\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −648.000 | −0.150213 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1992.00 | −0.451503 | −0.225752 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225752 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3362.00 | 0.753605 | 0.376803 | − | 0.926294i | \(-0.377024\pi\) | ||||
0.376803 | + | 0.926294i | \(0.377024\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6292.00 | 1.37972 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1506.00 | 0.326667 | 0.163334 | − | 0.986571i | \(-0.447775\pi\) | ||||
0.163334 | + | 0.986571i | \(0.447775\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3638.00 | −0.772331 | −0.386165 | − | 0.922430i | \(-0.626201\pi\) | ||||
−0.386165 | + | 0.922430i | \(0.626201\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5404.00 | −1.13510 | −0.567552 | − | 0.823338i | \(-0.692109\pi\) | ||||
−0.567552 | + | 0.823338i | \(0.692109\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8580.00 | 1.76467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2609.00 | −0.531040 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4994.00 | −0.995743 | −0.497871 | − | 0.867251i | \(-0.665885\pi\) | ||||
−0.497871 | + | 0.867251i | \(0.665885\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −376.000 | −0.0742087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −676.000 | −0.130749 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8528.00 | −1.63304 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −220.000 | −0.0413022 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2474.00 | −0.459930 | −0.229965 | − | 0.973199i | \(-0.573861\pi\) | ||||
−0.229965 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9156.00 | 1.66942 | 0.834709 | − | 0.550691i | \(-0.185636\pi\) | ||||
0.834709 | + | 0.550691i | \(0.185636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3818.00 | 0.689476 | 0.344738 | − | 0.938699i | \(-0.387968\pi\) | ||||
0.344738 | + | 0.938699i | \(0.387968\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6234.00 | 1.10453 | 0.552265 | − | 0.833668i | \(-0.313763\pi\) | ||||
0.552265 | + | 0.833668i | \(0.313763\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11648.0 | −2.04440 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −864.000 | −0.148837 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1573.00 | 0.268475 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16016.0 | −2.68386 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5054.00 | −0.839254 | −0.419627 | − | 0.907697i | \(-0.637839\pi\) | ||||
−0.419627 | + | 0.907697i | \(0.637839\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −236.000 | −0.0384897 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10238.0 | 1.65489 | 0.827447 | − | 0.561544i | \(-0.189792\pi\) | ||||
0.827447 | + | 0.561544i | \(0.189792\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16120.0 | 2.55996 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −260.000 | −0.0409291 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2184.00 | 0.337877 | 0.168938 | − | 0.985627i | \(-0.445966\pi\) | ||||
0.168938 | + | 0.985627i | \(0.445966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6766.00 | 1.03775 | 0.518876 | − | 0.854849i | \(-0.326351\pi\) | ||||
0.518876 | + | 0.854849i | \(0.326351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8290.00 | 1.24995 | 0.624975 | − | 0.780645i | \(-0.285109\pi\) | ||||
0.624975 | + | 0.780645i | \(0.285109\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1312.00 | 0.196151 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9456.00 | 1.39016 | 0.695082 | − | 0.718931i | \(-0.255368\pi\) | ||||
0.695082 | + | 0.718931i | \(0.255368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6535.00 | −0.952763 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −356.000 | −0.0510518 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10096.0 | 1.43599 | 0.717993 | − | 0.696050i | \(-0.245061\pi\) | ||||
0.717993 | + | 0.696050i | \(0.245061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8424.00 | −1.17885 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1234.00 | −0.171298 | −0.0856489 | − | 0.996325i | \(-0.527296\pi\) | ||||
−0.0856489 | + | 0.996325i | \(0.527296\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2912.00 | −0.397813 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11218.0 | −1.52040 | −0.760198 | − | 0.649692i | \(-0.774898\pi\) | ||||
−0.760198 | + | 0.649692i | \(0.774898\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7488.00 | 0.999005 | 0.499503 | − | 0.866312i | \(-0.333516\pi\) | ||||
0.499503 | + | 0.866312i | \(0.333516\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2704.00 | −0.357944 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14364.0 | −1.87219 | −0.936097 | − | 0.351741i | \(-0.885590\pi\) | ||||
−0.936097 | + | 0.351741i | \(0.885590\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2496.00 | 0.322834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1672.00 | −0.212981 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7454.00 | 0.942331 | 0.471166 | − | 0.882045i | \(-0.343833\pi\) | ||||
0.471166 | + | 0.882045i | \(0.343833\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5766.00 | 0.718056 | 0.359028 | − | 0.933327i | \(-0.383108\pi\) | ||||
0.359028 | + | 0.933327i | \(0.383108\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4030.00 | 0.498135 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 936.000 | 0.113995 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11926.0 | 1.44182 | 0.720908 | − | 0.693031i | \(-0.243725\pi\) | ||||
0.720908 | + | 0.693031i | \(0.243725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4888.00 | −0.582380 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −120.000 | −0.0141941 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9996.00 | −1.16548 | −0.582741 | − | 0.812658i | \(-0.698020\pi\) | ||||
−0.582741 | + | 0.812658i | \(0.698020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2030.00 | −0.235003 | −0.117501 | − | 0.993073i | \(-0.537488\pi\) | ||||
−0.117501 | + | 0.993073i | \(0.537488\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5808.00 | −0.662893 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2860.00 | −0.324134 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15888.0 | −1.77563 | −0.887817 | − | 0.460197i | \(-0.847779\pi\) | ||||
−0.887817 | + | 0.460197i | \(0.847779\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14402.0 | −1.59842 | −0.799210 | − | 0.601052i | \(-0.794749\pi\) | ||||
−0.799210 | + | 0.601052i | \(0.794749\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −936.000 | −0.102460 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −404.000 | −0.0439223 | −0.0219611 | − | 0.999759i | \(-0.506991\pi\) | ||||
−0.0219611 | + | 0.999759i | \(0.506991\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16692.0 | 1.79021 | 0.895103 | − | 0.445860i | \(-0.147102\pi\) | ||||
0.895103 | + | 0.445860i | \(0.147102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1740.00 | 0.185357 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4058.00 | −0.426523 | −0.213262 | − | 0.976995i | \(-0.568409\pi\) | ||||
−0.213262 | + | 0.976995i | \(0.568409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17160.0 | −1.79165 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −676.000 | −0.0696514 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14642.0 | −1.49874 | −0.749370 | − | 0.662152i | \(-0.769643\pi\) | ||||
−0.749370 | + | 0.662152i | \(0.769643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17970.0 | 1.81550 | 0.907751 | − | 0.419510i | \(-0.137798\pi\) | ||||
0.907751 | + | 0.419510i | \(0.137798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6242.00 | 0.626545 | 0.313273 | − | 0.949663i | \(-0.398575\pi\) | ||||
0.313273 | + | 0.949663i | \(0.398575\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5000.00 | −0.495444 | −0.247722 | − | 0.968831i | \(-0.579682\pi\) | ||||
−0.247722 | + | 0.968831i | \(0.579682\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3068.00 | −0.302062 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17056.0 | 1.65800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2178.00 | 0.210386 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9408.00 | −0.897416 | −0.448708 | − | 0.893678i | \(-0.648116\pi\) | ||||
−0.448708 | + | 0.893678i | \(0.648116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 234.000 | 0.0221819 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2476.00 | 0.231813 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7090.00 | 0.659710 | 0.329855 | − | 0.944032i | \(-0.393000\pi\) | ||||
0.329855 | + | 0.944032i | \(0.393000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8176.00 | −0.751482 | −0.375741 | − | 0.926725i | \(-0.622612\pi\) | ||||
−0.375741 | + | 0.926725i | \(0.622612\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10752.0 | 0.982243 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17056.0 | 1.53937 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9646.00 | −0.865359 | −0.432680 | − | 0.901548i | \(-0.642432\pi\) | ||||
−0.432680 | + | 0.901548i | \(0.642432\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4352.00 | 0.385778 | 0.192889 | − | 0.981221i | \(-0.438214\pi\) | ||||
0.192889 | + | 0.981221i | \(0.438214\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1840.00 | −0.162136 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14582.0 | −1.26981 | −0.634907 | − | 0.772588i | \(-0.718962\pi\) | ||||
−0.634907 | + | 0.772588i | \(0.718962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4628.00 | −0.400647 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1672.00 | 0.143062 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32032.0 | 2.72489 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11820.0 | −0.993942 | −0.496971 | − | 0.867767i | \(-0.665554\pi\) | ||||
−0.496971 | + | 0.867767i | \(0.665554\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2676.00 | −0.223735 | −0.111867 | − | 0.993723i | \(-0.535683\pi\) | ||||
−0.111867 | + | 0.993723i | \(0.535683\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14880.0 | −1.22995 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9463.00 | −0.777760 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4290.00 | −0.348631 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −520.000 | −0.0420216 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17316.0 | −1.38377 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 842.000 | 0.0669139 | 0.0334569 | − | 0.999440i | \(-0.489348\pi\) | ||||
0.0334569 | + | 0.999440i | \(0.489348\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4156.00 | −0.326649 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1036.00 | −0.0809802 | −0.0404901 | − | 0.999180i | \(-0.512892\pi\) | ||||
−0.0404901 | + | 0.999180i | \(0.512892\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4032.00 | −0.311740 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21736.0 | −1.67144 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3342.00 | 0.254228 | 0.127114 | − | 0.991888i | \(-0.459429\pi\) | ||||
0.127114 | + | 0.991888i | \(0.459429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4264.00 | 0.322626 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12412.0 | 0.929136 | 0.464568 | − | 0.885538i | \(-0.346210\pi\) | ||||
0.464568 | + | 0.885538i | \(0.346210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2312.00 | −0.172153 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21556.0 | 1.58818 | 0.794090 | − | 0.607800i | \(-0.207948\pi\) | ||||
0.794090 | + | 0.607800i | \(0.207948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9012.00 | −0.660491 | −0.330246 | − | 0.943895i | \(-0.607132\pi\) | ||||
−0.330246 | + | 0.943895i | \(0.607132\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6292.00 | −0.456338 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10446.0 | −0.753679 | −0.376839 | − | 0.926279i | \(-0.622989\pi\) | ||||
−0.376839 | + | 0.926279i | \(0.622989\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1560.00 | −0.111394 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16848.0 | 1.19687 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23452.0 | 1.64901 | 0.824504 | − | 0.565856i | \(-0.191454\pi\) | ||||
0.824504 | + | 0.565856i | \(0.191454\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5580.00 | 0.390356 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23914.0 | −1.65604 | −0.828019 | − | 0.560700i | \(-0.810532\pi\) | ||||
−0.828019 | + | 0.560700i | \(0.810532\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2496.00 | 0.171977 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2552.00 | 0.174077 | 0.0870383 | − | 0.996205i | \(-0.472260\pi\) | ||||
0.0870383 | + | 0.996205i | \(0.472260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3418.00 | 0.231985 | 0.115993 | − | 0.993250i | \(-0.462995\pi\) | ||||
0.115993 | + | 0.993250i | \(0.462995\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2746.00 | 0.184530 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12336.0 | −0.824881 | −0.412441 | − | 0.910985i | \(-0.635324\pi\) | ||||
−0.412441 | + | 0.910985i | \(0.635324\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8008.00 | 0.530228 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21946.0 | −1.44599 | −0.722994 | − | 0.690854i | \(-0.757235\pi\) | ||||
−0.722994 | + | 0.690854i | \(0.757235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23890.0 | 1.55879 | 0.779396 | − | 0.626531i | \(-0.215526\pi\) | ||||
0.779396 | + | 0.626531i | \(0.215526\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10042.0 | −0.652055 | −0.326028 | − | 0.945360i | \(-0.605710\pi\) | ||||
−0.326028 | + | 0.945360i | \(0.605710\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22620.0 | 1.45466 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14141.0 | 0.905024 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −864.000 | −0.0547694 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21830.0 | 1.37724 | 0.688620 | − | 0.725122i | \(-0.258217\pi\) | ||||
0.688620 | + | 0.725122i | \(0.258217\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1504.00 | 0.0939912 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4329.00 | −0.269264 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −776.000 | −0.0478162 | −0.0239081 | − | 0.999714i | \(-0.507611\pi\) | ||||
−0.0239081 | + | 0.999714i | \(0.507611\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4094.00 | −0.251091 | −0.125546 | − | 0.992088i | \(-0.540068\pi\) | ||||
−0.125546 | + | 0.992088i | \(0.540068\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13064.0 | 0.793816 | 0.396908 | − | 0.917858i | \(-0.370083\pi\) | ||||
0.396908 | + | 0.917858i | \(0.370083\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9776.00 | 0.591281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24504.0 | −1.46848 | −0.734239 | − | 0.678891i | \(-0.762461\pi\) | ||||
−0.734239 | + | 0.678891i | \(0.762461\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3944.00 | 0.235275 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4752.00 | −0.280898 | −0.140449 | − | 0.990088i | \(-0.544855\pi\) | ||||
−0.140449 | + | 0.990088i | \(0.544855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9514.00 | −0.559836 | −0.279918 | − | 0.960024i | \(-0.590307\pi\) | ||||
−0.279918 | + | 0.960024i | \(0.590307\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −936.000 | −0.0545812 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11648.0 | 0.676180 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5720.00 | 0.329088 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8374.00 | 0.479634 | 0.239817 | − | 0.970818i | \(-0.422912\pi\) | ||||
0.239817 | + | 0.970818i | \(0.422912\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14556.0 | −0.826341 | −0.413170 | − | 0.910654i | \(-0.635579\pi\) | ||||
−0.413170 | + | 0.910654i | \(0.635579\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32188.0 | 1.81924 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23276.0 | 1.30400 | 0.652000 | − | 0.758219i | \(-0.273930\pi\) | ||||
0.652000 | + | 0.758219i | \(0.273930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 516.000 | 0.0287815 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4212.00 | 0.232895 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29522.0 | 1.62528 | 0.812641 | − | 0.582765i | \(-0.198029\pi\) | ||||
0.812641 | + | 0.582765i | \(0.198029\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2936.00 | −0.160243 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15840.0 | 0.860807 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27252.0 | 1.46832 | 0.734161 | − | 0.678975i | \(-0.237576\pi\) | ||||
0.734161 | + | 0.678975i | \(0.237576\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 324.000 | 0.0173825 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23920.0 | −1.27242 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2162.00 | 0.114521 | 0.0572607 | − | 0.998359i | \(-0.481763\pi\) | ||||
0.0572607 | + | 0.998359i | \(0.481763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16120.0 | −0.846702 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1352.00 | 0.0707160 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8044.00 | 0.417233 | 0.208617 | − | 0.977998i | \(-0.433104\pi\) | ||||
0.208617 | + | 0.977998i | \(0.433104\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21736.0 | 1.12273 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −27104.0 | −1.38844 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22496.0 | 1.14763 | 0.573817 | − | 0.818983i | \(-0.305462\pi\) | ||||
0.573817 | + | 0.818983i | \(0.305462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15744.0 | −0.796598 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15934.0 | −0.802914 | −0.401457 | − | 0.915878i | \(-0.631496\pi\) | ||||
−0.401457 | + | 0.915878i | \(0.631496\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6136.00 | 0.306679 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29838.0 | 1.48526 | 0.742631 | − | 0.669701i | \(-0.233578\pi\) | ||||
0.742631 | + | 0.669701i | \(0.233578\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10760.0 | 0.531287 | 0.265643 | − | 0.964071i | \(-0.414416\pi\) | ||||
0.265643 | + | 0.964071i | \(0.414416\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6828.00 | 0.335783 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6760.00 | −0.329780 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14916.0 | 0.724757 | 0.362379 | − | 0.932031i | \(-0.381965\pi\) | ||||
0.362379 | + | 0.932031i | \(0.381965\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4428.00 | 0.213446 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29046.0 | 1.39458 | 0.697289 | − | 0.716791i | \(-0.254390\pi\) | ||||
0.697289 | + | 0.716791i | \(0.254390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2766.00 | −0.131757 | −0.0658787 | − | 0.997828i | \(-0.520985\pi\) | ||||
−0.0658787 | + | 0.997828i | \(0.520985\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −54028.0 | −2.56349 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2444.00 | 0.115056 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5394.00 | 0.252942 | 0.126471 | − | 0.991970i | \(-0.459635\pi\) | ||||
0.126471 | + | 0.991970i | \(0.459635\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19378.0 | −0.901654 | −0.450827 | − | 0.892611i | \(-0.648871\pi\) | ||||
−0.450827 | + | 0.892611i | \(0.648871\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37510.0 | 1.73858 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5940.00 | −0.273200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34112.0 | −1.56290 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4460.00 | −0.202782 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8350.00 | 0.378202 | 0.189101 | − | 0.981958i | \(-0.439443\pi\) | ||||
0.189101 | + | 0.981958i | \(0.439443\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30056.0 | −1.35103 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1430.00 | 0.0640363 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22116.0 | 0.982922 | 0.491461 | − | 0.870900i | \(-0.336463\pi\) | ||||
0.491461 | + | 0.870900i | \(0.336463\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29568.0 | −1.30919 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9256.00 | 0.406771 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2704.00 | 0.118389 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6444.00 | 0.280048 | 0.140024 | − | 0.990148i | \(-0.455282\pi\) | ||||
0.140024 | + | 0.990148i | \(0.455282\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8998.00 | 0.389596 | 0.194798 | − | 0.980843i | \(-0.437595\pi\) | ||||
0.194798 | + | 0.980843i | \(0.437595\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2236.00 | −0.0961027 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5904.00 | 0.252821 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11938.0 | −0.507478 | −0.253739 | − | 0.967273i | \(-0.581660\pi\) | ||||
−0.253739 | + | 0.967273i | \(0.581660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41028.0 | 1.73772 | 0.868862 | − | 0.495055i | \(-0.164852\pi\) | ||||
0.868862 | + | 0.495055i | \(0.164852\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20460.0 | −0.860295 | −0.430147 | − | 0.902759i | \(-0.641538\pi\) | ||||
−0.430147 | + | 0.902759i | \(0.641538\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27814.0 | 1.16528 | 0.582642 | − | 0.812729i | \(-0.302019\pi\) | ||||
0.582642 | + | 0.812729i | \(0.302019\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15984.0 | 0.664841 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 576.000 | 0.0238722 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24880.0 | 1.02378 | 0.511891 | − | 0.859050i | \(-0.328945\pi\) | ||||
0.511891 | + | 0.859050i | \(0.328945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25787.0 | 1.05732 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 338.000 | 0.0137604 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 35698.0 | 1.44817 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −936.000 | −0.0377035 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37678.0 | 1.51239 | 0.756196 | − | 0.654345i | \(-0.227056\pi\) | ||||
0.756196 | + | 0.654345i | \(0.227056\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14708.0 | −0.586249 | −0.293125 | − | 0.956074i | \(-0.594695\pi\) | ||||
−0.293125 | + | 0.956074i | \(0.594695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16472.0 | −0.654269 | −0.327135 | − | 0.944978i | \(-0.606083\pi\) | ||||
−0.327135 | + | 0.944978i | \(0.606083\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13640.0 | 0.538020 | 0.269010 | − | 0.963137i | \(-0.413304\pi\) | ||||
0.269010 | + | 0.963137i | \(0.413304\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −656.000 | −0.0257857 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43472.0 | 1.69699 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1534.00 | 0.0596758 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12792.0 | −0.494227 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44430.0 | 1.71071 | 0.855356 | − | 0.518041i | \(-0.173338\pi\) | ||||
0.855356 | + | 0.518041i | \(0.173338\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6684.00 | 0.255607 | 0.127803 | − | 0.991800i | \(-0.459207\pi\) | ||||
0.127803 | + | 0.991800i | \(0.459207\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9196.00 | −0.350476 | −0.175238 | − | 0.984526i | \(-0.556069\pi\) | ||||
−0.175238 | + | 0.984526i | \(0.556069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34852.0 | −1.31930 | −0.659648 | − | 0.751575i | \(-0.729295\pi\) | ||||
−0.659648 | + | 0.751575i | \(0.729295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19552.0 | 0.737630 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11088.0 | 0.415505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5640.00 | −0.210642 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −69440.0 | −2.57614 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15552.0 | −0.575041 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4500.00 | −0.165287 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36780.0 | −1.34648 | −0.673241 | − | 0.739423i | \(-0.735099\pi\) | ||||
−0.673241 | + | 0.739423i | \(0.735099\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22980.0 | −0.835742 | −0.417871 | − | 0.908506i | \(-0.637224\pi\) | ||||
−0.417871 | + | 0.908506i | \(0.637224\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3120.00 | 0.113096 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 51272.0 | 1.84640 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19980.0 | 0.717170 | 0.358585 | − | 0.933497i | \(-0.383259\pi\) | ||||
0.358585 | + | 0.933497i | \(0.383259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8528.00 | −0.304120 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2178.00 | 0.0774186 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51486.0 | −1.81830 | −0.909150 | − | 0.416469i | \(-0.863268\pi\) | ||||
−0.909150 | + | 0.416469i | \(0.863268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5994.00 | −0.211005 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4992.00 | −0.174605 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21774.0 | 0.759152 | 0.379576 | − | 0.925161i | \(-0.376070\pi\) | ||||
0.379576 | + | 0.925161i | \(0.376070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29158.0 | 1.01012 | 0.505060 | − | 0.863084i | \(-0.331470\pi\) | ||||
0.505060 | + | 0.863084i | \(0.331470\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17160.0 | 0.592584 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47844.0 | 1.64173 | 0.820866 | − | 0.571120i | \(-0.193491\pi\) | ||||
0.820866 | + | 0.571120i | \(0.193491\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2314.00 | 0.0791524 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20716.0 | −0.704152 | −0.352076 | − | 0.935971i | \(-0.614524\pi\) | ||||
−0.352076 | + | 0.935971i | \(0.614524\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7208.00 | −0.244236 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6708.00 | 0.225873 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 66309.0 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2396.00 | −0.0799274 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1406.00 | −0.0467569 | −0.0233784 | − | 0.999727i | \(-0.507442\pi\) | ||||
−0.0233784 | + | 0.999727i | \(0.507442\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40176.0 | 1.32782 | 0.663908 | − | 0.747814i | \(-0.268897\pi\) | ||||
0.663908 | + | 0.747814i | \(0.268897\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −38168.0 | −1.25756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20910.0 | 0.684719 | 0.342359 | − | 0.939569i | \(-0.388774\pi\) | ||||
0.342359 | + | 0.939569i | \(0.388774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45240.0 | −1.47689 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26288.0 | −0.852957 | −0.426479 | − | 0.904498i | \(-0.640246\pi\) | ||||
−0.426479 | + | 0.904498i | \(0.640246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2052.00 | 0.0663778 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17056.0 | −0.548381 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25608.0 | 0.820853 | 0.410426 | − | 0.911894i | \(-0.365380\pi\) | ||||
0.410426 | + | 0.911894i | \(0.365380\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5056.00 | −0.161091 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20098.0 | −0.638425 | −0.319213 | − | 0.947683i | \(-0.603418\pi\) | ||||
−0.319213 | + | 0.947683i | \(0.603418\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1872.4.a.h.1.1 | 1 | ||
3.2 | odd | 2 | 1872.4.a.g.1.1 | 1 | |||
4.3 | odd | 2 | 234.4.a.d.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 234.4.a.i.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
234.4.a.d.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
234.4.a.i.1.1 | yes | 1 | 12.11 | even | 2 | ||
1872.4.a.g.1.1 | 1 | 3.2 | odd | 2 | |||
1872.4.a.h.1.1 | 1 | 1.1 | even | 1 | trivial |