Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(1,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, 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("1344.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 168) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1344.1 |
$q$-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 | ||||||||
\(5\) | 10.0000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.0000 | −0.640039 | −0.320019 | − | 0.947411i | \(-0.603689\pi\) | ||||
−0.320019 | + | 0.947411i | \(0.603689\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 30.0000 | 0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 34.0000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −148.000 | −1.78703 | −0.893514 | − | 0.449036i | \(-0.851768\pi\) | ||||
−0.893514 | + | 0.449036i | \(0.851768\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 152.000 | 1.37801 | 0.689004 | − | 0.724757i | \(-0.258048\pi\) | ||||
0.689004 | + | 0.724757i | \(0.258048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 106.000 | 0.678748 | 0.339374 | − | 0.940651i | \(-0.389785\pi\) | ||||
0.339374 | + | 0.940651i | \(0.389785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 304.000 | 1.76129 | 0.880645 | − | 0.473776i | \(-0.157109\pi\) | ||||
0.880645 | + | 0.473776i | \(0.157109\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 36.0000 | 0.189903 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 70.0000 | 0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 114.000 | 0.506527 | 0.253263 | − | 0.967397i | \(-0.418496\pi\) | ||||
0.253263 | + | 0.967397i | \(0.418496\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −90.0000 | −0.369527 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 202.000 | 0.769441 | 0.384721 | − | 0.923033i | \(-0.374298\pi\) | ||||
0.384721 | + | 0.923033i | \(0.374298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −116.000 | −0.411391 | −0.205696 | − | 0.978616i | \(-0.565946\pi\) | ||||
−0.205696 | + | 0.978616i | \(0.565946\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 90.0000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 224.000 | 0.695186 | 0.347593 | − | 0.937645i | \(-0.386999\pi\) | ||||
0.347593 | + | 0.937645i | \(0.386999\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 102.000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 274.000 | 0.710128 | 0.355064 | − | 0.934842i | \(-0.384459\pi\) | ||||
0.355064 | + | 0.934842i | \(0.384459\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 120.000 | 0.294196 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −444.000 | −1.03174 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 660.000 | 1.45635 | 0.728175 | − | 0.685391i | \(-0.240369\pi\) | ||||
0.728175 | + | 0.685391i | \(0.240369\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −382.000 | −0.801805 | −0.400902 | − | 0.916121i | \(-0.631303\pi\) | ||||
−0.400902 | + | 0.916121i | \(0.631303\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −300.000 | −0.572468 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0000 | −0.0218811 | −0.0109405 | − | 0.999940i | \(-0.503483\pi\) | ||||
−0.0109405 | + | 0.999940i | \(0.503483\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 456.000 | 0.795593 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −552.000 | −0.922681 | −0.461340 | − | 0.887223i | \(-0.652631\pi\) | ||||
−0.461340 | + | 0.887223i | \(0.652631\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −614.000 | −0.984428 | −0.492214 | − | 0.870474i | \(-0.663812\pi\) | ||||
−0.492214 | + | 0.870474i | \(0.663812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 84.0000 | 0.124321 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 880.000 | 1.25326 | 0.626631 | − | 0.779316i | \(-0.284433\pi\) | ||||
0.626631 | + | 0.779316i | \(0.284433\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 108.000 | 0.142826 | 0.0714129 | − | 0.997447i | \(-0.477249\pi\) | ||||
0.0714129 | + | 0.997447i | \(0.477249\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 340.000 | 0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 318.000 | 0.391876 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −86.0000 | −0.102427 | −0.0512134 | − | 0.998688i | \(-0.516309\pi\) | ||||
−0.0512134 | + | 0.998688i | \(0.516309\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −210.000 | −0.241912 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 912.000 | 1.01688 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1480.00 | −1.59837 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1426.00 | 1.49266 | 0.746332 | − | 0.665574i | \(-0.231813\pi\) | ||||
0.746332 | + | 0.665574i | \(0.231813\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 108.000 | 0.109640 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 810.000 | 0.798000 | 0.399000 | − | 0.916951i | \(-0.369357\pi\) | ||||
0.399000 | + | 0.916951i | \(0.369357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1032.00 | 0.987243 | 0.493621 | − | 0.869677i | \(-0.335673\pi\) | ||||
0.493621 | + | 0.869677i | \(0.335673\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 210.000 | 0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −900.000 | −0.813143 | −0.406571 | − | 0.913619i | \(-0.633276\pi\) | ||||
−0.406571 | + | 0.913619i | \(0.633276\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −454.000 | −0.398948 | −0.199474 | − | 0.979903i | \(-0.563923\pi\) | ||||
−0.199474 | + | 0.979903i | \(0.563923\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 342.000 | 0.292443 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 0.0149849 | 0.00749247 | − | 0.999972i | \(-0.497615\pi\) | ||||
0.00749247 | + | 0.999972i | \(0.497615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1520.00 | 1.23253 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −270.000 | −0.213346 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 238.000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 606.000 | 0.444237 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1500.00 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1072.00 | −0.749013 | −0.374506 | − | 0.927224i | \(-0.622188\pi\) | ||||
−0.374506 | + | 0.927224i | \(0.622188\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −348.000 | −0.237517 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1084.00 | 0.722973 | 0.361487 | − | 0.932377i | \(-0.382269\pi\) | ||||
0.361487 | + | 0.932377i | \(0.382269\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1036.00 | −0.675433 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 270.000 | 0.172133 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2426.00 | 1.51290 | 0.756450 | − | 0.654052i | \(-0.226932\pi\) | ||||
0.756450 | + | 0.654052i | \(0.226932\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −684.000 | −0.417382 | −0.208691 | − | 0.977982i | \(-0.566920\pi\) | ||||
−0.208691 | + | 0.977982i | \(0.566920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 672.000 | 0.401366 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −360.000 | −0.210522 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1060.00 | 0.607091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3598.00 | −1.97825 | −0.989126 | − | 0.147068i | \(-0.953016\pi\) | ||||
−0.989126 | + | 0.147068i | \(0.953016\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2680.00 | 1.44434 | 0.722170 | − | 0.691716i | \(-0.243145\pi\) | ||||
0.722170 | + | 0.691716i | \(0.243145\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 306.000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3040.00 | 1.57535 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1422.00 | −0.722853 | −0.361427 | − | 0.932401i | \(-0.617710\pi\) | ||||
−0.361427 | + | 0.932401i | \(0.617710\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 822.000 | 0.409993 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1064.00 | 0.520838 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −220.000 | −0.105716 | −0.0528581 | − | 0.998602i | \(-0.516833\pi\) | ||||
−0.0528581 | + | 0.998602i | \(0.516833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 360.000 | 0.169854 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1992.00 | 0.923027 | 0.461514 | − | 0.887133i | \(-0.347307\pi\) | ||||
0.461514 | + | 0.887133i | \(0.347307\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1297.00 | −0.590350 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1332.00 | −0.595676 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4286.00 | −1.88358 | −0.941788 | − | 0.336208i | \(-0.890855\pi\) | ||||
−0.941788 | + | 0.336208i | \(0.890855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −175.000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1980.00 | 0.840824 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4516.00 | 1.88571 | 0.942854 | − | 0.333206i | \(-0.108131\pi\) | ||||
0.942854 | + | 0.333206i | \(0.108131\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2218.00 | 0.910843 | 0.455422 | − | 0.890276i | \(-0.349489\pi\) | ||||
0.455422 | + | 0.890276i | \(0.349489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1146.00 | −0.462922 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1140.00 | 0.453051 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 408.000 | 0.159550 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3136.00 | 1.18803 | 0.594013 | − | 0.804455i | \(-0.297543\pi\) | ||||
0.594013 | + | 0.804455i | \(0.297543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3198.00 | −1.19273 | −0.596365 | − | 0.802713i | \(-0.703389\pi\) | ||||
−0.596365 | + | 0.802713i | \(0.703389\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −900.000 | −0.330515 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3714.00 | 1.34321 | 0.671603 | − | 0.740911i | \(-0.265606\pi\) | ||||
0.671603 | + | 0.740911i | \(0.265606\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3256.00 | −1.15986 | −0.579929 | − | 0.814667i | \(-0.696920\pi\) | ||||
−0.579929 | + | 0.814667i | \(0.696920\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −36.0000 | −0.0126331 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 742.000 | 0.256543 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2020.00 | 0.688209 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1368.00 | 0.459336 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1776.00 | −0.587792 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4612.00 | 1.50475 | 0.752377 | − | 0.658733i | \(-0.228907\pi\) | ||||
0.752377 | + | 0.658733i | \(0.228907\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1656.00 | −0.532710 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1160.00 | −0.367960 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2128.00 | 0.665705 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1842.00 | −0.568360 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1020.00 | −0.310464 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2976.00 | 0.893667 | 0.446833 | − | 0.894617i | \(-0.352552\pi\) | ||||
0.446833 | + | 0.894617i | \(0.352552\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −225.000 | −0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1084.00 | 0.316950 | 0.158475 | − | 0.987363i | \(-0.449342\pi\) | ||||
0.158475 | + | 0.987363i | \(0.449342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2746.00 | 0.792405 | 0.396203 | − | 0.918163i | \(-0.370328\pi\) | ||||
0.396203 | + | 0.918163i | \(0.370328\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 252.000 | 0.0717765 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5062.00 | −1.42327 | −0.711637 | − | 0.702548i | \(-0.752046\pi\) | ||||
−0.711637 | + | 0.702548i | \(0.752046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2240.00 | 0.621794 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2640.00 | 0.723571 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 320.000 | 0.0866070 | 0.0433035 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433035 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6974.00 | −1.86404 | −0.932022 | − | 0.362400i | \(-0.881957\pi\) | ||||
−0.932022 | + | 0.362400i | \(0.881957\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 490.000 | 0.127775 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4440.00 | 1.14377 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 324.000 | 0.0824605 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 356.000 | 0.0895240 | 0.0447620 | − | 0.998998i | \(-0.485747\pi\) | ||||
0.0447620 | + | 0.998998i | \(0.485747\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1824.00 | 0.453257 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1020.00 | 0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4770.00 | 1.15776 | 0.578880 | − | 0.815413i | \(-0.303490\pi\) | ||||
0.578880 | + | 0.815413i | \(0.303490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 798.000 | 0.191449 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 954.000 | 0.226249 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2712.00 | 0.635852 | 0.317926 | − | 0.948116i | \(-0.397014\pi\) | ||||
0.317926 | + | 0.948116i | \(0.397014\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2740.00 | 0.635158 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −258.000 | −0.0591361 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6942.00 | −1.57346 | −0.786731 | − | 0.617296i | \(-0.788228\pi\) | ||||
−0.786731 | + | 0.617296i | \(0.788228\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4720.00 | −1.05801 | −0.529003 | − | 0.848620i | \(-0.677434\pi\) | ||||
−0.529003 | + | 0.848620i | \(0.677434\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −630.000 | −0.139668 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −300.000 | −0.0657843 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1490.00 | 0.323196 | 0.161598 | − | 0.986857i | \(-0.448335\pi\) | ||||
0.161598 | + | 0.986857i | \(0.448335\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2736.00 | 0.587097 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7926.00 | −1.68265 | −0.841327 | − | 0.540527i | \(-0.818225\pi\) | ||||
−0.841327 | + | 0.540527i | \(0.818225\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8596.00 | 1.80558 | 0.902790 | − | 0.430082i | \(-0.141515\pi\) | ||||
0.902790 | + | 0.430082i | \(0.141515\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4440.00 | −0.922817 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1414.00 | 0.290822 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3757.00 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4278.00 | 0.861790 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −438.000 | −0.0873319 | −0.0436659 | − | 0.999046i | \(-0.513904\pi\) | ||||
−0.0436659 | + | 0.999046i | \(0.513904\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6600.00 | 1.30260 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 324.000 | 0.0633010 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4560.00 | −0.881979 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −812.000 | −0.155491 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2430.00 | 0.460726 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3820.00 | −0.717156 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5140.00 | −0.955555 | −0.477777 | − | 0.878481i | \(-0.658557\pi\) | ||||
−0.477777 | + | 0.878481i | \(0.658557\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3096.00 | 0.569985 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4296.00 | 0.783292 | 0.391646 | − | 0.920116i | \(-0.371906\pi\) | ||||
0.391646 | + | 0.920116i | \(0.371906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2714.00 | 0.490110 | 0.245055 | − | 0.969509i | \(-0.421194\pi\) | ||||
0.245055 | + | 0.969509i | \(0.421194\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 630.000 | 0.112687 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4314.00 | 0.764348 | 0.382174 | − | 0.924090i | \(-0.375175\pi\) | ||||
0.382174 | + | 0.924090i | \(0.375175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1272.00 | 0.223255 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2700.00 | −0.469468 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5032.00 | −0.866836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 750.000 | 0.128008 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1362.00 | −0.230333 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1568.00 | 0.262756 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2284.00 | 0.379275 | 0.189637 | − | 0.981854i | \(-0.439269\pi\) | ||||
0.189637 | + | 0.981854i | \(0.439269\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1026.00 | 0.168842 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −120.000 | −0.0195710 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9650.00 | 1.55985 | 0.779924 | − | 0.625874i | \(-0.215258\pi\) | ||||
0.779924 | + | 0.625874i | \(0.215258\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 54.0000 | 0.00865156 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3648.00 | 0.579326 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4560.00 | 0.711600 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4068.00 | −0.629342 | −0.314671 | − | 0.949201i | \(-0.601894\pi\) | ||||
−0.314671 | + | 0.949201i | \(0.601894\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3922.00 | 0.601547 | 0.300773 | − | 0.953696i | \(-0.402755\pi\) | ||||
0.300773 | + | 0.953696i | \(0.402755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −810.000 | −0.123176 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −414.000 | −0.0624221 | −0.0312110 | − | 0.999513i | \(-0.509936\pi\) | ||||
−0.0312110 | + | 0.999513i | \(0.509936\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5520.00 | −0.825271 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 714.000 | 0.105851 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5160.00 | 0.758592 | 0.379296 | − | 0.925275i | \(-0.376166\pi\) | ||||
0.379296 | + | 0.925275i | \(0.376166\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15045.0 | 2.19347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3561.00 | −0.514887 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6140.00 | −0.880499 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11056.0 | −1.57253 | −0.786265 | − | 0.617889i | \(-0.787988\pi\) | ||||
−0.786265 | + | 0.617889i | \(0.787988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1818.00 | 0.256480 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1918.00 | 0.268403 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7762.00 | 1.07748 | 0.538741 | − | 0.842471i | \(-0.318900\pi\) | ||||
0.538741 | + | 0.842471i | \(0.318900\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4500.00 | −0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3180.00 | −0.434425 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12228.0 | −1.65728 | −0.828641 | − | 0.559780i | \(-0.810886\pi\) | ||||
−0.828641 | + | 0.559780i | \(0.810886\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3216.00 | −0.432443 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 336.000 | 0.0448271 | 0.0224136 | − | 0.999749i | \(-0.492865\pi\) | ||||
0.0224136 | + | 0.999749i | \(0.492865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 840.000 | 0.111196 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1044.00 | −0.137130 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1966.00 | −0.256247 | −0.128124 | − | 0.991758i | \(-0.540895\pi\) | ||||
−0.128124 | + | 0.991758i | \(0.540895\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5168.00 | 0.668432 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3252.00 | 0.417409 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8800.00 | 1.12095 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4606.00 | −0.582288 | −0.291144 | − | 0.956679i | \(-0.594036\pi\) | ||||
−0.291144 | + | 0.956679i | \(0.594036\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3108.00 | −0.389961 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13038.0 | −1.62366 | −0.811829 | − | 0.583896i | \(-0.801528\pi\) | ||||
−0.811829 | + | 0.583896i | \(0.801528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9120.00 | −1.12729 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 810.000 | 0.0993808 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1368.00 | 0.166607 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7290.00 | 0.881338 | 0.440669 | − | 0.897670i | \(-0.354741\pi\) | ||||
0.440669 | + | 0.897670i | \(0.354741\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7278.00 | 0.873473 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4620.00 | 0.550449 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1080.00 | 0.127747 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2052.00 | −0.240976 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5836.00 | 0.680447 | 0.340223 | − | 0.940345i | \(-0.389497\pi\) | ||||
0.340223 | + | 0.940345i | \(0.389497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2398.00 | −0.277604 | −0.138802 | − | 0.990320i | \(-0.544325\pi\) | ||||
−0.138802 | + | 0.990320i | \(0.544325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2016.00 | 0.231729 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −850.000 | −0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2674.00 | −0.303054 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1080.00 | −0.121545 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17568.0 | −1.96339 | −0.981695 | − | 0.190462i | \(-0.939002\pi\) | ||||
−0.981695 | + | 0.190462i | \(0.939002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4354.00 | 0.483233 | 0.241616 | − | 0.970372i | \(-0.422322\pi\) | ||||
0.241616 | + | 0.970372i | \(0.422322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3180.00 | 0.350504 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22496.0 | −2.46254 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14616.0 | −1.58903 | −0.794514 | − | 0.607245i | \(-0.792275\pi\) | ||||
−0.794514 | + | 0.607245i | \(0.792275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14516.0 | −1.55683 | −0.778415 | − | 0.627750i | \(-0.783976\pi\) | ||||
−0.778415 | + | 0.627750i | \(0.783976\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −860.000 | −0.0916133 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10794.0 | −1.14214 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14462.0 | −1.52005 | −0.760027 | − | 0.649892i | \(-0.774814\pi\) | ||||
−0.760027 | + | 0.649892i | \(0.774814\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2424.00 | 0.253086 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8040.00 | 0.833890 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2100.00 | −0.216373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3610.00 | 0.369516 | 0.184758 | − | 0.982784i | \(-0.440850\pi\) | ||||
0.184758 | + | 0.982784i | \(0.440850\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 918.000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3138.00 | 0.317031 | 0.158515 | − | 0.987356i | \(-0.449329\pi\) | ||||
0.158515 | + | 0.987356i | \(0.449329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6896.00 | 0.692191 | 0.346095 | − | 0.938199i | \(-0.387507\pi\) | ||||
0.346095 | + | 0.938199i | \(0.387507\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9120.00 | 0.909527 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1356.00 | 0.134364 | 0.0671822 | − | 0.997741i | \(-0.478599\pi\) | ||||
0.0671822 | + | 0.997741i | \(0.478599\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −84.0000 | −0.00827028 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4266.00 | −0.417339 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1392.00 | −0.135315 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3700.00 | 0.357406 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2466.00 | 0.236709 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9136.00 | 0.871471 | 0.435735 | − | 0.900075i | \(-0.356488\pi\) | ||||
0.435735 | + | 0.900075i | \(0.356488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3420.00 | −0.324197 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3192.00 | 0.300706 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14260.0 | 1.33508 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4072.00 | 0.378891 | 0.189446 | − | 0.981891i | \(-0.439331\pi\) | ||||
0.189446 | + | 0.981891i | \(0.439331\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −660.000 | −0.0610352 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12420.0 | −1.14156 | −0.570781 | − | 0.821102i | \(-0.693359\pi\) | ||||
−0.570781 | + | 0.821102i | \(0.693359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3604.00 | 0.329241 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1080.00 | 0.0980654 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3864.00 | −0.348741 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13892.0 | 1.24628 | 0.623138 | − | 0.782112i | \(-0.285858\pi\) | ||||
0.623138 | + | 0.782112i | \(0.285858\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5976.00 | 0.532910 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20408.0 | −1.80904 | −0.904521 | − | 0.426430i | \(-0.859771\pi\) | ||||
−0.904521 | + | 0.426430i | \(0.859771\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8100.00 | 0.713753 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3891.00 | −0.340839 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3666.00 | 0.319239 | 0.159619 | − | 0.987179i | \(-0.448973\pi\) | ||||
0.159619 | + | 0.987179i | \(0.448973\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4298.00 | −0.372079 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3996.00 | −0.343914 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10320.0 | 0.883017 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2688.00 | 0.228662 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12858.0 | −1.08748 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5046.00 | −0.424317 | −0.212159 | − | 0.977235i | \(-0.568049\pi\) | ||||
−0.212159 | + | 0.977235i | \(0.568049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18628.0 | 1.55745 | 0.778724 | − | 0.627366i | \(-0.215867\pi\) | ||||
0.778724 | + | 0.627366i | \(0.215867\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −525.000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10336.0 | 0.854351 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5940.00 | 0.485450 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6060.00 | −0.492472 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9000.00 | −0.727297 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13548.0 | 1.08871 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 588.000 | 0.0469888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5594.00 | 0.444556 | 0.222278 | − | 0.974983i | \(-0.428651\pi\) | ||||
0.222278 | + | 0.974983i | \(0.428651\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6654.00 | 0.525876 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4540.00 | −0.356830 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13372.0 | −1.04524 | −0.522619 | − | 0.852566i | \(-0.675045\pi\) | ||||
−0.522619 | + | 0.852566i | \(0.675045\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3438.00 | −0.267268 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15688.0 | −1.21294 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6160.00 | 0.473689 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3420.00 | 0.261569 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15478.0 | −1.17742 | −0.588711 | − | 0.808344i | \(-0.700364\pi\) | ||||
−0.588711 | + | 0.808344i | \(0.700364\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3480.00 | 0.263306 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1224.00 | 0.0921164 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12964.0 | −0.970457 | −0.485229 | − | 0.874387i | \(-0.661264\pi\) | ||||
−0.485229 | + | 0.874387i | \(0.661264\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 180.000 | 0.0134029 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10506.0 | 0.774050 | 0.387025 | − | 0.922069i | \(-0.373503\pi\) | ||||
0.387025 | + | 0.922069i | \(0.373503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6268.00 | 0.459383 | 0.229691 | − | 0.973263i | \(-0.426228\pi\) | ||||
0.229691 | + | 0.973263i | \(0.426228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9408.00 | 0.685907 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3800.00 | −0.275602 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5790.00 | −0.417748 | −0.208874 | − | 0.977943i | \(-0.566980\pi\) | ||||
−0.208874 | + | 0.977943i | \(0.566980\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9594.00 | −0.688624 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 756.000 | 0.0539831 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3288.00 | 0.233576 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2700.00 | −0.190823 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8332.00 | −0.585858 | −0.292929 | − | 0.956134i | \(-0.594630\pi\) | ||||
−0.292929 | + | 0.956134i | \(0.594630\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −44992.0 | −3.14748 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11142.0 | 0.775500 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23310.0 | −1.61421 | −0.807105 | − | 0.590407i | \(-0.798967\pi\) | ||||
−0.807105 | + | 0.590407i | \(0.798967\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2380.00 | 0.163984 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9768.00 | −0.669644 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18184.0 | 1.24036 | 0.620182 | − | 0.784458i | \(-0.287059\pi\) | ||||
0.620182 | + | 0.784458i | \(0.287059\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9398.00 | −0.637858 | −0.318929 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318929 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −108.000 | −0.00729370 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11870.0 | −0.797660 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20192.0 | −1.35019 | −0.675097 | − | 0.737729i | \(-0.735898\pi\) | ||||
−0.675097 | + | 0.737729i | \(0.735898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2226.00 | 0.148115 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6720.00 | −0.444946 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11758.0 | −0.774716 | −0.387358 | − | 0.921929i | \(-0.626612\pi\) | ||||
−0.387358 | + | 0.921929i | \(0.626612\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6060.00 | 0.397338 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2310.00 | −0.150725 | −0.0753623 | − | 0.997156i | \(-0.524011\pi\) | ||||
−0.0753623 | + | 0.997156i | \(0.524011\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19356.0 | −1.25684 | −0.628419 | − | 0.777875i | \(-0.716298\pi\) | ||||
−0.628419 | + | 0.777875i | \(0.716298\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4104.00 | 0.265198 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −602.000 | −0.0387137 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11875.0 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5328.00 | −0.339362 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3876.00 | 0.245701 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7768.00 | −0.490078 | −0.245039 | − | 0.969513i | \(-0.578801\pi\) | ||||
−0.245039 | + | 0.969513i | \(0.578801\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13836.0 | 0.868770 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10720.0 | −0.669937 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1470.00 | −0.0914341 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4968.00 | −0.307560 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11102.0 | −0.684091 | −0.342046 | − | 0.939683i | \(-0.611120\pi\) | ||||
−0.342046 | + | 0.939683i | \(0.611120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22612.0 | −1.38683 | −0.693414 | − | 0.720540i | \(-0.743894\pi\) | ||||
−0.693414 | + | 0.720540i | \(0.743894\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3480.00 | −0.212442 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1656.00 | −0.100625 | −0.0503123 | − | 0.998734i | \(-0.516022\pi\) | ||||
−0.0503123 | + | 0.998734i | \(0.516022\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7920.00 | 0.479025 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6384.00 | 0.384345 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16070.0 | −0.963044 | −0.481522 | − | 0.876434i | \(-0.659916\pi\) | ||||
−0.481522 | + | 0.876434i | \(0.659916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10840.0 | 0.646647 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5526.00 | −0.328143 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21740.0 | −1.28508 | −0.642542 | − | 0.766251i | \(-0.722120\pi\) | ||||
−0.642542 | + | 0.766251i | \(0.722120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31642.0 | 1.86192 | 0.930962 | − | 0.365117i | \(-0.118971\pi\) | ||||
0.930962 | + | 0.365117i | \(0.118971\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3060.00 | −0.179247 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10360.0 | −0.604126 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16112.0 | 0.935321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8928.00 | 0.515959 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4584.00 | −0.263731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27518.0 | −1.57614 | −0.788069 | − | 0.615587i | \(-0.788919\pi\) | ||||
−0.788069 | + | 0.615587i | \(0.788919\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −675.000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7290.00 | 0.413851 | 0.206926 | − | 0.978357i | \(-0.433654\pi\) | ||||
0.206926 | + | 0.978357i | \(0.433654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9982.00 | 0.564174 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3252.00 | 0.182991 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3684.00 | −0.206390 | −0.103195 | − | 0.994661i | \(-0.532907\pi\) | ||||
−0.103195 | + | 0.994661i | \(0.532907\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24260.0 | 1.35318 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8238.00 | 0.457495 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8220.00 | −0.454510 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24788.0 | −1.36466 | −0.682330 | − | 0.731044i | \(-0.739033\pi\) | ||||
−0.682330 | + | 0.731044i | \(0.739033\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 756.000 | 0.0414402 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6840.00 | −0.373318 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6868.00 | 0.373234 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15186.0 | −0.821727 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −15574.0 | −0.839118 | −0.419559 | − | 0.907728i | \(-0.637815\pi\) | ||||
−0.419559 | + | 0.907728i | \(0.637815\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16872.0 | −0.905177 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6720.00 | 0.358993 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5670.00 | 0.301616 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24338.0 | 1.28919 | 0.644593 | − | 0.764526i | \(-0.277027\pi\) | ||||
0.644593 | + | 0.764526i | \(0.277027\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7920.00 | 0.417754 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46208.0 | 2.42707 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3600.00 | −0.188297 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 960.000 | 0.0500026 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17760.0 | 0.921191 | 0.460595 | − | 0.887610i | \(-0.347636\pi\) | ||||
0.460595 | + | 0.887610i | \(0.347636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7224.00 | 0.373143 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20922.0 | −1.07621 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2650.00 | −0.135750 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3704.00 | 0.188960 | 0.0944799 | − | 0.995527i | \(-0.469881\pi\) | ||||
0.0944799 | + | 0.995527i | \(0.469881\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3944.00 | −0.199554 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32354.0 | 1.63032 | 0.815158 | − | 0.579238i | \(-0.196650\pi\) | ||||
0.815158 | + | 0.579238i | \(0.196650\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1470.00 | 0.0737711 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −144.000 | −0.00719716 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8860.00 | −0.441029 | −0.220514 | − | 0.975384i | \(-0.570774\pi\) | ||||
−0.220514 | + | 0.975384i | \(0.570774\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13320.0 | 0.660354 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8168.00 | 0.403304 | 0.201652 | − | 0.979457i | \(-0.435369\pi\) | ||||
0.201652 | + | 0.979457i | \(0.435369\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35980.0 | −1.76940 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 972.000 | 0.0476086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6300.00 | −0.307339 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25600.0 | −1.24388 | −0.621942 | − | 0.783063i | \(-0.713656\pi\) | ||||
−0.621942 | + | 0.783063i | \(0.713656\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1068.00 | 0.0516867 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26800.0 | 1.29186 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14878.0 | −0.714333 | −0.357167 | − | 0.934041i | \(-0.616257\pi\) | ||||
−0.357167 | + | 0.934041i | \(0.616257\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5472.00 | 0.261688 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9690.00 | 0.461580 | 0.230790 | − | 0.973004i | \(-0.425869\pi\) | ||||
0.230790 | + | 0.973004i | \(0.425869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3178.00 | −0.150788 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3060.00 | 0.144620 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19800.0 | −0.932121 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10670.0 | −0.500351 | −0.250176 | − | 0.968200i | \(-0.580488\pi\) | ||||
−0.250176 | + | 0.968200i | \(0.580488\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14310.0 | 0.668433 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2326.00 | −0.108228 | −0.0541141 | − | 0.998535i | \(-0.517233\pi\) | ||||
−0.0541141 | + | 0.998535i | \(0.517233\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7600.00 | −0.352258 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2394.00 | 0.110533 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29896.0 | −1.37501 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6624.00 | −0.303490 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2862.00 | 0.130625 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14220.0 | −0.646540 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10612.0 | −0.480657 | −0.240328 | − | 0.970692i | \(-0.577255\pi\) | ||||
−0.240328 | + | 0.970692i | \(0.577255\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8136.00 | 0.367109 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 126.000 | 0.00566377 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11460.0 | 0.513186 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8220.00 | 0.366709 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41166.0 | −1.82958 | −0.914790 | − | 0.403931i | \(-0.867644\pi\) | ||||
−0.914790 | + | 0.403931i | \(0.867644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7616.00 | 0.337215 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −774.000 | −0.0341423 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7368.00 | −0.323800 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10640.0 | 0.465852 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −20826.0 | −0.908439 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34182.0 | −1.48551 | −0.742753 | − | 0.669565i | \(-0.766481\pi\) | ||||
−0.742753 | + | 0.669565i | \(0.766481\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10308.0 | 0.446317 | 0.223158 | − | 0.974782i | \(-0.428363\pi\) | ||||
0.223158 | + | 0.974782i | \(0.428363\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14160.0 | −0.610840 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2200.00 | −0.0945554 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17168.0 | 0.735168 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1890.00 | −0.0806373 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37362.0 | 1.58824 | 0.794119 | − | 0.607763i | \(-0.207933\pi\) | ||||
0.794119 | + | 0.607763i | \(0.207933\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30808.0 | −1.30486 | −0.652430 | − | 0.757849i | \(-0.726250\pi\) | ||||
−0.652430 | + | 0.757849i | \(0.726250\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −900.000 | −0.0379806 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43596.0 | 1.83311 | 0.916555 | − | 0.399909i | \(-0.130958\pi\) | ||||
0.916555 | + | 0.399909i | \(0.130958\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8578.00 | 0.359380 | 0.179690 | − | 0.983723i | \(-0.442490\pi\) | ||||
0.179690 | + | 0.983723i | \(0.442490\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4470.00 | 0.186598 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1666.00 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19920.0 | 0.825581 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8208.00 | 0.338961 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41304.0 | −1.69961 | −0.849805 | − | 0.527098i | \(-0.823280\pi\) | ||||
−0.849805 | + | 0.527098i | \(0.823280\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13153.0 | −0.539301 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23778.0 | −0.971480 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12970.0 | −0.528026 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8309.00 | −0.337073 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25788.0 | 1.04245 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17328.0 | 0.697998 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11498.0 | 0.461529 | 0.230764 | − | 0.973010i | \(-0.425877\pi\) | ||||
0.230764 | + | 0.973010i | \(0.425877\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13320.0 | −0.532789 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21210.0 | 0.845414 | 0.422707 | − | 0.906266i | \(-0.361080\pi\) | ||||
0.422707 | + | 0.906266i | \(0.361080\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3580.00 | −0.142198 | −0.0710990 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0710990 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4242.00 | 0.167906 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10144.0 | −0.400123 | −0.200061 | − | 0.979783i | \(-0.564114\pi\) | ||||
−0.200061 | + | 0.979783i | \(0.564114\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −42860.0 | −1.68472 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11271.0 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10560.0 | 0.412225 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 360.000 | 0.0140047 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12834.0 | 0.497555 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10500.0 | −0.405674 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45926.0 | −1.76831 | −0.884157 | − | 0.467190i | \(-0.845266\pi\) | ||||
−0.884157 | + | 0.467190i | \(0.845266\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1314.00 | −0.0504211 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9038.00 | −0.345628 | −0.172814 | − | 0.984955i | \(-0.555286\pi\) | ||||
−0.172814 | + | 0.984955i | \(0.555286\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30692.0 | 1.16973 | 0.584863 | − | 0.811132i | \(-0.301148\pi\) | ||||
0.584863 | + | 0.811132i | \(0.301148\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19800.0 | 0.752056 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22104.0 | 0.836730 | 0.418365 | − | 0.908279i | \(-0.362603\pi\) | ||||
0.418365 | + | 0.908279i | \(0.362603\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7504.00 | −0.283100 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 972.000 | 0.0365468 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33152.0 | −1.24232 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45160.0 | 1.68663 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13680.0 | −0.509211 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32224.0 | 1.19547 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9316.00 | 0.344463 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2436.00 | −0.0897730 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 22180.0 | 0.814683 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42212.0 | −1.54534 | −0.772672 | − | 0.634806i | \(-0.781080\pi\) | ||||
−0.772672 | + | 0.634806i | \(0.781080\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7290.00 | 0.266000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24512.0 | −0.891459 | −0.445729 | − | 0.895168i | \(-0.647056\pi\) | ||||
−0.445729 | + | 0.895168i | \(0.647056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1296.00 | 0.0469785 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11460.0 | −0.414050 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7588.00 | 0.273258 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19912.0 | 0.714729 | 0.357365 | − | 0.933965i | \(-0.383675\pi\) | ||||
0.357365 | + | 0.933965i | \(0.383675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15420.0 | −0.551690 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16560.0 | 0.590552 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2850.00 | −0.101305 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9288.00 | 0.329081 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6802.00 | 0.240222 | 0.120111 | − | 0.992760i | \(-0.461675\pi\) | ||||
0.120111 | + | 0.992760i | \(0.461675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7252.00 | −0.255290 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12888.0 | 0.452234 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4080.00 | 0.142706 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55482.0 | 1.93438 | 0.967192 | − | 0.254046i | \(-0.0817616\pi\) | ||||
0.967192 | + | 0.254046i | \(0.0817616\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8142.00 | 0.282965 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3630.00 | −0.125754 | −0.0628771 | − | 0.998021i | \(-0.520028\pi\) | ||||
−0.0628771 | + | 0.998021i | \(0.520028\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30704.0 | 1.06030 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1890.00 | 0.0650600 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32372.0 | 1.11082 | 0.555411 | − | 0.831576i | \(-0.312561\pi\) | ||||
0.555411 | + | 0.831576i | \(0.312561\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18420.0 | 0.630072 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12942.0 | 0.441297 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43286.0 | −1.47132 | −0.735662 | − | 0.677349i | \(-0.763129\pi\) | ||||
−0.735662 | + | 0.677349i | \(0.763129\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31360.0 | 1.06260 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3816.00 | 0.128896 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16982.0 | 0.571822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62625.0 | 2.10214 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8100.00 | −0.271048 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31980.0 | −1.06681 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15864.0 | −0.527561 | −0.263781 | − | 0.964583i | \(-0.584970\pi\) | ||||
−0.263781 | + | 0.964583i | \(0.584970\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15096.0 | −0.500468 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9956.00 | 0.329046 | 0.164523 | − | 0.986373i | \(-0.447392\pi\) | ||||
0.164523 | + | 0.986373i | \(0.447392\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4788.00 | −0.157756 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2250.00 | 0.0739053 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28818.0 | 0.943674 | 0.471837 | − | 0.881686i | \(-0.343591\pi\) | ||||
0.471837 | + | 0.881686i | \(0.343591\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1032.00 | −0.0336904 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4086.00 | −0.132983 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40920.0 | 1.32772 | 0.663858 | − | 0.747858i | \(-0.268918\pi\) | ||||
0.663858 | + | 0.747858i | \(0.268918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 37140.0 | 1.20140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4704.00 | 0.151702 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17632.0 | −0.566901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3072.00 | 0.0984715 | 0.0492358 | − | 0.998787i | \(-0.484321\pi\) | ||||
0.0492358 | + | 0.998787i | \(0.484321\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6852.00 | 0.218974 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32560.0 | −1.03741 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11306.0 | 0.359142 | 0.179571 | − | 0.983745i | \(-0.442529\pi\) | ||||
0.179571 | + | 0.983745i | \(0.442529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3078.00 | 0.0974811 |
(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 | 1344.4.a.y.1.1 | 1 | ||
4.3 | odd | 2 | 1344.4.a.j.1.1 | 1 | |||
8.3 | odd | 2 | 336.4.a.g.1.1 | 1 | |||
8.5 | even | 2 | 168.4.a.a.1.1 | ✓ | 1 | ||
24.5 | odd | 2 | 504.4.a.f.1.1 | 1 | |||
24.11 | even | 2 | 1008.4.a.p.1.1 | 1 | |||
56.13 | odd | 2 | 1176.4.a.m.1.1 | 1 | |||
56.27 | even | 2 | 2352.4.a.n.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.4.a.a.1.1 | ✓ | 1 | 8.5 | even | 2 | ||
336.4.a.g.1.1 | 1 | 8.3 | odd | 2 | |||
504.4.a.f.1.1 | 1 | 24.5 | odd | 2 | |||
1008.4.a.p.1.1 | 1 | 24.11 | even | 2 | |||
1176.4.a.m.1.1 | 1 | 56.13 | odd | 2 | |||
1344.4.a.j.1.1 | 1 | 4.3 | odd | 2 | |||
1344.4.a.y.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2352.4.a.n.1.1 | 1 | 56.27 | even | 2 |