Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [726,4,Mod(1,726)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(726, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("726.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 726 = 2 \cdot 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 726.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: | \(42.8353866642\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 726.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 11.0000 | 0.593944 | 0.296972 | − | 0.954886i | \(-0.404023\pi\) | ||||
0.296972 | + | 0.954886i | \(0.404023\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −34.0000 | −0.725377 | −0.362689 | − | 0.931910i | \(-0.618141\pi\) | ||||
−0.362689 | + | 0.931910i | \(0.618141\pi\) | |||||||
\(14\) | −22.0000 | −0.419982 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 36.0000 | 0.513605 | 0.256802 | − | 0.966464i | \(-0.417331\pi\) | ||||
0.256802 | + | 0.966464i | \(0.417331\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −37.0000 | −0.446757 | −0.223378 | − | 0.974732i | \(-0.571709\pi\) | ||||
−0.223378 | + | 0.974732i | \(0.571709\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −33.0000 | −0.342914 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 0.0543951 | 0.0271975 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271975 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | −125.000 | −1.00000 | ||||||||
\(26\) | 68.0000 | 0.512919 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 44.0000 | 0.296972 | ||||||||
\(29\) | −42.0000 | −0.268938 | −0.134469 | − | 0.990918i | \(-0.542933\pi\) | ||||
−0.134469 | + | 0.990918i | \(0.542933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 113.000 | 0.654690 | 0.327345 | − | 0.944905i | \(-0.393846\pi\) | ||||
0.327345 | + | 0.944905i | \(0.393846\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −72.0000 | −0.363173 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 311.000 | 1.38184 | 0.690920 | − | 0.722931i | \(-0.257206\pi\) | ||||
0.690920 | + | 0.722931i | \(0.257206\pi\) | |||||||
\(38\) | 74.0000 | 0.315905 | ||||||||
\(39\) | 102.000 | 0.418797 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.0000 | 0.0685641 | 0.0342820 | − | 0.999412i | \(-0.489086\pi\) | ||||
0.0342820 | + | 0.999412i | \(0.489086\pi\) | |||||||
\(42\) | 66.0000 | 0.242477 | ||||||||
\(43\) | −412.000 | −1.46115 | −0.730575 | − | 0.682833i | \(-0.760748\pi\) | ||||
−0.730575 | + | 0.682833i | \(0.760748\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.0000 | −0.0384631 | ||||||||
\(47\) | 18.0000 | 0.0558632 | 0.0279316 | − | 0.999610i | \(-0.491108\pi\) | ||||
0.0279316 | + | 0.999610i | \(0.491108\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | −222.000 | −0.647230 | ||||||||
\(50\) | 250.000 | 0.707107 | ||||||||
\(51\) | −108.000 | −0.296530 | ||||||||
\(52\) | −136.000 | −0.362689 | ||||||||
\(53\) | 750.000 | 1.94378 | 0.971891 | − | 0.235432i | \(-0.0756506\pi\) | ||||
0.971891 | + | 0.235432i | \(0.0756506\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −88.0000 | −0.209991 | ||||||||
\(57\) | 111.000 | 0.257935 | ||||||||
\(58\) | 84.0000 | 0.190168 | ||||||||
\(59\) | 546.000 | 1.20480 | 0.602400 | − | 0.798195i | \(-0.294211\pi\) | ||||
0.602400 | + | 0.798195i | \(0.294211\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −25.0000 | −0.0524741 | −0.0262371 | − | 0.999656i | \(-0.508352\pi\) | ||||
−0.0262371 | + | 0.999656i | \(0.508352\pi\) | |||||||
\(62\) | −226.000 | −0.462936 | ||||||||
\(63\) | 99.0000 | 0.197981 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −535.000 | −0.975532 | −0.487766 | − | 0.872974i | \(-0.662188\pi\) | ||||
−0.487766 | + | 0.872974i | \(0.662188\pi\) | |||||||
\(68\) | 144.000 | 0.256802 | ||||||||
\(69\) | −18.0000 | −0.0314050 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 300.000 | 0.501457 | 0.250729 | − | 0.968057i | \(-0.419330\pi\) | ||||
0.250729 | + | 0.968057i | \(0.419330\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −499.000 | −0.800048 | −0.400024 | − | 0.916505i | \(-0.630998\pi\) | ||||
−0.400024 | + | 0.916505i | \(0.630998\pi\) | |||||||
\(74\) | −622.000 | −0.977109 | ||||||||
\(75\) | 375.000 | 0.577350 | ||||||||
\(76\) | −148.000 | −0.223378 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −204.000 | −0.296134 | ||||||||
\(79\) | −343.000 | −0.488488 | −0.244244 | − | 0.969714i | \(-0.578540\pi\) | ||||
−0.244244 | + | 0.969714i | \(0.578540\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −36.0000 | −0.0484821 | ||||||||
\(83\) | −1386.00 | −1.83293 | −0.916465 | − | 0.400114i | \(-0.868971\pi\) | ||||
−0.916465 | + | 0.400114i | \(0.868971\pi\) | |||||||
\(84\) | −132.000 | −0.171457 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 824.000 | 1.03319 | ||||||||
\(87\) | 126.000 | 0.155271 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1392.00 | −1.65788 | −0.828942 | − | 0.559334i | \(-0.811057\pi\) | ||||
−0.828942 | + | 0.559334i | \(0.811057\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −374.000 | −0.430834 | ||||||||
\(92\) | 24.0000 | 0.0271975 | ||||||||
\(93\) | −339.000 | −0.377986 | ||||||||
\(94\) | −36.0000 | −0.0395012 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 53.0000 | 0.0554777 | 0.0277388 | − | 0.999615i | \(-0.491169\pi\) | ||||
0.0277388 | + | 0.999615i | \(0.491169\pi\) | |||||||
\(98\) | 444.000 | 0.457661 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −500.000 | −0.500000 | ||||||||
\(101\) | 210.000 | 0.206889 | 0.103444 | − | 0.994635i | \(-0.467014\pi\) | ||||
0.103444 | + | 0.994635i | \(0.467014\pi\) | |||||||
\(102\) | 216.000 | 0.209678 | ||||||||
\(103\) | 1139.00 | 1.08960 | 0.544801 | − | 0.838565i | \(-0.316605\pi\) | ||||
0.544801 | + | 0.838565i | \(0.316605\pi\) | |||||||
\(104\) | 272.000 | 0.256460 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1500.00 | −1.37446 | ||||||||
\(107\) | 30.0000 | 0.0271048 | 0.0135524 | − | 0.999908i | \(-0.495686\pi\) | ||||
0.0135524 | + | 0.999908i | \(0.495686\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −1435.00 | −1.26099 | −0.630496 | − | 0.776193i | \(-0.717148\pi\) | ||||
−0.630496 | + | 0.776193i | \(0.717148\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −933.000 | −0.797806 | ||||||||
\(112\) | 176.000 | 0.148486 | ||||||||
\(113\) | −1434.00 | −1.19380 | −0.596900 | − | 0.802316i | \(-0.703601\pi\) | ||||
−0.596900 | + | 0.802316i | \(0.703601\pi\) | |||||||
\(114\) | −222.000 | −0.182388 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −168.000 | −0.134469 | ||||||||
\(117\) | −306.000 | −0.241792 | ||||||||
\(118\) | −1092.00 | −0.851922 | ||||||||
\(119\) | 396.000 | 0.305053 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 50.0000 | 0.0371048 | ||||||||
\(123\) | −54.0000 | −0.0395855 | ||||||||
\(124\) | 452.000 | 0.327345 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −198.000 | −0.139994 | ||||||||
\(127\) | −1183.00 | −0.826569 | −0.413285 | − | 0.910602i | \(-0.635619\pi\) | ||||
−0.413285 | + | 0.910602i | \(0.635619\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 1236.00 | 0.843595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 318.000 | 0.212090 | 0.106045 | − | 0.994361i | \(-0.466181\pi\) | ||||
0.106045 | + | 0.994361i | \(0.466181\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −407.000 | −0.265349 | ||||||||
\(134\) | 1070.00 | 0.689805 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −288.000 | −0.181587 | ||||||||
\(137\) | 168.000 | 0.104768 | 0.0523840 | − | 0.998627i | \(-0.483318\pi\) | ||||
0.0523840 | + | 0.998627i | \(0.483318\pi\) | |||||||
\(138\) | 36.0000 | 0.0222067 | ||||||||
\(139\) | −2536.00 | −1.54749 | −0.773744 | − | 0.633499i | \(-0.781618\pi\) | ||||
−0.773744 | + | 0.633499i | \(0.781618\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −54.0000 | −0.0322526 | ||||||||
\(142\) | −600.000 | −0.354584 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 998.000 | 0.565720 | ||||||||
\(147\) | 666.000 | 0.373679 | ||||||||
\(148\) | 1244.00 | 0.690920 | ||||||||
\(149\) | −3336.00 | −1.83420 | −0.917100 | − | 0.398657i | \(-0.869476\pi\) | ||||
−0.917100 | + | 0.398657i | \(0.869476\pi\) | |||||||
\(150\) | −750.000 | −0.408248 | ||||||||
\(151\) | −520.000 | −0.280245 | −0.140123 | − | 0.990134i | \(-0.544750\pi\) | ||||
−0.140123 | + | 0.990134i | \(0.544750\pi\) | |||||||
\(152\) | 296.000 | 0.157952 | ||||||||
\(153\) | 324.000 | 0.171202 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 408.000 | 0.209398 | ||||||||
\(157\) | −3661.00 | −1.86102 | −0.930508 | − | 0.366271i | \(-0.880634\pi\) | ||||
−0.930508 | + | 0.366271i | \(0.880634\pi\) | |||||||
\(158\) | 686.000 | 0.345413 | ||||||||
\(159\) | −2250.00 | −1.12224 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 66.0000 | 0.0323076 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | −1393.00 | −0.669375 | −0.334688 | − | 0.942329i | \(-0.608631\pi\) | ||||
−0.334688 | + | 0.942329i | \(0.608631\pi\) | |||||||
\(164\) | 72.0000 | 0.0342820 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2772.00 | 1.29608 | ||||||||
\(167\) | 246.000 | 0.113988 | 0.0569942 | − | 0.998375i | \(-0.481848\pi\) | ||||
0.0569942 | + | 0.998375i | \(0.481848\pi\) | |||||||
\(168\) | 264.000 | 0.121238 | ||||||||
\(169\) | −1041.00 | −0.473828 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −333.000 | −0.148919 | ||||||||
\(172\) | −1648.00 | −0.730575 | ||||||||
\(173\) | −1968.00 | −0.864880 | −0.432440 | − | 0.901663i | \(-0.642347\pi\) | ||||
−0.432440 | + | 0.901663i | \(0.642347\pi\) | |||||||
\(174\) | −252.000 | −0.109794 | ||||||||
\(175\) | −1375.00 | −0.593944 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1638.00 | −0.695591 | ||||||||
\(178\) | 2784.00 | 1.17230 | ||||||||
\(179\) | −2442.00 | −1.01969 | −0.509843 | − | 0.860268i | \(-0.670296\pi\) | ||||
−0.509843 | + | 0.860268i | \(0.670296\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 461.000 | 0.189314 | 0.0946571 | − | 0.995510i | \(-0.469825\pi\) | ||||
0.0946571 | + | 0.995510i | \(0.469825\pi\) | |||||||
\(182\) | 748.000 | 0.304645 | ||||||||
\(183\) | 75.0000 | 0.0302960 | ||||||||
\(184\) | −48.0000 | −0.0192316 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 678.000 | 0.267276 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 72.0000 | 0.0279316 | ||||||||
\(189\) | −297.000 | −0.114305 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2172.00 | 0.822829 | 0.411415 | − | 0.911448i | \(-0.365035\pi\) | ||||
0.411415 | + | 0.911448i | \(0.365035\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 2315.00 | 0.863406 | 0.431703 | − | 0.902016i | \(-0.357913\pi\) | ||||
0.431703 | + | 0.902016i | \(0.357913\pi\) | |||||||
\(194\) | −106.000 | −0.0392286 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −888.000 | −0.323615 | ||||||||
\(197\) | 4152.00 | 1.50161 | 0.750806 | − | 0.660522i | \(-0.229665\pi\) | ||||
0.750806 | + | 0.660522i | \(0.229665\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1457.00 | 0.519015 | 0.259508 | − | 0.965741i | \(-0.416440\pi\) | ||||
0.259508 | + | 0.965741i | \(0.416440\pi\) | |||||||
\(200\) | 1000.00 | 0.353553 | ||||||||
\(201\) | 1605.00 | 0.563224 | ||||||||
\(202\) | −420.000 | −0.146293 | ||||||||
\(203\) | −462.000 | −0.159734 | ||||||||
\(204\) | −432.000 | −0.148265 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2278.00 | −0.770465 | ||||||||
\(207\) | 54.0000 | 0.0181317 | ||||||||
\(208\) | −544.000 | −0.181344 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3475.00 | −1.13379 | −0.566893 | − | 0.823791i | \(-0.691855\pi\) | ||||
−0.566893 | + | 0.823791i | \(0.691855\pi\) | |||||||
\(212\) | 3000.00 | 0.971891 | ||||||||
\(213\) | −900.000 | −0.289516 | ||||||||
\(214\) | −60.0000 | −0.0191660 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 1243.00 | 0.388849 | ||||||||
\(218\) | 2870.00 | 0.891656 | ||||||||
\(219\) | 1497.00 | 0.461908 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1224.00 | −0.372557 | ||||||||
\(222\) | 1866.00 | 0.564134 | ||||||||
\(223\) | −4387.00 | −1.31738 | −0.658689 | − | 0.752415i | \(-0.728889\pi\) | ||||
−0.658689 | + | 0.752415i | \(0.728889\pi\) | |||||||
\(224\) | −352.000 | −0.104995 | ||||||||
\(225\) | −1125.00 | −0.333333 | ||||||||
\(226\) | 2868.00 | 0.844144 | ||||||||
\(227\) | 5724.00 | 1.67364 | 0.836818 | − | 0.547482i | \(-0.184413\pi\) | ||||
0.836818 | + | 0.547482i | \(0.184413\pi\) | |||||||
\(228\) | 444.000 | 0.128968 | ||||||||
\(229\) | −2986.00 | −0.861661 | −0.430831 | − | 0.902433i | \(-0.641779\pi\) | ||||
−0.430831 | + | 0.902433i | \(0.641779\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 336.000 | 0.0950840 | ||||||||
\(233\) | −474.000 | −0.133274 | −0.0666369 | − | 0.997777i | \(-0.521227\pi\) | ||||
−0.0666369 | + | 0.997777i | \(0.521227\pi\) | |||||||
\(234\) | 612.000 | 0.170973 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2184.00 | 0.602400 | ||||||||
\(237\) | 1029.00 | 0.282028 | ||||||||
\(238\) | −792.000 | −0.215705 | ||||||||
\(239\) | 3174.00 | 0.859033 | 0.429517 | − | 0.903059i | \(-0.358684\pi\) | ||||
0.429517 | + | 0.903059i | \(0.358684\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3454.00 | −0.923202 | −0.461601 | − | 0.887088i | \(-0.652725\pi\) | ||||
−0.461601 | + | 0.887088i | \(0.652725\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −100.000 | −0.0262371 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 108.000 | 0.0279912 | ||||||||
\(247\) | 1258.00 | 0.324067 | ||||||||
\(248\) | −904.000 | −0.231468 | ||||||||
\(249\) | 4158.00 | 1.05824 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3546.00 | −0.891719 | −0.445860 | − | 0.895103i | \(-0.647102\pi\) | ||||
−0.445860 | + | 0.895103i | \(0.647102\pi\) | |||||||
\(252\) | 396.000 | 0.0989907 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 2366.00 | 0.584473 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −918.000 | −0.222814 | −0.111407 | − | 0.993775i | \(-0.535536\pi\) | ||||
−0.111407 | + | 0.993775i | \(0.535536\pi\) | |||||||
\(258\) | −2472.00 | −0.596512 | ||||||||
\(259\) | 3421.00 | 0.820736 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −378.000 | −0.0896460 | ||||||||
\(262\) | −636.000 | −0.149970 | ||||||||
\(263\) | 6162.00 | 1.44473 | 0.722367 | − | 0.691510i | \(-0.243054\pi\) | ||||
0.722367 | + | 0.691510i | \(0.243054\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 814.000 | 0.187630 | ||||||||
\(267\) | 4176.00 | 0.957180 | ||||||||
\(268\) | −2140.00 | −0.487766 | ||||||||
\(269\) | −4890.00 | −1.10836 | −0.554179 | − | 0.832397i | \(-0.686968\pi\) | ||||
−0.554179 | + | 0.832397i | \(0.686968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2072.00 | 0.464447 | 0.232223 | − | 0.972662i | \(-0.425400\pi\) | ||||
0.232223 | + | 0.972662i | \(0.425400\pi\) | |||||||
\(272\) | 576.000 | 0.128401 | ||||||||
\(273\) | 1122.00 | 0.248742 | ||||||||
\(274\) | −336.000 | −0.0740821 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −72.0000 | −0.0157025 | ||||||||
\(277\) | −6511.00 | −1.41230 | −0.706152 | − | 0.708061i | \(-0.749570\pi\) | ||||
−0.706152 | + | 0.708061i | \(0.749570\pi\) | |||||||
\(278\) | 5072.00 | 1.09424 | ||||||||
\(279\) | 1017.00 | 0.218230 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −432.000 | −0.0917116 | −0.0458558 | − | 0.998948i | \(-0.514601\pi\) | ||||
−0.0458558 | + | 0.998948i | \(0.514601\pi\) | |||||||
\(282\) | 108.000 | 0.0228061 | ||||||||
\(283\) | 6827.00 | 1.43400 | 0.717002 | − | 0.697071i | \(-0.245514\pi\) | ||||
0.717002 | + | 0.697071i | \(0.245514\pi\) | |||||||
\(284\) | 1200.00 | 0.250729 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 198.000 | 0.0407232 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −3617.00 | −0.736210 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −159.000 | −0.0320301 | ||||||||
\(292\) | −1996.00 | −0.400024 | ||||||||
\(293\) | 6216.00 | 1.23939 | 0.619697 | − | 0.784841i | \(-0.287255\pi\) | ||||
0.619697 | + | 0.784841i | \(0.287255\pi\) | |||||||
\(294\) | −1332.00 | −0.264231 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2488.00 | −0.488554 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6672.00 | 1.29698 | ||||||||
\(299\) | −204.000 | −0.0394569 | ||||||||
\(300\) | 1500.00 | 0.288675 | ||||||||
\(301\) | −4532.00 | −0.867841 | ||||||||
\(302\) | 1040.00 | 0.198163 | ||||||||
\(303\) | −630.000 | −0.119447 | ||||||||
\(304\) | −592.000 | −0.111689 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −648.000 | −0.121058 | ||||||||
\(307\) | −8389.00 | −1.55956 | −0.779781 | − | 0.626052i | \(-0.784670\pi\) | ||||
−0.779781 | + | 0.626052i | \(0.784670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3417.00 | −0.629082 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8268.00 | 1.50751 | 0.753754 | − | 0.657156i | \(-0.228241\pi\) | ||||
0.753754 | + | 0.657156i | \(0.228241\pi\) | |||||||
\(312\) | −816.000 | −0.148067 | ||||||||
\(313\) | 8318.00 | 1.50211 | 0.751056 | − | 0.660238i | \(-0.229545\pi\) | ||||
0.751056 | + | 0.660238i | \(0.229545\pi\) | |||||||
\(314\) | 7322.00 | 1.31594 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1372.00 | −0.244244 | ||||||||
\(317\) | −372.000 | −0.0659104 | −0.0329552 | − | 0.999457i | \(-0.510492\pi\) | ||||
−0.0329552 | + | 0.999457i | \(0.510492\pi\) | |||||||
\(318\) | 4500.00 | 0.793546 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −90.0000 | −0.0156489 | ||||||||
\(322\) | −132.000 | −0.0228449 | ||||||||
\(323\) | −1332.00 | −0.229457 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 4250.00 | 0.725377 | ||||||||
\(326\) | 2786.00 | 0.473320 | ||||||||
\(327\) | 4305.00 | 0.728034 | ||||||||
\(328\) | −144.000 | −0.0242411 | ||||||||
\(329\) | 198.000 | 0.0331796 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10763.0 | 1.78727 | 0.893637 | − | 0.448790i | \(-0.148145\pi\) | ||||
0.893637 | + | 0.448790i | \(0.148145\pi\) | |||||||
\(332\) | −5544.00 | −0.916465 | ||||||||
\(333\) | 2799.00 | 0.460613 | ||||||||
\(334\) | −492.000 | −0.0806019 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −528.000 | −0.0857285 | ||||||||
\(337\) | 8141.00 | 1.31593 | 0.657965 | − | 0.753048i | \(-0.271417\pi\) | ||||
0.657965 | + | 0.753048i | \(0.271417\pi\) | |||||||
\(338\) | 2082.00 | 0.335047 | ||||||||
\(339\) | 4302.00 | 0.689241 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 666.000 | 0.105302 | ||||||||
\(343\) | −6215.00 | −0.978363 | ||||||||
\(344\) | 3296.00 | 0.516594 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3936.00 | 0.611563 | ||||||||
\(347\) | −1110.00 | −0.171723 | −0.0858616 | − | 0.996307i | \(-0.527364\pi\) | ||||
−0.0858616 | + | 0.996307i | \(0.527364\pi\) | |||||||
\(348\) | 504.000 | 0.0776357 | ||||||||
\(349\) | −6205.00 | −0.951708 | −0.475854 | − | 0.879524i | \(-0.657861\pi\) | ||||
−0.475854 | + | 0.879524i | \(0.657861\pi\) | |||||||
\(350\) | 2750.00 | 0.419982 | ||||||||
\(351\) | 918.000 | 0.139599 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1752.00 | 0.264163 | 0.132082 | − | 0.991239i | \(-0.457834\pi\) | ||||
0.132082 | + | 0.991239i | \(0.457834\pi\) | |||||||
\(354\) | 3276.00 | 0.491857 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5568.00 | −0.828942 | ||||||||
\(357\) | −1188.00 | −0.176122 | ||||||||
\(358\) | 4884.00 | 0.721026 | ||||||||
\(359\) | 1716.00 | 0.252276 | 0.126138 | − | 0.992013i | \(-0.459742\pi\) | ||||
0.126138 | + | 0.992013i | \(0.459742\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5490.00 | −0.800408 | ||||||||
\(362\) | −922.000 | −0.133865 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1496.00 | −0.215417 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −150.000 | −0.0214225 | ||||||||
\(367\) | −1024.00 | −0.145647 | −0.0728234 | − | 0.997345i | \(-0.523201\pi\) | ||||
−0.0728234 | + | 0.997345i | \(0.523201\pi\) | |||||||
\(368\) | 96.0000 | 0.0135988 | ||||||||
\(369\) | 162.000 | 0.0228547 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8250.00 | 1.15450 | ||||||||
\(372\) | −1356.00 | −0.188993 | ||||||||
\(373\) | −6661.00 | −0.924647 | −0.462324 | − | 0.886711i | \(-0.652984\pi\) | ||||
−0.462324 | + | 0.886711i | \(0.652984\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −144.000 | −0.0197506 | ||||||||
\(377\) | 1428.00 | 0.195082 | ||||||||
\(378\) | 594.000 | 0.0808256 | ||||||||
\(379\) | 9560.00 | 1.29568 | 0.647842 | − | 0.761775i | \(-0.275672\pi\) | ||||
0.647842 | + | 0.761775i | \(0.275672\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3549.00 | 0.477220 | ||||||||
\(382\) | −4344.00 | −0.581828 | ||||||||
\(383\) | −6102.00 | −0.814093 | −0.407047 | − | 0.913407i | \(-0.633441\pi\) | ||||
−0.407047 | + | 0.913407i | \(0.633441\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4630.00 | −0.610520 | ||||||||
\(387\) | −3708.00 | −0.487050 | ||||||||
\(388\) | 212.000 | 0.0277388 | ||||||||
\(389\) | −10002.0 | −1.30365 | −0.651827 | − | 0.758368i | \(-0.725997\pi\) | ||||
−0.651827 | + | 0.758368i | \(0.725997\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 216.000 | 0.0279376 | ||||||||
\(392\) | 1776.00 | 0.228830 | ||||||||
\(393\) | −954.000 | −0.122450 | ||||||||
\(394\) | −8304.00 | −1.06180 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4259.00 | 0.538421 | 0.269210 | − | 0.963081i | \(-0.413237\pi\) | ||||
0.269210 | + | 0.963081i | \(0.413237\pi\) | |||||||
\(398\) | −2914.00 | −0.366999 | ||||||||
\(399\) | 1221.00 | 0.153199 | ||||||||
\(400\) | −2000.00 | −0.250000 | ||||||||
\(401\) | −5772.00 | −0.718803 | −0.359401 | − | 0.933183i | \(-0.617019\pi\) | ||||
−0.359401 | + | 0.933183i | \(0.617019\pi\) | |||||||
\(402\) | −3210.00 | −0.398259 | ||||||||
\(403\) | −3842.00 | −0.474897 | ||||||||
\(404\) | 840.000 | 0.103444 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 924.000 | 0.112949 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 864.000 | 0.104839 | ||||||||
\(409\) | −3091.00 | −0.373692 | −0.186846 | − | 0.982389i | \(-0.559827\pi\) | ||||
−0.186846 | + | 0.982389i | \(0.559827\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −504.000 | −0.0604878 | ||||||||
\(412\) | 4556.00 | 0.544801 | ||||||||
\(413\) | 6006.00 | 0.715583 | ||||||||
\(414\) | −108.000 | −0.0128210 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1088.00 | 0.128230 | ||||||||
\(417\) | 7608.00 | 0.893442 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1542.00 | 0.179789 | 0.0898945 | − | 0.995951i | \(-0.471347\pi\) | ||||
0.0898945 | + | 0.995951i | \(0.471347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −0.00393601 | −0.00196800 | − | 0.999998i | \(-0.500626\pi\) | ||||
−0.00196800 | + | 0.999998i | \(0.500626\pi\) | |||||||
\(422\) | 6950.00 | 0.801708 | ||||||||
\(423\) | 162.000 | 0.0186211 | ||||||||
\(424\) | −6000.00 | −0.687231 | ||||||||
\(425\) | −4500.00 | −0.513605 | ||||||||
\(426\) | 1800.00 | 0.204719 | ||||||||
\(427\) | −275.000 | −0.0311667 | ||||||||
\(428\) | 120.000 | 0.0135524 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8334.00 | 0.931403 | 0.465701 | − | 0.884942i | \(-0.345802\pi\) | ||||
0.465701 | + | 0.884942i | \(0.345802\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | 1559.00 | 0.173027 | 0.0865136 | − | 0.996251i | \(-0.472427\pi\) | ||||
0.0865136 | + | 0.996251i | \(0.472427\pi\) | |||||||
\(434\) | −2486.00 | −0.274958 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5740.00 | −0.630496 | ||||||||
\(437\) | −222.000 | −0.0243014 | ||||||||
\(438\) | −2994.00 | −0.326618 | ||||||||
\(439\) | −3025.00 | −0.328873 | −0.164437 | − | 0.986388i | \(-0.552581\pi\) | ||||
−0.164437 | + | 0.986388i | \(0.552581\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1998.00 | −0.215743 | ||||||||
\(442\) | 2448.00 | 0.263438 | ||||||||
\(443\) | −5448.00 | −0.584294 | −0.292147 | − | 0.956373i | \(-0.594370\pi\) | ||||
−0.292147 | + | 0.956373i | \(0.594370\pi\) | |||||||
\(444\) | −3732.00 | −0.398903 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8774.00 | 0.931527 | ||||||||
\(447\) | 10008.0 | 1.05898 | ||||||||
\(448\) | 704.000 | 0.0742430 | ||||||||
\(449\) | −7272.00 | −0.764336 | −0.382168 | − | 0.924093i | \(-0.624822\pi\) | ||||
−0.382168 | + | 0.924093i | \(0.624822\pi\) | |||||||
\(450\) | 2250.00 | 0.235702 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −5736.00 | −0.596900 | ||||||||
\(453\) | 1560.00 | 0.161800 | ||||||||
\(454\) | −11448.0 | −1.18344 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −888.000 | −0.0911939 | ||||||||
\(457\) | 5402.00 | 0.552943 | 0.276471 | − | 0.961022i | \(-0.410835\pi\) | ||||
0.276471 | + | 0.961022i | \(0.410835\pi\) | |||||||
\(458\) | 5972.00 | 0.609287 | ||||||||
\(459\) | −972.000 | −0.0988433 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9258.00 | 0.935332 | 0.467666 | − | 0.883905i | \(-0.345095\pi\) | ||||
0.467666 | + | 0.883905i | \(0.345095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13592.0 | 1.36431 | 0.682153 | − | 0.731209i | \(-0.261044\pi\) | ||||
0.682153 | + | 0.731209i | \(0.261044\pi\) | |||||||
\(464\) | −672.000 | −0.0672345 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 948.000 | 0.0942387 | ||||||||
\(467\) | −15444.0 | −1.53033 | −0.765164 | − | 0.643836i | \(-0.777342\pi\) | ||||
−0.765164 | + | 0.643836i | \(0.777342\pi\) | |||||||
\(468\) | −1224.00 | −0.120896 | ||||||||
\(469\) | −5885.00 | −0.579412 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10983.0 | 1.07446 | ||||||||
\(472\) | −4368.00 | −0.425961 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2058.00 | −0.199424 | ||||||||
\(475\) | 4625.00 | 0.446757 | ||||||||
\(476\) | 1584.00 | 0.152526 | ||||||||
\(477\) | 6750.00 | 0.647927 | ||||||||
\(478\) | −6348.00 | −0.607428 | ||||||||
\(479\) | −18822.0 | −1.79541 | −0.897703 | − | 0.440602i | \(-0.854765\pi\) | ||||
−0.897703 | + | 0.440602i | \(0.854765\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10574.0 | −1.00236 | ||||||||
\(482\) | 6908.00 | 0.652802 | ||||||||
\(483\) | −198.000 | −0.0186528 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | 3656.00 | 0.340183 | 0.170092 | − | 0.985428i | \(-0.445594\pi\) | ||||
0.170092 | + | 0.985428i | \(0.445594\pi\) | |||||||
\(488\) | 200.000 | 0.0185524 | ||||||||
\(489\) | 4179.00 | 0.386464 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15126.0 | −1.39028 | −0.695139 | − | 0.718875i | \(-0.744657\pi\) | ||||
−0.695139 | + | 0.718875i | \(0.744657\pi\) | |||||||
\(492\) | −216.000 | −0.0197927 | ||||||||
\(493\) | −1512.00 | −0.138128 | ||||||||
\(494\) | −2516.00 | −0.229150 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1808.00 | 0.163673 | ||||||||
\(497\) | 3300.00 | 0.297837 | ||||||||
\(498\) | −8316.00 | −0.748291 | ||||||||
\(499\) | 10961.0 | 0.983330 | 0.491665 | − | 0.870784i | \(-0.336388\pi\) | ||||
0.491665 | + | 0.870784i | \(0.336388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −738.000 | −0.0658112 | ||||||||
\(502\) | 7092.00 | 0.630541 | ||||||||
\(503\) | 13068.0 | 1.15840 | 0.579198 | − | 0.815187i | \(-0.303366\pi\) | ||||
0.579198 | + | 0.815187i | \(0.303366\pi\) | |||||||
\(504\) | −792.000 | −0.0699970 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3123.00 | 0.273565 | ||||||||
\(508\) | −4732.00 | −0.413285 | ||||||||
\(509\) | −2082.00 | −0.181303 | −0.0906513 | − | 0.995883i | \(-0.528895\pi\) | ||||
−0.0906513 | + | 0.995883i | \(0.528895\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5489.00 | −0.475184 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 999.000 | 0.0859784 | ||||||||
\(514\) | 1836.00 | 0.157553 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4944.00 | 0.421797 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −6842.00 | −0.580348 | ||||||||
\(519\) | 5904.00 | 0.499339 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2538.00 | −0.213420 | −0.106710 | − | 0.994290i | \(-0.534032\pi\) | ||||
−0.106710 | + | 0.994290i | \(0.534032\pi\) | |||||||
\(522\) | 756.000 | 0.0633893 | ||||||||
\(523\) | −3589.00 | −0.300069 | −0.150034 | − | 0.988681i | \(-0.547938\pi\) | ||||
−0.150034 | + | 0.988681i | \(0.547938\pi\) | |||||||
\(524\) | 1272.00 | 0.106045 | ||||||||
\(525\) | 4125.00 | 0.342914 | ||||||||
\(526\) | −12324.0 | −1.02158 | ||||||||
\(527\) | 4068.00 | 0.336252 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12131.0 | −0.997041 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4914.00 | 0.401600 | ||||||||
\(532\) | −1628.00 | −0.132674 | ||||||||
\(533\) | −612.000 | −0.0497348 | ||||||||
\(534\) | −8352.00 | −0.676828 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4280.00 | 0.344903 | ||||||||
\(537\) | 7326.00 | 0.588716 | ||||||||
\(538\) | 9780.00 | 0.783728 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10838.0 | 0.861298 | 0.430649 | − | 0.902520i | \(-0.358285\pi\) | ||||
0.430649 | + | 0.902520i | \(0.358285\pi\) | |||||||
\(542\) | −4144.00 | −0.328413 | ||||||||
\(543\) | −1383.00 | −0.109301 | ||||||||
\(544\) | −1152.00 | −0.0907934 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2244.00 | −0.175887 | ||||||||
\(547\) | −13372.0 | −1.04524 | −0.522619 | − | 0.852566i | \(-0.675045\pi\) | ||||
−0.522619 | + | 0.852566i | \(0.675045\pi\) | |||||||
\(548\) | 672.000 | 0.0523840 | ||||||||
\(549\) | −225.000 | −0.0174914 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1554.00 | 0.120150 | ||||||||
\(552\) | 144.000 | 0.0111033 | ||||||||
\(553\) | −3773.00 | −0.290134 | ||||||||
\(554\) | 13022.0 | 0.998649 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10144.0 | −0.773744 | ||||||||
\(557\) | −19332.0 | −1.47060 | −0.735299 | − | 0.677743i | \(-0.762958\pi\) | ||||
−0.735299 | + | 0.677743i | \(0.762958\pi\) | |||||||
\(558\) | −2034.00 | −0.154312 | ||||||||
\(559\) | 14008.0 | 1.05988 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 864.000 | 0.0648499 | ||||||||
\(563\) | 19584.0 | 1.46602 | 0.733008 | − | 0.680220i | \(-0.238116\pi\) | ||||
0.733008 | + | 0.680220i | \(0.238116\pi\) | |||||||
\(564\) | −216.000 | −0.0161263 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13654.0 | −1.01399 | ||||||||
\(567\) | 891.000 | 0.0659938 | ||||||||
\(568\) | −2400.00 | −0.177292 | ||||||||
\(569\) | −20352.0 | −1.49947 | −0.749737 | − | 0.661736i | \(-0.769820\pi\) | ||||
−0.749737 | + | 0.661736i | \(0.769820\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6703.00 | −0.491264 | −0.245632 | − | 0.969363i | \(-0.578995\pi\) | ||||
−0.245632 | + | 0.969363i | \(0.578995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6516.00 | −0.475061 | ||||||||
\(574\) | −396.000 | −0.0287957 | ||||||||
\(575\) | −750.000 | −0.0543951 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 7103.00 | 0.512481 | 0.256241 | − | 0.966613i | \(-0.417516\pi\) | ||||
0.256241 | + | 0.966613i | \(0.417516\pi\) | |||||||
\(578\) | 7234.00 | 0.520579 | ||||||||
\(579\) | −6945.00 | −0.498488 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15246.0 | −1.08866 | ||||||||
\(582\) | 318.000 | 0.0226487 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3992.00 | 0.282860 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12432.0 | −0.876384 | ||||||||
\(587\) | 7344.00 | 0.516387 | 0.258194 | − | 0.966093i | \(-0.416873\pi\) | ||||
0.258194 | + | 0.966093i | \(0.416873\pi\) | |||||||
\(588\) | 2664.00 | 0.186839 | ||||||||
\(589\) | −4181.00 | −0.292487 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12456.0 | −0.866957 | ||||||||
\(592\) | 4976.00 | 0.345460 | ||||||||
\(593\) | 13470.0 | 0.932794 | 0.466397 | − | 0.884576i | \(-0.345552\pi\) | ||||
0.466397 | + | 0.884576i | \(0.345552\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13344.0 | −0.917100 | ||||||||
\(597\) | −4371.00 | −0.299653 | ||||||||
\(598\) | 408.000 | 0.0279003 | ||||||||
\(599\) | 9348.00 | 0.637644 | 0.318822 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318822 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(600\) | −3000.00 | −0.204124 | ||||||||
\(601\) | −17377.0 | −1.17941 | −0.589703 | − | 0.807620i | \(-0.700755\pi\) | ||||
−0.589703 | + | 0.807620i | \(0.700755\pi\) | |||||||
\(602\) | 9064.00 | 0.613656 | ||||||||
\(603\) | −4815.00 | −0.325177 | ||||||||
\(604\) | −2080.00 | −0.140123 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1260.00 | 0.0844620 | ||||||||
\(607\) | 15824.0 | 1.05812 | 0.529058 | − | 0.848586i | \(-0.322545\pi\) | ||||
0.529058 | + | 0.848586i | \(0.322545\pi\) | |||||||
\(608\) | 1184.00 | 0.0789762 | ||||||||
\(609\) | 1386.00 | 0.0922226 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −612.000 | −0.0405219 | ||||||||
\(612\) | 1296.00 | 0.0856008 | ||||||||
\(613\) | −3217.00 | −0.211963 | −0.105982 | − | 0.994368i | \(-0.533798\pi\) | ||||
−0.105982 | + | 0.994368i | \(0.533798\pi\) | |||||||
\(614\) | 16778.0 | 1.10278 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22212.0 | −1.44931 | −0.724653 | − | 0.689114i | \(-0.758000\pi\) | ||||
−0.724653 | + | 0.689114i | \(0.758000\pi\) | |||||||
\(618\) | 6834.00 | 0.444828 | ||||||||
\(619\) | −3076.00 | −0.199733 | −0.0998666 | − | 0.995001i | \(-0.531842\pi\) | ||||
−0.0998666 | + | 0.995001i | \(0.531842\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −162.000 | −0.0104683 | ||||||||
\(622\) | −16536.0 | −1.06597 | ||||||||
\(623\) | −15312.0 | −0.984691 | ||||||||
\(624\) | 1632.00 | 0.104699 | ||||||||
\(625\) | 15625.0 | 1.00000 | ||||||||
\(626\) | −16636.0 | −1.06215 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14644.0 | −0.930508 | ||||||||
\(629\) | 11196.0 | 0.709720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10568.0 | 0.666728 | 0.333364 | − | 0.942798i | \(-0.391816\pi\) | ||||
0.333364 | + | 0.942798i | \(0.391816\pi\) | |||||||
\(632\) | 2744.00 | 0.172706 | ||||||||
\(633\) | 10425.0 | 0.654592 | ||||||||
\(634\) | 744.000 | 0.0466057 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9000.00 | −0.561121 | ||||||||
\(637\) | 7548.00 | 0.469486 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2700.00 | 0.167152 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11904.0 | 0.733510 | 0.366755 | − | 0.930318i | \(-0.380469\pi\) | ||||
0.366755 | + | 0.930318i | \(0.380469\pi\) | |||||||
\(642\) | 180.000 | 0.0110655 | ||||||||
\(643\) | 3005.00 | 0.184301 | 0.0921506 | − | 0.995745i | \(-0.470626\pi\) | ||||
0.0921506 | + | 0.995745i | \(0.470626\pi\) | |||||||
\(644\) | 264.000 | 0.0161538 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2664.00 | 0.162250 | ||||||||
\(647\) | 9324.00 | 0.566560 | 0.283280 | − | 0.959037i | \(-0.408577\pi\) | ||||
0.283280 | + | 0.959037i | \(0.408577\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −8500.00 | −0.512919 | ||||||||
\(651\) | −3729.00 | −0.224502 | ||||||||
\(652\) | −5572.00 | −0.334688 | ||||||||
\(653\) | −21018.0 | −1.25957 | −0.629784 | − | 0.776770i | \(-0.716857\pi\) | ||||
−0.629784 | + | 0.776770i | \(0.716857\pi\) | |||||||
\(654\) | −8610.00 | −0.514798 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 288.000 | 0.0171410 | ||||||||
\(657\) | −4491.00 | −0.266683 | ||||||||
\(658\) | −396.000 | −0.0234615 | ||||||||
\(659\) | −22482.0 | −1.32894 | −0.664472 | − | 0.747313i | \(-0.731344\pi\) | ||||
−0.664472 | + | 0.747313i | \(0.731344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28273.0 | −1.66368 | −0.831840 | − | 0.555016i | \(-0.812712\pi\) | ||||
−0.831840 | + | 0.555016i | \(0.812712\pi\) | |||||||
\(662\) | −21526.0 | −1.26379 | ||||||||
\(663\) | 3672.00 | 0.215096 | ||||||||
\(664\) | 11088.0 | 0.648039 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5598.00 | −0.325703 | ||||||||
\(667\) | −252.000 | −0.0146289 | ||||||||
\(668\) | 984.000 | 0.0569942 | ||||||||
\(669\) | 13161.0 | 0.760588 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1056.00 | 0.0606192 | ||||||||
\(673\) | −26101.0 | −1.49498 | −0.747489 | − | 0.664275i | \(-0.768741\pi\) | ||||
−0.747489 | + | 0.664275i | \(0.768741\pi\) | |||||||
\(674\) | −16282.0 | −0.930503 | ||||||||
\(675\) | 3375.00 | 0.192450 | ||||||||
\(676\) | −4164.00 | −0.236914 | ||||||||
\(677\) | 3468.00 | 0.196877 | 0.0984387 | − | 0.995143i | \(-0.468615\pi\) | ||||
0.0984387 | + | 0.995143i | \(0.468615\pi\) | |||||||
\(678\) | −8604.00 | −0.487367 | ||||||||
\(679\) | 583.000 | 0.0329506 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17172.0 | −0.966274 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14478.0 | 0.811106 | 0.405553 | − | 0.914072i | \(-0.367079\pi\) | ||||
0.405553 | + | 0.914072i | \(0.367079\pi\) | |||||||
\(684\) | −1332.00 | −0.0744595 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12430.0 | 0.691807 | ||||||||
\(687\) | 8958.00 | 0.497480 | ||||||||
\(688\) | −6592.00 | −0.365287 | ||||||||
\(689\) | −25500.0 | −1.40997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7349.00 | 0.404586 | 0.202293 | − | 0.979325i | \(-0.435161\pi\) | ||||
0.202293 | + | 0.979325i | \(0.435161\pi\) | |||||||
\(692\) | −7872.00 | −0.432440 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2220.00 | 0.121427 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1008.00 | −0.0548968 | ||||||||
\(697\) | 648.000 | 0.0352148 | ||||||||
\(698\) | 12410.0 | 0.672959 | ||||||||
\(699\) | 1422.00 | 0.0769456 | ||||||||
\(700\) | −5500.00 | −0.296972 | ||||||||
\(701\) | −16782.0 | −0.904205 | −0.452102 | − | 0.891966i | \(-0.649326\pi\) | ||||
−0.452102 | + | 0.891966i | \(0.649326\pi\) | |||||||
\(702\) | −1836.00 | −0.0987113 | ||||||||
\(703\) | −11507.0 | −0.617347 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3504.00 | −0.186791 | ||||||||
\(707\) | 2310.00 | 0.122880 | ||||||||
\(708\) | −6552.00 | −0.347796 | ||||||||
\(709\) | 16418.0 | 0.869663 | 0.434831 | − | 0.900512i | \(-0.356808\pi\) | ||||
0.434831 | + | 0.900512i | \(0.356808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3087.00 | −0.162829 | ||||||||
\(712\) | 11136.0 | 0.586151 | ||||||||
\(713\) | 678.000 | 0.0356119 | ||||||||
\(714\) | 2376.00 | 0.124537 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9768.00 | −0.509843 | ||||||||
\(717\) | −9522.00 | −0.495963 | ||||||||
\(718\) | −3432.00 | −0.178386 | ||||||||
\(719\) | 16374.0 | 0.849301 | 0.424650 | − | 0.905357i | \(-0.360397\pi\) | ||||
0.424650 | + | 0.905357i | \(0.360397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12529.0 | 0.647163 | ||||||||
\(722\) | 10980.0 | 0.565974 | ||||||||
\(723\) | 10362.0 | 0.533011 | ||||||||
\(724\) | 1844.00 | 0.0946571 | ||||||||
\(725\) | 5250.00 | 0.268938 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5596.00 | −0.285480 | −0.142740 | − | 0.989760i | \(-0.545591\pi\) | ||||
−0.142740 | + | 0.989760i | \(0.545591\pi\) | |||||||
\(728\) | 2992.00 | 0.152323 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14832.0 | −0.750453 | ||||||||
\(732\) | 300.000 | 0.0151480 | ||||||||
\(733\) | 3962.00 | 0.199645 | 0.0998225 | − | 0.995005i | \(-0.468172\pi\) | ||||
0.0998225 | + | 0.995005i | \(0.468172\pi\) | |||||||
\(734\) | 2048.00 | 0.102988 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −192.000 | −0.00961578 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −324.000 | −0.0161607 | ||||||||
\(739\) | 6815.00 | 0.339234 | 0.169617 | − | 0.985510i | \(-0.445747\pi\) | ||||
0.169617 | + | 0.985510i | \(0.445747\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3774.00 | −0.187100 | ||||||||
\(742\) | −16500.0 | −0.816353 | ||||||||
\(743\) | −30360.0 | −1.49906 | −0.749529 | − | 0.661971i | \(-0.769720\pi\) | ||||
−0.749529 | + | 0.661971i | \(0.769720\pi\) | |||||||
\(744\) | 2712.00 | 0.133638 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 13322.0 | 0.653824 | ||||||||
\(747\) | −12474.0 | −0.610977 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 330.000 | 0.0160987 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32825.0 | 1.59494 | 0.797471 | − | 0.603357i | \(-0.206171\pi\) | ||||
0.797471 | + | 0.603357i | \(0.206171\pi\) | |||||||
\(752\) | 288.000 | 0.0139658 | ||||||||
\(753\) | 10638.0 | 0.514834 | ||||||||
\(754\) | −2856.00 | −0.137943 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1188.00 | −0.0571523 | ||||||||
\(757\) | 21641.0 | 1.03904 | 0.519521 | − | 0.854457i | \(-0.326110\pi\) | ||||
0.519521 | + | 0.854457i | \(0.326110\pi\) | |||||||
\(758\) | −19120.0 | −0.916187 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1176.00 | −0.0560184 | −0.0280092 | − | 0.999608i | \(-0.508917\pi\) | ||||
−0.0280092 | + | 0.999608i | \(0.508917\pi\) | |||||||
\(762\) | −7098.00 | −0.337445 | ||||||||
\(763\) | −15785.0 | −0.748959 | ||||||||
\(764\) | 8688.00 | 0.411415 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12204.0 | 0.575651 | ||||||||
\(767\) | −18564.0 | −0.873934 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 21779.0 | 1.02129 | 0.510644 | − | 0.859792i | \(-0.329407\pi\) | ||||
0.510644 | + | 0.859792i | \(0.329407\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2754.00 | 0.128642 | ||||||||
\(772\) | 9260.00 | 0.431703 | ||||||||
\(773\) | −16212.0 | −0.754340 | −0.377170 | − | 0.926144i | \(-0.623103\pi\) | ||||
−0.377170 | + | 0.926144i | \(0.623103\pi\) | |||||||
\(774\) | 7416.00 | 0.344396 | ||||||||
\(775\) | −14125.0 | −0.654690 | ||||||||
\(776\) | −424.000 | −0.0196143 | ||||||||
\(777\) | −10263.0 | −0.473852 | ||||||||
\(778\) | 20004.0 | 0.921823 | ||||||||
\(779\) | −666.000 | −0.0306315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −432.000 | −0.0197548 | ||||||||
\(783\) | 1134.00 | 0.0517572 | ||||||||
\(784\) | −3552.00 | −0.161808 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1908.00 | 0.0865854 | ||||||||
\(787\) | −4084.00 | −0.184980 | −0.0924898 | − | 0.995714i | \(-0.529483\pi\) | ||||
−0.0924898 | + | 0.995714i | \(0.529483\pi\) | |||||||
\(788\) | 16608.0 | 0.750806 | ||||||||
\(789\) | −18486.0 | −0.834118 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15774.0 | −0.709050 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 850.000 | 0.0380635 | ||||||||
\(794\) | −8518.00 | −0.380721 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5828.00 | 0.259508 | ||||||||
\(797\) | 38586.0 | 1.71491 | 0.857457 | − | 0.514556i | \(-0.172043\pi\) | ||||
0.857457 | + | 0.514556i | \(0.172043\pi\) | |||||||
\(798\) | −2442.00 | −0.108328 | ||||||||
\(799\) | 648.000 | 0.0286916 | ||||||||
\(800\) | 4000.00 | 0.176777 | ||||||||
\(801\) | −12528.0 | −0.552628 | ||||||||
\(802\) | 11544.0 | 0.508270 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6420.00 | 0.281612 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7684.00 | 0.335803 | ||||||||
\(807\) | 14670.0 | 0.639911 | ||||||||
\(808\) | −1680.00 | −0.0731463 | ||||||||
\(809\) | 9132.00 | 0.396865 | 0.198433 | − | 0.980115i | \(-0.436415\pi\) | ||||
0.198433 | + | 0.980115i | \(0.436415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37217.0 | 1.61142 | 0.805712 | − | 0.592307i | \(-0.201783\pi\) | ||||
0.805712 | + | 0.592307i | \(0.201783\pi\) | |||||||
\(812\) | −1848.00 | −0.0798671 | ||||||||
\(813\) | −6216.00 | −0.268148 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1728.00 | −0.0741325 | ||||||||
\(817\) | 15244.0 | 0.652779 | ||||||||
\(818\) | 6182.00 | 0.264240 | ||||||||
\(819\) | −3366.00 | −0.143611 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −558.000 | −0.0237203 | −0.0118601 | − | 0.999930i | \(-0.503775\pi\) | ||||
−0.0118601 | + | 0.999930i | \(0.503775\pi\) | |||||||
\(822\) | 1008.00 | 0.0427713 | ||||||||
\(823\) | 33839.0 | 1.43324 | 0.716618 | − | 0.697466i | \(-0.245689\pi\) | ||||
0.716618 | + | 0.697466i | \(0.245689\pi\) | |||||||
\(824\) | −9112.00 | −0.385232 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12012.0 | −0.505994 | ||||||||
\(827\) | 9402.00 | 0.395332 | 0.197666 | − | 0.980269i | \(-0.436664\pi\) | ||||
0.197666 | + | 0.980269i | \(0.436664\pi\) | |||||||
\(828\) | 216.000 | 0.00906584 | ||||||||
\(829\) | 5705.00 | 0.239014 | 0.119507 | − | 0.992833i | \(-0.461869\pi\) | ||||
0.119507 | + | 0.992833i | \(0.461869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19533.0 | 0.815394 | ||||||||
\(832\) | −2176.00 | −0.0906721 | ||||||||
\(833\) | −7992.00 | −0.332421 | ||||||||
\(834\) | −15216.0 | −0.631759 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3051.00 | −0.125995 | ||||||||
\(838\) | −3084.00 | −0.127130 | ||||||||
\(839\) | −24972.0 | −1.02757 | −0.513784 | − | 0.857920i | \(-0.671757\pi\) | ||||
−0.513784 | + | 0.857920i | \(0.671757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22625.0 | −0.927672 | ||||||||
\(842\) | 68.0000 | 0.00278318 | ||||||||
\(843\) | 1296.00 | 0.0529497 | ||||||||
\(844\) | −13900.0 | −0.566893 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −324.000 | −0.0131671 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12000.0 | 0.485945 | ||||||||
\(849\) | −20481.0 | −0.827922 | ||||||||
\(850\) | 9000.00 | 0.363173 | ||||||||
\(851\) | 1866.00 | 0.0751653 | ||||||||
\(852\) | −3600.00 | −0.144758 | ||||||||
\(853\) | 40487.0 | 1.62514 | 0.812572 | − | 0.582860i | \(-0.198067\pi\) | ||||
0.812572 | + | 0.582860i | \(0.198067\pi\) | |||||||
\(854\) | 550.000 | 0.0220382 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −240.000 | −0.00958298 | ||||||||
\(857\) | 40080.0 | 1.59756 | 0.798779 | − | 0.601625i | \(-0.205480\pi\) | ||||
0.798779 | + | 0.601625i | \(0.205480\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2875.00 | −0.114195 | −0.0570976 | − | 0.998369i | \(-0.518185\pi\) | ||||
−0.0570976 | + | 0.998369i | \(0.518185\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −594.000 | −0.0235116 | ||||||||
\(862\) | −16668.0 | −0.658601 | ||||||||
\(863\) | −2646.00 | −0.104370 | −0.0521848 | − | 0.998637i | \(-0.516618\pi\) | ||||
−0.0521848 | + | 0.998637i | \(0.516618\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3118.00 | −0.122349 | ||||||||
\(867\) | 10851.0 | 0.425051 | ||||||||
\(868\) | 4972.00 | 0.194425 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18190.0 | 0.707629 | ||||||||
\(872\) | 11480.0 | 0.445828 | ||||||||
\(873\) | 477.000 | 0.0184926 | ||||||||
\(874\) | 444.000 | 0.0171837 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5988.00 | 0.230954 | ||||||||
\(877\) | −12145.0 | −0.467625 | −0.233813 | − | 0.972282i | \(-0.575120\pi\) | ||||
−0.233813 | + | 0.972282i | \(0.575120\pi\) | |||||||
\(878\) | 6050.00 | 0.232549 | ||||||||
\(879\) | −18648.0 | −0.715565 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27834.0 | 1.06442 | 0.532208 | − | 0.846613i | \(-0.321362\pi\) | ||||
0.532208 | + | 0.846613i | \(0.321362\pi\) | |||||||
\(882\) | 3996.00 | 0.152554 | ||||||||
\(883\) | 47951.0 | 1.82750 | 0.913748 | − | 0.406281i | \(-0.133174\pi\) | ||||
0.913748 | + | 0.406281i | \(0.133174\pi\) | |||||||
\(884\) | −4896.00 | −0.186279 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10896.0 | 0.413158 | ||||||||
\(887\) | 48246.0 | 1.82632 | 0.913158 | − | 0.407606i | \(-0.133636\pi\) | ||||
0.913158 | + | 0.407606i | \(0.133636\pi\) | |||||||
\(888\) | 7464.00 | 0.282067 | ||||||||
\(889\) | −13013.0 | −0.490936 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −17548.0 | −0.658689 | ||||||||
\(893\) | −666.000 | −0.0249573 | ||||||||
\(894\) | −20016.0 | −0.748809 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1408.00 | −0.0524977 | ||||||||
\(897\) | 612.000 | 0.0227805 | ||||||||
\(898\) | 14544.0 | 0.540467 | ||||||||
\(899\) | −4746.00 | −0.176071 | ||||||||
\(900\) | −4500.00 | −0.166667 | ||||||||
\(901\) | 27000.0 | 0.998336 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13596.0 | 0.501048 | ||||||||
\(904\) | 11472.0 | 0.422072 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3120.00 | −0.114410 | ||||||||
\(907\) | −27937.0 | −1.02275 | −0.511374 | − | 0.859358i | \(-0.670863\pi\) | ||||
−0.511374 | + | 0.859358i | \(0.670863\pi\) | |||||||
\(908\) | 22896.0 | 0.836818 | ||||||||
\(909\) | 1890.00 | 0.0689630 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18204.0 | −0.662048 | −0.331024 | − | 0.943622i | \(-0.607394\pi\) | ||||
−0.331024 | + | 0.943622i | \(0.607394\pi\) | |||||||
\(912\) | 1776.00 | 0.0644838 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −10804.0 | −0.390990 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11944.0 | −0.430831 | ||||||||
\(917\) | 3498.00 | 0.125970 | ||||||||
\(918\) | 1944.00 | 0.0698928 | ||||||||
\(919\) | −19279.0 | −0.692008 | −0.346004 | − | 0.938233i | \(-0.612462\pi\) | ||||
−0.346004 | + | 0.938233i | \(0.612462\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25167.0 | 0.900414 | ||||||||
\(922\) | −18516.0 | −0.661380 | ||||||||
\(923\) | −10200.0 | −0.363745 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38875.0 | −1.38184 | ||||||||
\(926\) | −27184.0 | −0.964710 | ||||||||
\(927\) | 10251.0 | 0.363201 | ||||||||
\(928\) | 1344.00 | 0.0475420 | ||||||||
\(929\) | 16074.0 | 0.567676 | 0.283838 | − | 0.958872i | \(-0.408392\pi\) | ||||
0.283838 | + | 0.958872i | \(0.408392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8214.00 | 0.289155 | ||||||||
\(932\) | −1896.00 | −0.0666369 | ||||||||
\(933\) | −24804.0 | −0.870361 | ||||||||
\(934\) | 30888.0 | 1.08211 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2448.00 | 0.0854865 | ||||||||
\(937\) | 12287.0 | 0.428387 | 0.214194 | − | 0.976791i | \(-0.431288\pi\) | ||||
0.214194 | + | 0.976791i | \(0.431288\pi\) | |||||||
\(938\) | 11770.0 | 0.409706 | ||||||||
\(939\) | −24954.0 | −0.867245 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26514.0 | 0.918525 | 0.459262 | − | 0.888301i | \(-0.348114\pi\) | ||||
0.459262 | + | 0.888301i | \(0.348114\pi\) | |||||||
\(942\) | −21966.0 | −0.759757 | ||||||||
\(943\) | 108.000 | 0.00372955 | ||||||||
\(944\) | 8736.00 | 0.301200 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 55278.0 | 1.89683 | 0.948413 | − | 0.317038i | \(-0.102688\pi\) | ||||
0.948413 | + | 0.317038i | \(0.102688\pi\) | |||||||
\(948\) | 4116.00 | 0.141014 | ||||||||
\(949\) | 16966.0 | 0.580337 | ||||||||
\(950\) | −9250.00 | −0.315905 | ||||||||
\(951\) | 1116.00 | 0.0380534 | ||||||||
\(952\) | −3168.00 | −0.107852 | ||||||||
\(953\) | 17298.0 | 0.587972 | 0.293986 | − | 0.955810i | \(-0.405018\pi\) | ||||
0.293986 | + | 0.955810i | \(0.405018\pi\) | |||||||
\(954\) | −13500.0 | −0.458154 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12696.0 | 0.429517 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 37644.0 | 1.26954 | ||||||||
\(959\) | 1848.00 | 0.0622263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17022.0 | −0.571381 | ||||||||
\(962\) | 21148.0 | 0.708772 | ||||||||
\(963\) | 270.000 | 0.00903492 | ||||||||
\(964\) | −13816.0 | −0.461601 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 396.000 | 0.0131895 | ||||||||
\(967\) | 29567.0 | 0.983258 | 0.491629 | − | 0.870805i | \(-0.336402\pi\) | ||||
0.491629 | + | 0.870805i | \(0.336402\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3996.00 | 0.132477 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27294.0 | −0.902066 | −0.451033 | − | 0.892507i | \(-0.648944\pi\) | ||||
−0.451033 | + | 0.892507i | \(0.648944\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −27896.0 | −0.919121 | ||||||||
\(974\) | −7312.00 | −0.240546 | ||||||||
\(975\) | −12750.0 | −0.418797 | ||||||||
\(976\) | −400.000 | −0.0131185 | ||||||||
\(977\) | −41334.0 | −1.35352 | −0.676761 | − | 0.736202i | \(-0.736617\pi\) | ||||
−0.676761 | + | 0.736202i | \(0.736617\pi\) | |||||||
\(978\) | −8358.00 | −0.273271 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12915.0 | −0.420330 | ||||||||
\(982\) | 30252.0 | 0.983075 | ||||||||
\(983\) | −41922.0 | −1.36023 | −0.680114 | − | 0.733106i | \(-0.738070\pi\) | ||||
−0.680114 | + | 0.733106i | \(0.738070\pi\) | |||||||
\(984\) | 432.000 | 0.0139956 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3024.00 | 0.0976712 | ||||||||
\(987\) | −594.000 | −0.0191563 | ||||||||
\(988\) | 5032.00 | 0.162034 | ||||||||
\(989\) | −2472.00 | −0.0794793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44948.0 | 1.44079 | 0.720394 | − | 0.693565i | \(-0.243961\pi\) | ||||
0.720394 | + | 0.693565i | \(0.243961\pi\) | |||||||
\(992\) | −3616.00 | −0.115734 | ||||||||
\(993\) | −32289.0 | −1.03188 | ||||||||
\(994\) | −6600.00 | −0.210603 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16632.0 | 0.529122 | ||||||||
\(997\) | 60011.0 | 1.90629 | 0.953143 | − | 0.302520i | \(-0.0978278\pi\) | ||||
0.953143 | + | 0.302520i | \(0.0978278\pi\) | |||||||
\(998\) | −21922.0 | −0.695319 | ||||||||
\(999\) | −8397.00 | −0.265935 |
(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 | 726.4.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 2178.4.a.q.1.1 | 1 | |||
11.10 | odd | 2 | 726.4.a.e.1.1 | yes | 1 | ||
33.32 | even | 2 | 2178.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
726.4.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
726.4.a.e.1.1 | yes | 1 | 11.10 | odd | 2 | ||
2178.4.a.h.1.1 | 1 | 33.32 | even | 2 | |||
2178.4.a.q.1.1 | 1 | 3.2 | odd | 2 |