Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,4,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("784.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(46.2574974445\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1929.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 10x + 13 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.36922\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.261560 | −0.0503372 | −0.0251686 | − | 0.999683i | \(-0.508012\pi\) | ||||
−0.0251686 | + | 0.999683i | \(0.508012\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −19.5009 | −1.74422 | −0.872109 | − | 0.489312i | \(-0.837248\pi\) | ||||
−0.872109 | + | 0.489312i | \(0.837248\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.9316 | −0.997466 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 56.2875 | 1.54285 | 0.771424 | − | 0.636322i | \(-0.219545\pi\) | ||||
0.771424 | + | 0.636322i | \(0.219545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.0260 | 1.40864 | 0.704319 | − | 0.709883i | \(-0.251252\pi\) | ||||
0.704319 | + | 0.709883i | \(0.251252\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.10067 | 0.0877991 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.8372 | 0.268747 | 0.134373 | − | 0.990931i | \(-0.457098\pi\) | ||||
0.134373 | + | 0.990931i | \(0.457098\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −80.8106 | −0.975749 | −0.487875 | − | 0.872914i | \(-0.662228\pi\) | ||||
−0.487875 | + | 0.872914i | \(0.662228\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 89.3559 | 0.810087 | 0.405043 | − | 0.914297i | \(-0.367256\pi\) | ||||
0.405043 | + | 0.914297i | \(0.367256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 255.287 | 2.04230 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.1063 | 0.100547 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 104.118 | 0.666700 | 0.333350 | − | 0.942803i | \(-0.391821\pi\) | ||||
0.333350 | + | 0.942803i | \(0.391821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −148.437 | −0.860002 | −0.430001 | − | 0.902828i | \(-0.641487\pi\) | ||||
−0.430001 | + | 0.902828i | \(0.641487\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −14.7226 | −0.0776627 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 13.8119 | 0.0613693 | 0.0306847 | − | 0.999529i | \(-0.490231\pi\) | ||||
0.0306847 | + | 0.999529i | \(0.490231\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −17.2697 | −0.0709070 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −174.403 | −0.664323 | −0.332161 | − | 0.943223i | \(-0.607778\pi\) | ||||
−0.332161 | + | 0.943223i | \(0.607778\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −205.353 | −0.728279 | −0.364139 | − | 0.931344i | \(-0.618637\pi\) | ||||
−0.364139 | + | 0.931344i | \(0.618637\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 525.191 | 1.73980 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −116.634 | −0.361976 | −0.180988 | − | 0.983485i | \(-0.557930\pi\) | ||||
−0.180988 | + | 0.983485i | \(0.557930\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.92706 | −0.0135280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −316.249 | −0.819625 | −0.409813 | − | 0.912170i | \(-0.634406\pi\) | ||||
−0.409813 | + | 0.912170i | \(0.634406\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1097.66 | −2.69106 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 21.1368 | 0.0491165 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −539.585 | −1.19064 | −0.595322 | − | 0.803487i | \(-0.702976\pi\) | ||||
−0.595322 | + | 0.803487i | \(0.702976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −145.313 | −0.305007 | −0.152503 | − | 0.988303i | \(-0.548734\pi\) | ||||
−0.152503 | + | 0.988303i | \(0.548734\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1287.57 | −2.45697 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −476.094 | −0.868122 | −0.434061 | − | 0.900883i | \(-0.642920\pi\) | ||||
−0.434061 | + | 0.900883i | \(0.642920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −23.3719 | −0.0407775 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −131.763 | −0.220245 | −0.110123 | − | 0.993918i | \(-0.535124\pi\) | ||||
−0.110123 | + | 0.993918i | \(0.535124\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −349.608 | −0.560528 | −0.280264 | − | 0.959923i | \(-0.590422\pi\) | ||||
−0.280264 | + | 0.959923i | \(0.590422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −66.7728 | −0.102803 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 806.906 | 1.14917 | 0.574583 | − | 0.818447i | \(-0.305164\pi\) | ||||
0.574583 | + | 0.818447i | \(0.305164\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 723.463 | 0.992405 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −233.648 | −0.308990 | −0.154495 | − | 0.987994i | \(-0.549375\pi\) | ||||
−0.154495 | + | 0.987994i | \(0.549375\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −367.344 | −0.468753 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −27.2332 | −0.0335599 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 535.483 | 0.637765 | 0.318882 | − | 0.947794i | \(-0.396693\pi\) | ||||
0.318882 | + | 0.947794i | \(0.396693\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 38.8252 | 0.0432901 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1575.88 | 1.70192 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −80.7221 | −0.0844958 | −0.0422479 | − | 0.999107i | \(-0.513452\pi\) | ||||
−0.0422479 | + | 0.999107i | \(0.513452\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1515.91 | −1.53894 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 173.472 | 0.170902 | 0.0854509 | − | 0.996342i | \(-0.472767\pi\) | ||||
0.0854509 | + | 0.996342i | \(0.472767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −195.751 | −0.187262 | −0.0936308 | − | 0.995607i | \(-0.529847\pi\) | ||||
−0.0936308 | + | 0.995607i | \(0.529847\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2048.92 | −1.85118 | −0.925591 | − | 0.378524i | \(-0.876432\pi\) | ||||
−0.925591 | + | 0.378524i | \(0.876432\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1557.94 | 1.36902 | 0.684512 | − | 0.729001i | \(-0.260015\pi\) | ||||
0.684512 | + | 0.729001i | \(0.260015\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.61264 | −0.00308916 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −652.982 | −0.543605 | −0.271802 | − | 0.962353i | \(-0.587620\pi\) | ||||
−0.271802 | + | 0.962353i | \(0.587620\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1742.53 | −1.41297 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1778.18 | −1.40507 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1837.28 | 1.38038 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 45.6170 | 0.0334402 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2540.72 | −1.81799 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 819.069 | 0.572288 | 0.286144 | − | 0.958187i | \(-0.407626\pi\) | ||||
0.286144 | + | 0.958187i | \(0.407626\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 53.7120 | 0.0366595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2428.30 | −1.61955 | −0.809777 | − | 0.586737i | \(-0.800412\pi\) | ||||
−0.809777 | + | 0.586737i | \(0.800412\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −275.087 | −0.175376 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 100.337 | 0.0625719 | 0.0312859 | − | 0.999510i | \(-0.490040\pi\) | ||||
0.0312859 | + | 0.999510i | \(0.490040\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −634.299 | −0.387054 | −0.193527 | − | 0.981095i | \(-0.561993\pi\) | ||||
−0.193527 | + | 0.981095i | \(0.561993\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 30.5069 | 0.0182209 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3716.44 | 2.17332 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2030.41 | −1.16287 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2105.19 | −1.15747 | −0.578737 | − | 0.815514i | \(-0.696454\pi\) | ||||
−0.578737 | + | 0.815514i | \(0.696454\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2868.57 | 1.54596 | 0.772982 | − | 0.634428i | \(-0.218764\pi\) | ||||
0.772982 | + | 0.634428i | \(0.218764\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −507.316 | −0.268066 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2894.66 | 1.50003 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3087.39 | −1.56943 | −0.784714 | − | 0.619858i | \(-0.787190\pi\) | ||||
−0.784714 | + | 0.619858i | \(0.787190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 82.7180 | 0.0412577 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1011.12 | 0.485869 | 0.242935 | − | 0.970043i | \(-0.421890\pi\) | ||||
0.242935 | + | 0.970043i | \(0.421890\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 287.104 | 0.135461 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1052.69 | −0.487784 | −0.243892 | − | 0.969802i | \(-0.578424\pi\) | ||||
−0.243892 | + | 0.969802i | \(0.578424\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2162.43 | 0.984264 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2176.36 | 0.973277 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 306.144 | 0.134542 | 0.0672708 | − | 0.997735i | \(-0.478571\pi\) | ||||
0.0672708 | + | 0.997735i | \(0.478571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 141.134 | 0.0599337 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 188.964 | 0.0789040 | 0.0394520 | − | 0.999221i | \(-0.487439\pi\) | ||||
0.0394520 | + | 0.999221i | \(0.487439\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 468.520 | 0.192402 | 0.0962011 | − | 0.995362i | \(-0.469331\pi\) | ||||
0.0962011 | + | 0.995362i | \(0.469331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 38.0081 | 0.0153532 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −269.345 | −0.107041 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1060.30 | 0.414635 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4200.00 | −1.59111 | −0.795553 | − | 0.605884i | \(-0.792820\pi\) | ||||
−0.795553 | + | 0.605884i | \(0.792820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2925.26 | −1.09101 | −0.545505 | − | 0.838108i | \(-0.683662\pi\) | ||||
−0.545505 | + | 0.838108i | \(0.683662\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 336.776 | 0.123677 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3402.39 | −1.23051 | −0.615254 | − | 0.788329i | \(-0.710947\pi\) | ||||
−0.615254 | + | 0.788329i | \(0.710947\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −98.3992 | −0.0350519 | −0.0175260 | − | 0.999846i | \(-0.505579\pi\) | ||||
−0.0175260 | + | 0.999846i | \(0.505579\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 124.527 | 0.0436989 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3401.03 | 1.15872 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2406.50 | −0.808034 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4548.63 | −1.50543 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2692.24 | −0.878396 | −0.439198 | − | 0.898390i | \(-0.644737\pi\) | ||||
−0.439198 | + | 0.898390i | \(0.644737\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.4640 | 0.0110865 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4004.57 | 1.27028 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 91.4435 | 0.0282154 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1243.75 | 0.378567 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6075.65 | 1.82447 | 0.912233 | − | 0.409672i | \(-0.134357\pi\) | ||||
0.912233 | + | 0.409672i | \(0.134357\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6875.28 | −2.03712 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2991.15 | −0.874581 | −0.437290 | − | 0.899320i | \(-0.644062\pi\) | ||||
−0.437290 | + | 0.899320i | \(0.644062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6181.17 | 1.78368 | 0.891841 | − | 0.452349i | \(-0.149414\pi\) | ||||
0.891841 | + | 0.452349i | \(0.149414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2913.44 | 0.819166 | 0.409583 | − | 0.912273i | \(-0.365674\pi\) | ||||
0.409583 | + | 0.912273i | \(0.365674\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2274.48 | 0.631366 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −211.054 | −0.0578458 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3407.25 | −0.922163 | −0.461081 | − | 0.887358i | \(-0.652538\pi\) | ||||
−0.461081 | + | 0.887358i | \(0.652538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −244.124 | −0.0652508 | −0.0326254 | − | 0.999468i | \(-0.510387\pi\) | ||||
−0.0326254 | + | 0.999468i | \(0.510387\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −570.100 | −0.150502 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5335.60 | −1.37448 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 61.1129 | 0.0155537 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4795.49 | −1.20593 | −0.602966 | − | 0.797767i | \(-0.706014\pi\) | ||||
−0.602966 | + | 0.797767i | \(0.706014\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5029.62 | 1.24984 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 96.0824 | 0.0235957 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4782.35 | −1.16076 | −0.580380 | − | 0.814346i | \(-0.697096\pi\) | ||||
−0.580380 | + | 0.814346i | \(0.697096\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2804.07 | −0.665011 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7649.05 | −1.79339 | −0.896693 | − | 0.442652i | \(-0.854038\pi\) | ||||
−0.896693 | + | 0.442652i | \(0.854038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6167.15 | 1.42960 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −140.061 | −0.0321033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4200.71 | −0.952125 | −0.476062 | − | 0.879412i | \(-0.657936\pi\) | ||||
−0.476062 | + | 0.879412i | \(0.657936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5063.22 | −1.13494 | −0.567470 | − | 0.823394i | \(-0.692078\pi\) | ||||
−0.567470 | + | 0.823394i | \(0.692078\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14369.5 | 3.15095 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5346.39 | −1.15969 | −0.579843 | − | 0.814728i | \(-0.696886\pi\) | ||||
−0.579843 | + | 0.814728i | \(0.696886\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3997.64 | 0.857823 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6367.90 | 1.35188 | 0.675938 | − | 0.736958i | \(-0.263739\pi\) | ||||
0.675938 | + | 0.736958i | \(0.263739\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2124.38 | −0.446224 | −0.223112 | − | 0.974793i | \(-0.571622\pi\) | ||||
−0.223112 | + | 0.974793i | \(0.571622\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −412.188 | −0.0856699 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4558.16 | −0.927775 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.1137 | 0.00425328 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5921.90 | 1.18075 | 0.590377 | − | 0.807128i | \(-0.298979\pi\) | ||||
0.590377 | + | 0.807128i | \(0.298979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10522.4 | 2.07674 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 794.011 | 0.155129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5899.81 | 1.14112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −45.3733 | −0.00860273 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2833.74 | 0.531998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6630.60 | −1.23267 | −0.616333 | − | 0.787486i | \(-0.711382\pi\) | ||||
−0.616333 | + | 0.787486i | \(0.711382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51.2007 | 0.00942623 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2181.45 | 0.397746 | 0.198873 | − | 0.980025i | \(-0.436272\pi\) | ||||
0.198873 | + | 0.980025i | \(0.436272\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8996.44 | 1.62463 | 0.812314 | − | 0.583220i | \(-0.198208\pi\) | ||||
0.812314 | + | 0.583220i | \(0.198208\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −314.569 | −0.0557348 | −0.0278674 | − | 0.999612i | \(-0.508872\pi\) | ||||
−0.0278674 | + | 0.999612i | \(0.508872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5860.57 | 1.02862 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 535.915 | 0.0931834 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1522.25 | −0.262229 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16855.6 | 2.87686 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −407.495 | −0.0689129 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7006.07 | 1.16341 | 0.581704 | − | 0.813400i | \(-0.302386\pi\) | ||||
0.581704 | + | 0.813400i | \(0.302386\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −371.977 | −0.0612138 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9284.29 | 1.51419 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4697.83 | 0.759368 | 0.379684 | − | 0.925116i | \(-0.376033\pi\) | ||||
0.379684 | + | 0.925116i | \(0.376033\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 170.794 | 0.0273636 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8355.15 | −1.32685 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 455.775 | 0.0711249 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8094.65 | −1.25229 | −0.626143 | − | 0.779708i | \(-0.715368\pi\) | ||||
−0.626143 | + | 0.779708i | \(0.715368\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10531.7 | 1.61532 | 0.807662 | − | 0.589646i | \(-0.200733\pi\) | ||||
0.807662 | + | 0.589646i | \(0.200733\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 931.385 | 0.141634 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11986.5 | 1.80730 | 0.903648 | − | 0.428276i | \(-0.140879\pi\) | ||||
0.903648 | + | 0.428276i | \(0.140879\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2569.51 | 0.384155 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8073.90 | −1.18698 | −0.593488 | − | 0.804843i | \(-0.702250\pi\) | ||||
−0.593488 | + | 0.804843i | \(0.702250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −328.641 | −0.0479138 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −480.560 | −0.0694845 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6817.69 | 0.977683 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2904.85 | 0.413166 | 0.206583 | − | 0.978429i | \(-0.433766\pi\) | ||||
0.206583 | + | 0.978429i | \(0.433766\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4696.96 | 0.662640 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5116.71 | 0.710277 | 0.355139 | − | 0.934814i | \(-0.384434\pi\) | ||||
0.355139 | + | 0.934814i | \(0.384434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 664.550 | 0.0915126 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6874.52 | 0.939140 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7841.91 | −1.06283 | −0.531414 | − | 0.847112i | \(-0.678339\pi\) | ||||
−0.531414 | + | 0.847112i | \(0.678339\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −214.236 | −0.0288074 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4959.17 | −0.661623 | −0.330812 | − | 0.943697i | \(-0.607322\pi\) | ||||
−0.330812 | + | 0.943697i | \(0.607322\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5530.47 | 0.726433 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2188.94 | 0.285306 | 0.142653 | − | 0.989773i | \(-0.454437\pi\) | ||||
0.142653 | + | 0.989773i | \(0.454437\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1683.22 | 0.217708 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 635.146 | 0.0815239 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15735.4 | −2.00439 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6953.85 | 0.879103 | 0.439551 | − | 0.898217i | \(-0.355137\pi\) | ||||
0.439551 | + | 0.898217i | \(0.355137\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3768.06 | −0.469246 | −0.234623 | − | 0.972086i | \(-0.575386\pi\) | ||||
−0.234623 | + | 0.972086i | \(0.575386\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9800.69 | −1.21143 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14108.2 | −1.73097 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 777.438 | 0.0946835 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16138.5 | −1.95110 | −0.975548 | − | 0.219787i | \(-0.929464\pi\) | ||||
−0.975548 | + | 0.219787i | \(0.929464\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −26.2441 | −0.00314969 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4556.36 | 0.538946 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 165.907 | 0.0194832 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9445.77 | 1.10133 | 0.550664 | − | 0.834727i | \(-0.314375\pi\) | ||||
0.550664 | + | 0.834727i | \(0.314375\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11555.5 | −1.33772 | −0.668858 | − | 0.743390i | \(-0.733217\pi\) | ||||
−0.668858 | + | 0.743390i | \(0.733217\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3141.15 | 0.361059 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4808.89 | 0.548860 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −972.071 | −0.109399 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9497.23 | −1.06141 | −0.530703 | − | 0.847558i | \(-0.678072\pi\) | ||||
−0.530703 | + | 0.847558i | \(0.678072\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10826.5 | 1.20160 | 0.600798 | − | 0.799401i | \(-0.294850\pi\) | ||||
0.600798 | + | 0.799401i | \(0.294850\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 531.073 | 0.0585357 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7220.91 | −0.790442 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12635.7 | 1.37373 | 0.686867 | − | 0.726783i | \(-0.258985\pi\) | ||||
0.686867 | + | 0.726783i | \(0.258985\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4875.92 | 0.522939 | 0.261470 | − | 0.965212i | \(-0.415793\pi\) | ||||
0.261470 | + | 0.965212i | \(0.415793\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10442.4 | −1.11240 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 550.632 | 0.0582640 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5294.85 | −0.556524 | −0.278262 | − | 0.960505i | \(-0.589758\pi\) | ||||
−0.278262 | + | 0.960505i | \(0.589758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9816.74 | −1.02495 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −750.302 | −0.0778196 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1899.61 | 0.194442 | 0.0972211 | − | 0.995263i | \(-0.469005\pi\) | ||||
0.0972211 | + | 0.995263i | \(0.469005\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 265.724 | 0.0270217 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4665.78 | 0.471382 | 0.235691 | − | 0.971828i | \(-0.424265\pi\) | ||||
0.235691 | + | 0.971828i | \(0.424265\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1960.56 | −0.196792 | −0.0983962 | − | 0.995147i | \(-0.531371\pi\) | ||||
−0.0983962 | + | 0.995147i | \(0.531371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −757.127 | −0.0755074 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10206.4 | −1.01134 | −0.505671 | − | 0.862726i | \(-0.668755\pi\) | ||||
−0.505671 | + | 0.862726i | \(0.668755\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 807.537 | 0.0790007 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11558.8 | −1.12362 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20629.9 | −1.99277 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8517.08 | 0.817548 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10961.2 | 1.04558 | 0.522789 | − | 0.852462i | \(-0.324892\pi\) | ||||
0.522789 | + | 0.852462i | \(0.324892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 911.945 | 0.0864472 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1574.16 | 0.147379 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17409.7 | 1.61994 | 0.809970 | − | 0.586471i | \(-0.199483\pi\) | ||||
0.809970 | + | 0.586471i | \(0.199483\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −264.467 | −0.0244573 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5282.62 | 0.485543 | 0.242771 | − | 0.970084i | \(-0.421944\pi\) | ||||
0.242771 | + | 0.970084i | \(0.421944\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1961.30 | 0.179174 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29561.7 | 2.68424 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18977.1 | −1.70246 | −0.851232 | − | 0.524789i | \(-0.824144\pi\) | ||||
−0.851232 | + | 0.524789i | \(0.824144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 275.343 | 0.0245537 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8525.73 | 0.755753 | 0.377876 | − | 0.925856i | \(-0.376654\pi\) | ||||
0.377876 | + | 0.925856i | \(0.376654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3382.86 | −0.298090 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −565.604 | −0.0495451 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10235.7 | −0.891333 | −0.445666 | − | 0.895199i | \(-0.647033\pi\) | ||||
−0.445666 | + | 0.895199i | \(0.647033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1139.94 | −0.0981086 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3817.34 | 0.326625 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6565.07 | −0.558474 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −80.0750 | −0.00677245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1592.37 | −0.133902 | −0.0669511 | − | 0.997756i | \(-0.521327\pi\) | ||||
−0.0669511 | + | 0.997756i | \(0.521327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14008.0 | −1.17118 | −0.585589 | − | 0.810608i | \(-0.699137\pi\) | ||||
−0.585589 | + | 0.810608i | \(0.699137\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2796.14 | −0.231123 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4182.52 | −0.343759 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14531.9 | 1.18763 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11515.2 | −0.935791 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 39955.9 | 3.22887 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −49.4254 | −0.00397181 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8928.02 | 0.709511 | 0.354755 | − | 0.934959i | \(-0.384564\pi\) | ||||
0.354755 | + | 0.934959i | \(0.384564\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −122.546 | −0.00968500 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −30381.3 | −2.38788 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9736.48 | −0.761063 | −0.380532 | − | 0.924768i | \(-0.624259\pi\) | ||||
−0.380532 | + | 0.924768i | \(0.624259\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3913.51 | 0.304234 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8413.88 | −0.650532 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 70.4500 | 0.00538817 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4432.76 | 0.337203 | 0.168602 | − | 0.985684i | \(-0.446075\pi\) | ||||
0.168602 | + | 0.985684i | \(0.446075\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13558.6 | −1.02588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −277.332 | −0.0208716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1402.96 | 0.105022 | 0.0525112 | − | 0.998620i | \(-0.483277\pi\) | ||||
0.0525112 | + | 0.998620i | \(0.483277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12733.8 | 0.948165 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5798.54 | 0.427218 | 0.213609 | − | 0.976919i | \(-0.431478\pi\) | ||||
0.213609 | + | 0.976919i | \(0.431478\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13761.8 | −1.00861 | −0.504303 | − | 0.863527i | \(-0.668250\pi\) | ||||
−0.504303 | + | 0.863527i | \(0.668250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1098.55 | 0.0800919 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22811.4 | 1.65444 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7420.50 | 0.535389 | 0.267695 | − | 0.963504i | \(-0.413738\pi\) | ||||
0.267695 | + | 0.963504i | \(0.413738\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 765.131 | 0.0549184 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17800.9 | −1.26456 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 34676.3 | 2.45075 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19685.1 | 1.38414 | 0.692072 | − | 0.721828i | \(-0.256698\pi\) | ||||
0.692072 | + | 0.721828i | \(0.256698\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11995.3 | 0.839146 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 889.928 | 0.0619404 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24079.3 | −1.66749 | −0.833743 | − | 0.552153i | \(-0.813807\pi\) | ||||
−0.833743 | + | 0.552153i | \(0.813807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 25.7373 | 0.00176442 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17966.4 | 1.22552 | 0.612759 | − | 0.790270i | \(-0.290060\pi\) | ||||
0.612759 | + | 0.790270i | \(0.290060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12893.6 | −0.875111 | −0.437555 | − | 0.899192i | \(-0.644156\pi\) | ||||
−0.437555 | + | 0.899192i | \(0.644156\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12822.0 | 0.865922 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −35828.8 | −2.40768 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25200.5 | −1.68510 | −0.842550 | − | 0.538619i | \(-0.818946\pi\) | ||||
−0.842550 | + | 0.538619i | \(0.818946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7700.90 | −0.509894 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12814.9 | 0.844357 | 0.422178 | − | 0.906513i | \(-0.361266\pi\) | ||||
0.422178 | + | 0.906513i | \(0.361266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −889.574 | −0.0583270 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7597.02 | 0.495696 | 0.247848 | − | 0.968799i | \(-0.420277\pi\) | ||||
0.247848 | + | 0.968799i | \(0.420277\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22412.8 | −1.45533 | −0.727664 | − | 0.685934i | \(-0.759394\pi\) | ||||
−0.727664 | + | 0.685934i | \(0.759394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1260.49 | 0.0814518 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17635.5 | 1.12867 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1189.74 | 0.0757793 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 260.178 | 0.0164928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8993.43 | −0.567389 | −0.283695 | − | 0.958915i | \(-0.591560\pi\) | ||||
−0.283695 | + | 0.958915i | \(0.591560\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 704.183 | 0.0442160 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15972.6 | −0.998195 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3548.59 | 0.219687 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18152.7 | −1.11855 | −0.559273 | − | 0.828983i | \(-0.688920\pi\) | ||||
−0.559273 | + | 0.828983i | \(0.688920\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25767.3 | −1.58034 | −0.790172 | − | 0.612885i | \(-0.790009\pi\) | ||||
−0.790172 | + | 0.612885i | \(0.790009\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1047.44 | −0.0639422 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6962.52 | −0.423068 | −0.211534 | − | 0.977371i | \(-0.567846\pi\) | ||||
−0.211534 | + | 0.977371i | \(0.567846\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −30371.9 | −1.83698 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12157.8 | −0.728595 | −0.364297 | − | 0.931283i | \(-0.618691\pi\) | ||||
−0.364297 | + | 0.931283i | \(0.618691\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 47354.2 | 2.82486 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9415.50 | 0.559108 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3853.23 | 0.227770 | 0.113885 | − | 0.993494i | \(-0.463670\pi\) | ||||
0.113885 | + | 0.993494i | \(0.463670\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4579.02 | 0.269445 | 0.134723 | − | 0.990883i | \(-0.456986\pi\) | ||||
0.134723 | + | 0.990883i | \(0.456986\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −325.314 | −0.0190560 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9303.60 | 0.540085 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1589.15 | −0.0918386 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8179.31 | −0.470579 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21847.0 | −1.25132 | −0.625661 | − | 0.780095i | \(-0.715171\pi\) | ||||
−0.625661 | + | 0.780095i | \(0.715171\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3601.16 | 0.205347 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4823.04 | −0.273803 | −0.136901 | − | 0.990585i | \(-0.543714\pi\) | ||||
−0.136901 | + | 0.990585i | \(0.543714\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 782.366 | 0.0440240 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16222.7 | 0.908850 | 0.454425 | − | 0.890785i | \(-0.349845\pi\) | ||||
0.454425 | + | 0.890785i | \(0.349845\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1956.66 | −0.109139 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1616.75 | −0.0897856 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −20880.6 | −1.15456 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25356.2 | 1.39594 | 0.697971 | − | 0.716126i | \(-0.254086\pi\) | ||||
0.697971 | + | 0.716126i | \(0.254086\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12369.4 | 0.675107 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3285.28 | −0.178535 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −762.039 | −0.0412345 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11538.7 | −0.621701 | −0.310850 | − | 0.950459i | \(-0.600614\pi\) | ||||
−0.310850 | + | 0.950459i | \(0.600614\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1116.15 | −0.0598810 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −594.914 | −0.0317812 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33771.6 | −1.78888 | −0.894442 | − | 0.447185i | \(-0.852427\pi\) | ||||
−0.894442 | + | 0.447185i | \(0.852427\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21731.3 | −1.14625 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13263.7 | −0.696676 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −72474.0 | −3.79074 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 891.201 | 0.0464191 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14047.9 | 0.728647 | 0.364324 | − | 0.931272i | \(-0.381300\pi\) | ||||
0.364324 | + | 0.931272i | \(0.381300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 63.8532 | 0.00328454 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26580.1 | 1.36160 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10726.8 | 0.547226 | 0.273613 | − | 0.961840i | \(-0.411781\pi\) | ||||
0.273613 | + | 0.961840i | \(0.411781\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19384.4 | −0.984829 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3868.27 | −0.195723 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10039.3 | 0.505880 | 0.252940 | − | 0.967482i | \(-0.418603\pi\) | ||||
0.252940 | + | 0.967482i | \(0.418603\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −26798.2 | −1.33938 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6984.31 | −0.347661 | −0.173831 | − | 0.984776i | \(-0.555615\pi\) | ||||
−0.173831 | + | 0.984776i | \(0.555615\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1395.58 | 0.0691874 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20657.2 | 1.01997 | 0.509986 | − | 0.860183i | \(-0.329651\pi\) | ||||
0.509986 | + | 0.860183i | \(0.329651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 41053.1 | 2.01889 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6292.51 | 0.308207 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29782.2 | −1.44709 | −0.723547 | − | 0.690275i | \(-0.757489\pi\) | ||||
−0.723547 | + | 0.690275i | \(0.757489\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1254.31 | 0.0607032 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −55939.7 | −2.69650 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17157.0 | −0.823754 | −0.411877 | − | 0.911240i | \(-0.635127\pi\) | ||||
−0.411877 | + | 0.911240i | \(0.635127\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1315.55 | −0.0629135 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38481.4 | 1.83305 | 0.916523 | − | 0.399981i | \(-0.130983\pi\) | ||||
0.916523 | + | 0.399981i | \(0.130983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9893.14 | 0.467565 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35626.6 | −1.67719 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17934.4 | 0.841002 | 0.420501 | − | 0.907292i | \(-0.361854\pi\) | ||||
0.420501 | + | 0.907292i | \(0.361854\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1250.87 | 0.0584294 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11443.2 | 0.532451 | 0.266226 | − | 0.963911i | \(-0.414223\pi\) | ||||
0.266226 | + | 0.963911i | \(0.414223\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37894.0 | −1.75638 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14093.7 | 0.648213 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7416.62 | −0.339805 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1468.73 | 0.0670347 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 60207.0 | 2.73743 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11578.5 | −0.524431 | −0.262216 | − | 0.965009i | \(-0.584453\pi\) | ||||
−0.262216 | + | 0.965009i | \(0.584453\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2000.69 | 0.0902741 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9594.43 | −0.429645 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1613.08 | −0.0719623 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36578.7 | −1.62570 | −0.812850 | − | 0.582473i | \(-0.802085\pi\) | ||||
−0.812850 | + | 0.582473i | \(0.802085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2197.07 | −0.0972800 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14421.4 | −0.636149 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19678.6 | −0.864809 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1098.74 | 0.0479273 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5876.16 | 0.255370 | 0.127685 | − | 0.991815i | \(-0.459245\pi\) | ||||
0.127685 | + | 0.991815i | \(0.459245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3272.77 | −0.141705 | −0.0708523 | − | 0.997487i | \(-0.522572\pi\) | ||||
−0.0708523 | + | 0.997487i | \(0.522572\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1324.33 | 0.0571297 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19717.7 | −0.847462 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16594.7 | 0.710617 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11801.6 | 0.501679 | 0.250840 | − | 0.968029i | \(-0.419293\pi\) | ||||
0.250840 | + | 0.968029i | \(0.419293\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9636.61 | −0.408154 | −0.204077 | − | 0.978955i | \(-0.565419\pi\) | ||||
−0.204077 | + | 0.978955i | \(0.565419\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3758.48 | −0.158610 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28192.3 | 1.18542 | 0.592710 | − | 0.805416i | \(-0.298058\pi\) | ||||
0.592710 | + | 0.805416i | \(0.298058\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24633.1 | 1.03202 | 0.516010 | − | 0.856583i | \(-0.327417\pi\) | ||||
0.516010 | + | 0.856583i | \(0.327417\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1398.40 | 0.0583754 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20528.5 | 0.850801 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2093.90 | −0.0864706 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3682.43 | −0.151527 | −0.0757637 | − | 0.997126i | \(-0.524139\pi\) | ||||
−0.0757637 | + | 0.997126i | \(0.524139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13548.4 | −0.555511 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1665.59 | −0.0680497 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −42169.4 | −1.71677 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 555.654 | 0.0224617 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1234.18 | 0.0497145 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 790.015 | 0.0317112 | 0.0158556 | − | 0.999874i | \(-0.494953\pi\) | ||||
0.0158556 | + | 0.999874i | \(0.494953\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −42441.1 | −1.69761 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15450.3 | 0.615835 | 0.307918 | − | 0.951413i | \(-0.400368\pi\) | ||||
0.307918 | + | 0.951413i | \(0.400368\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19601.6 | 0.778579 | 0.389289 | − | 0.921116i | \(-0.372721\pi\) | ||||
0.389289 | + | 0.921116i | \(0.372721\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −38572.6 | −1.52147 | −0.760734 | − | 0.649064i | \(-0.775161\pi\) | ||||
−0.760734 | + | 0.649064i | \(0.775161\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5970.10 | −0.234670 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1192.23 | 0.0467016 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 45418.7 | 1.77299 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31434.6 | −1.22287 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2173.97 | 0.0842817 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6319.27 | −0.243314 | −0.121657 | − | 0.992572i | \(-0.538821\pi\) | ||||
−0.121657 | + | 0.992572i | \(0.538821\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1548.93 | −0.0594359 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15224.6 | 0.582213 | 0.291106 | − | 0.956691i | \(-0.405977\pi\) | ||||
0.291106 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33244.2 | 1.26700 | 0.633498 | − | 0.773744i | \(-0.281618\pi\) | ||||
0.633498 | + | 0.773744i | \(0.281618\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2752.24 | −0.104537 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15940.1 | 0.603401 | 0.301700 | − | 0.953403i | \(-0.402446\pi\) | ||||
0.301700 | + | 0.953403i | \(0.402446\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40721.9 | 1.53113 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9425.31 | 0.353198 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3684.97 | −0.137626 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1543.15 | −0.0574408 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15455.0 | −0.573364 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5957.25 | −0.220272 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9136.58 | −0.335591 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22038.3 | 0.806804 | 0.403402 | − | 0.915023i | \(-0.367828\pi\) | ||||
0.403402 | + | 0.915023i | \(0.367828\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4671.87 | −0.170469 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2241.91 | −0.0815342 | −0.0407671 | − | 0.999169i | \(-0.512980\pi\) | ||||
−0.0407671 | + | 0.999169i | \(0.512980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13151.5 | −0.476725 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −741.193 | −0.0267793 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35585.4 | 1.27732 | 0.638658 | − | 0.769491i | \(-0.279490\pi\) | ||||
0.638658 | + | 0.769491i | \(0.279490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1734.30 | 0.0620490 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8699.79 | −0.310246 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3526.00 | 0.125334 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5271.89 | 0.186787 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45914.2 | −1.62153 | −0.810763 | − | 0.585375i | \(-0.800947\pi\) | ||||
−0.810763 | + | 0.585375i | \(0.800947\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −570.581 | −0.0200214 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20676.9 | −0.723214 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42963.4 | 1.49792 | 0.748962 | − | 0.662613i | \(-0.230553\pi\) | ||||
0.748962 | + | 0.662613i | \(0.230553\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2353.11 | −0.0817793 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21420.7 | 0.742077 | 0.371039 | − | 0.928617i | \(-0.379002\pi\) | ||||
0.371039 | + | 0.928617i | \(0.379002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15584.0 | −0.538159 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6523.67 | 0.223855 | 0.111928 | − | 0.993716i | \(-0.464298\pi\) | ||||
0.111928 | + | 0.993716i | \(0.464298\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23083.2 | −0.789581 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 82.2786 | 0.00280554 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32537.1 | −1.10596 | −0.552979 | − | 0.833195i | \(-0.686509\pi\) | ||||
−0.552979 | + | 0.833195i | \(0.686509\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 81904.0 | 2.77524 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1532.89 | −0.0517777 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7757.48 | −0.260397 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 55180.7 | 1.84649 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57045.4 | 1.90296 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9013.22 | −0.299737 | −0.149868 | − | 0.988706i | \(-0.547885\pi\) | ||||
−0.149868 | + | 0.988706i | \(0.547885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 398.159 | 0.0131999 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −47164.6 | −1.55879 | −0.779395 | − | 0.626533i | \(-0.784473\pi\) | ||||
−0.779395 | + | 0.626533i | \(0.784473\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4408.74 | −0.144813 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29115.2 | 0.953407 | 0.476703 | − | 0.879064i | \(-0.341832\pi\) | ||||
0.476703 | + | 0.879064i | \(0.341832\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30141.0 | 0.983974 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41957.8 | −1.36556 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38771.1 | −1.25799 | −0.628996 | − | 0.777409i | \(-0.716534\pi\) | ||||
−0.628996 | + | 0.777409i | \(0.716534\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 66349.8 | 2.14627 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18349.5 | −0.589969 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18648.2 | 0.597760 | 0.298880 | − | 0.954291i | \(-0.403387\pi\) | ||||
0.298880 | + | 0.954291i | \(0.403387\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1832.51 | −0.0585628 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1918.88 | 0.0611382 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16939.6 | −0.538097 | −0.269049 | − | 0.963127i | \(-0.586709\pi\) | ||||
−0.269049 | + | 0.963127i | \(0.586709\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 194.836 | 0.00617050 |
(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 | 784.4.a.bb.1.2 | 3 | ||
4.3 | odd | 2 | 392.4.a.l.1.2 | 3 | |||
7.3 | odd | 6 | 112.4.i.e.65.2 | 6 | |||
7.5 | odd | 6 | 112.4.i.e.81.2 | 6 | |||
7.6 | odd | 2 | 784.4.a.be.1.2 | 3 | |||
28.3 | even | 6 | 56.4.i.b.9.2 | ✓ | 6 | ||
28.11 | odd | 6 | 392.4.i.m.177.2 | 6 | |||
28.19 | even | 6 | 56.4.i.b.25.2 | yes | 6 | ||
28.23 | odd | 6 | 392.4.i.m.361.2 | 6 | |||
28.27 | even | 2 | 392.4.a.i.1.2 | 3 | |||
56.3 | even | 6 | 448.4.i.j.65.2 | 6 | |||
56.5 | odd | 6 | 448.4.i.m.193.2 | 6 | |||
56.19 | even | 6 | 448.4.i.j.193.2 | 6 | |||
56.45 | odd | 6 | 448.4.i.m.65.2 | 6 | |||
84.47 | odd | 6 | 504.4.s.h.361.3 | 6 | |||
84.59 | odd | 6 | 504.4.s.h.289.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.4.i.b.9.2 | ✓ | 6 | 28.3 | even | 6 | ||
56.4.i.b.25.2 | yes | 6 | 28.19 | even | 6 | ||
112.4.i.e.65.2 | 6 | 7.3 | odd | 6 | |||
112.4.i.e.81.2 | 6 | 7.5 | odd | 6 | |||
392.4.a.i.1.2 | 3 | 28.27 | even | 2 | |||
392.4.a.l.1.2 | 3 | 4.3 | odd | 2 | |||
392.4.i.m.177.2 | 6 | 28.11 | odd | 6 | |||
392.4.i.m.361.2 | 6 | 28.23 | odd | 6 | |||
448.4.i.j.65.2 | 6 | 56.3 | even | 6 | |||
448.4.i.j.193.2 | 6 | 56.19 | even | 6 | |||
448.4.i.m.65.2 | 6 | 56.45 | odd | 6 | |||
448.4.i.m.193.2 | 6 | 56.5 | odd | 6 | |||
504.4.s.h.289.3 | 6 | 84.59 | odd | 6 | |||
504.4.s.h.361.3 | 6 | 84.47 | odd | 6 | |||
784.4.a.bb.1.2 | 3 | 1.1 | even | 1 | trivial | ||
784.4.a.be.1.2 | 3 | 7.6 | odd | 2 |