Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(1,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.36248.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 54x - 90 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 312) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-5.70213\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.8819 | 1.68885 | 0.844423 | − | 0.535676i | \(-0.179943\pi\) | ||||
0.844423 | + | 0.535676i | \(0.179943\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 17.9266 | 0.967948 | 0.483974 | − | 0.875082i | \(-0.339193\pi\) | ||||
0.483974 | + | 0.875082i | \(0.339193\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −44.5723 | −1.22173 | −0.610866 | − | 0.791734i | \(-0.709179\pi\) | ||||
−0.610866 | + | 0.791734i | \(0.709179\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 56.6456 | 0.975056 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 34.0000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 152.835 | 1.84541 | 0.922704 | − | 0.385510i | \(-0.125974\pi\) | ||||
0.922704 | + | 0.385510i | \(0.125974\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 53.7799 | 0.558845 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −107.234 | −0.972168 | −0.486084 | − | 0.873912i | \(-0.661575\pi\) | ||||
−0.486084 | + | 0.873912i | \(0.661575\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 231.525 | 1.85220 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 149.674 | 0.958407 | 0.479204 | − | 0.877704i | \(-0.340926\pi\) | ||||
0.479204 | + | 0.877704i | \(0.340926\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.162885 | −0.000943710 0 | −0.000471855 | − | 1.00000i | \(-0.500150\pi\) | ||||
−0.000471855 | 1.00000i | \(0.500150\pi\) | ||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −133.717 | −0.705367 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 338.489 | 1.63472 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −256.342 | −1.13898 | −0.569491 | − | 0.821997i | \(-0.692860\pi\) | ||||
−0.569491 | + | 0.821997i | \(0.692860\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 39.0000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 414.723 | 1.57973 | 0.789865 | − | 0.613281i | \(-0.210151\pi\) | ||||
0.789865 | + | 0.613281i | \(0.210151\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −471.076 | −1.67066 | −0.835330 | − | 0.549749i | \(-0.814723\pi\) | ||||
−0.835330 | + | 0.549749i | \(0.814723\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 169.937 | 0.562949 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −632.710 | −1.96362 | −0.981812 | − | 0.189857i | \(-0.939197\pi\) | ||||
−0.981812 | + | 0.189857i | \(0.939197\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.6354 | −0.0630771 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 102.000 | 0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −236.489 | −0.612910 | −0.306455 | − | 0.951885i | \(-0.599143\pi\) | ||||
−0.306455 | + | 0.951885i | \(0.599143\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −841.608 | −2.06332 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 458.505 | 1.06545 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 108.018 | 0.238351 | 0.119176 | − | 0.992873i | \(-0.461975\pi\) | ||||
0.119176 | + | 0.992873i | \(0.461975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 888.292 | 1.86449 | 0.932247 | − | 0.361822i | \(-0.117845\pi\) | ||||
0.932247 | + | 0.361822i | \(0.117845\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 161.340 | 0.322649 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 245.464 | 0.468402 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −637.149 | −1.16179 | −0.580897 | − | 0.813977i | \(-0.697298\pi\) | ||||
−0.580897 | + | 0.813977i | \(0.697298\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −321.702 | −0.561281 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 362.597 | 0.606090 | 0.303045 | − | 0.952976i | \(-0.401997\pi\) | ||||
0.303045 | + | 0.952976i | \(0.401997\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 723.177 | 1.15947 | 0.579736 | − | 0.814804i | \(-0.303156\pi\) | ||||
0.579736 | + | 0.814804i | \(0.303156\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 694.576 | 1.06937 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −799.031 | −1.18257 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 964.684 | 1.37387 | 0.686933 | − | 0.726721i | \(-0.258957\pi\) | ||||
0.686933 | + | 0.726721i | \(0.258957\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 431.868 | 0.571128 | 0.285564 | − | 0.958360i | \(-0.407819\pi\) | ||||
0.285564 | + | 0.958360i | \(0.407819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 641.984 | 0.819211 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 449.023 | 0.553337 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 117.359 | 0.139775 | 0.0698877 | − | 0.997555i | \(-0.477736\pi\) | ||||
0.0698877 | + | 0.997555i | \(0.477736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 233.046 | 0.268460 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.488655 | −0.000544851 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2885.81 | 3.11661 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1153.38 | −1.20730 | −0.603652 | − | 0.797248i | \(-0.706288\pi\) | ||||
−0.603652 | + | 0.797248i | \(0.706288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −401.151 | −0.407244 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −848.183 | −0.835618 | −0.417809 | − | 0.908535i | \(-0.637202\pi\) | ||||
−0.417809 | + | 0.908535i | \(0.637202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 710.562 | 0.679745 | 0.339873 | − | 0.940471i | \(-0.389616\pi\) | ||||
0.339873 | + | 0.940471i | \(0.389616\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1015.47 | 0.943803 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −533.245 | −0.481782 | −0.240891 | − | 0.970552i | \(-0.577440\pi\) | ||||
−0.240891 | + | 0.970552i | \(0.577440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −667.057 | −0.586170 | −0.293085 | − | 0.956086i | \(-0.594682\pi\) | ||||
−0.293085 | + | 0.956086i | \(0.594682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −769.026 | −0.657592 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 302.916 | 0.252176 | 0.126088 | − | 0.992019i | \(-0.459758\pi\) | ||||
0.126088 | + | 0.992019i | \(0.459758\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2024.78 | −1.64184 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 117.000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 609.506 | 0.469524 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 655.688 | 0.492628 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1244.17 | 0.912057 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2011.40 | 1.43924 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 459.472 | 0.321035 | 0.160518 | − | 0.987033i | \(-0.448684\pi\) | ||||
0.160518 | + | 0.987033i | \(0.448684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1413.23 | −0.964556 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −496.848 | −0.331373 | −0.165686 | − | 0.986179i | \(-0.552984\pi\) | ||||
−0.165686 | + | 0.986179i | \(0.552984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2739.82 | 1.78626 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 509.811 | 0.325019 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2684.75 | −1.67426 | −0.837129 | − | 0.547006i | \(-0.815768\pi\) | ||||
−0.837129 | + | 0.547006i | \(0.815768\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1728.99 | 1.05504 | 0.527522 | − | 0.849541i | \(-0.323121\pi\) | ||||
0.527522 | + | 0.849541i | \(0.323121\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1898.13 | −1.13370 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −579.440 | −0.338847 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2826.13 | 1.61860 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −64.9063 | −0.0364176 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1132.89 | −0.622887 | −0.311444 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311444 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1258.52 | 0.678259 | 0.339130 | − | 0.940740i | \(-0.389867\pi\) | ||||
0.339130 | + | 0.940740i | \(0.389867\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 306.000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.07558 | −0.00159378 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2469.89 | 1.25553 | 0.627766 | − | 0.778402i | \(-0.283970\pi\) | ||||
0.627766 | + | 0.778402i | \(0.283970\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −709.466 | −0.353864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1922.35 | −0.941007 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 733.892 | 0.352656 | 0.176328 | − | 0.984331i | \(-0.443578\pi\) | ||||
0.176328 | + | 0.984331i | \(0.443578\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2524.83 | −1.19126 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2610.39 | −1.20957 | −0.604784 | − | 0.796389i | \(-0.706741\pi\) | ||||
−0.604784 | + | 0.796389i | \(0.706741\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1375.51 | 0.615136 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1164.04 | 0.511564 | 0.255782 | − | 0.966734i | \(-0.417667\pi\) | ||||
0.255782 | + | 0.966734i | \(0.417667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4150.47 | 1.79284 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 324.053 | 0.137612 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −911.229 | −0.380494 | −0.190247 | − | 0.981736i | \(-0.560929\pi\) | ||||
−0.190247 | + | 0.981736i | \(0.560929\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4817.82 | −1.97848 | −0.989242 | − | 0.146291i | \(-0.953266\pi\) | ||||
−0.989242 | + | 0.146291i | \(0.953266\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2664.88 | 1.07647 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4840.22 | −1.92357 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1515.46 | −0.592627 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 484.019 | 0.186282 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −674.312 | −0.255453 | −0.127726 | − | 0.991809i | \(-0.540768\pi\) | ||||
−0.127726 | + | 0.991809i | \(0.540768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −963.634 | −0.359398 | −0.179699 | − | 0.983722i | \(-0.557512\pi\) | ||||
−0.179699 | + | 0.983722i | \(0.557512\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 736.393 | 0.270432 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3995.21 | 1.44491 | 0.722454 | − | 0.691418i | \(-0.243014\pi\) | ||||
0.722454 | + | 0.691418i | \(0.243014\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1619.07 | 0.576749 | 0.288374 | − | 0.957518i | \(-0.406885\pi\) | ||||
0.288374 | + | 0.957518i | \(0.406885\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1911.45 | −0.670762 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2683.16 | 0.927688 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7830.76 | 2.66792 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −965.107 | −0.324056 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6812.20 | −2.25459 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −543.991 | −0.177488 | −0.0887438 | − | 0.996054i | \(-0.528285\pi\) | ||||
−0.0887438 | + | 0.996054i | \(0.528285\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1087.79 | 0.349926 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8894.79 | −2.82149 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.91998 | −0.000913462 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2169.53 | 0.669421 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 442.000 | 0.134535 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2447.45 | −0.734949 | −0.367474 | − | 0.930034i | \(-0.619777\pi\) | ||||
−0.367474 | + | 0.930034i | \(0.619777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2083.73 | 0.617401 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −467.798 | −0.136779 | −0.0683896 | − | 0.997659i | \(-0.521786\pi\) | ||||
−0.0683896 | + | 0.997659i | \(0.521786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −361.180 | −0.104225 | −0.0521123 | − | 0.998641i | \(-0.516595\pi\) | ||||
−0.0521123 | + | 0.998641i | \(0.516595\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2397.09 | −0.682759 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3068.38 | −0.862732 | −0.431366 | − | 0.902177i | \(-0.641968\pi\) | ||||
−0.431366 | + | 0.902177i | \(0.641968\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11946.8 | −3.31626 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2894.05 | 0.793202 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −334.108 | −0.0904253 | −0.0452127 | − | 0.998977i | \(-0.514397\pi\) | ||||
−0.0452127 | + | 0.998977i | \(0.514397\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 514.961 | 0.137641 | 0.0688207 | − | 0.997629i | \(-0.478076\pi\) | ||||
0.0688207 | + | 0.997629i | \(0.478076\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −408.518 | −0.106528 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1986.85 | 0.511824 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1295.60 | 0.329741 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7028.13 | 1.76738 | 0.883688 | − | 0.468076i | \(-0.155053\pi\) | ||||
0.883688 | + | 0.468076i | \(0.155053\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4779.67 | 1.18773 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1925.95 | 0.472972 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3572.23 | −0.867040 | −0.433520 | − | 0.901144i | \(-0.642729\pi\) | ||||
−0.433520 | + | 0.901144i | \(0.642729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4595.35 | −1.10248 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1347.07 | 0.319469 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4276.74 | −1.00272 | −0.501359 | − | 0.865239i | \(-0.667166\pi\) | ||||
−0.501359 | + | 0.865239i | \(0.667166\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4465.35 | −1.03511 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 352.076 | 0.0806993 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2128.08 | 0.482347 | 0.241173 | − | 0.970482i | \(-0.422468\pi\) | ||||
0.241173 | + | 0.970482i | \(0.422468\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4386.94 | 0.983350 | 0.491675 | − | 0.870779i | \(-0.336385\pi\) | ||||
0.491675 | + | 0.870779i | \(0.336385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 699.139 | 0.154996 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10319.6 | −2.26290 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3411.86 | 0.740067 | 0.370034 | − | 0.929018i | \(-0.379346\pi\) | ||||
0.370034 | + | 0.929018i | \(0.379346\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.46597 | −0.000314570 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4466.83 | −0.948286 | −0.474143 | − | 0.880448i | \(-0.657242\pi\) | ||||
−0.474143 | + | 0.880448i | \(0.657242\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1879.30 | 0.394746 | 0.197373 | − | 0.980329i | \(-0.436759\pi\) | ||||
0.197373 | + | 0.980329i | \(0.436759\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8657.43 | 1.79938 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7434.60 | 1.52910 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3757.00 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3460.15 | −0.697037 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −207.996 | −0.0414718 | −0.0207359 | − | 0.999785i | \(-0.506601\pi\) | ||||
−0.0207359 | + | 0.999785i | \(0.506601\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2039.58 | 0.402539 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1203.45 | −0.235122 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1394.04 | −0.269631 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8444.80 | −1.61711 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2544.55 | −0.482444 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16772.6 | 3.14885 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1743.07 | 0.324046 | 0.162023 | − | 0.986787i | \(-0.448198\pi\) | ||||
0.162023 | + | 0.986787i | \(0.448198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2131.69 | 0.392451 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10027.9 | −1.82840 | −0.914198 | − | 0.405267i | \(-0.867178\pi\) | ||||
−0.914198 | + | 0.405267i | \(0.867178\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2092.80 | −0.377929 | −0.188965 | − | 0.981984i | \(-0.560513\pi\) | ||||
−0.188965 | + | 0.981984i | \(0.560513\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3046.40 | 0.544905 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10481.8 | −1.85715 | −0.928573 | − | 0.371151i | \(-0.878963\pi\) | ||||
−0.928573 | + | 0.371151i | \(0.878963\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6671.32 | −1.17092 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1599.73 | −0.278157 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5196.39 | 0.895154 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3009.83 | 0.513709 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2001.17 | −0.338425 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11342.4 | −1.90068 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3954.25 | −0.656631 | −0.328316 | − | 0.944568i | \(-0.606481\pi\) | ||||
−0.328316 | + | 0.944568i | \(0.606481\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2307.08 | −0.379661 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12030.6 | −1.96209 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7823.04 | −1.26454 | −0.632268 | − | 0.774750i | \(-0.717876\pi\) | ||||
−0.632268 | + | 0.774750i | \(0.717876\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 908.748 | 0.145594 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.26016 | 0.00115296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6536.69 | −1.02900 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6074.34 | −0.947918 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4248.15 | −0.657213 | −0.328606 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328606 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3202.79 | −0.491236 | −0.245618 | − | 0.969367i | \(-0.578991\pi\) | ||||
−0.245618 | + | 0.969367i | \(0.578991\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 351.000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2667.60 | −0.402216 | −0.201108 | − | 0.979569i | \(-0.564454\pi\) | ||||
−0.201108 | + | 0.979569i | \(0.564454\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6846.52 | 1.02359 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1828.52 | 0.271080 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9062.64 | −1.33233 | −0.666167 | − | 0.745803i | \(-0.732066\pi\) | ||||
−0.666167 | + | 0.745803i | \(0.732066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16499.5 | 2.40553 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1967.06 | 0.284419 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13654.9 | 1.95817 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4141.93 | 0.589120 | 0.294560 | − | 0.955633i | \(-0.404827\pi\) | ||||
0.294560 | + | 0.955633i | \(0.404827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3732.51 | 0.526576 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4239.45 | −0.593265 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5350.96 | −0.742794 | −0.371397 | − | 0.928474i | \(-0.621121\pi\) | ||||
−0.371397 | + | 0.928474i | \(0.621121\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6034.20 | 0.830946 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1945.76 | 0.265814 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9360.54 | 1.26865 | 0.634325 | − | 0.773066i | \(-0.281278\pi\) | ||||
0.634325 | + | 0.773066i | \(0.281278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1378.41 | 0.185350 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7241.39 | −0.966104 | −0.483052 | − | 0.875592i | \(-0.660472\pi\) | ||||
−0.483052 | + | 0.875592i | \(0.660472\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15087.2 | −1.99718 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4239.68 | −0.556886 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6258.22 | 0.815692 | 0.407846 | − | 0.913051i | \(-0.366280\pi\) | ||||
0.407846 | + | 0.913051i | \(0.366280\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3645.96 | −0.471571 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1490.54 | −0.191318 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18215.0 | 2.32025 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10114.6 | −1.27868 | −0.639342 | − | 0.768923i | \(-0.720793\pi\) | ||||
−0.639342 | + | 0.768923i | \(0.720793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8219.45 | 1.03130 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12414.5 | −1.54601 | −0.773006 | − | 0.634398i | \(-0.781248\pi\) | ||||
−0.773006 | + | 0.634398i | \(0.781248\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.11751 | −0.000261738 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1529.43 | 0.187650 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11425.7 | 1.39153 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14052.1 | −1.69885 | −0.849425 | − | 0.527709i | \(-0.823051\pi\) | ||||
−0.849425 | + | 0.527709i | \(0.823051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8054.24 | −0.966633 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1936.40 | 0.230711 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8154.48 | 0.964548 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5186.98 | 0.609130 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1003.68 | −0.117024 | −0.0585119 | − | 0.998287i | \(-0.518636\pi\) | ||||
−0.0585119 | + | 0.998287i | \(0.518636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8376.14 | 0.969663 | 0.484832 | − | 0.874608i | \(-0.338881\pi\) | ||||
0.484832 | + | 0.874608i | \(0.338881\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5694.39 | −0.654541 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7871.86 | 0.898450 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15924.1 | 1.80473 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1738.32 | −0.195634 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12296.3 | 1.37423 | 0.687116 | − | 0.726548i | \(-0.258877\pi\) | ||||
0.687116 | + | 0.726548i | \(0.258877\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1010.07 | 0.112104 | 0.0560518 | − | 0.998428i | \(-0.482149\pi\) | ||||
0.0560518 | + | 0.998428i | \(0.482149\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8478.39 | 0.934501 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16389.1 | −1.79405 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1845.70 | −0.200662 | −0.100331 | − | 0.994954i | \(-0.531990\pi\) | ||||
−0.100331 | + | 0.994954i | \(0.531990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −194.719 | −0.0210257 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7313.67 | −0.784386 | −0.392193 | − | 0.919883i | \(-0.628283\pi\) | ||||
−0.392193 | + | 0.919883i | \(0.628283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2215.95 | 0.236059 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3398.68 | −0.359624 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8443.62 | 0.887481 | 0.443740 | − | 0.896155i | \(-0.353651\pi\) | ||||
0.443740 | + | 0.896155i | \(0.353651\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18485.2 | −1.93001 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3775.57 | 0.391593 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4400.35 | 0.453388 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14302.7 | 1.46401 | 0.732004 | − | 0.681301i | \(-0.238585\pi\) | ||||
0.732004 | + | 0.681301i | \(0.238585\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 918.000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3862.08 | −0.390184 | −0.195092 | − | 0.980785i | \(-0.562501\pi\) | ||||
−0.195092 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14364.6 | 1.44186 | 0.720929 | − | 0.693009i | \(-0.243715\pi\) | ||||
0.720929 | + | 0.693009i | \(0.243715\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.22673 | −0.000920171 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14181.4 | −1.40522 | −0.702610 | − | 0.711575i | \(-0.747982\pi\) | ||||
−0.702610 | + | 0.711575i | \(0.747982\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11421.9 | −1.12455 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7409.66 | 0.724881 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 20996.9 | 2.04110 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 35385.2 | 3.41807 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2128.40 | −0.204303 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1182.57 | −0.112804 | −0.0564019 | − | 0.998408i | \(-0.517963\pi\) | ||||
−0.0564019 | + | 0.998408i | \(0.517963\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3332.45 | −0.315897 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5767.04 | −0.543291 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21778.1 | −2.03895 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16039.2 | 1.49242 | 0.746209 | − | 0.665712i | \(-0.231872\pi\) | ||||
0.746209 | + | 0.665712i | \(0.231872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2201.68 | 0.203606 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11867.2 | 1.09075 | 0.545376 | − | 0.838191i | \(-0.316387\pi\) | ||||
0.545376 | + | 0.838191i | \(0.316387\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5088.92 | 0.464896 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7574.48 | −0.687772 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6500.15 | 0.586663 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6945.54 | 0.623097 | 0.311548 | − | 0.950230i | \(-0.399152\pi\) | ||||
0.311548 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7831.17 | −0.698345 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5631.84 | −0.499227 | −0.249614 | − | 0.968346i | \(-0.580304\pi\) | ||||
−0.249614 | + | 0.968346i | \(0.580304\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16015.3 | −1.41123 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10395.3 | 0.905229 | 0.452614 | − | 0.891706i | \(-0.350491\pi\) | ||||
0.452614 | + | 0.891706i | \(0.350491\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12964.1 | 1.12231 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4126.54 | 0.355149 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13416.7 | 1.14799 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28201.3 | 2.39902 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3492.13 | 0.295352 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7846.89 | 0.659844 | 0.329922 | − | 0.944008i | \(-0.392978\pi\) | ||||
0.329922 | + | 0.944008i | \(0.392978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13670.9 | −1.14299 | −0.571497 | − | 0.820604i | \(-0.693637\pi\) | ||||
−0.571497 | + | 0.820604i | \(0.693637\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12451.4 | 1.03509 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.53809 | −0.000457767 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −667.849 | −0.0548902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 972.160 | 0.0794504 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5391.40 | 0.438138 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10068.7 | −0.813657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2733.69 | −0.219678 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 964.341 | 0.0770633 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6194.38 | 0.492269 | 0.246134 | − | 0.969236i | \(-0.420840\pi\) | ||||
0.246134 | + | 0.969236i | \(0.420840\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14453.4 | −1.14228 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12595.3 | −0.989951 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1856.88 | 0.145145 | 0.0725726 | − | 0.997363i | \(-0.476879\pi\) | ||||
0.0725726 | + | 0.997363i | \(0.476879\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7994.63 | 0.621498 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22875.5 | 1.76865 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17293.5 | 1.32983 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14520.7 | −1.11057 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15017.2 | 1.14237 | 0.571183 | − | 0.820822i | \(-0.306484\pi\) | ||||
0.571183 | + | 0.820822i | \(0.306484\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6123.98 | −0.463358 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4546.37 | −0.342153 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13842.2 | −1.03620 | −0.518098 | − | 0.855321i | \(-0.673360\pi\) | ||||
−0.518098 | + | 0.855321i | \(0.673360\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5719.62 | 0.425887 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1452.06 | 0.107550 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17621.0 | −1.29826 | −0.649131 | − | 0.760677i | \(-0.724867\pi\) | ||||
−0.649131 | + | 0.760677i | \(0.724867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16472.6 | −1.20728 | −0.603639 | − | 0.797258i | \(-0.706283\pi\) | ||||
−0.603639 | + | 0.797258i | \(0.706283\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2022.94 | −0.147486 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24827.4 | −1.80065 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19638.6 | −1.41693 | −0.708463 | − | 0.705748i | \(-0.750611\pi\) | ||||
−0.708463 | + | 0.705748i | \(0.750611\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2890.90 | −0.207499 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7741.94 | 0.552822 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10540.8 | 0.748811 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2209.18 | 0.156134 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15965.5 | 1.12260 | 0.561300 | − | 0.827612i | \(-0.310301\pi\) | ||||
0.561300 | + | 0.827612i | \(0.310301\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.8945 | −0.00174153 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11985.6 | 0.834219 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16128.6 | −1.11690 | −0.558452 | − | 0.829537i | \(-0.688604\pi\) | ||||
−0.558452 | + | 0.829537i | \(0.688604\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11508.6 | 0.792953 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4857.22 | 0.332986 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18322.6 | −1.24982 | −0.624910 | − | 0.780697i | \(-0.714864\pi\) | ||||
−0.624910 | + | 0.780697i | \(0.714864\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10528.6 | 0.714594 | 0.357297 | − | 0.933991i | \(-0.383698\pi\) | ||||
0.357297 | + | 0.933991i | \(0.383698\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5734.34 | −0.387264 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 12380.6 | 0.831974 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16560.5 | −1.10737 | −0.553683 | − | 0.832728i | \(-0.686778\pi\) | ||||
−0.553683 | + | 0.832728i | \(0.686778\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8049.47 | 0.535601 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8225.24 | −0.544611 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23354.0 | 1.53876 | 0.769379 | − | 0.638793i | \(-0.220566\pi\) | ||||
0.769379 | + | 0.638793i | \(0.220566\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 23492.3 | 1.54032 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23424.3 | −1.52840 | −0.764202 | − | 0.644977i | \(-0.776867\pi\) | ||||
−0.764202 | + | 0.644977i | \(0.776867\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3275.77 | 0.212705 | 0.106352 | − | 0.994328i | \(-0.466083\pi\) | ||||
0.106352 | + | 0.994328i | \(0.466083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2895.32 | −0.187094 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2103.85 | 0.135295 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9038.33 | 0.578453 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20436.6 | −1.30169 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8715.63 | −0.552488 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24146.4 | 1.52338 | 0.761691 | − | 0.647941i | \(-0.224369\pi\) | ||||
0.761691 | + | 0.647941i | \(0.224369\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1631.97 | −0.102473 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8675.69 | 0.542180 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −281.261 | −0.0174944 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3263.37 | 0.202030 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23506.8 | −1.44846 | −0.724230 | − | 0.689558i | \(-0.757805\pi\) | ||||
−0.724230 | + | 0.689558i | \(0.757805\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5273.79 | −0.323449 | −0.161725 | − | 0.986836i | \(-0.551706\pi\) | ||||
−0.161725 | + | 0.986836i | \(0.551706\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −26684.4 | −1.62899 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7106.47 | 0.431815 | 0.215907 | − | 0.976414i | \(-0.430729\pi\) | ||||
0.215907 | + | 0.976414i | \(0.430729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4814.60 | −0.291201 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.75995 | −0.000527388 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8474.11 | −0.507837 | −0.253918 | − | 0.967226i | \(-0.581719\pi\) | ||||
−0.253918 | + | 0.967226i | \(0.581719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9381.43 | −0.559638 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6508.59 | 0.386491 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18444.7 | 1.09030 | 0.545148 | − | 0.838340i | \(-0.316474\pi\) | ||||
0.545148 | + | 0.838340i | \(0.316474\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29184.5 | 1.71732 | 0.858659 | − | 0.512547i | \(-0.171298\pi\) | ||||
0.858659 | + | 0.512547i | \(0.171298\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1326.00 | 0.0776736 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 51732.9 | 3.01672 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16050.2 | −0.931732 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7342.36 | −0.424323 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −39593.2 | −2.27791 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28477.5 | −1.63110 | −0.815548 | − | 0.578689i | \(-0.803564\pi\) | ||||
−0.815548 | + | 0.578689i | \(0.803564\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6251.18 | 0.356457 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6422.80 | 0.364621 | 0.182310 | − | 0.983241i | \(-0.441642\pi\) | ||||
0.182310 | + | 0.983241i | \(0.441642\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20676.3 | −1.16861 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1403.40 | −0.0789695 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 54.3801 | 0.00304655 | 0.00152328 | − | 0.999999i | \(-0.499515\pi\) | ||||
0.00152328 | + | 0.999999i | \(0.499515\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50693.1 | −2.82756 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1083.54 | −0.0601741 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3074.35 | −0.169991 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14382.3 | −0.791794 | −0.395897 | − | 0.918295i | \(-0.629566\pi\) | ||||
−0.395897 | + | 0.918295i | \(0.629566\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7191.28 | −0.394191 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32646.6 | 1.78181 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14100.6 | 0.766281 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9205.15 | −0.498098 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32081.3 | 1.72852 | 0.864262 | − | 0.503042i | \(-0.167786\pi\) | ||||
0.864262 | + | 0.503042i | \(0.167786\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39178.0 | −2.10189 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35840.3 | −1.91464 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15205.1 | −0.808835 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11549.8 | 0.611793 | 0.305896 | − | 0.952065i | \(-0.401044\pi\) | ||||
0.305896 | + | 0.952065i | \(0.401044\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8682.16 | 0.457955 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.4668 | 0.000917445 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10940.9 | −0.572261 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1002.32 | −0.0522071 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33235.7 | 1.72390 | 0.861949 | − | 0.506995i | \(-0.169244\pi\) | ||||
0.861949 | + | 0.506995i | \(0.169244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12738.0 | 0.657958 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1544.88 | 0.0794672 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34653.4 | 1.77516 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13863.5 | −0.707249 | −0.353625 | − | 0.935387i | \(-0.615051\pi\) | ||||
−0.353625 | + | 0.935387i | \(0.615051\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16016.6 | −0.810389 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13448.6 | 0.677675 | 0.338838 | − | 0.940845i | \(-0.389966\pi\) | ||||
0.338838 | + | 0.940845i | \(0.389966\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1225.55 | −0.0615037 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28399.2 | 1.41940 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36402.4 | 1.81202 | 0.906012 | − | 0.423252i | \(-0.139112\pi\) | ||||
0.906012 | + | 0.423252i | \(0.139112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5960.56 | 0.295502 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23695.5 | −1.16999 | −0.584996 | − | 0.811036i | \(-0.698904\pi\) | ||||
−0.584996 | + | 0.811036i | \(0.698904\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21391.1 | −1.05196 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3886.81 | 0.190376 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9559.29 | −0.466340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4052.82 | 0.196923 | 0.0984617 | − | 0.995141i | \(-0.468608\pi\) | ||||
0.0984617 | + | 0.995141i | \(0.468608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21084.4 | 1.02040 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23763.3 | 1.14548 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15508.4 | 0.744603 | 0.372301 | − | 0.928112i | \(-0.378569\pi\) | ||||
0.372301 | + | 0.928112i | \(0.378569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14339.0 | 0.685735 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29272.1 | 1.39436 | 0.697182 | − | 0.716894i | \(-0.254437\pi\) | ||||
0.697182 | + | 0.716894i | \(0.254437\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11958.1 | −0.567382 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5777.86 | 0.273070 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1404.23 | 0.0661067 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35088.4 | 1.64541 | 0.822706 | − | 0.568468i | \(-0.192464\pi\) | ||||
0.822706 | + | 0.568468i | \(0.192464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10716.7 | −0.500586 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11475.6 | −0.533956 | −0.266978 | − | 0.963703i | \(-0.586025\pi\) | ||||
−0.266978 | + | 0.963703i | \(0.586025\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.7120 | −0.00174794 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13786.1 | −0.636515 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 63384.2 | 2.91524 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16161.8 | −0.740479 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4041.20 | 0.184446 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 46636.1 | 2.12040 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17215.7 | 0.779761 | 0.389881 | − | 0.920865i | \(-0.372516\pi\) | ||||
0.389881 | + | 0.920865i | \(0.372516\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12830.2 | −0.578920 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5430.27 | 0.244094 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11547.8 | 0.517118 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13396.1 | −0.597622 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 43951.6 | 1.95338 | 0.976692 | − | 0.214646i | \(-0.0688599\pi\) | ||||
0.976692 | + | 0.214646i | \(0.0688599\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21512.2 | −0.952497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1056.23 | 0.0465918 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32233.6 | −1.41656 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36297.5 | −1.58922 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6384.24 | 0.278483 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27914.7 | −1.21314 | −0.606569 | − | 0.795031i | \(-0.707455\pi\) | ||||
−0.606569 | + | 0.795031i | \(0.707455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38016.3 | −1.64603 | −0.823017 | − | 0.568016i | \(-0.807711\pi\) | ||||
−0.823017 | + | 0.568016i | \(0.807711\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13160.8 | 0.567737 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13857.3 | 0.595581 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −71996.8 | −3.08305 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2097.42 | 0.0894868 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15367.7 | −0.653273 | −0.326637 | − | 0.945150i | \(-0.605915\pi\) | ||||
−0.326637 | + | 0.945150i | \(0.605915\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −377.068 | −0.0159705 | −0.00798527 | − | 0.999968i | \(-0.502542\pi\) | ||||
−0.00798527 | + | 0.999968i | \(0.502542\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30958.8 | −1.30648 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5466.15 | 0.229839 | 0.114919 | − | 0.993375i | \(-0.463339\pi\) | ||||
0.114919 | + | 0.993375i | \(0.463339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18760.0 | −0.785962 | −0.392981 | − | 0.919547i | \(-0.628556\pi\) | ||||
−0.392981 | + | 0.919547i | \(0.628556\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10235.6 | 0.427278 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −735.605 | −0.0305969 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −49289.1 | −2.04278 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.39790 | −0.000181617 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46530.4 | 1.91467 | 0.957334 | − | 0.288983i | \(-0.0933170\pi\) | ||||
0.957334 | + | 0.288983i | \(0.0933170\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1986.62 | −0.0814558 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13400.5 | −0.547493 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3191.04 | 0.129911 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11754.3 | 0.476839 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5637.91 | 0.227906 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27488.6 | 1.10728 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11378.2 | −0.456719 | −0.228359 | − | 0.973577i | \(-0.573336\pi\) | ||||
−0.228359 | + | 0.973577i | \(0.573336\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 25972.3 | 1.03887 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 16515.4 | 0.658289 | 0.329145 | − | 0.944280i | \(-0.393240\pi\) | ||||
0.329145 | + | 0.944280i | \(0.393240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1477.37 | −0.0586811 | −0.0293406 | − | 0.999569i | \(-0.509341\pi\) | ||||
−0.0293406 | + | 0.999569i | \(0.509341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22303.8 | 0.882824 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14215.0 | −0.560702 | −0.280351 | − | 0.959898i | \(-0.590451\pi\) | ||||
−0.280351 | + | 0.959898i | \(0.590451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21979.3 | 0.863953 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11271.0 | −0.441503 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42998.2 | −1.67850 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8282.94 | −0.322223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10380.5 | −0.402434 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 36057.6 | 1.39311 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15634.9 | 0.602001 | 0.301000 | − | 0.953624i | \(-0.402679\pi\) | ||||
0.301000 | + | 0.953624i | \(0.402679\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −623.987 | −0.0239438 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35793.2 | −1.36879 | −0.684395 | − | 0.729111i | \(-0.739934\pi\) | ||||
−0.684395 | + | 0.729111i | \(0.739934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18937.7 | 0.721749 | 0.360875 | − | 0.932614i | \(-0.382478\pi\) | ||||
0.360875 | + | 0.932614i | \(0.382478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6118.74 | 0.232406 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16591.7 | 0.628066 | 0.314033 | − | 0.949412i | \(-0.398320\pi\) | ||||
0.314033 | + | 0.949412i | \(0.398320\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8236.78 | 0.310746 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3610.35 | −0.135748 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −96700.3 | −3.62369 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17205.7 | −0.642596 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4182.13 | −0.155671 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.3797 | −0.000904459 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8040.62 | −0.297305 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −25334.4 | −0.933639 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −90969.4 | −3.34135 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28947.7 | −1.05975 | −0.529875 | − | 0.848076i | \(-0.677761\pi\) | ||||
−0.529875 | + | 0.848076i | \(0.677761\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7633.65 | −0.278539 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13179.1 | −0.479302 | −0.239651 | − | 0.970859i | \(-0.577033\pi\) | ||||
−0.239651 | + | 0.970859i | \(0.577033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19249.3 | −0.697766 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 50317.9 | 1.81799 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8906.82 | −0.320751 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29617.7 | −1.06311 | −0.531555 | − | 0.847024i | \(-0.678392\pi\) | ||||
−0.531555 | + | 0.847024i | \(0.678392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5229.21 | 0.187088 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4713.76 | 0.168099 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −59349.7 | −2.10963 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6395.06 | 0.226582 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36633.5 | −1.29376 | −0.646882 | − | 0.762590i | \(-0.723927\pi\) | ||||
−0.646882 | + | 0.762590i | \(0.723927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3306.65 | −0.116403 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30083.8 | −1.05563 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −28614.7 | −1.00086 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3252.46 | 0.113397 | 0.0566986 | − | 0.998391i | \(-0.481943\pi\) | ||||
0.0566986 | + | 0.998391i | \(0.481943\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6278.39 | −0.218198 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20638.9 | −0.714995 | −0.357497 | − | 0.933914i | \(-0.616370\pi\) | ||||
−0.357497 | + | 0.933914i | \(0.616370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44472.5 | −1.53576 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9139.20 | 0.314601 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 21790.8 | 0.747737 | 0.373869 | − | 0.927482i | \(-0.378031\pi\) | ||||
0.373869 | + | 0.927482i | \(0.378031\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9401.30 | 0.321580 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31445.3 | −1.07222 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31780.0 | 1.08023 | 0.540114 | − | 0.841592i | \(-0.318381\pi\) | ||||
0.540114 | + | 0.841592i | \(0.318381\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12732.3 | −0.431421 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20014.0 | −0.676029 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −48128.5 | −1.62059 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29791.0 | −0.999999 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4799.20 | −0.160594 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −18195.2 | −0.606969 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 38528.7 | 1.28128 | 0.640640 | − | 0.767841i | \(-0.278669\pi\) | ||||
0.640640 | + | 0.767841i | \(0.278669\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15589.2 | 0.516818 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22579.5 | −0.746252 | −0.373126 | − | 0.927781i | \(-0.621714\pi\) | ||||
−0.373126 | + | 0.927781i | \(0.621714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30995.0 | 1.02123 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9029.49 | 0.296590 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30254.4 | 0.990712 | 0.495356 | − | 0.868690i | \(-0.335038\pi\) | ||||
0.495356 | + | 0.868690i | \(0.335038\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5230.95 | −0.170768 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6003.51 | −0.195390 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7071.61 | 0.229450 | 0.114725 | − | 0.993397i | \(-0.463401\pi\) | ||||
0.114725 | + | 0.993397i | \(0.463401\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 75437.1 | 2.44023 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34027.1 | −1.09736 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 50515.4 | 1.62416 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2808.28 | −0.0900180 | −0.0450090 | − | 0.998987i | \(-0.514332\pi\) | ||||
−0.0450090 | + | 0.998987i | \(0.514332\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11862.7 | −0.379106 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30571.1 | 0.974040 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15225.5 | −0.483648 | −0.241824 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241824 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6921.23 | −0.219197 |
(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 | 624.4.a.u.1.3 | 3 | ||
3.2 | odd | 2 | 1872.4.a.bj.1.1 | 3 | |||
4.3 | odd | 2 | 312.4.a.g.1.3 | ✓ | 3 | ||
8.3 | odd | 2 | 2496.4.a.bo.1.1 | 3 | |||
8.5 | even | 2 | 2496.4.a.bk.1.1 | 3 | |||
12.11 | even | 2 | 936.4.a.k.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.4.a.g.1.3 | ✓ | 3 | 4.3 | odd | 2 | ||
624.4.a.u.1.3 | 3 | 1.1 | even | 1 | trivial | ||
936.4.a.k.1.1 | 3 | 12.11 | even | 2 | |||
1872.4.a.bj.1.1 | 3 | 3.2 | odd | 2 | |||
2496.4.a.bk.1.1 | 3 | 8.5 | even | 2 | |||
2496.4.a.bo.1.1 | 3 | 8.3 | odd | 2 |