Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 58) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −3.44949 | −0.663855 | −0.331927 | − | 0.943305i | \(-0.607699\pi\) | ||||
−0.331927 | + | 0.943305i | \(0.607699\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.69694 | −0.867321 | −0.433660 | − | 0.901076i | \(-0.642778\pi\) | ||||
−0.433660 | + | 0.901076i | \(0.642778\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 27.5959 | 1.49004 | 0.745020 | − | 0.667042i | \(-0.232440\pi\) | ||||
0.745020 | + | 0.667042i | \(0.232440\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −15.1010 | −0.559297 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −52.3485 | −1.43488 | −0.717439 | − | 0.696621i | \(-0.754686\pi\) | ||||
−0.717439 | + | 0.696621i | \(0.754686\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.40408 | 0.115294 | 0.0576470 | − | 0.998337i | \(-0.481640\pi\) | ||||
0.0576470 | + | 0.998337i | \(0.481640\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 33.4495 | 0.575775 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 17.1918 | 0.245273 | 0.122636 | − | 0.992452i | \(-0.460865\pi\) | ||||
0.122636 | + | 0.992452i | \(0.460865\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 44.2020 | 0.533718 | 0.266859 | − | 0.963736i | \(-0.414014\pi\) | ||||
0.266859 | + | 0.963736i | \(0.414014\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −95.1918 | −0.989170 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 205.060 | 1.85904 | 0.929522 | − | 0.368767i | \(-0.120220\pi\) | ||||
0.929522 | + | 0.368767i | \(0.120220\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −30.9694 | −0.247755 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 145.227 | 1.03515 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −299.994 | −1.73808 | −0.869042 | − | 0.494739i | \(-0.835264\pi\) | ||||
−0.869042 | + | 0.494739i | \(0.835264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 180.576 | 0.952550 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −267.596 | −1.29234 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −29.7980 | −0.132399 | −0.0661994 | − | 0.997806i | \(-0.521087\pi\) | ||||
−0.0661994 | + | 0.997806i | \(0.521087\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.6413 | −0.0765385 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −43.9592 | −0.167446 | −0.0837228 | − | 0.996489i | \(-0.526681\pi\) | ||||
−0.0837228 | + | 0.996489i | \(0.526681\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 64.8230 | 0.229893 | 0.114947 | − | 0.993372i | \(-0.463330\pi\) | ||||
0.114947 | + | 0.993372i | \(0.463330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 146.434 | 0.485090 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 499.499 | 1.55020 | 0.775101 | − | 0.631837i | \(-0.217699\pi\) | ||||
0.775101 | + | 0.631837i | \(0.217699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 418.535 | 1.22022 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −59.3031 | −0.162825 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 351.627 | 0.911314 | 0.455657 | − | 0.890156i | \(-0.349404\pi\) | ||||
0.455657 | + | 0.890156i | \(0.349404\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 507.620 | 1.24450 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −152.474 | −0.354311 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 522.372 | 1.15266 | 0.576331 | − | 0.817216i | \(-0.304484\pi\) | ||||
0.576331 | + | 0.817216i | \(0.304484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −484.606 | −1.01717 | −0.508586 | − | 0.861011i | \(-0.669832\pi\) | ||||
−0.508586 | + | 0.861011i | \(0.669832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −416.727 | −0.833375 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −52.4031 | −0.0999969 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −504.990 | −0.920811 | −0.460405 | − | 0.887709i | \(-0.652296\pi\) | ||||
−0.460405 | + | 0.887709i | \(0.652296\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −707.353 | −1.23413 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −481.283 | −0.804475 | −0.402238 | − | 0.915535i | \(-0.631767\pi\) | ||||
−0.402238 | + | 0.915535i | \(0.631767\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.11019 | 0.00498659 | 0.00249329 | − | 0.999997i | \(-0.499206\pi\) | ||||
0.00249329 | + | 0.999997i | \(0.499206\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 106.829 | 0.164473 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1444.60 | −2.13802 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1043.27 | 1.48578 | 0.742890 | − | 0.669414i | \(-0.233455\pi\) | ||||
0.742890 | + | 0.669414i | \(0.233455\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −93.2316 | −0.127890 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1007.08 | −1.33182 | −0.665912 | − | 0.746030i | \(-0.731958\pi\) | ||||
−0.665912 | + | 0.746030i | \(0.731958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −166.708 | −0.212730 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 100.035 | 0.123275 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −295.637 | −0.352106 | −0.176053 | − | 0.984381i | \(-0.556333\pi\) | ||||
−0.176053 | + | 0.984381i | \(0.556333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 149.131 | 0.171793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1034.83 | 1.15383 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −428.624 | −0.462905 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 428.949 | 0.449002 | 0.224501 | − | 0.974474i | \(-0.427925\pi\) | ||||
0.224501 | + | 0.974474i | \(0.427925\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 790.515 | 0.802523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1212.16 | 1.19420 | 0.597101 | − | 0.802166i | \(-0.296319\pi\) | ||||
0.597101 | + | 0.802166i | \(0.296319\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1032.07 | −0.987310 | −0.493655 | − | 0.869658i | \(-0.664339\pi\) | ||||
−0.493655 | + | 0.869658i | \(0.664339\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 923.069 | 0.857927 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1176.06 | −1.06256 | −0.531280 | − | 0.847196i | \(-0.678289\pi\) | ||||
−0.531280 | + | 0.847196i | \(0.678289\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2167.86 | 1.90498 | 0.952491 | − | 0.304568i | \(-0.0985121\pi\) | ||||
0.952491 | + | 0.304568i | \(0.0985121\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 102.788 | 0.0878935 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1623.65 | 1.35169 | 0.675843 | − | 0.737046i | \(-0.263780\pi\) | ||||
0.675843 | + | 0.737046i | \(0.263780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1988.46 | −1.61239 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −81.6072 | −0.0644836 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 474.424 | 0.365466 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1409.36 | 1.05887 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 151.637 | 0.111160 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1512.43 | 1.08220 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −333.473 | −0.233000 | −0.116500 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116500 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −223.606 | −0.152616 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −933.492 | −0.622592 | −0.311296 | − | 0.950313i | \(-0.600763\pi\) | ||||
−0.311296 | + | 0.950313i | \(0.600763\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1219.80 | 0.795261 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1408.26 | −0.897804 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1090.32 | −0.679944 | −0.339972 | − | 0.940436i | \(-0.610418\pi\) | ||||
−0.339972 | + | 0.940436i | \(0.610418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1924.60 | −1.17440 | −0.587202 | − | 0.809440i | \(-0.699771\pi\) | ||||
−0.587202 | + | 0.809440i | \(0.699771\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1723.02 | −1.02911 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −282.895 | −0.165433 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 281.211 | 0.161057 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1443.73 | −0.810047 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1703.62 | 0.936687 | 0.468343 | − | 0.883546i | \(-0.344851\pi\) | ||||
0.468343 | + | 0.883546i | \(0.344851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1082.81 | −0.583560 | −0.291780 | − | 0.956486i | \(-0.594247\pi\) | ||||
−0.291780 | + | 0.956486i | \(0.594247\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −259.614 | −0.137180 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2909.03 | 1.50748 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2407.90 | −1.22402 | −0.612010 | − | 0.790850i | \(-0.709639\pi\) | ||||
−0.612010 | + | 0.790850i | \(0.709639\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1212.93 | −0.604980 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5658.82 | 2.77005 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1061.59 | 0.510123 | 0.255061 | − | 0.966925i | \(-0.417904\pi\) | ||||
0.255061 | + | 0.966925i | \(0.417904\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1751.03 | −0.826166 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1315.63 | −0.609618 | −0.304809 | − | 0.952414i | \(-0.598593\pi\) | ||||
−0.304809 | + | 0.952414i | \(0.598593\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2167.80 | −0.986707 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −667.496 | −0.298507 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 653.800 | 0.287327 | 0.143663 | − | 0.989627i | \(-0.454112\pi\) | ||||
0.143663 | + | 0.989627i | \(0.454112\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −854.629 | −0.369165 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1801.92 | −0.765200 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2055.28 | 0.858208 | 0.429104 | − | 0.903255i | \(-0.358829\pi\) | ||||
0.429104 | + | 0.903255i | \(0.358829\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3398.36 | −1.39557 | −0.697785 | − | 0.716307i | \(-0.745831\pi\) | ||||
−0.697785 | + | 0.716307i | \(0.745831\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1671.64 | 0.675254 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 288.949 | 0.114832 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −899.966 | −0.351936 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4007.67 | 1.54241 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4853.92 | −1.83883 | −0.919417 | − | 0.393285i | \(-0.871339\pi\) | ||||
−0.919417 | + | 0.393285i | \(0.871339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4877.24 | −1.81902 | −0.909512 | − | 0.415677i | \(-0.863545\pi\) | ||||
−0.909512 | + | 0.415677i | \(0.863545\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 180.764 | 0.0663834 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1031.42 | 0.373022 | 0.186511 | − | 0.982453i | \(-0.440282\pi\) | ||||
0.186511 | + | 0.982453i | \(0.440282\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1167.70 | 0.415960 | 0.207980 | − | 0.978133i | \(-0.433311\pi\) | ||||
0.207980 | + | 0.978133i | \(0.433311\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1741.96 | 0.611284 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −800.282 | −0.276693 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 426.269 | 0.145229 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3096.62 | −1.03976 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2313.91 | −0.765820 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 794.341 | 0.259169 | 0.129585 | − | 0.991568i | \(-0.458636\pi\) | ||||
0.129585 | + | 0.991568i | \(0.458636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1660.18 | 0.534055 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −628.584 | −0.199391 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8278.62 | −2.58981 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.7286 | −0.00331037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 92.9061 | 0.0282785 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5136.08 | −1.54232 | −0.771161 | − | 0.636641i | \(-0.780324\pi\) | ||||
−0.771161 | + | 0.636641i | \(0.780324\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 467.669 | 0.138569 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5032.84 | −1.47155 | −0.735774 | − | 0.677228i | \(-0.763181\pi\) | ||||
−0.735774 | + | 0.677228i | \(0.763181\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6213.12 | 1.79290 | 0.896451 | − | 0.443142i | \(-0.146136\pi\) | ||||
0.896451 | + | 0.443142i | \(0.146136\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4983.15 | 1.41934 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3117.59 | −0.876566 | −0.438283 | − | 0.898837i | \(-0.644413\pi\) | ||||
−0.438283 | + | 0.898837i | \(0.644413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4843.62 | −1.34452 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3598.73 | −0.986342 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7193.09 | −1.94679 | −0.973394 | − | 0.229136i | \(-0.926410\pi\) | ||||
−0.973394 | + | 0.229136i | \(0.926410\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −837.347 | −0.223810 | −0.111905 | − | 0.993719i | \(-0.535695\pi\) | ||||
−0.111905 | + | 0.993719i | \(0.535695\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3599.53 | −0.950246 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4058.51 | −1.05832 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 238.871 | 0.0615345 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3473.91 | 0.884138 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4306.56 | 1.08298 | 0.541489 | − | 0.840708i | \(-0.317861\pi\) | ||||
0.541489 | + | 0.840708i | \(0.317861\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10734.6 | −2.66750 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 575.058 | 0.141222 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 401.238 | 0.0973873 | 0.0486936 | − | 0.998814i | \(-0.484494\pi\) | ||||
0.0486936 | + | 0.998814i | \(0.484494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −822.302 | −0.197279 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 437.930 | 0.103859 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2682.72 | 0.628988 | 0.314494 | − | 0.949260i | \(-0.398165\pi\) | ||||
0.314494 | + | 0.949260i | \(0.398165\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3409.70 | −0.790401 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1019.80 | 0.233747 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4732.38 | 1.07263 | 0.536316 | − | 0.844017i | \(-0.319816\pi\) | ||||
0.536316 | + | 0.844017i | \(0.319816\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4529.66 | −1.01534 | −0.507670 | − | 0.861552i | \(-0.669493\pi\) | ||||
−0.507670 | + | 0.861552i | \(0.669493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −514.424 | −0.114045 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1621.20 | 0.355498 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7158.69 | −1.55279 | −0.776397 | − | 0.630245i | \(-0.782955\pi\) | ||||
−0.776397 | + | 0.630245i | \(0.782955\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4530.22 | 0.972105 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5769.75 | −1.22489 | −0.612446 | − | 0.790512i | \(-0.709814\pi\) | ||||
−0.612446 | + | 0.790512i | \(0.709814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3815.25 | −0.801389 | −0.400694 | − | 0.916212i | \(-0.631231\pi\) | ||||
−0.400694 | + | 0.916212i | \(0.631231\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1478.54 | 0.307301 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1213.09 | −0.249501 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4617.44 | −0.939841 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1479.66 | −0.298072 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5416.66 | −1.08002 | −0.540008 | − | 0.841660i | \(-0.681579\pi\) | ||||
−0.540008 | + | 0.841660i | \(0.681579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5065.41 | −0.999728 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7602.41 | −1.48531 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1108.16 | 0.214337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1788.85 | 0.342550 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4181.33 | −0.792776 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4699.20 | 0.882214 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4929.06 | 0.916339 | 0.458169 | − | 0.888865i | \(-0.348505\pi\) | ||||
0.458169 | + | 0.888865i | \(0.348505\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3560.12 | 0.655430 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1117.93 | −0.203832 | −0.101916 | − | 0.994793i | \(-0.532497\pi\) | ||||
−0.101916 | + | 0.994793i | \(0.532497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2032.21 | 0.366988 | 0.183494 | − | 0.983021i | \(-0.441259\pi\) | ||||
0.183494 | + | 0.983021i | \(0.441259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4040.97 | 0.722803 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2051.75 | −0.363526 | −0.181763 | − | 0.983342i | \(-0.558180\pi\) | ||||
−0.181763 | + | 0.983342i | \(0.558180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1518.11 | 0.266450 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4056.80 | 0.705385 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 759.914 | 0.130906 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −167.361 | −0.0285647 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7478.00 | −1.26463 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13784.1 | 2.30986 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9652.92 | −1.60294 | −0.801469 | − | 0.598036i | \(-0.795948\pi\) | ||||
−0.801469 | + | 0.598036i | \(0.795948\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 449.980 | 0.0740502 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4896.85 | 0.798638 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4277.57 | 0.691437 | 0.345719 | − | 0.938338i | \(-0.387635\pi\) | ||||
0.345719 | + | 0.938338i | \(0.387635\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5600.77 | −0.897322 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15704.2 | 2.49394 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2084.45 | 0.328133 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6859.16 | 1.07039 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9475.83 | −1.46596 | −0.732982 | − | 0.680248i | \(-0.761872\pi\) | ||||
−0.732982 | + | 0.680248i | \(0.761872\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2968.57 | −0.455313 | −0.227656 | − | 0.973742i | \(-0.573106\pi\) | ||||
−0.227656 | + | 0.973742i | \(0.573106\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 784.819 | 0.119346 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3969.16 | 0.598461 | 0.299231 | − | 0.954181i | \(-0.403270\pi\) | ||||
0.299231 | + | 0.954181i | \(0.403270\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4666.97 | 0.697738 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1636.52 | −0.242616 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3503.03 | 0.514994 | 0.257497 | − | 0.966279i | \(-0.417102\pi\) | ||||
0.257497 | + | 0.966279i | \(0.417102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4905.18 | −0.715145 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4861.58 | −0.702939 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.1594 | −0.00432497 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8253.53 | 1.17393 | 0.586963 | − | 0.809614i | \(-0.300323\pi\) | ||||
0.586963 | + | 0.809614i | \(0.300323\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 663.828 | 0.0936518 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9703.46 | 1.35789 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1253.95 | −0.174067 | −0.0870335 | − | 0.996205i | \(-0.527739\pi\) | ||||
−0.0870335 | + | 0.996205i | \(0.527739\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5217.10 | −0.718426 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −156.718 | −0.0214096 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6966.52 | −0.944185 | −0.472092 | − | 0.881549i | \(-0.656501\pi\) | ||||
−0.472092 | + | 0.881549i | \(0.656501\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1150.31 | 0.154678 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9821.84 | 1.31037 | 0.655186 | − | 0.755467i | \(-0.272590\pi\) | ||||
0.655186 | + | 0.755467i | \(0.272590\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14008.2 | 1.85435 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −978.893 | −0.128579 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3942.96 | −0.513923 | −0.256962 | − | 0.966422i | \(-0.582721\pi\) | ||||
−0.256962 | + | 0.966422i | \(0.582721\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3525.36 | 0.455972 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3220.07 | 0.413311 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10116.5 | −1.28865 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8725.50 | −1.10307 | −0.551537 | − | 0.834150i | \(-0.685959\pi\) | ||||
−0.551537 | + | 0.834150i | \(0.685959\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4207.67 | −0.527938 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3986.86 | 0.496494 | 0.248247 | − | 0.968697i | \(-0.420146\pi\) | ||||
0.248247 | + | 0.968697i | \(0.420146\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1621.19 | −0.200391 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 904.061 | 0.110921 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1559.88 | 0.189976 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −704.847 | −0.0852138 | −0.0426069 | − | 0.999092i | \(-0.513566\pi\) | ||||
−0.0426069 | + | 0.999092i | \(0.513566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3761.05 | 0.451384 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14415.3 | 1.71751 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9765.60 | 1.15512 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6638.88 | 0.779634 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6705.33 | 0.781807 | 0.390903 | − | 0.920432i | \(-0.372163\pi\) | ||||
0.390903 | + | 0.920432i | \(0.372163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8996.55 | −1.04148 | −0.520742 | − | 0.853714i | \(-0.674345\pi\) | ||||
−0.520742 | + | 0.853714i | \(0.674345\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7542.95 | −0.867023 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −532.421 | −0.0607675 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13373.2 | −1.51563 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 975.845 | 0.109823 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5383.16 | −0.601619 | −0.300810 | − | 0.953684i | \(-0.597257\pi\) | ||||
−0.300810 | + | 0.953684i | \(0.597257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6901.64 | −0.765985 | −0.382993 | − | 0.923751i | \(-0.625107\pi\) | ||||
−0.382993 | + | 0.923751i | \(0.625107\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −970.035 | −0.106919 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9064.08 | 0.992205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12119.4 | −1.31760 | −0.658802 | − | 0.752316i | \(-0.728937\pi\) | ||||
−0.658802 | + | 0.752316i | \(0.728937\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6320.30 | −0.682464 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5229.40 | 0.560849 | 0.280425 | − | 0.959876i | \(-0.409525\pi\) | ||||
0.280425 | + | 0.959876i | \(0.409525\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2866.77 | 0.305389 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5876.64 | −0.621824 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10220.3 | −1.07422 | −0.537112 | − | 0.843511i | \(-0.680485\pi\) | ||||
−0.537112 | + | 0.843511i | \(0.680485\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2301.20 | 0.240264 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3735.13 | 0.387399 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1446.11 | −0.148999 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12030.6 | 1.23143 | 0.615717 | − | 0.787967i | \(-0.288866\pi\) | ||||
0.615717 | + | 0.787967i | \(0.288866\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2496.72 | 0.253893 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1063.24 | −0.107418 | −0.0537092 | − | 0.998557i | \(-0.517104\pi\) | ||||
−0.0537092 | + | 0.998557i | \(0.517104\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15498.8 | −1.55570 | −0.777851 | − | 0.628449i | \(-0.783690\pi\) | ||||
−0.777851 | + | 0.628449i | \(0.783690\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10034.7 | −1.00074 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13215.6 | 1.30952 | 0.654759 | − | 0.755838i | \(-0.272770\pi\) | ||||
0.654759 | + | 0.755838i | \(0.272770\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13935.7 | −1.37204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8306.01 | 0.812571 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3393.38 | −0.329869 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1368.91 | −0.132231 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5309.92 | −0.509695 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19058.5 | 1.81796 | 0.908981 | − | 0.416837i | \(-0.136861\pi\) | ||||
0.908981 | + | 0.416837i | \(0.136861\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −161.031 | −0.0152648 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19520.1 | −1.83891 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4159.49 | −0.389428 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 487.214 | 0.0453343 | 0.0226671 | − | 0.999743i | \(-0.492784\pi\) | ||||
0.0226671 | + | 0.999743i | \(0.492784\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3661.94 | −0.338647 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6462.89 | −0.594025 | −0.297013 | − | 0.954874i | \(-0.595990\pi\) | ||||
−0.297013 | + | 0.954874i | \(0.595990\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −498.563 | −0.0455460 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7665.58 | −0.696045 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13281.4 | −1.19870 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7947.79 | −0.713010 | −0.356505 | − | 0.934293i | \(-0.616032\pi\) | ||||
−0.356505 | + | 0.934293i | \(0.616032\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4538.24 | 0.404698 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2307.81 | 0.204573 | 0.102287 | − | 0.994755i | \(-0.467384\pi\) | ||||
0.102287 | + | 0.994755i | \(0.467384\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11754.2 | −1.03576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7477.79 | 0.655030 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16496.2 | 1.43651 | 0.718253 | − | 0.695782i | \(-0.244942\pi\) | ||||
0.718253 | + | 0.695782i | \(0.244942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 85.8287 | 0.00743021 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6419.33 | 0.552476 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10007.9 | 0.856314 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26148.0 | −2.22435 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2255.28 | −0.190743 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10386.5 | −0.873398 | −0.436699 | − | 0.899608i | \(-0.643853\pi\) | ||||
−0.436699 | + | 0.899608i | \(0.643853\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −918.174 | −0.0767666 | −0.0383833 | − | 0.999263i | \(-0.512221\pi\) | ||||
−0.0383833 | + | 0.999263i | \(0.512221\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2948.03 | 0.245072 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5157.45 | −0.426304 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29882.7 | 2.45604 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7888.36 | −0.644681 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −237.559 | −0.0193055 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11404.2 | 0.921580 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7089.68 | −0.569725 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21909.7 | −1.75086 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12860.2 | 1.02200 | 0.511001 | − | 0.859580i | \(-0.329275\pi\) | ||||
0.511001 | + | 0.859580i | \(0.329275\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11722.6 | 0.926456 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21021.6 | −1.65223 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4471.84 | 0.349547 | 0.174774 | − | 0.984609i | \(-0.444081\pi\) | ||||
0.174774 | + | 0.984609i | \(0.444081\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7318.05 | 0.568901 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1281.86 | −0.0991090 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28789.9 | 2.21387 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −996.727 | −0.0762319 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2649.40 | −0.201542 | −0.100771 | − | 0.994910i | \(-0.532131\pi\) | ||||
−0.100771 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 350.309 | 0.0265053 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3104.42 | 0.233634 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12615.8 | 0.944395 | 0.472198 | − | 0.881493i | \(-0.343461\pi\) | ||||
0.472198 | + | 0.881493i | \(0.343461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15744.5 | −1.17234 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2572.81 | −0.190561 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 617.443 | 0.0454913 | 0.0227456 | − | 0.999741i | \(-0.492759\pi\) | ||||
0.0227456 | + | 0.999741i | \(0.492759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8005.50 | 0.586725 | 0.293362 | − | 0.956001i | \(-0.405226\pi\) | ||||
0.293362 | + | 0.956001i | \(0.405226\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16743.5 | 1.22072 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6350.59 | −0.460588 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11761.1 | 0.848565 | 0.424282 | − | 0.905530i | \(-0.360526\pi\) | ||||
0.424282 | + | 0.905530i | \(0.360526\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16824.0 | 1.20757 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27791.3 | −1.98447 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18407.1 | −1.30762 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 791.340 | 0.0559280 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1211.03 | −0.0851528 | −0.0425764 | − | 0.999093i | \(-0.513557\pi\) | ||||
−0.0425764 | + | 0.999093i | \(0.513557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13260.4 | −0.927646 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3557.86 | −0.247633 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 459.376 | 0.0318117 | 0.0159058 | − | 0.999873i | \(-0.494937\pi\) | ||||
0.0159058 | + | 0.999873i | \(0.494937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4600.47 | −0.316976 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4027.97 | −0.276137 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16686.2 | −1.13820 | −0.569099 | − | 0.822269i | \(-0.692708\pi\) | ||||
−0.569099 | + | 0.822269i | \(0.692708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11625.9 | 0.789072 | 0.394536 | − | 0.918881i | \(-0.370905\pi\) | ||||
0.394536 | + | 0.918881i | \(0.370905\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7625.86 | 0.515007 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13666.5 | −0.918384 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21556.9 | 1.44146 | 0.720731 | − | 0.693215i | \(-0.243806\pi\) | ||||
0.720731 | + | 0.693215i | \(0.243806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2760.56 | 0.183684 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2699.34 | 0.178729 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19273.2 | 1.26988 | 0.634940 | − | 0.772561i | \(-0.281025\pi\) | ||||
0.634940 | + | 0.772561i | \(0.281025\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1470.41 | −0.0964110 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3270.70 | −0.213409 | −0.106704 | − | 0.994291i | \(-0.534030\pi\) | ||||
−0.106704 | + | 0.994291i | \(0.534030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 75.8068 | 0.00492234 | 0.00246117 | − | 0.999997i | \(-0.499217\pi\) | ||||
0.00246117 | + | 0.999997i | \(0.499217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29780.3 | 1.92438 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8158.37 | −0.524652 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10794.7 | −0.690862 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7981.81 | 0.508393 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −512.282 | −0.0324738 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4915.71 | 0.310129 | 0.155064 | − | 0.987904i | \(-0.450441\pi\) | ||||
0.155064 | + | 0.987904i | \(0.450441\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2740.07 | −0.172051 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3233.67 | 0.202086 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2261.80 | 0.140684 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7267.86 | 0.449941 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3317.63 | 0.204428 | 0.102214 | − | 0.994762i | \(-0.467407\pi\) | ||||
0.102214 | + | 0.994762i | \(0.467407\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27222.7 | −1.66961 | −0.834805 | − | 0.550546i | \(-0.814420\pi\) | ||||
−0.834805 | + | 0.550546i | \(0.814420\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2168.29 | 0.132367 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24433.6 | −1.48468 | −0.742338 | − | 0.670025i | \(-0.766283\pi\) | ||||
−0.742338 | + | 0.670025i | \(0.766283\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27345.4 | −1.65393 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28557.0 | 1.71926 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5755.36 | −0.344907 | −0.172454 | − | 0.985018i | \(-0.555170\pi\) | ||||
−0.172454 | + | 0.985018i | \(0.555170\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9052.01 | 0.539987 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −46.9671 | −0.00278898 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 965.300 | 0.0570603 | 0.0285301 | − | 0.999593i | \(-0.490917\pi\) | ||||
0.0285301 | + | 0.999593i | \(0.490917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22791.0 | 1.34110 | 0.670549 | − | 0.741866i | \(-0.266059\pi\) | ||||
0.670549 | + | 0.741866i | \(0.266059\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −320.479 | −0.0187728 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11828.3 | −0.689746 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5946.75 | −0.345216 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17716.9 | 1.02388 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25368.4 | 1.45952 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12412.1 | 0.710925 | 0.355463 | − | 0.934690i | \(-0.384323\pi\) | ||||
0.355463 | + | 0.934690i | \(0.384323\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4497.59 | −0.256463 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8998.03 | −0.510816 | −0.255408 | − | 0.966833i | \(-0.582210\pi\) | ||||
−0.255408 | + | 0.966833i | \(0.582210\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11837.2 | 0.669030 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17360.7 | 0.976893 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13439.1 | 0.752904 | 0.376452 | − | 0.926436i | \(-0.377144\pi\) | ||||
0.376452 | + | 0.926436i | \(0.377144\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10572.8 | 0.589730 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21432.1 | −1.19023 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1900.22 | 0.105069 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16220.4 | −0.892983 | −0.446492 | − | 0.894788i | \(-0.647327\pi\) | ||||
−0.446492 | + | 0.894788i | \(0.647327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21815.0 | 1.19579 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18662.7 | 1.01858 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −755.739 | −0.0410698 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10754.1 | 0.581912 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18919.6 | 1.01938 | 0.509689 | − | 0.860359i | \(-0.329761\pi\) | ||||
0.509689 | + | 0.860359i | \(0.329761\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1317.13 | −0.0706636 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16708.0 | 0.892567 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33450.6 | 1.77941 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4781.99 | 0.253302 | 0.126651 | − | 0.991947i | \(-0.459577\pi\) | ||||
0.126651 | + | 0.991947i | \(0.459577\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15754.4 | −0.830992 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −61516.9 | −3.23117 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2743.22 | 0.143483 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24812.5 | 1.29238 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13020.1 | −0.675336 | −0.337668 | − | 0.941265i | \(-0.609638\pi\) | ||||
−0.337668 | + | 0.941265i | \(0.609638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28480.9 | −1.47113 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2888.42 | 0.148577 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 898.112 | 0.0460070 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8738.68 | 0.445804 | 0.222902 | − | 0.974841i | \(-0.428447\pi\) | ||||
0.222902 | + | 0.974841i | \(0.428447\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14933.8 | 0.758715 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1114.43 | 0.0563865 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12775.2 | 0.643744 | 0.321872 | − | 0.946783i | \(-0.395688\pi\) | ||||
0.321872 | + | 0.946783i | \(0.395688\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13999.8 | 0.702571 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26435.4 | 1.32125 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5397.68 | 0.268683 | 0.134342 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134342 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −823.985 | −0.0408500 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37984.2 | 1.87551 | 0.937757 | − | 0.347293i | \(-0.112899\pi\) | ||||
0.937757 | + | 0.347293i | \(0.112899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16519.9 | −0.812408 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15207.9 | 0.744886 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −32454.4 | −1.58326 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26384.8 | −1.28202 | −0.641009 | − | 0.767534i | \(-0.721484\pi\) | ||||
−0.641009 | + | 0.767534i | \(0.721484\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14855.4 | −0.718940 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10499.9 | 0.506133 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6889.95 | −0.330805 | −0.165403 | − | 0.986226i | \(-0.552892\pi\) | ||||
−0.165403 | + | 0.986226i | \(0.552892\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 37028.8 | 1.77083 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31579.3 | 1.50427 | 0.752134 | − | 0.659010i | \(-0.229025\pi\) | ||||
0.752134 | + | 0.659010i | \(0.229025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 59824.0 | 2.83850 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2517.46 | 0.118979 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2822.94 | 0.132895 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12232.7 | −0.573632 | −0.286816 | − | 0.957986i | \(-0.592597\pi\) | ||||
−0.286816 | + | 0.957986i | \(0.592597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1384.07 | −0.0646510 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9958.46 | −0.463365 | −0.231682 | − | 0.972792i | \(-0.574423\pi\) | ||||
−0.231682 | + | 0.972792i | \(0.574423\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9290.64 | 0.430619 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2836.52 | 0.130965 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1943.09 | −0.0893688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25194.4 | 1.15432 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4211.58 | −0.192222 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23349.2 | 1.06162 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 103.911 | 0.00470653 | 0.00235326 | − | 0.999997i | \(-0.499251\pi\) | ||||
0.00235326 | + | 0.999997i | \(0.499251\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9254.02 | −0.417556 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44806.2 | 2.01406 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2618.85 | −0.117274 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 11761.7 | 0.524711 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30624.4 | −1.36107 | −0.680534 | − | 0.732717i | \(-0.738252\pi\) | ||||
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8587.31 | 0.380222 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4464.42 | 0.196932 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −162.814 | −0.00715514 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −54873.3 | −2.40252 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16324.3 | −0.712072 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7737.50 | −0.336262 | −0.168131 | − | 0.985765i | \(-0.553773\pi\) | ||||
−0.168131 | + | 0.985765i | \(0.553773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12974.1 | −0.561756 | −0.280878 | − | 0.959744i | \(-0.590626\pi\) | ||||
−0.280878 | + | 0.959744i | \(0.590626\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15625.0 | 0.674038 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10294.2 | −0.442440 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2865.31 | 0.122698 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2252.02 | −0.0960831 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3264.26 | −0.138762 | −0.0693809 | − | 0.997590i | \(-0.522102\pi\) | ||||
−0.0693809 | + | 0.997590i | \(0.522102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23509.7 | −0.995745 | −0.497872 | − | 0.867250i | \(-0.665885\pi\) | ||||
−0.497872 | + | 0.867250i | \(0.665885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5592.31 | −0.235999 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27116.5 | 1.14019 | 0.570093 | − | 0.821580i | \(-0.306907\pi\) | ||||
0.570093 | + | 0.821580i | \(0.306907\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15393.6 | −0.644923 | −0.322462 | − | 0.946583i | \(-0.604510\pi\) | ||||
−0.322462 | + | 0.946583i | \(0.604510\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24693.8 | 1.03083 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7195.38 | 0.299286 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12757.5 | 0.528734 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43567.3 | −1.79917 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7906.51 | 0.325343 | 0.162672 | − | 0.986680i | \(-0.447989\pi\) | ||||
0.162672 | + | 0.986680i | \(0.447989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19902.7 | 0.813150 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21021.0 | 0.855791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38892.6 | 1.57777 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13160.7 | 0.532005 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6110.38 | −0.246135 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11887.1 | 0.477146 | 0.238573 | − | 0.971125i | \(-0.423320\pi\) | ||||
0.238573 | + | 0.971125i | \(0.423320\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6472.67 | 0.258901 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −655.328 | −0.0261208 | −0.0130604 | − | 0.999915i | \(-0.504157\pi\) | ||||
−0.0130604 | + | 0.999915i | \(0.504157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48758.4 | −1.93669 | −0.968345 | − | 0.249617i | \(-0.919695\pi\) | ||||
−0.968345 | + | 0.249617i | \(0.919695\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4184.55 | 0.165632 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10398.2 | 0.410150 | 0.205075 | − | 0.978746i | \(-0.434256\pi\) | ||||
0.205075 | + | 0.978746i | \(0.434256\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6339.86 | −0.249204 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15927.8 | 0.623918 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −54613.4 | −2.13191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2729.01 | −0.106164 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6477.57 | −0.251125 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41736.8 | 1.61253 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31024.2 | 1.19454 | 0.597272 | − | 0.802039i | \(-0.296251\pi\) | ||||
0.597272 | + | 0.802039i | \(0.296251\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18684.7 | 0.716973 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1510.50 | −0.0577641 | −0.0288821 | − | 0.999583i | \(-0.509195\pi\) | ||||
−0.0288821 | + | 0.999583i | \(0.509195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32376.4 | −1.23392 | −0.616961 | − | 0.786993i | \(-0.711637\pi\) | ||||
−0.616961 | + | 0.786993i | \(0.711637\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 17473.1 | 0.663674 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10474.6 | −0.396510 | −0.198255 | − | 0.980150i | \(-0.563527\pi\) | ||||
−0.198255 | + | 0.980150i | \(0.563527\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9202.51 | −0.347179 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4880.53 | 0.183506 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22078.9 | 0.827371 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19930.0 | −0.744341 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3822.59 | −0.142288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8699.84 | 0.322754 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6045.11 | 0.223520 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6170.62 | −0.227403 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32953.7 | 1.21041 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34634.3 | −1.26793 | −0.633965 | − | 0.773362i | \(-0.718574\pi\) | ||||
−0.633965 | + | 0.773362i | \(0.718574\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18304.8 | −0.667913 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1186.14 | −0.0431377 | −0.0215688 | − | 0.999767i | \(-0.506866\pi\) | ||||
−0.0215688 | + | 0.999767i | \(0.506866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52719.1 | 1.91101 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16209.8 | −0.585662 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25760.6 | −0.927687 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5685.58 | 0.204080 | 0.102040 | − | 0.994780i | \(-0.467463\pi\) | ||||
0.102040 | + | 0.994780i | \(0.467463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17002.7 | −0.608316 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2600.89 | −0.0927512 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 922.824 | 0.0328025 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15585.3 | 0.552200 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19143.7 | −0.676087 | −0.338044 | − | 0.941130i | \(-0.609765\pi\) | ||||
−0.338044 | + | 0.941130i | \(0.609765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18500.1 | 0.651252 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3856.28 | 0.135315 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8726.92 | 0.305241 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53623.5 | −1.86959 | −0.934794 | − | 0.355191i | \(-0.884416\pi\) | ||||
−0.934794 | + | 0.355191i | \(0.884416\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7010.08 | −0.243626 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7947.57 | 0.275328 | 0.137664 | − | 0.990479i | \(-0.456041\pi\) | ||||
0.137664 | + | 0.990479i | \(0.456041\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9014.28 | −0.311289 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −38862.2 | −1.33776 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41047.8 | −1.40853 | −0.704263 | − | 0.709939i | \(-0.748723\pi\) | ||||
−0.704263 | + | 0.709939i | \(0.748723\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.8077 | 0.000574924 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7077.49 | 0.241328 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12000.8 | −0.407915 | −0.203957 | − | 0.978980i | \(-0.565380\pi\) | ||||
−0.203957 | + | 0.978980i | \(0.565380\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 47068.1 | 1.59486 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5236.69 | −0.176884 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30088.4 | −1.01314 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60205.6 | 2.02093 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17759.7 | 0.594287 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 47294.3 | 1.57768 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55391.0 | 1.84204 | 0.921021 | − | 0.389514i | \(-0.127357\pi\) | ||||
0.921021 | + | 0.389514i | \(0.127357\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2621.32 | −0.0869028 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23937.0 | −0.791117 | −0.395558 | − | 0.918441i | \(-0.629449\pi\) | ||||
−0.395558 | + | 0.918441i | \(0.629449\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −53111.0 | −1.74991 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 577.310 | 0.0189628 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43982.3 | −1.44024 | −0.720122 | − | 0.693847i | \(-0.755914\pi\) | ||||
−0.720122 | + | 0.693847i | \(0.755914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15476.1 | 0.505229 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −32736.8 | −1.06545 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2724.78 | −0.0884100 | −0.0442050 | − | 0.999022i | \(-0.514075\pi\) | ||||
−0.0442050 | + | 0.999022i | \(0.514075\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10001.6 | −0.323530 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47548.3 | −1.53341 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13292.6 | 0.427382 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23748.6 | 0.761250 | 0.380625 | − | 0.924729i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924729i | \(0.375709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33297.7 | 1.06412 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11323.1 | −0.360771 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24718.0 | −0.785182 | −0.392591 | − | 0.919713i | \(-0.628421\pi\) | ||||
−0.392591 | + | 0.919713i | \(0.628421\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4327.47 | −0.137052 |
(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 | 1856.4.a.i.1.1 | 2 | ||
4.3 | odd | 2 | 1856.4.a.l.1.2 | 2 | |||
8.3 | odd | 2 | 58.4.a.c.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 464.4.a.e.1.2 | 2 | |||
24.11 | even | 2 | 522.4.a.j.1.1 | 2 | |||
40.19 | odd | 2 | 1450.4.a.g.1.2 | 2 | |||
232.115 | odd | 2 | 1682.4.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
58.4.a.c.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
464.4.a.e.1.2 | 2 | 8.5 | even | 2 | |||
522.4.a.j.1.1 | 2 | 24.11 | even | 2 | |||
1450.4.a.g.1.2 | 2 | 40.19 | odd | 2 | |||
1682.4.a.c.1.2 | 2 | 232.115 | odd | 2 | |||
1856.4.a.i.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1856.4.a.l.1.2 | 2 | 4.3 | odd | 2 |