Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.915825 | −0.323793 | −0.161896 | − | 0.986808i | \(-0.551761\pi\) | ||||
−0.161896 | + | 0.986808i | \(0.551761\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −7.16127 | −0.895158 | ||||||||
\(5\) | −7.54581 | −0.674918 | −0.337459 | − | 0.941340i | \(-0.609567\pi\) | ||||
−0.337459 | + | 0.941340i | \(0.609567\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 24.7091 | 1.33416 | 0.667082 | − | 0.744984i | \(-0.267543\pi\) | ||||
0.667082 | + | 0.744984i | \(0.267543\pi\) | |||||||
\(8\) | 13.8851 | 0.613639 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.91064 | 0.218534 | ||||||||
\(11\) | 49.4899 | 1.35652 | 0.678262 | − | 0.734820i | \(-0.262733\pi\) | ||||
0.678262 | + | 0.734820i | \(0.262733\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −26.5926 | −0.567343 | −0.283671 | − | 0.958922i | \(-0.591552\pi\) | ||||
−0.283671 | + | 0.958922i | \(0.591552\pi\) | |||||||
\(14\) | −22.6292 | −0.431993 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 44.5738 | 0.696466 | ||||||||
\(17\) | −21.6855 | −0.309382 | −0.154691 | − | 0.987963i | \(-0.549438\pi\) | ||||
−0.154691 | + | 0.987963i | \(0.549438\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −36.0776 | −0.435619 | −0.217810 | − | 0.975991i | \(-0.569891\pi\) | ||||
−0.217810 | + | 0.975991i | \(0.569891\pi\) | |||||||
\(20\) | 54.0376 | 0.604158 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −45.3241 | −0.439233 | ||||||||
\(23\) | −137.325 | −1.24497 | −0.622483 | − | 0.782633i | \(-0.713876\pi\) | ||||
−0.622483 | + | 0.782633i | \(0.713876\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −68.0607 | −0.544486 | ||||||||
\(26\) | 24.3541 | 0.183702 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −176.948 | −1.19429 | ||||||||
\(29\) | 0.350892 | 0.00224686 | 0.00112343 | − | 0.999999i | \(-0.499642\pi\) | ||||
0.00112343 | + | 0.999999i | \(0.499642\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 302.936 | 1.75512 | 0.877562 | − | 0.479464i | \(-0.159169\pi\) | ||||
0.877562 | + | 0.479464i | \(0.159169\pi\) | |||||||
\(32\) | −151.902 | −0.839150 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 19.8601 | 0.100176 | ||||||||
\(35\) | −186.450 | −0.900451 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −340.352 | −1.51226 | −0.756128 | − | 0.654424i | \(-0.772911\pi\) | ||||
−0.756128 | + | 0.654424i | \(0.772911\pi\) | |||||||
\(38\) | 33.0407 | 0.141050 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −104.774 | −0.414156 | ||||||||
\(41\) | 31.5267 | 0.120089 | 0.0600444 | − | 0.998196i | \(-0.480876\pi\) | ||||
0.0600444 | + | 0.998196i | \(0.480876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −291.827 | −1.03496 | −0.517478 | − | 0.855696i | \(-0.673129\pi\) | ||||
−0.517478 | + | 0.855696i | \(0.673129\pi\) | |||||||
\(44\) | −354.410 | −1.21430 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 125.766 | 0.403111 | ||||||||
\(47\) | 576.423 | 1.78893 | 0.894467 | − | 0.447134i | \(-0.147555\pi\) | ||||
0.894467 | + | 0.447134i | \(0.147555\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 267.538 | 0.779993 | ||||||||
\(50\) | 62.3317 | 0.176301 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 190.437 | 0.507861 | ||||||||
\(53\) | −108.321 | −0.280737 | −0.140368 | − | 0.990099i | \(-0.544829\pi\) | ||||
−0.140368 | + | 0.990099i | \(0.544829\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −373.442 | −0.915543 | ||||||||
\(56\) | 343.087 | 0.818695 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.321356 | −0.000727519 0 | ||||||||
\(59\) | −138.023 | −0.304561 | −0.152281 | − | 0.988337i | \(-0.548662\pi\) | ||||
−0.152281 | + | 0.988337i | \(0.548662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 622.364 | 1.30632 | 0.653160 | − | 0.757220i | \(-0.273443\pi\) | ||||
0.653160 | + | 0.757220i | \(0.273443\pi\) | |||||||
\(62\) | −277.436 | −0.568297 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −217.475 | −0.424755 | ||||||||
\(65\) | 200.663 | 0.382910 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 348.715 | 0.635856 | 0.317928 | − | 0.948115i | \(-0.397013\pi\) | ||||
0.317928 | + | 0.948115i | \(0.397013\pi\) | |||||||
\(68\) | 155.295 | 0.276946 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 170.755 | 0.291560 | ||||||||
\(71\) | 322.287 | 0.538711 | 0.269355 | − | 0.963041i | \(-0.413189\pi\) | ||||
0.269355 | + | 0.963041i | \(0.413189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1219.41 | −1.95509 | −0.977543 | − | 0.210737i | \(-0.932414\pi\) | ||||
−0.977543 | + | 0.210737i | \(0.932414\pi\) | |||||||
\(74\) | 311.703 | 0.489658 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 258.361 | 0.389948 | ||||||||
\(77\) | 1222.85 | 1.80983 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1116.69 | −1.59035 | −0.795177 | − | 0.606378i | \(-0.792622\pi\) | ||||
−0.795177 | + | 0.606378i | \(0.792622\pi\) | |||||||
\(80\) | −336.346 | −0.470058 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −28.8729 | −0.0388839 | ||||||||
\(83\) | 379.080 | 0.501319 | 0.250659 | − | 0.968075i | \(-0.419353\pi\) | ||||
0.250659 | + | 0.968075i | \(0.419353\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 163.634 | 0.208808 | ||||||||
\(86\) | 267.262 | 0.335112 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 687.170 | 0.832416 | ||||||||
\(89\) | 1277.30 | 1.52127 | 0.760637 | − | 0.649177i | \(-0.224887\pi\) | ||||
0.760637 | + | 0.649177i | \(0.224887\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −657.078 | −0.756928 | ||||||||
\(92\) | 983.420 | 1.11444 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −527.902 | −0.579244 | ||||||||
\(95\) | 272.235 | 0.294007 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −814.774 | −0.852864 | −0.426432 | − | 0.904520i | \(-0.640230\pi\) | ||||
−0.426432 | + | 0.904520i | \(0.640230\pi\) | |||||||
\(98\) | −245.017 | −0.252556 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 487.401 | 0.487401 | ||||||||
\(101\) | 421.449 | 0.415206 | 0.207603 | − | 0.978213i | \(-0.433434\pi\) | ||||
0.207603 | + | 0.978213i | \(0.433434\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 32.5268 | 0.0311161 | 0.0155581 | − | 0.999879i | \(-0.495048\pi\) | ||||
0.0155581 | + | 0.999879i | \(0.495048\pi\) | |||||||
\(104\) | −369.240 | −0.348143 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 99.2032 | 0.0909007 | ||||||||
\(107\) | 1387.59 | 1.25368 | 0.626840 | − | 0.779148i | \(-0.284348\pi\) | ||||
0.626840 | + | 0.779148i | \(0.284348\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1069.15 | −0.939503 | −0.469752 | − | 0.882799i | \(-0.655657\pi\) | ||||
−0.469752 | + | 0.882799i | \(0.655657\pi\) | |||||||
\(110\) | 342.007 | 0.296446 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1101.38 | 0.929200 | ||||||||
\(113\) | 519.470 | 0.432457 | 0.216228 | − | 0.976343i | \(-0.430624\pi\) | ||||
0.216228 | + | 0.976343i | \(0.430624\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1036.23 | 0.840250 | ||||||||
\(116\) | −2.51283 | −0.00201130 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 126.405 | 0.0986147 | ||||||||
\(119\) | −535.827 | −0.412767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1118.25 | 0.840158 | ||||||||
\(122\) | −569.976 | −0.422977 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2169.40 | −1.57111 | ||||||||
\(125\) | 1456.80 | 1.04240 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1420.46 | 0.992486 | 0.496243 | − | 0.868184i | \(-0.334713\pi\) | ||||
0.496243 | + | 0.868184i | \(0.334713\pi\) | |||||||
\(128\) | 1414.39 | 0.976682 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −183.772 | −0.123983 | ||||||||
\(131\) | 1795.64 | 1.19760 | 0.598799 | − | 0.800899i | \(-0.295645\pi\) | ||||
0.598799 | + | 0.800899i | \(0.295645\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −891.443 | −0.581187 | ||||||||
\(134\) | −319.362 | −0.205886 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −301.104 | −0.189849 | ||||||||
\(137\) | −1581.74 | −0.986405 | −0.493203 | − | 0.869914i | \(-0.664174\pi\) | ||||
−0.493203 | + | 0.869914i | \(0.664174\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −816.896 | −0.498477 | −0.249238 | − | 0.968442i | \(-0.580180\pi\) | ||||
−0.249238 | + | 0.968442i | \(0.580180\pi\) | |||||||
\(140\) | 1335.22 | 0.806046 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −295.159 | −0.174431 | ||||||||
\(143\) | −1316.06 | −0.769614 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.64777 | −0.00151645 | ||||||||
\(146\) | 1116.77 | 0.633043 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2437.35 | 1.35371 | ||||||||
\(149\) | −3569.30 | −1.96247 | −0.981236 | − | 0.192810i | \(-0.938240\pi\) | ||||
−0.981236 | + | 0.192810i | \(0.938240\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2320.85 | −1.25078 | −0.625391 | − | 0.780311i | \(-0.715061\pi\) | ||||
−0.625391 | + | 0.780311i | \(0.715061\pi\) | |||||||
\(152\) | −500.939 | −0.267313 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1119.92 | −0.586009 | ||||||||
\(155\) | −2285.89 | −1.18456 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3209.19 | 1.63135 | 0.815673 | − | 0.578513i | \(-0.196367\pi\) | ||||
0.815673 | + | 0.578513i | \(0.196367\pi\) | |||||||
\(158\) | 1022.70 | 0.514945 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1146.23 | 0.566357 | ||||||||
\(161\) | −3393.17 | −1.66099 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2042.28 | −0.981370 | −0.490685 | − | 0.871337i | \(-0.663253\pi\) | ||||
−0.490685 | + | 0.871337i | \(0.663253\pi\) | |||||||
\(164\) | −225.771 | −0.107498 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −347.171 | −0.162323 | ||||||||
\(167\) | −884.456 | −0.409828 | −0.204914 | − | 0.978780i | \(-0.565691\pi\) | ||||
−0.204914 | + | 0.978780i | \(0.565691\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1489.83 | −0.678122 | ||||||||
\(170\) | −149.861 | −0.0676105 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2089.85 | 0.926450 | ||||||||
\(173\) | −410.066 | −0.180212 | −0.0901062 | − | 0.995932i | \(-0.528721\pi\) | ||||
−0.0901062 | + | 0.995932i | \(0.528721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1681.72 | −0.726433 | ||||||||
\(176\) | 2205.95 | 0.944773 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1169.78 | −0.492578 | ||||||||
\(179\) | 2521.04 | 1.05269 | 0.526346 | − | 0.850271i | \(-0.323562\pi\) | ||||
0.526346 | + | 0.850271i | \(0.323562\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 947.700 | 0.389182 | 0.194591 | − | 0.980884i | \(-0.437662\pi\) | ||||
0.194591 | + | 0.980884i | \(0.437662\pi\) | |||||||
\(182\) | 601.768 | 0.245088 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1906.76 | −0.763959 | ||||||||
\(185\) | 2568.23 | 1.02065 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1073.21 | −0.419685 | ||||||||
\(188\) | −4127.92 | −1.60138 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −249.319 | −0.0951975 | ||||||||
\(191\) | −3979.72 | −1.50766 | −0.753829 | − | 0.657071i | \(-0.771795\pi\) | ||||
−0.753829 | + | 0.657071i | \(0.771795\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3640.34 | 1.35771 | 0.678853 | − | 0.734274i | \(-0.262477\pi\) | ||||
0.678853 | + | 0.734274i | \(0.262477\pi\) | |||||||
\(194\) | 746.191 | 0.276151 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1915.91 | −0.698217 | ||||||||
\(197\) | −1661.13 | −0.600766 | −0.300383 | − | 0.953819i | \(-0.597115\pi\) | ||||
−0.300383 | + | 0.953819i | \(0.597115\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1317.39 | −0.469283 | −0.234641 | − | 0.972082i | \(-0.575392\pi\) | ||||
−0.234641 | + | 0.972082i | \(0.575392\pi\) | |||||||
\(200\) | −945.027 | −0.334117 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −385.974 | −0.134441 | ||||||||
\(203\) | 8.67022 | 0.00299768 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −237.895 | −0.0810501 | ||||||||
\(206\) | −29.7889 | −0.0100752 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1185.33 | −0.395135 | ||||||||
\(209\) | −1785.48 | −0.590928 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4554.14 | −1.48588 | −0.742939 | − | 0.669359i | \(-0.766569\pi\) | ||||
−0.742939 | + | 0.669359i | \(0.766569\pi\) | |||||||
\(212\) | 775.717 | 0.251304 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1270.79 | −0.405933 | ||||||||
\(215\) | 2202.07 | 0.698511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7485.25 | 2.34162 | ||||||||
\(218\) | 979.153 | 0.304205 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2674.31 | 0.819556 | ||||||||
\(221\) | 576.672 | 0.175526 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1217.03 | 0.365462 | 0.182731 | − | 0.983163i | \(-0.441506\pi\) | ||||
0.182731 | + | 0.983163i | \(0.441506\pi\) | |||||||
\(224\) | −3753.36 | −1.11956 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −475.743 | −0.140026 | ||||||||
\(227\) | −5712.96 | −1.67041 | −0.835203 | − | 0.549942i | \(-0.814650\pi\) | ||||
−0.835203 | + | 0.549942i | \(0.814650\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5241.04 | −1.51239 | −0.756196 | − | 0.654345i | \(-0.772944\pi\) | ||||
−0.756196 | + | 0.654345i | \(0.772944\pi\) | |||||||
\(230\) | −949.003 | −0.272067 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.87216 | 0.00137876 | ||||||||
\(233\) | −4672.74 | −1.31382 | −0.656912 | − | 0.753967i | \(-0.728138\pi\) | ||||
−0.656912 | + | 0.753967i | \(0.728138\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4349.58 | −1.20738 | ||||||||
\(236\) | 988.422 | 0.272630 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 490.724 | 0.133651 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3779.64 | 1.01024 | 0.505120 | − | 0.863049i | \(-0.331448\pi\) | ||||
0.505120 | + | 0.863049i | \(0.331448\pi\) | |||||||
\(242\) | −1024.12 | −0.272037 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4456.91 | −1.16936 | ||||||||
\(245\) | −2018.79 | −0.526431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 959.396 | 0.247145 | ||||||||
\(248\) | 4206.28 | 1.07701 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1334.17 | −0.337522 | ||||||||
\(251\) | −4718.47 | −1.18656 | −0.593281 | − | 0.804995i | \(-0.702168\pi\) | ||||
−0.593281 | + | 0.804995i | \(0.702168\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6796.19 | −1.68883 | ||||||||
\(254\) | −1300.90 | −0.321360 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 444.467 | 0.108513 | ||||||||
\(257\) | 1973.28 | 0.478949 | 0.239474 | − | 0.970903i | \(-0.423025\pi\) | ||||
0.239474 | + | 0.970903i | \(0.423025\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8409.77 | −2.01760 | ||||||||
\(260\) | −1437.00 | −0.342765 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1644.49 | −0.387774 | ||||||||
\(263\) | 3962.75 | 0.929102 | 0.464551 | − | 0.885546i | \(-0.346216\pi\) | ||||
0.464551 | + | 0.885546i | \(0.346216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 817.372 | 0.189474 | ||||||||
\(266\) | 816.406 | 0.188184 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2497.24 | −0.569191 | ||||||||
\(269\) | 3186.72 | 0.722296 | 0.361148 | − | 0.932508i | \(-0.382385\pi\) | ||||
0.361148 | + | 0.932508i | \(0.382385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4140.92 | −0.928203 | −0.464101 | − | 0.885782i | \(-0.653623\pi\) | ||||
−0.464101 | + | 0.885782i | \(0.653623\pi\) | |||||||
\(272\) | −966.604 | −0.215474 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1448.60 | 0.319391 | ||||||||
\(275\) | −3368.32 | −0.738608 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4612.25 | −1.00044 | −0.500222 | − | 0.865897i | \(-0.666748\pi\) | ||||
−0.500222 | + | 0.865897i | \(0.666748\pi\) | |||||||
\(278\) | 748.134 | 0.161403 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2588.87 | −0.552552 | ||||||||
\(281\) | −3827.71 | −0.812604 | −0.406302 | − | 0.913739i | \(-0.633182\pi\) | ||||
−0.406302 | + | 0.913739i | \(0.633182\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8715.37 | −1.83065 | −0.915326 | − | 0.402713i | \(-0.868067\pi\) | ||||
−0.915326 | + | 0.402713i | \(0.868067\pi\) | |||||||
\(284\) | −2307.98 | −0.482231 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1205.28 | 0.249196 | ||||||||
\(287\) | 778.995 | 0.160218 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4442.74 | −0.904283 | ||||||||
\(290\) | 2.42489 | 0.000491016 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8732.53 | 1.75011 | ||||||||
\(293\) | 5279.18 | 1.05260 | 0.526302 | − | 0.850298i | \(-0.323578\pi\) | ||||
0.526302 | + | 0.850298i | \(0.323578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1041.50 | 0.205554 | ||||||||
\(296\) | −4725.80 | −0.927979 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3268.85 | 0.635435 | ||||||||
\(299\) | 3651.82 | 0.706322 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7210.76 | −1.38080 | ||||||||
\(302\) | 2125.49 | 0.404995 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1608.12 | −0.303394 | ||||||||
\(305\) | −4696.24 | −0.881659 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 644.834 | 0.119878 | 0.0599391 | − | 0.998202i | \(-0.480909\pi\) | ||||
0.0599391 | + | 0.998202i | \(0.480909\pi\) | |||||||
\(308\) | −8757.14 | −1.62008 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2093.48 | 0.383554 | ||||||||
\(311\) | −7145.34 | −1.30281 | −0.651407 | − | 0.758728i | \(-0.725821\pi\) | ||||
−0.651407 | + | 0.758728i | \(0.725821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5382.86 | 0.972069 | 0.486034 | − | 0.873940i | \(-0.338443\pi\) | ||||
0.486034 | + | 0.873940i | \(0.338443\pi\) | |||||||
\(314\) | −2939.06 | −0.528218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7996.95 | 1.42362 | ||||||||
\(317\) | 832.861 | 0.147565 | 0.0737826 | − | 0.997274i | \(-0.476493\pi\) | ||||
0.0737826 | + | 0.997274i | \(0.476493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.3656 | 0.00304793 | ||||||||
\(320\) | 1641.02 | 0.286675 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3107.55 | 0.537816 | ||||||||
\(323\) | 782.359 | 0.134773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1809.91 | 0.308910 | ||||||||
\(326\) | 1870.37 | 0.317761 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 437.750 | 0.0736912 | ||||||||
\(329\) | 14242.9 | 2.38673 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5984.19 | 0.993718 | 0.496859 | − | 0.867831i | \(-0.334487\pi\) | ||||
0.496859 | + | 0.867831i | \(0.334487\pi\) | |||||||
\(332\) | −2714.69 | −0.448759 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 810.007 | 0.132699 | ||||||||
\(335\) | −2631.34 | −0.429150 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9699.50 | 1.56785 | 0.783925 | − | 0.620855i | \(-0.213215\pi\) | ||||
0.783925 | + | 0.620855i | \(0.213215\pi\) | |||||||
\(338\) | 1364.43 | 0.219571 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1171.83 | −0.186916 | ||||||||
\(341\) | 14992.2 | 2.38087 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1864.61 | −0.293526 | ||||||||
\(344\) | −4052.03 | −0.635090 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 375.549 | 0.0583515 | ||||||||
\(347\) | 11627.2 | 1.79879 | 0.899397 | − | 0.437132i | \(-0.144006\pi\) | ||||
0.899397 | + | 0.437132i | \(0.144006\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4284.59 | −0.657160 | −0.328580 | − | 0.944476i | \(-0.606570\pi\) | ||||
−0.328580 | + | 0.944476i | \(0.606570\pi\) | |||||||
\(350\) | 1540.16 | 0.235214 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7517.63 | −1.13833 | ||||||||
\(353\) | −1870.98 | −0.282103 | −0.141051 | − | 0.990002i | \(-0.545048\pi\) | ||||
−0.141051 | + | 0.990002i | \(0.545048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2431.92 | −0.363586 | ||||||||
\(356\) | −9147.08 | −1.36178 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2308.83 | −0.340854 | ||||||||
\(359\) | −6816.46 | −1.00211 | −0.501057 | − | 0.865414i | \(-0.667055\pi\) | ||||
−0.501057 | + | 0.865414i | \(0.667055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5557.41 | −0.810236 | ||||||||
\(362\) | −867.927 | −0.126014 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4705.51 | 0.677570 | ||||||||
\(365\) | 9201.45 | 1.31952 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 785.509 | 0.111725 | 0.0558627 | − | 0.998438i | \(-0.482209\pi\) | ||||
0.0558627 | + | 0.998438i | \(0.482209\pi\) | |||||||
\(368\) | −6121.10 | −0.867077 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2352.05 | −0.330479 | ||||||||
\(371\) | −2676.51 | −0.374549 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1641.96 | −0.227929 | −0.113965 | − | 0.993485i | \(-0.536355\pi\) | ||||
−0.113965 | + | 0.993485i | \(0.536355\pi\) | |||||||
\(374\) | 982.874 | 0.135891 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8003.67 | 1.09776 | ||||||||
\(377\) | −9.33113 | −0.00127474 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7525.41 | 1.01993 | 0.509966 | − | 0.860194i | \(-0.329658\pi\) | ||||
0.509966 | + | 0.860194i | \(0.329658\pi\) | |||||||
\(380\) | −1949.54 | −0.263183 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3644.73 | 0.488169 | ||||||||
\(383\) | 2465.18 | 0.328890 | 0.164445 | − | 0.986386i | \(-0.447417\pi\) | ||||
0.164445 | + | 0.986386i | \(0.447417\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9227.39 | −1.22148 | ||||||||
\(386\) | −3333.91 | −0.439616 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5834.82 | 0.763448 | ||||||||
\(389\) | −10287.3 | −1.34085 | −0.670423 | − | 0.741979i | \(-0.733887\pi\) | ||||
−0.670423 | + | 0.741979i | \(0.733887\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2977.95 | 0.385170 | ||||||||
\(392\) | 3714.78 | 0.478634 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1521.31 | 0.194524 | ||||||||
\(395\) | 8426.37 | 1.07336 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −916.280 | −0.115836 | −0.0579179 | − | 0.998321i | \(-0.518446\pi\) | ||||
−0.0579179 | + | 0.998321i | \(0.518446\pi\) | |||||||
\(398\) | 1206.50 | 0.151950 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3033.73 | −0.379216 | ||||||||
\(401\) | −13110.9 | −1.63274 | −0.816369 | − | 0.577530i | \(-0.804017\pi\) | ||||
−0.816369 | + | 0.577530i | \(0.804017\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8055.84 | −0.995756 | ||||||||
\(404\) | −3018.11 | −0.371675 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.94040 | −0.000970629 0 | ||||||||
\(407\) | −16844.0 | −2.05141 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9105.34 | −1.10081 | −0.550403 | − | 0.834899i | \(-0.685526\pi\) | ||||
−0.550403 | + | 0.834899i | \(0.685526\pi\) | |||||||
\(410\) | 217.870 | 0.0262435 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −232.933 | −0.0278539 | ||||||||
\(413\) | −3410.43 | −0.406334 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2860.47 | −0.338349 | ||||||||
\(416\) | 4039.47 | 0.476085 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1635.18 | 0.191338 | ||||||||
\(419\) | 3712.52 | 0.432861 | 0.216430 | − | 0.976298i | \(-0.430559\pi\) | ||||
0.216430 | + | 0.976298i | \(0.430559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −471.976 | −0.0546383 | −0.0273191 | − | 0.999627i | \(-0.508697\pi\) | ||||
−0.0273191 | + | 0.999627i | \(0.508697\pi\) | |||||||
\(422\) | 4170.80 | 0.481117 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1504.05 | −0.172271 | ||||||||
\(425\) | 1475.93 | 0.168454 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15378.0 | 1.74284 | ||||||||
\(428\) | −9936.93 | −1.12224 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2016.71 | −0.226173 | ||||||||
\(431\) | 559.067 | 0.0624810 | 0.0312405 | − | 0.999512i | \(-0.490054\pi\) | ||||
0.0312405 | + | 0.999512i | \(0.490054\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9113.61 | 1.01148 | 0.505742 | − | 0.862685i | \(-0.331219\pi\) | ||||
0.505742 | + | 0.862685i | \(0.331219\pi\) | |||||||
\(434\) | −6855.18 | −0.758201 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7656.46 | 0.841004 | ||||||||
\(437\) | 4954.35 | 0.542331 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6031.78 | 0.655766 | 0.327883 | − | 0.944718i | \(-0.393665\pi\) | ||||
0.327883 | + | 0.944718i | \(0.393665\pi\) | |||||||
\(440\) | −5185.26 | −0.561813 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −528.131 | −0.0568340 | ||||||||
\(443\) | 16257.9 | 1.74365 | 0.871823 | − | 0.489821i | \(-0.162938\pi\) | ||||
0.871823 | + | 0.489821i | \(0.162938\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9638.26 | −1.02674 | ||||||||
\(446\) | −1114.58 | −0.118334 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5373.60 | −0.566693 | ||||||||
\(449\) | −8313.62 | −0.873817 | −0.436909 | − | 0.899506i | \(-0.643927\pi\) | ||||
−0.436909 | + | 0.899506i | \(0.643927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1560.25 | 0.162903 | ||||||||
\(452\) | −3720.06 | −0.387117 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5232.07 | 0.540866 | ||||||||
\(455\) | 4958.18 | 0.510864 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17797.2 | 1.82170 | 0.910852 | − | 0.412733i | \(-0.135426\pi\) | ||||
0.910852 | + | 0.412733i | \(0.135426\pi\) | |||||||
\(458\) | 4799.87 | 0.489702 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7420.70 | −0.752157 | ||||||||
\(461\) | 1209.43 | 0.122188 | 0.0610940 | − | 0.998132i | \(-0.480541\pi\) | ||||
0.0610940 | + | 0.998132i | \(0.480541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18160.0 | −1.82282 | −0.911410 | − | 0.411501i | \(-0.865005\pi\) | ||||
−0.911410 | + | 0.411501i | \(0.865005\pi\) | |||||||
\(464\) | 15.6406 | 0.00156486 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4279.41 | 0.425407 | ||||||||
\(467\) | −3033.10 | −0.300546 | −0.150273 | − | 0.988645i | \(-0.548015\pi\) | ||||
−0.150273 | + | 0.988645i | \(0.548015\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8616.42 | 0.848336 | ||||||||
\(470\) | 3983.45 | 0.390942 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1916.46 | −0.186891 | ||||||||
\(473\) | −14442.5 | −1.40394 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2455.47 | 0.237188 | ||||||||
\(476\) | 3837.20 | 0.369491 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 218.882 | 0.0209444 | ||||||||
\(479\) | 1205.11 | 0.114953 | 0.0574767 | − | 0.998347i | \(-0.481695\pi\) | ||||
0.0574767 | + | 0.998347i | \(0.481695\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9050.83 | 0.857967 | ||||||||
\(482\) | −3461.48 | −0.327108 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8008.09 | −0.752074 | ||||||||
\(485\) | 6148.14 | 0.575613 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18893.4 | −1.75799 | −0.878995 | − | 0.476831i | \(-0.841786\pi\) | ||||
−0.878995 | + | 0.476831i | \(0.841786\pi\) | |||||||
\(488\) | 8641.56 | 0.801609 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1848.86 | 0.170455 | ||||||||
\(491\) | −7189.48 | −0.660808 | −0.330404 | − | 0.943840i | \(-0.607185\pi\) | ||||
−0.330404 | + | 0.943840i | \(0.607185\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.60926 | −0.000695140 0 | ||||||||
\(494\) | −878.638 | −0.0800239 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13503.0 | 1.22238 | ||||||||
\(497\) | 7963.41 | 0.718728 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8363.23 | −0.750279 | −0.375140 | − | 0.926968i | \(-0.622405\pi\) | ||||
−0.375140 | + | 0.926968i | \(0.622405\pi\) | |||||||
\(500\) | −10432.5 | −0.933114 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4321.29 | 0.384201 | ||||||||
\(503\) | −16512.4 | −1.46372 | −0.731859 | − | 0.681456i | \(-0.761347\pi\) | ||||
−0.731859 | + | 0.681456i | \(0.761347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3180.18 | −0.280230 | ||||||||
\(506\) | 6224.12 | 0.546830 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10172.3 | −0.888432 | ||||||||
\(509\) | 20223.3 | 1.76106 | 0.880532 | − | 0.473987i | \(-0.157186\pi\) | ||||
0.880532 | + | 0.473987i | \(0.157186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30130.5 | −2.60840 | ||||||||
\(512\) | −11722.2 | −1.01182 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1807.18 | −0.155080 | ||||||||
\(515\) | −245.441 | −0.0210009 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 28527.1 | 2.42673 | ||||||||
\(518\) | 7701.88 | 0.653284 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2786.21 | 0.234968 | ||||||||
\(521\) | 5376.56 | 0.452114 | 0.226057 | − | 0.974114i | \(-0.427416\pi\) | ||||
0.226057 | + | 0.974114i | \(0.427416\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12438.5 | 1.03996 | 0.519981 | − | 0.854178i | \(-0.325939\pi\) | ||||
0.519981 | + | 0.854178i | \(0.325939\pi\) | |||||||
\(524\) | −12859.0 | −1.07204 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3629.19 | −0.300837 | ||||||||
\(527\) | −6569.30 | −0.543004 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6691.12 | 0.549940 | ||||||||
\(530\) | −748.569 | −0.0613505 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6383.86 | 0.520255 | ||||||||
\(533\) | −838.376 | −0.0681315 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10470.5 | −0.846131 | ||||||||
\(536\) | 4841.93 | 0.390186 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2918.48 | −0.233874 | ||||||||
\(539\) | 13240.4 | 1.05808 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 655.093 | 0.0520604 | 0.0260302 | − | 0.999661i | \(-0.491713\pi\) | ||||
0.0260302 | + | 0.999661i | \(0.491713\pi\) | |||||||
\(542\) | 3792.36 | 0.300545 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3294.07 | 0.259618 | ||||||||
\(545\) | 8067.60 | 0.634088 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 761.634 | 0.0595341 | 0.0297670 | − | 0.999557i | \(-0.490523\pi\) | ||||
0.0297670 | + | 0.999557i | \(0.490523\pi\) | |||||||
\(548\) | 11327.3 | 0.882989 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3084.79 | 0.239156 | ||||||||
\(551\) | −12.6593 | −0.000978777 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27592.5 | −2.12179 | ||||||||
\(554\) | 4224.01 | 0.323937 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5850.01 | 0.446215 | ||||||||
\(557\) | −12915.3 | −0.982475 | −0.491238 | − | 0.871026i | \(-0.663455\pi\) | ||||
−0.491238 | + | 0.871026i | \(0.663455\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7760.42 | 0.587175 | ||||||||
\(560\) | −8310.79 | −0.627134 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3505.51 | 0.263116 | ||||||||
\(563\) | −2721.26 | −0.203707 | −0.101854 | − | 0.994799i | \(-0.532477\pi\) | ||||
−0.101854 | + | 0.994799i | \(0.532477\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3919.82 | −0.291873 | ||||||||
\(566\) | 7981.75 | 0.592753 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4474.98 | 0.330574 | ||||||||
\(569\) | −17019.8 | −1.25397 | −0.626984 | − | 0.779032i | \(-0.715711\pi\) | ||||
−0.626984 | + | 0.779032i | \(0.715711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8436.61 | −0.618321 | −0.309160 | − | 0.951010i | \(-0.600048\pi\) | ||||
−0.309160 | + | 0.951010i | \(0.600048\pi\) | |||||||
\(572\) | 9424.68 | 0.688926 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −713.423 | −0.0518775 | ||||||||
\(575\) | 9346.43 | 0.677866 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10300.6 | −0.743191 | −0.371595 | − | 0.928395i | \(-0.621189\pi\) | ||||
−0.371595 | + | 0.928395i | \(0.621189\pi\) | |||||||
\(578\) | 4068.77 | 0.292800 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 18.9614 | 0.00135746 | ||||||||
\(581\) | 9366.71 | 0.668841 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5360.81 | −0.380827 | ||||||||
\(584\) | −16931.6 | −1.19972 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4834.80 | −0.340826 | ||||||||
\(587\) | 1605.22 | 0.112870 | 0.0564350 | − | 0.998406i | \(-0.482027\pi\) | ||||
0.0564350 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10929.2 | −0.764565 | ||||||||
\(590\) | −953.830 | −0.0665569 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15170.8 | −1.05324 | ||||||||
\(593\) | 13691.9 | 0.948159 | 0.474079 | − | 0.880482i | \(-0.342781\pi\) | ||||
0.474079 | + | 0.880482i | \(0.342781\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4043.25 | 0.278584 | ||||||||
\(596\) | 25560.7 | 1.75672 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3344.43 | −0.228702 | ||||||||
\(599\) | −26216.9 | −1.78830 | −0.894151 | − | 0.447765i | \(-0.852220\pi\) | ||||
−0.894151 | + | 0.447765i | \(0.852220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11341.8 | −0.769787 | −0.384894 | − | 0.922961i | \(-0.625762\pi\) | ||||
−0.384894 | + | 0.922961i | \(0.625762\pi\) | |||||||
\(602\) | 6603.79 | 0.447094 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16620.2 | 1.11965 | ||||||||
\(605\) | −8438.11 | −0.567038 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11101.0 | −0.742303 | −0.371151 | − | 0.928572i | \(-0.621037\pi\) | ||||
−0.371151 | + | 0.928572i | \(0.621037\pi\) | |||||||
\(608\) | 5480.27 | 0.365550 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4300.93 | 0.285475 | ||||||||
\(611\) | −15328.6 | −1.01494 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17017.3 | 1.12124 | 0.560620 | − | 0.828073i | \(-0.310563\pi\) | ||||
0.560620 | + | 0.828073i | \(0.310563\pi\) | |||||||
\(614\) | −590.555 | −0.0388157 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16979.3 | 1.11058 | ||||||||
\(617\) | −14467.0 | −0.943956 | −0.471978 | − | 0.881610i | \(-0.656460\pi\) | ||||
−0.471978 | + | 0.881610i | \(0.656460\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14990.7 | −0.973385 | −0.486693 | − | 0.873573i | \(-0.661797\pi\) | ||||
−0.486693 | + | 0.873573i | \(0.661797\pi\) | |||||||
\(620\) | 16369.9 | 1.06037 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6543.88 | 0.421842 | ||||||||
\(623\) | 31560.9 | 2.02963 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2485.15 | −0.159050 | ||||||||
\(626\) | −4929.76 | −0.314749 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22981.9 | −1.46031 | ||||||||
\(629\) | 7380.69 | 0.467865 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16047.2 | −1.01241 | −0.506203 | − | 0.862414i | \(-0.668951\pi\) | ||||
−0.506203 | + | 0.862414i | \(0.668951\pi\) | |||||||
\(632\) | −15505.4 | −0.975903 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −762.755 | −0.0477806 | ||||||||
\(635\) | −10718.5 | −0.669847 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7114.51 | −0.442523 | ||||||||
\(638\) | −15.9039 | −0.000986897 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10672.7 | −0.659181 | ||||||||
\(641\) | 20880.9 | 1.28666 | 0.643328 | − | 0.765591i | \(-0.277553\pi\) | ||||
0.643328 | + | 0.765591i | \(0.277553\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10675.4 | 0.654738 | 0.327369 | − | 0.944897i | \(-0.393838\pi\) | ||||
0.327369 | + | 0.944897i | \(0.393838\pi\) | |||||||
\(644\) | 24299.4 | 1.48685 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −716.504 | −0.0436385 | ||||||||
\(647\) | −23770.6 | −1.44439 | −0.722195 | − | 0.691690i | \(-0.756867\pi\) | ||||
−0.722195 | + | 0.691690i | \(0.756867\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6830.76 | −0.413145 | ||||||||
\(650\) | −1657.56 | −0.100023 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14625.3 | 0.878482 | ||||||||
\(653\) | 7609.84 | 0.456043 | 0.228022 | − | 0.973656i | \(-0.426774\pi\) | ||||
0.228022 | + | 0.973656i | \(0.426774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13549.5 | −0.808281 | ||||||||
\(656\) | 1405.27 | 0.0836378 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13044.0 | −0.772807 | ||||||||
\(659\) | −5332.02 | −0.315184 | −0.157592 | − | 0.987504i | \(-0.550373\pi\) | ||||
−0.157592 | + | 0.987504i | \(0.550373\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9421.86 | −0.554415 | −0.277207 | − | 0.960810i | \(-0.589409\pi\) | ||||
−0.277207 | + | 0.960810i | \(0.589409\pi\) | |||||||
\(662\) | −5480.47 | −0.321759 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5263.55 | 0.307629 | ||||||||
\(665\) | 6726.66 | 0.392254 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.1862 | −0.00279727 | ||||||||
\(668\) | 6333.83 | 0.366861 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2409.85 | 0.138956 | ||||||||
\(671\) | 30800.7 | 1.77205 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9723.05 | 0.556903 | 0.278452 | − | 0.960450i | \(-0.410179\pi\) | ||||
0.278452 | + | 0.960450i | \(0.410179\pi\) | |||||||
\(674\) | −8883.04 | −0.507659 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10669.1 | 0.607027 | ||||||||
\(677\) | −4577.67 | −0.259873 | −0.129937 | − | 0.991522i | \(-0.541477\pi\) | ||||
−0.129937 | + | 0.991522i | \(0.541477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20132.3 | −1.13786 | ||||||||
\(680\) | 2272.08 | 0.128132 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13730.3 | −0.770908 | ||||||||
\(683\) | −26280.5 | −1.47232 | −0.736160 | − | 0.676808i | \(-0.763363\pi\) | ||||
−0.736160 | + | 0.676808i | \(0.763363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11935.5 | 0.665743 | ||||||||
\(686\) | 1707.65 | 0.0950415 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13007.8 | −0.720812 | ||||||||
\(689\) | 2880.54 | 0.159274 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14534.8 | −0.800190 | −0.400095 | − | 0.916474i | \(-0.631023\pi\) | ||||
−0.400095 | + | 0.916474i | \(0.631023\pi\) | |||||||
\(692\) | 2936.59 | 0.161319 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10648.5 | −0.582437 | ||||||||
\(695\) | 6164.15 | 0.336431 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −683.671 | −0.0371533 | ||||||||
\(698\) | 3923.93 | 0.212784 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 12043.2 | 0.650272 | ||||||||
\(701\) | −22046.9 | −1.18788 | −0.593938 | − | 0.804511i | \(-0.702428\pi\) | ||||
−0.593938 | + | 0.804511i | \(0.702428\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12279.1 | 0.658768 | ||||||||
\(704\) | −10762.8 | −0.576191 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1713.49 | 0.0913428 | ||||||||
\(707\) | 10413.6 | 0.553952 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1160.25 | −0.0614583 | −0.0307292 | − | 0.999528i | \(-0.509783\pi\) | ||||
−0.0307292 | + | 0.999528i | \(0.509783\pi\) | |||||||
\(710\) | 2227.21 | 0.117726 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 17735.4 | 0.933513 | ||||||||
\(713\) | −41600.6 | −2.18507 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9930.77 | 0.519426 | ||||||||
\(716\) | −18053.9 | −0.942325 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6242.68 | 0.324477 | ||||||||
\(719\) | −26058.1 | −1.35161 | −0.675803 | − | 0.737082i | \(-0.736203\pi\) | ||||
−0.675803 | + | 0.737082i | \(0.736203\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 803.707 | 0.0415140 | ||||||||
\(722\) | 5089.61 | 0.262349 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6786.73 | −0.348380 | ||||||||
\(725\) | −23.8820 | −0.00122339 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34483.7 | −1.75919 | −0.879594 | − | 0.475725i | \(-0.842186\pi\) | ||||
−0.879594 | + | 0.475725i | \(0.842186\pi\) | |||||||
\(728\) | −9123.56 | −0.464480 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8426.91 | −0.427252 | ||||||||
\(731\) | 6328.40 | 0.320197 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1508.37 | 0.0760067 | 0.0380034 | − | 0.999278i | \(-0.487900\pi\) | ||||
0.0380034 | + | 0.999278i | \(0.487900\pi\) | |||||||
\(734\) | −719.389 | −0.0361759 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20860.0 | 1.04471 | ||||||||
\(737\) | 17257.9 | 0.862554 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13898.1 | −0.691813 | −0.345907 | − | 0.938269i | \(-0.612429\pi\) | ||||
−0.345907 | + | 0.938269i | \(0.612429\pi\) | |||||||
\(740\) | −18391.8 | −0.913642 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2451.22 | 0.121276 | ||||||||
\(743\) | −24303.8 | −1.20003 | −0.600013 | − | 0.799990i | \(-0.704838\pi\) | ||||
−0.600013 | + | 0.799990i | \(0.704838\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26933.3 | 1.32451 | ||||||||
\(746\) | 1503.75 | 0.0738018 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 7685.55 | 0.375684 | ||||||||
\(749\) | 34286.1 | 1.67261 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29770.3 | 1.44652 | 0.723259 | − | 0.690577i | \(-0.242643\pi\) | ||||
0.723259 | + | 0.690577i | \(0.242643\pi\) | |||||||
\(752\) | 25693.4 | 1.24593 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.54568 | 0.000412752 0 | ||||||||
\(755\) | 17512.7 | 0.844176 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1684.16 | 0.0808610 | 0.0404305 | − | 0.999182i | \(-0.487127\pi\) | ||||
0.0404305 | + | 0.999182i | \(0.487127\pi\) | |||||||
\(758\) | −6891.96 | −0.330247 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3780.00 | 0.180414 | ||||||||
\(761\) | 10307.3 | 0.490986 | 0.245493 | − | 0.969398i | \(-0.421050\pi\) | ||||
0.245493 | + | 0.969398i | \(0.421050\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26417.7 | −1.25345 | ||||||||
\(764\) | 28499.8 | 1.34959 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2257.67 | −0.106492 | ||||||||
\(767\) | 3670.40 | 0.172791 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33644.6 | 1.57771 | 0.788853 | − | 0.614582i | \(-0.210675\pi\) | ||||
0.788853 | + | 0.614582i | \(0.210675\pi\) | |||||||
\(770\) | 8450.67 | 0.395508 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26069.4 | −1.21536 | ||||||||
\(773\) | 3463.13 | 0.161139 | 0.0805693 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805693 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20618.0 | −0.955639 | ||||||||
\(776\) | −11313.2 | −0.523351 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9421.41 | 0.434157 | ||||||||
\(779\) | −1137.41 | −0.0523130 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15950.0 | 0.730774 | ||||||||
\(782\) | −2727.28 | −0.124715 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11925.2 | 0.543239 | ||||||||
\(785\) | −24216.0 | −1.10102 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30239.6 | −1.36966 | −0.684832 | − | 0.728701i | \(-0.740125\pi\) | ||||
−0.684832 | + | 0.728701i | \(0.740125\pi\) | |||||||
\(788\) | 11895.8 | 0.537781 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7717.08 | −0.347546 | ||||||||
\(791\) | 12835.6 | 0.576968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16550.3 | −0.741131 | ||||||||
\(794\) | 839.152 | 0.0375068 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9434.17 | 0.420082 | ||||||||
\(797\) | 30267.7 | 1.34522 | 0.672609 | − | 0.739998i | \(-0.265174\pi\) | ||||
0.672609 | + | 0.739998i | \(0.265174\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12500.0 | −0.553464 | ||||||||
\(800\) | 10338.6 | 0.456905 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12007.3 | 0.528669 | ||||||||
\(803\) | −60348.5 | −2.65212 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25604.2 | 1.12103 | ||||||||
\(806\) | 7377.73 | 0.322419 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5851.85 | 0.254786 | ||||||||
\(809\) | −21323.9 | −0.926710 | −0.463355 | − | 0.886173i | \(-0.653355\pi\) | ||||
−0.463355 | + | 0.886173i | \(0.653355\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4544.15 | 0.196753 | 0.0983766 | − | 0.995149i | \(-0.468635\pi\) | ||||
0.0983766 | + | 0.995149i | \(0.468635\pi\) | |||||||
\(812\) | −62.0897 | −0.00268340 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15426.1 | 0.664233 | ||||||||
\(815\) | 15410.6 | 0.662345 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10528.4 | 0.450847 | ||||||||
\(818\) | 8338.89 | 0.356433 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1703.63 | 0.0725527 | ||||||||
\(821\) | −15313.0 | −0.650949 | −0.325474 | − | 0.945551i | \(-0.605524\pi\) | ||||
−0.325474 | + | 0.945551i | \(0.605524\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10661.7 | 0.451573 | 0.225786 | − | 0.974177i | \(-0.427505\pi\) | ||||
0.225786 | + | 0.974177i | \(0.427505\pi\) | |||||||
\(824\) | 451.637 | 0.0190941 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3123.35 | 0.131568 | ||||||||
\(827\) | 17341.6 | 0.729172 | 0.364586 | − | 0.931170i | \(-0.381211\pi\) | ||||
0.364586 | + | 0.931170i | \(0.381211\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20108.0 | −0.842435 | −0.421217 | − | 0.906960i | \(-0.638397\pi\) | ||||
−0.421217 | + | 0.906960i | \(0.638397\pi\) | |||||||
\(830\) | 2619.69 | 0.109555 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5783.22 | 0.240982 | ||||||||
\(833\) | −5801.68 | −0.241316 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6673.94 | 0.276600 | ||||||||
\(836\) | 12786.3 | 0.528974 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3400.02 | −0.140157 | ||||||||
\(839\) | 30229.1 | 1.24389 | 0.621946 | − | 0.783060i | \(-0.286342\pi\) | ||||
0.621946 | + | 0.783060i | \(0.286342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24388.9 | −0.999995 | ||||||||
\(842\) | 432.248 | 0.0176915 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 32613.4 | 1.33010 | ||||||||
\(845\) | 11242.0 | 0.457677 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27630.9 | 1.12091 | ||||||||
\(848\) | −4828.29 | −0.195524 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1351.69 | −0.0545443 | ||||||||
\(851\) | 46738.8 | 1.88271 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5756.55 | −0.231067 | −0.115534 | − | 0.993304i | \(-0.536858\pi\) | ||||
−0.115534 | + | 0.993304i | \(0.536858\pi\) | |||||||
\(854\) | −14083.6 | −0.564321 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19266.8 | 0.769307 | ||||||||
\(857\) | −7273.51 | −0.289916 | −0.144958 | − | 0.989438i | \(-0.546305\pi\) | ||||
−0.144958 | + | 0.989438i | \(0.546305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20497.9 | −0.814179 | −0.407090 | − | 0.913388i | \(-0.633456\pi\) | ||||
−0.407090 | + | 0.913388i | \(0.633456\pi\) | |||||||
\(860\) | −15769.6 | −0.625278 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −512.007 | −0.0202309 | ||||||||
\(863\) | 34895.9 | 1.37644 | 0.688221 | − | 0.725501i | \(-0.258392\pi\) | ||||
0.688221 | + | 0.725501i | \(0.258392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3094.28 | 0.121629 | ||||||||
\(866\) | −8346.47 | −0.327511 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −53603.9 | −2.09612 | ||||||||
\(869\) | −55265.1 | −2.15735 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9273.23 | −0.360748 | ||||||||
\(872\) | −14845.2 | −0.576516 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4537.32 | −0.175603 | ||||||||
\(875\) | 35996.2 | 1.39073 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15900.6 | 0.612229 | 0.306114 | − | 0.951995i | \(-0.400971\pi\) | ||||
0.306114 | + | 0.951995i | \(0.400971\pi\) | |||||||
\(878\) | −5524.05 | −0.212332 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −16645.7 | −0.637645 | ||||||||
\(881\) | 25571.7 | 0.977904 | 0.488952 | − | 0.872311i | \(-0.337379\pi\) | ||||
0.488952 | + | 0.872311i | \(0.337379\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18259.8 | −0.695912 | −0.347956 | − | 0.937511i | \(-0.613124\pi\) | ||||
−0.347956 | + | 0.937511i | \(0.613124\pi\) | |||||||
\(884\) | −4129.70 | −0.157123 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14889.4 | −0.564580 | ||||||||
\(887\) | 14766.5 | 0.558973 | 0.279487 | − | 0.960150i | \(-0.409836\pi\) | ||||
0.279487 | + | 0.960150i | \(0.409836\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35098.3 | 1.32414 | ||||||||
\(890\) | 8826.96 | 0.332450 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8715.45 | −0.327147 | ||||||||
\(893\) | −20795.9 | −0.779294 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19023.3 | −0.710480 | ||||||||
\(896\) | 34948.2 | 1.30305 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7613.82 | 0.282936 | ||||||||
\(899\) | 106.298 | 0.00394352 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2349.00 | 0.0868550 | ||||||||
\(902\) | −1428.92 | −0.0527470 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7212.87 | 0.265372 | ||||||||
\(905\) | −7151.17 | −0.262666 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 289.782 | 0.0106087 | 0.00530433 | − | 0.999986i | \(-0.498312\pi\) | ||||
0.00530433 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(908\) | 40912.0 | 1.49528 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4540.83 | −0.165414 | ||||||||
\(911\) | −8011.03 | −0.291347 | −0.145674 | − | 0.989333i | \(-0.546535\pi\) | ||||
−0.145674 | + | 0.989333i | \(0.546535\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18760.6 | 0.680051 | ||||||||
\(914\) | −16299.1 | −0.589855 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 37532.5 | 1.35383 | ||||||||
\(917\) | 44368.5 | 1.59779 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40447.3 | 1.45183 | 0.725916 | − | 0.687783i | \(-0.241416\pi\) | ||||
0.725916 | + | 0.687783i | \(0.241416\pi\) | |||||||
\(920\) | 14388.1 | 0.515610 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1107.62 | −0.0395636 | ||||||||
\(923\) | −8570.45 | −0.305633 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23164.6 | 0.823402 | ||||||||
\(926\) | 16631.3 | 0.590216 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −53.3014 | −0.00188546 | ||||||||
\(929\) | −4973.47 | −0.175645 | −0.0878225 | − | 0.996136i | \(-0.527991\pi\) | ||||
−0.0878225 | + | 0.996136i | \(0.527991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9652.11 | −0.339780 | ||||||||
\(932\) | 33462.7 | 1.17608 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2777.79 | 0.0973147 | ||||||||
\(935\) | 8098.26 | 0.283253 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30016.5 | 1.04653 | 0.523264 | − | 0.852171i | \(-0.324714\pi\) | ||||
0.523264 | + | 0.852171i | \(0.324714\pi\) | |||||||
\(938\) | −7891.13 | −0.274685 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 31148.5 | 1.08080 | ||||||||
\(941\) | 37395.5 | 1.29549 | 0.647745 | − | 0.761857i | \(-0.275712\pi\) | ||||
0.647745 | + | 0.761857i | \(0.275712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4329.40 | −0.149506 | ||||||||
\(944\) | −6152.23 | −0.212117 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13226.8 | 0.454587 | ||||||||
\(947\) | 14566.8 | 0.499848 | 0.249924 | − | 0.968265i | \(-0.419594\pi\) | ||||
0.249924 | + | 0.968265i | \(0.419594\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32427.3 | 1.10920 | ||||||||
\(950\) | −2248.78 | −0.0767999 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7440.00 | −0.253290 | ||||||||
\(953\) | 18307.3 | 0.622278 | 0.311139 | − | 0.950364i | \(-0.399290\pi\) | ||||
0.311139 | + | 0.950364i | \(0.399290\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30030.2 | 1.01755 | ||||||||
\(956\) | 1711.54 | 0.0579030 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1103.67 | −0.0372211 | ||||||||
\(959\) | −39083.4 | −1.31603 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61978.9 | 2.08046 | ||||||||
\(962\) | −8288.97 | −0.277804 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27067.0 | −0.904324 | ||||||||
\(965\) | −27469.3 | −0.916340 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27458.7 | −0.913145 | −0.456572 | − | 0.889686i | \(-0.650923\pi\) | ||||
−0.456572 | + | 0.889686i | \(0.650923\pi\) | |||||||
\(968\) | 15527.0 | 0.515554 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5630.62 | −0.186380 | ||||||||
\(971\) | −52683.2 | −1.74118 | −0.870590 | − | 0.492010i | \(-0.836262\pi\) | ||||
−0.870590 | + | 0.492010i | \(0.836262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20184.7 | −0.665049 | ||||||||
\(974\) | 17303.0 | 0.569225 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 27741.1 | 0.909808 | ||||||||
\(977\) | −26057.2 | −0.853270 | −0.426635 | − | 0.904424i | \(-0.640301\pi\) | ||||
−0.426635 | + | 0.904424i | \(0.640301\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63213.4 | 2.06365 | ||||||||
\(980\) | 14457.1 | 0.471239 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6584.30 | 0.213965 | ||||||||
\(983\) | −14618.3 | −0.474314 | −0.237157 | − | 0.971471i | \(-0.576216\pi\) | ||||
−0.237157 | + | 0.971471i | \(0.576216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12534.6 | 0.405468 | ||||||||
\(986\) | 6.96875 | 0.000225081 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6870.49 | −0.221234 | ||||||||
\(989\) | 40075.0 | 1.28849 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12768.4 | 0.409285 | 0.204642 | − | 0.978837i | \(-0.434397\pi\) | ||||
0.204642 | + | 0.978837i | \(0.434397\pi\) | |||||||
\(992\) | −46016.6 | −1.47281 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7293.09 | −0.232719 | ||||||||
\(995\) | 9940.77 | 0.316727 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42906.2 | 1.36294 | 0.681472 | − | 0.731845i | \(-0.261340\pi\) | ||||
0.681472 | + | 0.731845i | \(0.261340\pi\) | |||||||
\(998\) | 7659.25 | 0.242935 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.b.1.12 | 28 | ||
3.2 | odd | 2 | 717.4.a.b.1.17 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.4.a.b.1.17 | ✓ | 28 | 3.2 | odd | 2 | ||
2151.4.a.b.1.12 | 28 | 1.1 | even | 1 | trivial |