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: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 717) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.64745 | 0.582460 | 0.291230 | − | 0.956653i | \(-0.405936\pi\) | ||||
0.291230 | + | 0.956653i | \(0.405936\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.28592 | −0.660740 | ||||||||
\(5\) | −5.57976 | −0.499069 | −0.249534 | − | 0.968366i | \(-0.580278\pi\) | ||||
−0.249534 | + | 0.968366i | \(0.580278\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 35.6078 | 1.92264 | 0.961321 | − | 0.275431i | \(-0.0888204\pi\) | ||||
0.961321 | + | 0.275431i | \(0.0888204\pi\) | |||||||
\(8\) | −21.8878 | −0.967315 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −9.19235 | −0.290687 | ||||||||
\(11\) | 54.2616 | 1.48732 | 0.743658 | − | 0.668560i | \(-0.233089\pi\) | ||||
0.743658 | + | 0.668560i | \(0.233089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.0551 | −0.406533 | −0.203266 | − | 0.979123i | \(-0.565156\pi\) | ||||
−0.203266 | + | 0.979123i | \(0.565156\pi\) | |||||||
\(14\) | 58.6620 | 1.11986 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.22837 | 0.0973183 | ||||||||
\(17\) | 90.4987 | 1.29113 | 0.645564 | − | 0.763706i | \(-0.276622\pi\) | ||||
0.645564 | + | 0.763706i | \(0.276622\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −78.5936 | −0.948979 | −0.474490 | − | 0.880261i | \(-0.657367\pi\) | ||||
−0.474490 | + | 0.880261i | \(0.657367\pi\) | |||||||
\(20\) | 29.4942 | 0.329755 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 89.3930 | 0.866302 | ||||||||
\(23\) | 172.386 | 1.56283 | 0.781413 | − | 0.624014i | \(-0.214499\pi\) | ||||
0.781413 | + | 0.624014i | \(0.214499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −93.8663 | −0.750930 | ||||||||
\(26\) | −31.3922 | −0.236789 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −188.220 | −1.27037 | ||||||||
\(29\) | −79.9221 | −0.511764 | −0.255882 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255882 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 48.5690 | 0.281395 | 0.140698 | − | 0.990053i | \(-0.455065\pi\) | ||||
0.140698 | + | 0.990053i | \(0.455065\pi\) | |||||||
\(32\) | 185.364 | 1.02400 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 149.092 | 0.752030 | ||||||||
\(35\) | −198.683 | −0.959530 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 437.671 | 1.94467 | 0.972333 | − | 0.233599i | \(-0.0750503\pi\) | ||||
0.972333 | + | 0.233599i | \(0.0750503\pi\) | |||||||
\(38\) | −129.479 | −0.552742 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 122.129 | 0.482756 | ||||||||
\(41\) | −64.7499 | −0.246640 | −0.123320 | − | 0.992367i | \(-0.539354\pi\) | ||||
−0.123320 | + | 0.992367i | \(0.539354\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −440.739 | −1.56307 | −0.781536 | − | 0.623860i | \(-0.785564\pi\) | ||||
−0.781536 | + | 0.623860i | \(0.785564\pi\) | |||||||
\(44\) | −286.823 | −0.982730 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 283.997 | 0.910283 | ||||||||
\(47\) | 210.972 | 0.654755 | 0.327377 | − | 0.944894i | \(-0.393835\pi\) | ||||
0.327377 | + | 0.944894i | \(0.393835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 924.917 | 2.69655 | ||||||||
\(50\) | −154.640 | −0.437387 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 100.724 | 0.268613 | ||||||||
\(53\) | −19.8918 | −0.0515538 | −0.0257769 | − | 0.999668i | \(-0.508206\pi\) | ||||
−0.0257769 | + | 0.999668i | \(0.508206\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −302.766 | −0.742273 | ||||||||
\(56\) | −779.378 | −1.85980 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −131.667 | −0.298082 | ||||||||
\(59\) | 163.118 | 0.359935 | 0.179967 | − | 0.983673i | \(-0.442401\pi\) | ||||
0.179967 | + | 0.983673i | \(0.442401\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −439.784 | −0.923091 | −0.461545 | − | 0.887117i | \(-0.652705\pi\) | ||||
−0.461545 | + | 0.887117i | \(0.652705\pi\) | |||||||
\(62\) | 80.0148 | 0.163902 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 255.549 | 0.499120 | ||||||||
\(65\) | 106.323 | 0.202888 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −889.752 | −1.62240 | −0.811198 | − | 0.584772i | \(-0.801184\pi\) | ||||
−0.811198 | + | 0.584772i | \(0.801184\pi\) | |||||||
\(68\) | −478.369 | −0.853100 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −327.319 | −0.558888 | ||||||||
\(71\) | 5.50954 | 0.00920933 | 0.00460466 | − | 0.999989i | \(-0.498534\pi\) | ||||
0.00460466 | + | 0.999989i | \(0.498534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −601.222 | −0.963941 | −0.481970 | − | 0.876188i | \(-0.660079\pi\) | ||||
−0.481970 | + | 0.876188i | \(0.660079\pi\) | |||||||
\(74\) | 721.039 | 1.13269 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 415.440 | 0.627029 | ||||||||
\(77\) | 1932.14 | 2.85958 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −93.0720 | −0.132550 | −0.0662748 | − | 0.997801i | \(-0.521111\pi\) | ||||
−0.0662748 | + | 0.997801i | \(0.521111\pi\) | |||||||
\(80\) | −34.7528 | −0.0485685 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −106.672 | −0.143658 | ||||||||
\(83\) | −212.225 | −0.280659 | −0.140330 | − | 0.990105i | \(-0.544816\pi\) | ||||
−0.140330 | + | 0.990105i | \(0.544816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −504.961 | −0.644361 | ||||||||
\(86\) | −726.094 | −0.910427 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1187.67 | −1.43870 | ||||||||
\(89\) | 461.248 | 0.549351 | 0.274675 | − | 0.961537i | \(-0.411430\pi\) | ||||
0.274675 | + | 0.961537i | \(0.411430\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −678.509 | −0.781617 | ||||||||
\(92\) | −911.220 | −1.03262 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 347.565 | 0.381369 | ||||||||
\(95\) | 438.533 | 0.473606 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 885.983 | 0.927401 | 0.463701 | − | 0.885992i | \(-0.346521\pi\) | ||||
0.463701 | + | 0.885992i | \(0.346521\pi\) | |||||||
\(98\) | 1523.75 | 1.57063 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 496.170 | 0.496170 | ||||||||
\(101\) | 265.340 | 0.261409 | 0.130705 | − | 0.991421i | \(-0.458276\pi\) | ||||
0.130705 | + | 0.991421i | \(0.458276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −498.373 | −0.476759 | −0.238380 | − | 0.971172i | \(-0.576616\pi\) | ||||
−0.238380 | + | 0.971172i | \(0.576616\pi\) | |||||||
\(104\) | 417.074 | 0.393245 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −32.7707 | −0.0300281 | ||||||||
\(107\) | −330.252 | −0.298380 | −0.149190 | − | 0.988809i | \(-0.547667\pi\) | ||||
−0.149190 | + | 0.988809i | \(0.547667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 179.639 | 0.157856 | 0.0789282 | − | 0.996880i | \(-0.474850\pi\) | ||||
0.0789282 | + | 0.996880i | \(0.474850\pi\) | |||||||
\(110\) | −498.791 | −0.432344 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 221.779 | 0.187108 | ||||||||
\(113\) | 1527.27 | 1.27145 | 0.635725 | − | 0.771915i | \(-0.280701\pi\) | ||||
0.635725 | + | 0.771915i | \(0.280701\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −961.873 | −0.779957 | ||||||||
\(116\) | 422.462 | 0.338143 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 268.728 | 0.209648 | ||||||||
\(119\) | 3222.46 | 2.48238 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1613.32 | 1.21211 | ||||||||
\(122\) | −724.520 | −0.537663 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −256.732 | −0.185929 | ||||||||
\(125\) | 1221.22 | 0.873834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1374.93 | 0.960670 | 0.480335 | − | 0.877085i | \(-0.340515\pi\) | ||||
0.480335 | + | 0.877085i | \(0.340515\pi\) | |||||||
\(128\) | −1061.90 | −0.733281 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 175.161 | 0.118174 | ||||||||
\(131\) | −1046.00 | −0.697627 | −0.348813 | − | 0.937192i | \(-0.613415\pi\) | ||||
−0.348813 | + | 0.937192i | \(0.613415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2798.55 | −1.82455 | ||||||||
\(134\) | −1465.82 | −0.944981 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1980.82 | −1.24893 | ||||||||
\(137\) | −956.425 | −0.596445 | −0.298222 | − | 0.954496i | \(-0.596394\pi\) | ||||
−0.298222 | + | 0.954496i | \(0.596394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1779.97 | 1.08615 | 0.543075 | − | 0.839684i | \(-0.317260\pi\) | ||||
0.543075 | + | 0.839684i | \(0.317260\pi\) | |||||||
\(140\) | 1050.22 | 0.634000 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.07667 | 0.00536406 | ||||||||
\(143\) | −1033.96 | −0.604643 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 445.946 | 0.255405 | ||||||||
\(146\) | −990.480 | −0.561457 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2313.49 | −1.28492 | ||||||||
\(149\) | −2389.19 | −1.31363 | −0.656813 | − | 0.754054i | \(-0.728096\pi\) | ||||
−0.656813 | + | 0.754054i | \(0.728096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2983.32 | 1.60781 | 0.803904 | − | 0.594759i | \(-0.202752\pi\) | ||||
0.803904 | + | 0.594759i | \(0.202752\pi\) | |||||||
\(152\) | 1720.24 | 0.917962 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3183.09 | 1.66559 | ||||||||
\(155\) | −271.003 | −0.140436 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1895.07 | 0.963330 | 0.481665 | − | 0.876355i | \(-0.340032\pi\) | ||||
0.481665 | + | 0.876355i | \(0.340032\pi\) | |||||||
\(158\) | −153.331 | −0.0772048 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1034.28 | −0.511046 | ||||||||
\(161\) | 6138.30 | 3.00475 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −874.514 | −0.420228 | −0.210114 | − | 0.977677i | \(-0.567384\pi\) | ||||
−0.210114 | + | 0.977677i | \(0.567384\pi\) | |||||||
\(164\) | 342.263 | 0.162965 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −349.629 | −0.163473 | ||||||||
\(167\) | 4191.06 | 1.94200 | 0.971001 | − | 0.239076i | \(-0.0768444\pi\) | ||||
0.971001 | + | 0.239076i | \(0.0768444\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1833.90 | −0.834731 | ||||||||
\(170\) | −831.896 | −0.375315 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2329.71 | 1.03279 | ||||||||
\(173\) | 1048.67 | 0.460861 | 0.230431 | − | 0.973089i | \(-0.425987\pi\) | ||||
0.230431 | + | 0.973089i | \(0.425987\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3342.38 | −1.44377 | ||||||||
\(176\) | 337.961 | 0.144743 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 759.882 | 0.319975 | ||||||||
\(179\) | 4139.45 | 1.72848 | 0.864238 | − | 0.503083i | \(-0.167801\pi\) | ||||
0.864238 | + | 0.503083i | \(0.167801\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3662.97 | −1.50423 | −0.752117 | − | 0.659030i | \(-0.770967\pi\) | ||||
−0.752117 | + | 0.659030i | \(0.770967\pi\) | |||||||
\(182\) | −1117.81 | −0.455260 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3773.16 | −1.51174 | ||||||||
\(185\) | −2442.10 | −0.970522 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4910.60 | 1.92032 | ||||||||
\(188\) | −1115.18 | −0.432623 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 722.459 | 0.275856 | ||||||||
\(191\) | 2845.69 | 1.07805 | 0.539023 | − | 0.842291i | \(-0.318794\pi\) | ||||
0.539023 | + | 0.842291i | \(0.318794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4714.14 | 1.75819 | 0.879096 | − | 0.476645i | \(-0.158147\pi\) | ||||
0.879096 | + | 0.476645i | \(0.158147\pi\) | |||||||
\(194\) | 1459.61 | 0.540174 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4889.04 | −1.78172 | ||||||||
\(197\) | 4032.32 | 1.45833 | 0.729165 | − | 0.684337i | \(-0.239908\pi\) | ||||
0.729165 | + | 0.684337i | \(0.239908\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −933.417 | −0.332503 | −0.166252 | − | 0.986083i | \(-0.553166\pi\) | ||||
−0.166252 | + | 0.986083i | \(0.553166\pi\) | |||||||
\(200\) | 2054.53 | 0.726386 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 437.133 | 0.152260 | ||||||||
\(203\) | −2845.85 | −0.983939 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 361.289 | 0.123090 | ||||||||
\(206\) | −821.043 | −0.277693 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −118.682 | −0.0395631 | ||||||||
\(209\) | −4264.61 | −1.41143 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1813.40 | −0.591658 | −0.295829 | − | 0.955241i | \(-0.595596\pi\) | ||||
−0.295829 | + | 0.955241i | \(0.595596\pi\) | |||||||
\(212\) | 105.147 | 0.0340637 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −544.072 | −0.173794 | ||||||||
\(215\) | 2459.22 | 0.780081 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1729.44 | 0.541022 | ||||||||
\(218\) | 295.946 | 0.0919450 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1600.40 | 0.490450 | ||||||||
\(221\) | −1724.46 | −0.524885 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2352.07 | 0.706306 | 0.353153 | − | 0.935566i | \(-0.385110\pi\) | ||||
0.353153 | + | 0.935566i | \(0.385110\pi\) | |||||||
\(224\) | 6600.39 | 1.96878 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2516.10 | 0.740569 | ||||||||
\(227\) | 3432.14 | 1.00352 | 0.501761 | − | 0.865006i | \(-0.332686\pi\) | ||||
0.501761 | + | 0.865006i | \(0.332686\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4121.07 | 1.18920 | 0.594602 | − | 0.804020i | \(-0.297310\pi\) | ||||
0.594602 | + | 0.804020i | \(0.297310\pi\) | |||||||
\(230\) | −1584.63 | −0.454294 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1749.32 | 0.495037 | ||||||||
\(233\) | 1117.49 | 0.314202 | 0.157101 | − | 0.987583i | \(-0.449785\pi\) | ||||
0.157101 | + | 0.987583i | \(0.449785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1177.17 | −0.326768 | ||||||||
\(236\) | −862.229 | −0.237823 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5308.83 | 1.44588 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4803.11 | −1.28380 | −0.641899 | − | 0.766789i | \(-0.721853\pi\) | ||||
−0.641899 | + | 0.766789i | \(0.721853\pi\) | |||||||
\(242\) | 2657.86 | 0.706006 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2324.66 | 0.609923 | ||||||||
\(245\) | −5160.81 | −1.34576 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1497.61 | 0.385791 | ||||||||
\(248\) | −1063.07 | −0.272198 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2011.89 | 0.508974 | ||||||||
\(251\) | −3912.29 | −0.983831 | −0.491915 | − | 0.870643i | \(-0.663703\pi\) | ||||
−0.491915 | + | 0.870643i | \(0.663703\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9353.94 | 2.32442 | ||||||||
\(254\) | 2265.12 | 0.559552 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3793.83 | −0.926227 | ||||||||
\(257\) | −6174.12 | −1.49856 | −0.749282 | − | 0.662251i | \(-0.769601\pi\) | ||||
−0.749282 | + | 0.662251i | \(0.769601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15584.5 | 3.73890 | ||||||||
\(260\) | −562.013 | −0.134056 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1723.22 | −0.406340 | ||||||||
\(263\) | 6934.32 | 1.62581 | 0.812906 | − | 0.582395i | \(-0.197884\pi\) | ||||
0.812906 | + | 0.582395i | \(0.197884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 110.992 | 0.0257289 | ||||||||
\(266\) | −4610.45 | −1.06273 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4703.16 | 1.07198 | ||||||||
\(269\) | 5537.65 | 1.25515 | 0.627577 | − | 0.778555i | \(-0.284047\pi\) | ||||
0.627577 | + | 0.778555i | \(0.284047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7680.70 | 1.72166 | 0.860829 | − | 0.508894i | \(-0.169945\pi\) | ||||
0.860829 | + | 0.508894i | \(0.169945\pi\) | |||||||
\(272\) | 563.660 | 0.125650 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1575.66 | −0.347405 | ||||||||
\(275\) | −5093.33 | −1.11687 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4927.67 | −1.06886 | −0.534432 | − | 0.845212i | \(-0.679474\pi\) | ||||
−0.534432 | + | 0.845212i | \(0.679474\pi\) | |||||||
\(278\) | 2932.40 | 0.632639 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4348.74 | 0.928168 | ||||||||
\(281\) | 2240.98 | 0.475751 | 0.237875 | − | 0.971296i | \(-0.423549\pi\) | ||||
0.237875 | + | 0.971296i | \(0.423549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4151.98 | 0.872119 | 0.436059 | − | 0.899918i | \(-0.356374\pi\) | ||||
0.436059 | + | 0.899918i | \(0.356374\pi\) | |||||||
\(284\) | −29.1230 | −0.00608497 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1703.39 | −0.352180 | ||||||||
\(287\) | −2305.60 | −0.474200 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3277.02 | 0.667011 | ||||||||
\(290\) | 734.671 | 0.148763 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3178.01 | 0.636914 | ||||||||
\(293\) | −3487.66 | −0.695396 | −0.347698 | − | 0.937607i | \(-0.613037\pi\) | ||||
−0.347698 | + | 0.937607i | \(0.613037\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −910.159 | −0.179632 | ||||||||
\(296\) | −9579.67 | −1.88110 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3936.06 | −0.765134 | ||||||||
\(299\) | −3284.83 | −0.635340 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15693.8 | −3.00523 | ||||||||
\(302\) | 4914.86 | 0.936484 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −489.510 | −0.0923531 | ||||||||
\(305\) | 2453.89 | 0.460686 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1383.54 | −0.257209 | −0.128604 | − | 0.991696i | \(-0.541050\pi\) | ||||
−0.128604 | + | 0.991696i | \(0.541050\pi\) | |||||||
\(308\) | −10213.1 | −1.88944 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −446.463 | −0.0817981 | ||||||||
\(311\) | 6117.12 | 1.11534 | 0.557669 | − | 0.830063i | \(-0.311696\pi\) | ||||
0.557669 | + | 0.830063i | \(0.311696\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2006.29 | −0.362308 | −0.181154 | − | 0.983455i | \(-0.557983\pi\) | ||||
−0.181154 | + | 0.983455i | \(0.557983\pi\) | |||||||
\(314\) | 3122.02 | 0.561101 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 491.972 | 0.0875809 | ||||||||
\(317\) | −5133.38 | −0.909525 | −0.454763 | − | 0.890613i | \(-0.650276\pi\) | ||||
−0.454763 | + | 0.890613i | \(0.650276\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4336.70 | −0.761155 | ||||||||
\(320\) | −1425.90 | −0.249095 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10112.5 | 1.75015 | ||||||||
\(323\) | −7112.62 | −1.22525 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1788.63 | 0.305278 | ||||||||
\(326\) | −1440.71 | −0.244766 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1417.24 | 0.238578 | ||||||||
\(329\) | 7512.27 | 1.25886 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1703.75 | 0.282920 | 0.141460 | − | 0.989944i | \(-0.454820\pi\) | ||||
0.141460 | + | 0.989944i | \(0.454820\pi\) | |||||||
\(332\) | 1121.81 | 0.185443 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6904.55 | 1.13114 | ||||||||
\(335\) | 4964.60 | 0.809687 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5307.52 | 0.857920 | 0.428960 | − | 0.903324i | \(-0.358880\pi\) | ||||
0.428960 | + | 0.903324i | \(0.358880\pi\) | |||||||
\(338\) | −3021.26 | −0.486198 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2669.19 | 0.425756 | ||||||||
\(341\) | 2635.43 | 0.418524 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20720.8 | 3.26186 | ||||||||
\(344\) | 9646.83 | 1.51198 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1727.63 | 0.268433 | ||||||||
\(347\) | −11128.3 | −1.72161 | −0.860804 | − | 0.508937i | \(-0.830039\pi\) | ||||
−0.860804 | + | 0.508937i | \(0.830039\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 498.178 | 0.0764093 | 0.0382047 | − | 0.999270i | \(-0.487836\pi\) | ||||
0.0382047 | + | 0.999270i | \(0.487836\pi\) | |||||||
\(350\) | −5506.38 | −0.840938 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10058.1 | 1.52301 | ||||||||
\(353\) | 4016.63 | 0.605619 | 0.302809 | − | 0.953051i | \(-0.402075\pi\) | ||||
0.302809 | + | 0.953051i | \(0.402075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.7419 | −0.00459609 | ||||||||
\(356\) | −2438.12 | −0.362978 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6819.52 | 1.00677 | ||||||||
\(359\) | −864.748 | −0.127130 | −0.0635650 | − | 0.997978i | \(-0.520247\pi\) | ||||
−0.0635650 | + | 0.997978i | \(0.520247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −682.047 | −0.0994383 | ||||||||
\(362\) | −6034.54 | −0.876156 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3586.55 | 0.516446 | ||||||||
\(365\) | 3354.67 | 0.481073 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2722.63 | −0.387249 | −0.193624 | − | 0.981076i | \(-0.562024\pi\) | ||||
−0.193624 | + | 0.981076i | \(0.562024\pi\) | |||||||
\(368\) | 1073.68 | 0.152092 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4023.22 | −0.565290 | ||||||||
\(371\) | −708.305 | −0.0991196 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8534.44 | −1.18471 | −0.592354 | − | 0.805677i | \(-0.701801\pi\) | ||||
−0.592354 | + | 0.805677i | \(0.701801\pi\) | |||||||
\(374\) | 8089.95 | 1.11851 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4617.73 | −0.633354 | ||||||||
\(377\) | 1522.92 | 0.208049 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3521.92 | −0.477331 | −0.238666 | − | 0.971102i | \(-0.576710\pi\) | ||||
−0.238666 | + | 0.971102i | \(0.576710\pi\) | |||||||
\(380\) | −2318.05 | −0.312930 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4688.11 | 0.627918 | ||||||||
\(383\) | 3611.09 | 0.481770 | 0.240885 | − | 0.970554i | \(-0.422562\pi\) | ||||
0.240885 | + | 0.970554i | \(0.422562\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10780.9 | −1.42713 | ||||||||
\(386\) | 7766.28 | 1.02408 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4683.24 | −0.612771 | ||||||||
\(389\) | 6408.88 | 0.835329 | 0.417665 | − | 0.908601i | \(-0.362849\pi\) | ||||
0.417665 | + | 0.908601i | \(0.362849\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15600.7 | 2.01781 | ||||||||
\(392\) | −20244.4 | −2.60841 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6643.03 | 0.849419 | ||||||||
\(395\) | 519.319 | 0.0661514 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9621.06 | 1.21629 | 0.608145 | − | 0.793826i | \(-0.291914\pi\) | ||||
0.608145 | + | 0.793826i | \(0.291914\pi\) | |||||||
\(398\) | −1537.75 | −0.193670 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −584.634 | −0.0730793 | ||||||||
\(401\) | −12078.8 | −1.50421 | −0.752105 | − | 0.659043i | \(-0.770962\pi\) | ||||
−0.752105 | + | 0.659043i | \(0.770962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −925.486 | −0.114396 | ||||||||
\(404\) | −1402.57 | −0.172724 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4688.38 | −0.573105 | ||||||||
\(407\) | 23748.7 | 2.89233 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9252.85 | −1.11864 | −0.559320 | − | 0.828952i | \(-0.688938\pi\) | ||||
−0.559320 | + | 0.828952i | \(0.688938\pi\) | |||||||
\(410\) | 595.204 | 0.0716951 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2634.36 | 0.315014 | ||||||||
\(413\) | 5808.28 | 0.692026 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1184.16 | 0.140068 | ||||||||
\(416\) | −3532.11 | −0.416289 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7025.72 | −0.822103 | ||||||||
\(419\) | −3089.02 | −0.360164 | −0.180082 | − | 0.983652i | \(-0.557636\pi\) | ||||
−0.180082 | + | 0.983652i | \(0.557636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1044.46 | 0.120912 | 0.0604558 | − | 0.998171i | \(-0.480745\pi\) | ||||
0.0604558 | + | 0.998171i | \(0.480745\pi\) | |||||||
\(422\) | −2987.48 | −0.344617 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 435.389 | 0.0498688 | ||||||||
\(425\) | −8494.78 | −0.969547 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15659.7 | −1.77477 | ||||||||
\(428\) | 1745.68 | 0.197152 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4051.43 | 0.454366 | ||||||||
\(431\) | −2532.27 | −0.283005 | −0.141502 | − | 0.989938i | \(-0.545193\pi\) | ||||
−0.141502 | + | 0.989938i | \(0.545193\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17903.2 | 1.98700 | 0.993501 | − | 0.113827i | \(-0.0363109\pi\) | ||||
0.993501 | + | 0.113827i | \(0.0363109\pi\) | |||||||
\(434\) | 2849.15 | 0.315124 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −949.560 | −0.104302 | ||||||||
\(437\) | −13548.4 | −1.48309 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13212.4 | −1.43643 | −0.718214 | − | 0.695822i | \(-0.755040\pi\) | ||||
−0.718214 | + | 0.695822i | \(0.755040\pi\) | |||||||
\(440\) | 6626.90 | 0.718012 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2840.95 | −0.305725 | ||||||||
\(443\) | −4677.28 | −0.501635 | −0.250818 | − | 0.968034i | \(-0.580699\pi\) | ||||
−0.250818 | + | 0.968034i | \(0.580699\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2573.65 | −0.274164 | ||||||||
\(446\) | 3874.91 | 0.411395 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9099.56 | 0.959629 | ||||||||
\(449\) | −12810.1 | −1.34643 | −0.673216 | − | 0.739446i | \(-0.735088\pi\) | ||||
−0.673216 | + | 0.739446i | \(0.735088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3513.43 | −0.366832 | ||||||||
\(452\) | −8073.06 | −0.840099 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5654.27 | 0.584511 | ||||||||
\(455\) | 3785.92 | 0.390080 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19402.9 | −1.98606 | −0.993032 | − | 0.117846i | \(-0.962401\pi\) | ||||
−0.993032 | + | 0.117846i | \(0.962401\pi\) | |||||||
\(458\) | 6789.24 | 0.692664 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5084.39 | 0.515349 | ||||||||
\(461\) | 13983.8 | 1.41278 | 0.706388 | − | 0.707825i | \(-0.250323\pi\) | ||||
0.706388 | + | 0.707825i | \(0.250323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7800.22 | −0.782953 | −0.391476 | − | 0.920188i | \(-0.628036\pi\) | ||||
−0.391476 | + | 0.920188i | \(0.628036\pi\) | |||||||
\(464\) | −497.784 | −0.0498040 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1841.00 | 0.183010 | ||||||||
\(467\) | 13713.3 | 1.35883 | 0.679415 | − | 0.733754i | \(-0.262234\pi\) | ||||
0.679415 | + | 0.733754i | \(0.262234\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31682.1 | −3.11929 | ||||||||
\(470\) | −1939.33 | −0.190329 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3570.30 | −0.348170 | ||||||||
\(473\) | −23915.2 | −2.32478 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7377.29 | 0.712618 | ||||||||
\(476\) | −17033.7 | −1.64021 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 393.739 | 0.0376762 | ||||||||
\(479\) | −15954.9 | −1.52192 | −0.760958 | − | 0.648801i | \(-0.775271\pi\) | ||||
−0.760958 | + | 0.648801i | \(0.775271\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8339.85 | −0.790570 | ||||||||
\(482\) | −7912.86 | −0.747761 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8527.88 | −0.800890 | ||||||||
\(485\) | −4943.57 | −0.462837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5449.51 | 0.507065 | 0.253533 | − | 0.967327i | \(-0.418408\pi\) | ||||
0.253533 | + | 0.967327i | \(0.418408\pi\) | |||||||
\(488\) | 9625.91 | 0.892919 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8502.16 | −0.783854 | ||||||||
\(491\) | −7614.50 | −0.699873 | −0.349936 | − | 0.936773i | \(-0.613797\pi\) | ||||
−0.349936 | + | 0.936773i | \(0.613797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7232.85 | −0.660753 | ||||||||
\(494\) | 2467.22 | 0.224708 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 302.506 | 0.0273849 | ||||||||
\(497\) | 196.183 | 0.0177062 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3547.26 | 0.318231 | 0.159115 | − | 0.987260i | \(-0.449136\pi\) | ||||
0.159115 | + | 0.987260i | \(0.449136\pi\) | |||||||
\(500\) | −6455.28 | −0.577378 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6445.28 | −0.573042 | ||||||||
\(503\) | −15506.5 | −1.37455 | −0.687276 | − | 0.726397i | \(-0.741194\pi\) | ||||
−0.687276 | + | 0.726397i | \(0.741194\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1480.53 | −0.130461 | ||||||||
\(506\) | 15410.1 | 1.35388 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7267.76 | −0.634753 | ||||||||
\(509\) | −18965.4 | −1.65153 | −0.825763 | − | 0.564018i | \(-0.809255\pi\) | ||||
−0.825763 | + | 0.564018i | \(0.809255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21408.2 | −1.85331 | ||||||||
\(512\) | 2245.12 | 0.193791 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10171.5 | −0.872854 | ||||||||
\(515\) | 2780.80 | 0.237936 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11447.7 | 0.973828 | ||||||||
\(518\) | 25674.6 | 2.17776 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2327.17 | −0.196256 | ||||||||
\(521\) | 4545.27 | 0.382211 | 0.191105 | − | 0.981570i | \(-0.438793\pi\) | ||||
0.191105 | + | 0.981570i | \(0.438793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19500.8 | 1.63042 | 0.815210 | − | 0.579165i | \(-0.196621\pi\) | ||||
0.815210 | + | 0.579165i | \(0.196621\pi\) | |||||||
\(524\) | 5529.06 | 0.460950 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11423.9 | 0.946971 | ||||||||
\(527\) | 4395.44 | 0.363317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17550.0 | 1.44242 | ||||||||
\(530\) | 182.853 | 0.0149861 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14792.9 | 1.20555 | ||||||||
\(533\) | 1233.81 | 0.100267 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1842.72 | 0.148912 | ||||||||
\(536\) | 19474.7 | 1.56937 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9122.97 | 0.731077 | ||||||||
\(539\) | 50187.5 | 4.01063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14008.5 | −1.11325 | −0.556627 | − | 0.830762i | \(-0.687905\pi\) | ||||
−0.556627 | + | 0.830762i | \(0.687905\pi\) | |||||||
\(542\) | 12653.5 | 1.00280 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16775.2 | 1.32211 | ||||||||
\(545\) | −1002.34 | −0.0787811 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12009.3 | −0.938720 | −0.469360 | − | 0.883007i | \(-0.655515\pi\) | ||||
−0.469360 | + | 0.883007i | \(0.655515\pi\) | |||||||
\(548\) | 5055.59 | 0.394095 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8390.99 | −0.650533 | ||||||||
\(551\) | 6281.36 | 0.485653 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3314.09 | −0.254845 | ||||||||
\(554\) | −8118.07 | −0.622570 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9408.76 | −0.717663 | ||||||||
\(557\) | 13403.1 | 1.01958 | 0.509790 | − | 0.860299i | \(-0.329723\pi\) | ||||
0.509790 | + | 0.860299i | \(0.329723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8398.32 | 0.635440 | ||||||||
\(560\) | −1237.47 | −0.0933799 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3691.90 | 0.277106 | ||||||||
\(563\) | 13027.5 | 0.975210 | 0.487605 | − | 0.873064i | \(-0.337871\pi\) | ||||
0.487605 | + | 0.873064i | \(0.337871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8521.82 | −0.634541 | ||||||||
\(566\) | 6840.16 | 0.507974 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −120.592 | −0.00890832 | ||||||||
\(569\) | −7195.64 | −0.530153 | −0.265076 | − | 0.964227i | \(-0.585397\pi\) | ||||
−0.265076 | + | 0.964227i | \(0.585397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13680.8 | −1.00267 | −0.501333 | − | 0.865255i | \(-0.667157\pi\) | ||||
−0.501333 | + | 0.865255i | \(0.667157\pi\) | |||||||
\(572\) | 5465.42 | 0.399512 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3798.36 | −0.276203 | ||||||||
\(575\) | −16181.2 | −1.17357 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19096.2 | 1.37779 | 0.688897 | − | 0.724859i | \(-0.258095\pi\) | ||||
0.688897 | + | 0.724859i | \(0.258095\pi\) | |||||||
\(578\) | 5398.72 | 0.388507 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2357.23 | −0.168757 | ||||||||
\(581\) | −7556.87 | −0.539607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1079.36 | −0.0766769 | ||||||||
\(584\) | 13159.4 | 0.932434 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5745.73 | −0.405041 | ||||||||
\(587\) | −16405.3 | −1.15353 | −0.576763 | − | 0.816911i | \(-0.695685\pi\) | ||||
−0.576763 | + | 0.816911i | \(0.695685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3817.21 | −0.267038 | ||||||||
\(590\) | −1499.44 | −0.104629 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2725.98 | 0.189252 | ||||||||
\(593\) | −19025.6 | −1.31751 | −0.658757 | − | 0.752356i | \(-0.728917\pi\) | ||||
−0.658757 | + | 0.752356i | \(0.728917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17980.6 | −1.23888 | ||||||||
\(596\) | 12629.1 | 0.867965 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5411.58 | −0.370060 | ||||||||
\(599\) | 3751.43 | 0.255892 | 0.127946 | − | 0.991781i | \(-0.459162\pi\) | ||||
0.127946 | + | 0.991781i | \(0.459162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12654.5 | −0.858881 | −0.429440 | − | 0.903095i | \(-0.641289\pi\) | ||||
−0.429440 | + | 0.903095i | \(0.641289\pi\) | |||||||
\(602\) | −25854.6 | −1.75043 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15769.6 | −1.06234 | ||||||||
\(605\) | −9001.93 | −0.604926 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5552.85 | 0.371307 | 0.185653 | − | 0.982615i | \(-0.440560\pi\) | ||||
0.185653 | + | 0.982615i | \(0.440560\pi\) | |||||||
\(608\) | −14568.4 | −0.971754 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4042.64 | 0.268331 | ||||||||
\(611\) | −4020.09 | −0.266179 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19445.2 | 1.28122 | 0.640609 | − | 0.767868i | \(-0.278682\pi\) | ||||
0.640609 | + | 0.767868i | \(0.278682\pi\) | |||||||
\(614\) | −2279.31 | −0.149814 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −42290.3 | −2.76611 | ||||||||
\(617\) | 7681.31 | 0.501196 | 0.250598 | − | 0.968091i | \(-0.419373\pi\) | ||||
0.250598 | + | 0.968091i | \(0.419373\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23937.0 | 1.55430 | 0.777149 | − | 0.629317i | \(-0.216665\pi\) | ||||
0.777149 | + | 0.629317i | \(0.216665\pi\) | |||||||
\(620\) | 1432.50 | 0.0927915 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10077.6 | 0.649640 | ||||||||
\(623\) | 16424.1 | 1.05621 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4919.17 | 0.314827 | ||||||||
\(626\) | −3305.26 | −0.211030 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10017.2 | −0.636511 | ||||||||
\(629\) | 39608.7 | 2.51081 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11248.1 | 0.709632 | 0.354816 | − | 0.934936i | \(-0.384543\pi\) | ||||
0.354816 | + | 0.934936i | \(0.384543\pi\) | |||||||
\(632\) | 2037.14 | 0.128217 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8456.97 | −0.529762 | ||||||||
\(635\) | −7671.76 | −0.479440 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17624.4 | −1.09624 | ||||||||
\(638\) | −7144.47 | −0.443342 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5925.17 | 0.365958 | ||||||||
\(641\) | −17640.5 | −1.08699 | −0.543493 | − | 0.839414i | \(-0.682899\pi\) | ||||
−0.543493 | + | 0.839414i | \(0.682899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13020.3 | −0.798555 | −0.399278 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399278 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(644\) | −32446.6 | −1.98536 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11717.7 | −0.713661 | ||||||||
\(647\) | 2580.88 | 0.156824 | 0.0784119 | − | 0.996921i | \(-0.475015\pi\) | ||||
0.0784119 | + | 0.996921i | \(0.475015\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8851.04 | 0.535337 | ||||||||
\(650\) | 2946.67 | 0.177812 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4622.61 | 0.277662 | ||||||||
\(653\) | 9853.27 | 0.590487 | 0.295244 | − | 0.955422i | \(-0.404599\pi\) | ||||
0.295244 | + | 0.955422i | \(0.404599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5836.41 | 0.348164 | ||||||||
\(656\) | −403.286 | −0.0240026 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12376.1 | 0.733235 | ||||||||
\(659\) | 3950.82 | 0.233539 | 0.116769 | − | 0.993159i | \(-0.462746\pi\) | ||||
0.116769 | + | 0.993159i | \(0.462746\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23360.3 | 1.37460 | 0.687299 | − | 0.726374i | \(-0.258796\pi\) | ||||
0.687299 | + | 0.726374i | \(0.258796\pi\) | |||||||
\(662\) | 2806.83 | 0.164789 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4645.15 | 0.271486 | ||||||||
\(665\) | 15615.2 | 0.910574 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13777.5 | −0.799798 | ||||||||
\(668\) | −22153.6 | −1.28316 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8178.91 | 0.471610 | ||||||||
\(671\) | −23863.4 | −1.37293 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20404.8 | 1.16872 | 0.584360 | − | 0.811495i | \(-0.301346\pi\) | ||||
0.584360 | + | 0.811495i | \(0.301346\pi\) | |||||||
\(674\) | 8743.85 | 0.499704 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9693.88 | 0.551541 | ||||||||
\(677\) | 17244.1 | 0.978941 | 0.489470 | − | 0.872020i | \(-0.337190\pi\) | ||||
0.489470 | + | 0.872020i | \(0.337190\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31547.9 | 1.78306 | ||||||||
\(680\) | 11052.5 | 0.623300 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4341.73 | 0.243773 | ||||||||
\(683\) | 22468.3 | 1.25875 | 0.629374 | − | 0.777102i | \(-0.283311\pi\) | ||||
0.629374 | + | 0.777102i | \(0.283311\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5336.62 | 0.297667 | ||||||||
\(686\) | 34136.4 | 1.89990 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2745.09 | −0.152116 | ||||||||
\(689\) | 379.040 | 0.0209583 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1335.99 | −0.0735508 | −0.0367754 | − | 0.999324i | \(-0.511709\pi\) | ||||
−0.0367754 | + | 0.999324i | \(0.511709\pi\) | |||||||
\(692\) | −5543.19 | −0.304510 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18333.3 | −1.00277 | ||||||||
\(695\) | −9931.78 | −0.542063 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5859.79 | −0.318444 | ||||||||
\(698\) | 820.721 | 0.0445054 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17667.5 | 0.953957 | ||||||||
\(701\) | −14909.4 | −0.803308 | −0.401654 | − | 0.915792i | \(-0.631565\pi\) | ||||
−0.401654 | + | 0.915792i | \(0.631565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34398.1 | −1.84545 | ||||||||
\(704\) | 13866.5 | 0.742349 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6617.17 | 0.352749 | ||||||||
\(707\) | 9448.18 | 0.502596 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 543.498 | 0.0287891 | 0.0143946 | − | 0.999896i | \(-0.495418\pi\) | ||||
0.0143946 | + | 0.999896i | \(0.495418\pi\) | |||||||
\(710\) | −50.6456 | −0.00267704 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10095.7 | −0.531395 | ||||||||
\(713\) | 8372.63 | 0.439772 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5769.23 | 0.301758 | ||||||||
\(716\) | −21880.8 | −1.14207 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1424.63 | −0.0740481 | ||||||||
\(719\) | 25212.4 | 1.30774 | 0.653870 | − | 0.756607i | \(-0.273144\pi\) | ||||
0.653870 | + | 0.756607i | \(0.273144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17746.0 | −0.916637 | ||||||||
\(722\) | −1123.64 | −0.0579188 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19362.2 | 0.993908 | ||||||||
\(725\) | 7501.99 | 0.384299 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17816.1 | 0.908890 | 0.454445 | − | 0.890775i | \(-0.349838\pi\) | ||||
0.454445 | + | 0.890775i | \(0.349838\pi\) | |||||||
\(728\) | 14851.1 | 0.756069 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5526.64 | 0.280205 | ||||||||
\(731\) | −39886.4 | −2.01813 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27700.5 | −1.39583 | −0.697914 | − | 0.716181i | \(-0.745888\pi\) | ||||
−0.697914 | + | 0.716181i | \(0.745888\pi\) | |||||||
\(734\) | −4485.39 | −0.225557 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31954.1 | 1.60033 | ||||||||
\(737\) | −48279.4 | −2.41302 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 177.348 | 0.00882794 | 0.00441397 | − | 0.999990i | \(-0.498595\pi\) | ||||
0.00441397 | + | 0.999990i | \(0.498595\pi\) | |||||||
\(740\) | 12908.7 | 0.641263 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1166.89 | −0.0577332 | ||||||||
\(743\) | 17677.9 | 0.872865 | 0.436432 | − | 0.899737i | \(-0.356242\pi\) | ||||
0.436432 | + | 0.899737i | \(0.356242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13331.1 | 0.655589 | ||||||||
\(746\) | −14060.0 | −0.690046 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25957.1 | −1.26883 | ||||||||
\(749\) | −11759.5 | −0.573677 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27506.4 | 1.33652 | 0.668258 | − | 0.743930i | \(-0.267040\pi\) | ||||
0.668258 | + | 0.743930i | \(0.267040\pi\) | |||||||
\(752\) | 1314.01 | 0.0637196 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2508.93 | 0.121180 | ||||||||
\(755\) | −16646.2 | −0.802407 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5969.17 | −0.286596 | −0.143298 | − | 0.989680i | \(-0.545771\pi\) | ||||
−0.143298 | + | 0.989680i | \(0.545771\pi\) | |||||||
\(758\) | −5802.16 | −0.278026 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9598.54 | −0.458126 | ||||||||
\(761\) | 13976.6 | 0.665772 | 0.332886 | − | 0.942967i | \(-0.391978\pi\) | ||||
0.332886 | + | 0.942967i | \(0.391978\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6396.57 | 0.303501 | ||||||||
\(764\) | −15042.1 | −0.712308 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5949.07 | 0.280612 | ||||||||
\(767\) | −3108.22 | −0.146325 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21818.2 | 1.02313 | 0.511564 | − | 0.859245i | \(-0.329066\pi\) | ||||
0.511564 | + | 0.859245i | \(0.329066\pi\) | |||||||
\(770\) | −17760.9 | −0.831243 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24918.6 | −1.16171 | ||||||||
\(773\) | −2656.81 | −0.123621 | −0.0618104 | − | 0.998088i | \(-0.519687\pi\) | ||||
−0.0618104 | + | 0.998088i | \(0.519687\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4559.00 | −0.211308 | ||||||||
\(776\) | −19392.2 | −0.897089 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 10558.3 | 0.486546 | ||||||||
\(779\) | 5088.93 | 0.234056 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 298.956 | 0.0136972 | ||||||||
\(782\) | 25701.3 | 1.17529 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5760.73 | 0.262424 | ||||||||
\(785\) | −10574.0 | −0.480768 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19700.1 | −0.892292 | −0.446146 | − | 0.894960i | \(-0.647204\pi\) | ||||
−0.446146 | + | 0.894960i | \(0.647204\pi\) | |||||||
\(788\) | −21314.6 | −0.963578 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 855.550 | 0.0385305 | ||||||||
\(791\) | 54382.9 | 2.44454 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8380.11 | 0.375267 | ||||||||
\(794\) | 15850.2 | 0.708440 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4933.97 | 0.219698 | ||||||||
\(797\) | 18458.3 | 0.820362 | 0.410181 | − | 0.912004i | \(-0.365466\pi\) | ||||
0.410181 | + | 0.912004i | \(0.365466\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19092.7 | 0.845372 | ||||||||
\(800\) | −17399.4 | −0.768952 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19899.2 | −0.876143 | ||||||||
\(803\) | −32623.2 | −1.43368 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −34250.2 | −1.49958 | ||||||||
\(806\) | −1524.69 | −0.0666313 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5807.72 | −0.252865 | ||||||||
\(809\) | −17976.7 | −0.781246 | −0.390623 | − | 0.920551i | \(-0.627740\pi\) | ||||
−0.390623 | + | 0.920551i | \(0.627740\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28715.6 | −1.24333 | −0.621665 | − | 0.783283i | \(-0.713544\pi\) | ||||
−0.621665 | + | 0.783283i | \(0.713544\pi\) | |||||||
\(812\) | 15042.9 | 0.650128 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 39124.7 | 1.68467 | ||||||||
\(815\) | 4879.57 | 0.209723 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34639.3 | 1.48332 | ||||||||
\(818\) | −15243.6 | −0.651563 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1909.74 | −0.0813307 | ||||||||
\(821\) | 2245.35 | 0.0954487 | 0.0477243 | − | 0.998861i | \(-0.484803\pi\) | ||||
0.0477243 | + | 0.998861i | \(0.484803\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6607.49 | −0.279857 | −0.139929 | − | 0.990162i | \(-0.544687\pi\) | ||||
−0.139929 | + | 0.990162i | \(0.544687\pi\) | |||||||
\(824\) | 10908.3 | 0.461176 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9568.82 | 0.403077 | ||||||||
\(827\) | 6354.94 | 0.267210 | 0.133605 | − | 0.991035i | \(-0.457345\pi\) | ||||
0.133605 | + | 0.991035i | \(0.457345\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16373.2 | −0.685963 | −0.342982 | − | 0.939342i | \(-0.611437\pi\) | ||||
−0.342982 | + | 0.939342i | \(0.611437\pi\) | |||||||
\(830\) | 1950.85 | 0.0815842 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4869.51 | −0.202909 | ||||||||
\(833\) | 83703.9 | 3.48159 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23385.1 | −0.969192 | ||||||||
\(836\) | 22542.4 | 0.932591 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5089.00 | −0.209781 | ||||||||
\(839\) | −17839.6 | −0.734076 | −0.367038 | − | 0.930206i | \(-0.619628\pi\) | ||||
−0.367038 | + | 0.930206i | \(0.619628\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18001.5 | −0.738098 | ||||||||
\(842\) | 1720.69 | 0.0704262 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9585.51 | 0.390932 | ||||||||
\(845\) | 10232.7 | 0.416588 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57446.8 | 2.33045 | ||||||||
\(848\) | −123.894 | −0.00501713 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13994.7 | −0.564722 | ||||||||
\(851\) | 75448.4 | 3.03917 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9279.28 | −0.372469 | −0.186235 | − | 0.982505i | \(-0.559628\pi\) | ||||
−0.186235 | + | 0.982505i | \(0.559628\pi\) | |||||||
\(854\) | −25798.6 | −1.03373 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7228.49 | 0.288627 | ||||||||
\(857\) | −9631.39 | −0.383900 | −0.191950 | − | 0.981405i | \(-0.561481\pi\) | ||||
−0.191950 | + | 0.981405i | \(0.561481\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4086.40 | −0.162312 | −0.0811560 | − | 0.996701i | \(-0.525861\pi\) | ||||
−0.0811560 | + | 0.996701i | \(0.525861\pi\) | |||||||
\(860\) | −12999.2 | −0.515431 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4171.77 | −0.164839 | ||||||||
\(863\) | −34804.9 | −1.37285 | −0.686426 | − | 0.727200i | \(-0.740821\pi\) | ||||
−0.686426 | + | 0.727200i | \(0.740821\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5851.33 | −0.230001 | ||||||||
\(866\) | 29494.5 | 1.15735 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9141.67 | −0.357475 | ||||||||
\(869\) | −5050.23 | −0.197143 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16954.3 | 0.659557 | ||||||||
\(872\) | −3931.92 | −0.152697 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −22320.3 | −0.863840 | ||||||||
\(875\) | 43485.0 | 1.68007 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16077.5 | −0.619041 | −0.309521 | − | 0.950893i | \(-0.600169\pi\) | ||||
−0.309521 | + | 0.950893i | \(0.600169\pi\) | |||||||
\(878\) | −21766.7 | −0.836662 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1885.74 | −0.0722368 | ||||||||
\(881\) | 29258.8 | 1.11890 | 0.559452 | − | 0.828863i | \(-0.311012\pi\) | ||||
0.559452 | + | 0.828863i | \(0.311012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9180.31 | −0.349878 | −0.174939 | − | 0.984579i | \(-0.555973\pi\) | ||||
−0.174939 | + | 0.984579i | \(0.555973\pi\) | |||||||
\(884\) | 9115.36 | 0.346813 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7705.57 | −0.292182 | ||||||||
\(887\) | 27405.2 | 1.03740 | 0.518701 | − | 0.854956i | \(-0.326416\pi\) | ||||
0.518701 | + | 0.854956i | \(0.326416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48958.2 | 1.84702 | ||||||||
\(890\) | −4239.95 | −0.159689 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12432.9 | −0.466685 | ||||||||
\(893\) | −16581.1 | −0.621349 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23097.1 | −0.862628 | ||||||||
\(896\) | −37812.1 | −1.40984 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21104.0 | −0.784243 | ||||||||
\(899\) | −3881.74 | −0.144008 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1800.19 | −0.0665626 | ||||||||
\(902\) | −5788.19 | −0.213665 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33428.7 | −1.22989 | ||||||||
\(905\) | 20438.5 | 0.750716 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23293.7 | −0.852760 | −0.426380 | − | 0.904544i | \(-0.640211\pi\) | ||||
−0.426380 | + | 0.904544i | \(0.640211\pi\) | |||||||
\(908\) | −18142.0 | −0.663067 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6237.09 | 0.227206 | ||||||||
\(911\) | 37781.1 | 1.37403 | 0.687017 | − | 0.726642i | \(-0.258920\pi\) | ||||
0.687017 | + | 0.726642i | \(0.258920\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11515.7 | −0.417429 | ||||||||
\(914\) | −31965.3 | −1.15680 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21783.7 | −0.785756 | ||||||||
\(917\) | −37245.7 | −1.34129 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32968.9 | 1.18340 | 0.591699 | − | 0.806159i | \(-0.298457\pi\) | ||||
0.591699 | + | 0.806159i | \(0.298457\pi\) | |||||||
\(920\) | 21053.3 | 0.754464 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23037.5 | 0.822886 | ||||||||
\(923\) | −104.985 | −0.00374389 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −41082.5 | −1.46031 | ||||||||
\(926\) | −12850.4 | −0.456039 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14814.6 | −0.524046 | ||||||||
\(929\) | −27745.8 | −0.979881 | −0.489940 | − | 0.871756i | \(-0.662981\pi\) | ||||
−0.489940 | + | 0.871756i | \(0.662981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −72692.6 | −2.55897 | ||||||||
\(932\) | −5906.96 | −0.207606 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22591.8 | 0.791464 | ||||||||
\(935\) | −27400.0 | −0.958369 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3424.81 | −0.119406 | −0.0597032 | − | 0.998216i | \(-0.519015\pi\) | ||||
−0.0597032 | + | 0.998216i | \(0.519015\pi\) | |||||||
\(938\) | −52194.6 | −1.81686 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6222.45 | 0.215909 | ||||||||
\(941\) | −29835.8 | −1.03360 | −0.516800 | − | 0.856106i | \(-0.672877\pi\) | ||||
−0.516800 | + | 0.856106i | \(0.672877\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11162.0 | −0.385455 | ||||||||
\(944\) | 1015.96 | 0.0350282 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −39399.0 | −1.35409 | ||||||||
\(947\) | −7223.68 | −0.247875 | −0.123938 | − | 0.992290i | \(-0.539552\pi\) | ||||
−0.123938 | + | 0.992290i | \(0.539552\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11456.3 | 0.391873 | ||||||||
\(950\) | 12153.7 | 0.415071 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −70532.8 | −2.40124 | ||||||||
\(953\) | −50384.7 | −1.71261 | −0.856306 | − | 0.516469i | \(-0.827246\pi\) | ||||
−0.856306 | + | 0.516469i | \(0.827246\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15878.2 | −0.538018 | ||||||||
\(956\) | −1263.34 | −0.0427397 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26284.8 | −0.886455 | ||||||||
\(959\) | −34056.2 | −1.14675 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27432.0 | −0.920817 | ||||||||
\(962\) | −13739.4 | −0.460475 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25388.9 | 0.848257 | ||||||||
\(965\) | −26303.7 | −0.877458 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17397.6 | 0.578562 | 0.289281 | − | 0.957244i | \(-0.406584\pi\) | ||||
0.289281 | + | 0.957244i | \(0.406584\pi\) | |||||||
\(968\) | −35312.1 | −1.17249 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8144.26 | −0.269584 | ||||||||
\(971\) | −712.563 | −0.0235502 | −0.0117751 | − | 0.999931i | \(-0.503748\pi\) | ||||
−0.0117751 | + | 0.999931i | \(0.503748\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 63380.7 | 2.08828 | ||||||||
\(974\) | 8977.76 | 0.295345 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2739.14 | −0.0898336 | ||||||||
\(977\) | 39634.3 | 1.29786 | 0.648932 | − | 0.760847i | \(-0.275216\pi\) | ||||
0.648932 | + | 0.760847i | \(0.275216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25028.1 | 0.817059 | ||||||||
\(980\) | 27279.7 | 0.889201 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12544.5 | −0.407648 | ||||||||
\(983\) | 37996.8 | 1.23287 | 0.616434 | − | 0.787406i | \(-0.288577\pi\) | ||||
0.616434 | + | 0.787406i | \(0.288577\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22499.4 | −0.727807 | ||||||||
\(986\) | −11915.7 | −0.384862 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7916.23 | −0.254908 | ||||||||
\(989\) | −75977.4 | −2.44281 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26751.3 | −0.857502 | −0.428751 | − | 0.903423i | \(-0.641046\pi\) | ||||
−0.428751 | + | 0.903423i | \(0.641046\pi\) | |||||||
\(992\) | 9002.93 | 0.288148 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 323.200 | 0.0103132 | ||||||||
\(995\) | 5208.24 | 0.165942 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28884.7 | −0.917541 | −0.458770 | − | 0.888555i | \(-0.651710\pi\) | ||||
−0.458770 | + | 0.888555i | \(0.651710\pi\) | |||||||
\(998\) | 5843.91 | 0.185357 | ||||||||
\(999\) | 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.c.1.17 | 28 | ||
3.2 | odd | 2 | 717.4.a.a.1.12 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
717.4.a.a.1.12 | ✓ | 28 | 3.2 | odd | 2 | ||
2151.4.a.c.1.17 | 28 | 1.1 | even | 1 | trivial |