Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,4,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, 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("2166.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(127.798137072\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.14457.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 32x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-5.12716\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 14.2543 | 1.27494 | 0.637472 | − | 0.770473i | \(-0.279980\pi\) | ||||
0.637472 | + | 0.770473i | \(0.279980\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 13.2543 | 0.715666 | 0.357833 | − | 0.933786i | \(-0.383516\pi\) | ||||
0.357833 | + | 0.933786i | \(0.383516\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 28.5086 | 0.901522 | ||||||||
\(11\) | −65.9138 | −1.80671 | −0.903353 | − | 0.428898i | \(-0.858902\pi\) | ||||
−0.903353 | + | 0.428898i | \(0.858902\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | −68.5259 | −1.46197 | −0.730987 | − | 0.682392i | \(-0.760940\pi\) | ||||
−0.730987 | + | 0.682392i | \(0.760940\pi\) | |||||||
\(14\) | 26.5086 | 0.506052 | ||||||||
\(15\) | −42.7629 | −0.736089 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 99.6940 | 1.42231 | 0.711157 | − | 0.703033i | \(-0.248171\pi\) | ||||
0.711157 | + | 0.703033i | \(0.248171\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 57.0172 | 0.637472 | ||||||||
\(21\) | −39.7629 | −0.413190 | ||||||||
\(22\) | −131.828 | −1.27753 | ||||||||
\(23\) | 3.53886 | 0.0320828 | 0.0160414 | − | 0.999871i | \(-0.494894\pi\) | ||||
0.0160414 | + | 0.999871i | \(0.494894\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 78.1854 | 0.625483 | ||||||||
\(26\) | −137.052 | −1.03377 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 53.0172 | 0.357833 | ||||||||
\(29\) | −81.9008 | −0.524435 | −0.262217 | − | 0.965009i | \(-0.584454\pi\) | ||||
−0.262217 | + | 0.965009i | \(0.584454\pi\) | |||||||
\(30\) | −85.5259 | −0.520494 | ||||||||
\(31\) | −247.190 | −1.43215 | −0.716074 | − | 0.698025i | \(-0.754063\pi\) | ||||
−0.716074 | + | 0.698025i | \(0.754063\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 197.741 | 1.04310 | ||||||||
\(34\) | 199.388 | 1.00573 | ||||||||
\(35\) | 188.931 | 0.912434 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 421.065 | 1.87088 | 0.935441 | − | 0.353483i | \(-0.115003\pi\) | ||||
0.935441 | + | 0.353483i | \(0.115003\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 205.578 | 0.844071 | ||||||||
\(40\) | 114.034 | 0.450761 | ||||||||
\(41\) | −345.259 | −1.31513 | −0.657565 | − | 0.753398i | \(-0.728413\pi\) | ||||
−0.657565 | + | 0.753398i | \(0.728413\pi\) | |||||||
\(42\) | −79.5259 | −0.292169 | ||||||||
\(43\) | −366.168 | −1.29861 | −0.649304 | − | 0.760529i | \(-0.724940\pi\) | ||||
−0.649304 | + | 0.760529i | \(0.724940\pi\) | |||||||
\(44\) | −263.655 | −0.903353 | ||||||||
\(45\) | 128.289 | 0.424981 | ||||||||
\(46\) | 7.07773 | 0.0226860 | ||||||||
\(47\) | −90.9399 | −0.282233 | −0.141116 | − | 0.989993i | \(-0.545069\pi\) | ||||
−0.141116 | + | 0.989993i | \(0.545069\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | −167.323 | −0.487823 | ||||||||
\(50\) | 156.371 | 0.442283 | ||||||||
\(51\) | −299.082 | −0.821174 | ||||||||
\(52\) | −274.103 | −0.730987 | ||||||||
\(53\) | −688.491 | −1.78437 | −0.892185 | − | 0.451671i | \(-0.850828\pi\) | ||||
−0.892185 | + | 0.451671i | \(0.850828\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −939.556 | −2.30345 | ||||||||
\(56\) | 106.034 | 0.253026 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −163.802 | −0.370831 | ||||||||
\(59\) | 182.289 | 0.402237 | 0.201118 | − | 0.979567i | \(-0.435542\pi\) | ||||
0.201118 | + | 0.979567i | \(0.435542\pi\) | |||||||
\(60\) | −171.052 | −0.368045 | ||||||||
\(61\) | −0.517370 | −0.00108594 | −0.000542971 | − | 1.00000i | \(-0.500173\pi\) | ||||
−0.000542971 | 1.00000i | \(0.500173\pi\) | ||||||||
\(62\) | −494.379 | −1.01268 | ||||||||
\(63\) | 119.289 | 0.238555 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −976.789 | −1.86393 | ||||||||
\(66\) | 395.483 | 0.737585 | ||||||||
\(67\) | −159.862 | −0.291496 | −0.145748 | − | 0.989322i | \(-0.546559\pi\) | ||||
−0.145748 | + | 0.989322i | \(0.546559\pi\) | |||||||
\(68\) | 398.776 | 0.711157 | ||||||||
\(69\) | −10.6166 | −0.0185230 | ||||||||
\(70\) | 377.862 | 0.645188 | ||||||||
\(71\) | −791.884 | −1.32365 | −0.661826 | − | 0.749657i | \(-0.730218\pi\) | ||||
−0.661826 | + | 0.749657i | \(0.730218\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 322.129 | 0.516471 | 0.258235 | − | 0.966082i | \(-0.416859\pi\) | ||||
0.258235 | + | 0.966082i | \(0.416859\pi\) | |||||||
\(74\) | 842.130 | 1.32291 | ||||||||
\(75\) | −234.556 | −0.361123 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −873.642 | −1.29300 | ||||||||
\(78\) | 411.155 | 0.596848 | ||||||||
\(79\) | 318.371 | 0.453412 | 0.226706 | − | 0.973963i | \(-0.427204\pi\) | ||||
0.226706 | + | 0.973963i | \(0.427204\pi\) | |||||||
\(80\) | 228.069 | 0.318736 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −690.517 | −0.929937 | ||||||||
\(83\) | 684.160 | 0.904774 | 0.452387 | − | 0.891822i | \(-0.350573\pi\) | ||||
0.452387 | + | 0.891822i | \(0.350573\pi\) | |||||||
\(84\) | −159.052 | −0.206595 | ||||||||
\(85\) | 1421.07 | 1.81337 | ||||||||
\(86\) | −732.336 | −0.918254 | ||||||||
\(87\) | 245.703 | 0.302782 | ||||||||
\(88\) | −527.311 | −0.638767 | ||||||||
\(89\) | 720.406 | 0.858009 | 0.429005 | − | 0.903302i | \(-0.358864\pi\) | ||||
0.429005 | + | 0.903302i | \(0.358864\pi\) | |||||||
\(90\) | 256.578 | 0.300507 | ||||||||
\(91\) | −908.263 | −1.04628 | ||||||||
\(92\) | 14.1555 | 0.0160414 | ||||||||
\(93\) | 741.569 | 0.826851 | ||||||||
\(94\) | −181.880 | −0.199569 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 415.392 | 0.434811 | 0.217406 | − | 0.976081i | \(-0.430241\pi\) | ||||
0.217406 | + | 0.976081i | \(0.430241\pi\) | |||||||
\(98\) | −334.646 | −0.344943 | ||||||||
\(99\) | −593.224 | −0.602235 | ||||||||
\(100\) | 312.742 | 0.312742 | ||||||||
\(101\) | 337.341 | 0.332343 | 0.166172 | − | 0.986097i | \(-0.446859\pi\) | ||||
0.166172 | + | 0.986097i | \(0.446859\pi\) | |||||||
\(102\) | −598.164 | −0.580658 | ||||||||
\(103\) | −1467.05 | −1.40342 | −0.701711 | − | 0.712462i | \(-0.747580\pi\) | ||||
−0.701711 | + | 0.712462i | \(0.747580\pi\) | |||||||
\(104\) | −548.207 | −0.516886 | ||||||||
\(105\) | −566.793 | −0.526794 | ||||||||
\(106\) | −1376.98 | −1.26174 | ||||||||
\(107\) | 382.014 | 0.345146 | 0.172573 | − | 0.984997i | \(-0.444792\pi\) | ||||
0.172573 | + | 0.984997i | \(0.444792\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −132.857 | −0.116747 | −0.0583736 | − | 0.998295i | \(-0.518591\pi\) | ||||
−0.0583736 | + | 0.998295i | \(0.518591\pi\) | |||||||
\(110\) | −1879.11 | −1.62879 | ||||||||
\(111\) | −1263.19 | −1.08015 | ||||||||
\(112\) | 212.069 | 0.178916 | ||||||||
\(113\) | −1137.94 | −0.947331 | −0.473665 | − | 0.880705i | \(-0.657069\pi\) | ||||
−0.473665 | + | 0.880705i | \(0.657069\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 50.4441 | 0.0409038 | ||||||||
\(116\) | −327.603 | −0.262217 | ||||||||
\(117\) | −616.733 | −0.487325 | ||||||||
\(118\) | 364.578 | 0.284424 | ||||||||
\(119\) | 1321.38 | 1.01790 | ||||||||
\(120\) | −342.103 | −0.260247 | ||||||||
\(121\) | 3013.63 | 2.26419 | ||||||||
\(122\) | −1.03474 | −0.000767877 0 | ||||||||
\(123\) | 1035.78 | 0.759291 | ||||||||
\(124\) | −988.759 | −0.716074 | ||||||||
\(125\) | −667.310 | −0.477488 | ||||||||
\(126\) | 238.578 | 0.168684 | ||||||||
\(127\) | −1509.97 | −1.05503 | −0.527514 | − | 0.849546i | \(-0.676876\pi\) | ||||
−0.527514 | + | 0.849546i | \(0.676876\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 1098.50 | 0.749751 | ||||||||
\(130\) | −1953.58 | −1.31800 | ||||||||
\(131\) | −370.944 | −0.247401 | −0.123701 | − | 0.992320i | \(-0.539476\pi\) | ||||
−0.123701 | + | 0.992320i | \(0.539476\pi\) | |||||||
\(132\) | 790.966 | 0.521551 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −319.724 | −0.206119 | ||||||||
\(135\) | −384.866 | −0.245363 | ||||||||
\(136\) | 797.552 | 0.502864 | ||||||||
\(137\) | −1690.37 | −1.05415 | −0.527075 | − | 0.849819i | \(-0.676711\pi\) | ||||
−0.527075 | + | 0.849819i | \(0.676711\pi\) | |||||||
\(138\) | −21.2332 | −0.0130977 | ||||||||
\(139\) | −2711.52 | −1.65459 | −0.827296 | − | 0.561766i | \(-0.810122\pi\) | ||||
−0.827296 | + | 0.561766i | \(0.810122\pi\) | |||||||
\(140\) | 755.724 | 0.456217 | ||||||||
\(141\) | 272.820 | 0.162947 | ||||||||
\(142\) | −1583.77 | −0.935964 | ||||||||
\(143\) | 4516.80 | 2.64136 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −1167.44 | −0.668625 | ||||||||
\(146\) | 644.258 | 0.365200 | ||||||||
\(147\) | 501.970 | 0.281645 | ||||||||
\(148\) | 1684.26 | 0.935441 | ||||||||
\(149\) | 2598.90 | 1.42893 | 0.714464 | − | 0.699672i | \(-0.246671\pi\) | ||||
0.714464 | + | 0.699672i | \(0.246671\pi\) | |||||||
\(150\) | −469.112 | −0.255352 | ||||||||
\(151\) | 594.863 | 0.320591 | 0.160296 | − | 0.987069i | \(-0.448755\pi\) | ||||
0.160296 | + | 0.987069i | \(0.448755\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 897.246 | 0.474105 | ||||||||
\(154\) | −1747.28 | −0.914287 | ||||||||
\(155\) | −3523.52 | −1.82591 | ||||||||
\(156\) | 822.310 | 0.422035 | ||||||||
\(157\) | −58.2549 | −0.0296130 | −0.0148065 | − | 0.999890i | \(-0.504713\pi\) | ||||
−0.0148065 | + | 0.999890i | \(0.504713\pi\) | |||||||
\(158\) | 636.742 | 0.320610 | ||||||||
\(159\) | 2065.47 | 1.03021 | ||||||||
\(160\) | 456.138 | 0.225380 | ||||||||
\(161\) | 46.9052 | 0.0229605 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 1152.53 | 0.553825 | 0.276912 | − | 0.960895i | \(-0.410689\pi\) | ||||
0.276912 | + | 0.960895i | \(0.410689\pi\) | |||||||
\(164\) | −1381.03 | −0.657565 | ||||||||
\(165\) | 2818.67 | 1.32990 | ||||||||
\(166\) | 1368.32 | 0.639772 | ||||||||
\(167\) | 1259.11 | 0.583430 | 0.291715 | − | 0.956505i | \(-0.405774\pi\) | ||||
0.291715 | + | 0.956505i | \(0.405774\pi\) | |||||||
\(168\) | −318.103 | −0.146085 | ||||||||
\(169\) | 2498.79 | 1.13737 | ||||||||
\(170\) | 2842.14 | 1.28225 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1464.67 | −0.649304 | ||||||||
\(173\) | −1274.10 | −0.559931 | −0.279965 | − | 0.960010i | \(-0.590323\pi\) | ||||
−0.279965 | + | 0.960010i | \(0.590323\pi\) | |||||||
\(174\) | 491.405 | 0.214100 | ||||||||
\(175\) | 1036.29 | 0.447637 | ||||||||
\(176\) | −1054.62 | −0.451677 | ||||||||
\(177\) | −546.866 | −0.232232 | ||||||||
\(178\) | 1440.81 | 0.606704 | ||||||||
\(179\) | 2034.50 | 0.849528 | 0.424764 | − | 0.905304i | \(-0.360357\pi\) | ||||
0.424764 | + | 0.905304i | \(0.360357\pi\) | |||||||
\(180\) | 513.155 | 0.212491 | ||||||||
\(181\) | 1033.31 | 0.424340 | 0.212170 | − | 0.977233i | \(-0.431947\pi\) | ||||
0.212170 | + | 0.977233i | \(0.431947\pi\) | |||||||
\(182\) | −1816.53 | −0.739835 | ||||||||
\(183\) | 1.55211 | 0.000626969 0 | ||||||||
\(184\) | 28.3109 | 0.0113430 | ||||||||
\(185\) | 6001.99 | 2.38527 | ||||||||
\(186\) | 1483.14 | 0.584672 | ||||||||
\(187\) | −6571.21 | −2.56970 | ||||||||
\(188\) | −363.760 | −0.141116 | ||||||||
\(189\) | −357.866 | −0.137730 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1135.46 | −0.430154 | −0.215077 | − | 0.976597i | \(-0.569000\pi\) | ||||
−0.215077 | + | 0.976597i | \(0.569000\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 1091.07 | 0.406928 | 0.203464 | − | 0.979082i | \(-0.434780\pi\) | ||||
0.203464 | + | 0.979082i | \(0.434780\pi\) | |||||||
\(194\) | 830.784 | 0.307458 | ||||||||
\(195\) | 2930.37 | 1.07614 | ||||||||
\(196\) | −669.293 | −0.243911 | ||||||||
\(197\) | 4138.08 | 1.49658 | 0.748289 | − | 0.663373i | \(-0.230876\pi\) | ||||
0.748289 | + | 0.663373i | \(0.230876\pi\) | |||||||
\(198\) | −1186.45 | −0.425845 | ||||||||
\(199\) | −2734.23 | −0.973993 | −0.486997 | − | 0.873404i | \(-0.661908\pi\) | ||||
−0.486997 | + | 0.873404i | \(0.661908\pi\) | |||||||
\(200\) | 625.483 | 0.221142 | ||||||||
\(201\) | 479.586 | 0.168296 | ||||||||
\(202\) | 674.682 | 0.235002 | ||||||||
\(203\) | −1085.54 | −0.375320 | ||||||||
\(204\) | −1196.33 | −0.410587 | ||||||||
\(205\) | −4921.42 | −1.67672 | ||||||||
\(206\) | −2934.10 | −0.992369 | ||||||||
\(207\) | 31.8498 | 0.0106943 | ||||||||
\(208\) | −1096.41 | −0.365493 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1133.59 | −0.372500 | ||||||||
\(211\) | 3058.01 | 0.997734 | 0.498867 | − | 0.866679i | \(-0.333750\pi\) | ||||
0.498867 | + | 0.866679i | \(0.333750\pi\) | |||||||
\(212\) | −2753.97 | −0.892185 | ||||||||
\(213\) | 2375.65 | 0.764211 | ||||||||
\(214\) | 764.027 | 0.244055 | ||||||||
\(215\) | −5219.48 | −1.65565 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −3276.33 | −1.02494 | ||||||||
\(218\) | −265.715 | −0.0825527 | ||||||||
\(219\) | −966.388 | −0.298185 | ||||||||
\(220\) | −3758.23 | −1.15172 | ||||||||
\(221\) | −6831.62 | −2.07939 | ||||||||
\(222\) | −2526.39 | −0.763784 | ||||||||
\(223\) | 1618.27 | 0.485951 | 0.242976 | − | 0.970032i | \(-0.421876\pi\) | ||||
0.242976 | + | 0.970032i | \(0.421876\pi\) | |||||||
\(224\) | 424.138 | 0.126513 | ||||||||
\(225\) | 703.668 | 0.208494 | ||||||||
\(226\) | −2275.88 | −0.669864 | ||||||||
\(227\) | −6065.43 | −1.77347 | −0.886733 | − | 0.462282i | \(-0.847031\pi\) | ||||
−0.886733 | + | 0.462282i | \(0.847031\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1916.36 | −0.552999 | −0.276500 | − | 0.961014i | \(-0.589174\pi\) | ||||
−0.276500 | + | 0.961014i | \(0.589174\pi\) | |||||||
\(230\) | 100.888 | 0.0289233 | ||||||||
\(231\) | 2620.93 | 0.746512 | ||||||||
\(232\) | −655.207 | −0.185416 | ||||||||
\(233\) | −4008.54 | −1.12707 | −0.563537 | − | 0.826091i | \(-0.690560\pi\) | ||||
−0.563537 | + | 0.826091i | \(0.690560\pi\) | |||||||
\(234\) | −1233.47 | −0.344590 | ||||||||
\(235\) | −1296.29 | −0.359831 | ||||||||
\(236\) | 729.155 | 0.201118 | ||||||||
\(237\) | −955.112 | −0.261777 | ||||||||
\(238\) | 2642.75 | 0.719765 | ||||||||
\(239\) | 530.292 | 0.143522 | 0.0717610 | − | 0.997422i | \(-0.477138\pi\) | ||||
0.0717610 | + | 0.997422i | \(0.477138\pi\) | |||||||
\(240\) | −684.207 | −0.184022 | ||||||||
\(241\) | 1271.23 | 0.339779 | 0.169890 | − | 0.985463i | \(-0.445659\pi\) | ||||
0.169890 | + | 0.985463i | \(0.445659\pi\) | |||||||
\(242\) | 6027.27 | 1.60102 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −2.06948 | −0.000542971 0 | ||||||||
\(245\) | −2385.08 | −0.621947 | ||||||||
\(246\) | 2071.55 | 0.536900 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1977.52 | −0.506341 | ||||||||
\(249\) | −2052.48 | −0.522372 | ||||||||
\(250\) | −1334.62 | −0.337635 | ||||||||
\(251\) | 551.989 | 0.138810 | 0.0694048 | − | 0.997589i | \(-0.477890\pi\) | ||||
0.0694048 | + | 0.997589i | \(0.477890\pi\) | |||||||
\(252\) | 477.155 | 0.119278 | ||||||||
\(253\) | −233.260 | −0.0579642 | ||||||||
\(254\) | −3019.95 | −0.746018 | ||||||||
\(255\) | −4263.21 | −1.04695 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5235.84 | −1.27083 | −0.635414 | − | 0.772172i | \(-0.719170\pi\) | ||||
−0.635414 | + | 0.772172i | \(0.719170\pi\) | |||||||
\(258\) | 2197.01 | 0.530154 | ||||||||
\(259\) | 5580.92 | 1.33893 | ||||||||
\(260\) | −3907.16 | −0.931967 | ||||||||
\(261\) | −737.108 | −0.174812 | ||||||||
\(262\) | −741.888 | −0.174939 | ||||||||
\(263\) | −1814.26 | −0.425368 | −0.212684 | − | 0.977121i | \(-0.568221\pi\) | ||||
−0.212684 | + | 0.977121i | \(0.568221\pi\) | |||||||
\(264\) | 1581.93 | 0.368792 | ||||||||
\(265\) | −9813.97 | −2.27497 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2161.22 | −0.495372 | ||||||||
\(268\) | −639.448 | −0.145748 | ||||||||
\(269\) | 1013.40 | 0.229695 | 0.114848 | − | 0.993383i | \(-0.463362\pi\) | ||||
0.114848 | + | 0.993383i | \(0.463362\pi\) | |||||||
\(270\) | −769.733 | −0.173498 | ||||||||
\(271\) | −1918.52 | −0.430043 | −0.215021 | − | 0.976609i | \(-0.568982\pi\) | ||||
−0.215021 | + | 0.976609i | \(0.568982\pi\) | |||||||
\(272\) | 1595.10 | 0.355579 | ||||||||
\(273\) | 2724.79 | 0.604072 | ||||||||
\(274\) | −3380.75 | −0.745396 | ||||||||
\(275\) | −5153.50 | −1.13006 | ||||||||
\(276\) | −42.4664 | −0.00926150 | ||||||||
\(277\) | 6283.45 | 1.36295 | 0.681473 | − | 0.731844i | \(-0.261340\pi\) | ||||
0.681473 | + | 0.731844i | \(0.261340\pi\) | |||||||
\(278\) | −5423.04 | −1.16997 | ||||||||
\(279\) | −2224.71 | −0.477382 | ||||||||
\(280\) | 1511.45 | 0.322594 | ||||||||
\(281\) | −8057.36 | −1.71054 | −0.855270 | − | 0.518182i | \(-0.826609\pi\) | ||||
−0.855270 | + | 0.518182i | \(0.826609\pi\) | |||||||
\(282\) | 545.639 | 0.115221 | ||||||||
\(283\) | −193.417 | −0.0406269 | −0.0203135 | − | 0.999794i | \(-0.506466\pi\) | ||||
−0.0203135 | + | 0.999794i | \(0.506466\pi\) | |||||||
\(284\) | −3167.54 | −0.661826 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9033.61 | 1.86772 | ||||||||
\(287\) | −4576.16 | −0.941193 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 5025.90 | 1.02298 | ||||||||
\(290\) | −2334.88 | −0.472789 | ||||||||
\(291\) | −1246.18 | −0.251038 | ||||||||
\(292\) | 1288.52 | 0.258235 | ||||||||
\(293\) | −4735.47 | −0.944194 | −0.472097 | − | 0.881547i | \(-0.656503\pi\) | ||||
−0.472097 | + | 0.881547i | \(0.656503\pi\) | |||||||
\(294\) | 1003.94 | 0.199153 | ||||||||
\(295\) | 2598.40 | 0.512830 | ||||||||
\(296\) | 3368.52 | 0.661457 | ||||||||
\(297\) | 1779.67 | 0.347701 | ||||||||
\(298\) | 5197.80 | 1.01040 | ||||||||
\(299\) | −242.504 | −0.0469042 | ||||||||
\(300\) | −938.225 | −0.180561 | ||||||||
\(301\) | −4853.31 | −0.929369 | ||||||||
\(302\) | 1189.73 | 0.226692 | ||||||||
\(303\) | −1012.02 | −0.191879 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.37475 | −0.00138451 | ||||||||
\(306\) | 1794.49 | 0.335243 | ||||||||
\(307\) | −28.7122 | −0.00533775 | −0.00266888 | − | 0.999996i | \(-0.500850\pi\) | ||||
−0.00266888 | + | 0.999996i | \(0.500850\pi\) | |||||||
\(308\) | −3494.57 | −0.646499 | ||||||||
\(309\) | 4401.14 | 0.810266 | ||||||||
\(310\) | −7047.04 | −1.29111 | ||||||||
\(311\) | −1165.69 | −0.212540 | −0.106270 | − | 0.994337i | \(-0.533891\pi\) | ||||
−0.106270 | + | 0.994337i | \(0.533891\pi\) | |||||||
\(312\) | 1644.62 | 0.298424 | ||||||||
\(313\) | 2512.75 | 0.453767 | 0.226884 | − | 0.973922i | \(-0.427146\pi\) | ||||
0.226884 | + | 0.973922i | \(0.427146\pi\) | |||||||
\(314\) | −116.510 | −0.0209396 | ||||||||
\(315\) | 1700.38 | 0.304145 | ||||||||
\(316\) | 1273.48 | 0.226706 | ||||||||
\(317\) | −1727.57 | −0.306087 | −0.153044 | − | 0.988219i | \(-0.548908\pi\) | ||||
−0.153044 | + | 0.988219i | \(0.548908\pi\) | |||||||
\(318\) | 4130.95 | 0.728466 | ||||||||
\(319\) | 5398.40 | 0.947499 | ||||||||
\(320\) | 912.276 | 0.159368 | ||||||||
\(321\) | −1146.04 | −0.199270 | ||||||||
\(322\) | 93.8104 | 0.0162356 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −5357.72 | −0.914440 | ||||||||
\(326\) | 2305.07 | 0.391613 | ||||||||
\(327\) | 398.572 | 0.0674040 | ||||||||
\(328\) | −2762.07 | −0.464969 | ||||||||
\(329\) | −1205.35 | −0.201984 | ||||||||
\(330\) | 5637.34 | 0.940379 | ||||||||
\(331\) | −6816.13 | −1.13187 | −0.565934 | − | 0.824450i | \(-0.691484\pi\) | ||||
−0.565934 | + | 0.824450i | \(0.691484\pi\) | |||||||
\(332\) | 2736.64 | 0.452387 | ||||||||
\(333\) | 3789.58 | 0.623627 | ||||||||
\(334\) | 2518.22 | 0.412547 | ||||||||
\(335\) | −2278.72 | −0.371642 | ||||||||
\(336\) | −636.207 | −0.103297 | ||||||||
\(337\) | −10408.4 | −1.68244 | −0.841218 | − | 0.540696i | \(-0.818161\pi\) | ||||
−0.841218 | + | 0.540696i | \(0.818161\pi\) | |||||||
\(338\) | 4997.59 | 0.804240 | ||||||||
\(339\) | 3413.82 | 0.546942 | ||||||||
\(340\) | 5684.28 | 0.906686 | ||||||||
\(341\) | 16293.2 | 2.58747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6763.98 | −1.06478 | ||||||||
\(344\) | −2929.35 | −0.459127 | ||||||||
\(345\) | −151.332 | −0.0236158 | ||||||||
\(346\) | −2548.20 | −0.395931 | ||||||||
\(347\) | −5584.03 | −0.863881 | −0.431940 | − | 0.901902i | \(-0.642171\pi\) | ||||
−0.431940 | + | 0.901902i | \(0.642171\pi\) | |||||||
\(348\) | 982.810 | 0.151391 | ||||||||
\(349\) | 5505.82 | 0.844470 | 0.422235 | − | 0.906486i | \(-0.361246\pi\) | ||||
0.422235 | + | 0.906486i | \(0.361246\pi\) | |||||||
\(350\) | 2072.59 | 0.316527 | ||||||||
\(351\) | 1850.20 | 0.281357 | ||||||||
\(352\) | −2109.24 | −0.319384 | ||||||||
\(353\) | −5782.46 | −0.871868 | −0.435934 | − | 0.899979i | \(-0.643582\pi\) | ||||
−0.435934 | + | 0.899979i | \(0.643582\pi\) | |||||||
\(354\) | −1093.73 | −0.164213 | ||||||||
\(355\) | −11287.8 | −1.68758 | ||||||||
\(356\) | 2881.62 | 0.429005 | ||||||||
\(357\) | −3964.13 | −0.587686 | ||||||||
\(358\) | 4068.99 | 0.600707 | ||||||||
\(359\) | −1903.64 | −0.279861 | −0.139931 | − | 0.990161i | \(-0.544688\pi\) | ||||
−0.139931 | + | 0.990161i | \(0.544688\pi\) | |||||||
\(360\) | 1026.31 | 0.150254 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 2066.63 | 0.300054 | ||||||||
\(363\) | −9040.90 | −1.30723 | ||||||||
\(364\) | −3633.05 | −0.523142 | ||||||||
\(365\) | 4591.73 | 0.658472 | ||||||||
\(366\) | 3.10422 | 0.000443334 0 | ||||||||
\(367\) | −12748.0 | −1.81319 | −0.906597 | − | 0.421998i | \(-0.861329\pi\) | ||||
−0.906597 | + | 0.421998i | \(0.861329\pi\) | |||||||
\(368\) | 56.6218 | 0.00802070 | ||||||||
\(369\) | −3107.33 | −0.438377 | ||||||||
\(370\) | 12004.0 | 1.68664 | ||||||||
\(371\) | −9125.48 | −1.27701 | ||||||||
\(372\) | 2966.28 | 0.413425 | ||||||||
\(373\) | −736.660 | −0.102260 | −0.0511298 | − | 0.998692i | \(-0.516282\pi\) | ||||
−0.0511298 | + | 0.998692i | \(0.516282\pi\) | |||||||
\(374\) | −13142.4 | −1.81706 | ||||||||
\(375\) | 2001.93 | 0.275678 | ||||||||
\(376\) | −727.519 | −0.0997844 | ||||||||
\(377\) | 5612.33 | 0.766710 | ||||||||
\(378\) | −715.733 | −0.0973897 | ||||||||
\(379\) | 1543.57 | 0.209202 | 0.104601 | − | 0.994514i | \(-0.466643\pi\) | ||||
0.104601 | + | 0.994514i | \(0.466643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4529.92 | 0.609121 | ||||||||
\(382\) | −2270.93 | −0.304165 | ||||||||
\(383\) | 6564.36 | 0.875779 | 0.437889 | − | 0.899029i | \(-0.355726\pi\) | ||||
0.437889 | + | 0.899029i | \(0.355726\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | −12453.2 | −1.64850 | ||||||||
\(386\) | 2182.15 | 0.287742 | ||||||||
\(387\) | −3295.51 | −0.432869 | ||||||||
\(388\) | 1661.57 | 0.217406 | ||||||||
\(389\) | −3498.27 | −0.455962 | −0.227981 | − | 0.973666i | \(-0.573212\pi\) | ||||
−0.227981 | + | 0.973666i | \(0.573212\pi\) | |||||||
\(390\) | 5860.73 | 0.760948 | ||||||||
\(391\) | 352.803 | 0.0456318 | ||||||||
\(392\) | −1338.59 | −0.172471 | ||||||||
\(393\) | 1112.83 | 0.142837 | ||||||||
\(394\) | 8276.16 | 1.05824 | ||||||||
\(395\) | 4538.16 | 0.578075 | ||||||||
\(396\) | −2372.90 | −0.301118 | ||||||||
\(397\) | 8610.60 | 1.08855 | 0.544274 | − | 0.838908i | \(-0.316805\pi\) | ||||
0.544274 | + | 0.838908i | \(0.316805\pi\) | |||||||
\(398\) | −5468.47 | −0.688717 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1250.97 | 0.156371 | ||||||||
\(401\) | 1765.74 | 0.219893 | 0.109946 | − | 0.993938i | \(-0.464932\pi\) | ||||
0.109946 | + | 0.993938i | \(0.464932\pi\) | |||||||
\(402\) | 959.173 | 0.119003 | ||||||||
\(403\) | 16938.9 | 2.09376 | ||||||||
\(404\) | 1349.36 | 0.166172 | ||||||||
\(405\) | 1154.60 | 0.141660 | ||||||||
\(406\) | −2171.08 | −0.265391 | ||||||||
\(407\) | −27754.0 | −3.38013 | ||||||||
\(408\) | −2392.66 | −0.290329 | ||||||||
\(409\) | 13395.7 | 1.61950 | 0.809751 | − | 0.586774i | \(-0.199602\pi\) | ||||
0.809751 | + | 0.586774i | \(0.199602\pi\) | |||||||
\(410\) | −9842.85 | −1.18562 | ||||||||
\(411\) | 5071.12 | 0.608613 | ||||||||
\(412\) | −5868.19 | −0.701711 | ||||||||
\(413\) | 2416.11 | 0.287867 | ||||||||
\(414\) | 63.6995 | 0.00756198 | ||||||||
\(415\) | 9752.22 | 1.15354 | ||||||||
\(416\) | −2192.83 | −0.258443 | ||||||||
\(417\) | 8134.57 | 0.955279 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9117.71 | 1.06308 | 0.531539 | − | 0.847034i | \(-0.321614\pi\) | ||||
0.531539 | + | 0.847034i | \(0.321614\pi\) | |||||||
\(420\) | −2267.17 | −0.263397 | ||||||||
\(421\) | 8204.45 | 0.949788 | 0.474894 | − | 0.880043i | \(-0.342486\pi\) | ||||
0.474894 | + | 0.880043i | \(0.342486\pi\) | |||||||
\(422\) | 6116.01 | 0.705504 | ||||||||
\(423\) | −818.459 | −0.0940776 | ||||||||
\(424\) | −5507.93 | −0.630870 | ||||||||
\(425\) | 7794.61 | 0.889634 | ||||||||
\(426\) | 4751.30 | 0.540379 | ||||||||
\(427\) | −6.85738 | −0.000777171 0 | ||||||||
\(428\) | 1528.05 | 0.172573 | ||||||||
\(429\) | −13550.4 | −1.52499 | ||||||||
\(430\) | −10439.0 | −1.17072 | ||||||||
\(431\) | −1271.34 | −0.142085 | −0.0710423 | − | 0.997473i | \(-0.522633\pi\) | ||||
−0.0710423 | + | 0.997473i | \(0.522633\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −3967.59 | −0.440347 | −0.220173 | − | 0.975461i | \(-0.570662\pi\) | ||||
−0.220173 | + | 0.975461i | \(0.570662\pi\) | |||||||
\(434\) | −6552.66 | −0.724741 | ||||||||
\(435\) | 3502.32 | 0.386031 | ||||||||
\(436\) | −531.430 | −0.0583736 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −1932.78 | −0.210848 | ||||||||
\(439\) | 209.038 | 0.0227263 | 0.0113632 | − | 0.999935i | \(-0.496383\pi\) | ||||
0.0113632 | + | 0.999935i | \(0.496383\pi\) | |||||||
\(440\) | −7516.45 | −0.814393 | ||||||||
\(441\) | −1505.91 | −0.162608 | ||||||||
\(442\) | −13663.2 | −1.47035 | ||||||||
\(443\) | 5734.04 | 0.614972 | 0.307486 | − | 0.951553i | \(-0.400512\pi\) | ||||
0.307486 | + | 0.951553i | \(0.400512\pi\) | |||||||
\(444\) | −5052.78 | −0.540077 | ||||||||
\(445\) | 10268.9 | 1.09391 | ||||||||
\(446\) | 3236.53 | 0.343619 | ||||||||
\(447\) | −7796.70 | −0.824992 | ||||||||
\(448\) | 848.276 | 0.0894582 | ||||||||
\(449\) | 9741.13 | 1.02386 | 0.511929 | − | 0.859028i | \(-0.328931\pi\) | ||||
0.511929 | + | 0.859028i | \(0.328931\pi\) | |||||||
\(450\) | 1407.34 | 0.147428 | ||||||||
\(451\) | 22757.3 | 2.37605 | ||||||||
\(452\) | −4551.76 | −0.473665 | ||||||||
\(453\) | −1784.59 | −0.185093 | ||||||||
\(454\) | −12130.9 | −1.25403 | ||||||||
\(455\) | −12946.7 | −1.33395 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17233.8 | −1.76403 | −0.882016 | − | 0.471220i | \(-0.843814\pi\) | ||||
−0.882016 | + | 0.471220i | \(0.843814\pi\) | |||||||
\(458\) | −3832.73 | −0.391029 | ||||||||
\(459\) | −2691.74 | −0.273725 | ||||||||
\(460\) | 201.776 | 0.0204519 | ||||||||
\(461\) | 1665.23 | 0.168238 | 0.0841190 | − | 0.996456i | \(-0.473192\pi\) | ||||
0.0841190 | + | 0.996456i | \(0.473192\pi\) | |||||||
\(462\) | 5241.85 | 0.527864 | ||||||||
\(463\) | −10694.0 | −1.07342 | −0.536710 | − | 0.843767i | \(-0.680333\pi\) | ||||
−0.536710 | + | 0.843767i | \(0.680333\pi\) | |||||||
\(464\) | −1310.41 | −0.131109 | ||||||||
\(465\) | 10570.6 | 1.05419 | ||||||||
\(466\) | −8017.08 | −0.796961 | ||||||||
\(467\) | 13212.7 | 1.30923 | 0.654614 | − | 0.755963i | \(-0.272831\pi\) | ||||
0.654614 | + | 0.755963i | \(0.272831\pi\) | |||||||
\(468\) | −2466.93 | −0.243662 | ||||||||
\(469\) | −2118.86 | −0.208614 | ||||||||
\(470\) | −2592.57 | −0.254439 | ||||||||
\(471\) | 174.765 | 0.0170971 | ||||||||
\(472\) | 1458.31 | 0.142212 | ||||||||
\(473\) | 24135.5 | 2.34620 | ||||||||
\(474\) | −1910.22 | −0.185105 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5285.50 | 0.508951 | ||||||||
\(477\) | −6196.42 | −0.594790 | ||||||||
\(478\) | 1060.58 | 0.101485 | ||||||||
\(479\) | 5409.53 | 0.516008 | 0.258004 | − | 0.966144i | \(-0.416935\pi\) | ||||
0.258004 | + | 0.966144i | \(0.416935\pi\) | |||||||
\(480\) | −1368.41 | −0.130123 | ||||||||
\(481\) | −28853.8 | −2.73518 | ||||||||
\(482\) | 2542.45 | 0.240260 | ||||||||
\(483\) | −140.716 | −0.0132563 | ||||||||
\(484\) | 12054.5 | 1.13209 | ||||||||
\(485\) | 5921.13 | 0.554360 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 14297.0 | 1.33031 | 0.665154 | − | 0.746706i | \(-0.268366\pi\) | ||||
0.665154 | + | 0.746706i | \(0.268366\pi\) | |||||||
\(488\) | −4.13896 | −0.000383938 0 | ||||||||
\(489\) | −3457.60 | −0.319751 | ||||||||
\(490\) | −4770.15 | −0.439783 | ||||||||
\(491\) | 2802.42 | 0.257580 | 0.128790 | − | 0.991672i | \(-0.458891\pi\) | ||||
0.128790 | + | 0.991672i | \(0.458891\pi\) | |||||||
\(492\) | 4143.10 | 0.379645 | ||||||||
\(493\) | −8165.02 | −0.745911 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8456.01 | −0.767817 | ||||||||
\(496\) | −3955.03 | −0.358037 | ||||||||
\(497\) | −10495.9 | −0.947293 | ||||||||
\(498\) | −4104.96 | −0.369373 | ||||||||
\(499\) | 14178.3 | 1.27196 | 0.635978 | − | 0.771708i | \(-0.280597\pi\) | ||||
0.635978 | + | 0.771708i | \(0.280597\pi\) | |||||||
\(500\) | −2669.24 | −0.238744 | ||||||||
\(501\) | −3777.33 | −0.336843 | ||||||||
\(502\) | 1103.98 | 0.0981533 | ||||||||
\(503\) | −5537.85 | −0.490896 | −0.245448 | − | 0.969410i | \(-0.578935\pi\) | ||||
−0.245448 | + | 0.969410i | \(0.578935\pi\) | |||||||
\(504\) | 954.310 | 0.0843420 | ||||||||
\(505\) | 4808.56 | 0.423719 | ||||||||
\(506\) | −466.520 | −0.0409869 | ||||||||
\(507\) | −7496.38 | −0.656659 | ||||||||
\(508\) | −6039.90 | −0.527514 | ||||||||
\(509\) | 9115.09 | 0.793751 | 0.396876 | − | 0.917872i | \(-0.370094\pi\) | ||||
0.396876 | + | 0.917872i | \(0.370094\pi\) | |||||||
\(510\) | −8526.42 | −0.740306 | ||||||||
\(511\) | 4269.60 | 0.369620 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10471.7 | −0.898610 | ||||||||
\(515\) | −20911.8 | −1.78929 | ||||||||
\(516\) | 4394.02 | 0.374876 | ||||||||
\(517\) | 5994.20 | 0.509912 | ||||||||
\(518\) | 11161.8 | 0.946763 | ||||||||
\(519\) | 3822.30 | 0.323276 | ||||||||
\(520\) | −7814.31 | −0.659001 | ||||||||
\(521\) | −2705.46 | −0.227502 | −0.113751 | − | 0.993509i | \(-0.536287\pi\) | ||||
−0.113751 | + | 0.993509i | \(0.536287\pi\) | |||||||
\(522\) | −1474.22 | −0.123610 | ||||||||
\(523\) | −23128.3 | −1.93371 | −0.966856 | − | 0.255323i | \(-0.917818\pi\) | ||||
−0.966856 | + | 0.255323i | \(0.917818\pi\) | |||||||
\(524\) | −1483.78 | −0.123701 | ||||||||
\(525\) | −3108.88 | −0.258443 | ||||||||
\(526\) | −3628.52 | −0.300781 | ||||||||
\(527\) | −24643.3 | −2.03696 | ||||||||
\(528\) | 3163.86 | 0.260776 | ||||||||
\(529\) | −12154.5 | −0.998971 | ||||||||
\(530\) | −19627.9 | −1.60865 | ||||||||
\(531\) | 1640.60 | 0.134079 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23659.1 | 1.92269 | ||||||||
\(534\) | −4322.43 | −0.350281 | ||||||||
\(535\) | 5445.34 | 0.440042 | ||||||||
\(536\) | −1278.90 | −0.103060 | ||||||||
\(537\) | −6103.49 | −0.490475 | ||||||||
\(538\) | 2026.80 | 0.162419 | ||||||||
\(539\) | 11028.9 | 0.881353 | ||||||||
\(540\) | −1539.47 | −0.122682 | ||||||||
\(541\) | −9641.17 | −0.766185 | −0.383093 | − | 0.923710i | \(-0.625141\pi\) | ||||
−0.383093 | + | 0.923710i | \(0.625141\pi\) | |||||||
\(542\) | −3837.03 | −0.304086 | ||||||||
\(543\) | −3099.94 | −0.244993 | ||||||||
\(544\) | 3190.21 | 0.251432 | ||||||||
\(545\) | −1893.79 | −0.148846 | ||||||||
\(546\) | 5449.58 | 0.427144 | ||||||||
\(547\) | −17377.0 | −1.35829 | −0.679147 | − | 0.734002i | \(-0.737650\pi\) | ||||
−0.679147 | + | 0.734002i | \(0.737650\pi\) | |||||||
\(548\) | −6761.50 | −0.527075 | ||||||||
\(549\) | −4.65633 | −0.000361980 0 | ||||||||
\(550\) | −10307.0 | −0.799076 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −84.9327 | −0.00654887 | ||||||||
\(553\) | 4219.79 | 0.324491 | ||||||||
\(554\) | 12566.9 | 0.963748 | ||||||||
\(555\) | −18006.0 | −1.37714 | ||||||||
\(556\) | −10846.1 | −0.827296 | ||||||||
\(557\) | 18744.3 | 1.42589 | 0.712945 | − | 0.701220i | \(-0.247361\pi\) | ||||
0.712945 | + | 0.701220i | \(0.247361\pi\) | |||||||
\(558\) | −4449.41 | −0.337560 | ||||||||
\(559\) | 25092.0 | 1.89853 | ||||||||
\(560\) | 3022.90 | 0.228108 | ||||||||
\(561\) | 19713.6 | 1.48362 | ||||||||
\(562\) | −16114.7 | −1.20953 | ||||||||
\(563\) | −7618.70 | −0.570320 | −0.285160 | − | 0.958480i | \(-0.592047\pi\) | ||||
−0.285160 | + | 0.958480i | \(0.592047\pi\) | |||||||
\(564\) | 1091.28 | 0.0814736 | ||||||||
\(565\) | −16220.6 | −1.20779 | ||||||||
\(566\) | −386.833 | −0.0287276 | ||||||||
\(567\) | 1073.60 | 0.0795184 | ||||||||
\(568\) | −6335.07 | −0.467982 | ||||||||
\(569\) | −13081.6 | −0.963816 | −0.481908 | − | 0.876222i | \(-0.660056\pi\) | ||||
−0.481908 | + | 0.876222i | \(0.660056\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8643.49 | 0.633483 | 0.316741 | − | 0.948512i | \(-0.397411\pi\) | ||||
0.316741 | + | 0.948512i | \(0.397411\pi\) | |||||||
\(572\) | 18067.2 | 1.32068 | ||||||||
\(573\) | 3406.39 | 0.248349 | ||||||||
\(574\) | −9152.33 | −0.665524 | ||||||||
\(575\) | 276.687 | 0.0200672 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 9841.26 | 0.710047 | 0.355024 | − | 0.934857i | \(-0.384473\pi\) | ||||
0.355024 | + | 0.934857i | \(0.384473\pi\) | |||||||
\(578\) | 10051.8 | 0.723355 | ||||||||
\(579\) | −3273.22 | −0.234940 | ||||||||
\(580\) | −4669.76 | −0.334312 | ||||||||
\(581\) | 9068.06 | 0.647516 | ||||||||
\(582\) | −2492.35 | −0.177511 | ||||||||
\(583\) | 45381.1 | 3.22383 | ||||||||
\(584\) | 2577.03 | 0.182600 | ||||||||
\(585\) | −8791.10 | −0.621312 | ||||||||
\(586\) | −9470.93 | −0.667646 | ||||||||
\(587\) | 19898.5 | 1.39915 | 0.699573 | − | 0.714562i | \(-0.253374\pi\) | ||||
0.699573 | + | 0.714562i | \(0.253374\pi\) | |||||||
\(588\) | 2007.88 | 0.140822 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 5196.80 | 0.362625 | ||||||||
\(591\) | −12414.2 | −0.864050 | ||||||||
\(592\) | 6737.04 | 0.467720 | ||||||||
\(593\) | 22195.0 | 1.53699 | 0.768497 | − | 0.639853i | \(-0.221005\pi\) | ||||
0.768497 | + | 0.639853i | \(0.221005\pi\) | |||||||
\(594\) | 3559.35 | 0.245862 | ||||||||
\(595\) | 18835.3 | 1.29777 | ||||||||
\(596\) | 10395.6 | 0.714464 | ||||||||
\(597\) | 8202.70 | 0.562335 | ||||||||
\(598\) | −485.007 | −0.0331663 | ||||||||
\(599\) | 19696.2 | 1.34352 | 0.671758 | − | 0.740771i | \(-0.265540\pi\) | ||||
0.671758 | + | 0.740771i | \(0.265540\pi\) | |||||||
\(600\) | −1876.45 | −0.127676 | ||||||||
\(601\) | −14626.5 | −0.992724 | −0.496362 | − | 0.868116i | \(-0.665331\pi\) | ||||
−0.496362 | + | 0.868116i | \(0.665331\pi\) | |||||||
\(602\) | −9706.61 | −0.657163 | ||||||||
\(603\) | −1438.76 | −0.0971655 | ||||||||
\(604\) | 2379.45 | 0.160296 | ||||||||
\(605\) | 42957.3 | 2.88671 | ||||||||
\(606\) | −2024.05 | −0.135679 | ||||||||
\(607\) | −16312.0 | −1.09075 | −0.545375 | − | 0.838192i | \(-0.683613\pi\) | ||||
−0.545375 | + | 0.838192i | \(0.683613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3256.62 | 0.216691 | ||||||||
\(610\) | −14.7495 | −0.000979000 0 | ||||||||
\(611\) | 6231.73 | 0.412617 | ||||||||
\(612\) | 3588.98 | 0.237052 | ||||||||
\(613\) | 17748.7 | 1.16944 | 0.584718 | − | 0.811237i | \(-0.301205\pi\) | ||||
0.584718 | + | 0.811237i | \(0.301205\pi\) | |||||||
\(614\) | −57.4243 | −0.00377436 | ||||||||
\(615\) | 14764.3 | 0.968053 | ||||||||
\(616\) | −6989.14 | −0.457144 | ||||||||
\(617\) | 3729.80 | 0.243365 | 0.121682 | − | 0.992569i | \(-0.461171\pi\) | ||||
0.121682 | + | 0.992569i | \(0.461171\pi\) | |||||||
\(618\) | 8802.29 | 0.572945 | ||||||||
\(619\) | −1003.67 | −0.0651714 | −0.0325857 | − | 0.999469i | \(-0.510374\pi\) | ||||
−0.0325857 | + | 0.999469i | \(0.510374\pi\) | |||||||
\(620\) | −14094.1 | −0.912954 | ||||||||
\(621\) | −95.5493 | −0.00617433 | ||||||||
\(622\) | −2331.37 | −0.150289 | ||||||||
\(623\) | 9548.48 | 0.614048 | ||||||||
\(624\) | 3289.24 | 0.211018 | ||||||||
\(625\) | −19285.2 | −1.23425 | ||||||||
\(626\) | 5025.51 | 0.320862 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −233.019 | −0.0148065 | ||||||||
\(629\) | 41977.6 | 2.66098 | ||||||||
\(630\) | 3400.76 | 0.215063 | ||||||||
\(631\) | 16846.8 | 1.06285 | 0.531426 | − | 0.847105i | \(-0.321656\pi\) | ||||
0.531426 | + | 0.847105i | \(0.321656\pi\) | |||||||
\(632\) | 2546.97 | 0.160305 | ||||||||
\(633\) | −9174.02 | −0.576042 | ||||||||
\(634\) | −3455.13 | −0.216437 | ||||||||
\(635\) | −21523.7 | −1.34510 | ||||||||
\(636\) | 8261.90 | 0.515103 | ||||||||
\(637\) | 11466.0 | 0.713184 | ||||||||
\(638\) | 10796.8 | 0.669983 | ||||||||
\(639\) | −7126.96 | −0.441218 | ||||||||
\(640\) | 1824.55 | 0.112690 | ||||||||
\(641\) | −161.995 | −0.00998196 | −0.00499098 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499098 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(642\) | −2292.08 | −0.140905 | ||||||||
\(643\) | 6290.91 | 0.385831 | 0.192915 | − | 0.981215i | \(-0.438206\pi\) | ||||
0.192915 | + | 0.981215i | \(0.438206\pi\) | |||||||
\(644\) | 187.621 | 0.0114803 | ||||||||
\(645\) | 15658.4 | 0.955891 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28249.8 | 1.71656 | 0.858280 | − | 0.513181i | \(-0.171533\pi\) | ||||
0.858280 | + | 0.513181i | \(0.171533\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −12015.4 | −0.726724 | ||||||||
\(650\) | −10715.4 | −0.646607 | ||||||||
\(651\) | 9828.99 | 0.591749 | ||||||||
\(652\) | 4610.14 | 0.276912 | ||||||||
\(653\) | 11423.5 | 0.684587 | 0.342293 | − | 0.939593i | \(-0.388796\pi\) | ||||
0.342293 | + | 0.939593i | \(0.388796\pi\) | |||||||
\(654\) | 797.145 | 0.0476618 | ||||||||
\(655\) | −5287.55 | −0.315423 | ||||||||
\(656\) | −5524.14 | −0.328782 | ||||||||
\(657\) | 2899.16 | 0.172157 | ||||||||
\(658\) | −2410.69 | −0.142824 | ||||||||
\(659\) | 200.138 | 0.0118304 | 0.00591522 | − | 0.999983i | \(-0.498117\pi\) | ||||
0.00591522 | + | 0.999983i | \(0.498117\pi\) | |||||||
\(660\) | 11274.7 | 0.664949 | ||||||||
\(661\) | −2607.01 | −0.153405 | −0.0767026 | − | 0.997054i | \(-0.524439\pi\) | ||||
−0.0767026 | + | 0.997054i | \(0.524439\pi\) | |||||||
\(662\) | −13632.3 | −0.800352 | ||||||||
\(663\) | 20494.9 | 1.20053 | ||||||||
\(664\) | 5473.28 | 0.319886 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7579.17 | 0.440971 | ||||||||
\(667\) | −289.836 | −0.0168253 | ||||||||
\(668\) | 5036.44 | 0.291715 | ||||||||
\(669\) | −4854.80 | −0.280564 | ||||||||
\(670\) | −4557.45 | −0.262790 | ||||||||
\(671\) | 34.1018 | 0.00196198 | ||||||||
\(672\) | −1272.41 | −0.0730423 | ||||||||
\(673\) | 14561.2 | 0.834015 | 0.417007 | − | 0.908903i | \(-0.363079\pi\) | ||||
0.417007 | + | 0.908903i | \(0.363079\pi\) | |||||||
\(674\) | −20816.8 | −1.18966 | ||||||||
\(675\) | −2111.01 | −0.120374 | ||||||||
\(676\) | 9995.18 | 0.568683 | ||||||||
\(677\) | 12684.6 | 0.720100 | 0.360050 | − | 0.932933i | \(-0.382760\pi\) | ||||
0.360050 | + | 0.932933i | \(0.382760\pi\) | |||||||
\(678\) | 6827.64 | 0.386746 | ||||||||
\(679\) | 5505.74 | 0.311179 | ||||||||
\(680\) | 11368.6 | 0.641124 | ||||||||
\(681\) | 18196.3 | 1.02391 | ||||||||
\(682\) | 32586.4 | 1.82962 | ||||||||
\(683\) | 12054.5 | 0.675332 | 0.337666 | − | 0.941266i | \(-0.390363\pi\) | ||||
0.337666 | + | 0.941266i | \(0.390363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −24095.1 | −1.34398 | ||||||||
\(686\) | −13528.0 | −0.752916 | ||||||||
\(687\) | 5749.09 | 0.319274 | ||||||||
\(688\) | −5858.69 | −0.324652 | ||||||||
\(689\) | 47179.5 | 2.60870 | ||||||||
\(690\) | −302.664 | −0.0166989 | ||||||||
\(691\) | 3338.42 | 0.183791 | 0.0918953 | − | 0.995769i | \(-0.470707\pi\) | ||||
0.0918953 | + | 0.995769i | \(0.470707\pi\) | |||||||
\(692\) | −5096.40 | −0.279965 | ||||||||
\(693\) | −7862.78 | −0.430999 | ||||||||
\(694\) | −11168.1 | −0.610856 | ||||||||
\(695\) | −38650.9 | −2.10951 | ||||||||
\(696\) | 1965.62 | 0.107050 | ||||||||
\(697\) | −34420.2 | −1.87053 | ||||||||
\(698\) | 11011.6 | 0.597130 | ||||||||
\(699\) | 12025.6 | 0.650716 | ||||||||
\(700\) | 4145.17 | 0.223818 | ||||||||
\(701\) | −23782.8 | −1.28140 | −0.640702 | − | 0.767790i | \(-0.721356\pi\) | ||||
−0.640702 | + | 0.767790i | \(0.721356\pi\) | |||||||
\(702\) | 3700.40 | 0.198949 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −4218.49 | −0.225838 | ||||||||
\(705\) | 3888.86 | 0.207749 | ||||||||
\(706\) | −11564.9 | −0.616504 | ||||||||
\(707\) | 4471.22 | 0.237847 | ||||||||
\(708\) | −2187.47 | −0.116116 | ||||||||
\(709\) | 32185.1 | 1.70485 | 0.852424 | − | 0.522851i | \(-0.175132\pi\) | ||||
0.852424 | + | 0.522851i | \(0.175132\pi\) | |||||||
\(710\) | −22575.5 | −1.19330 | ||||||||
\(711\) | 2865.34 | 0.151137 | ||||||||
\(712\) | 5763.24 | 0.303352 | ||||||||
\(713\) | −874.770 | −0.0459473 | ||||||||
\(714\) | −7928.25 | −0.415557 | ||||||||
\(715\) | 64383.9 | 3.36758 | ||||||||
\(716\) | 8137.99 | 0.424764 | ||||||||
\(717\) | −1590.88 | −0.0828624 | ||||||||
\(718\) | −3807.28 | −0.197892 | ||||||||
\(719\) | −38319.4 | −1.98758 | −0.993791 | − | 0.111266i | \(-0.964509\pi\) | ||||
−0.993791 | + | 0.111266i | \(0.964509\pi\) | |||||||
\(720\) | 2052.62 | 0.106245 | ||||||||
\(721\) | −19444.7 | −1.00438 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3813.68 | −0.196172 | ||||||||
\(724\) | 4133.26 | 0.212170 | ||||||||
\(725\) | −6403.45 | −0.328025 | ||||||||
\(726\) | −18081.8 | −0.924351 | ||||||||
\(727\) | −36543.1 | −1.86425 | −0.932125 | − | 0.362138i | \(-0.882047\pi\) | ||||
−0.932125 | + | 0.362138i | \(0.882047\pi\) | |||||||
\(728\) | −7266.11 | −0.369917 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 9183.46 | 0.465610 | ||||||||
\(731\) | −36504.8 | −1.84703 | ||||||||
\(732\) | 6.20844 | 0.000313484 0 | ||||||||
\(733\) | −15689.3 | −0.790584 | −0.395292 | − | 0.918555i | \(-0.629357\pi\) | ||||
−0.395292 | + | 0.918555i | \(0.629357\pi\) | |||||||
\(734\) | −25496.1 | −1.28212 | ||||||||
\(735\) | 7155.23 | 0.359081 | ||||||||
\(736\) | 113.244 | 0.00567149 | ||||||||
\(737\) | 10537.1 | 0.526648 | ||||||||
\(738\) | −6214.65 | −0.309979 | ||||||||
\(739\) | −36445.7 | −1.81418 | −0.907088 | − | 0.420940i | \(-0.861700\pi\) | ||||
−0.907088 | + | 0.420940i | \(0.861700\pi\) | |||||||
\(740\) | 24008.0 | 1.19264 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18251.0 | −0.902984 | ||||||||
\(743\) | 1678.29 | 0.0828673 | 0.0414337 | − | 0.999141i | \(-0.486807\pi\) | ||||
0.0414337 | + | 0.999141i | \(0.486807\pi\) | |||||||
\(744\) | 5932.55 | 0.292336 | ||||||||
\(745\) | 37045.6 | 1.82180 | ||||||||
\(746\) | −1473.32 | −0.0723084 | ||||||||
\(747\) | 6157.44 | 0.301591 | ||||||||
\(748\) | −26284.9 | −1.28485 | ||||||||
\(749\) | 5063.33 | 0.247009 | ||||||||
\(750\) | 4003.86 | 0.194934 | ||||||||
\(751\) | 8641.67 | 0.419892 | 0.209946 | − | 0.977713i | \(-0.432671\pi\) | ||||
0.209946 | + | 0.977713i | \(0.432671\pi\) | |||||||
\(752\) | −1455.04 | −0.0705582 | ||||||||
\(753\) | −1655.97 | −0.0801418 | ||||||||
\(754\) | 11224.7 | 0.542145 | ||||||||
\(755\) | 8479.36 | 0.408736 | ||||||||
\(756\) | −1431.47 | −0.0688649 | ||||||||
\(757\) | 3586.79 | 0.172212 | 0.0861058 | − | 0.996286i | \(-0.472558\pi\) | ||||
0.0861058 | + | 0.996286i | \(0.472558\pi\) | |||||||
\(758\) | 3087.13 | 0.147928 | ||||||||
\(759\) | 699.780 | 0.0334656 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11615.4 | −0.553297 | −0.276649 | − | 0.960971i | \(-0.589224\pi\) | ||||
−0.276649 | + | 0.960971i | \(0.589224\pi\) | |||||||
\(762\) | 9059.85 | 0.430714 | ||||||||
\(763\) | −1760.93 | −0.0835519 | ||||||||
\(764\) | −4541.86 | −0.215077 | ||||||||
\(765\) | 12789.6 | 0.604457 | ||||||||
\(766\) | 13128.7 | 0.619269 | ||||||||
\(767\) | −12491.5 | −0.588060 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 6021.83 | 0.282383 | 0.141192 | − | 0.989982i | \(-0.454907\pi\) | ||||
0.141192 | + | 0.989982i | \(0.454907\pi\) | |||||||
\(770\) | −24906.3 | −1.16567 | ||||||||
\(771\) | 15707.5 | 0.733712 | ||||||||
\(772\) | 4364.29 | 0.203464 | ||||||||
\(773\) | −1508.99 | −0.0702128 | −0.0351064 | − | 0.999384i | \(-0.511177\pi\) | ||||
−0.0351064 | + | 0.999384i | \(0.511177\pi\) | |||||||
\(774\) | −6591.03 | −0.306085 | ||||||||
\(775\) | −19326.6 | −0.895784 | ||||||||
\(776\) | 3323.14 | 0.153729 | ||||||||
\(777\) | −16742.8 | −0.773029 | ||||||||
\(778\) | −6996.54 | −0.322414 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 11721.5 | 0.538072 | ||||||||
\(781\) | 52196.1 | 2.39145 | ||||||||
\(782\) | 705.607 | 0.0322666 | ||||||||
\(783\) | 2211.32 | 0.100927 | ||||||||
\(784\) | −2677.17 | −0.121956 | ||||||||
\(785\) | −830.383 | −0.0377550 | ||||||||
\(786\) | 2225.67 | 0.101001 | ||||||||
\(787\) | 3255.84 | 0.147469 | 0.0737346 | − | 0.997278i | \(-0.476508\pi\) | ||||
0.0737346 | + | 0.997278i | \(0.476508\pi\) | |||||||
\(788\) | 16552.3 | 0.748289 | ||||||||
\(789\) | 5442.77 | 0.245587 | ||||||||
\(790\) | 9076.31 | 0.408760 | ||||||||
\(791\) | −15082.6 | −0.677972 | ||||||||
\(792\) | −4745.80 | −0.212922 | ||||||||
\(793\) | 35.4532 | 0.00158762 | ||||||||
\(794\) | 17221.2 | 0.769720 | ||||||||
\(795\) | 29441.9 | 1.31346 | ||||||||
\(796\) | −10936.9 | −0.486997 | ||||||||
\(797\) | 31732.8 | 1.41033 | 0.705164 | − | 0.709044i | \(-0.250873\pi\) | ||||
0.705164 | + | 0.709044i | \(0.250873\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9066.16 | −0.401424 | ||||||||
\(800\) | 2501.93 | 0.110571 | ||||||||
\(801\) | 6483.65 | 0.286003 | ||||||||
\(802\) | 3531.49 | 0.155488 | ||||||||
\(803\) | −21232.8 | −0.933111 | ||||||||
\(804\) | 1918.35 | 0.0841478 | ||||||||
\(805\) | 668.601 | 0.0292734 | ||||||||
\(806\) | 33877.8 | 1.48051 | ||||||||
\(807\) | −3040.20 | −0.132615 | ||||||||
\(808\) | 2698.73 | 0.117501 | ||||||||
\(809\) | 3853.96 | 0.167488 | 0.0837441 | − | 0.996487i | \(-0.473312\pi\) | ||||
0.0837441 | + | 0.996487i | \(0.473312\pi\) | |||||||
\(810\) | 2309.20 | 0.100169 | ||||||||
\(811\) | 31871.8 | 1.37999 | 0.689995 | − | 0.723814i | \(-0.257613\pi\) | ||||
0.689995 | + | 0.723814i | \(0.257613\pi\) | |||||||
\(812\) | −4342.16 | −0.187660 | ||||||||
\(813\) | 5755.55 | 0.248285 | ||||||||
\(814\) | −55508.0 | −2.39012 | ||||||||
\(815\) | 16428.6 | 0.706096 | ||||||||
\(816\) | −4785.31 | −0.205293 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 26791.4 | 1.14516 | ||||||||
\(819\) | −8174.37 | −0.348761 | ||||||||
\(820\) | −19685.7 | −0.838359 | ||||||||
\(821\) | −39170.0 | −1.66509 | −0.832547 | − | 0.553954i | \(-0.813118\pi\) | ||||
−0.832547 | + | 0.553954i | \(0.813118\pi\) | |||||||
\(822\) | 10142.2 | 0.430355 | ||||||||
\(823\) | −18838.8 | −0.797910 | −0.398955 | − | 0.916971i | \(-0.630627\pi\) | ||||
−0.398955 | + | 0.916971i | \(0.630627\pi\) | |||||||
\(824\) | −11736.4 | −0.496185 | ||||||||
\(825\) | 15460.5 | 0.652443 | ||||||||
\(826\) | 4832.22 | 0.203553 | ||||||||
\(827\) | 887.307 | 0.0373092 | 0.0186546 | − | 0.999826i | \(-0.494062\pi\) | ||||
0.0186546 | + | 0.999826i | \(0.494062\pi\) | |||||||
\(828\) | 127.399 | 0.00534713 | ||||||||
\(829\) | 32877.0 | 1.37740 | 0.688700 | − | 0.725046i | \(-0.258182\pi\) | ||||
0.688700 | + | 0.725046i | \(0.258182\pi\) | |||||||
\(830\) | 19504.4 | 0.815674 | ||||||||
\(831\) | −18850.3 | −0.786897 | ||||||||
\(832\) | −4385.66 | −0.182747 | ||||||||
\(833\) | −16681.1 | −0.693838 | ||||||||
\(834\) | 16269.1 | 0.675484 | ||||||||
\(835\) | 17947.7 | 0.743840 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6674.12 | 0.275617 | ||||||||
\(838\) | 18235.4 | 0.751709 | ||||||||
\(839\) | −41512.7 | −1.70820 | −0.854099 | − | 0.520110i | \(-0.825891\pi\) | ||||
−0.854099 | + | 0.520110i | \(0.825891\pi\) | |||||||
\(840\) | −4534.35 | −0.186250 | ||||||||
\(841\) | −17681.3 | −0.724968 | ||||||||
\(842\) | 16408.9 | 0.671601 | ||||||||
\(843\) | 24172.1 | 0.987581 | ||||||||
\(844\) | 12232.0 | 0.498867 | ||||||||
\(845\) | 35618.6 | 1.45008 | ||||||||
\(846\) | −1636.92 | −0.0665229 | ||||||||
\(847\) | 39943.6 | 1.62040 | ||||||||
\(848\) | −11015.9 | −0.446092 | ||||||||
\(849\) | 580.250 | 0.0234560 | ||||||||
\(850\) | 15589.2 | 0.629066 | ||||||||
\(851\) | 1490.09 | 0.0600231 | ||||||||
\(852\) | 9502.61 | 0.382106 | ||||||||
\(853\) | 1487.75 | 0.0597182 | 0.0298591 | − | 0.999554i | \(-0.490494\pi\) | ||||
0.0298591 | + | 0.999554i | \(0.490494\pi\) | |||||||
\(854\) | −13.7148 | −0.000549543 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3056.11 | 0.122028 | ||||||||
\(857\) | 20276.1 | 0.808188 | 0.404094 | − | 0.914718i | \(-0.367587\pi\) | ||||
0.404094 | + | 0.914718i | \(0.367587\pi\) | |||||||
\(858\) | −27100.8 | −1.07833 | ||||||||
\(859\) | 7436.86 | 0.295393 | 0.147696 | − | 0.989033i | \(-0.452814\pi\) | ||||
0.147696 | + | 0.989033i | \(0.452814\pi\) | |||||||
\(860\) | −20877.9 | −0.827826 | ||||||||
\(861\) | 13728.5 | 0.543398 | ||||||||
\(862\) | −2542.69 | −0.100469 | ||||||||
\(863\) | 35570.4 | 1.40305 | 0.701524 | − | 0.712646i | \(-0.252503\pi\) | ||||
0.701524 | + | 0.712646i | \(0.252503\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −18161.4 | −0.713880 | ||||||||
\(866\) | −7935.18 | −0.311372 | ||||||||
\(867\) | −15077.7 | −0.590617 | ||||||||
\(868\) | −13105.3 | −0.512469 | ||||||||
\(869\) | −20985.0 | −0.819182 | ||||||||
\(870\) | 7004.64 | 0.272965 | ||||||||
\(871\) | 10954.7 | 0.426160 | ||||||||
\(872\) | −1062.86 | −0.0412764 | ||||||||
\(873\) | 3738.53 | 0.144937 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8844.74 | −0.341722 | ||||||||
\(876\) | −3865.55 | −0.149092 | ||||||||
\(877\) | 3868.42 | 0.148948 | 0.0744740 | − | 0.997223i | \(-0.476272\pi\) | ||||
0.0744740 | + | 0.997223i | \(0.476272\pi\) | |||||||
\(878\) | 418.076 | 0.0160699 | ||||||||
\(879\) | 14206.4 | 0.545131 | ||||||||
\(880\) | −15032.9 | −0.575862 | ||||||||
\(881\) | −20877.4 | −0.798384 | −0.399192 | − | 0.916867i | \(-0.630709\pi\) | ||||
−0.399192 | + | 0.916867i | \(0.630709\pi\) | |||||||
\(882\) | −3011.82 | −0.114981 | ||||||||
\(883\) | −24206.8 | −0.922565 | −0.461283 | − | 0.887253i | \(-0.652611\pi\) | ||||
−0.461283 | + | 0.887253i | \(0.652611\pi\) | |||||||
\(884\) | −27326.5 | −1.03969 | ||||||||
\(885\) | −7795.20 | −0.296082 | ||||||||
\(886\) | 11468.1 | 0.434851 | ||||||||
\(887\) | −27117.5 | −1.02651 | −0.513256 | − | 0.858235i | \(-0.671561\pi\) | ||||
−0.513256 | + | 0.858235i | \(0.671561\pi\) | |||||||
\(888\) | −10105.6 | −0.381892 | ||||||||
\(889\) | −20013.7 | −0.755047 | ||||||||
\(890\) | 20537.8 | 0.773514 | ||||||||
\(891\) | −5339.02 | −0.200745 | ||||||||
\(892\) | 6473.07 | 0.242976 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −15593.4 | −0.583357 | ||||||||
\(895\) | 29000.4 | 1.08310 | ||||||||
\(896\) | 1696.55 | 0.0632565 | ||||||||
\(897\) | 727.511 | 0.0270801 | ||||||||
\(898\) | 19482.3 | 0.723977 | ||||||||
\(899\) | 20245.0 | 0.751068 | ||||||||
\(900\) | 2814.67 | 0.104247 | ||||||||
\(901\) | −68638.5 | −2.53793 | ||||||||
\(902\) | 45514.6 | 1.68012 | ||||||||
\(903\) | 14559.9 | 0.536571 | ||||||||
\(904\) | −9103.52 | −0.334932 | ||||||||
\(905\) | 14729.2 | 0.541010 | ||||||||
\(906\) | −3569.18 | −0.130881 | ||||||||
\(907\) | −35594.9 | −1.30310 | −0.651548 | − | 0.758608i | \(-0.725880\pi\) | ||||
−0.651548 | + | 0.758608i | \(0.725880\pi\) | |||||||
\(908\) | −24261.7 | −0.886733 | ||||||||
\(909\) | 3036.07 | 0.110781 | ||||||||
\(910\) | −25893.3 | −0.943248 | ||||||||
\(911\) | 27909.5 | 1.01502 | 0.507510 | − | 0.861646i | \(-0.330566\pi\) | ||||
0.507510 | + | 0.861646i | \(0.330566\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45095.6 | −1.63466 | ||||||||
\(914\) | −34467.6 | −1.24736 | ||||||||
\(915\) | 22.1243 | 0.000799350 0 | ||||||||
\(916\) | −7665.45 | −0.276500 | ||||||||
\(917\) | −4916.61 | −0.177056 | ||||||||
\(918\) | −5383.48 | −0.193553 | ||||||||
\(919\) | −48960.0 | −1.75739 | −0.878696 | − | 0.477383i | \(-0.841586\pi\) | ||||
−0.878696 | + | 0.477383i | \(0.841586\pi\) | |||||||
\(920\) | 403.552 | 0.0144617 | ||||||||
\(921\) | 86.1365 | 0.00308175 | ||||||||
\(922\) | 3330.47 | 0.118962 | ||||||||
\(923\) | 54264.5 | 1.93515 | ||||||||
\(924\) | 10483.7 | 0.373256 | ||||||||
\(925\) | 32921.1 | 1.17020 | ||||||||
\(926\) | −21388.1 | −0.759023 | ||||||||
\(927\) | −13203.4 | −0.467807 | ||||||||
\(928\) | −2620.83 | −0.0927078 | ||||||||
\(929\) | −11971.7 | −0.422799 | −0.211399 | − | 0.977400i | \(-0.567802\pi\) | ||||
−0.211399 | + | 0.977400i | \(0.567802\pi\) | |||||||
\(930\) | 21141.1 | 0.745424 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16034.2 | −0.563537 | ||||||||
\(933\) | 3497.06 | 0.122710 | ||||||||
\(934\) | 26425.4 | 0.925765 | ||||||||
\(935\) | −93668.1 | −3.27623 | ||||||||
\(936\) | −4933.86 | −0.172295 | ||||||||
\(937\) | −50434.2 | −1.75839 | −0.879197 | − | 0.476459i | \(-0.841920\pi\) | ||||
−0.879197 | + | 0.476459i | \(0.841920\pi\) | |||||||
\(938\) | −4237.72 | −0.147512 | ||||||||
\(939\) | −7538.26 | −0.261983 | ||||||||
\(940\) | −5185.14 | −0.179916 | ||||||||
\(941\) | 12594.3 | 0.436303 | 0.218151 | − | 0.975915i | \(-0.429997\pi\) | ||||
0.218151 | + | 0.975915i | \(0.429997\pi\) | |||||||
\(942\) | 349.529 | 0.0120895 | ||||||||
\(943\) | −1221.82 | −0.0421930 | ||||||||
\(944\) | 2916.62 | 0.100559 | ||||||||
\(945\) | −5101.14 | −0.175598 | ||||||||
\(946\) | 48271.1 | 1.65902 | ||||||||
\(947\) | 27632.6 | 0.948192 | 0.474096 | − | 0.880473i | \(-0.342775\pi\) | ||||
0.474096 | + | 0.880473i | \(0.342775\pi\) | |||||||
\(948\) | −3820.45 | −0.130889 | ||||||||
\(949\) | −22074.2 | −0.755067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5182.70 | 0.176720 | ||||||||
\(952\) | 10571.0 | 0.359883 | ||||||||
\(953\) | 32021.7 | 1.08844 | 0.544221 | − | 0.838942i | \(-0.316825\pi\) | ||||
0.544221 | + | 0.838942i | \(0.316825\pi\) | |||||||
\(954\) | −12392.8 | −0.420580 | ||||||||
\(955\) | −16185.3 | −0.548422 | ||||||||
\(956\) | 2121.17 | 0.0717610 | ||||||||
\(957\) | −16195.2 | −0.547039 | ||||||||
\(958\) | 10819.1 | 0.364873 | ||||||||
\(959\) | −22404.8 | −0.754418 | ||||||||
\(960\) | −2736.83 | −0.0920112 | ||||||||
\(961\) | 31311.7 | 1.05105 | ||||||||
\(962\) | −57707.7 | −1.93406 | ||||||||
\(963\) | 3438.12 | 0.115049 | ||||||||
\(964\) | 5084.90 | 0.169890 | ||||||||
\(965\) | 15552.5 | 0.518811 | ||||||||
\(966\) | −281.431 | −0.00937360 | ||||||||
\(967\) | −12876.4 | −0.428209 | −0.214104 | − | 0.976811i | \(-0.568683\pi\) | ||||
−0.214104 | + | 0.976811i | \(0.568683\pi\) | |||||||
\(968\) | 24109.1 | 0.800511 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11842.3 | 0.391992 | ||||||||
\(971\) | 2414.51 | 0.0797996 | 0.0398998 | − | 0.999204i | \(-0.487296\pi\) | ||||
0.0398998 | + | 0.999204i | \(0.487296\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | −35939.4 | −1.18413 | ||||||||
\(974\) | 28594.0 | 0.940670 | ||||||||
\(975\) | 16073.2 | 0.527952 | ||||||||
\(976\) | −8.27792 | −0.000271485 0 | ||||||||
\(977\) | −14131.4 | −0.462746 | −0.231373 | − | 0.972865i | \(-0.574322\pi\) | ||||
−0.231373 | + | 0.972865i | \(0.574322\pi\) | |||||||
\(978\) | −6915.21 | −0.226098 | ||||||||
\(979\) | −47484.7 | −1.55017 | ||||||||
\(980\) | −9540.31 | −0.310973 | ||||||||
\(981\) | −1195.72 | −0.0389157 | ||||||||
\(982\) | 5604.85 | 0.182136 | ||||||||
\(983\) | −20268.2 | −0.657634 | −0.328817 | − | 0.944394i | \(-0.606650\pi\) | ||||
−0.328817 | + | 0.944394i | \(0.606650\pi\) | |||||||
\(984\) | 8286.21 | 0.268450 | ||||||||
\(985\) | 58985.5 | 1.90805 | ||||||||
\(986\) | −16330.0 | −0.527439 | ||||||||
\(987\) | 3616.04 | 0.116616 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1295.82 | −0.0416629 | ||||||||
\(990\) | −16912.0 | −0.542928 | ||||||||
\(991\) | 15550.2 | 0.498453 | 0.249226 | − | 0.968445i | \(-0.419824\pi\) | ||||
0.249226 | + | 0.968445i | \(0.419824\pi\) | |||||||
\(992\) | −7910.07 | −0.253170 | ||||||||
\(993\) | 20448.4 | 0.653485 | ||||||||
\(994\) | −20991.8 | −0.669837 | ||||||||
\(995\) | −38974.6 | −1.24179 | ||||||||
\(996\) | −8209.92 | −0.261186 | ||||||||
\(997\) | 12715.8 | 0.403925 | 0.201962 | − | 0.979393i | \(-0.435268\pi\) | ||||
0.201962 | + | 0.979393i | \(0.435268\pi\) | |||||||
\(998\) | 28356.5 | 0.899408 | ||||||||
\(999\) | −11368.7 | −0.360051 |
(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 | 2166.4.a.u.1.3 | 3 | ||
19.7 | even | 3 | 114.4.e.d.49.1 | yes | 6 | ||
19.11 | even | 3 | 114.4.e.d.7.1 | ✓ | 6 | ||
19.18 | odd | 2 | 2166.4.a.t.1.3 | 3 | |||
57.11 | odd | 6 | 342.4.g.h.235.3 | 6 | |||
57.26 | odd | 6 | 342.4.g.h.163.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.4.e.d.7.1 | ✓ | 6 | 19.11 | even | 3 | ||
114.4.e.d.49.1 | yes | 6 | 19.7 | even | 3 | ||
342.4.g.h.163.3 | 6 | 57.26 | odd | 6 | |||
342.4.g.h.235.3 | 6 | 57.11 | odd | 6 | |||
2166.4.a.t.1.3 | 3 | 19.18 | odd | 2 | |||
2166.4.a.u.1.3 | 3 | 1.1 | even | 1 | trivial |