Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,4,Mod(1,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(110.628581261\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 1875.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.60577 | −1.62838 | −0.814192 | − | 0.580596i | \(-0.802820\pi\) | ||||
−0.814192 | + | 0.580596i | \(0.802820\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 13.2131 | 1.65163 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −13.8173 | −0.940148 | ||||||||
\(7\) | 33.5484 | 1.81144 | 0.905722 | − | 0.423872i | \(-0.139329\pi\) | ||||
0.905722 | + | 0.423872i | \(0.139329\pi\) | |||||||
\(8\) | −24.0102 | −1.06111 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −43.8194 | −1.20109 | −0.600547 | − | 0.799589i | \(-0.705050\pi\) | ||||
−0.600547 | + | 0.799589i | \(0.705050\pi\) | |||||||
\(12\) | 39.6392 | 0.953572 | ||||||||
\(13\) | 7.37003 | 0.157237 | 0.0786184 | − | 0.996905i | \(-0.474949\pi\) | ||||
0.0786184 | + | 0.996905i | \(0.474949\pi\) | |||||||
\(14\) | −154.516 | −2.94973 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.88082 | 0.0762628 | ||||||||
\(17\) | 22.6283 | 0.322834 | 0.161417 | − | 0.986886i | \(-0.448394\pi\) | ||||
0.161417 | + | 0.986886i | \(0.448394\pi\) | |||||||
\(18\) | −41.4519 | −0.542795 | ||||||||
\(19\) | 128.610 | 1.55291 | 0.776454 | − | 0.630174i | \(-0.217017\pi\) | ||||
0.776454 | + | 0.630174i | \(0.217017\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 100.645 | 1.04584 | ||||||||
\(22\) | 201.822 | 1.95584 | ||||||||
\(23\) | −165.615 | −1.50144 | −0.750719 | − | 0.660622i | \(-0.770293\pi\) | ||||
−0.750719 | + | 0.660622i | \(0.770293\pi\) | |||||||
\(24\) | −72.0307 | −0.612633 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −33.9446 | −0.256042 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 443.278 | 2.99184 | ||||||||
\(29\) | −172.004 | −1.10139 | −0.550697 | − | 0.834705i | \(-0.685638\pi\) | ||||
−0.550697 | + | 0.834705i | \(0.685638\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −91.3035 | −0.528987 | −0.264493 | − | 0.964388i | \(-0.585205\pi\) | ||||
−0.264493 | + | 0.964388i | \(0.585205\pi\) | |||||||
\(32\) | 169.602 | 0.936927 | ||||||||
\(33\) | −131.458 | −0.693452 | ||||||||
\(34\) | −104.221 | −0.525698 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 118.918 | 0.550545 | ||||||||
\(37\) | −235.949 | −1.04837 | −0.524186 | − | 0.851604i | \(-0.675630\pi\) | ||||
−0.524186 | + | 0.851604i | \(0.675630\pi\) | |||||||
\(38\) | −592.349 | −2.52873 | ||||||||
\(39\) | 22.1101 | 0.0907808 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 238.726 | 0.909335 | 0.454667 | − | 0.890661i | \(-0.349758\pi\) | ||||
0.454667 | + | 0.890661i | \(0.349758\pi\) | |||||||
\(42\) | −463.548 | −1.70303 | ||||||||
\(43\) | 48.3382 | 0.171430 | 0.0857152 | − | 0.996320i | \(-0.472682\pi\) | ||||
0.0857152 | + | 0.996320i | \(0.472682\pi\) | |||||||
\(44\) | −578.989 | −1.98377 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 762.783 | 2.44492 | ||||||||
\(47\) | −289.512 | −0.898503 | −0.449252 | − | 0.893405i | \(-0.648309\pi\) | ||||
−0.449252 | + | 0.893405i | \(0.648309\pi\) | |||||||
\(48\) | 14.6425 | 0.0440304 | ||||||||
\(49\) | 782.496 | 2.28133 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 67.8850 | 0.186388 | ||||||||
\(52\) | 97.3808 | 0.259698 | ||||||||
\(53\) | 154.553 | 0.400556 | 0.200278 | − | 0.979739i | \(-0.435815\pi\) | ||||
0.200278 | + | 0.979739i | \(0.435815\pi\) | |||||||
\(54\) | −124.356 | −0.313383 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −805.505 | −1.92214 | ||||||||
\(57\) | 385.831 | 0.896571 | ||||||||
\(58\) | 792.212 | 1.79349 | ||||||||
\(59\) | 218.931 | 0.483091 | 0.241545 | − | 0.970390i | \(-0.422346\pi\) | ||||
0.241545 | + | 0.970390i | \(0.422346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 546.945 | 1.14802 | 0.574010 | − | 0.818849i | \(-0.305387\pi\) | ||||
0.574010 | + | 0.818849i | \(0.305387\pi\) | |||||||
\(62\) | 420.522 | 0.861394 | ||||||||
\(63\) | 301.936 | 0.603815 | ||||||||
\(64\) | −820.193 | −1.60194 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 605.465 | 1.12921 | ||||||||
\(67\) | 791.301 | 1.44288 | 0.721439 | − | 0.692478i | \(-0.243481\pi\) | ||||
0.721439 | + | 0.692478i | \(0.243481\pi\) | |||||||
\(68\) | 298.990 | 0.533204 | ||||||||
\(69\) | −496.845 | −0.866856 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1142.61 | 1.90990 | 0.954951 | − | 0.296763i | \(-0.0959070\pi\) | ||||
0.954951 | + | 0.296763i | \(0.0959070\pi\) | |||||||
\(72\) | −216.092 | −0.353704 | ||||||||
\(73\) | −251.151 | −0.402672 | −0.201336 | − | 0.979522i | \(-0.564528\pi\) | ||||
−0.201336 | + | 0.979522i | \(0.564528\pi\) | |||||||
\(74\) | 1086.72 | 1.70715 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1699.34 | 2.56484 | ||||||||
\(77\) | −1470.07 | −2.17571 | ||||||||
\(78\) | −101.834 | −0.147826 | ||||||||
\(79\) | −402.769 | −0.573609 | −0.286804 | − | 0.957989i | \(-0.592593\pi\) | ||||
−0.286804 | + | 0.957989i | \(0.592593\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −1099.52 | −1.48075 | ||||||||
\(83\) | 106.577 | 0.140944 | 0.0704720 | − | 0.997514i | \(-0.477549\pi\) | ||||
0.0704720 | + | 0.997514i | \(0.477549\pi\) | |||||||
\(84\) | 1329.83 | 1.72734 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −222.634 | −0.279154 | ||||||||
\(87\) | −516.013 | −0.635890 | ||||||||
\(88\) | 1052.11 | 1.27449 | ||||||||
\(89\) | 1608.81 | 1.91611 | 0.958053 | − | 0.286592i | \(-0.0925223\pi\) | ||||
0.958053 | + | 0.286592i | \(0.0925223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 247.253 | 0.284826 | ||||||||
\(92\) | −2188.28 | −2.47983 | ||||||||
\(93\) | −273.910 | −0.305411 | ||||||||
\(94\) | 1333.42 | 1.46311 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 508.806 | 0.540935 | ||||||||
\(97\) | −984.943 | −1.03099 | −0.515494 | − | 0.856893i | \(-0.672392\pi\) | ||||
−0.515494 | + | 0.856893i | \(0.672392\pi\) | |||||||
\(98\) | −3603.99 | −3.71488 | ||||||||
\(99\) | −394.374 | −0.400365 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −805.442 | −0.793509 | −0.396755 | − | 0.917925i | \(-0.629864\pi\) | ||||
−0.396755 | + | 0.917925i | \(0.629864\pi\) | |||||||
\(102\) | −312.662 | −0.303512 | ||||||||
\(103\) | 1782.70 | 1.70538 | 0.852691 | − | 0.522416i | \(-0.174969\pi\) | ||||
0.852691 | + | 0.522416i | \(0.174969\pi\) | |||||||
\(104\) | −176.956 | −0.166846 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −711.834 | −0.652259 | ||||||||
\(107\) | −953.536 | −0.861512 | −0.430756 | − | 0.902468i | \(-0.641753\pi\) | ||||
−0.430756 | + | 0.902468i | \(0.641753\pi\) | |||||||
\(108\) | 356.753 | 0.317857 | ||||||||
\(109\) | 2214.01 | 1.94554 | 0.972769 | − | 0.231777i | \(-0.0744540\pi\) | ||||
0.972769 | + | 0.231777i | \(0.0744540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −707.846 | −0.605277 | ||||||||
\(112\) | 163.744 | 0.138146 | ||||||||
\(113\) | 1437.28 | 1.19653 | 0.598265 | − | 0.801298i | \(-0.295857\pi\) | ||||
0.598265 | + | 0.801298i | \(0.295857\pi\) | |||||||
\(114\) | −1777.05 | −1.45996 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2272.71 | −1.81910 | ||||||||
\(117\) | 66.3303 | 0.0524123 | ||||||||
\(118\) | −1008.34 | −0.786657 | ||||||||
\(119\) | 759.145 | 0.584796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 589.136 | 0.442627 | ||||||||
\(122\) | −2519.10 | −1.86942 | ||||||||
\(123\) | 716.178 | 0.525005 | ||||||||
\(124\) | −1206.40 | −0.873693 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1390.65 | −0.983242 | ||||||||
\(127\) | −713.871 | −0.498786 | −0.249393 | − | 0.968402i | \(-0.580231\pi\) | ||||
−0.249393 | + | 0.968402i | \(0.580231\pi\) | |||||||
\(128\) | 2420.80 | 1.67165 | ||||||||
\(129\) | 145.015 | 0.0989753 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 42.7900 | 0.0285388 | 0.0142694 | − | 0.999898i | \(-0.495458\pi\) | ||||
0.0142694 | + | 0.999898i | \(0.495458\pi\) | |||||||
\(132\) | −1736.97 | −1.14533 | ||||||||
\(133\) | 4314.67 | 2.81300 | ||||||||
\(134\) | −3644.55 | −2.34956 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −543.311 | −0.342563 | ||||||||
\(137\) | 2155.68 | 1.34432 | 0.672162 | − | 0.740404i | \(-0.265366\pi\) | ||||
0.672162 | + | 0.740404i | \(0.265366\pi\) | |||||||
\(138\) | 2288.35 | 1.41157 | ||||||||
\(139\) | −88.9660 | −0.0542878 | −0.0271439 | − | 0.999632i | \(-0.508641\pi\) | ||||
−0.0271439 | + | 0.999632i | \(0.508641\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −868.536 | −0.518751 | ||||||||
\(142\) | −5262.60 | −3.11006 | ||||||||
\(143\) | −322.950 | −0.188856 | ||||||||
\(144\) | 43.9274 | 0.0254209 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1156.74 | 0.655705 | ||||||||
\(147\) | 2347.49 | 1.31713 | ||||||||
\(148\) | −3117.61 | −1.73153 | ||||||||
\(149\) | 2041.54 | 1.12248 | 0.561240 | − | 0.827653i | \(-0.310324\pi\) | ||||
0.561240 | + | 0.827653i | \(0.310324\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 892.328 | 0.480905 | 0.240452 | − | 0.970661i | \(-0.422704\pi\) | ||||
0.240452 | + | 0.970661i | \(0.422704\pi\) | |||||||
\(152\) | −3087.96 | −1.64781 | ||||||||
\(153\) | 203.655 | 0.107611 | ||||||||
\(154\) | 6770.80 | 3.54290 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 292.142 | 0.149937 | ||||||||
\(157\) | −1567.05 | −0.796585 | −0.398292 | − | 0.917258i | \(-0.630397\pi\) | ||||
−0.398292 | + | 0.917258i | \(0.630397\pi\) | |||||||
\(158\) | 1855.06 | 0.934055 | ||||||||
\(159\) | 463.659 | 0.231261 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5556.11 | −2.71977 | ||||||||
\(162\) | −373.067 | −0.180932 | ||||||||
\(163\) | −1325.13 | −0.636762 | −0.318381 | − | 0.947963i | \(-0.603139\pi\) | ||||
−0.318381 | + | 0.947963i | \(0.603139\pi\) | |||||||
\(164\) | 3154.30 | 1.50189 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −490.869 | −0.229511 | ||||||||
\(167\) | 156.572 | 0.0725501 | 0.0362751 | − | 0.999342i | \(-0.488451\pi\) | ||||
0.0362751 | + | 0.999342i | \(0.488451\pi\) | |||||||
\(168\) | −2416.51 | −1.10975 | ||||||||
\(169\) | −2142.68 | −0.975277 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1157.49 | 0.517636 | ||||||||
\(172\) | 638.696 | 0.283140 | ||||||||
\(173\) | 1673.87 | 0.735618 | 0.367809 | − | 0.929901i | \(-0.380108\pi\) | ||||
0.367809 | + | 0.929901i | \(0.380108\pi\) | |||||||
\(174\) | 2376.64 | 1.03547 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −213.874 | −0.0915988 | ||||||||
\(177\) | 656.792 | 0.278912 | ||||||||
\(178\) | −7409.80 | −3.12016 | ||||||||
\(179\) | −2925.86 | −1.22173 | −0.610863 | − | 0.791736i | \(-0.709177\pi\) | ||||
−0.610863 | + | 0.791736i | \(0.709177\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1613.12 | −0.662443 | −0.331222 | − | 0.943553i | \(-0.607461\pi\) | ||||
−0.331222 | + | 0.943553i | \(0.607461\pi\) | |||||||
\(182\) | −1138.79 | −0.463806 | ||||||||
\(183\) | 1640.84 | 0.662809 | ||||||||
\(184\) | 3976.45 | 1.59319 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1261.57 | 0.497326 | ||||||||
\(187\) | −991.559 | −0.387754 | ||||||||
\(188\) | −3825.34 | −1.48400 | ||||||||
\(189\) | 905.807 | 0.348613 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1599.27 | 0.605860 | 0.302930 | − | 0.953013i | \(-0.402035\pi\) | ||||
0.302930 | + | 0.953013i | \(0.402035\pi\) | |||||||
\(192\) | −2460.58 | −0.924880 | ||||||||
\(193\) | −2419.25 | −0.902288 | −0.451144 | − | 0.892451i | \(-0.648984\pi\) | ||||
−0.451144 | + | 0.892451i | \(0.648984\pi\) | |||||||
\(194\) | 4536.42 | 1.67884 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10339.2 | 3.76792 | ||||||||
\(197\) | 1654.27 | 0.598285 | 0.299143 | − | 0.954208i | \(-0.403299\pi\) | ||||
0.299143 | + | 0.954208i | \(0.403299\pi\) | |||||||
\(198\) | 1816.40 | 0.651947 | ||||||||
\(199\) | −5102.28 | −1.81754 | −0.908771 | − | 0.417296i | \(-0.862978\pi\) | ||||
−0.908771 | + | 0.417296i | \(0.862978\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2373.90 | 0.833046 | ||||||||
\(202\) | 3709.68 | 1.29214 | ||||||||
\(203\) | −5770.47 | −1.99511 | ||||||||
\(204\) | 896.970 | 0.307845 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8210.68 | −2.77702 | ||||||||
\(207\) | −1490.53 | −0.500479 | ||||||||
\(208\) | 35.9718 | 0.0119913 | ||||||||
\(209\) | −5635.62 | −1.86519 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6033.10 | 1.96842 | 0.984208 | − | 0.177015i | \(-0.0566441\pi\) | ||||
0.984208 | + | 0.177015i | \(0.0566441\pi\) | |||||||
\(212\) | 2042.12 | 0.661572 | ||||||||
\(213\) | 3427.84 | 1.10268 | ||||||||
\(214\) | 4391.76 | 1.40287 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −648.276 | −0.204211 | ||||||||
\(217\) | −3063.09 | −0.958230 | ||||||||
\(218\) | −10197.2 | −3.16808 | ||||||||
\(219\) | −753.454 | −0.232483 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 166.772 | 0.0507614 | ||||||||
\(222\) | 3260.17 | 0.985624 | ||||||||
\(223\) | 5350.14 | 1.60660 | 0.803301 | − | 0.595574i | \(-0.203075\pi\) | ||||
0.803301 | + | 0.595574i | \(0.203075\pi\) | |||||||
\(224\) | 5689.87 | 1.69719 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6619.78 | −1.94841 | ||||||||
\(227\) | −3065.13 | −0.896211 | −0.448106 | − | 0.893981i | \(-0.647901\pi\) | ||||
−0.448106 | + | 0.893981i | \(0.647901\pi\) | |||||||
\(228\) | 5098.02 | 1.48081 | ||||||||
\(229\) | 5829.96 | 1.68234 | 0.841168 | − | 0.540774i | \(-0.181869\pi\) | ||||
0.841168 | + | 0.540774i | \(0.181869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4410.21 | −1.25615 | ||||||||
\(232\) | 4129.86 | 1.16870 | ||||||||
\(233\) | −1555.52 | −0.437363 | −0.218681 | − | 0.975796i | \(-0.570176\pi\) | ||||
−0.218681 | + | 0.975796i | \(0.570176\pi\) | |||||||
\(234\) | −305.502 | −0.0853473 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2892.75 | 0.797889 | ||||||||
\(237\) | −1208.31 | −0.331173 | ||||||||
\(238\) | −3496.44 | −0.952272 | ||||||||
\(239\) | −1588.23 | −0.429849 | −0.214924 | − | 0.976631i | \(-0.568950\pi\) | ||||
−0.214924 | + | 0.976631i | \(0.568950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4225.08 | 1.12930 | 0.564651 | − | 0.825330i | \(-0.309011\pi\) | ||||
0.564651 | + | 0.825330i | \(0.309011\pi\) | |||||||
\(242\) | −2713.42 | −0.720766 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 7226.83 | 1.89611 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3298.55 | −0.854909 | ||||||||
\(247\) | 947.863 | 0.244174 | ||||||||
\(248\) | 2192.22 | 0.561314 | ||||||||
\(249\) | 319.731 | 0.0813740 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1084.74 | −0.272782 | −0.136391 | − | 0.990655i | \(-0.543550\pi\) | ||||
−0.136391 | + | 0.990655i | \(0.543550\pi\) | |||||||
\(252\) | 3989.50 | 0.997281 | ||||||||
\(253\) | 7257.14 | 1.80337 | ||||||||
\(254\) | 3287.92 | 0.812214 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4588.10 | −1.12014 | ||||||||
\(257\) | −3686.21 | −0.894705 | −0.447353 | − | 0.894358i | \(-0.647633\pi\) | ||||
−0.447353 | + | 0.894358i | \(0.647633\pi\) | |||||||
\(258\) | −667.903 | −0.161170 | ||||||||
\(259\) | −7915.71 | −1.89907 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1548.04 | −0.367131 | ||||||||
\(262\) | −197.081 | −0.0464721 | ||||||||
\(263\) | −2756.15 | −0.646204 | −0.323102 | − | 0.946364i | \(-0.604726\pi\) | ||||
−0.323102 | + | 0.946364i | \(0.604726\pi\) | |||||||
\(264\) | 3156.34 | 0.735830 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −19872.4 | −4.58065 | ||||||||
\(267\) | 4826.43 | 1.10626 | ||||||||
\(268\) | 10455.5 | 2.38311 | ||||||||
\(269\) | 4914.24 | 1.11385 | 0.556927 | − | 0.830561i | \(-0.311980\pi\) | ||||
0.556927 | + | 0.830561i | \(0.311980\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −608.390 | −0.136373 | −0.0681865 | − | 0.997673i | \(-0.521721\pi\) | ||||
−0.0681865 | + | 0.997673i | \(0.521721\pi\) | |||||||
\(272\) | 110.445 | 0.0246202 | ||||||||
\(273\) | 741.759 | 0.164444 | ||||||||
\(274\) | −9928.58 | −2.18908 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6564.85 | −1.43173 | ||||||||
\(277\) | −3408.79 | −0.739402 | −0.369701 | − | 0.929151i | \(-0.620540\pi\) | ||||
−0.369701 | + | 0.929151i | \(0.620540\pi\) | |||||||
\(278\) | 409.757 | 0.0884014 | ||||||||
\(279\) | −821.731 | −0.176329 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4436.65 | −0.941881 | −0.470940 | − | 0.882165i | \(-0.656085\pi\) | ||||
−0.470940 | + | 0.882165i | \(0.656085\pi\) | |||||||
\(282\) | 4000.27 | 0.844726 | ||||||||
\(283\) | 3358.79 | 0.705511 | 0.352755 | − | 0.935716i | \(-0.385245\pi\) | ||||
0.352755 | + | 0.935716i | \(0.385245\pi\) | |||||||
\(284\) | 15097.4 | 3.15446 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1487.43 | 0.307531 | ||||||||
\(287\) | 8008.88 | 1.64721 | ||||||||
\(288\) | 1526.42 | 0.312309 | ||||||||
\(289\) | −4400.96 | −0.895778 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2954.83 | −0.595241 | ||||||||
\(292\) | −3318.48 | −0.665067 | ||||||||
\(293\) | −2749.27 | −0.548171 | −0.274085 | − | 0.961705i | \(-0.588375\pi\) | ||||
−0.274085 | + | 0.961705i | \(0.588375\pi\) | |||||||
\(294\) | −10812.0 | −2.14479 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5665.18 | 1.11244 | ||||||||
\(297\) | −1183.12 | −0.231151 | ||||||||
\(298\) | −9402.86 | −1.82783 | ||||||||
\(299\) | −1220.59 | −0.236081 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1621.67 | 0.310536 | ||||||||
\(302\) | −4109.85 | −0.783098 | ||||||||
\(303\) | −2416.32 | −0.458133 | ||||||||
\(304\) | 627.724 | 0.118429 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −937.987 | −0.175233 | ||||||||
\(307\) | −6981.55 | −1.29791 | −0.648954 | − | 0.760827i | \(-0.724793\pi\) | ||||
−0.648954 | + | 0.760827i | \(0.724793\pi\) | |||||||
\(308\) | −19424.1 | −3.59349 | ||||||||
\(309\) | 5348.09 | 0.984603 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7031.46 | 1.28205 | 0.641025 | − | 0.767520i | \(-0.278509\pi\) | ||||
0.641025 | + | 0.767520i | \(0.278509\pi\) | |||||||
\(312\) | −530.868 | −0.0963285 | ||||||||
\(313\) | −3182.12 | −0.574646 | −0.287323 | − | 0.957834i | \(-0.592765\pi\) | ||||
−0.287323 | + | 0.957834i | \(0.592765\pi\) | |||||||
\(314\) | 7217.44 | 1.29715 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5321.82 | −0.947392 | ||||||||
\(317\) | 3964.31 | 0.702390 | 0.351195 | − | 0.936302i | \(-0.385775\pi\) | ||||
0.351195 | + | 0.936302i | \(0.385775\pi\) | |||||||
\(318\) | −2135.50 | −0.376582 | ||||||||
\(319\) | 7537.12 | 1.32288 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2860.61 | −0.497394 | ||||||||
\(322\) | 25590.2 | 4.42883 | ||||||||
\(323\) | 2910.24 | 0.501331 | ||||||||
\(324\) | 1070.26 | 0.183515 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6103.24 | 1.03689 | ||||||||
\(327\) | 6642.03 | 1.12326 | ||||||||
\(328\) | −5731.86 | −0.964906 | ||||||||
\(329\) | −9712.67 | −1.62759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11219.5 | 1.86308 | 0.931541 | − | 0.363637i | \(-0.118465\pi\) | ||||
0.931541 | + | 0.363637i | \(0.118465\pi\) | |||||||
\(332\) | 1408.21 | 0.232788 | ||||||||
\(333\) | −2123.54 | −0.349457 | ||||||||
\(334\) | −721.132 | −0.118139 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 491.231 | 0.0797585 | ||||||||
\(337\) | 2956.56 | 0.477905 | 0.238952 | − | 0.971031i | \(-0.423196\pi\) | ||||
0.238952 | + | 0.971031i | \(0.423196\pi\) | |||||||
\(338\) | 9868.69 | 1.58812 | ||||||||
\(339\) | 4311.84 | 0.690817 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4000.86 | 0.635363 | ||||||||
\(342\) | −5331.14 | −0.842910 | ||||||||
\(343\) | 14744.4 | 2.32106 | ||||||||
\(344\) | −1160.61 | −0.181907 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7709.45 | −1.19787 | ||||||||
\(347\) | 5466.64 | 0.845720 | 0.422860 | − | 0.906195i | \(-0.361026\pi\) | ||||
0.422860 | + | 0.906195i | \(0.361026\pi\) | |||||||
\(348\) | −6818.12 | −1.05026 | ||||||||
\(349\) | 7548.63 | 1.15779 | 0.578895 | − | 0.815402i | \(-0.303484\pi\) | ||||
0.578895 | + | 0.815402i | \(0.303484\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 198.991 | 0.0302603 | ||||||||
\(352\) | −7431.84 | −1.12534 | ||||||||
\(353\) | 3170.61 | 0.478058 | 0.239029 | − | 0.971012i | \(-0.423171\pi\) | ||||
0.239029 | + | 0.971012i | \(0.423171\pi\) | |||||||
\(354\) | −3025.03 | −0.454177 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 21257.3 | 3.16471 | ||||||||
\(357\) | 2277.43 | 0.337632 | ||||||||
\(358\) | 13475.8 | 1.98944 | ||||||||
\(359\) | 1784.51 | 0.262347 | 0.131174 | − | 0.991359i | \(-0.458125\pi\) | ||||
0.131174 | + | 0.991359i | \(0.458125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9681.62 | 1.41152 | ||||||||
\(362\) | 7429.65 | 1.07871 | ||||||||
\(363\) | 1767.41 | 0.255551 | ||||||||
\(364\) | 3266.97 | 0.470428 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7557.31 | −1.07931 | ||||||||
\(367\) | 6511.59 | 0.926164 | 0.463082 | − | 0.886315i | \(-0.346743\pi\) | ||||
0.463082 | + | 0.886315i | \(0.346743\pi\) | |||||||
\(368\) | −808.336 | −0.114504 | ||||||||
\(369\) | 2148.53 | 0.303112 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5185.00 | 0.725585 | ||||||||
\(372\) | −3619.20 | −0.504427 | ||||||||
\(373\) | 3936.95 | 0.546509 | 0.273254 | − | 0.961942i | \(-0.411900\pi\) | ||||
0.273254 | + | 0.961942i | \(0.411900\pi\) | |||||||
\(374\) | 4566.89 | 0.631412 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6951.25 | 0.953413 | ||||||||
\(377\) | −1267.68 | −0.173180 | ||||||||
\(378\) | −4171.94 | −0.567675 | ||||||||
\(379\) | 1134.62 | 0.153777 | 0.0768885 | − | 0.997040i | \(-0.475501\pi\) | ||||
0.0768885 | + | 0.997040i | \(0.475501\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2141.61 | −0.287974 | ||||||||
\(382\) | −7365.87 | −0.986572 | ||||||||
\(383\) | −7387.51 | −0.985599 | −0.492799 | − | 0.870143i | \(-0.664026\pi\) | ||||
−0.492799 | + | 0.870143i | \(0.664026\pi\) | |||||||
\(384\) | 7262.41 | 0.965125 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11142.5 | 1.46927 | ||||||||
\(387\) | 435.044 | 0.0571434 | ||||||||
\(388\) | −13014.1 | −1.70282 | ||||||||
\(389\) | −2561.11 | −0.333814 | −0.166907 | − | 0.985973i | \(-0.553378\pi\) | ||||
−0.166907 | + | 0.985973i | \(0.553378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3747.59 | −0.484715 | ||||||||
\(392\) | −18787.9 | −2.42075 | ||||||||
\(393\) | 128.370 | 0.0164769 | ||||||||
\(394\) | −7619.20 | −0.974238 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5210.90 | −0.661256 | ||||||||
\(397\) | 4075.29 | 0.515196 | 0.257598 | − | 0.966252i | \(-0.417069\pi\) | ||||
0.257598 | + | 0.966252i | \(0.417069\pi\) | |||||||
\(398\) | 23499.9 | 2.95966 | ||||||||
\(399\) | 12944.0 | 1.62409 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4491.11 | 0.559290 | 0.279645 | − | 0.960103i | \(-0.409783\pi\) | ||||
0.279645 | + | 0.960103i | \(0.409783\pi\) | |||||||
\(402\) | −10933.6 | −1.35652 | ||||||||
\(403\) | −672.910 | −0.0831762 | ||||||||
\(404\) | −10642.4 | −1.31059 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 26577.4 | 3.24881 | ||||||||
\(407\) | 10339.1 | 1.25919 | ||||||||
\(408\) | −1629.93 | −0.197779 | ||||||||
\(409\) | −6325.03 | −0.764677 | −0.382338 | − | 0.924022i | \(-0.624881\pi\) | ||||
−0.382338 | + | 0.924022i | \(0.624881\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6467.05 | 0.776146 | ||||||||
\(412\) | 23554.9 | 2.81667 | ||||||||
\(413\) | 7344.77 | 0.875091 | ||||||||
\(414\) | 6865.05 | 0.814973 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1249.97 | 0.147319 | ||||||||
\(417\) | −266.898 | −0.0313431 | ||||||||
\(418\) | 25956.4 | 3.03724 | ||||||||
\(419\) | −1052.63 | −0.122732 | −0.0613658 | − | 0.998115i | \(-0.519546\pi\) | ||||
−0.0613658 | + | 0.998115i | \(0.519546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10994.5 | 1.27277 | 0.636387 | − | 0.771370i | \(-0.280428\pi\) | ||||
0.636387 | + | 0.771370i | \(0.280428\pi\) | |||||||
\(422\) | −27787.1 | −3.20534 | ||||||||
\(423\) | −2605.61 | −0.299501 | ||||||||
\(424\) | −3710.85 | −0.425035 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −15787.8 | −1.79559 | ||||||||
\(427\) | 18349.1 | 2.07957 | ||||||||
\(428\) | −12599.1 | −1.42290 | ||||||||
\(429\) | −968.850 | −0.109036 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17481.3 | 1.95370 | 0.976849 | − | 0.213931i | \(-0.0686266\pi\) | ||||
0.976849 | + | 0.213931i | \(0.0686266\pi\) | |||||||
\(432\) | 131.782 | 0.0146768 | ||||||||
\(433\) | 3057.99 | 0.339394 | 0.169697 | − | 0.985496i | \(-0.445721\pi\) | ||||
0.169697 | + | 0.985496i | \(0.445721\pi\) | |||||||
\(434\) | 14107.9 | 1.56037 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 29253.9 | 3.21332 | ||||||||
\(437\) | −21299.8 | −2.33159 | ||||||||
\(438\) | 3470.23 | 0.378571 | ||||||||
\(439\) | −12594.8 | −1.36929 | −0.684646 | − | 0.728876i | \(-0.740043\pi\) | ||||
−0.684646 | + | 0.728876i | \(0.740043\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7042.46 | 0.760443 | ||||||||
\(442\) | −768.111 | −0.0826591 | ||||||||
\(443\) | 6599.93 | 0.707838 | 0.353919 | − | 0.935276i | \(-0.384849\pi\) | ||||
0.353919 | + | 0.935276i | \(0.384849\pi\) | |||||||
\(444\) | −9352.83 | −0.999697 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24641.5 | −2.61616 | ||||||||
\(447\) | 6124.62 | 0.648064 | ||||||||
\(448\) | −27516.2 | −2.90182 | ||||||||
\(449\) | 12479.4 | 1.31167 | 0.655837 | − | 0.754903i | \(-0.272316\pi\) | ||||
0.655837 | + | 0.754903i | \(0.272316\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10460.8 | −1.09220 | ||||||||
\(452\) | 18990.9 | 1.97623 | ||||||||
\(453\) | 2676.98 | 0.277651 | ||||||||
\(454\) | 14117.3 | 1.45938 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9263.89 | −0.951363 | ||||||||
\(457\) | −436.301 | −0.0446593 | −0.0223296 | − | 0.999751i | \(-0.507108\pi\) | ||||
−0.0223296 | + | 0.999751i | \(0.507108\pi\) | |||||||
\(458\) | −26851.5 | −2.73949 | ||||||||
\(459\) | 610.965 | 0.0621294 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11749.4 | −1.18704 | −0.593521 | − | 0.804819i | \(-0.702262\pi\) | ||||
−0.593521 | + | 0.804819i | \(0.702262\pi\) | |||||||
\(462\) | 20312.4 | 2.04549 | ||||||||
\(463\) | −8031.27 | −0.806144 | −0.403072 | − | 0.915168i | \(-0.632058\pi\) | ||||
−0.403072 | + | 0.915168i | \(0.632058\pi\) | |||||||
\(464\) | −839.522 | −0.0839954 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7164.36 | 0.712194 | ||||||||
\(467\) | 3981.50 | 0.394522 | 0.197261 | − | 0.980351i | \(-0.436795\pi\) | ||||
0.197261 | + | 0.980351i | \(0.436795\pi\) | |||||||
\(468\) | 876.427 | 0.0865660 | ||||||||
\(469\) | 26546.9 | 2.61369 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4701.14 | −0.459908 | ||||||||
\(472\) | −5256.57 | −0.512613 | ||||||||
\(473\) | −2118.15 | −0.205904 | ||||||||
\(474\) | 5565.18 | 0.539277 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10030.6 | 0.965869 | ||||||||
\(477\) | 1390.98 | 0.133519 | ||||||||
\(478\) | 7315.00 | 0.699959 | ||||||||
\(479\) | 3852.79 | 0.367513 | 0.183756 | − | 0.982972i | \(-0.441174\pi\) | ||||
0.183756 | + | 0.982972i | \(0.441174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1738.95 | −0.164843 | ||||||||
\(482\) | −19459.7 | −1.83894 | ||||||||
\(483\) | −16668.3 | −1.57026 | ||||||||
\(484\) | 7784.30 | 0.731057 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1119.20 | −0.104461 | ||||||||
\(487\) | −8404.63 | −0.782033 | −0.391016 | − | 0.920384i | \(-0.627876\pi\) | ||||
−0.391016 | + | 0.920384i | \(0.627876\pi\) | |||||||
\(488\) | −13132.3 | −1.21818 | ||||||||
\(489\) | −3975.39 | −0.367635 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16071.8 | −1.47721 | −0.738607 | − | 0.674136i | \(-0.764516\pi\) | ||||
−0.738607 | + | 0.674136i | \(0.764516\pi\) | |||||||
\(492\) | 9462.91 | 0.867116 | ||||||||
\(493\) | −3892.17 | −0.355567 | ||||||||
\(494\) | −4365.63 | −0.397610 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −445.636 | −0.0403420 | ||||||||
\(497\) | 38332.8 | 3.45968 | ||||||||
\(498\) | −1472.61 | −0.132508 | ||||||||
\(499\) | 2752.94 | 0.246971 | 0.123485 | − | 0.992346i | \(-0.460593\pi\) | ||||
0.123485 | + | 0.992346i | \(0.460593\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 469.715 | 0.0418868 | ||||||||
\(502\) | 4996.07 | 0.444195 | ||||||||
\(503\) | 21243.4 | 1.88310 | 0.941549 | − | 0.336875i | \(-0.109370\pi\) | ||||
0.941549 | + | 0.336875i | \(0.109370\pi\) | |||||||
\(504\) | −7249.54 | −0.640715 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −33424.7 | −2.93658 | ||||||||
\(507\) | −6428.05 | −0.563076 | ||||||||
\(508\) | −9432.43 | −0.823812 | ||||||||
\(509\) | 3168.44 | 0.275911 | 0.137955 | − | 0.990438i | \(-0.455947\pi\) | ||||
0.137955 | + | 0.990438i | \(0.455947\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8425.73 | −0.729418 | ||||||||
\(512\) | 1765.31 | 0.152376 | ||||||||
\(513\) | 3472.48 | 0.298857 | ||||||||
\(514\) | 16977.8 | 1.45692 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1916.09 | 0.163471 | ||||||||
\(517\) | 12686.2 | 1.07919 | ||||||||
\(518\) | 36457.9 | 3.09241 | ||||||||
\(519\) | 5021.61 | 0.424709 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3701.03 | 0.311219 | 0.155609 | − | 0.987819i | \(-0.450266\pi\) | ||||
0.155609 | + | 0.987819i | \(0.450266\pi\) | |||||||
\(522\) | 7129.91 | 0.597830 | ||||||||
\(523\) | 7547.89 | 0.631064 | 0.315532 | − | 0.948915i | \(-0.397817\pi\) | ||||
0.315532 | + | 0.948915i | \(0.397817\pi\) | |||||||
\(524\) | 565.387 | 0.0471356 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12694.2 | 1.05227 | ||||||||
\(527\) | −2066.05 | −0.170775 | ||||||||
\(528\) | −641.623 | −0.0528846 | ||||||||
\(529\) | 15261.3 | 1.25432 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1970.38 | 0.161030 | ||||||||
\(532\) | 57010.1 | 4.64606 | ||||||||
\(533\) | 1759.42 | 0.142981 | ||||||||
\(534\) | −22229.4 | −1.80142 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −18999.3 | −1.53105 | ||||||||
\(537\) | −8777.58 | −0.705364 | ||||||||
\(538\) | −22633.9 | −1.81378 | ||||||||
\(539\) | −34288.5 | −2.74009 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7164.72 | 0.569382 | 0.284691 | − | 0.958619i | \(-0.408109\pi\) | ||||
0.284691 | + | 0.958619i | \(0.408109\pi\) | |||||||
\(542\) | 2802.10 | 0.222068 | ||||||||
\(543\) | −4839.36 | −0.382462 | ||||||||
\(544\) | 3837.81 | 0.302472 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3416.37 | −0.267778 | ||||||||
\(547\) | −17819.3 | −1.39287 | −0.696434 | − | 0.717621i | \(-0.745231\pi\) | ||||
−0.696434 | + | 0.717621i | \(0.745231\pi\) | |||||||
\(548\) | 28483.2 | 2.22033 | ||||||||
\(549\) | 4922.51 | 0.382673 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22121.5 | −1.71036 | ||||||||
\(552\) | 11929.3 | 0.919831 | ||||||||
\(553\) | −13512.3 | −1.03906 | ||||||||
\(554\) | 15700.1 | 1.20403 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1175.52 | −0.0896636 | ||||||||
\(557\) | −9017.26 | −0.685949 | −0.342975 | − | 0.939345i | \(-0.611434\pi\) | ||||
−0.342975 | + | 0.939345i | \(0.611434\pi\) | |||||||
\(558\) | 3784.70 | 0.287131 | ||||||||
\(559\) | 356.254 | 0.0269552 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2974.68 | −0.223870 | ||||||||
\(562\) | 20434.2 | 1.53374 | ||||||||
\(563\) | 12636.2 | 0.945916 | 0.472958 | − | 0.881085i | \(-0.343186\pi\) | ||||
0.472958 | + | 0.881085i | \(0.343186\pi\) | |||||||
\(564\) | −11476.0 | −0.856787 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −15469.8 | −1.14884 | ||||||||
\(567\) | 2717.42 | 0.201272 | ||||||||
\(568\) | −27434.4 | −2.02662 | ||||||||
\(569\) | −8645.88 | −0.637002 | −0.318501 | − | 0.947922i | \(-0.603179\pi\) | ||||
−0.318501 | + | 0.947922i | \(0.603179\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12085.9 | −0.885781 | −0.442890 | − | 0.896576i | \(-0.646047\pi\) | ||||
−0.442890 | + | 0.896576i | \(0.646047\pi\) | |||||||
\(572\) | −4267.17 | −0.311922 | ||||||||
\(573\) | 4797.81 | 0.349793 | ||||||||
\(574\) | −36887.0 | −2.68229 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7381.74 | −0.533980 | ||||||||
\(577\) | 4644.56 | 0.335105 | 0.167553 | − | 0.985863i | \(-0.446414\pi\) | ||||
0.167553 | + | 0.985863i | \(0.446414\pi\) | |||||||
\(578\) | 20269.8 | 1.45867 | ||||||||
\(579\) | −7257.76 | −0.520936 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3575.49 | 0.255312 | ||||||||
\(582\) | 13609.3 | 0.969281 | ||||||||
\(583\) | −6772.41 | −0.481105 | ||||||||
\(584\) | 6030.20 | 0.427280 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12662.5 | 0.892632 | ||||||||
\(587\) | 7797.47 | 0.548272 | 0.274136 | − | 0.961691i | \(-0.411608\pi\) | ||||
0.274136 | + | 0.961691i | \(0.411608\pi\) | |||||||
\(588\) | 31017.5 | 2.17541 | ||||||||
\(589\) | −11742.6 | −0.821467 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4962.82 | 0.345420 | ||||||||
\(592\) | −1151.62 | −0.0799518 | ||||||||
\(593\) | −21835.1 | −1.51207 | −0.756037 | − | 0.654529i | \(-0.772867\pi\) | ||||
−0.756037 | + | 0.654529i | \(0.772867\pi\) | |||||||
\(594\) | 5449.19 | 0.376402 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26975.0 | 1.85393 | ||||||||
\(597\) | −15306.8 | −1.04936 | ||||||||
\(598\) | 5621.74 | 0.384431 | ||||||||
\(599\) | 9744.09 | 0.664662 | 0.332331 | − | 0.943163i | \(-0.392165\pi\) | ||||
0.332331 | + | 0.943163i | \(0.392165\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11576.7 | 0.785726 | 0.392863 | − | 0.919597i | \(-0.371485\pi\) | ||||
0.392863 | + | 0.919597i | \(0.371485\pi\) | |||||||
\(602\) | −7469.03 | −0.505673 | ||||||||
\(603\) | 7121.71 | 0.480959 | ||||||||
\(604\) | 11790.4 | 0.794279 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11129.0 | 0.746016 | ||||||||
\(607\) | 6719.64 | 0.449327 | 0.224664 | − | 0.974436i | \(-0.427872\pi\) | ||||
0.224664 | + | 0.974436i | \(0.427872\pi\) | |||||||
\(608\) | 21812.6 | 1.45496 | ||||||||
\(609\) | −17311.4 | −1.15188 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2133.71 | −0.141278 | ||||||||
\(612\) | 2690.91 | 0.177735 | ||||||||
\(613\) | 3880.73 | 0.255695 | 0.127848 | − | 0.991794i | \(-0.459193\pi\) | ||||
0.127848 | + | 0.991794i | \(0.459193\pi\) | |||||||
\(614\) | 32155.4 | 2.11349 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 35296.7 | 2.30868 | ||||||||
\(617\) | −22898.6 | −1.49410 | −0.747052 | − | 0.664766i | \(-0.768531\pi\) | ||||
−0.747052 | + | 0.664766i | \(0.768531\pi\) | |||||||
\(618\) | −24632.1 | −1.60331 | ||||||||
\(619\) | 13421.8 | 0.871516 | 0.435758 | − | 0.900064i | \(-0.356480\pi\) | ||||
0.435758 | + | 0.900064i | \(0.356480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4471.60 | −0.288952 | ||||||||
\(622\) | −32385.3 | −2.08767 | ||||||||
\(623\) | 53973.0 | 3.47092 | ||||||||
\(624\) | 107.915 | 0.00692320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14656.1 | 0.935745 | ||||||||
\(627\) | −16906.9 | −1.07687 | ||||||||
\(628\) | −20705.5 | −1.31567 | ||||||||
\(629\) | −5339.13 | −0.338450 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13089.3 | −0.825797 | −0.412898 | − | 0.910777i | \(-0.635484\pi\) | ||||
−0.412898 | + | 0.910777i | \(0.635484\pi\) | |||||||
\(632\) | 9670.58 | 0.608663 | ||||||||
\(633\) | 18099.3 | 1.13647 | ||||||||
\(634\) | −18258.7 | −1.14376 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6126.36 | 0.381959 | ||||||||
\(637\) | 5767.02 | 0.358709 | ||||||||
\(638\) | −34714.2 | −2.15415 | ||||||||
\(639\) | 10283.5 | 0.636634 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1160.65 | 0.0715179 | 0.0357590 | − | 0.999360i | \(-0.488615\pi\) | ||||
0.0357590 | + | 0.999360i | \(0.488615\pi\) | |||||||
\(642\) | 13175.3 | 0.809949 | ||||||||
\(643\) | 2318.80 | 0.142215 | 0.0711076 | − | 0.997469i | \(-0.477347\pi\) | ||||
0.0711076 | + | 0.997469i | \(0.477347\pi\) | |||||||
\(644\) | −73413.4 | −4.49207 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13403.9 | −0.816360 | ||||||||
\(647\) | 26809.3 | 1.62903 | 0.814515 | − | 0.580143i | \(-0.197003\pi\) | ||||
0.814515 | + | 0.580143i | \(0.197003\pi\) | |||||||
\(648\) | −1944.83 | −0.117901 | ||||||||
\(649\) | −9593.40 | −0.580237 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9189.26 | −0.553234 | ||||||||
\(652\) | −17509.0 | −1.05170 | ||||||||
\(653\) | 3318.86 | 0.198893 | 0.0994465 | − | 0.995043i | \(-0.468293\pi\) | ||||
0.0994465 | + | 0.995043i | \(0.468293\pi\) | |||||||
\(654\) | −30591.6 | −1.82909 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1165.18 | 0.0693485 | ||||||||
\(657\) | −2260.36 | −0.134224 | ||||||||
\(658\) | 44734.3 | 2.65034 | ||||||||
\(659\) | −26163.5 | −1.54656 | −0.773281 | − | 0.634063i | \(-0.781386\pi\) | ||||
−0.773281 | + | 0.634063i | \(0.781386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10785.7 | 0.634669 | 0.317335 | − | 0.948314i | \(-0.397212\pi\) | ||||
0.317335 | + | 0.948314i | \(0.397212\pi\) | |||||||
\(662\) | −51674.4 | −3.03381 | ||||||||
\(663\) | 500.315 | 0.0293071 | ||||||||
\(664\) | −2558.94 | −0.149557 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9780.52 | 0.569050 | ||||||||
\(667\) | 28486.5 | 1.65367 | ||||||||
\(668\) | 2068.79 | 0.119826 | ||||||||
\(669\) | 16050.4 | 0.927572 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23966.8 | −1.37888 | ||||||||
\(672\) | 17069.6 | 0.979873 | ||||||||
\(673\) | −12388.0 | −0.709541 | −0.354770 | − | 0.934953i | \(-0.615441\pi\) | ||||
−0.354770 | + | 0.934953i | \(0.615441\pi\) | |||||||
\(674\) | −13617.2 | −0.778212 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28311.4 | −1.61080 | ||||||||
\(677\) | −18741.0 | −1.06392 | −0.531960 | − | 0.846769i | \(-0.678544\pi\) | ||||
−0.531960 | + | 0.846769i | \(0.678544\pi\) | |||||||
\(678\) | −19859.3 | −1.12492 | ||||||||
\(679\) | −33043.3 | −1.86758 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9195.39 | −0.517428 | ||||||||
\(682\) | −18427.0 | −1.03461 | ||||||||
\(683\) | 557.263 | 0.0312198 | 0.0156099 | − | 0.999878i | \(-0.495031\pi\) | ||||
0.0156099 | + | 0.999878i | \(0.495031\pi\) | |||||||
\(684\) | 15294.0 | 0.854945 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −67909.2 | −3.77957 | ||||||||
\(687\) | 17489.9 | 0.971297 | ||||||||
\(688\) | 235.930 | 0.0130738 | ||||||||
\(689\) | 1139.06 | 0.0629822 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11777.2 | −0.648374 | −0.324187 | − | 0.945993i | \(-0.605091\pi\) | ||||
−0.324187 | + | 0.945993i | \(0.605091\pi\) | |||||||
\(692\) | 22117.0 | 1.21497 | ||||||||
\(693\) | −13230.6 | −0.725238 | ||||||||
\(694\) | −25178.1 | −1.37716 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12389.6 | 0.674750 | ||||||||
\(697\) | 5401.97 | 0.293564 | ||||||||
\(698\) | −34767.2 | −1.88533 | ||||||||
\(699\) | −4666.56 | −0.252511 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15025.5 | 0.809563 | 0.404782 | − | 0.914413i | \(-0.367348\pi\) | ||||
0.404782 | + | 0.914413i | \(0.367348\pi\) | |||||||
\(702\) | −916.505 | −0.0492753 | ||||||||
\(703\) | −30345.5 | −1.62802 | ||||||||
\(704\) | 35940.3 | 1.92408 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14603.1 | −0.778462 | ||||||||
\(707\) | −27021.3 | −1.43740 | ||||||||
\(708\) | 8678.24 | 0.460662 | ||||||||
\(709\) | −16819.9 | −0.890950 | −0.445475 | − | 0.895294i | \(-0.646965\pi\) | ||||
−0.445475 | + | 0.895294i | \(0.646965\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3624.92 | −0.191203 | ||||||||
\(712\) | −38627.9 | −2.03320 | ||||||||
\(713\) | 15121.2 | 0.794241 | ||||||||
\(714\) | −10489.3 | −0.549794 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −38659.6 | −2.01785 | ||||||||
\(717\) | −4764.68 | −0.248173 | ||||||||
\(718\) | −8219.02 | −0.427202 | ||||||||
\(719\) | 3172.56 | 0.164557 | 0.0822784 | − | 0.996609i | \(-0.473780\pi\) | ||||
0.0822784 | + | 0.996609i | \(0.473780\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 59806.6 | 3.08920 | ||||||||
\(722\) | −44591.3 | −2.29850 | ||||||||
\(723\) | 12675.3 | 0.652002 | ||||||||
\(724\) | −21314.3 | −1.09411 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8140.27 | −0.416134 | ||||||||
\(727\) | 3030.09 | 0.154580 | 0.0772901 | − | 0.997009i | \(-0.475373\pi\) | ||||
0.0772901 | + | 0.997009i | \(0.475373\pi\) | |||||||
\(728\) | −5936.60 | −0.302232 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1093.81 | 0.0553435 | ||||||||
\(732\) | 21680.5 | 1.09472 | ||||||||
\(733\) | 7784.47 | 0.392259 | 0.196130 | − | 0.980578i | \(-0.437163\pi\) | ||||
0.196130 | + | 0.980578i | \(0.437163\pi\) | |||||||
\(734\) | −29990.9 | −1.50815 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28088.6 | −1.40674 | ||||||||
\(737\) | −34674.3 | −1.73303 | ||||||||
\(738\) | −9895.64 | −0.493582 | ||||||||
\(739\) | 5925.54 | 0.294959 | 0.147479 | − | 0.989065i | \(-0.452884\pi\) | ||||
0.147479 | + | 0.989065i | \(0.452884\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2843.59 | 0.140974 | ||||||||
\(742\) | −23880.9 | −1.18153 | ||||||||
\(743\) | 5801.80 | 0.286470 | 0.143235 | − | 0.989689i | \(-0.454250\pi\) | ||||
0.143235 | + | 0.989689i | \(0.454250\pi\) | |||||||
\(744\) | 6576.65 | 0.324075 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18132.7 | −0.889926 | ||||||||
\(747\) | 959.193 | 0.0469813 | ||||||||
\(748\) | −13101.5 | −0.640428 | ||||||||
\(749\) | −31989.6 | −1.56058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25182.5 | 1.22360 | 0.611799 | − | 0.791013i | \(-0.290446\pi\) | ||||
0.611799 | + | 0.791013i | \(0.290446\pi\) | |||||||
\(752\) | −1413.06 | −0.0685224 | ||||||||
\(753\) | −3254.23 | −0.157491 | ||||||||
\(754\) | 5838.63 | 0.282003 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11968.5 | 0.575781 | ||||||||
\(757\) | −37908.7 | −1.82010 | −0.910050 | − | 0.414498i | \(-0.863957\pi\) | ||||
−0.910050 | + | 0.414498i | \(0.863957\pi\) | |||||||
\(758\) | −5225.79 | −0.250408 | ||||||||
\(759\) | 21771.4 | 1.04118 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12693.8 | −0.604666 | −0.302333 | − | 0.953202i | \(-0.597765\pi\) | ||||
−0.302333 | + | 0.953202i | \(0.597765\pi\) | |||||||
\(762\) | 9863.76 | 0.468932 | ||||||||
\(763\) | 74276.5 | 3.52423 | ||||||||
\(764\) | 21131.3 | 1.00066 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 34025.2 | 1.60493 | ||||||||
\(767\) | 1613.53 | 0.0759596 | ||||||||
\(768\) | −13764.3 | −0.646714 | ||||||||
\(769\) | 19956.2 | 0.935811 | 0.467905 | − | 0.883779i | \(-0.345009\pi\) | ||||
0.467905 | + | 0.883779i | \(0.345009\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11058.6 | −0.516558 | ||||||||
\(772\) | −31965.8 | −1.49025 | ||||||||
\(773\) | −26532.8 | −1.23456 | −0.617282 | − | 0.786742i | \(-0.711766\pi\) | ||||
−0.617282 | + | 0.786742i | \(0.711766\pi\) | |||||||
\(774\) | −2003.71 | −0.0930515 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23648.7 | 1.09399 | ||||||||
\(777\) | −23747.1 | −1.09643 | ||||||||
\(778\) | 11795.9 | 0.543577 | ||||||||
\(779\) | 30702.6 | 1.41211 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50068.5 | −2.29397 | ||||||||
\(782\) | 17260.5 | 0.789303 | ||||||||
\(783\) | −4644.12 | −0.211963 | ||||||||
\(784\) | 3819.22 | 0.173981 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −591.242 | −0.0268307 | ||||||||
\(787\) | 22108.9 | 1.00139 | 0.500697 | − | 0.865622i | \(-0.333077\pi\) | ||||
0.500697 | + | 0.865622i | \(0.333077\pi\) | |||||||
\(788\) | 21858.1 | 0.988149 | ||||||||
\(789\) | −8268.46 | −0.373086 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48218.5 | 2.16745 | ||||||||
\(792\) | 9469.01 | 0.424832 | ||||||||
\(793\) | 4031.00 | 0.180511 | ||||||||
\(794\) | −18769.8 | −0.838937 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −67416.8 | −3.00191 | ||||||||
\(797\) | −39363.4 | −1.74946 | −0.874731 | − | 0.484608i | \(-0.838962\pi\) | ||||
−0.874731 | + | 0.484608i | \(0.838962\pi\) | |||||||
\(798\) | −59617.1 | −2.64464 | ||||||||
\(799\) | −6551.17 | −0.290067 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14479.3 | 0.638702 | ||||||||
\(802\) | −20685.0 | −0.910739 | ||||||||
\(803\) | 11005.3 | 0.483647 | ||||||||
\(804\) | 31366.6 | 1.37589 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3099.26 | 0.135443 | ||||||||
\(807\) | 14742.7 | 0.643084 | ||||||||
\(808\) | 19338.8 | 0.842002 | ||||||||
\(809\) | 14593.9 | 0.634231 | 0.317116 | − | 0.948387i | \(-0.397286\pi\) | ||||
0.317116 | + | 0.948387i | \(0.397286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6792.04 | 0.294082 | 0.147041 | − | 0.989130i | \(-0.453025\pi\) | ||||
0.147041 | + | 0.989130i | \(0.453025\pi\) | |||||||
\(812\) | −76245.7 | −3.29520 | ||||||||
\(813\) | −1825.17 | −0.0787350 | ||||||||
\(814\) | −47619.6 | −2.05045 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 331.335 | 0.0142145 | ||||||||
\(817\) | 6216.79 | 0.266215 | ||||||||
\(818\) | 29131.6 | 1.24519 | ||||||||
\(819\) | 2225.28 | 0.0949419 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13142.0 | −0.558659 | −0.279329 | − | 0.960195i | \(-0.590112\pi\) | ||||
−0.279329 | + | 0.960195i | \(0.590112\pi\) | |||||||
\(822\) | −29785.7 | −1.26386 | ||||||||
\(823\) | −2536.89 | −0.107449 | −0.0537245 | − | 0.998556i | \(-0.517109\pi\) | ||||
−0.0537245 | + | 0.998556i | \(0.517109\pi\) | |||||||
\(824\) | −42802.9 | −1.80960 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33828.3 | −1.42498 | ||||||||
\(827\) | −3502.79 | −0.147284 | −0.0736421 | − | 0.997285i | \(-0.523462\pi\) | ||||
−0.0736421 | + | 0.997285i | \(0.523462\pi\) | |||||||
\(828\) | −19694.5 | −0.826609 | ||||||||
\(829\) | −4725.94 | −0.197996 | −0.0989979 | − | 0.995088i | \(-0.531564\pi\) | ||||
−0.0989979 | + | 0.995088i | \(0.531564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10226.4 | −0.426894 | ||||||||
\(832\) | −6044.85 | −0.251884 | ||||||||
\(833\) | 17706.6 | 0.736490 | ||||||||
\(834\) | 1229.27 | 0.0510385 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −74463.9 | −3.08061 | ||||||||
\(837\) | −2465.19 | −0.101804 | ||||||||
\(838\) | 4848.19 | 0.199854 | ||||||||
\(839\) | −7199.51 | −0.296251 | −0.148126 | − | 0.988969i | \(-0.547324\pi\) | ||||
−0.148126 | + | 0.988969i | \(0.547324\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5196.49 | 0.213067 | ||||||||
\(842\) | −50638.0 | −2.07257 | ||||||||
\(843\) | −13310.0 | −0.543795 | ||||||||
\(844\) | 79715.8 | 3.25111 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12000.8 | 0.487703 | ||||||||
\(847\) | 19764.6 | 0.801793 | ||||||||
\(848\) | 754.345 | 0.0305475 | ||||||||
\(849\) | 10076.4 | 0.407327 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39076.6 | 1.57406 | ||||||||
\(852\) | 45292.3 | 1.82123 | ||||||||
\(853\) | 42311.1 | 1.69836 | 0.849182 | − | 0.528100i | \(-0.177096\pi\) | ||||
0.849182 | + | 0.528100i | \(0.177096\pi\) | |||||||
\(854\) | −84511.9 | −3.38634 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22894.6 | 0.914161 | ||||||||
\(857\) | −28565.5 | −1.13860 | −0.569300 | − | 0.822130i | \(-0.692786\pi\) | ||||
−0.569300 | + | 0.822130i | \(0.692786\pi\) | |||||||
\(858\) | 4462.30 | 0.177553 | ||||||||
\(859\) | −11851.8 | −0.470755 | −0.235378 | − | 0.971904i | \(-0.575633\pi\) | ||||
−0.235378 | + | 0.971904i | \(0.575633\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24026.6 | 0.951017 | ||||||||
\(862\) | −80514.7 | −3.18137 | ||||||||
\(863\) | −27207.3 | −1.07317 | −0.536585 | − | 0.843846i | \(-0.680286\pi\) | ||||
−0.536585 | + | 0.843846i | \(0.680286\pi\) | |||||||
\(864\) | 4579.25 | 0.180312 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14084.4 | −0.552665 | ||||||||
\(867\) | −13202.9 | −0.517178 | ||||||||
\(868\) | −40472.8 | −1.58265 | ||||||||
\(869\) | 17649.1 | 0.688958 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5831.91 | 0.226874 | ||||||||
\(872\) | −53158.8 | −2.06443 | ||||||||
\(873\) | −8864.49 | −0.343663 | ||||||||
\(874\) | 98101.8 | 3.79673 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9955.45 | −0.383977 | ||||||||
\(877\) | 13750.0 | 0.529425 | 0.264712 | − | 0.964327i | \(-0.414723\pi\) | ||||
0.264712 | + | 0.964327i | \(0.414723\pi\) | |||||||
\(878\) | 58008.9 | 2.22973 | ||||||||
\(879\) | −8247.81 | −0.316486 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1662.82 | −0.0635890 | −0.0317945 | − | 0.999494i | \(-0.510122\pi\) | ||||
−0.0317945 | + | 0.999494i | \(0.510122\pi\) | |||||||
\(882\) | −32435.9 | −1.23829 | ||||||||
\(883\) | 4944.07 | 0.188427 | 0.0942136 | − | 0.995552i | \(-0.469966\pi\) | ||||
0.0942136 | + | 0.995552i | \(0.469966\pi\) | |||||||
\(884\) | 2203.57 | 0.0838393 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −30397.7 | −1.15263 | ||||||||
\(887\) | 23974.0 | 0.907519 | 0.453759 | − | 0.891124i | \(-0.350083\pi\) | ||||
0.453759 | + | 0.891124i | \(0.350083\pi\) | |||||||
\(888\) | 16995.5 | 0.642267 | ||||||||
\(889\) | −23949.2 | −0.903522 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3549.37 | −0.133455 | ||||||||
\(892\) | 70691.9 | 2.65352 | ||||||||
\(893\) | −37234.2 | −1.39529 | ||||||||
\(894\) | −28208.6 | −1.05530 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 81214.1 | 3.02809 | ||||||||
\(897\) | −3661.76 | −0.136302 | ||||||||
\(898\) | −57477.4 | −2.13591 | ||||||||
\(899\) | 15704.6 | 0.582622 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3497.27 | 0.129313 | ||||||||
\(902\) | 48180.1 | 1.77852 | ||||||||
\(903\) | 4865.01 | 0.179288 | ||||||||
\(904\) | −34509.4 | −1.26965 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −12329.6 | −0.452122 | ||||||||
\(907\) | −40692.0 | −1.48970 | −0.744850 | − | 0.667232i | \(-0.767479\pi\) | ||||
−0.744850 | + | 0.667232i | \(0.767479\pi\) | |||||||
\(908\) | −40499.8 | −1.48021 | ||||||||
\(909\) | −7248.97 | −0.264503 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5532.73 | 0.201216 | 0.100608 | − | 0.994926i | \(-0.467921\pi\) | ||||
0.100608 | + | 0.994926i | \(0.467921\pi\) | |||||||
\(912\) | 1883.17 | 0.0683751 | ||||||||
\(913\) | −4670.14 | −0.169287 | ||||||||
\(914\) | 2009.50 | 0.0727225 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 77031.8 | 2.77860 | ||||||||
\(917\) | 1435.54 | 0.0516964 | ||||||||
\(918\) | −2813.96 | −0.101171 | ||||||||
\(919\) | −29602.2 | −1.06255 | −0.531277 | − | 0.847198i | \(-0.678288\pi\) | ||||
−0.531277 | + | 0.847198i | \(0.678288\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20944.6 | −0.749348 | ||||||||
\(922\) | 54115.2 | 1.93296 | ||||||||
\(923\) | 8421.09 | 0.300307 | ||||||||
\(924\) | −58272.4 | −2.07470 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 36990.1 | 1.31271 | ||||||||
\(927\) | 16044.3 | 0.568461 | ||||||||
\(928\) | −29172.3 | −1.03192 | ||||||||
\(929\) | −8456.51 | −0.298654 | −0.149327 | − | 0.988788i | \(-0.547711\pi\) | ||||
−0.149327 | + | 0.988788i | \(0.547711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 100637. | 3.54269 | ||||||||
\(932\) | −20553.2 | −0.722363 | ||||||||
\(933\) | 21094.4 | 0.740192 | ||||||||
\(934\) | −18337.9 | −0.642434 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1592.61 | −0.0556153 | ||||||||
\(937\) | −28862.3 | −1.00629 | −0.503143 | − | 0.864203i | \(-0.667823\pi\) | ||||
−0.503143 | + | 0.864203i | \(0.667823\pi\) | |||||||
\(938\) | −122269. | −4.25609 | ||||||||
\(939\) | −9546.37 | −0.331772 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20891.0 | 0.723727 | 0.361863 | − | 0.932231i | \(-0.382141\pi\) | ||||
0.361863 | + | 0.932231i | \(0.382141\pi\) | |||||||
\(942\) | 21652.3 | 0.748908 | ||||||||
\(943\) | −39536.6 | −1.36531 | ||||||||
\(944\) | 1068.56 | 0.0368419 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9755.69 | 0.335291 | ||||||||
\(947\) | −1974.72 | −0.0677610 | −0.0338805 | − | 0.999426i | \(-0.510787\pi\) | ||||
−0.0338805 | + | 0.999426i | \(0.510787\pi\) | |||||||
\(948\) | −15965.5 | −0.546977 | ||||||||
\(949\) | −1850.99 | −0.0633149 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11892.9 | 0.405525 | ||||||||
\(952\) | −18227.2 | −0.620534 | ||||||||
\(953\) | −16786.4 | −0.570583 | −0.285292 | − | 0.958441i | \(-0.592090\pi\) | ||||
−0.285292 | + | 0.958441i | \(0.592090\pi\) | |||||||
\(954\) | −6406.51 | −0.217420 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20985.4 | −0.709953 | ||||||||
\(957\) | 22611.4 | 0.763763 | ||||||||
\(958\) | −17745.1 | −0.598452 | ||||||||
\(959\) | 72319.8 | 2.43517 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21454.7 | −0.720173 | ||||||||
\(962\) | 8009.20 | 0.268427 | ||||||||
\(963\) | −8581.82 | −0.287171 | ||||||||
\(964\) | 55826.4 | 1.86519 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 76770.5 | 2.55699 | ||||||||
\(967\) | 15006.2 | 0.499036 | 0.249518 | − | 0.968370i | \(-0.419728\pi\) | ||||
0.249518 | + | 0.968370i | \(0.419728\pi\) | |||||||
\(968\) | −14145.3 | −0.469676 | ||||||||
\(969\) | 8730.71 | 0.289444 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40317.1 | 1.33248 | 0.666240 | − | 0.745737i | \(-0.267902\pi\) | ||||
0.666240 | + | 0.745737i | \(0.267902\pi\) | |||||||
\(972\) | 3210.78 | 0.105952 | ||||||||
\(973\) | −2984.67 | −0.0983393 | ||||||||
\(974\) | 38709.7 | 1.27345 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2669.54 | 0.0875512 | ||||||||
\(977\) | −3389.00 | −0.110976 | −0.0554881 | − | 0.998459i | \(-0.517671\pi\) | ||||
−0.0554881 | + | 0.998459i | \(0.517671\pi\) | |||||||
\(978\) | 18309.7 | 0.598650 | ||||||||
\(979\) | −70497.0 | −2.30142 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19926.1 | 0.648513 | ||||||||
\(982\) | 74023.2 | 2.40547 | ||||||||
\(983\) | 57501.0 | 1.86571 | 0.932857 | − | 0.360246i | \(-0.117307\pi\) | ||||
0.932857 | + | 0.360246i | \(0.117307\pi\) | |||||||
\(984\) | −17195.6 | −0.557089 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 17926.4 | 0.579000 | ||||||||
\(987\) | −29138.0 | −0.939689 | ||||||||
\(988\) | 12524.2 | 0.403287 | ||||||||
\(989\) | −8005.52 | −0.257392 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1372.94 | 0.0440090 | 0.0220045 | − | 0.999758i | \(-0.492995\pi\) | ||||
0.0220045 | + | 0.999758i | \(0.492995\pi\) | |||||||
\(992\) | −15485.2 | −0.495622 | ||||||||
\(993\) | 33658.5 | 1.07565 | ||||||||
\(994\) | −176552. | −5.63369 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4224.63 | 0.134400 | ||||||||
\(997\) | −18947.7 | −0.601884 | −0.300942 | − | 0.953642i | \(-0.597301\pi\) | ||||
−0.300942 | + | 0.953642i | \(0.597301\pi\) | |||||||
\(998\) | −12679.4 | −0.402163 | ||||||||
\(999\) | −6370.62 | −0.201759 |
(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 | 1875.4.a.l.1.4 | yes | 24 | |
5.4 | even | 2 | 1875.4.a.k.1.21 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.4.a.k.1.21 | ✓ | 24 | 5.4 | even | 2 | ||
1875.4.a.l.1.4 | yes | 24 | 1.1 | even | 1 | trivial |