Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, 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("147.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.57516.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 24x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(5.30829\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.30829 | 1.87677 | 0.938383 | − | 0.345598i | \(-0.112324\pi\) | ||||
0.938383 | + | 0.345598i | \(0.112324\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 20.1780 | 2.52225 | ||||||||
\(5\) | 5.56140 | 0.497427 | 0.248713 | − | 0.968577i | \(-0.419992\pi\) | ||||
0.248713 | + | 0.968577i | \(0.419992\pi\) | |||||||
\(6\) | −15.9249 | −1.08355 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 64.6443 | 2.85690 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 29.5215 | 0.933553 | ||||||||
\(11\) | −13.9174 | −0.381477 | −0.190738 | − | 0.981641i | \(-0.561088\pi\) | ||||
−0.190738 | + | 0.981641i | \(0.561088\pi\) | |||||||
\(12\) | −60.5340 | −1.45622 | ||||||||
\(13\) | 38.6718 | 0.825048 | 0.412524 | − | 0.910947i | \(-0.364647\pi\) | ||||
0.412524 | + | 0.910947i | \(0.364647\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −16.6842 | −0.287189 | ||||||||
\(16\) | 181.727 | 2.83949 | ||||||||
\(17\) | 43.4788 | 0.620303 | 0.310152 | − | 0.950687i | \(-0.399620\pi\) | ||||
0.310152 | + | 0.950687i | \(0.399620\pi\) | |||||||
\(18\) | 47.7746 | 0.625588 | ||||||||
\(19\) | −109.028 | −1.31646 | −0.658228 | − | 0.752818i | \(-0.728694\pi\) | ||||
−0.658228 | + | 0.752818i | \(0.728694\pi\) | |||||||
\(20\) | 112.218 | 1.25463 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −73.8775 | −0.715943 | ||||||||
\(23\) | −74.8778 | −0.678831 | −0.339415 | − | 0.940637i | \(-0.610229\pi\) | ||||
−0.339415 | + | 0.940637i | \(0.610229\pi\) | |||||||
\(24\) | −193.933 | −1.64943 | ||||||||
\(25\) | −94.0708 | −0.752567 | ||||||||
\(26\) | 205.281 | 1.54842 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −72.3589 | −0.463335 | −0.231667 | − | 0.972795i | \(-0.574418\pi\) | ||||
−0.231667 | + | 0.972795i | \(0.574418\pi\) | |||||||
\(30\) | −88.5646 | −0.538987 | ||||||||
\(31\) | 64.0431 | 0.371048 | 0.185524 | − | 0.982640i | \(-0.440602\pi\) | ||||
0.185524 | + | 0.982640i | \(0.440602\pi\) | |||||||
\(32\) | 447.507 | 2.47215 | ||||||||
\(33\) | 41.7521 | 0.220246 | ||||||||
\(34\) | 230.798 | 1.16416 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 181.602 | 0.840749 | ||||||||
\(37\) | 188.727 | 0.838556 | 0.419278 | − | 0.907858i | \(-0.362283\pi\) | ||||
0.419278 | + | 0.907858i | \(0.362283\pi\) | |||||||
\(38\) | −578.751 | −2.47068 | ||||||||
\(39\) | −116.015 | −0.476342 | ||||||||
\(40\) | 359.513 | 1.42110 | ||||||||
\(41\) | −24.7923 | −0.0944367 | −0.0472184 | − | 0.998885i | \(-0.515036\pi\) | ||||
−0.0472184 | + | 0.998885i | \(0.515036\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −243.881 | −0.864920 | −0.432460 | − | 0.901653i | \(-0.642354\pi\) | ||||
−0.432460 | + | 0.901653i | \(0.642354\pi\) | |||||||
\(44\) | −280.825 | −0.962180 | ||||||||
\(45\) | 50.0526 | 0.165809 | ||||||||
\(46\) | −397.474 | −1.27401 | ||||||||
\(47\) | −620.549 | −1.92588 | −0.962940 | − | 0.269717i | \(-0.913070\pi\) | ||||
−0.962940 | + | 0.269717i | \(0.913070\pi\) | |||||||
\(48\) | −545.182 | −1.63938 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −499.356 | −1.41239 | ||||||||
\(51\) | −130.436 | −0.358132 | ||||||||
\(52\) | 780.319 | 2.08098 | ||||||||
\(53\) | −287.839 | −0.745995 | −0.372997 | − | 0.927832i | \(-0.621670\pi\) | ||||
−0.372997 | + | 0.927832i | \(0.621670\pi\) | |||||||
\(54\) | −143.324 | −0.361184 | ||||||||
\(55\) | −77.4001 | −0.189757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 327.083 | 0.760057 | ||||||||
\(58\) | −384.102 | −0.869571 | ||||||||
\(59\) | 525.051 | 1.15857 | 0.579287 | − | 0.815124i | \(-0.303331\pi\) | ||||
0.579287 | + | 0.815124i | \(0.303331\pi\) | |||||||
\(60\) | −336.654 | −0.724363 | ||||||||
\(61\) | −383.436 | −0.804818 | −0.402409 | − | 0.915460i | \(-0.631827\pi\) | ||||
−0.402409 | + | 0.915460i | \(0.631827\pi\) | |||||||
\(62\) | 339.960 | 0.696369 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 921.681 | 1.80016 | ||||||||
\(65\) | 215.069 | 0.410401 | ||||||||
\(66\) | 221.633 | 0.413350 | ||||||||
\(67\) | 198.117 | 0.361251 | 0.180625 | − | 0.983552i | \(-0.442188\pi\) | ||||
0.180625 | + | 0.983552i | \(0.442188\pi\) | |||||||
\(68\) | 877.314 | 1.56456 | ||||||||
\(69\) | 224.634 | 0.391923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 785.432 | 1.31287 | 0.656434 | − | 0.754384i | \(-0.272064\pi\) | ||||
0.656434 | + | 0.754384i | \(0.272064\pi\) | |||||||
\(72\) | 581.799 | 0.952301 | ||||||||
\(73\) | −331.141 | −0.530919 | −0.265459 | − | 0.964122i | \(-0.585524\pi\) | ||||
−0.265459 | + | 0.964122i | \(0.585524\pi\) | |||||||
\(74\) | 1001.82 | 1.57377 | ||||||||
\(75\) | 282.213 | 0.434495 | ||||||||
\(76\) | −2199.96 | −3.32043 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −615.844 | −0.893981 | ||||||||
\(79\) | 437.647 | 0.623280 | 0.311640 | − | 0.950200i | \(-0.399122\pi\) | ||||
0.311640 | + | 0.950200i | \(0.399122\pi\) | |||||||
\(80\) | 1010.66 | 1.41244 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −131.605 | −0.177236 | ||||||||
\(83\) | 241.241 | 0.319032 | 0.159516 | − | 0.987195i | \(-0.449007\pi\) | ||||
0.159516 | + | 0.987195i | \(0.449007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 241.803 | 0.308555 | ||||||||
\(86\) | −1294.59 | −1.62325 | ||||||||
\(87\) | 217.077 | 0.267506 | ||||||||
\(88\) | −899.680 | −1.08984 | ||||||||
\(89\) | 1585.54 | 1.88840 | 0.944198 | − | 0.329378i | \(-0.106839\pi\) | ||||
0.944198 | + | 0.329378i | \(0.106839\pi\) | |||||||
\(90\) | 265.694 | 0.311184 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1510.88 | −1.71218 | ||||||||
\(93\) | −192.129 | −0.214224 | ||||||||
\(94\) | −3294.05 | −3.61442 | ||||||||
\(95\) | −606.347 | −0.654841 | ||||||||
\(96\) | −1342.52 | −1.42730 | ||||||||
\(97\) | 79.2754 | 0.0829814 | 0.0414907 | − | 0.999139i | \(-0.486789\pi\) | ||||
0.0414907 | + | 0.999139i | \(0.486789\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −125.256 | −0.127159 | ||||||||
\(100\) | −1898.16 | −1.89816 | ||||||||
\(101\) | 1154.97 | 1.13786 | 0.568931 | − | 0.822385i | \(-0.307357\pi\) | ||||
0.568931 | + | 0.822385i | \(0.307357\pi\) | |||||||
\(102\) | −692.394 | −0.672130 | ||||||||
\(103\) | −1444.86 | −1.38220 | −0.691098 | − | 0.722761i | \(-0.742873\pi\) | ||||
−0.691098 | + | 0.722761i | \(0.742873\pi\) | |||||||
\(104\) | 2499.91 | 2.35708 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1527.93 | −1.40006 | ||||||||
\(107\) | 990.960 | 0.895325 | 0.447662 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447662 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(108\) | −544.806 | −0.485407 | ||||||||
\(109\) | 1953.17 | 1.71633 | 0.858164 | − | 0.513376i | \(-0.171605\pi\) | ||||
0.858164 | + | 0.513376i | \(0.171605\pi\) | |||||||
\(110\) | −410.862 | −0.356129 | ||||||||
\(111\) | −566.182 | −0.484141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 672.882 | 0.560172 | 0.280086 | − | 0.959975i | \(-0.409637\pi\) | ||||
0.280086 | + | 0.959975i | \(0.409637\pi\) | |||||||
\(114\) | 1736.25 | 1.42645 | ||||||||
\(115\) | −416.426 | −0.337669 | ||||||||
\(116\) | −1460.06 | −1.16865 | ||||||||
\(117\) | 348.046 | 0.275016 | ||||||||
\(118\) | 2787.13 | 2.17437 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1078.54 | −0.820472 | ||||||||
\(121\) | −1137.31 | −0.854475 | ||||||||
\(122\) | −2035.39 | −1.51045 | ||||||||
\(123\) | 74.3769 | 0.0545231 | ||||||||
\(124\) | 1292.26 | 0.935874 | ||||||||
\(125\) | −1218.34 | −0.871773 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 175.815 | 0.122843 | 0.0614216 | − | 0.998112i | \(-0.480437\pi\) | ||||
0.0614216 | + | 0.998112i | \(0.480437\pi\) | |||||||
\(128\) | 1312.50 | 0.906325 | ||||||||
\(129\) | 731.644 | 0.499362 | ||||||||
\(130\) | 1141.65 | 0.770226 | ||||||||
\(131\) | 1125.93 | 0.750939 | 0.375470 | − | 0.926835i | \(-0.377481\pi\) | ||||
0.375470 | + | 0.926835i | \(0.377481\pi\) | |||||||
\(132\) | 842.474 | 0.555515 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1051.66 | 0.677983 | ||||||||
\(135\) | −150.158 | −0.0957298 | ||||||||
\(136\) | 2810.66 | 1.77215 | ||||||||
\(137\) | 1868.70 | 1.16536 | 0.582678 | − | 0.812703i | \(-0.302005\pi\) | ||||
0.582678 | + | 0.812703i | \(0.302005\pi\) | |||||||
\(138\) | 1192.42 | 0.735548 | ||||||||
\(139\) | −2817.19 | −1.71907 | −0.859537 | − | 0.511074i | \(-0.829248\pi\) | ||||
−0.859537 | + | 0.511074i | \(0.829248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1861.65 | 1.11191 | ||||||||
\(142\) | 4169.30 | 2.46394 | ||||||||
\(143\) | −538.210 | −0.314737 | ||||||||
\(144\) | 1635.55 | 0.946496 | ||||||||
\(145\) | −402.417 | −0.230475 | ||||||||
\(146\) | −1757.79 | −0.996410 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3808.14 | 2.11505 | ||||||||
\(149\) | 1800.33 | 0.989855 | 0.494928 | − | 0.868934i | \(-0.335195\pi\) | ||||
0.494928 | + | 0.868934i | \(0.335195\pi\) | |||||||
\(150\) | 1498.07 | 0.815444 | ||||||||
\(151\) | −452.984 | −0.244128 | −0.122064 | − | 0.992522i | \(-0.538951\pi\) | ||||
−0.122064 | + | 0.992522i | \(0.538951\pi\) | |||||||
\(152\) | −7048.03 | −3.76099 | ||||||||
\(153\) | 391.309 | 0.206768 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 356.169 | 0.184569 | ||||||||
\(156\) | −2340.96 | −1.20145 | ||||||||
\(157\) | −1863.66 | −0.947364 | −0.473682 | − | 0.880696i | \(-0.657075\pi\) | ||||
−0.473682 | + | 0.880696i | \(0.657075\pi\) | |||||||
\(158\) | 2323.16 | 1.16975 | ||||||||
\(159\) | 863.517 | 0.430700 | ||||||||
\(160\) | 2488.77 | 1.22971 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 429.972 | 0.208529 | ||||||||
\(163\) | 2321.14 | 1.11537 | 0.557686 | − | 0.830052i | \(-0.311689\pi\) | ||||
0.557686 | + | 0.830052i | \(0.311689\pi\) | |||||||
\(164\) | −500.259 | −0.238193 | ||||||||
\(165\) | 232.200 | 0.109556 | ||||||||
\(166\) | 1280.58 | 0.598749 | ||||||||
\(167\) | 3211.62 | 1.48816 | 0.744079 | − | 0.668092i | \(-0.232889\pi\) | ||||
0.744079 | + | 0.668092i | \(0.232889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −701.494 | −0.319296 | ||||||||
\(170\) | 1283.56 | 0.579086 | ||||||||
\(171\) | −981.250 | −0.438819 | ||||||||
\(172\) | −4921.04 | −2.18154 | ||||||||
\(173\) | 214.277 | 0.0941687 | 0.0470844 | − | 0.998891i | \(-0.485007\pi\) | ||||
0.0470844 | + | 0.998891i | \(0.485007\pi\) | |||||||
\(174\) | 1152.31 | 0.502047 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2529.17 | −1.08320 | ||||||||
\(177\) | −1575.15 | −0.668903 | ||||||||
\(178\) | 8416.53 | 3.54408 | ||||||||
\(179\) | −2437.22 | −1.01769 | −0.508845 | − | 0.860858i | \(-0.669927\pi\) | ||||
−0.508845 | + | 0.860858i | \(0.669927\pi\) | |||||||
\(180\) | 1009.96 | 0.418211 | ||||||||
\(181\) | −248.631 | −0.102103 | −0.0510514 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510514 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1150.31 | 0.464662 | ||||||||
\(184\) | −4840.43 | −1.93935 | ||||||||
\(185\) | 1049.59 | 0.417120 | ||||||||
\(186\) | −1019.88 | −0.402049 | ||||||||
\(187\) | −605.110 | −0.236631 | ||||||||
\(188\) | −12521.4 | −4.85755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3218.67 | −1.22898 | ||||||||
\(191\) | −4313.08 | −1.63394 | −0.816972 | − | 0.576677i | \(-0.804349\pi\) | ||||
−0.816972 | + | 0.576677i | \(0.804349\pi\) | |||||||
\(192\) | −2765.04 | −1.03932 | ||||||||
\(193\) | 2060.85 | 0.768618 | 0.384309 | − | 0.923205i | \(-0.374440\pi\) | ||||
0.384309 | + | 0.923205i | \(0.374440\pi\) | |||||||
\(194\) | 420.817 | 0.155737 | ||||||||
\(195\) | −645.208 | −0.236945 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1666.09 | −0.602557 | −0.301279 | − | 0.953536i | \(-0.597413\pi\) | ||||
−0.301279 | + | 0.953536i | \(0.597413\pi\) | |||||||
\(198\) | −664.898 | −0.238648 | ||||||||
\(199\) | −1087.53 | −0.387403 | −0.193702 | − | 0.981061i | \(-0.562049\pi\) | ||||
−0.193702 | + | 0.981061i | \(0.562049\pi\) | |||||||
\(200\) | −6081.15 | −2.15001 | ||||||||
\(201\) | −594.350 | −0.208568 | ||||||||
\(202\) | 6130.94 | 2.13550 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2631.94 | −0.903298 | ||||||||
\(205\) | −137.880 | −0.0469754 | ||||||||
\(206\) | −7669.74 | −2.59406 | ||||||||
\(207\) | −673.901 | −0.226277 | ||||||||
\(208\) | 7027.72 | 2.34271 | ||||||||
\(209\) | 1517.38 | 0.502198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4676.47 | −1.52579 | −0.762895 | − | 0.646522i | \(-0.776223\pi\) | ||||
−0.762895 | + | 0.646522i | \(0.776223\pi\) | |||||||
\(212\) | −5808.01 | −1.88158 | ||||||||
\(213\) | −2356.29 | −0.757984 | ||||||||
\(214\) | 5260.31 | 1.68031 | ||||||||
\(215\) | −1356.32 | −0.430234 | ||||||||
\(216\) | −1745.40 | −0.549811 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10368.0 | 3.22114 | ||||||||
\(219\) | 993.422 | 0.306526 | ||||||||
\(220\) | −1561.78 | −0.478614 | ||||||||
\(221\) | 1681.40 | 0.511780 | ||||||||
\(222\) | −3005.46 | −0.908618 | ||||||||
\(223\) | 3246.03 | 0.974754 | 0.487377 | − | 0.873192i | \(-0.337954\pi\) | ||||
0.487377 | + | 0.873192i | \(0.337954\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −846.638 | −0.250856 | ||||||||
\(226\) | 3571.86 | 1.05131 | ||||||||
\(227\) | 5138.16 | 1.50234 | 0.751171 | − | 0.660108i | \(-0.229490\pi\) | ||||
0.751171 | + | 0.660108i | \(0.229490\pi\) | |||||||
\(228\) | 6599.88 | 1.91705 | ||||||||
\(229\) | 614.806 | 0.177413 | 0.0887064 | − | 0.996058i | \(-0.471727\pi\) | ||||
0.0887064 | + | 0.996058i | \(0.471727\pi\) | |||||||
\(230\) | −2210.51 | −0.633725 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4677.59 | −1.32370 | ||||||||
\(233\) | 2827.42 | 0.794979 | 0.397490 | − | 0.917607i | \(-0.369881\pi\) | ||||
0.397490 | + | 0.917607i | \(0.369881\pi\) | |||||||
\(234\) | 1847.53 | 0.516140 | ||||||||
\(235\) | −3451.12 | −0.957984 | ||||||||
\(236\) | 10594.5 | 2.92221 | ||||||||
\(237\) | −1312.94 | −0.359851 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3432.45 | −0.928983 | −0.464491 | − | 0.885578i | \(-0.653763\pi\) | ||||
−0.464491 | + | 0.885578i | \(0.653763\pi\) | |||||||
\(240\) | −3031.97 | −0.815471 | ||||||||
\(241\) | −2636.11 | −0.704593 | −0.352296 | − | 0.935888i | \(-0.614599\pi\) | ||||
−0.352296 | + | 0.935888i | \(0.614599\pi\) | |||||||
\(242\) | −6037.16 | −1.60365 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −7736.96 | −2.02995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 394.814 | 0.102327 | ||||||||
\(247\) | −4216.30 | −1.08614 | ||||||||
\(248\) | 4140.02 | 1.06005 | ||||||||
\(249\) | −723.724 | −0.184193 | ||||||||
\(250\) | −6467.31 | −1.63611 | ||||||||
\(251\) | 2057.57 | 0.517422 | 0.258711 | − | 0.965955i | \(-0.416702\pi\) | ||||
0.258711 | + | 0.965955i | \(0.416702\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1042.10 | 0.258958 | ||||||||
\(254\) | 933.279 | 0.230548 | ||||||||
\(255\) | −725.408 | −0.178144 | ||||||||
\(256\) | −406.321 | −0.0991996 | ||||||||
\(257\) | 2150.21 | 0.521892 | 0.260946 | − | 0.965353i | \(-0.415966\pi\) | ||||
0.260946 | + | 0.965353i | \(0.415966\pi\) | |||||||
\(258\) | 3883.78 | 0.937185 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4339.66 | 1.03513 | ||||||||
\(261\) | −651.230 | −0.154445 | ||||||||
\(262\) | 5976.77 | 1.40934 | ||||||||
\(263\) | −4590.15 | −1.07620 | −0.538100 | − | 0.842881i | \(-0.680858\pi\) | ||||
−0.538100 | + | 0.842881i | \(0.680858\pi\) | |||||||
\(264\) | 2699.04 | 0.629221 | ||||||||
\(265\) | −1600.79 | −0.371078 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4756.63 | −1.09027 | ||||||||
\(268\) | 3997.59 | 0.911164 | ||||||||
\(269\) | −379.378 | −0.0859891 | −0.0429945 | − | 0.999075i | \(-0.513690\pi\) | ||||
−0.0429945 | + | 0.999075i | \(0.513690\pi\) | |||||||
\(270\) | −797.082 | −0.179662 | ||||||||
\(271\) | −5368.84 | −1.20345 | −0.601723 | − | 0.798705i | \(-0.705519\pi\) | ||||
−0.601723 | + | 0.798705i | \(0.705519\pi\) | |||||||
\(272\) | 7901.28 | 1.76134 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9919.61 | 2.18710 | ||||||||
\(275\) | 1309.22 | 0.287087 | ||||||||
\(276\) | 4532.65 | 0.988528 | ||||||||
\(277\) | −4781.60 | −1.03718 | −0.518590 | − | 0.855023i | \(-0.673543\pi\) | ||||
−0.518590 | + | 0.855023i | \(0.673543\pi\) | |||||||
\(278\) | −14954.5 | −3.22630 | ||||||||
\(279\) | 576.388 | 0.123683 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2076.57 | −0.440845 | −0.220423 | − | 0.975404i | \(-0.570744\pi\) | ||||
−0.220423 | + | 0.975404i | \(0.570744\pi\) | |||||||
\(282\) | 9882.16 | 2.08679 | ||||||||
\(283\) | 2557.62 | 0.537224 | 0.268612 | − | 0.963248i | \(-0.413435\pi\) | ||||
0.268612 | + | 0.963248i | \(0.413435\pi\) | |||||||
\(284\) | 15848.4 | 3.31138 | ||||||||
\(285\) | 1819.04 | 0.378073 | ||||||||
\(286\) | −2856.97 | −0.590687 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4027.56 | 0.824050 | ||||||||
\(289\) | −3022.60 | −0.615224 | ||||||||
\(290\) | −2136.15 | −0.432548 | ||||||||
\(291\) | −237.826 | −0.0479093 | ||||||||
\(292\) | −6681.75 | −1.33911 | ||||||||
\(293\) | 560.049 | 0.111667 | 0.0558335 | − | 0.998440i | \(-0.482218\pi\) | ||||
0.0558335 | + | 0.998440i | \(0.482218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2920.02 | 0.576305 | ||||||||
\(296\) | 12200.2 | 2.39567 | ||||||||
\(297\) | 375.769 | 0.0734153 | ||||||||
\(298\) | 9556.66 | 1.85773 | ||||||||
\(299\) | −2895.66 | −0.560068 | ||||||||
\(300\) | 5694.48 | 1.09590 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2404.57 | −0.458171 | ||||||||
\(303\) | −3464.92 | −0.656945 | ||||||||
\(304\) | −19813.3 | −3.73806 | ||||||||
\(305\) | −2132.44 | −0.400338 | ||||||||
\(306\) | 2077.18 | 0.388054 | ||||||||
\(307\) | 3653.02 | 0.679117 | 0.339558 | − | 0.940585i | \(-0.389722\pi\) | ||||
0.339558 | + | 0.940585i | \(0.389722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4334.58 | 0.798011 | ||||||||
\(310\) | 1890.65 | 0.346393 | ||||||||
\(311\) | 3492.27 | 0.636747 | 0.318374 | − | 0.947965i | \(-0.396863\pi\) | ||||
0.318374 | + | 0.947965i | \(0.396863\pi\) | |||||||
\(312\) | −7499.73 | −1.36086 | ||||||||
\(313\) | 8712.09 | 1.57328 | 0.786640 | − | 0.617412i | \(-0.211819\pi\) | ||||
0.786640 | + | 0.617412i | \(0.211819\pi\) | |||||||
\(314\) | −9892.85 | −1.77798 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8830.83 | 1.57207 | ||||||||
\(317\) | 1940.33 | 0.343785 | 0.171892 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171892 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(318\) | 4583.80 | 0.808323 | ||||||||
\(319\) | 1007.05 | 0.176752 | ||||||||
\(320\) | 5125.84 | 0.895447 | ||||||||
\(321\) | −2972.88 | −0.516916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4740.39 | −0.816602 | ||||||||
\(324\) | 1634.42 | 0.280250 | ||||||||
\(325\) | −3637.89 | −0.620904 | ||||||||
\(326\) | 12321.3 | 2.09329 | ||||||||
\(327\) | −5859.51 | −0.990922 | ||||||||
\(328\) | −1602.68 | −0.269797 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1232.59 | 0.205611 | ||||||||
\(331\) | −5731.51 | −0.951759 | −0.475879 | − | 0.879510i | \(-0.657870\pi\) | ||||
−0.475879 | + | 0.879510i | \(0.657870\pi\) | |||||||
\(332\) | 4867.76 | 0.804678 | ||||||||
\(333\) | 1698.55 | 0.279519 | ||||||||
\(334\) | 17048.2 | 2.79292 | ||||||||
\(335\) | 1101.81 | 0.179696 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2403.74 | 0.388547 | 0.194273 | − | 0.980947i | \(-0.437765\pi\) | ||||
0.194273 | + | 0.980947i | \(0.437765\pi\) | |||||||
\(338\) | −3723.73 | −0.599244 | ||||||||
\(339\) | −2018.65 | −0.323416 | ||||||||
\(340\) | 4879.09 | 0.778253 | ||||||||
\(341\) | −891.312 | −0.141546 | ||||||||
\(342\) | −5208.76 | −0.823560 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −15765.6 | −2.47099 | ||||||||
\(345\) | 1249.28 | 0.194953 | ||||||||
\(346\) | 1137.45 | 0.176733 | ||||||||
\(347\) | −3336.44 | −0.516166 | −0.258083 | − | 0.966123i | \(-0.583091\pi\) | ||||
−0.258083 | + | 0.966123i | \(0.583091\pi\) | |||||||
\(348\) | 4380.17 | 0.674718 | ||||||||
\(349\) | −2424.54 | −0.371870 | −0.185935 | − | 0.982562i | \(-0.559531\pi\) | ||||
−0.185935 | + | 0.982562i | \(0.559531\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1044.14 | −0.158781 | ||||||||
\(352\) | −6228.12 | −0.943069 | ||||||||
\(353\) | −12403.1 | −1.87012 | −0.935059 | − | 0.354491i | \(-0.884654\pi\) | ||||
−0.935059 | + | 0.354491i | \(0.884654\pi\) | |||||||
\(354\) | −8361.38 | −1.25537 | ||||||||
\(355\) | 4368.10 | 0.653055 | ||||||||
\(356\) | 31993.1 | 4.76300 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12937.5 | −1.90997 | ||||||||
\(359\) | 1353.84 | 0.199034 | 0.0995168 | − | 0.995036i | \(-0.468270\pi\) | ||||
0.0995168 | + | 0.995036i | \(0.468270\pi\) | |||||||
\(360\) | 3235.62 | 0.473700 | ||||||||
\(361\) | 5028.05 | 0.733059 | ||||||||
\(362\) | −1319.81 | −0.191623 | ||||||||
\(363\) | 3411.92 | 0.493332 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1841.61 | −0.264093 | ||||||||
\(366\) | 6106.17 | 0.872061 | ||||||||
\(367\) | −1378.06 | −0.196006 | −0.0980031 | − | 0.995186i | \(-0.531246\pi\) | ||||
−0.0980031 | + | 0.995186i | \(0.531246\pi\) | |||||||
\(368\) | −13607.3 | −1.92753 | ||||||||
\(369\) | −223.131 | −0.0314789 | ||||||||
\(370\) | 5571.52 | 0.782837 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3876.78 | −0.540327 | ||||||||
\(373\) | 5456.92 | 0.757503 | 0.378752 | − | 0.925498i | \(-0.376353\pi\) | ||||
0.378752 | + | 0.925498i | \(0.376353\pi\) | |||||||
\(374\) | −3212.10 | −0.444101 | ||||||||
\(375\) | 3655.02 | 0.503319 | ||||||||
\(376\) | −40115.0 | −5.50205 | ||||||||
\(377\) | −2798.25 | −0.382273 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 554.675 | 0.0751761 | 0.0375881 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375881 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(380\) | −12234.9 | −1.65167 | ||||||||
\(381\) | −527.446 | −0.0709235 | ||||||||
\(382\) | −22895.1 | −3.06653 | ||||||||
\(383\) | 5860.66 | 0.781895 | 0.390948 | − | 0.920413i | \(-0.372147\pi\) | ||||
0.390948 | + | 0.920413i | \(0.372147\pi\) | |||||||
\(384\) | −3937.50 | −0.523267 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10939.6 | 1.44252 | ||||||||
\(387\) | −2194.93 | −0.288307 | ||||||||
\(388\) | 1599.62 | 0.209300 | ||||||||
\(389\) | 7778.86 | 1.01389 | 0.506946 | − | 0.861978i | \(-0.330774\pi\) | ||||
0.506946 | + | 0.861978i | \(0.330774\pi\) | |||||||
\(390\) | −3424.95 | −0.444690 | ||||||||
\(391\) | −3255.60 | −0.421081 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3377.79 | −0.433555 | ||||||||
\(394\) | −8844.08 | −1.13086 | ||||||||
\(395\) | 2433.93 | 0.310036 | ||||||||
\(396\) | −2527.42 | −0.320727 | ||||||||
\(397\) | 8027.88 | 1.01488 | 0.507440 | − | 0.861687i | \(-0.330592\pi\) | ||||
0.507440 | + | 0.861687i | \(0.330592\pi\) | |||||||
\(398\) | −5772.95 | −0.727065 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17095.2 | −2.13690 | ||||||||
\(401\) | 779.980 | 0.0971330 | 0.0485665 | − | 0.998820i | \(-0.484535\pi\) | ||||
0.0485665 | + | 0.998820i | \(0.484535\pi\) | |||||||
\(402\) | −3154.98 | −0.391434 | ||||||||
\(403\) | 2476.66 | 0.306132 | ||||||||
\(404\) | 23305.0 | 2.86997 | ||||||||
\(405\) | 450.473 | 0.0552696 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2626.59 | −0.319890 | ||||||||
\(408\) | −8431.97 | −1.02315 | ||||||||
\(409\) | 14692.5 | 1.77628 | 0.888139 | − | 0.459575i | \(-0.151998\pi\) | ||||
0.888139 | + | 0.459575i | \(0.151998\pi\) | |||||||
\(410\) | −731.907 | −0.0881617 | ||||||||
\(411\) | −5606.10 | −0.672819 | ||||||||
\(412\) | −29154.4 | −3.48624 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3577.26 | −0.424669 | ||||||||
\(415\) | 1341.64 | 0.158695 | ||||||||
\(416\) | 17305.9 | 2.03964 | ||||||||
\(417\) | 8451.58 | 0.992508 | ||||||||
\(418\) | 8054.70 | 0.942508 | ||||||||
\(419\) | 3370.31 | 0.392960 | 0.196480 | − | 0.980508i | \(-0.437049\pi\) | ||||
0.196480 | + | 0.980508i | \(0.437049\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15651.0 | 1.81184 | 0.905919 | − | 0.423450i | \(-0.139181\pi\) | ||||
0.905919 | + | 0.423450i | \(0.139181\pi\) | |||||||
\(422\) | −24824.1 | −2.86355 | ||||||||
\(423\) | −5584.94 | −0.641960 | ||||||||
\(424\) | −18607.2 | −2.13123 | ||||||||
\(425\) | −4090.08 | −0.466819 | ||||||||
\(426\) | −12507.9 | −1.42256 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19995.6 | 2.25823 | ||||||||
\(429\) | 1614.63 | 0.181713 | ||||||||
\(430\) | −7199.75 | −0.807449 | ||||||||
\(431\) | 4888.12 | 0.546294 | 0.273147 | − | 0.961972i | \(-0.411936\pi\) | ||||
0.273147 | + | 0.961972i | \(0.411936\pi\) | |||||||
\(432\) | −4906.64 | −0.546460 | ||||||||
\(433\) | −5255.73 | −0.583313 | −0.291656 | − | 0.956523i | \(-0.594206\pi\) | ||||
−0.291656 | + | 0.956523i | \(0.594206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1207.25 | 0.133065 | ||||||||
\(436\) | 39411.0 | 4.32901 | ||||||||
\(437\) | 8163.76 | 0.893651 | ||||||||
\(438\) | 5273.38 | 0.575278 | ||||||||
\(439\) | −824.977 | −0.0896902 | −0.0448451 | − | 0.998994i | \(-0.514279\pi\) | ||||
−0.0448451 | + | 0.998994i | \(0.514279\pi\) | |||||||
\(440\) | −5003.48 | −0.542117 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8925.37 | 0.960490 | ||||||||
\(443\) | 13027.3 | 1.39717 | 0.698583 | − | 0.715529i | \(-0.253814\pi\) | ||||
0.698583 | + | 0.715529i | \(0.253814\pi\) | |||||||
\(444\) | −11424.4 | −1.22112 | ||||||||
\(445\) | 8817.84 | 0.939339 | ||||||||
\(446\) | 17230.9 | 1.82939 | ||||||||
\(447\) | −5400.98 | −0.571493 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16526.1 | 1.73700 | 0.868500 | − | 0.495689i | \(-0.165084\pi\) | ||||
0.868500 | + | 0.495689i | \(0.165084\pi\) | |||||||
\(450\) | −4494.20 | −0.470797 | ||||||||
\(451\) | 345.044 | 0.0360254 | ||||||||
\(452\) | 13577.4 | 1.41289 | ||||||||
\(453\) | 1358.95 | 0.140947 | ||||||||
\(454\) | 27274.9 | 2.81954 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21144.1 | 2.17141 | ||||||||
\(457\) | −3710.82 | −0.379836 | −0.189918 | − | 0.981800i | \(-0.560822\pi\) | ||||
−0.189918 | + | 0.981800i | \(0.560822\pi\) | |||||||
\(458\) | 3263.57 | 0.332962 | ||||||||
\(459\) | −1173.93 | −0.119377 | ||||||||
\(460\) | −8402.63 | −0.851684 | ||||||||
\(461\) | −9714.00 | −0.981401 | −0.490701 | − | 0.871328i | \(-0.663259\pi\) | ||||
−0.490701 | + | 0.871328i | \(0.663259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −43.2780 | −0.00434406 | −0.00217203 | − | 0.999998i | \(-0.500691\pi\) | ||||
−0.00217203 | + | 0.999998i | \(0.500691\pi\) | |||||||
\(464\) | −13149.6 | −1.31563 | ||||||||
\(465\) | −1068.51 | −0.106561 | ||||||||
\(466\) | 15008.8 | 1.49199 | ||||||||
\(467\) | −1533.24 | −0.151927 | −0.0759633 | − | 0.997111i | \(-0.524203\pi\) | ||||
−0.0759633 | + | 0.997111i | \(0.524203\pi\) | |||||||
\(468\) | 7022.87 | 0.693659 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −18319.6 | −1.79791 | ||||||||
\(471\) | 5590.98 | 0.546961 | ||||||||
\(472\) | 33941.6 | 3.30993 | ||||||||
\(473\) | 3394.19 | 0.329947 | ||||||||
\(474\) | −6969.47 | −0.675355 | ||||||||
\(475\) | 10256.3 | 0.990722 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2590.55 | −0.248665 | ||||||||
\(478\) | −18220.5 | −1.74348 | ||||||||
\(479\) | −7035.37 | −0.671095 | −0.335547 | − | 0.942023i | \(-0.608921\pi\) | ||||
−0.335547 | + | 0.942023i | \(0.608921\pi\) | |||||||
\(480\) | −7466.30 | −0.709976 | ||||||||
\(481\) | 7298.42 | 0.691849 | ||||||||
\(482\) | −13993.3 | −1.32236 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22948.6 | −2.15520 | ||||||||
\(485\) | 440.882 | 0.0412772 | ||||||||
\(486\) | −1289.92 | −0.120395 | ||||||||
\(487\) | −15371.3 | −1.43026 | −0.715132 | − | 0.698989i | \(-0.753634\pi\) | ||||
−0.715132 | + | 0.698989i | \(0.753634\pi\) | |||||||
\(488\) | −24786.9 | −2.29929 | ||||||||
\(489\) | −6963.41 | −0.643960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2393.35 | −0.219980 | −0.109990 | − | 0.993933i | \(-0.535082\pi\) | ||||
−0.109990 | + | 0.993933i | \(0.535082\pi\) | |||||||
\(492\) | 1500.78 | 0.137521 | ||||||||
\(493\) | −3146.08 | −0.287408 | ||||||||
\(494\) | −22381.3 | −2.03843 | ||||||||
\(495\) | −696.601 | −0.0632523 | ||||||||
\(496\) | 11638.4 | 1.05359 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3841.74 | −0.345688 | ||||||||
\(499\) | 693.520 | 0.0622169 | 0.0311084 | − | 0.999516i | \(-0.490096\pi\) | ||||
0.0311084 | + | 0.999516i | \(0.490096\pi\) | |||||||
\(500\) | −24583.7 | −2.19883 | ||||||||
\(501\) | −9634.85 | −0.859188 | ||||||||
\(502\) | 10922.2 | 0.971079 | ||||||||
\(503\) | −8646.95 | −0.766498 | −0.383249 | − | 0.923645i | \(-0.625195\pi\) | ||||
−0.383249 | + | 0.923645i | \(0.625195\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6423.27 | 0.566003 | ||||||||
\(506\) | 5531.79 | 0.486004 | ||||||||
\(507\) | 2104.48 | 0.184346 | ||||||||
\(508\) | 3547.60 | 0.309841 | ||||||||
\(509\) | −15500.9 | −1.34983 | −0.674916 | − | 0.737895i | \(-0.735820\pi\) | ||||
−0.674916 | + | 0.737895i | \(0.735820\pi\) | |||||||
\(510\) | −3850.68 | −0.334335 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12656.9 | −1.09250 | ||||||||
\(513\) | 2943.75 | 0.253352 | ||||||||
\(514\) | 11413.9 | 0.979469 | ||||||||
\(515\) | −8035.44 | −0.687541 | ||||||||
\(516\) | 14763.1 | 1.25951 | ||||||||
\(517\) | 8636.41 | 0.734678 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −642.831 | −0.0543683 | ||||||||
\(520\) | 13903.0 | 1.17248 | ||||||||
\(521\) | 864.707 | 0.0727131 | 0.0363565 | − | 0.999339i | \(-0.488425\pi\) | ||||
0.0363565 | + | 0.999339i | \(0.488425\pi\) | |||||||
\(522\) | −3456.92 | −0.289857 | ||||||||
\(523\) | −6255.61 | −0.523019 | −0.261509 | − | 0.965201i | \(-0.584220\pi\) | ||||
−0.261509 | + | 0.965201i | \(0.584220\pi\) | |||||||
\(524\) | 22719.0 | 1.89406 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24365.9 | −2.01978 | ||||||||
\(527\) | 2784.51 | 0.230162 | ||||||||
\(528\) | 7587.50 | 0.625386 | ||||||||
\(529\) | −6560.31 | −0.539189 | ||||||||
\(530\) | −8497.45 | −0.696426 | ||||||||
\(531\) | 4725.46 | 0.386191 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −958.762 | −0.0779148 | ||||||||
\(534\) | −25249.6 | −2.04617 | ||||||||
\(535\) | 5511.13 | 0.445358 | ||||||||
\(536\) | 12807.1 | 1.03206 | ||||||||
\(537\) | 7311.67 | 0.587564 | ||||||||
\(538\) | −2013.85 | −0.161381 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3029.88 | −0.241454 | ||||||||
\(541\) | 143.871 | 0.0114334 | 0.00571671 | − | 0.999984i | \(-0.498180\pi\) | ||||
0.00571671 | + | 0.999984i | \(0.498180\pi\) | |||||||
\(542\) | −28499.4 | −2.25858 | ||||||||
\(543\) | 745.893 | 0.0589490 | ||||||||
\(544\) | 19457.1 | 1.53348 | ||||||||
\(545\) | 10862.4 | 0.853747 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5455.65 | 0.426448 | 0.213224 | − | 0.977003i | \(-0.431604\pi\) | ||||
0.213224 | + | 0.977003i | \(0.431604\pi\) | |||||||
\(548\) | 37706.6 | 2.93932 | ||||||||
\(549\) | −3450.92 | −0.268273 | ||||||||
\(550\) | 6949.72 | 0.538795 | ||||||||
\(551\) | 7889.13 | 0.609960 | ||||||||
\(552\) | 14521.3 | 1.11969 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25382.2 | −1.94654 | ||||||||
\(555\) | −3148.76 | −0.240824 | ||||||||
\(556\) | −56845.3 | −4.33593 | ||||||||
\(557\) | 24809.9 | 1.88730 | 0.943652 | − | 0.330940i | \(-0.107366\pi\) | ||||
0.943652 | + | 0.330940i | \(0.107366\pi\) | |||||||
\(558\) | 3059.64 | 0.232123 | ||||||||
\(559\) | −9431.33 | −0.713600 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1815.33 | 0.136619 | ||||||||
\(562\) | −11023.0 | −0.827363 | ||||||||
\(563\) | 16369.8 | 1.22541 | 0.612705 | − | 0.790312i | \(-0.290081\pi\) | ||||
0.612705 | + | 0.790312i | \(0.290081\pi\) | |||||||
\(564\) | 37564.3 | 2.80451 | ||||||||
\(565\) | 3742.17 | 0.278645 | ||||||||
\(566\) | 13576.6 | 1.00824 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 50773.7 | 3.75074 | ||||||||
\(569\) | −18450.6 | −1.35938 | −0.679691 | − | 0.733498i | \(-0.737886\pi\) | ||||
−0.679691 | + | 0.733498i | \(0.737886\pi\) | |||||||
\(570\) | 9656.00 | 0.709553 | ||||||||
\(571\) | −7108.69 | −0.520997 | −0.260499 | − | 0.965474i | \(-0.583887\pi\) | ||||
−0.260499 | + | 0.965474i | \(0.583887\pi\) | |||||||
\(572\) | −10860.0 | −0.793844 | ||||||||
\(573\) | 12939.2 | 0.943358 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7043.82 | 0.510865 | ||||||||
\(576\) | 8295.13 | 0.600053 | ||||||||
\(577\) | 7594.17 | 0.547919 | 0.273960 | − | 0.961741i | \(-0.411667\pi\) | ||||
0.273960 | + | 0.961741i | \(0.411667\pi\) | |||||||
\(578\) | −16044.8 | −1.15463 | ||||||||
\(579\) | −6182.55 | −0.443762 | ||||||||
\(580\) | −8119.96 | −0.581315 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1262.45 | −0.0899146 | ||||||||
\(583\) | 4005.96 | 0.284580 | ||||||||
\(584\) | −21406.4 | −1.51678 | ||||||||
\(585\) | 1935.62 | 0.136800 | ||||||||
\(586\) | 2972.91 | 0.209573 | ||||||||
\(587\) | −1763.34 | −0.123988 | −0.0619939 | − | 0.998077i | \(-0.519746\pi\) | ||||
−0.0619939 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6982.47 | −0.488468 | ||||||||
\(590\) | 15500.3 | 1.08159 | ||||||||
\(591\) | 4998.26 | 0.347887 | ||||||||
\(592\) | 34296.9 | 2.38107 | ||||||||
\(593\) | −12316.1 | −0.852889 | −0.426445 | − | 0.904514i | \(-0.640234\pi\) | ||||
−0.426445 | + | 0.904514i | \(0.640234\pi\) | |||||||
\(594\) | 1994.69 | 0.137783 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36327.0 | 2.49666 | ||||||||
\(597\) | 3262.60 | 0.223667 | ||||||||
\(598\) | −15371.0 | −1.05112 | ||||||||
\(599\) | −8903.40 | −0.607317 | −0.303659 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303659 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(600\) | 18243.4 | 1.24131 | ||||||||
\(601\) | −19157.1 | −1.30022 | −0.650112 | − | 0.759838i | \(-0.725278\pi\) | ||||
−0.650112 | + | 0.759838i | \(0.725278\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1783.05 | 0.120417 | ||||||||
\(604\) | −9140.31 | −0.615751 | ||||||||
\(605\) | −6325.02 | −0.425039 | ||||||||
\(606\) | −18392.8 | −1.23293 | ||||||||
\(607\) | −7569.93 | −0.506184 | −0.253092 | − | 0.967442i | \(-0.581448\pi\) | ||||
−0.253092 | + | 0.967442i | \(0.581448\pi\) | |||||||
\(608\) | −48790.7 | −3.25448 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11319.6 | −0.751340 | ||||||||
\(611\) | −23997.7 | −1.58894 | ||||||||
\(612\) | 7895.83 | 0.521519 | ||||||||
\(613\) | 2907.13 | 0.191546 | 0.0957730 | − | 0.995403i | \(-0.469468\pi\) | ||||
0.0957730 | + | 0.995403i | \(0.469468\pi\) | |||||||
\(614\) | 19391.3 | 1.27454 | ||||||||
\(615\) | 413.640 | 0.0271212 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12510.9 | −0.816320 | −0.408160 | − | 0.912910i | \(-0.633829\pi\) | ||||
−0.408160 | + | 0.912910i | \(0.633829\pi\) | |||||||
\(618\) | 23009.2 | 1.49768 | ||||||||
\(619\) | 10065.6 | 0.653585 | 0.326792 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326792 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(620\) | 7186.78 | 0.465529 | ||||||||
\(621\) | 2021.70 | 0.130641 | ||||||||
\(622\) | 18538.0 | 1.19503 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −21083.2 | −1.35257 | ||||||||
\(625\) | 4983.18 | 0.318923 | ||||||||
\(626\) | 46246.4 | 2.95268 | ||||||||
\(627\) | −4552.14 | −0.289944 | ||||||||
\(628\) | −37604.9 | −2.38949 | ||||||||
\(629\) | 8205.63 | 0.520159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25146.6 | −1.58648 | −0.793242 | − | 0.608907i | \(-0.791608\pi\) | ||||
−0.793242 | + | 0.608907i | \(0.791608\pi\) | |||||||
\(632\) | 28291.4 | 1.78065 | ||||||||
\(633\) | 14029.4 | 0.880915 | ||||||||
\(634\) | 10299.8 | 0.645203 | ||||||||
\(635\) | 977.779 | 0.0611055 | ||||||||
\(636\) | 17424.0 | 1.08633 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5345.70 | 0.331721 | ||||||||
\(639\) | 7068.88 | 0.437622 | ||||||||
\(640\) | 7299.33 | 0.450830 | ||||||||
\(641\) | −28958.9 | −1.78441 | −0.892206 | − | 0.451629i | \(-0.850843\pi\) | ||||
−0.892206 | + | 0.451629i | \(0.850843\pi\) | |||||||
\(642\) | −15780.9 | −0.970130 | ||||||||
\(643\) | 7341.90 | 0.450290 | 0.225145 | − | 0.974325i | \(-0.427714\pi\) | ||||
0.225145 | + | 0.974325i | \(0.427714\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4068.97 | 0.248396 | ||||||||
\(646\) | −25163.4 | −1.53257 | ||||||||
\(647\) | 6071.98 | 0.368955 | 0.184478 | − | 0.982837i | \(-0.440941\pi\) | ||||
0.184478 | + | 0.982837i | \(0.440941\pi\) | |||||||
\(648\) | 5236.19 | 0.317434 | ||||||||
\(649\) | −7307.33 | −0.441969 | ||||||||
\(650\) | −19311.0 | −1.16529 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 46835.9 | 2.81324 | ||||||||
\(653\) | 26262.1 | 1.57384 | 0.786920 | − | 0.617056i | \(-0.211675\pi\) | ||||
0.786920 | + | 0.617056i | \(0.211675\pi\) | |||||||
\(654\) | −31104.0 | −1.85973 | ||||||||
\(655\) | 6261.75 | 0.373537 | ||||||||
\(656\) | −4505.44 | −0.268152 | ||||||||
\(657\) | −2980.27 | −0.176973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26130.1 | 1.54459 | 0.772296 | − | 0.635263i | \(-0.219108\pi\) | ||||
0.772296 | + | 0.635263i | \(0.219108\pi\) | |||||||
\(660\) | 4685.33 | 0.276328 | ||||||||
\(661\) | −11925.5 | −0.701737 | −0.350868 | − | 0.936425i | \(-0.614114\pi\) | ||||
−0.350868 | + | 0.936425i | \(0.614114\pi\) | |||||||
\(662\) | −30424.5 | −1.78623 | ||||||||
\(663\) | −5044.20 | −0.295476 | ||||||||
\(664\) | 15594.9 | 0.911444 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9016.38 | 0.524591 | ||||||||
\(667\) | 5418.08 | 0.314526 | ||||||||
\(668\) | 64804.0 | 3.75350 | ||||||||
\(669\) | −9738.09 | −0.562775 | ||||||||
\(670\) | 5848.71 | 0.337247 | ||||||||
\(671\) | 5336.42 | 0.307019 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6359.85 | −0.364271 | −0.182135 | − | 0.983273i | \(-0.558301\pi\) | ||||
−0.182135 | + | 0.983273i | \(0.558301\pi\) | |||||||
\(674\) | 12759.8 | 0.729211 | ||||||||
\(675\) | 2539.91 | 0.144832 | ||||||||
\(676\) | −14154.7 | −0.805344 | ||||||||
\(677\) | 8561.61 | 0.486041 | 0.243020 | − | 0.970021i | \(-0.421862\pi\) | ||||
0.243020 | + | 0.970021i | \(0.421862\pi\) | |||||||
\(678\) | −10715.6 | −0.606975 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15631.2 | 0.881513 | ||||||||
\(681\) | −15414.5 | −0.867377 | ||||||||
\(682\) | −4731.34 | −0.265649 | ||||||||
\(683\) | −6705.88 | −0.375686 | −0.187843 | − | 0.982199i | \(-0.560150\pi\) | ||||
−0.187843 | + | 0.982199i | \(0.560150\pi\) | |||||||
\(684\) | −19799.6 | −1.10681 | ||||||||
\(685\) | 10392.6 | 0.579679 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1844.42 | −0.102429 | ||||||||
\(688\) | −44319.9 | −2.45593 | ||||||||
\(689\) | −11131.2 | −0.615481 | ||||||||
\(690\) | 6631.53 | 0.365881 | ||||||||
\(691\) | −25330.6 | −1.39453 | −0.697267 | − | 0.716811i | \(-0.745601\pi\) | ||||
−0.697267 | + | 0.716811i | \(0.745601\pi\) | |||||||
\(692\) | 4323.68 | 0.237517 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17710.8 | −0.968723 | ||||||||
\(695\) | −15667.5 | −0.855113 | ||||||||
\(696\) | 14032.8 | 0.764240 | ||||||||
\(697\) | −1077.94 | −0.0585794 | ||||||||
\(698\) | −12870.2 | −0.697912 | ||||||||
\(699\) | −8482.25 | −0.458981 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27184.1 | −1.46467 | −0.732333 | − | 0.680947i | \(-0.761568\pi\) | ||||
−0.732333 | + | 0.680947i | \(0.761568\pi\) | |||||||
\(702\) | −5542.59 | −0.297994 | ||||||||
\(703\) | −20576.5 | −1.10392 | ||||||||
\(704\) | −12827.4 | −0.686719 | ||||||||
\(705\) | 10353.4 | 0.553092 | ||||||||
\(706\) | −65839.5 | −3.50977 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −31783.4 | −1.68714 | ||||||||
\(709\) | 16145.5 | 0.855228 | 0.427614 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427614 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(710\) | 23187.2 | 1.22563 | ||||||||
\(711\) | 3938.82 | 0.207760 | ||||||||
\(712\) | 102496. | 5.39496 | ||||||||
\(713\) | −4795.41 | −0.251879 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2993.20 | −0.156558 | ||||||||
\(716\) | −49178.2 | −2.56687 | ||||||||
\(717\) | 10297.4 | 0.536348 | ||||||||
\(718\) | 7186.59 | 0.373539 | ||||||||
\(719\) | 17297.5 | 0.897200 | 0.448600 | − | 0.893733i | \(-0.351923\pi\) | ||||
0.448600 | + | 0.893733i | \(0.351923\pi\) | |||||||
\(720\) | 9095.92 | 0.470812 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26690.4 | 1.37578 | ||||||||
\(723\) | 7908.34 | 0.406797 | ||||||||
\(724\) | −5016.87 | −0.257528 | ||||||||
\(725\) | 6806.86 | 0.348690 | ||||||||
\(726\) | 18111.5 | 0.925868 | ||||||||
\(727\) | 3514.71 | 0.179303 | 0.0896516 | − | 0.995973i | \(-0.471425\pi\) | ||||
0.0896516 | + | 0.995973i | \(0.471425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −9775.78 | −0.495641 | ||||||||
\(731\) | −10603.7 | −0.536513 | ||||||||
\(732\) | 23210.9 | 1.17199 | ||||||||
\(733\) | −27511.2 | −1.38629 | −0.693144 | − | 0.720799i | \(-0.743775\pi\) | ||||
−0.693144 | + | 0.720799i | \(0.743775\pi\) | |||||||
\(734\) | −7315.16 | −0.367858 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33508.4 | −1.67817 | ||||||||
\(737\) | −2757.26 | −0.137809 | ||||||||
\(738\) | −1184.44 | −0.0590785 | ||||||||
\(739\) | 16101.6 | 0.801497 | 0.400749 | − | 0.916188i | \(-0.368750\pi\) | ||||
0.400749 | + | 0.916188i | \(0.368750\pi\) | |||||||
\(740\) | 21178.6 | 1.05208 | ||||||||
\(741\) | 12648.9 | 0.627083 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14682.4 | 0.724961 | 0.362480 | − | 0.931991i | \(-0.381930\pi\) | ||||
0.362480 | + | 0.931991i | \(0.381930\pi\) | |||||||
\(744\) | −12420.1 | −0.612019 | ||||||||
\(745\) | 10012.3 | 0.492380 | ||||||||
\(746\) | 28966.9 | 1.42166 | ||||||||
\(747\) | 2171.17 | 0.106344 | ||||||||
\(748\) | −12209.9 | −0.596843 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19401.9 | 0.944611 | ||||||||
\(751\) | −7273.06 | −0.353393 | −0.176696 | − | 0.984265i | \(-0.556541\pi\) | ||||
−0.176696 | + | 0.984265i | \(0.556541\pi\) | |||||||
\(752\) | −112771. | −5.46851 | ||||||||
\(753\) | −6172.72 | −0.298734 | ||||||||
\(754\) | −14853.9 | −0.717437 | ||||||||
\(755\) | −2519.23 | −0.121436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8505.93 | 0.408393 | 0.204196 | − | 0.978930i | \(-0.434542\pi\) | ||||
0.204196 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(758\) | 2944.38 | 0.141088 | ||||||||
\(759\) | −3126.31 | −0.149510 | ||||||||
\(760\) | −39196.9 | −1.87082 | ||||||||
\(761\) | 14217.7 | 0.677256 | 0.338628 | − | 0.940920i | \(-0.390037\pi\) | ||||
0.338628 | + | 0.940920i | \(0.390037\pi\) | |||||||
\(762\) | −2799.84 | −0.133107 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −87029.3 | −4.12121 | ||||||||
\(765\) | 2176.23 | 0.102852 | ||||||||
\(766\) | 31110.1 | 1.46743 | ||||||||
\(767\) | 20304.7 | 0.955879 | ||||||||
\(768\) | 1218.96 | 0.0572729 | ||||||||
\(769\) | 16379.1 | 0.768068 | 0.384034 | − | 0.923319i | \(-0.374534\pi\) | ||||
0.384034 | + | 0.923319i | \(0.374534\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6450.62 | −0.301314 | ||||||||
\(772\) | 41583.8 | 1.93865 | ||||||||
\(773\) | −39896.7 | −1.85638 | −0.928192 | − | 0.372102i | \(-0.878637\pi\) | ||||
−0.928192 | + | 0.372102i | \(0.878637\pi\) | |||||||
\(774\) | −11651.3 | −0.541084 | ||||||||
\(775\) | −6024.59 | −0.279238 | ||||||||
\(776\) | 5124.70 | 0.237070 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41292.5 | 1.90284 | ||||||||
\(779\) | 2703.05 | 0.124322 | ||||||||
\(780\) | −13019.0 | −0.597634 | ||||||||
\(781\) | −10931.1 | −0.500829 | ||||||||
\(782\) | −17281.7 | −0.790270 | ||||||||
\(783\) | 1953.69 | 0.0891688 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10364.5 | −0.471244 | ||||||||
\(786\) | −17930.3 | −0.813681 | ||||||||
\(787\) | −33128.5 | −1.50051 | −0.750257 | − | 0.661146i | \(-0.770070\pi\) | ||||
−0.750257 | + | 0.661146i | \(0.770070\pi\) | |||||||
\(788\) | −33618.3 | −1.51980 | ||||||||
\(789\) | 13770.5 | 0.621345 | ||||||||
\(790\) | 12920.0 | 0.581865 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8097.12 | −0.363281 | ||||||||
\(793\) | −14828.1 | −0.664013 | ||||||||
\(794\) | 42614.3 | 1.90469 | ||||||||
\(795\) | 4802.36 | 0.214242 | ||||||||
\(796\) | −21944.2 | −0.977127 | ||||||||
\(797\) | −17851.5 | −0.793390 | −0.396695 | − | 0.917951i | \(-0.629843\pi\) | ||||
−0.396695 | + | 0.917951i | \(0.629843\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26980.7 | −1.19463 | ||||||||
\(800\) | −42097.4 | −1.86046 | ||||||||
\(801\) | 14269.9 | 0.629465 | ||||||||
\(802\) | 4140.36 | 0.182296 | ||||||||
\(803\) | 4608.61 | 0.202533 | ||||||||
\(804\) | −11992.8 | −0.526061 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13146.8 | 0.574538 | ||||||||
\(807\) | 1138.13 | 0.0496458 | ||||||||
\(808\) | 74662.5 | 3.25076 | ||||||||
\(809\) | −5057.03 | −0.219772 | −0.109886 | − | 0.993944i | \(-0.535049\pi\) | ||||
−0.109886 | + | 0.993944i | \(0.535049\pi\) | |||||||
\(810\) | 2391.24 | 0.103728 | ||||||||
\(811\) | −17535.4 | −0.759251 | −0.379626 | − | 0.925140i | \(-0.623947\pi\) | ||||
−0.379626 | + | 0.925140i | \(0.623947\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16106.5 | 0.694810 | ||||||||
\(814\) | −13942.7 | −0.600358 | ||||||||
\(815\) | 12908.8 | 0.554815 | ||||||||
\(816\) | −23703.8 | −1.01691 | ||||||||
\(817\) | 26589.8 | 1.13863 | ||||||||
\(818\) | 77992.1 | 3.33366 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2782.14 | −0.118484 | ||||||||
\(821\) | −18700.8 | −0.794959 | −0.397480 | − | 0.917611i | \(-0.630115\pi\) | ||||
−0.397480 | + | 0.917611i | \(0.630115\pi\) | |||||||
\(822\) | −29758.8 | −1.26272 | ||||||||
\(823\) | 22222.6 | 0.941230 | 0.470615 | − | 0.882339i | \(-0.344032\pi\) | ||||
0.470615 | + | 0.882339i | \(0.344032\pi\) | |||||||
\(824\) | −93402.0 | −3.94880 | ||||||||
\(825\) | −3927.66 | −0.165750 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25178.9 | 1.05872 | 0.529358 | − | 0.848399i | \(-0.322433\pi\) | ||||
0.529358 | + | 0.848399i | \(0.322433\pi\) | |||||||
\(828\) | −13598.0 | −0.570727 | ||||||||
\(829\) | 12278.9 | 0.514432 | 0.257216 | − | 0.966354i | \(-0.417195\pi\) | ||||
0.257216 | + | 0.966354i | \(0.417195\pi\) | |||||||
\(830\) | 7121.81 | 0.297834 | ||||||||
\(831\) | 14344.8 | 0.598816 | ||||||||
\(832\) | 35643.1 | 1.48522 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 44863.5 | 1.86270 | ||||||||
\(835\) | 17861.1 | 0.740249 | ||||||||
\(836\) | 30617.7 | 1.26667 | ||||||||
\(837\) | −1729.16 | −0.0714082 | ||||||||
\(838\) | 17890.6 | 0.737494 | ||||||||
\(839\) | −25765.0 | −1.06020 | −0.530098 | − | 0.847936i | \(-0.677845\pi\) | ||||
−0.530098 | + | 0.847936i | \(0.677845\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19153.2 | −0.785321 | ||||||||
\(842\) | 83080.2 | 3.40040 | ||||||||
\(843\) | 6229.70 | 0.254522 | ||||||||
\(844\) | −94361.8 | −3.84842 | ||||||||
\(845\) | −3901.29 | −0.158826 | ||||||||
\(846\) | −29646.5 | −1.20481 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −52308.2 | −2.11824 | ||||||||
\(849\) | −7672.85 | −0.310167 | ||||||||
\(850\) | −21711.4 | −0.876111 | ||||||||
\(851\) | −14131.5 | −0.569238 | ||||||||
\(852\) | −47545.3 | −1.91182 | ||||||||
\(853\) | 37864.5 | 1.51988 | 0.759939 | − | 0.649995i | \(-0.225229\pi\) | ||||
0.759939 | + | 0.649995i | \(0.225229\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5457.12 | −0.218280 | ||||||||
\(856\) | 64060.0 | 2.55786 | ||||||||
\(857\) | −29208.7 | −1.16424 | −0.582118 | − | 0.813104i | \(-0.697776\pi\) | ||||
−0.582118 | + | 0.813104i | \(0.697776\pi\) | |||||||
\(858\) | 8570.92 | 0.341033 | ||||||||
\(859\) | 34902.9 | 1.38635 | 0.693173 | − | 0.720771i | \(-0.256212\pi\) | ||||
0.693173 | + | 0.720771i | \(0.256212\pi\) | |||||||
\(860\) | −27367.8 | −1.08516 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25947.6 | 1.02527 | ||||||||
\(863\) | −13589.3 | −0.536021 | −0.268011 | − | 0.963416i | \(-0.586366\pi\) | ||||
−0.268011 | + | 0.963416i | \(0.586366\pi\) | |||||||
\(864\) | −12082.7 | −0.475766 | ||||||||
\(865\) | 1191.68 | 0.0468420 | ||||||||
\(866\) | −27899.0 | −1.09474 | ||||||||
\(867\) | 9067.79 | 0.355200 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6090.89 | −0.237767 | ||||||||
\(870\) | 6408.44 | 0.249731 | ||||||||
\(871\) | 7661.52 | 0.298049 | ||||||||
\(872\) | 126261. | 4.90338 | ||||||||
\(873\) | 713.478 | 0.0276605 | ||||||||
\(874\) | 43335.7 | 1.67717 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20045.3 | 0.773135 | ||||||||
\(877\) | −2379.75 | −0.0916288 | −0.0458144 | − | 0.998950i | \(-0.514588\pi\) | ||||
−0.0458144 | + | 0.998950i | \(0.514588\pi\) | |||||||
\(878\) | −4379.22 | −0.168327 | ||||||||
\(879\) | −1680.15 | −0.0644709 | ||||||||
\(880\) | −14065.7 | −0.538812 | ||||||||
\(881\) | −24235.5 | −0.926803 | −0.463401 | − | 0.886148i | \(-0.653371\pi\) | ||||
−0.463401 | + | 0.886148i | \(0.653371\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9844.13 | −0.375177 | −0.187589 | − | 0.982248i | \(-0.560067\pi\) | ||||
−0.187589 | + | 0.982248i | \(0.560067\pi\) | |||||||
\(884\) | 33927.3 | 1.29084 | ||||||||
\(885\) | −8760.06 | −0.332730 | ||||||||
\(886\) | 69152.6 | 2.62215 | ||||||||
\(887\) | 28609.9 | 1.08300 | 0.541502 | − | 0.840699i | \(-0.317856\pi\) | ||||
0.541502 | + | 0.840699i | \(0.317856\pi\) | |||||||
\(888\) | −36600.5 | −1.38314 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 46807.7 | 1.76292 | ||||||||
\(891\) | −1127.31 | −0.0423863 | ||||||||
\(892\) | 65498.4 | 2.45857 | ||||||||
\(893\) | 67657.0 | 2.53534 | ||||||||
\(894\) | −28670.0 | −1.07256 | ||||||||
\(895\) | −13554.4 | −0.506226 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8686.98 | 0.323355 | ||||||||
\(898\) | 87725.2 | 3.25994 | ||||||||
\(899\) | −4634.09 | −0.171919 | ||||||||
\(900\) | −17083.4 | −0.632720 | ||||||||
\(901\) | −12514.9 | −0.462743 | ||||||||
\(902\) | 1831.59 | 0.0676113 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 43498.0 | 1.60036 | ||||||||
\(905\) | −1382.74 | −0.0507886 | ||||||||
\(906\) | 7213.72 | 0.264525 | ||||||||
\(907\) | 44578.3 | 1.63197 | 0.815986 | − | 0.578071i | \(-0.196194\pi\) | ||||
0.815986 | + | 0.578071i | \(0.196194\pi\) | |||||||
\(908\) | 103678. | 3.78928 | ||||||||
\(909\) | 10394.8 | 0.379288 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45870.6 | 1.66823 | 0.834116 | − | 0.551589i | \(-0.185978\pi\) | ||||
0.834116 | + | 0.551589i | \(0.185978\pi\) | |||||||
\(912\) | 59440.0 | 2.15817 | ||||||||
\(913\) | −3357.45 | −0.121703 | ||||||||
\(914\) | −19698.1 | −0.712863 | ||||||||
\(915\) | 6397.31 | 0.231135 | ||||||||
\(916\) | 12405.6 | 0.447479 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6231.55 | −0.224043 | ||||||||
\(919\) | 31088.3 | 1.11590 | 0.557948 | − | 0.829876i | \(-0.311589\pi\) | ||||
0.557948 | + | 0.829876i | \(0.311589\pi\) | |||||||
\(920\) | −26919.6 | −0.964686 | ||||||||
\(921\) | −10959.1 | −0.392088 | ||||||||
\(922\) | −51564.8 | −1.84186 | ||||||||
\(923\) | 30374.0 | 1.08318 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17753.7 | −0.631069 | ||||||||
\(926\) | −229.732 | −0.00815278 | ||||||||
\(927\) | −13003.7 | −0.460732 | ||||||||
\(928\) | −32381.1 | −1.14543 | ||||||||
\(929\) | −42094.5 | −1.48663 | −0.743313 | − | 0.668943i | \(-0.766747\pi\) | ||||
−0.743313 | + | 0.668943i | \(0.766747\pi\) | |||||||
\(930\) | −5671.95 | −0.199990 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 57051.5 | 2.00513 | ||||||||
\(933\) | −10476.8 | −0.367626 | ||||||||
\(934\) | −8138.87 | −0.285130 | ||||||||
\(935\) | −3365.26 | −0.117707 | ||||||||
\(936\) | 22499.2 | 0.785694 | ||||||||
\(937\) | −44385.1 | −1.54749 | −0.773745 | − | 0.633497i | \(-0.781619\pi\) | ||||
−0.773745 | + | 0.633497i | \(0.781619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26136.3 | −0.908334 | ||||||||
\(940\) | −69636.6 | −2.41627 | ||||||||
\(941\) | 40991.6 | 1.42007 | 0.710036 | − | 0.704165i | \(-0.248679\pi\) | ||||
0.710036 | + | 0.704165i | \(0.248679\pi\) | |||||||
\(942\) | 29678.5 | 1.02652 | ||||||||
\(943\) | 1856.39 | 0.0641066 | ||||||||
\(944\) | 95416.1 | 3.28976 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18017.4 | 0.619233 | ||||||||
\(947\) | −52622.4 | −1.80570 | −0.902851 | − | 0.429955i | \(-0.858530\pi\) | ||||
−0.902851 | + | 0.429955i | \(0.858530\pi\) | |||||||
\(948\) | −26492.5 | −0.907633 | ||||||||
\(949\) | −12805.8 | −0.438034 | ||||||||
\(950\) | 54443.6 | 1.85935 | ||||||||
\(951\) | −5820.99 | −0.198484 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10798.1 | −0.367035 | −0.183517 | − | 0.983016i | \(-0.558748\pi\) | ||||
−0.183517 | + | 0.983016i | \(0.558748\pi\) | |||||||
\(954\) | −13751.4 | −0.466686 | ||||||||
\(955\) | −23986.8 | −0.812768 | ||||||||
\(956\) | −69260.0 | −2.34313 | ||||||||
\(957\) | −3021.14 | −0.102048 | ||||||||
\(958\) | −37345.8 | −1.25949 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15377.5 | −0.516987 | ||||||||
\(961\) | −25689.5 | −0.862324 | ||||||||
\(962\) | 38742.2 | 1.29844 | ||||||||
\(963\) | 8918.64 | 0.298442 | ||||||||
\(964\) | −53191.4 | −1.77716 | ||||||||
\(965\) | 11461.2 | 0.382331 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15648.9 | 0.520408 | 0.260204 | − | 0.965554i | \(-0.416210\pi\) | ||||
0.260204 | + | 0.965554i | \(0.416210\pi\) | |||||||
\(968\) | −73520.4 | −2.44115 | ||||||||
\(969\) | 14221.2 | 0.471466 | ||||||||
\(970\) | 2340.33 | 0.0774675 | ||||||||
\(971\) | 47259.8 | 1.56194 | 0.780968 | − | 0.624571i | \(-0.214726\pi\) | ||||
0.780968 | + | 0.624571i | \(0.214726\pi\) | |||||||
\(972\) | −4903.25 | −0.161802 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −81595.2 | −2.68427 | ||||||||
\(975\) | 10913.7 | 0.358479 | ||||||||
\(976\) | −69680.7 | −2.28527 | ||||||||
\(977\) | −48966.5 | −1.60346 | −0.801728 | − | 0.597689i | \(-0.796086\pi\) | ||||
−0.801728 | + | 0.597689i | \(0.796086\pi\) | |||||||
\(978\) | −36963.8 | −1.20856 | ||||||||
\(979\) | −22066.6 | −0.720380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17578.5 | 0.572109 | ||||||||
\(982\) | −12704.6 | −0.412851 | ||||||||
\(983\) | −19111.3 | −0.620097 | −0.310049 | − | 0.950721i | \(-0.600345\pi\) | ||||
−0.310049 | + | 0.950721i | \(0.600345\pi\) | |||||||
\(984\) | 4808.04 | 0.155767 | ||||||||
\(985\) | −9265.77 | −0.299728 | ||||||||
\(986\) | −16700.3 | −0.539397 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −85076.4 | −2.73951 | ||||||||
\(989\) | 18261.3 | 0.587134 | ||||||||
\(990\) | −3697.76 | −0.118710 | ||||||||
\(991\) | −54102.5 | −1.73423 | −0.867115 | − | 0.498107i | \(-0.834029\pi\) | ||||
−0.867115 | + | 0.498107i | \(0.834029\pi\) | |||||||
\(992\) | 28659.7 | 0.917286 | ||||||||
\(993\) | 17194.5 | 0.549498 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6048.21 | −0.192705 | ||||||||
\(996\) | −14603.3 | −0.464581 | ||||||||
\(997\) | 9192.80 | 0.292015 | 0.146008 | − | 0.989283i | \(-0.453358\pi\) | ||||
0.146008 | + | 0.989283i | \(0.453358\pi\) | |||||||
\(998\) | 3681.41 | 0.116766 | ||||||||
\(999\) | −5095.64 | −0.161380 |
(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 | 147.4.a.l.1.3 | 3 | ||
3.2 | odd | 2 | 441.4.a.s.1.1 | 3 | |||
4.3 | odd | 2 | 2352.4.a.ci.1.2 | 3 | |||
7.2 | even | 3 | 21.4.e.b.4.1 | ✓ | 6 | ||
7.3 | odd | 6 | 147.4.e.n.79.1 | 6 | |||
7.4 | even | 3 | 21.4.e.b.16.1 | yes | 6 | ||
7.5 | odd | 6 | 147.4.e.n.67.1 | 6 | |||
7.6 | odd | 2 | 147.4.a.m.1.3 | 3 | |||
21.2 | odd | 6 | 63.4.e.c.46.3 | 6 | |||
21.5 | even | 6 | 441.4.e.w.361.3 | 6 | |||
21.11 | odd | 6 | 63.4.e.c.37.3 | 6 | |||
21.17 | even | 6 | 441.4.e.w.226.3 | 6 | |||
21.20 | even | 2 | 441.4.a.t.1.1 | 3 | |||
28.11 | odd | 6 | 336.4.q.k.289.2 | 6 | |||
28.23 | odd | 6 | 336.4.q.k.193.2 | 6 | |||
28.27 | even | 2 | 2352.4.a.cg.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.1 | ✓ | 6 | 7.2 | even | 3 | ||
21.4.e.b.16.1 | yes | 6 | 7.4 | even | 3 | ||
63.4.e.c.37.3 | 6 | 21.11 | odd | 6 | |||
63.4.e.c.46.3 | 6 | 21.2 | odd | 6 | |||
147.4.a.l.1.3 | 3 | 1.1 | even | 1 | trivial | ||
147.4.a.m.1.3 | 3 | 7.6 | odd | 2 | |||
147.4.e.n.67.1 | 6 | 7.5 | odd | 6 | |||
147.4.e.n.79.1 | 6 | 7.3 | odd | 6 | |||
336.4.q.k.193.2 | 6 | 28.23 | odd | 6 | |||
336.4.q.k.289.2 | 6 | 28.11 | odd | 6 | |||
441.4.a.s.1.1 | 3 | 3.2 | odd | 2 | |||
441.4.a.t.1.1 | 3 | 21.20 | even | 2 | |||
441.4.e.w.226.3 | 6 | 21.17 | even | 6 | |||
441.4.e.w.361.3 | 6 | 21.5 | even | 6 | |||
2352.4.a.cg.1.2 | 3 | 28.27 | even | 2 | |||
2352.4.a.ci.1.2 | 3 | 4.3 | odd | 2 |