Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.41");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.13 | ||
Character | \(\chi\) | \(=\) | 252.41 |
Dual form | 252.4.x.a.209.13 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0939923 | + | 5.19530i | 0.0180888 | + | 0.999836i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.82452 | − | 13.5525i | 0.699846 | − | 1.21217i | −0.268673 | − | 0.963231i | \(-0.586585\pi\) |
0.968519 | − | 0.248938i | \(-0.0800814\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −13.7444 | + | 12.4134i | −0.742126 | + | 0.670260i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.9823 | + | 0.976636i | −0.999346 | + | 0.0361717i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 34.2206 | − | 19.7573i | 0.937991 | − | 0.541549i | 0.0486610 | − | 0.998815i | \(-0.484505\pi\) |
0.889330 | + | 0.457266i | \(0.151171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.5318 | + | 32.0613i | 1.18475 | + | 0.684015i | 0.957109 | − | 0.289730i | \(-0.0935654\pi\) |
0.227641 | + | 0.973745i | \(0.426899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 71.1446 | + | 39.3769i | 1.22463 | + | 0.677805i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 56.6997 | 0.808923 | 0.404462 | − | 0.914555i | \(-0.367459\pi\) | ||||
0.404462 | + | 0.914555i | \(0.367459\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 117.055i | 1.41338i | 0.707525 | + | 0.706689i | \(0.249812\pi\) | ||||
−0.707525 | + | 0.706689i | \(0.750188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −65.7832 | − | 70.2394i | −0.683575 | − | 0.729880i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.59593 | − | 3.80816i | −0.0597976 | − | 0.0345242i | 0.469803 | − | 0.882771i | \(-0.344325\pi\) |
−0.529601 | + | 0.848247i | \(0.677658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −59.9462 | − | 103.830i | −0.479569 | − | 0.830638i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.61005 | − | 140.090i | −0.0542428 | − | 0.998528i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 39.8226 | − | 22.9916i | 0.254995 | − | 0.147222i | −0.367054 | − | 0.930200i | \(-0.619634\pi\) |
0.622049 | + | 0.782978i | \(0.286300\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 251.963 | + | 145.471i | 1.45980 | + | 0.842819i | 0.999001 | − | 0.0446836i | \(-0.0142280\pi\) |
0.460803 | + | 0.887502i | \(0.347561\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 105.861 | + | 175.929i | 0.558428 | + | 0.928042i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 60.6891 | + | 283.399i | 0.293095 | + | 1.36866i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −335.540 | −1.49088 | −0.745438 | − | 0.666575i | \(-0.767759\pi\) | ||||
−0.745438 | + | 0.666575i | \(0.767759\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −161.349 | + | 291.518i | −0.662473 | + | 1.19693i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 97.3000 | − | 168.529i | 0.370627 | − | 0.641945i | −0.619035 | − | 0.785363i | \(-0.712476\pi\) |
0.989662 | + | 0.143419i | \(0.0458095\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 152.264 | + | 263.729i | 0.540000 | + | 0.935308i | 0.998903 | + | 0.0468214i | \(0.0149092\pi\) |
−0.458903 | + | 0.888486i | \(0.651757\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −197.888 | + | 373.319i | −0.655542 | + | 1.23669i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 318.029 | + | 550.842i | 0.987006 | + | 1.70954i | 0.632659 | + | 0.774431i | \(0.281964\pi\) |
0.354347 | + | 0.935114i | \(0.384703\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 34.8151 | − | 341.229i | 0.101502 | − | 0.994835i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.32933 | + | 294.572i | 0.0146325 | + | 0.808791i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 274.953i | 0.712597i | 0.934372 | + | 0.356299i | \(0.115961\pi\) | ||||
−0.934372 | + | 0.356299i | \(0.884039\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 618.365i | − | 1.51600i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −608.134 | + | 11.0022i | −1.41315 | + | 0.0255663i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −258.871 | + | 448.377i | −0.571222 | + | 0.989385i | 0.425219 | + | 0.905090i | \(0.360197\pi\) |
−0.996441 | + | 0.0842947i | \(0.973136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 142.340 | − | 82.1801i | 0.298767 | − | 0.172493i | −0.343122 | − | 0.939291i | \(-0.611484\pi\) |
0.641889 | + | 0.766798i | \(0.278151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 358.732 | − | 348.366i | 0.717396 | − | 0.696666i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 869.019 | − | 501.728i | 1.65828 | − | 0.957411i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 368.103 | − | 637.573i | 0.671208 | − | 1.16257i | −0.306353 | − | 0.951918i | \(-0.599109\pi\) |
0.977562 | − | 0.210649i | \(-0.0675578\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.1646 | − | 34.6258i | 0.0334369 | − | 0.0604123i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 599.619i | − | 1.00228i | −0.865367 | − | 0.501139i | \(-0.832915\pi\) | ||
0.865367 | − | 0.501139i | \(-0.167085\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 214.435i | 0.343804i | 0.985114 | + | 0.171902i | \(0.0549913\pi\) | ||||
−0.985114 | + | 0.171902i | \(0.945009\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 533.793 | − | 321.198i | 0.821827 | − | 0.494516i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −225.086 | + | 696.345i | −0.333128 | + | 1.03060i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −454.345 | − | 786.949i | −0.647061 | − | 1.12074i | −0.983821 | − | 0.179152i | \(-0.942665\pi\) |
0.336761 | − | 0.941590i | \(-0.390669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 727.092 | − | 52.7039i | 0.997383 | − | 0.0722961i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −389.923 | − | 675.366i | −0.515658 | − | 0.893146i | −0.999835 | − | 0.0181755i | \(-0.994214\pi\) |
0.484177 | − | 0.874970i | \(-0.339119\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 443.648 | − | 768.420i | 0.566122 | − | 0.980552i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 123.191 | + | 204.729i | 0.151810 | + | 0.252290i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −443.089 | −0.527723 | −0.263862 | − | 0.964561i | \(-0.584996\pi\) | ||||
−0.263862 | + | 0.964561i | \(0.584996\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1161.24 | + | 248.676i | −1.33770 | + | 0.286465i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −732.084 | + | 1322.70i | −0.816275 | + | 1.47481i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1586.38 | + | 915.896i | 1.71325 | + | 0.989146i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 337.707 | − | 194.975i | 0.353495 | − | 0.204090i | −0.312729 | − | 0.949842i | \(-0.601243\pi\) |
0.666223 | + | 0.745752i | \(0.267910\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −904.056 | + | 566.518i | −0.917788 | + | 0.575124i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −701.270 | − | 1214.63i | −0.690881 | − | 1.19664i | −0.971550 | − | 0.236836i | \(-0.923890\pi\) |
0.280669 | − | 0.959805i | \(-0.409444\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −919.911 | − | 531.111i | −0.880015 | − | 0.508077i | −0.00935152 | − | 0.999956i | \(-0.502977\pi\) |
−0.870663 | + | 0.491879i | \(0.836310\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1466.64 | + | 341.935i | −1.36314 | + | 0.317805i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 216.811i | 0.195887i | 0.995192 | + | 0.0979433i | \(0.0312264\pi\) | ||||
−0.995192 | + | 0.0979433i | \(0.968774\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −947.744 | −0.832820 | −0.416410 | − | 0.909177i | \(-0.636712\pi\) | ||||
−0.416410 | + | 0.909177i | \(0.636712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −31.5381 | − | 1743.23i | −0.0269682 | − | 1.49063i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1219.08 | + | 703.838i | 1.01488 | + | 0.585942i | 0.912617 | − | 0.408815i | \(-0.134058\pi\) |
0.102265 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −103.220 | + | 59.5940i | −0.0836983 | + | 0.0483232i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1529.69 | − | 810.854i | −1.20872 | − | 0.640713i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −779.301 | + | 703.836i | −0.600323 | + | 0.542189i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 115.200 | − | 199.532i | 0.0865514 | − | 0.149911i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 884.702 | + | 489.662i | 0.648544 | + | 0.358954i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 79.9306 | 0.0571937 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1271.11 | 0.888131 | 0.444066 | − | 0.895994i | \(-0.353536\pi\) | ||||
0.444066 | + | 0.895994i | \(0.353536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1355.84 | + | 815.845i | −0.925387 | + | 0.556830i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 537.201 | − | 930.459i | 0.358286 | − | 0.620569i | −0.629389 | − | 0.777091i | \(-0.716695\pi\) |
0.987675 | + | 0.156521i | \(0.0500280\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1453.05 | − | 1608.84i | −0.947331 | − | 1.04890i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1958.10 | − | 992.998i | −1.24835 | − | 0.633064i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1303.13 | − | 752.364i | 0.812658 | − | 0.469188i | −0.0352200 | − | 0.999380i | \(-0.511213\pi\) |
0.847878 | + | 0.530191i | \(0.177880\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 738.300 | + | 426.257i | 0.450516 | + | 0.260106i | 0.708048 | − | 0.706164i | \(-0.249576\pi\) |
−0.257532 | + | 0.966270i | \(0.582909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2831.90 | + | 1704.03i | −1.69141 | + | 1.01777i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2533.77 | 1.48171 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 719.592i | − | 0.412130i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1776.06 | + | 148.802i | 0.996509 | + | 0.0834897i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −669.901 | − | 386.768i | −0.368325 | − | 0.212653i | 0.304401 | − | 0.952544i | \(-0.401544\pi\) |
−0.672727 | + | 0.739891i | \(0.734877\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1258.88 | − | 2180.44i | −0.678451 | − | 1.17511i | −0.975447 | − | 0.220232i | \(-0.929318\pi\) |
0.296997 | − | 0.954878i | \(-0.404015\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1529.89 | + | 55.3750i | −0.808394 | + | 0.0292601i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3942.98 | − | 2276.48i | 2.04328 | − | 1.17969i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −63.2586 | − | 36.5224i | −0.0321566 | − | 0.0185656i | 0.483836 | − | 0.875159i | \(-0.339243\pi\) |
−0.515992 | + | 0.856593i | \(0.672577\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1428.46 | + | 25.8434i | −0.712480 | + | 0.0128900i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 137.929 | − | 29.5371i | 0.0675176 | − | 0.0144587i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1604.80 | 0.771151 | 0.385576 | − | 0.922676i | \(-0.374003\pi\) | ||||
0.385576 | + | 0.922676i | \(0.374003\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3212.59 | − | 58.1215i | 1.51576 | − | 0.0274227i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −666.547 | + | 1154.49i | −0.308856 | + | 0.534954i | −0.978112 | − | 0.208077i | \(-0.933279\pi\) |
0.669257 | + | 0.743031i | \(0.266613\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 957.352 | + | 1658.18i | 0.435754 | + | 0.754749i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −114.320 | − | 3158.41i | −0.0511243 | − | 1.41245i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1234.93 | − | 2138.96i | −0.542717 | − | 0.940014i | −0.998747 | − | 0.0500494i | \(-0.984062\pi\) |
0.456029 | − | 0.889965i | \(-0.349271\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2112.80 | + | 682.939i | 0.912645 | + | 0.295002i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2353.79 | − | 1302.77i | −0.999556 | − | 0.553232i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4348.42i | 1.81573i | 0.419261 | + | 0.907866i | \(0.362289\pi\) | ||||
−0.419261 | + | 0.907866i | \(0.637711\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1523.82i | 0.625770i | 0.949791 | + | 0.312885i | \(0.101295\pi\) | ||||
−0.949791 | + | 0.312885i | \(0.898705\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 440.329 | + | 731.776i | 0.177869 | + | 0.295598i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2625.44 | + | 4547.39i | −1.04338 | + | 1.80719i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1940.30 | − | 1120.23i | 0.758763 | − | 0.438072i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1843.58 | + | 1830.98i | 0.709529 | + | 0.704677i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3370.81 | + | 1946.14i | −1.27698 | + | 0.737266i | −0.976292 | − | 0.216456i | \(-0.930550\pi\) |
−0.300690 | + | 0.953722i | \(0.597217\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −189.809 | + | 328.758i | −0.0707914 | + | 0.122614i | −0.899248 | − | 0.437438i | \(-0.855886\pi\) |
0.828457 | + | 0.560053i | \(0.189219\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2688.31 | + | 4467.66i | 0.987251 | + | 1.64070i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2916.71i | − | 1.05486i | −0.849599 | − | 0.527429i | \(-0.823156\pi\) | ||
0.849599 | − | 0.527429i | \(-0.176844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2913.59i | − | 1.03789i | −0.854809 | − | 0.518943i | \(-0.826326\pi\) | ||
0.854809 | − | 0.518943i | \(-0.173674\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3346.99 | + | 1852.48i | 1.17452 | + | 0.650069i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −261.932 | + | 810.338i | −0.0905618 | + | 0.280170i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1522.65 | − | 2637.31i | −0.518764 | − | 0.898525i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 181.693 | + | 96.3112i | 0.0610073 | + | 0.0323386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2312.68 | + | 4005.68i | 0.765413 | + | 1.32573i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −587.128 | + | 1016.93i | −0.191562 | + | 0.331795i | −0.945768 | − | 0.324843i | \(-0.894689\pi\) |
0.754206 | + | 0.656638i | \(0.228022\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3115.20 | − | 56.3596i | 1.00211 | − | 0.0181300i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4765.56 | 1.51167 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5268.87 | + | 1128.31i | −1.64827 | + | 0.352972i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1114.05 | + | 20.1552i | −0.343748 | + | 0.00621901i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3148.63 | + | 1817.86i | 0.958371 | + | 0.553316i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1611.22 | + | 930.237i | −0.483834 | + | 0.279342i | −0.722013 | − | 0.691879i | \(-0.756783\pi\) |
0.238179 | + | 0.971221i | \(0.423450\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1718.89 | + | 2743.02i | 0.509301 | + | 0.812748i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1240.21 | − | 2148.11i | −0.362624 | − | 0.628083i | 0.625768 | − | 0.780009i | \(-0.284786\pi\) |
−0.988392 | + | 0.151926i | \(0.951452\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2878.54 | − | 1661.92i | −0.830651 | − | 0.479577i | 0.0234243 | − | 0.999726i | \(-0.492543\pi\) |
−0.854076 | + | 0.520149i | \(0.825876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3638.88 | − | 1103.94i | −1.03645 | − | 0.314432i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 2378.25i | − | 0.668689i | −0.942451 | − | 0.334344i | \(-0.891485\pi\) | ||
0.942451 | − | 0.334344i | \(-0.108515\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9953.69 | 2.76301 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4045.73 | − | 2434.43i | 1.10885 | − | 0.667228i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5257.58 | − | 3035.47i | −1.42295 | − | 0.821539i | −0.426398 | − | 0.904536i | \(-0.640218\pi\) |
−0.996550 | + | 0.0829961i | \(0.973551\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3105.01 | + | 1792.68i | −0.829923 | + | 0.479156i | −0.853826 | − | 0.520558i | \(-0.825724\pi\) |
0.0239031 | + | 0.999714i | \(0.492391\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 342.154 | + | 3772.51i | 0.0903258 | + | 0.995912i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4352.08 | − | 3141.78i | −1.13487 | − | 0.819269i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3752.92 | + | 6500.25i | −0.966772 | + | 1.67450i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3472.08 | − | 2089.25i | 0.883672 | − | 0.531729i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4359.22 | −1.09622 | −0.548111 | − | 0.836406i | \(-0.684653\pi\) | ||||
−0.548111 | + | 0.836406i | \(0.684653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −300.955 | −0.0747862 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4033.88 | + | 2232.66i | 0.990632 | + | 0.548292i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1621.40 | + | 2808.35i | −0.393541 | + | 0.681634i | −0.992914 | − | 0.118837i | \(-0.962084\pi\) |
0.599372 | + | 0.800470i | \(0.295417\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4611.78 | − | 4165.19i | 1.10642 | − | 0.999275i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1052.05 | + | 659.258i | −0.249503 | + | 0.156349i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −302.312 | + | 174.540i | −0.0708796 | + | 0.0409223i | −0.535021 | − | 0.844839i | \(-0.679696\pi\) |
0.464141 | + | 0.885761i | \(0.346363\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3726.28 | + | 2151.37i | 0.863788 | + | 0.498708i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −41.6470 | − | 2301.98i | −0.00954589 | − | 0.527637i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7924.66 | 1.79619 | 0.898095 | − | 0.439802i | \(-0.144952\pi\) | ||||
0.898095 | + | 0.439802i | \(0.144952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6601.56i | 1.47976i | 0.672737 | + | 0.739882i | \(0.265119\pi\) | ||||
−0.672737 | + | 0.739882i | \(0.734881\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1401.09 | − | 6009.61i | −0.310616 | − | 1.33230i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4102.79 | − | 2368.75i | −0.899663 | − | 0.519421i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2868.51 | + | 4968.41i | 0.622210 | + | 1.07770i | 0.989073 | + | 0.147424i | \(0.0470983\pi\) |
−0.366863 | + | 0.930275i | \(0.619568\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6940.63 | − | 3679.07i | −1.48934 | − | 0.789463i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −640.561 | + | 369.828i | −0.135988 | + | 0.0785128i | −0.566451 | − | 0.824096i | \(-0.691684\pi\) |
0.430462 | + | 0.902608i | \(0.358350\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1367.20 | + | 789.355i | 0.287179 | + | 0.165803i | 0.636669 | − | 0.771137i | \(-0.280312\pi\) |
−0.349490 | + | 0.936940i | \(0.613645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4609.25 | + | 8327.80i | −0.957994 | + | 1.73086i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 754.685 | + | 3524.14i | 0.155218 | + | 0.724820i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1698.15 | −0.345643 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1044.70 | + | 1736.17i | 0.210451 | + | 0.349745i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −997.708 | + | 1728.08i | −0.198931 | + | 0.344558i | −0.948182 | − | 0.317728i | \(-0.897080\pi\) |
0.749251 | + | 0.662286i | \(0.230414\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4051.08 | + | 7016.67i | 0.799535 | + | 1.38483i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3028.21 | − | 4643.60i | −0.591631 | − | 0.907235i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −244.189 | − | 422.948i | −0.0472301 | − | 0.0818050i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5366.54 | − | 1734.67i | −1.02765 | − | 0.332175i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6244.48 | − | 3757.47i | 1.18395 | − | 0.712413i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2572.08i | − | 0.482875i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1713.47i | 0.318543i | 0.987235 | + | 0.159272i | \(0.0509146\pi\) | ||||
−0.987235 | + | 0.159272i | \(0.949085\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2672.82 | − | 4829.14i | 0.492075 | − | 0.889061i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3264.75 | − | 5654.71i | 0.595263 | − | 1.03103i | −0.398246 | − | 0.917278i | \(-0.630381\pi\) |
0.993510 | − | 0.113748i | \(-0.0362855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 377.873 | − | 218.165i | 0.0682384 | − | 0.0393975i | −0.465493 | − | 0.885052i | \(-0.654123\pi\) |
0.533731 | + | 0.845654i | \(0.320789\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1914.31 | − | 7587.49i | −0.342410 | − | 1.35716i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1201.15 | − | 693.486i | 0.212818 | − | 0.122871i | −0.389802 | − | 0.920899i | \(-0.627457\pi\) |
0.602621 | + | 0.798028i | \(0.294123\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 908.501 | − | 1573.57i | 0.159456 | − | 0.276185i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1126.40 | + | 20.3785i | −0.195855 | + | 0.00354336i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6636.96i | 1.14331i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 7687.80i | − | 1.31213i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −89.0806 | − | 4923.82i | −0.0150647 | − | 0.832684i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11208.9 | − | 3623.16i | −1.87832 | − | 0.607146i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 233.117 | + | 403.771i | 0.0387108 | + | 0.0670491i | 0.884732 | − | 0.466101i | \(-0.154342\pi\) |
−0.846021 | + | 0.533150i | \(0.821008\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9053.64 | − | 327.700i | 1.48990 | − | 0.0539275i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5760.46 | − | 9977.41i | −0.939485 | − | 1.62724i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 784.235 | − | 1358.34i | 0.126766 | − | 0.219565i | −0.795656 | − | 0.605749i | \(-0.792874\pi\) |
0.922422 | + | 0.386184i | \(0.126207\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3542.07 | + | 6399.66i | −0.567489 | + | 1.02532i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11496.4 | 1.82571 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3757.29 | + | 5122.14i | 0.591472 | + | 0.806326i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −319.311 | − | 530.657i | −0.0498293 | − | 0.0828105i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4674.58 | − | 2698.87i | −0.723184 | − | 0.417530i | 0.0927396 | − | 0.995690i | \(-0.470438\pi\) |
−0.815923 | + | 0.578160i | \(0.803771\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2247.57 | + | 1297.64i | −0.344727 | + | 0.199029i | −0.662361 | − | 0.749185i | \(-0.730445\pi\) |
0.317633 | + | 0.948214i | \(0.397112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4068.85 | − | 8023.41i | 0.618744 | − | 1.22011i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2303.43 | − | 3989.65i | −0.347306 | − | 0.601551i | 0.638464 | − | 0.769652i | \(-0.279570\pi\) |
−0.985770 | + | 0.168100i | \(0.946237\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8126.32 | − | 4691.73i | −1.21493 | − | 0.701440i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3729.89 | − | 3982.55i | −0.552960 | − | 0.590417i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2973.15i | 0.437095i | 0.975826 | + | 0.218547i | \(0.0701319\pi\) | ||||
−0.975826 | + | 0.218547i | \(0.929868\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6842.78 | −0.997635 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1047.46 | + | 579.744i | 0.151452 | + | 0.0838255i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2906.12 | + | 1677.85i | 0.416749 | + | 0.240610i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8243.22 | + | 4759.22i | −1.17246 | + | 0.676919i | −0.954258 | − | 0.298984i | \(-0.903352\pi\) |
−0.218201 | + | 0.975904i | \(0.570019\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2460.79 | + | 4642.32i | −0.347164 | + | 0.654931i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3413.10 | − | 3779.05i | −0.477626 | − | 0.528837i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 972.449 | − | 1684.33i | 0.134991 | − | 0.233811i | −0.790603 | − | 0.612329i | \(-0.790233\pi\) |
0.925594 | + | 0.378518i | \(0.123566\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.51285 | + | 415.263i | 0.00103457 | + | 0.0571843i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2948.56 | 0.402807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4140.33 | 0.561147 | 0.280573 | − | 0.959833i | \(-0.409475\pi\) | ||||
0.280573 | + | 0.959833i | \(0.409475\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 119.474 | + | 6603.80i | 0.0160652 | + | 0.887986i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 549.242 | − | 951.316i | 0.0732767 | − | 0.126919i | −0.827059 | − | 0.562115i | \(-0.809988\pi\) |
0.900336 | + | 0.435196i | \(0.143321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7676.01 | + | 8499.03i | 1.01612 | + | 1.12507i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4366.00 | − | 6967.31i | −0.573479 | − | 0.915163i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7971.13 | − | 4602.13i | 1.03895 | − | 0.599839i | 0.119416 | − | 0.992844i | \(-0.461898\pi\) |
0.919536 | + | 0.393005i | \(0.128564\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −373.987 | − | 215.921i | −0.0483717 | − | 0.0279274i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4884.51 | + | 2703.46i | 0.626949 | + | 0.347002i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14220.1 | −1.81137 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13251.6i | − | 1.67526i | −0.546237 | − | 0.837630i | \(-0.683940\pi\) | ||
0.546237 | − | 0.837630i | \(-0.316060\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8221.84 | − | 7700.23i | 1.03160 | − | 0.966149i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10109.5 | − | 5836.72i | −1.25896 | − | 0.726862i | −0.286090 | − | 0.958203i | \(-0.592356\pi\) |
−0.972873 | + | 0.231340i | \(0.925689\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9327.98 | + | 16156.5i | 1.15300 | + | 1.99706i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4974.88 | − | 10266.3i | 0.610380 | − | 1.25959i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11482.4 | + | 6629.35i | −1.39843 | + | 0.807382i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9968.20 | + | 5755.14i | 1.20512 | + | 0.695779i | 0.961690 | − | 0.274139i | \(-0.0883927\pi\) |
0.243434 | + | 0.969917i | \(0.421726\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4031.24 | + | 6699.45i | 0.483812 | + | 0.804038i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2007.87 | − | 9376.12i | −0.239227 | − | 1.11712i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12203.8 | −1.44352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2145.14 | + | 3875.75i | −0.251914 | + | 0.455148i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7814.88 | + | 13535.8i | −0.911174 | + | 1.57820i | −0.0987667 | + | 0.995111i | \(0.531490\pi\) |
−0.812408 | + | 0.583090i | \(0.801844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3771.44 | − | 6532.33i | −0.436600 | − | 0.756214i | 0.560824 | − | 0.827935i | \(-0.310484\pi\) |
−0.997425 | + | 0.0717208i | \(0.977151\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9119.13 | − | 14552.4i | −1.04820 | − | 1.67272i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3398.93 | − | 5887.12i | −0.387935 | − | 0.671922i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −936.240 | + | 2896.44i | −0.106107 | + | 0.328263i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 238.155 | + | 13163.7i | 0.0268024 | + | 1.48147i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13115.9i | − | 1.46582i | −0.680324 | − | 0.732911i | \(-0.738161\pi\) | ||
0.680324 | − | 0.732911i | \(-0.261839\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1126.39i | − | 0.125013i | −0.998045 | − | 0.0625065i | \(-0.980091\pi\) | ||
0.998045 | − | 0.0625065i | \(-0.0199094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3738.50 | − | 67.6360i | 0.412062 | − | 0.00745494i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 445.763 | − | 772.083i | 0.0487957 | − | 0.0845166i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11682.3 | + | 6744.81i | −1.27009 | + | 0.733285i | −0.975004 | − | 0.222187i | \(-0.928680\pi\) |
−0.295083 | + | 0.955472i | \(0.595347\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −606.136 | + | 9241.14i | −0.0654504 | + | 0.997856i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7184.54 | + | 4147.99i | −0.770536 | + | 0.444869i | −0.833066 | − | 0.553174i | \(-0.813417\pi\) |
0.0625295 | + | 0.998043i | \(0.480083\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3466.96 | + | 6004.95i | −0.369325 | + | 0.639690i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1946.41 | − | 3516.69i | 0.205955 | − | 0.372112i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14603.8i | 1.53496i | 0.641075 | + | 0.767478i | \(0.278489\pi\) | ||||
−0.641075 | + | 0.767478i | \(0.721511\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7689.53i | − | 0.802851i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11209.7 | − | 6745.20i | 1.16265 | − | 0.699596i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5715.96 | + | 17683.4i | −0.588941 | + | 1.82200i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 327.533 | + | 567.304i | 0.0335259 | + | 0.0580686i | 0.882302 | − | 0.470685i | \(-0.155993\pi\) |
−0.848776 | + | 0.528753i | \(0.822660\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −431.488 | − | 7943.03i | −0.0438782 | − | 0.807732i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6136.84 | − | 10629.3i | −0.620002 | − | 1.07387i | −0.989485 | − | 0.144637i | \(-0.953798\pi\) |
0.369483 | − | 0.929238i | \(-0.379535\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4612.44 | − | 7988.98i | 0.462977 | − | 0.801900i | −0.536131 | − | 0.844135i | \(-0.680115\pi\) |
0.999108 | + | 0.0422354i | \(0.0134479\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12197.6 | + | 20271.0i | 1.21645 | + | 2.02160i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14189.7 | 1.40605 | 0.703023 | − | 0.711167i | \(-0.251833\pi\) | ||||
0.703023 | + | 0.711167i | \(0.251833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2855.11 | + | 13332.5i | 0.281102 | + | 1.31266i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 183.799 | − | 332.080i | 0.0179809 | − | 0.0324872i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10421.1 | + | 6016.63i | 1.01303 | + | 0.584873i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12153.8 | − | 7016.97i | 1.17401 | − | 0.677812i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −268.529 | − | 7418.86i | −0.0257759 | − | 0.712131i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5260.23 | + | 9110.99i | 0.501766 | + | 0.869085i | 0.999998 | + | 0.00204079i | \(0.000649604\pi\) |
−0.498232 | + | 0.867044i | \(0.666017\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18633.1 | − | 10757.8i | −1.76631 | − | 1.01978i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 166.419 | + | 713.807i | 0.0156776 | + | 0.0672450i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 6102.35i | − | 0.571327i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19692.0 | 1.83230 | 0.916149 | − | 0.400838i | \(-0.131281\pi\) | ||||
0.916149 | + | 0.400838i | \(0.131281\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 150.839 | + | 8337.42i | 0.0139492 | + | 0.771025i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −585.724 | − | 338.168i | −0.0538358 | − | 0.0310821i | 0.472841 | − | 0.881148i | \(-0.343229\pi\) |
−0.526676 | + | 0.850066i | \(0.676562\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2257.93 | − | 1303.61i | 0.206272 | − | 0.119091i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 603.917 | + | 16684.9i | 0.0548365 | + | 1.51501i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7443.31 | + | 8241.38i | 0.671787 | + | 0.743816i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3095.81 | − | 5362.10i | 0.277730 | − | 0.481043i | −0.693090 | − | 0.720851i | \(-0.743751\pi\) |
0.970820 | + | 0.239808i | \(0.0770845\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6060.59 | − | 3354.40i | −0.540453 | − | 0.299129i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9490.52 | 0.841275 | 0.420638 | − | 0.907229i | \(-0.361806\pi\) | ||||
0.420638 | + | 0.907229i | \(0.361806\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21948.4 | −1.93404 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8524.78 | + | 5129.59i | −0.746743 | + | 0.449336i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6484.87 | − | 11232.1i | 0.564709 | − | 0.978104i | −0.432368 | − | 0.901697i | \(-0.642322\pi\) |
0.997077 | − | 0.0764070i | \(-0.0243448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2661.87 | − | 2947.27i | −0.230438 | − | 0.255146i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16398.1 | − | 890.792i | 1.41130 | − | 0.0766655i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −14395.7 | + | 8311.37i | −1.23175 | + | 0.711151i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21766.3 | + | 12566.8i | 1.85161 | + | 1.06902i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10996.5 | − | 6616.89i | 0.930043 | − | 0.559632i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20707.4 | 1.74128 | 0.870642 | − | 0.491917i | \(-0.163704\pi\) | ||||
0.870642 | + | 0.491917i | \(0.163704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 10537.8i | − | 0.881043i | −0.897742 | − | 0.440522i | \(-0.854794\pi\) | ||
0.897742 | − | 0.440522i | \(-0.145206\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3349.49 | + | 11040.8i | −0.278445 | + | 0.917832i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14286.2 | + | 8248.16i | 1.18087 | + | 0.681775i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6054.50 | − | 10486.7i | −0.497616 | − | 0.861896i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6547.03 | − | 12351.1i | 0.535060 | − | 1.00940i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10806.5 | − | 6239.13i | 0.878200 | − | 0.507029i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2938.32 | + | 1696.44i | 0.237448 | + | 0.137090i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22591.3 | + | 408.718i | −1.81543 | + | 0.0328444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5550.35 | − | 12364.9i | −0.443545 | − | 0.988115i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11394.7 | 0.905542 | 0.452771 | − | 0.891627i | \(-0.350436\pi\) | ||||
0.452771 | + | 0.891627i | \(0.350436\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7916.68 | + | 143.227i | −0.625667 | + | 0.0113194i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7415.64 | + | 12844.3i | −0.582846 | + | 1.00952i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11353.1 | − | 19664.1i | −0.887426 | − | 1.53707i | −0.842908 | − | 0.538058i | \(-0.819158\pi\) |
−0.0445177 | − | 0.999009i | \(-0.514175\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3760.41 | + | 2356.43i | −0.292332 | + | 0.183187i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2691.27 | + | 4661.41i | 0.208080 | + | 0.360404i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16013.4 | + | 5176.14i | 1.23139 | + | 0.398033i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −23871.8 | − | 13212.5i | −1.82577 | − | 1.01052i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6229.16i | 0.473857i | 0.971527 | + | 0.236928i | \(0.0761407\pi\) | ||||
−0.971527 | + | 0.236928i | \(0.923859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19527.1i | 1.47747i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6002.31 | + | 9975.14i | 0.451725 | + | 0.750714i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1558.81 | − | 2699.94i | 0.116689 | − | 0.202112i | −0.801764 | − | 0.597640i | \(-0.796105\pi\) |
0.918454 | + | 0.395528i | \(0.129438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19077.5 | − | 11014.4i | 1.42052 | − | 0.820139i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9339.19 | + | 9750.07i | −0.691727 | + | 0.722159i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10879.4 | − | 6281.22i | 0.801561 | − | 0.462781i | −0.0424558 | − | 0.999098i | \(-0.513518\pi\) |
0.844017 | + | 0.536317i | \(0.180185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3644.80 | − | 6312.98i | 0.267128 | − | 0.462679i | −0.700991 | − | 0.713170i | \(-0.747259\pi\) |
0.968119 | + | 0.250491i | \(0.0805920\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10427.6 | − | 17329.5i | −0.760244 | − | 1.26344i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 913.138i | 0.0662269i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5616.75i | 0.405248i | 0.979257 | + | 0.202624i | \(0.0649470\pi\) | ||||
−0.979257 | + | 0.202624i | \(0.935053\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1725.84 | − | 955.213i | −0.123875 | − | 0.0685618i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13742.8 | + | 4442.21i | 0.981323 | + | 0.317201i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5432.31 | + | 9409.04i | 0.385906 | + | 0.668410i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22958.1 | + | 14386.5i | −1.62257 | + | 1.01677i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −897.050 | − | 1553.74i | −0.0630753 | − | 0.109250i | 0.832763 | − | 0.553629i | \(-0.186758\pi\) |
−0.895839 | + | 0.444380i | \(0.853424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17028.1 | + | 29493.5i | −1.19122 | + | 2.06325i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15153.2 | − | 274.148i | 1.05469 | − | 0.0190811i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16863.9 | 1.16782 | 0.583912 | − | 0.811817i | \(-0.301521\pi\) | ||||
0.583912 | + | 0.811817i | \(0.301521\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3441.05 | + | 16068.6i | 0.237091 | + | 1.10714i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15137.0 | − | 273.855i | 1.03772 | − | 0.0187741i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12704.3 | − | 7334.84i | −0.866585 | − | 0.500323i | −0.000372774 | − | 1.00000i | \(-0.500119\pi\) |
−0.866212 | + | 0.499677i | \(0.833452\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −854.824 | + | 493.533i | −0.0580183 | + | 0.0334969i | −0.528729 | − | 0.848791i | \(-0.677331\pi\) |
0.470710 | + | 0.882288i | \(0.343998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9309.60 | + | 17562.7i | −0.628717 | + | 1.18608i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1802.77 | − | 3122.48i | −0.121145 | − | 0.209830i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12623.0 | − | 7287.87i | −0.844069 | − | 0.487323i | 0.0145763 | − | 0.999894i | \(-0.495360\pi\) |
−0.858645 | + | 0.512570i | \(0.828693\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4234.57 | − | 1284.65i | −0.281763 | − | 0.0854790i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 40785.7i | 2.70051i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20361.1 | −1.34156 | −0.670780 | − | 0.741656i | \(-0.734041\pi\) | ||||
−0.670780 | + | 0.741656i | \(0.734041\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 13558.5 | − | 8158.52i | 0.888994 | − | 0.534932i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3623.21 | − | 2091.86i | −0.236410 | − | 0.136491i | 0.377116 | − | 0.926166i | \(-0.376916\pi\) |
−0.613526 | + | 0.789675i | \(0.710249\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24006.3 | + | 13860.0i | −1.55879 | + | 0.899970i | −0.561421 | + | 0.827530i | \(0.689745\pi\) |
−0.997373 | + | 0.0724400i | \(0.976921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −483.288 | + | 953.001i | −0.0312298 | + | 0.0615823i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6089.98 | − | 5500.24i | 0.391637 | − | 0.353712i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8118.69 | − | 14062.0i | 0.519596 | − | 0.899967i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20593.3 | + | 12391.6i | −1.31167 | + | 0.789269i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19025.0 | −1.20600 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6437.94 | 0.406165 | 0.203083 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203083 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5338.47 | − | 2954.72i | −0.335206 | − | 0.185529i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9945.81 | − | 17226.7i | 0.621555 | − | 1.07657i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12873.6 | − | 17832.8i | 0.800737 | − | 1.10920i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 585.610 | + | 16179.1i | 0.0362541 | + | 1.00162i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25430.0 | − | 14682.0i | 1.56696 | − | 0.904687i | 0.570444 | − | 0.821336i | \(-0.306771\pi\) |
0.996520 | − | 0.0833510i | \(-0.0265622\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 951.096 | + | 549.116i | 0.0583321 | + | 0.0336781i | 0.528882 | − | 0.848695i | \(-0.322611\pi\) |
−0.470550 | + | 0.882373i | \(0.655945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 447.926 | + | 24758.5i | 0.0273443 | + | 1.51142i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8485.25 | −0.515595 | −0.257797 | − | 0.966199i | \(-0.582997\pi\) | ||||
−0.257797 | + | 0.966199i | \(0.582997\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20458.3i | 1.23738i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6357.16 | − | 27267.3i | −0.382729 | − | 1.64161i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2743.06 | + | 1583.71i | 0.164386 | + | 0.0949085i | 0.579936 | − | 0.814662i | \(-0.303077\pi\) |
−0.415550 | + | 0.909570i | \(0.636411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8406.67 | − | 14560.8i | −0.501490 | − | 0.868606i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −209.425 | − | 5785.95i | −0.0124360 | − | 0.343579i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13457.9 | − | 7769.91i | 0.795516 | − | 0.459291i | −0.0463851 | − | 0.998924i | \(-0.514770\pi\) |
0.841901 | + | 0.539632i | \(0.181437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9109.85 | − | 5259.57i | −0.536054 | − | 0.309491i | 0.207424 | − | 0.978251i | \(-0.433492\pi\) |
−0.743478 | + | 0.668760i | \(0.766825\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9148.41 | + | 16529.0i | −0.535890 | + | 0.968223i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33173.1 | + | 7103.94i | −1.93443 | + | 0.414254i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −350.222 | −0.0203308 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4984.30 | − | 8283.32i | −0.288048 | − | 0.478702i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3247.31 | − | 5624.51i | 0.186827 | − | 0.323594i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14642.5 | − | 25361.6i | −0.838674 | − | 1.45263i | −0.891004 | − | 0.453996i | \(-0.849998\pi\) |
0.0523297 | − | 0.998630i | \(-0.483335\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14089.3 | + | 9187.98i | −0.803402 | + | 0.523919i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2923.06 | + | 5062.89i | 0.165941 | + | 0.287419i | 0.936989 | − | 0.349358i | \(-0.113600\pi\) |
−0.771048 | + | 0.636777i | \(0.780267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2221.26 | + | 6871.91i | −0.125544 | + | 0.388394i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11043.5 | − | 6645.17i | 0.621421 | − | 0.373926i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 7438.18i | − | 0.416712i | −0.978053 | − | 0.208356i | \(-0.933189\pi\) | ||
0.978053 | − | 0.208356i | \(-0.0668112\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 23547.5i | − | 1.31344i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8363.64 | − | 15111.1i | 0.464473 | − | 0.839190i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8815.33 | + | 15268.6i | −0.487427 | + | 0.844249i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7016.10 | − | 4050.75i | 0.386259 | − | 0.223007i | −0.294279 | − | 0.955720i | \(-0.595079\pi\) |
0.680538 | + | 0.732713i | \(0.261746\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5393.26 | − | 19008.8i | 0.295632 | − | 1.04197i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11553.7 | − | 6670.52i | 0.630584 | − | 0.364068i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5516.88 | − | 9555.51i | 0.299809 | − | 0.519284i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12355.7 | − | 223.537i | 0.668579 | − | 0.0120958i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 80.5954i | 0.00434243i | 0.999998 | + | 0.00217122i | \(0.000691120\pi\) | ||||
−0.999998 | + | 0.00217122i | \(0.999309\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 39276.5i | − | 2.10717i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 935.570 | + | 51712.4i | 0.0499796 | + | 2.76256i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24716.2 | + | 7989.24i | 1.31478 | + | 0.424988i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10309.1 | − | 17855.8i | −0.546071 | − | 0.945823i | −0.998539 | − | 0.0540423i | \(-0.982789\pi\) |
0.452467 | − | 0.891781i | \(-0.350544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13027.8 | + | 20790.0i | 0.687177 | + | 1.09660i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1107.95 | − | 1919.03i | −0.0581952 | − | 0.100797i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19825.6 | − | 34338.9i | 1.03697 | − | 1.79609i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15276.0 | − | 27600.0i | 0.795666 | − | 1.43758i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7395.39 | 0.383591 | 0.191795 | − | 0.981435i | \(-0.438569\pi\) | ||||
0.191795 | + | 0.981435i | \(0.438569\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19236.5 | − | 4119.44i | 0.993626 | − | 0.212782i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9605.36 | − | 15963.0i | −0.494090 | − | 0.821120i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4774.42 | − | 2756.51i | −0.244576 | − | 0.141206i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2335.91 | + | 1348.64i | −0.119167 | + | 0.0688008i | −0.558398 | − | 0.829573i | \(-0.688584\pi\) |
0.439232 | + | 0.898374i | \(0.355251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19567.2 | + | 2132.18i | −0.994115 | + | 0.108326i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8633.31 | + | 14953.3i | 0.436819 | + | 0.756592i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34067.8 | − | 19669.0i | −1.71667 | − | 0.991122i | −0.924813 | − | 0.380421i | \(-0.875779\pi\) |
−0.791861 | − | 0.610701i | \(-0.790888\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15913.4 | − | 22905.6i | 0.798606 | − | 1.14951i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 29090.9i | − | 1.45397i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16780.5 | −0.835293 | −0.417646 | − | 0.908610i | \(-0.637145\pi\) | ||||
−0.417646 | + | 0.908610i | \(0.637145\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −34123.5 | − | 18886.6i | −1.69171 | − | 0.936324i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10852.9 | + | 6265.91i | 0.535873 | + | 0.309386i | 0.743405 | − | 0.668842i | \(-0.233210\pi\) |
−0.207532 | + | 0.978228i | \(0.566543\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10483.3 | + | 6052.54i | −0.515542 | + | 0.297648i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11180.6 | + | 17842.1i | 0.547627 | + | 0.873909i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2691.36 | − | 2979.92i | −0.131295 | − | 0.145373i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5313.64 | + | 9203.49i | −0.258186 | + | 0.447190i | −0.965756 | − | 0.259452i | \(-0.916458\pi\) |
0.707570 | + | 0.706643i | \(0.249791\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −409.733 | − | 22647.5i | −0.0198293 | − | 1.09604i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39400.5 | −1.89924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19420.8 | 0.932443 | 0.466221 | − | 0.884668i | \(-0.345615\pi\) | ||||
0.466221 | + | 0.884668i | \(0.345615\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.2875 | − | 1563.55i | −0.00135279 | − | 0.0747739i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1129.12 | − | 1955.70i | 0.0537854 | − | 0.0931591i | −0.837879 | − | 0.545856i | \(-0.816205\pi\) |
0.891665 | + | 0.452697i | \(0.149538\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13026.1 | − | 11764.7i | 0.618058 | − | 0.558207i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11220.2 | + | 21167.1i | −0.530283 | + | 1.00039i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28751.1 | + | 16599.5i | −1.35351 | + | 0.781449i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6652.81 | + | 3841.00i | 0.311972 | + | 0.180117i | 0.647809 | − | 0.761803i | \(-0.275686\pi\) |
−0.335837 | + | 0.941920i | \(0.609019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14742.6 | − | 8159.70i | −0.688641 | − | 0.381147i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13041.2 | 0.606804 | 0.303402 | − | 0.952863i | \(-0.401878\pi\) | ||||
0.303402 | + | 0.952863i | \(0.401878\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 34881.7i | − | 1.61676i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 22072.9 | + | 23568.1i | 1.01913 | + | 1.08816i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19727.0 | + | 11389.4i | 0.907310 | + | 0.523836i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11846.8 | − | 20519.3i | −0.542783 | − | 0.940127i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3523.93 | − | 5403.76i | −0.160836 | − | 0.246634i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −989.936 | + | 571.540i | −0.0450093 | + | 0.0259861i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7894.38 | + | 4557.83i | 0.357566 | + | 0.206441i | 0.668013 | − | 0.744150i | \(-0.267145\pi\) |
−0.310447 | + | 0.950591i | \(0.600479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −935.201 | − | 1554.19i | −0.0421978 | − | 0.0701277i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25492.5 | + | 5459.16i | −1.14590 | + | 0.245392i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10539.2 | 0.471952 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10826.8 | + | 19561.4i | −0.483002 | + | 0.872668i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22246.7 | + | 38532.4i | −0.988729 | + | 1.71253i | −0.364709 | + | 0.931122i | \(0.618831\pi\) |
−0.624021 | + | 0.781408i | \(0.714502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18032.1 | + | 31232.6i | 0.798412 | + | 1.38289i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11955.6 | − | 432.737i | 0.527378 | − | 0.0190887i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4236.65 | + | 7338.09i | 0.186187 | + | 0.322485i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 678.927 | − | 2100.39i | 0.0297255 | − | 0.0919616i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 744.857 | + | 41171.0i | 0.0324909 | + | 1.79590i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8457.35i | 0.367546i | 0.982969 | + | 0.183773i | \(0.0588311\pi\) | ||||
−0.982969 | + | 0.183773i | \(0.941169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26796.4i | 1.16023i | 0.814533 | + | 0.580117i | \(0.196993\pi\) | ||||
−0.814533 | + | 0.580117i | \(0.803007\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −34297.1 | + | 620.495i | −1.47952 | + | 0.0267672i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12556.8 | − | 21749.0i | 0.539687 | − | 0.934766i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30870.6 | + | 17823.2i | −1.32194 | + | 0.763224i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 31090.1 | − | 7843.97i | 1.32646 | − | 0.334665i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24830.3 | − | 14335.8i | 1.05552 | − | 0.609405i | 0.131331 | − | 0.991339i | \(-0.458075\pi\) |
0.924190 | + | 0.381933i | \(0.124742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11603.6 | + | 20098.0i | −0.491464 | + | 0.851241i | −0.999952 | − | 0.00982871i | \(-0.996871\pi\) |
0.508488 | + | 0.861069i | \(0.330205\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11920.7 | − | 21537.9i | 0.503062 | − | 0.908912i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1777.49i | 0.0747393i | 0.999302 | + | 0.0373696i | \(0.0118979\pi\) | ||||
−0.999302 | + | 0.0373696i | \(0.988102\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 13834.0i | − | 0.579585i | −0.957090 | − | 0.289792i | \(-0.906414\pi\) | ||
0.957090 | − | 0.289792i | \(-0.0935862\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25542.8 | + | 15369.8i | −1.06627 | + | 0.641602i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1974.00 | − | 19347.5i | 0.0821071 | − | 0.804745i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10430.8 | + | 18066.7i | 0.432303 | + | 0.748771i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18461.5 | − | 36404.5i | 0.762394 | − | 1.50337i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12455.4 | + | 21573.4i | 0.512526 | + | 0.887721i | 0.999895 | + | 0.0145243i | \(0.00462340\pi\) |
−0.487369 | + | 0.873196i | \(0.662043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11137.3 | + | 19290.3i | −0.456652 | + | 0.790944i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1981.58 | − | 3293.15i | −0.0809598 | − | 0.134546i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 29963.3 | 1.21984 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 893.522 | + | 4172.46i | 0.0362477 | + | 0.169265i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3972.43 | + | 7177.22i | −0.160581 | + | 0.290132i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2213.19 | + | 1277.79i | 0.0891508 | + | 0.0514712i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3041.79 | + | 1756.18i | −0.122097 | + | 0.0704928i | −0.559805 | − | 0.828625i | \(-0.689124\pi\) |
0.437708 | + | 0.899117i | \(0.355791\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43698.7 | − | 23163.7i | −1.74791 | − | 0.926528i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8211.64 | − | 14223.0i | −0.327310 | − | 0.566917i | 0.654667 | − | 0.755917i | \(-0.272809\pi\) |
−0.981977 | + | 0.189000i | \(0.939475\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1430.46 | + | 825.876i | 0.0568180 | + | 0.0328039i | 0.528140 | − | 0.849157i | \(-0.322890\pi\) |
−0.471322 | + | 0.881961i | \(0.656223\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18238.0 | + | 4252.06i | −0.721894 | + | 0.168304i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 20778.9i | − | 0.819610i | −0.912173 | − | 0.409805i | \(-0.865597\pi\) | ||
0.912173 | − | 0.409805i | \(-0.134403\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38651.0 | −1.51927 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −159.613 | − | 8822.38i | −0.00625228 | − | 0.345587i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31095.9 | − | 17953.2i | −1.21387 | − | 0.700831i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40882.8 | − | 23603.7i | 1.59043 | − | 0.918234i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8921.71 | + | 5590.71i | −0.345881 | + | 0.216743i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1098.59 | + | 992.210i | −0.0424449 | + | 0.0383346i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19789.9 | − | 34277.1i | 0.761981 | − | 1.31979i | −0.179846 | − | 0.983695i | \(-0.557560\pi\) |
0.941828 | − | 0.336096i | \(-0.109107\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9071.68 | − | 5020.97i | −0.348100 | − | 0.192666i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15881.0 | −0.607314 | −0.303657 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303657 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10903.6 | 0.415555 | 0.207778 | − | 0.978176i | \(-0.433377\pi\) | ||||
0.207778 | + | 0.978176i | \(0.433377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36072.9 | + | 21706.1i | −1.37015 | + | 0.824454i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23758.1 | − | 41150.3i | 0.899346 | − | 1.55771i | 0.0710149 | − | 0.997475i | \(-0.477376\pi\) |
0.828331 | − | 0.560238i | \(-0.189290\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17470.6 | + | 15778.8i | −0.659105 | + | 0.595279i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 23840.3 | − | 16168.9i | 0.896385 | − | 0.607945i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −64478.6 | + | 37226.7i | −2.41623 | + | 1.39501i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 58931.7 | + | 34024.3i | 2.20097 | + | 1.27073i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2174.39 | − | 1308.39i | 0.0809373 | − | 0.0487022i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13378.4 | 0.496324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15589.7i | 0.576436i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8507.73 | − | 28043.8i | 0.313532 | − | 1.03349i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20651.5 | + | 11923.1i | 0.758539 | + | 0.437942i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10606.5 | − | 18371.0i | −0.388294 | − | 0.672545i | 0.603926 | − | 0.797040i | \(-0.293602\pi\) |
−0.992220 | + | 0.124495i | \(0.960269\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20108.1 | + | 32088.8i | 0.733713 | + | 1.17087i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14559.0 | − | 8405.62i | 0.529484 | − | 0.305698i | −0.211322 | − | 0.977416i | \(-0.567777\pi\) |
0.740806 | + | 0.671719i | \(0.234444\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26686.8 | − | 15407.6i | −0.967365 | − | 0.558508i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13362.7 | − | 241.756i | 0.482796 | − | 0.00873464i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4166.68 | + | 19457.1i | 0.150050 | + | 0.700685i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34695.2 | −1.24536 | −0.622682 | − | 0.782475i | \(-0.713957\pi\) | ||||
−0.622682 | + | 0.782475i | \(0.713957\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8901.98 | + | 161.053i | −0.318491 | + | 0.00576207i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19224.6 | − | 33297.9i | 0.685573 | − | 1.18745i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20114.3 | + | 34839.0i | 0.714978 | + | 1.23838i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25340.0 | + | 13432.2i | 0.897817 | + | 0.475913i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22217.1 | + | 38481.2i | 0.784628 | + | 1.35902i | 0.929221 | + | 0.369525i | \(0.120480\pi\) |
−0.144592 | + | 0.989491i | \(0.546187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39942.4 | + | 4075.27i | 1.40608 | + | 0.143460i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29684.8 | + | 16429.9i | 1.04162 | + | 0.576516i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 35061.1i | − | 1.22633i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39975.1i | 1.39374i | 0.717199 | + | 0.696868i | \(0.245424\pi\) | ||||
−0.717199 | + | 0.696868i | \(0.754576\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1168.95 | + | 1942.66i | 0.0406254 | + | 0.0675146i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15218.5 | − | 26359.2i | 0.527214 | − | 0.913161i | −0.472283 | − | 0.881447i | \(-0.656570\pi\) |
0.999497 | − | 0.0317144i | \(-0.0100967\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1283.57 | + | 741.068i | −0.0443252 | + | 0.0255912i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 39239.4 | − | 10658.6i | 1.35075 | − | 0.366904i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13622.3 | + | 7864.86i | −0.467441 | + | 0.269877i | −0.715168 | − | 0.698953i | \(-0.753650\pi\) |
0.247727 | + | 0.968830i | \(0.420316\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6875.06 | + | 11908.0i | −0.235167 | + | 0.407322i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3715.77 | + | 6175.17i | 0.126700 | + | 0.210561i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1741.59i | − | 0.0591979i | −0.999562 | − | 0.0295990i | \(-0.990577\pi\) | ||
0.999562 | − | 0.0295990i | \(-0.00942302\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60910.4i | 2.06389i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8260.57 | + | 4572.04i | 0.279024 | + | 0.154434i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8571.34 | + | 26517.1i | −0.288616 | + | 0.892889i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27428.2 | + | 47507.0i | 0.920686 | + | 1.59468i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −211.745 | − | 5850.05i | −0.00708556 | − | 0.195758i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2970.32 | + | 5144.75i | 0.0990861 | + | 0.171622i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4096.53 | − | 7095.40i | 0.136231 | − | 0.235959i | −0.789836 | − | 0.613318i | \(-0.789834\pi\) |
0.926067 | + | 0.377359i | \(0.123168\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −34481.0 | + | 623.823i | −1.14313 | + | 0.0206812i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7844.92 | −0.259275 | −0.129637 | − | 0.991561i | \(-0.541381\pi\) | ||||
−0.129637 | + | 0.991561i | \(0.541381\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15438.8 | + | 3306.17i | −0.508678 | + | 0.108932i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39940.5 | − | 722.594i | 1.31192 | − | 0.0237349i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43445.7 | + | 25083.4i | 1.42267 | + | 0.821380i | 0.996527 | − | 0.0832744i | \(-0.0265378\pi\) |
0.426146 | + | 0.904655i | \(0.359871\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15162.8 | + | 8754.23i | −0.494999 | + | 0.285788i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25572.3 | − | 925.601i | 0.832275 | − | 0.0301245i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 653.927 | + | 1132.63i | 0.0212177 | + | 0.0367502i | 0.876439 | − | 0.481512i | \(-0.159912\pi\) |
−0.855222 | + | 0.518263i | \(0.826579\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39528.6 | − | 22821.9i | −1.27867 | − | 0.738238i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17769.8 | − | 58574.3i | 0.573070 | − | 1.88900i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2319.38i | − | 0.0745722i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43094.8 | −1.38138 | −0.690691 | − | 0.723150i | \(-0.742694\pi\) | ||||
−0.690691 | + | 0.723150i | \(0.742694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2075.80 | + | 1249.07i | −0.0663379 | + | 0.0399173i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39486.4 | − | 22797.5i | −1.25809 | − | 0.726360i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7444.26 | + | 4297.95i | −0.236471 | + | 0.136527i | −0.613554 | − | 0.789653i | \(-0.710261\pi\) |
0.377082 | + | 0.926180i | \(0.376927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2553.47 | + | 47005.6i | 0.0808692 | + | 1.48868i |
(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 | 252.4.x.a.41.13 | yes | 48 | |
3.2 | odd | 2 | 756.4.x.a.125.4 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.41.12 | ✓ | 48 | |
9.2 | odd | 6 | inner | 252.4.x.a.209.12 | yes | 48 | |
9.4 | even | 3 | 2268.4.f.a.1133.7 | 48 | |||
9.5 | odd | 6 | 2268.4.f.a.1133.42 | 48 | |||
9.7 | even | 3 | 756.4.x.a.629.21 | 48 | |||
21.20 | even | 2 | 756.4.x.a.125.21 | 48 | |||
63.13 | odd | 6 | 2268.4.f.a.1133.41 | 48 | |||
63.20 | even | 6 | inner | 252.4.x.a.209.13 | yes | 48 | |
63.34 | odd | 6 | 756.4.x.a.629.4 | 48 | |||
63.41 | even | 6 | 2268.4.f.a.1133.8 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.12 | ✓ | 48 | 7.6 | odd | 2 | inner | |
252.4.x.a.41.13 | yes | 48 | 1.1 | even | 1 | trivial | |
252.4.x.a.209.12 | yes | 48 | 9.2 | odd | 6 | inner | |
252.4.x.a.209.13 | yes | 48 | 63.20 | even | 6 | inner | |
756.4.x.a.125.4 | 48 | 3.2 | odd | 2 | |||
756.4.x.a.125.21 | 48 | 21.20 | even | 2 | |||
756.4.x.a.629.4 | 48 | 63.34 | odd | 6 | |||
756.4.x.a.629.21 | 48 | 9.7 | even | 3 | |||
2268.4.f.a.1133.7 | 48 | 9.4 | even | 3 | |||
2268.4.f.a.1133.8 | 48 | 63.41 | even | 6 | |||
2268.4.f.a.1133.41 | 48 | 63.13 | odd | 6 | |||
2268.4.f.a.1133.42 | 48 | 9.5 | odd | 6 |