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 | 209.13 | ||
Character | \(\chi\) | \(=\) | 252.209 |
Dual form | 252.4.x.a.41.13 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
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 | 0.968519 | + | 0.248938i | \(0.0800814\pi\) |
−0.268673 | + | 0.963231i | \(0.586585\pi\) | |||||||
\(6\) | 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 | 0.889330 | − | 0.457266i | \(-0.151171\pi\) |
0.0486610 | + | 0.998815i | \(0.484505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 55.5318 | − | 32.0613i | 1.18475 | − | 0.684015i | 0.227641 | − | 0.973745i | \(-0.426899\pi\) |
0.957109 | + | 0.289730i | \(0.0935654\pi\) | |||||||
\(14\) | 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 | \(-0.750188\pi\) | ||
0.707525 | − | 0.706689i | \(-0.249812\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −65.7832 | + | 70.2394i | −0.683575 | + | 0.729880i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.59593 | + | 3.80816i | −0.0597976 | + | 0.0345242i | −0.529601 | − | 0.848247i | \(-0.677658\pi\) |
0.469803 | + | 0.882771i | \(0.344325\pi\) | |||||||
\(24\) | 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 | 0.622049 | − | 0.782978i | \(-0.286300\pi\) |
−0.367054 | + | 0.930200i | \(0.619634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 251.963 | − | 145.471i | 1.45980 | − | 0.842819i | 0.460803 | − | 0.887502i | \(-0.347561\pi\) |
0.999001 | + | 0.0446836i | \(0.0142280\pi\) | |||||||
\(32\) | 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 | 0.989662 | − | 0.143419i | \(-0.0458095\pi\) |
−0.619035 | + | 0.785363i | \(0.712476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 152.264 | − | 263.729i | 0.540000 | − | 0.935308i | −0.458903 | − | 0.888486i | \(-0.651757\pi\) |
0.998903 | − | 0.0468214i | \(-0.0149092\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −197.888 | − | 373.319i | −0.655542 | − | 1.23669i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 318.029 | − | 550.842i | 0.987006 | − | 1.70954i | 0.354347 | − | 0.935114i | \(-0.384703\pi\) |
0.632659 | − | 0.774431i | \(-0.281964\pi\) | |||||||
\(48\) | 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 | \(-0.884039\pi\) | ||
0.934372 | − | 0.356299i | \(-0.115961\pi\) | |||||||
\(54\) | 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 | −0.996441 | − | 0.0842947i | \(-0.973136\pi\) |
0.425219 | − | 0.905090i | \(-0.360197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 142.340 | + | 82.1801i | 0.298767 | + | 0.172493i | 0.641889 | − | 0.766798i | \(-0.278151\pi\) |
−0.343122 | + | 0.939291i | \(0.611484\pi\) | |||||||
\(62\) | 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 | 0.977562 | + | 0.210649i | \(0.0675578\pi\) |
−0.306353 | + | 0.951918i | \(0.599109\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.1646 | + | 34.6258i | 0.0334369 | + | 0.0604123i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 599.619i | 1.00228i | 0.865367 | + | 0.501139i | \(0.167085\pi\) | ||||
−0.865367 | + | 0.501139i | \(0.832915\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 214.435i | − | 0.343804i | −0.985114 | − | 0.171902i | \(-0.945009\pi\) | ||
0.985114 | − | 0.171902i | \(-0.0549913\pi\) | |||||||
\(74\) | 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 | 0.336761 | + | 0.941590i | \(0.390669\pi\) |
−0.983821 | + | 0.179152i | \(0.942665\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 727.092 | + | 52.7039i | 0.997383 | + | 0.0722961i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −389.923 | + | 675.366i | −0.515658 | + | 0.893146i | 0.484177 | + | 0.874970i | \(0.339119\pi\) |
−0.999835 | + | 0.0181755i | \(0.994214\pi\) | |||||||
\(84\) | 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 | 0.666223 | − | 0.745752i | \(-0.267910\pi\) |
−0.312729 | + | 0.949842i | \(0.601243\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −904.056 | − | 566.518i | −0.917788 | − | 0.575124i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −701.270 | + | 1214.63i | −0.690881 | + | 1.19664i | 0.280669 | + | 0.959805i | \(0.409444\pi\) |
−0.971550 | + | 0.236836i | \(0.923890\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −919.911 | + | 531.111i | −0.880015 | + | 0.508077i | −0.870663 | − | 0.491879i | \(-0.836310\pi\) |
−0.00935152 | + | 0.999956i | \(0.502977\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1466.64 | − | 341.935i | −1.36314 | − | 0.317805i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 216.811i | − | 0.195887i | −0.995192 | − | 0.0979433i | \(-0.968774\pi\) | ||
0.995192 | − | 0.0979433i | \(-0.0312264\pi\) | |||||||
\(108\) | 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 | 0.102265 | − | 0.994757i | \(-0.467391\pi\) |
0.912617 | + | 0.408815i | \(0.134058\pi\) | |||||||
\(114\) | 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 | 0.987675 | − | 0.156521i | \(-0.0500280\pi\) |
−0.629389 | + | 0.777091i | \(0.716695\pi\) | |||||||
\(132\) | 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 | 0.847878 | − | 0.530191i | \(-0.177880\pi\) |
−0.0352200 | + | 0.999380i | \(0.511213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 738.300 | − | 426.257i | 0.450516 | − | 0.260106i | −0.257532 | − | 0.966270i | \(-0.582909\pi\) |
0.708048 | + | 0.706164i | \(0.249576\pi\) | |||||||
\(140\) | 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 | −0.672727 | − | 0.739891i | \(-0.734877\pi\) |
0.304401 | + | 0.952544i | \(0.401544\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1258.88 | + | 2180.44i | −0.678451 | + | 1.17511i | 0.296997 | + | 0.954878i | \(0.404015\pi\) |
−0.975447 | + | 0.220232i | \(0.929318\pi\) | |||||||
\(152\) | 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 | −0.515992 | − | 0.856593i | \(-0.672577\pi\) |
0.483836 | + | 0.875159i | \(0.339243\pi\) | |||||||
\(158\) | 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 | 0.669257 | − | 0.743031i | \(-0.266613\pi\) |
−0.978112 | + | 0.208077i | \(0.933279\pi\) | |||||||
\(168\) | 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 | 0.456029 | + | 0.889965i | \(0.349271\pi\) |
−0.998747 | + | 0.0500494i | \(0.984062\pi\) | |||||||
\(174\) | 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 | \(-0.637711\pi\) | ||
0.419261 | − | 0.907866i | \(-0.362289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1523.82i | − | 0.625770i | −0.949791 | − | 0.312885i | \(-0.898705\pi\) | ||
0.949791 | − | 0.312885i | \(-0.101295\pi\) | |||||||
\(182\) | 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 | −0.300690 | − | 0.953722i | \(-0.597217\pi\) |
−0.976292 | + | 0.216456i | \(0.930550\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −189.809 | − | 328.758i | −0.0707914 | − | 0.122614i | 0.828457 | − | 0.560053i | \(-0.189219\pi\) |
−0.899248 | + | 0.437438i | \(0.855886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2688.31 | − | 4467.66i | 0.987251 | − | 1.64070i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2916.71i | 1.05486i | 0.849599 | + | 0.527429i | \(0.176844\pi\) | ||||
−0.849599 | + | 0.527429i | \(0.823156\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2913.59i | 1.03789i | 0.854809 | + | 0.518943i | \(0.173674\pi\) | ||||
−0.854809 | + | 0.518943i | \(0.826326\pi\) | |||||||
\(200\) | 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 | 0.754206 | − | 0.656638i | \(-0.228022\pi\) |
−0.945768 | + | 0.324843i | \(0.894689\pi\) | |||||||
\(212\) | 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 | 0.238179 | − | 0.971221i | \(-0.423450\pi\) |
−0.722013 | + | 0.691879i | \(0.756783\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1718.89 | − | 2743.02i | 0.509301 | − | 0.812748i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1240.21 | + | 2148.11i | −0.362624 | + | 0.628083i | −0.988392 | − | 0.151926i | \(-0.951452\pi\) |
0.625768 | + | 0.780009i | \(0.284786\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2878.54 | + | 1661.92i | −0.830651 | + | 0.479577i | −0.854076 | − | 0.520149i | \(-0.825876\pi\) |
0.0234243 | + | 0.999726i | \(0.492543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3638.88 | + | 1103.94i | −1.03645 | + | 0.314432i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2378.25i | 0.668689i | 0.942451 | + | 0.334344i | \(0.108515\pi\) | ||||
−0.942451 | + | 0.334344i | \(0.891485\pi\) | |||||||
\(234\) | 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 | −0.996550 | − | 0.0829961i | \(-0.973551\pi\) |
−0.426398 | + | 0.904536i | \(0.640218\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3105.01 | − | 1792.68i | −0.829923 | − | 0.479156i | 0.0239031 | − | 0.999714i | \(-0.492391\pi\) |
−0.853826 | + | 0.520558i | \(0.825724\pi\) | |||||||
\(242\) | 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 | 0.599372 | − | 0.800470i | \(-0.295417\pi\) |
−0.992914 | + | 0.118837i | \(0.962084\pi\) | |||||||
\(258\) | 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 | 0.464141 | − | 0.885761i | \(-0.346363\pi\) |
−0.535021 | + | 0.844839i | \(0.679696\pi\) | |||||||
\(264\) | 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 | \(-0.734881\pi\) | ||
0.672737 | − | 0.739882i | \(-0.265119\pi\) | |||||||
\(272\) | 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 | −0.366863 | − | 0.930275i | \(-0.619568\pi\) |
0.989073 | − | 0.147424i | \(-0.0470983\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6940.63 | + | 3679.07i | −1.48934 | + | 0.789463i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −640.561 | − | 369.828i | −0.135988 | − | 0.0785128i | 0.430462 | − | 0.902608i | \(-0.358350\pi\) |
−0.566451 | + | 0.824096i | \(0.691684\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1367.20 | − | 789.355i | 0.287179 | − | 0.165803i | −0.349490 | − | 0.936940i | \(-0.613645\pi\) |
0.636669 | + | 0.771137i | \(0.280312\pi\) | |||||||
\(284\) | 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 | 0.749251 | − | 0.662286i | \(-0.230414\pi\) |
−0.948182 | + | 0.317728i | \(0.897080\pi\) | |||||||
\(294\) | 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 | \(-0.949085\pi\) | ||
0.987235 | − | 0.159272i | \(-0.0509146\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2672.82 | + | 4829.14i | 0.492075 | + | 0.889061i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3264.75 | + | 5654.71i | 0.595263 | + | 1.03103i | 0.993510 | + | 0.113748i | \(0.0362855\pi\) |
−0.398246 | + | 0.917278i | \(0.630381\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 377.873 | + | 218.165i | 0.0682384 | + | 0.0393975i | 0.533731 | − | 0.845654i | \(-0.320789\pi\) |
−0.465493 | + | 0.885052i | \(0.654123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1914.31 | + | 7587.49i | −0.342410 | + | 1.35716i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1201.15 | + | 693.486i | 0.212818 | + | 0.122871i | 0.602621 | − | 0.798028i | \(-0.294123\pi\) |
−0.389802 | + | 0.920899i | \(0.627457\pi\) | |||||||
\(318\) | 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 | −0.846021 | − | 0.533150i | \(-0.821008\pi\) |
0.884732 | + | 0.466101i | \(0.154342\pi\) | |||||||
\(332\) | 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 | 0.922422 | − | 0.386184i | \(-0.126207\pi\) |
−0.795656 | + | 0.605749i | \(0.792874\pi\) | |||||||
\(338\) | 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 | −0.815923 | − | 0.578160i | \(-0.803771\pi\) |
0.0927396 | + | 0.995690i | \(0.470438\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2247.57 | − | 1297.64i | −0.344727 | − | 0.199029i | 0.317633 | − | 0.948214i | \(-0.397112\pi\) |
−0.662361 | + | 0.749185i | \(0.730445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4068.85 | + | 8023.41i | 0.618744 | + | 1.22011i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2303.43 | + | 3989.65i | −0.347306 | + | 0.601551i | −0.985770 | − | 0.168100i | \(-0.946237\pi\) |
0.638464 | + | 0.769652i | \(0.279570\pi\) | |||||||
\(354\) | 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 | \(-0.929868\pi\) | ||
0.975826 | − | 0.218547i | \(-0.0701319\pi\) | |||||||
\(360\) | 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 | −0.218201 | − | 0.975904i | \(-0.570019\pi\) |
−0.954258 | + | 0.298984i | \(0.903352\pi\) | |||||||
\(368\) | 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 | 0.925594 | − | 0.378518i | \(-0.123566\pi\) |
−0.790603 | + | 0.612329i | \(0.790233\pi\) | |||||||
\(374\) | 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 | 0.900336 | − | 0.435196i | \(-0.143321\pi\) |
−0.827059 | + | 0.562115i | \(0.809988\pi\) | |||||||
\(384\) | 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 | 0.919536 | − | 0.393005i | \(-0.128564\pi\) |
0.119416 | + | 0.992844i | \(0.461898\pi\) | |||||||
\(390\) | 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 | \(0.316060\pi\) | ||||
−0.546237 | + | 0.837630i | \(0.683940\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8221.84 | + | 7700.23i | 1.03160 | + | 0.966149i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10109.5 | + | 5836.72i | −1.25896 | + | 0.726862i | −0.972873 | − | 0.231340i | \(-0.925689\pi\) |
−0.286090 | + | 0.958203i | \(0.592356\pi\) | |||||||
\(402\) | 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 | 0.243434 | − | 0.969917i | \(-0.421726\pi\) |
0.961690 | + | 0.274139i | \(0.0883927\pi\) | |||||||
\(410\) | 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 | −0.812408 | − | 0.583090i | \(-0.801844\pi\) |
−0.0987667 | − | 0.995111i | \(-0.531490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3771.44 | + | 6532.33i | −0.436600 | + | 0.756214i | −0.997425 | − | 0.0717208i | \(-0.977151\pi\) |
0.560824 | + | 0.827935i | \(0.310484\pi\) | |||||||
\(422\) | 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 | \(0.261839\pi\) | ||||
−0.680324 | + | 0.732911i | \(0.738161\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1126.39i | 0.125013i | 0.998045 | + | 0.0625065i | \(0.0199094\pi\) | ||||
−0.998045 | + | 0.0625065i | \(0.980091\pi\) | |||||||
\(434\) | 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 | −0.295083 | − | 0.955472i | \(-0.595347\pi\) |
−0.975004 | + | 0.222187i | \(0.928680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −606.136 | − | 9241.14i | −0.0654504 | − | 0.997856i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7184.54 | − | 4147.99i | −0.770536 | − | 0.444869i | 0.0625295 | − | 0.998043i | \(-0.480083\pi\) |
−0.833066 | + | 0.553174i | \(0.813417\pi\) | |||||||
\(444\) | 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 | \(-0.721511\pi\) | ||
0.641075 | − | 0.767478i | \(-0.278489\pi\) | |||||||
\(450\) | 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 | −0.848776 | − | 0.528753i | \(-0.822660\pi\) |
0.882302 | + | 0.470685i | \(0.155993\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −431.488 | + | 7943.03i | −0.0438782 | + | 0.807732i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6136.84 | + | 10629.3i | −0.620002 | + | 1.07387i | 0.369483 | + | 0.929238i | \(0.379535\pi\) |
−0.989485 | + | 0.144637i | \(0.953798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4612.44 | + | 7988.98i | 0.462977 | + | 0.801900i | 0.999108 | − | 0.0422354i | \(-0.0134479\pi\) |
−0.536131 | + | 0.844135i | \(0.680115\pi\) | |||||||
\(464\) | 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 | −0.498232 | − | 0.867044i | \(-0.666017\pi\) |
0.999998 | − | 0.00204079i | \(-0.000649604\pi\) | |||||||
\(480\) | 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 | −0.526676 | − | 0.850066i | \(-0.676562\pi\) |
0.472841 | + | 0.881148i | \(0.343229\pi\) | |||||||
\(492\) | 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 | 0.970820 | − | 0.239808i | \(-0.0770845\pi\) |
−0.693090 | + | 0.720851i | \(0.743751\pi\) | |||||||
\(500\) | 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 | 0.997077 | + | 0.0764070i | \(0.0243448\pi\) |
−0.432368 | + | 0.901697i | \(0.642322\pi\) | |||||||
\(510\) | 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 | \(0.145206\pi\) | ||||
−0.897742 | + | 0.440522i | \(0.854794\pi\) | |||||||
\(524\) | 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 | −0.0445177 | + | 0.999009i | \(0.514175\pi\) |
−0.842908 | + | 0.538058i | \(0.819158\pi\) | |||||||
\(548\) | 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 | \(-0.923859\pi\) | ||
0.971527 | − | 0.236928i | \(-0.0761407\pi\) | |||||||
\(558\) | 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 | 0.918454 | − | 0.395528i | \(-0.129438\pi\) |
−0.801764 | + | 0.597640i | \(0.796105\pi\) | |||||||
\(564\) | 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 | 0.844017 | − | 0.536317i | \(-0.180185\pi\) |
−0.0424558 | + | 0.999098i | \(0.513518\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3644.80 | + | 6312.98i | 0.267128 | + | 0.462679i | 0.968119 | − | 0.250491i | \(-0.0805920\pi\) |
−0.700991 | + | 0.713170i | \(0.747259\pi\) | |||||||
\(572\) | 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 | \(-0.935053\pi\) | ||
0.979257 | − | 0.202624i | \(-0.0649470\pi\) | |||||||
\(578\) | 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 | −0.895839 | − | 0.444380i | \(-0.853424\pi\) |
0.832763 | + | 0.553629i | \(0.186758\pi\) | |||||||
\(588\) | 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 | −0.866212 | − | 0.499677i | \(-0.833452\pi\) |
−0.000372774 | 1.00000i | \(0.500119\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −854.824 | − | 493.533i | −0.0580183 | − | 0.0334969i | 0.470710 | − | 0.882288i | \(-0.343998\pi\) |
−0.528729 | + | 0.848791i | \(0.677331\pi\) | |||||||
\(602\) | 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 | −0.858645 | − | 0.512570i | \(-0.828693\pi\) |
0.0145763 | + | 0.999894i | \(0.495360\pi\) | |||||||
\(608\) | 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 | −0.613526 | − | 0.789675i | \(-0.710249\pi\) |
0.377116 | + | 0.926166i | \(0.376916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24006.3 | − | 13860.0i | −1.55879 | − | 0.899970i | −0.997373 | − | 0.0724400i | \(-0.976921\pi\) |
−0.561421 | − | 0.827530i | \(-0.689745\pi\) | |||||||
\(620\) | 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 | 0.996520 | + | 0.0833510i | \(0.0265622\pi\) |
0.570444 | + | 0.821336i | \(0.306771\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 951.096 | − | 549.116i | 0.0583321 | − | 0.0336781i | −0.470550 | − | 0.882373i | \(-0.655945\pi\) |
0.528882 | + | 0.848695i | \(0.322611\pi\) | |||||||
\(644\) | 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 | −0.415550 | − | 0.909570i | \(-0.636411\pi\) |
0.579936 | + | 0.814662i | \(0.303077\pi\) | |||||||
\(654\) | 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 | 0.841901 | − | 0.539632i | \(-0.181437\pi\) |
−0.0463851 | + | 0.998924i | \(0.514770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9109.85 | + | 5259.57i | −0.536054 | + | 0.309491i | −0.743478 | − | 0.668760i | \(-0.766825\pi\) |
0.207424 | + | 0.978251i | \(0.433492\pi\) | |||||||
\(662\) | 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 | 0.0523297 | + | 0.998630i | \(0.483335\pi\) |
−0.891004 | + | 0.453996i | \(0.849998\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14089.3 | − | 9187.98i | −0.803402 | − | 0.523919i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2923.06 | − | 5062.89i | 0.165941 | − | 0.287419i | −0.771048 | − | 0.636777i | \(-0.780267\pi\) |
0.936989 | + | 0.349358i | \(0.113600\pi\) | |||||||
\(678\) | 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 | \(0.0668112\pi\) | ||||
−0.978053 | + | 0.208356i | \(0.933189\pi\) | |||||||
\(684\) | 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 | 0.680538 | − | 0.732713i | \(-0.261746\pi\) |
−0.294279 | + | 0.955720i | \(0.595079\pi\) | |||||||
\(692\) | 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 | \(-0.999309\pi\) | ||
0.999998 | − | 0.00217122i | \(-0.000691120\pi\) | |||||||
\(702\) | 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 | 0.452467 | + | 0.891781i | \(0.350544\pi\) |
−0.998539 | + | 0.0540423i | \(0.982789\pi\) | |||||||
\(710\) | 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 | 0.439232 | − | 0.898374i | \(-0.355251\pi\) |
−0.558398 | + | 0.829573i | \(0.688584\pi\) | |||||||
\(728\) | 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 | −0.791861 | + | 0.610701i | \(0.790888\pi\) |
−0.924813 | + | 0.380421i | \(0.875779\pi\) | |||||||
\(734\) | 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 | −0.207532 | − | 0.978228i | \(-0.566543\pi\) |
0.743405 | + | 0.668842i | \(0.233210\pi\) | |||||||
\(744\) | 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 | 0.707570 | − | 0.706643i | \(-0.249791\pi\) |
−0.965756 | + | 0.259452i | \(0.916458\pi\) | |||||||
\(752\) | 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 | 0.891665 | − | 0.452697i | \(-0.149538\pi\) |
−0.837879 | + | 0.545856i | \(0.816205\pi\) | |||||||
\(762\) | 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 | −0.335837 | − | 0.941920i | \(-0.609019\pi\) |
0.647809 | + | 0.761803i | \(0.275686\pi\) | |||||||
\(770\) | 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 | −0.310447 | − | 0.950591i | \(-0.600479\pi\) |
0.668013 | + | 0.744150i | \(0.267145\pi\) | |||||||
\(788\) | 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 | −0.624021 | − | 0.781408i | \(-0.714502\pi\) |
−0.364709 | − | 0.931122i | \(-0.618831\pi\) | |||||||
\(798\) | 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 | \(-0.941169\pi\) | ||
0.982969 | − | 0.183773i | \(-0.0588311\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 26796.4i | − | 1.16023i | −0.814533 | − | 0.580117i | \(-0.803007\pi\) | ||
0.814533 | − | 0.580117i | \(-0.196993\pi\) | |||||||
\(812\) | 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 | 0.924190 | − | 0.381933i | \(-0.124742\pi\) |
0.131331 | + | 0.991339i | \(0.458075\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11603.6 | − | 20098.0i | −0.491464 | − | 0.851241i | 0.508488 | − | 0.861069i | \(-0.330205\pi\) |
−0.999952 | + | 0.00982871i | \(0.996871\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11920.7 | + | 21537.9i | 0.503062 | + | 0.908912i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1777.49i | − | 0.0747393i | −0.999302 | − | 0.0373696i | \(-0.988102\pi\) | ||
0.999302 | − | 0.0373696i | \(-0.0118979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13834.0i | 0.579585i | 0.957090 | + | 0.289792i | \(0.0935862\pi\) | ||||
−0.957090 | + | 0.289792i | \(0.906414\pi\) | |||||||
\(830\) | 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 | −0.487369 | − | 0.873196i | \(-0.662043\pi\) |
0.999895 | − | 0.0145243i | \(-0.00462340\pi\) | |||||||
\(840\) | 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 | 0.437708 | − | 0.899117i | \(-0.355791\pi\) |
−0.559805 | + | 0.828625i | \(0.689124\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43698.7 | + | 23163.7i | −1.74791 | + | 0.926528i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8211.64 | + | 14223.0i | −0.327310 | + | 0.566917i | −0.981977 | − | 0.189000i | \(-0.939475\pi\) |
0.654667 | + | 0.755917i | \(0.272809\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1430.46 | − | 825.876i | 0.0568180 | − | 0.0328039i | −0.471322 | − | 0.881961i | \(-0.656223\pi\) |
0.528140 | + | 0.849157i | \(0.322890\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18238.0 | − | 4252.06i | −0.721894 | − | 0.168304i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20778.9i | 0.819610i | 0.912173 | + | 0.409805i | \(0.134403\pi\) | ||||
−0.912173 | + | 0.409805i | \(0.865597\pi\) | |||||||
\(864\) | 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 | 0.941828 | + | 0.336096i | \(0.109107\pi\) |
−0.179846 | + | 0.983695i | \(0.557560\pi\) | |||||||
\(878\) | 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 | 0.828331 | + | 0.560238i | \(0.189290\pi\) |
0.0710149 | + | 0.997475i | \(0.477376\pi\) | |||||||
\(888\) | 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 | −0.992220 | − | 0.124495i | \(-0.960269\pi\) |
0.603926 | + | 0.797040i | \(0.293602\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 20108.1 | − | 32088.8i | 0.733713 | − | 1.17087i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14559.0 | + | 8405.62i | 0.529484 | + | 0.305698i | 0.740806 | − | 0.671719i | \(-0.234444\pi\) |
−0.211322 | + | 0.977416i | \(0.567777\pi\) | |||||||
\(912\) | 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 | −0.144592 | − | 0.989491i | \(-0.546187\pi\) |
0.929221 | − | 0.369525i | \(-0.120480\pi\) | |||||||
\(930\) | 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 | \(-0.754576\pi\) | ||
0.717199 | − | 0.696868i | \(-0.245424\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1168.95 | − | 1942.66i | 0.0406254 | − | 0.0675146i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15218.5 | + | 26359.2i | 0.527214 | + | 0.913161i | 0.999497 | + | 0.0317144i | \(0.0100967\pi\) |
−0.472283 | + | 0.881447i | \(0.656570\pi\) | |||||||
\(942\) | 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 | 0.247727 | − | 0.968830i | \(-0.420316\pi\) |
−0.715168 | + | 0.698953i | \(0.753650\pi\) | |||||||
\(948\) | 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 | \(0.00942302\pi\) | ||||
−0.999562 | + | 0.0295990i | \(0.990577\pi\) | |||||||
\(954\) | 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 | 0.926067 | − | 0.377359i | \(-0.123168\pi\) |
−0.789836 | + | 0.613318i | \(0.789834\pi\) | |||||||
\(968\) | 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 | 0.426146 | − | 0.904655i | \(-0.359871\pi\) |
0.996527 | + | 0.0832744i | \(0.0265378\pi\) | |||||||
\(978\) | 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 | −0.855222 | − | 0.518263i | \(-0.826579\pi\) |
0.876439 | + | 0.481512i | \(0.159912\pi\) | |||||||
\(984\) | 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 | 0.377082 | − | 0.926180i | \(-0.376927\pi\) |
−0.613554 | + | 0.789653i | \(0.710261\pi\) | |||||||
\(998\) | 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.209.13 | yes | 48 | |
3.2 | odd | 2 | 756.4.x.a.629.4 | 48 | |||
7.6 | odd | 2 | inner | 252.4.x.a.209.12 | yes | 48 | |
9.2 | odd | 6 | 2268.4.f.a.1133.41 | 48 | |||
9.4 | even | 3 | 756.4.x.a.125.21 | 48 | |||
9.5 | odd | 6 | inner | 252.4.x.a.41.12 | ✓ | 48 | |
9.7 | even | 3 | 2268.4.f.a.1133.8 | 48 | |||
21.20 | even | 2 | 756.4.x.a.629.21 | 48 | |||
63.13 | odd | 6 | 756.4.x.a.125.4 | 48 | |||
63.20 | even | 6 | 2268.4.f.a.1133.7 | 48 | |||
63.34 | odd | 6 | 2268.4.f.a.1133.42 | 48 | |||
63.41 | even | 6 | inner | 252.4.x.a.41.13 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.x.a.41.12 | ✓ | 48 | 9.5 | odd | 6 | inner | |
252.4.x.a.41.13 | yes | 48 | 63.41 | even | 6 | inner | |
252.4.x.a.209.12 | yes | 48 | 7.6 | odd | 2 | inner | |
252.4.x.a.209.13 | yes | 48 | 1.1 | even | 1 | trivial | |
756.4.x.a.125.4 | 48 | 63.13 | odd | 6 | |||
756.4.x.a.125.21 | 48 | 9.4 | even | 3 | |||
756.4.x.a.629.4 | 48 | 3.2 | odd | 2 | |||
756.4.x.a.629.21 | 48 | 21.20 | even | 2 | |||
2268.4.f.a.1133.7 | 48 | 63.20 | even | 6 | |||
2268.4.f.a.1133.8 | 48 | 9.7 | even | 3 | |||
2268.4.f.a.1133.41 | 48 | 9.2 | odd | 6 | |||
2268.4.f.a.1133.42 | 48 | 63.34 | odd | 6 |