Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(226,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.226");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.e (of order \(3\), degree \(2\), not 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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 19x^{6} + 319x^{4} + 798x^{2} + 1764 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.1 | ||
Root | \(2.02770 + 3.51207i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.x.361.1 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.02770 | + | 3.51207i | −0.716899 | + | 1.24171i | 0.245323 | + | 0.969441i | \(0.421106\pi\) |
−0.962222 | + | 0.272264i | \(0.912227\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.22311 | − | 7.31464i | −0.527889 | − | 0.914330i | ||||
\(5\) | 4.96020 | − | 8.59131i | 0.443654 | − | 0.768430i | −0.554304 | − | 0.832314i | \(-0.687015\pi\) |
0.997957 | + | 0.0638840i | \(0.0203488\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.80961 | 0.0799740 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 20.1156 | + | 34.8412i | 0.636110 | + | 1.10177i | ||||
\(11\) | −6.76980 | − | 11.7256i | −0.185561 | − | 0.321401i | 0.758204 | − | 0.652017i | \(-0.226077\pi\) |
−0.943765 | + | 0.330616i | \(0.892744\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.5538 | −0.395838 | −0.197919 | − | 0.980218i | \(-0.563418\pi\) | ||||
−0.197919 | + | 0.980218i | \(0.563418\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 30.1156 | − | 52.1617i | 0.470556 | − | 0.815026i | ||||
\(17\) | 46.8551 | + | 81.1555i | 0.668473 | + | 1.15783i | 0.978331 | + | 0.207046i | \(0.0663850\pi\) |
−0.309858 | + | 0.950783i | \(0.600282\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 65.9542 | − | 114.236i | 0.796365 | − | 1.37934i | −0.125604 | − | 0.992080i | \(-0.540087\pi\) |
0.921969 | − | 0.387264i | \(-0.126580\pi\) | |||||||
\(20\) | −83.7899 | −0.936799 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 54.9084 | 0.532115 | ||||||||
\(23\) | −99.1391 | + | 171.714i | −0.898779 | + | 1.55673i | −0.0697230 | + | 0.997566i | \(0.522212\pi\) |
−0.829056 | + | 0.559165i | \(0.811122\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.2929 | + | 23.0240i | 0.106343 | + | 0.184192i | ||||
\(26\) | 37.6214 | − | 65.1622i | 0.283776 | − | 0.491514i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −188.358 | −1.20611 | −0.603054 | − | 0.797700i | \(-0.706050\pi\) | ||||
−0.603054 | + | 0.797700i | \(0.706050\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −41.9622 | − | 72.6807i | −0.243117 | − | 0.421092i | 0.718483 | − | 0.695544i | \(-0.244837\pi\) |
−0.961601 | + | 0.274453i | \(0.911503\pi\) | |||||||
\(32\) | 129.369 | + | 224.073i | 0.714669 | + | 1.23784i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −380.032 | −1.91691 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.0778 | + | 69.4167i | −0.178074 | + | 0.308434i | −0.941221 | − | 0.337792i | \(-0.890320\pi\) |
0.763147 | + | 0.646225i | \(0.223653\pi\) | |||||||
\(38\) | 267.470 | + | 463.272i | 1.14183 | + | 1.97770i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 8.97600 | − | 15.5469i | 0.0354808 | − | 0.0614545i | ||||
\(41\) | −385.828 | −1.46967 | −0.734833 | − | 0.678249i | \(-0.762739\pi\) | ||||
−0.734833 | + | 0.678249i | \(0.762739\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −397.048 | −1.40812 | −0.704061 | − | 0.710139i | \(-0.748632\pi\) | ||||
−0.704061 | + | 0.710139i | \(0.748632\pi\) | |||||||
\(44\) | −57.1793 | + | 99.0374i | −0.195911 | + | 0.339328i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −402.048 | − | 696.368i | −1.28867 | − | 2.23204i | ||||
\(47\) | −136.139 | + | 235.799i | −0.422508 | + | 0.731805i | −0.996184 | − | 0.0872772i | \(-0.972183\pi\) |
0.573676 | + | 0.819082i | \(0.305517\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −107.816 | −0.304949 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 78.3547 | + | 135.714i | 0.208958 | + | 0.361927i | ||||
\(53\) | −18.4998 | − | 32.0426i | −0.0479461 | − | 0.0830451i | 0.841056 | − | 0.540948i | \(-0.181934\pi\) |
−0.889002 | + | 0.457902i | \(0.848601\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −134.318 | −0.329299 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 381.932 | − | 661.526i | 0.864658 | − | 1.49763i | ||||
\(59\) | −197.874 | − | 342.728i | −0.436628 | − | 0.756262i | 0.560799 | − | 0.827952i | \(-0.310494\pi\) |
−0.997427 | + | 0.0716901i | \(0.977161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.73689 | − | 11.6686i | 0.0141405 | − | 0.0244921i | −0.858869 | − | 0.512196i | \(-0.828832\pi\) |
0.873009 | + | 0.487704i | \(0.162165\pi\) | |||||||
\(62\) | 340.347 | 0.697162 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −567.435 | −1.10827 | ||||||||
\(65\) | −92.0304 | + | 159.401i | −0.175615 | + | 0.304174i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −170.261 | − | 294.901i | −0.310458 | − | 0.537729i | 0.668004 | − | 0.744158i | \(-0.267149\pi\) |
−0.978462 | + | 0.206429i | \(0.933816\pi\) | |||||||
\(68\) | 395.749 | − | 685.457i | 0.705759 | − | 1.22241i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 211.140 | 0.352925 | 0.176463 | − | 0.984307i | \(-0.443534\pi\) | ||||
0.176463 | + | 0.984307i | \(0.443534\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 243.062 | + | 420.995i | 0.389702 | + | 0.674983i | 0.992409 | − | 0.122979i | \(-0.0392448\pi\) |
−0.602708 | + | 0.797962i | \(0.705911\pi\) | |||||||
\(74\) | −162.531 | − | 281.512i | −0.255323 | − | 0.442232i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1114.13 | −1.68157 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −146.871 | + | 254.387i | −0.209168 | + | 0.362289i | −0.951453 | − | 0.307795i | \(-0.900409\pi\) |
0.742285 | + | 0.670084i | \(0.233742\pi\) | |||||||
\(80\) | −298.758 | − | 517.464i | −0.417527 | − | 0.723178i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 782.343 | − | 1355.06i | 1.05360 | − | 1.82489i | ||||
\(83\) | 889.635 | 1.17651 | 0.588253 | − | 0.808677i | \(-0.299816\pi\) | ||||
0.588253 | + | 0.808677i | \(0.299816\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 929.643 | 1.18628 | ||||||||
\(86\) | 805.093 | − | 1394.46i | 1.00948 | − | 1.74847i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.2507 | − | 21.2188i | −0.0148401 | − | 0.0257038i | ||||
\(89\) | −572.182 | + | 991.048i | −0.681474 | + | 1.18035i | 0.293057 | + | 0.956095i | \(0.405327\pi\) |
−0.974531 | + | 0.224252i | \(0.928006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1674.70 | 1.89782 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −552.096 | − | 956.258i | −0.605791 | − | 1.04926i | ||||
\(95\) | −654.292 | − | 1133.27i | −0.706620 | − | 1.22390i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1384.61 | −1.44933 | −0.724667 | − | 0.689099i | \(-0.758007\pi\) | ||||
−0.724667 | + | 0.689099i | \(0.758007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 112.275 | − | 194.465i | 0.112275 | − | 0.194465i | ||||
\(101\) | −892.994 | − | 1546.71i | −0.879765 | − | 1.52380i | −0.851599 | − | 0.524194i | \(-0.824367\pi\) |
−0.0281660 | − | 0.999603i | \(-0.508967\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 244.831 | − | 424.059i | 0.234212 | − | 0.405668i | −0.724831 | − | 0.688927i | \(-0.758082\pi\) |
0.959044 | + | 0.283259i | \(0.0914155\pi\) | |||||||
\(104\) | −33.5750 | −0.0316568 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 150.048 | 0.137490 | ||||||||
\(107\) | 141.034 | − | 244.278i | 0.127423 | − | 0.220703i | −0.795254 | − | 0.606276i | \(-0.792663\pi\) |
0.922678 | + | 0.385573i | \(0.125996\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 143.616 | + | 248.749i | 0.126201 | + | 0.218586i | 0.922202 | − | 0.386709i | \(-0.126388\pi\) |
−0.796001 | + | 0.605295i | \(0.793055\pi\) | |||||||
\(110\) | 272.357 | − | 471.736i | 0.236074 | − | 0.408893i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1895.21 | −1.57776 | −0.788879 | − | 0.614548i | \(-0.789338\pi\) | ||||
−0.788879 | + | 0.614548i | \(0.789338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 983.499 | + | 1703.47i | 0.797493 | + | 1.38130i | ||||
\(116\) | 795.456 | + | 1377.77i | 0.636691 | + | 1.10278i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1604.92 | 1.25207 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 573.840 | − | 993.919i | 0.431134 | − | 0.746746i | ||||
\(122\) | 27.3208 | + | 47.3209i | 0.0202746 | + | 0.0351167i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −354.422 | + | 613.877i | −0.256678 | + | 0.444579i | ||||
\(125\) | 1503.79 | 1.07603 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1222.92 | −0.854463 | −0.427231 | − | 0.904142i | \(-0.640511\pi\) | ||||
−0.427231 | + | 0.904142i | \(0.640511\pi\) | |||||||
\(128\) | 115.635 | − | 200.285i | 0.0798496 | − | 0.138304i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −373.220 | − | 646.435i | −0.251796 | − | 0.436124i | ||||
\(131\) | −595.303 | + | 1031.10i | −0.397037 | + | 0.687689i | −0.993359 | − | 0.115057i | \(-0.963295\pi\) |
0.596322 | + | 0.802746i | \(0.296628\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1380.95 | 0.890268 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 84.7893 | + | 146.859i | 0.0534605 | + | 0.0925963i | ||||
\(137\) | 53.4807 | + | 92.6313i | 0.0333516 | + | 0.0577666i | 0.882219 | − | 0.470839i | \(-0.156049\pi\) |
−0.848868 | + | 0.528605i | \(0.822715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1096.78 | 0.669262 | 0.334631 | − | 0.942349i | \(-0.391388\pi\) | ||||
0.334631 | + | 0.942349i | \(0.391388\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −428.128 | + | 741.539i | −0.253012 | + | 0.438230i | ||||
\(143\) | 125.605 | + | 217.555i | 0.0734521 | + | 0.127223i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −934.292 | + | 1618.24i | −0.535094 | + | 0.926811i | ||||
\(146\) | −1971.42 | −1.11751 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 677.012 | 0.376014 | ||||||||
\(149\) | 358.331 | − | 620.647i | 0.197018 | − | 0.341244i | −0.750542 | − | 0.660822i | \(-0.770208\pi\) |
0.947560 | + | 0.319578i | \(0.103541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −77.1840 | − | 133.687i | −0.0415970 | − | 0.0720481i | 0.844477 | − | 0.535591i | \(-0.179911\pi\) |
−0.886074 | + | 0.463543i | \(0.846578\pi\) | |||||||
\(152\) | 119.351 | − | 206.722i | 0.0636885 | − | 0.110312i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −832.564 | −0.431439 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1046.87 | − | 1813.24i | −0.532163 | − | 0.921734i | −0.999295 | − | 0.0375459i | \(-0.988046\pi\) |
0.467132 | − | 0.884188i | \(-0.345287\pi\) | |||||||
\(158\) | −595.618 | − | 1031.64i | −0.299904 | − | 0.519449i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2566.78 | 1.26826 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1503.93 | + | 2604.88i | −0.722680 | + | 1.25172i | 0.237242 | + | 0.971451i | \(0.423757\pi\) |
−0.959922 | + | 0.280268i | \(0.909577\pi\) | |||||||
\(164\) | 1629.40 | + | 2822.20i | 0.775820 | + | 1.34376i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1803.91 | + | 3124.46i | −0.843437 | + | 1.46088i | ||||
\(167\) | −2230.43 | −1.03351 | −0.516754 | − | 0.856134i | \(-0.672860\pi\) | ||||
−0.516754 | + | 0.856134i | \(0.672860\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1852.76 | −0.843312 | ||||||||
\(170\) | −1885.03 | + | 3264.97i | −0.850444 | + | 1.47301i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1676.78 | + | 2904.26i | 0.743332 | + | 1.28749i | ||||
\(173\) | 281.585 | − | 487.719i | 0.123749 | − | 0.214339i | −0.797495 | − | 0.603326i | \(-0.793842\pi\) |
0.921243 | + | 0.388987i | \(0.127175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −815.506 | −0.349267 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2320.42 | − | 4019.09i | −0.977096 | − | 1.69238i | ||||
\(179\) | 919.749 | + | 1593.05i | 0.384052 | + | 0.665197i | 0.991637 | − | 0.129057i | \(-0.0411951\pi\) |
−0.607585 | + | 0.794254i | \(0.707862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2324.71 | −0.954664 | −0.477332 | − | 0.878723i | \(-0.658396\pi\) | ||||
−0.477332 | + | 0.878723i | \(0.658396\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −179.403 | + | 310.735i | −0.0718790 | + | 0.124498i | ||||
\(185\) | 397.587 | + | 688.641i | 0.158006 | + | 0.273675i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 634.400 | − | 1098.81i | 0.248085 | − | 0.429696i | ||||
\(188\) | 2299.71 | 0.892149 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5306.82 | 2.02630 | ||||||||
\(191\) | −1563.64 | + | 2708.30i | −0.592360 | + | 1.02600i | 0.401553 | + | 0.915836i | \(0.368470\pi\) |
−0.993914 | + | 0.110163i | \(0.964863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1854.64 | + | 3212.34i | 0.691711 | + | 1.19808i | 0.971277 | + | 0.237952i | \(0.0764761\pi\) |
−0.279566 | + | 0.960126i | \(0.590191\pi\) | |||||||
\(194\) | 2807.56 | − | 4862.84i | 1.03903 | − | 1.79965i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −851.150 | −0.307827 | −0.153913 | − | 0.988084i | \(-0.549188\pi\) | ||||
−0.153913 | + | 0.988084i | \(0.549188\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1698.89 | + | 2942.57i | 0.605182 | + | 1.04821i | 0.992023 | + | 0.126060i | \(0.0402331\pi\) |
−0.386840 | + | 0.922147i | \(0.626434\pi\) | |||||||
\(200\) | 24.0549 | + | 41.6643i | 0.00850469 | + | 0.0147306i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7242.89 | 2.52281 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1913.78 | + | 3314.77i | −0.652022 | + | 1.12934i | ||||
\(206\) | 992.885 | + | 1719.73i | 0.335813 | + | 0.581646i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −558.757 | + | 967.796i | −0.186264 | + | 0.322618i | ||||
\(209\) | −1785.99 | −0.591098 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 216.732 | 0.0707132 | 0.0353566 | − | 0.999375i | \(-0.488743\pi\) | ||||
0.0353566 | + | 0.999375i | \(0.488743\pi\) | |||||||
\(212\) | −156.253 | + | 270.639i | −0.0506204 | + | 0.0876772i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 571.948 | + | 990.644i | 0.182699 | + | 0.316444i | ||||
\(215\) | −1969.44 | + | 3411.16i | −0.624718 | + | 1.08204i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1164.84 | −0.361893 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 567.241 | + | 982.490i | 0.173833 | + | 0.301088i | ||||
\(221\) | −869.340 | − | 1505.74i | −0.264607 | − | 0.458312i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2254.86 | 0.677115 | 0.338558 | − | 0.940946i | \(-0.390061\pi\) | ||||
0.338558 | + | 0.940946i | \(0.390061\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3842.92 | − | 6656.13i | 1.13109 | − | 1.95911i | ||||
\(227\) | 1695.40 | + | 2936.52i | 0.495716 | + | 0.858606i | 0.999988 | − | 0.00493916i | \(-0.00157219\pi\) |
−0.504271 | + | 0.863545i | \(0.668239\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1293.92 | − | 2241.14i | 0.373384 | − | 0.646720i | −0.616700 | − | 0.787198i | \(-0.711531\pi\) |
0.990084 | + | 0.140479i | \(0.0448641\pi\) | |||||||
\(230\) | −7976.95 | −2.28689 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −340.853 | −0.0964574 | ||||||||
\(233\) | −477.210 | + | 826.552i | −0.134176 | + | 0.232400i | −0.925282 | − | 0.379279i | \(-0.876172\pi\) |
0.791106 | + | 0.611679i | \(0.209505\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1350.55 | + | 2339.22i | 0.374894 | + | 0.649336i | ||||
\(236\) | −1671.29 | + | 2894.76i | −0.460982 | + | 0.798444i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −199.504 | −0.0539951 | −0.0269976 | − | 0.999635i | \(-0.508595\pi\) | ||||
−0.0269976 | + | 0.999635i | \(0.508595\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2397.21 | + | 4152.10i | 0.640739 | + | 1.10979i | 0.985268 | + | 0.171017i | \(0.0547052\pi\) |
−0.344529 | + | 0.938776i | \(0.611961\pi\) | |||||||
\(242\) | 2327.15 | + | 4030.73i | 0.618159 | + | 1.07068i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −113.803 | −0.0298585 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1223.70 | + | 2119.51i | −0.315231 | + | 0.545997i | ||||
\(248\) | −75.9351 | − | 131.523i | −0.0194431 | − | 0.0336764i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3049.23 | + | 5281.42i | −0.771401 | + | 1.33611i | ||||
\(251\) | 6249.73 | 1.57163 | 0.785816 | − | 0.618460i | \(-0.212243\pi\) | ||||
0.785816 | + | 0.618460i | \(0.212243\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2684.61 | 0.667114 | ||||||||
\(254\) | 2479.71 | − | 4294.99i | 0.612564 | − | 1.06099i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1800.79 | − | 3119.07i | −0.439647 | − | 0.761491i | ||||
\(257\) | 1918.93 | − | 3323.68i | 0.465756 | − | 0.806713i | −0.533479 | − | 0.845813i | \(-0.679116\pi\) |
0.999235 | + | 0.0390999i | \(0.0124491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1554.62 | 0.370821 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2414.19 | − | 4181.50i | −0.569271 | − | 0.986007i | ||||
\(263\) | 103.602 | + | 179.443i | 0.0242903 | + | 0.0420721i | 0.877915 | − | 0.478816i | \(-0.158934\pi\) |
−0.853625 | + | 0.520889i | \(0.825601\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −367.051 | −0.0850858 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1438.06 | + | 2490.80i | −0.327775 | + | 0.567722i | ||||
\(269\) | −2402.04 | − | 4160.46i | −0.544442 | − | 0.943002i | −0.998642 | − | 0.0521018i | \(-0.983408\pi\) |
0.454199 | − | 0.890900i | \(-0.349925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1607.88 | − | 2784.92i | 0.360411 | − | 0.624251i | −0.627617 | − | 0.778522i | \(-0.715970\pi\) |
0.988029 | + | 0.154271i | \(0.0493030\pi\) | |||||||
\(272\) | 5644.27 | 1.25821 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −433.771 | −0.0956388 | ||||||||
\(275\) | 179.980 | − | 311.735i | 0.0394663 | − | 0.0683576i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1027.20 | − | 1779.16i | −0.222810 | − | 0.385918i | 0.732850 | − | 0.680390i | \(-0.238190\pi\) |
−0.955660 | + | 0.294472i | \(0.904856\pi\) | |||||||
\(278\) | −2223.93 | + | 3851.97i | −0.479794 | + | 0.831027i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1768.61 | −0.375468 | −0.187734 | − | 0.982220i | \(-0.560114\pi\) | ||||
−0.187734 | + | 0.982220i | \(0.560114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1170.26 | + | 2026.96i | 0.245813 | + | 0.425760i | 0.962360 | − | 0.271779i | \(-0.0876119\pi\) |
−0.716547 | + | 0.697539i | \(0.754279\pi\) | |||||||
\(284\) | −891.668 | − | 1544.41i | −0.186305 | − | 0.322690i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1018.76 | −0.210631 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1934.31 | + | 3350.32i | −0.393712 | + | 0.681929i | ||||
\(290\) | −3788.92 | − | 6562.60i | −0.767217 | − | 1.32886i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2052.95 | − | 3555.82i | 0.411438 | − | 0.712632i | ||||
\(293\) | −3633.47 | −0.724470 | −0.362235 | − | 0.932087i | \(-0.617986\pi\) | ||||
−0.362235 | + | 0.932087i | \(0.617986\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3925.98 | −0.774846 | ||||||||
\(296\) | −72.5250 | + | 125.617i | −0.0142413 | + | 0.0246667i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1453.17 | + | 2516.97i | 0.282483 | + | 0.489276i | ||||
\(299\) | 1839.40 | − | 3185.94i | 0.355771 | − | 0.616213i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 626.023 | 0.119283 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3972.50 | − | 6880.56i | −0.749468 | − | 1.29812i | ||||
\(305\) | −66.8326 | − | 115.758i | −0.0125470 | − | 0.0217320i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5954.32 | −1.10694 | −0.553471 | − | 0.832868i | \(-0.686697\pi\) | ||||
−0.553471 | + | 0.832868i | \(0.686697\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1688.19 | − | 2924.03i | 0.309299 | − | 0.535721i | ||||
\(311\) | −590.047 | − | 1021.99i | −0.107584 | − | 0.186340i | 0.807207 | − | 0.590268i | \(-0.200978\pi\) |
−0.914791 | + | 0.403928i | \(0.867645\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4873.12 | + | 8440.50i | −0.880017 | + | 1.52423i | −0.0286960 | + | 0.999588i | \(0.509135\pi\) |
−0.851321 | + | 0.524646i | \(0.824198\pi\) | |||||||
\(314\) | 8490.97 | 1.52603 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2481.00 | 0.441669 | ||||||||
\(317\) | 4295.96 | − | 7440.81i | 0.761151 | − | 1.31835i | −0.181106 | − | 0.983464i | \(-0.557968\pi\) |
0.942258 | − | 0.334889i | \(-0.108699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1275.14 | + | 2208.62i | 0.223807 | + | 0.387645i | ||||
\(320\) | −2814.59 | + | 4875.01i | −0.491688 | + | 0.851629i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12361.2 | 2.12939 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −246.633 | − | 427.181i | −0.0420946 | − | 0.0729100i | ||||
\(326\) | −6099.02 | − | 10563.8i | −1.03618 | − | 1.79471i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −698.197 | −0.117535 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2625.60 | − | 4547.67i | 0.436000 | − | 0.755174i | −0.561377 | − | 0.827560i | \(-0.689728\pi\) |
0.997377 | + | 0.0723864i | \(0.0230615\pi\) | |||||||
\(332\) | −3757.03 | − | 6507.36i | −0.621065 | − | 1.07572i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4522.64 | − | 7833.44i | 0.740921 | − | 1.28331i | ||||
\(335\) | −3378.11 | −0.550943 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8496.45 | −1.37339 | −0.686693 | − | 0.726947i | \(-0.740938\pi\) | ||||
−0.686693 | + | 0.726947i | \(0.740938\pi\) | |||||||
\(338\) | 3756.83 | − | 6507.02i | 0.604570 | − | 1.04715i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3925.98 | − | 6800.00i | −0.626225 | − | 1.08465i | ||||
\(341\) | −568.152 | + | 984.068i | −0.0902263 | + | 0.156276i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −718.500 | −0.112613 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1141.94 | + | 1977.89i | 0.177430 | + | 0.307319i | ||||
\(347\) | −2915.07 | − | 5049.06i | −0.450978 | − | 0.781117i | 0.547469 | − | 0.836826i | \(-0.315591\pi\) |
−0.998447 | + | 0.0557090i | \(0.982258\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1811.13 | −0.277786 | −0.138893 | − | 0.990307i | \(-0.544354\pi\) | ||||
−0.138893 | + | 0.990307i | \(0.544354\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1751.60 | − | 3033.87i | 0.265230 | − | 0.459391i | ||||
\(353\) | −1663.88 | − | 2881.92i | −0.250876 | − | 0.434531i | 0.712891 | − | 0.701275i | \(-0.247385\pi\) |
−0.963767 | + | 0.266744i | \(0.914052\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1047.30 | − | 1813.97i | 0.156577 | − | 0.271199i | ||||
\(356\) | 9665.55 | 1.43897 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7459.89 | −1.10131 | ||||||||
\(359\) | −435.430 | + | 754.188i | −0.0640143 | + | 0.110876i | −0.896256 | − | 0.443536i | \(-0.853724\pi\) |
0.832242 | + | 0.554413i | \(0.187057\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5270.42 | − | 9128.63i | −0.768395 | − | 1.33090i | ||||
\(362\) | 4713.80 | − | 8164.55i | 0.684398 | − | 1.18541i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4822.54 | 0.691570 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 587.358 | + | 1017.33i | 0.0835418 | + | 0.144699i | 0.904769 | − | 0.425903i | \(-0.140043\pi\) |
−0.821227 | + | 0.570601i | \(0.806710\pi\) | |||||||
\(368\) | 5971.26 | + | 10342.5i | 0.845851 | + | 1.46506i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3224.75 | −0.453099 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1814.17 | + | 3142.23i | −0.251834 | + | 0.436189i | −0.964031 | − | 0.265791i | \(-0.914367\pi\) |
0.712197 | + | 0.701980i | \(0.247700\pi\) | |||||||
\(374\) | 2572.74 | + | 4456.12i | 0.355704 | + | 0.616097i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −246.357 | + | 426.703i | −0.0337897 | + | 0.0585254i | ||||
\(377\) | 3494.75 | 0.477424 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7321.99 | 0.992362 | 0.496181 | − | 0.868219i | \(-0.334735\pi\) | ||||
0.496181 | + | 0.868219i | \(0.334735\pi\) | |||||||
\(380\) | −5526.29 | + | 9571.82i | −0.746034 | + | 1.29217i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6341.17 | − | 10983.2i | −0.849325 | − | 1.47107i | ||||
\(383\) | 3677.45 | − | 6369.52i | 0.490623 | − | 0.849784i | −0.509318 | − | 0.860578i | \(-0.670102\pi\) |
0.999942 | + | 0.0107937i | \(0.00343580\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −15042.6 | −1.98355 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5847.35 | + | 10127.9i | 0.765088 | + | 1.32517i | ||||
\(389\) | 4534.81 | + | 7854.52i | 0.591064 | + | 1.02375i | 0.994089 | + | 0.108564i | \(0.0346254\pi\) |
−0.403025 | + | 0.915189i | \(0.632041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18580.7 | −2.40324 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1725.87 | − | 2989.30i | 0.220681 | − | 0.382230i | ||||
\(395\) | 1457.01 | + | 2523.62i | 0.185596 | + | 0.321462i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3688.41 | − | 6388.52i | 0.466288 | − | 0.807634i | −0.532971 | − | 0.846134i | \(-0.678925\pi\) |
0.999259 | + | 0.0384997i | \(0.0122579\pi\) | |||||||
\(398\) | −13779.4 | −1.73542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1601.29 | 0.200161 | ||||||||
\(401\) | −1426.76 | + | 2471.21i | −0.177678 | + | 0.307747i | −0.941085 | − | 0.338171i | \(-0.890192\pi\) |
0.763407 | + | 0.645918i | \(0.223525\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 778.558 | + | 1348.50i | 0.0962350 | + | 0.166684i | ||||
\(404\) | −7542.43 | + | 13063.9i | −0.928836 | + | 1.60879i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1085.27 | 0.132175 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5630.03 | + | 9751.49i | 0.680652 | + | 1.17892i | 0.974782 | + | 0.223159i | \(0.0716369\pi\) |
−0.294130 | + | 0.955766i | \(0.595030\pi\) | |||||||
\(410\) | −7761.15 | − | 13442.7i | −0.934868 | − | 1.61924i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4135.79 | −0.494553 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4412.76 | − | 7643.13i | 0.521961 | − | 0.904064i | ||||
\(416\) | −2400.28 | − | 4157.41i | −0.282893 | − | 0.489985i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3621.44 | − | 6272.52i | 0.423757 | − | 0.733969i | ||||
\(419\) | −9221.47 | −1.07517 | −0.537587 | − | 0.843208i | \(-0.680664\pi\) | ||||
−0.537587 | + | 0.843208i | \(0.680664\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8520.28 | −0.986349 | −0.493175 | − | 0.869930i | \(-0.664164\pi\) | ||||
−0.493175 | + | 0.869930i | \(0.664164\pi\) | |||||||
\(422\) | −439.468 | + | 761.181i | −0.0506942 | + | 0.0878049i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −33.4774 | − | 57.9845i | −0.00383444 | − | 0.00664145i | ||||
\(425\) | −1245.68 | + | 2157.58i | −0.142175 | + | 0.246254i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2382.41 | −0.269061 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7986.84 | − | 13833.6i | −0.895720 | − | 1.55143i | ||||
\(431\) | 4581.05 | + | 7934.62i | 0.511976 | + | 0.886768i | 0.999904 | + | 0.0138840i | \(0.00441955\pi\) |
−0.487928 | + | 0.872884i | \(0.662247\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10976.2 | 1.21820 | 0.609100 | − | 0.793093i | \(-0.291531\pi\) | ||||
0.609100 | + | 0.793093i | \(0.291531\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1213.01 | − | 2100.99i | 0.133240 | − | 0.230778i | ||||
\(437\) | 13077.3 | + | 22650.5i | 1.43151 | + | 2.47945i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1991.59 | − | 3449.54i | 0.216523 | − | 0.375028i | −0.737220 | − | 0.675653i | \(-0.763862\pi\) |
0.953743 | + | 0.300625i | \(0.0971951\pi\) | |||||||
\(440\) | −243.063 | −0.0263354 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7051.03 | 0.758786 | ||||||||
\(443\) | 2262.22 | − | 3918.29i | 0.242622 | − | 0.420234i | −0.718838 | − | 0.695177i | \(-0.755326\pi\) |
0.961460 | + | 0.274944i | \(0.0886592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5676.27 | + | 9831.59i | 0.604676 | + | 1.04733i | ||||
\(446\) | −4572.18 | + | 7919.24i | −0.485423 | + | 0.840778i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2076.49 | 0.218253 | 0.109127 | − | 0.994028i | \(-0.465195\pi\) | ||||
0.109127 | + | 0.994028i | \(0.465195\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2611.98 | + | 4524.09i | 0.272713 | + | 0.472352i | ||||
\(452\) | 8003.70 | + | 13862.8i | 0.832881 | + | 1.44259i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13751.0 | −1.42151 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 923.795 | − | 1600.06i | 0.0945587 | − | 0.163780i | −0.814866 | − | 0.579650i | \(-0.803189\pi\) |
0.909424 | + | 0.415869i | \(0.136523\pi\) | |||||||
\(458\) | 5247.37 | + | 9088.71i | 0.535357 | + | 0.927266i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8306.85 | − | 14387.9i | 0.841976 | − | 1.45834i | ||||
\(461\) | 876.945 | 0.0885974 | 0.0442987 | − | 0.999018i | \(-0.485895\pi\) | ||||
0.0442987 | + | 0.999018i | \(0.485895\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16245.2 | 1.63062 | 0.815310 | − | 0.579025i | \(-0.196566\pi\) | ||||
0.815310 | + | 0.579025i | \(0.196566\pi\) | |||||||
\(464\) | −5672.50 | + | 9825.05i | −0.567541 | + | 0.983010i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1935.27 | − | 3351.99i | −0.192382 | − | 0.333215i | ||||
\(467\) | 9480.88 | − | 16421.4i | 0.939449 | − | 1.62717i | 0.172947 | − | 0.984931i | \(-0.444671\pi\) |
0.766502 | − | 0.642242i | \(-0.221996\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −10954.0 | −1.07505 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −358.075 | − | 620.204i | −0.0349189 | − | 0.0604813i | ||||
\(473\) | 2687.94 | + | 4655.64i | 0.261293 | + | 0.452572i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3506.89 | 0.338752 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 404.533 | − | 700.672i | 0.0387090 | − | 0.0670460i | ||||
\(479\) | 4188.88 | + | 7255.35i | 0.399572 | + | 0.692078i | 0.993673 | − | 0.112312i | \(-0.0358256\pi\) |
−0.594101 | + | 0.804390i | \(0.702492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 743.594 | − | 1287.94i | 0.0704885 | − | 0.122090i | ||||
\(482\) | −19443.3 | −1.83738 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9693.55 | −0.910364 | ||||||||
\(485\) | −6867.92 | + | 11895.6i | −0.643002 | + | 1.11371i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2279.42 | + | 3948.08i | 0.212096 | + | 0.367360i | 0.952370 | − | 0.304944i | \(-0.0986378\pi\) |
−0.740275 | + | 0.672305i | \(0.765304\pi\) | |||||||
\(488\) | 12.1911 | − | 21.1156i | 0.00113087 | − | 0.00195873i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15809.9 | −1.45314 | −0.726570 | − | 0.687092i | \(-0.758887\pi\) | ||||
−0.726570 | + | 0.687092i | \(0.758887\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8825.53 | − | 15286.3i | −0.806251 | − | 1.39647i | ||||
\(494\) | −4962.59 | − | 8595.45i | −0.451978 | − | 0.782849i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5054.86 | −0.457601 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6693.04 | + | 11592.7i | −0.600444 | + | 1.04000i | 0.392309 | + | 0.919833i | \(0.371676\pi\) |
−0.992754 | + | 0.120167i | \(0.961657\pi\) | |||||||
\(500\) | −6350.67 | − | 10999.7i | −0.568022 | − | 0.983842i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12672.6 | + | 21949.5i | −1.12670 | + | 1.95150i | ||||
\(503\) | 5720.55 | 0.507091 | 0.253545 | − | 0.967323i | \(-0.418403\pi\) | ||||
0.253545 | + | 0.967323i | \(0.418403\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17717.7 | −1.56124 | ||||||||
\(506\) | −5443.57 | + | 9428.54i | −0.478254 | + | 0.828359i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5164.53 | + | 8945.24i | 0.451061 | + | 0.781261i | ||||
\(509\) | 7646.59 | − | 13244.3i | 0.665873 | − | 1.15333i | −0.313175 | − | 0.949695i | \(-0.601393\pi\) |
0.979048 | − | 0.203630i | \(-0.0652740\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16456.0 | 1.42043 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7782.00 | + | 13478.8i | 0.667800 | + | 1.15666i | ||||
\(515\) | −2428.82 | − | 4206.83i | −0.207818 | − | 0.359952i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3686.53 | 0.313604 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −166.539 | + | 288.454i | −0.0140446 | + | 0.0243260i | ||||
\(521\) | −2184.35 | − | 3783.40i | −0.183681 | − | 0.318145i | 0.759450 | − | 0.650566i | \(-0.225468\pi\) |
−0.943131 | + | 0.332420i | \(0.892135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1211.08 | + | 2097.66i | −0.101256 | + | 0.175381i | −0.912202 | − | 0.409740i | \(-0.865619\pi\) |
0.810946 | + | 0.585121i | \(0.198953\pi\) | |||||||
\(524\) | 10056.1 | 0.838366 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −840.291 | −0.0696548 | ||||||||
\(527\) | 3932.29 | − | 6810.93i | 0.325035 | − | 0.562976i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13573.6 | − | 23510.2i | −1.11561 | − | 1.93229i | ||||
\(530\) | 744.268 | − | 1289.11i | 0.0609980 | − | 0.105652i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7158.57 | 0.581749 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1399.11 | − | 2423.33i | −0.113063 | − | 0.195832i | ||||
\(536\) | −308.105 | − | 533.654i | −0.0248286 | − | 0.0430044i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19482.4 | 1.56124 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6581.27 | + | 11399.1i | −0.523014 | + | 0.905888i | 0.476627 | + | 0.879106i | \(0.341859\pi\) |
−0.999641 | + | 0.0267819i | \(0.991474\pi\) | |||||||
\(542\) | 6520.57 | + | 11294.0i | 0.516757 | + | 0.895050i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12123.2 | + | 20998.0i | −0.955473 | + | 1.65493i | ||||
\(545\) | 2849.45 | 0.223958 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12112.4 | 0.946778 | 0.473389 | − | 0.880853i | \(-0.343031\pi\) | ||||
0.473389 | + | 0.880853i | \(0.343031\pi\) | |||||||
\(548\) | 451.710 | − | 782.384i | 0.0352118 | − | 0.0609887i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 729.892 | + | 1264.21i | 0.0565867 | + | 0.0980110i | ||||
\(551\) | −12423.0 | + | 21517.2i | −0.960503 | + | 1.66364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8331.38 | 0.638928 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4631.81 | − | 8022.54i | −0.353296 | − | 0.611927i | ||||
\(557\) | −4179.82 | − | 7239.67i | −0.317962 | − | 0.550726i | 0.662101 | − | 0.749415i | \(-0.269665\pi\) |
−0.980063 | + | 0.198689i | \(0.936332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7366.74 | 0.557388 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3586.21 | − | 6211.50i | 0.269173 | − | 0.466221i | ||||
\(563\) | −6819.20 | − | 11811.2i | −0.510471 | − | 0.884162i | −0.999926 | − | 0.0121334i | \(-0.996138\pi\) |
0.489455 | − | 0.872028i | \(-0.337196\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9400.63 | + | 16282.4i | −0.699978 | + | 1.21240i | ||||
\(566\) | −9491.76 | −0.704891 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 382.080 | 0.0282249 | ||||||||
\(569\) | 7745.67 | − | 13415.9i | 0.570677 | − | 0.988442i | −0.425820 | − | 0.904808i | \(-0.640014\pi\) |
0.996497 | − | 0.0836335i | \(-0.0266525\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2324.08 | + | 4025.42i | 0.170332 | + | 0.295024i | 0.938536 | − | 0.345182i | \(-0.112183\pi\) |
−0.768204 | + | 0.640205i | \(0.778849\pi\) | |||||||
\(572\) | 1060.89 | − | 1837.52i | 0.0775491 | − | 0.134319i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5271.38 | −0.382316 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2739.53 | − | 4745.01i | −0.197657 | − | 0.342352i | 0.750111 | − | 0.661312i | \(-0.230000\pi\) |
−0.947768 | + | 0.318959i | \(0.896667\pi\) | |||||||
\(578\) | −7844.37 | − | 13586.8i | −0.564503 | − | 0.977748i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15782.5 | 1.12988 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −250.480 | + | 433.844i | −0.0177939 | + | 0.0308199i | ||||
\(584\) | 439.846 | + | 761.836i | 0.0311660 | + | 0.0539811i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7367.59 | − | 12761.0i | 0.519372 | − | 0.899579i | ||||
\(587\) | 4408.22 | 0.309960 | 0.154980 | − | 0.987918i | \(-0.450469\pi\) | ||||
0.154980 | + | 0.987918i | \(0.450469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11070.3 | −0.774441 | ||||||||
\(590\) | 7960.71 | − | 13788.3i | 0.555487 | − | 0.962131i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2413.93 | + | 4181.05i | 0.167588 | + | 0.290270i | ||||
\(593\) | −1407.63 | + | 2438.08i | −0.0974779 | + | 0.168837i | −0.910640 | − | 0.413201i | \(-0.864411\pi\) |
0.813162 | + | 0.582037i | \(0.197744\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6053.09 | −0.416014 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7459.51 | + | 12920.2i | 0.510104 | + | 0.883526i | ||||
\(599\) | 9859.53 | + | 17077.2i | 0.672537 | + | 1.16487i | 0.977182 | + | 0.212402i | \(0.0681287\pi\) |
−0.304646 | + | 0.952466i | \(0.598538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13982.8 | 0.949033 | 0.474517 | − | 0.880247i | \(-0.342623\pi\) | ||||
0.474517 | + | 0.880247i | \(0.342623\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −651.913 | + | 1129.15i | −0.0439172 | + | 0.0760667i | ||||
\(605\) | −5692.71 | − | 9860.07i | −0.382548 | − | 0.662593i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6694.14 | − | 11594.6i | 0.447622 | − | 0.775305i | −0.550608 | − | 0.834764i | \(-0.685604\pi\) |
0.998231 | + | 0.0594590i | \(0.0189376\pi\) | |||||||
\(608\) | 34129.7 | 2.27655 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 542.065 | 0.0359797 | ||||||||
\(611\) | 2525.89 | − | 4374.96i | 0.167245 | − | 0.289676i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13895.9 | + | 24068.5i | 0.915582 | + | 1.58583i | 0.806047 | + | 0.591852i | \(0.201603\pi\) |
0.109535 | + | 0.993983i | \(0.465064\pi\) | |||||||
\(614\) | 12073.6 | − | 20912.0i | 0.793566 | − | 1.37450i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19107.2 | 1.24672 | 0.623361 | − | 0.781935i | \(-0.285767\pi\) | ||||
0.623361 | + | 0.781935i | \(0.285767\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 546.469 | + | 946.512i | 0.0354837 | + | 0.0614596i | 0.883222 | − | 0.468955i | \(-0.155369\pi\) |
−0.847738 | + | 0.530415i | \(0.822036\pi\) | |||||||
\(620\) | 3516.01 | + | 6089.90i | 0.227752 | + | 0.394478i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4785.75 | 0.308507 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5797.49 | − | 10041.5i | 0.371039 | − | 0.642659i | ||||
\(626\) | −19762.4 | − | 34229.5i | −1.26177 | − | 2.18544i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8842.13 | + | 15315.0i | −0.561846 | + | 0.973146i | ||||
\(629\) | −7511.40 | −0.476151 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19235.2 | 1.21353 | 0.606767 | − | 0.794879i | \(-0.292466\pi\) | ||||
0.606767 | + | 0.794879i | \(0.292466\pi\) | |||||||
\(632\) | −265.778 | + | 460.341i | −0.0167280 | + | 0.0289737i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 17421.8 | + | 30175.4i | 1.09134 | + | 1.89025i | ||||
\(635\) | −6065.93 | + | 10506.5i | −0.379085 | + | 0.656595i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −10342.4 | −0.641788 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1147.14 | − | 1986.91i | −0.0708511 | − | 0.122718i | ||||
\(641\) | −9975.33 | − | 17277.8i | −0.614667 | − | 1.06463i | −0.990443 | − | 0.137924i | \(-0.955957\pi\) |
0.375776 | − | 0.926711i | \(-0.377376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −688.125 | −0.0422037 | −0.0211019 | − | 0.999777i | \(-0.506717\pi\) | ||||
−0.0211019 | + | 0.999777i | \(0.506717\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25064.7 | + | 43413.4i | −1.52656 | + | 2.64408i | ||||
\(647\) | −5483.09 | − | 9497.00i | −0.333173 | − | 0.577072i | 0.649959 | − | 0.759969i | \(-0.274786\pi\) |
−0.983132 | + | 0.182897i | \(0.941453\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2679.14 | + | 4640.41i | −0.162042 | + | 0.280666i | ||||
\(650\) | 2000.39 | 0.120710 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 25405.0 | 1.52598 | ||||||||
\(653\) | −6462.54 | + | 11193.4i | −0.387287 | + | 0.670802i | −0.992084 | − | 0.125579i | \(-0.959921\pi\) |
0.604796 | + | 0.796380i | \(0.293255\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5905.64 | + | 10228.9i | 0.352294 | + | 0.610191i | ||||
\(656\) | −11619.4 | + | 20125.5i | −0.691559 | + | 1.19782i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11779.0 | 0.696273 | 0.348137 | − | 0.937444i | \(-0.386815\pi\) | ||||
0.348137 | + | 0.937444i | \(0.386815\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12520.0 | − | 21685.3i | −0.736721 | − | 1.27604i | −0.953964 | − | 0.299921i | \(-0.903040\pi\) |
0.217243 | − | 0.976118i | \(-0.430294\pi\) | |||||||
\(662\) | 10647.8 | + | 18442.6i | 0.625136 | + | 1.08277i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1609.89 | 0.0940900 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18673.6 | − | 32343.6i | 1.08403 | − | 1.87759i | ||||
\(668\) | 9419.36 | + | 16314.8i | 0.545578 | + | 0.944968i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6849.78 | − | 11864.2i | 0.394971 | − | 0.684109i | ||||
\(671\) | −182.430 | −0.0104957 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4104.64 | 0.235100 | 0.117550 | − | 0.993067i | \(-0.462496\pi\) | ||||
0.117550 | + | 0.993067i | \(0.462496\pi\) | |||||||
\(674\) | 17228.2 | − | 29840.2i | 0.984580 | − | 1.70534i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7824.40 | + | 13552.3i | 0.445175 | + | 0.771066i | ||||
\(677\) | −6076.70 | + | 10525.1i | −0.344973 | + | 0.597510i | −0.985349 | − | 0.170551i | \(-0.945445\pi\) |
0.640376 | + | 0.768061i | \(0.278778\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1682.29 | 0.0948717 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2304.08 | − | 3990.78i | −0.129366 | − | 0.224069i | ||||
\(683\) | −10207.0 | − | 17679.0i | −0.571830 | − | 0.990438i | −0.996378 | − | 0.0850328i | \(-0.972900\pi\) |
0.424549 | − | 0.905405i | \(-0.360433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1061.10 | 0.0591862 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11957.3 | + | 20710.7i | −0.662600 | + | 1.14766i | ||||
\(689\) | 343.241 | + | 594.511i | 0.0189789 | + | 0.0328724i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8046.76 | − | 13937.4i | 0.443000 | − | 0.767299i | −0.554910 | − | 0.831910i | \(-0.687247\pi\) |
0.997911 | + | 0.0646110i | \(0.0205807\pi\) | |||||||
\(692\) | −4756.66 | −0.261302 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23643.6 | 1.29322 | ||||||||
\(695\) | 5440.23 | − | 9422.76i | 0.296921 | − | 0.514282i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18078.0 | − | 31312.1i | −0.982431 | − | 1.70162i | ||||
\(698\) | 3672.42 | − | 6360.81i | 0.199145 | − | 0.344929i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20803.0 | −1.12085 | −0.560426 | − | 0.828204i | \(-0.689363\pi\) | ||||
−0.560426 | + | 0.828204i | \(0.689363\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5286.60 | + | 9156.65i | 0.283624 | + | 0.491251i | ||||
\(704\) | 3841.42 | + | 6653.54i | 0.205652 | + | 0.356200i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13495.4 | 0.719412 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −70.7460 | + | 122.536i | −0.00374742 | + | 0.00649073i | −0.867893 | − | 0.496751i | \(-0.834526\pi\) |
0.864146 | + | 0.503242i | \(0.167860\pi\) | |||||||
\(710\) | 4247.20 | + | 7356.36i | 0.224499 | + | 0.388844i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1035.42 | + | 1793.41i | −0.0545002 | + | 0.0943971i | ||||
\(713\) | 16640.4 | 0.874035 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2492.11 | 0.130349 | ||||||||
\(716\) | 7768.40 | − | 13455.3i | 0.405473 | − | 0.702300i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1765.84 | − | 3058.53i | −0.0917836 | − | 0.158974i | ||||
\(719\) | 3332.23 | − | 5771.59i | 0.172839 | − | 0.299366i | −0.766572 | − | 0.642158i | \(-0.778039\pi\) |
0.939411 | + | 0.342792i | \(0.111373\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 42747.2 | 2.20345 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9817.50 | + | 17004.4i | 0.503957 | + | 0.872878i | ||||
\(725\) | −2503.82 | − | 4336.74i | −0.128261 | − | 0.222155i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4837.23 | 0.246772 | 0.123386 | − | 0.992359i | \(-0.460625\pi\) | ||||
0.123386 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9778.65 | + | 16937.1i | −0.495786 | + | 0.858727i | ||||
\(731\) | −18603.7 | − | 32222.6i | −0.941291 | − | 1.63036i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15801.3 | + | 27368.6i | −0.796225 | + | 1.37910i | 0.125834 | + | 0.992051i | \(0.459839\pi\) |
−0.922059 | + | 0.387050i | \(0.873494\pi\) | |||||||
\(734\) | −4763.93 | −0.239564 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −51302.0 | −2.56932 | ||||||||
\(737\) | −2305.27 | + | 3992.84i | −0.115218 | + | 0.199563i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4113.79 | + | 7125.30i | 0.204774 | + | 0.354680i | 0.950061 | − | 0.312065i | \(-0.101021\pi\) |
−0.745286 | + | 0.666744i | \(0.767687\pi\) | |||||||
\(740\) | 3358.11 | − | 5816.42i | 0.166820 | − | 0.288940i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37020.3 | −1.82792 | −0.913959 | − | 0.405805i | \(-0.866991\pi\) | ||||
−0.913959 | + | 0.405805i | \(0.866991\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3554.78 | − | 6157.07i | −0.174815 | − | 0.302789i | ||||
\(746\) | −7357.16 | − | 12743.0i | −0.361079 | − | 0.625407i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10716.6 | −0.523846 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12575.0 | − | 21780.5i | 0.611008 | − | 1.05830i | −0.380063 | − | 0.924960i | \(-0.624098\pi\) |
0.991071 | − | 0.133336i | \(-0.0425689\pi\) | |||||||
\(752\) | 8199.78 | + | 14202.4i | 0.397627 | + | 0.688710i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7086.29 | + | 12273.8i | −0.342265 | + | 0.592820i | ||||
\(755\) | −1531.39 | −0.0738186 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20460.8 | 0.982377 | 0.491189 | − | 0.871053i | \(-0.336563\pi\) | ||||
0.491189 | + | 0.871053i | \(0.336563\pi\) | |||||||
\(758\) | −14846.8 | + | 25715.4i | −0.711424 | + | 1.23222i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1184.01 | − | 2050.77i | −0.0565113 | − | 0.0978804i | ||||
\(761\) | −16329.6 | + | 28283.6i | −0.777853 | + | 1.34728i | 0.155324 | + | 0.987864i | \(0.450358\pi\) |
−0.933177 | + | 0.359417i | \(0.882976\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 26413.7 | 1.25080 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14913.5 | + | 25830.9i | 0.703455 | + | 1.21842i | ||||
\(767\) | 3671.32 | + | 6358.91i | 0.172834 | + | 0.299357i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11005.3 | 0.516075 | 0.258037 | − | 0.966135i | \(-0.416924\pi\) | ||||
0.258037 | + | 0.966135i | \(0.416924\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 15664.7 | − | 27132.1i | 0.730293 | − | 1.26490i | ||||
\(773\) | 1519.09 | + | 2631.14i | 0.0706829 | + | 0.122426i | 0.899201 | − | 0.437536i | \(-0.144149\pi\) |
−0.828518 | + | 0.559963i | \(0.810815\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1115.60 | − | 1932.27i | 0.0517077 | − | 0.0895604i | ||||
\(776\) | −2505.59 | −0.115909 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −36780.9 | −1.69493 | ||||||||
\(779\) | −25447.0 | + | 44075.5i | −1.17039 | + | 2.02717i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1429.38 | − | 2475.75i | −0.0654893 | − | 0.113431i | ||||
\(782\) | 37676.0 | − | 65256.8i | 1.72288 | − | 2.98411i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20770.8 | −0.944384 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6153.38 | − | 10658.0i | −0.278710 | − | 0.482739i | 0.692355 | − | 0.721557i | \(-0.256573\pi\) |
−0.971064 | + | 0.238818i | \(0.923240\pi\) | |||||||
\(788\) | 3594.50 | + | 6225.86i | 0.162498 | + | 0.281455i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11817.5 | −0.532214 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −124.995 | + | 216.497i | −0.00559735 | + | 0.00969489i | ||||
\(794\) | 14958.0 | + | 25908.0i | 0.668562 | + | 1.15798i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14349.2 | − | 24853.6i | 0.638938 | − | 1.10667i | ||||
\(797\) | 3007.06 | 0.133646 | 0.0668228 | − | 0.997765i | \(-0.478714\pi\) | ||||
0.0668228 | + | 0.997765i | \(0.478714\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25515.2 | −1.12974 | ||||||||
\(800\) | −3439.37 | + | 5957.17i | −0.152000 | + | 0.263272i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5786.06 | − | 10021.7i | −0.254754 | − | 0.441247i | ||||
\(803\) | 3290.96 | − | 5700.11i | 0.144627 | − | 0.250501i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6314.72 | −0.275963 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1615.97 | − | 2798.94i | −0.0703584 | − | 0.121864i | ||||
\(809\) | −5292.48 | − | 9166.84i | −0.230005 | − | 0.398380i | 0.727805 | − | 0.685785i | \(-0.240541\pi\) |
−0.957809 | + | 0.287405i | \(0.907207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18217.8 | 0.788796 | 0.394398 | − | 0.918940i | \(-0.370953\pi\) | ||||
0.394398 | + | 0.918940i | \(0.370953\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2200.61 | + | 3811.57i | −0.0947559 | + | 0.164122i | ||||
\(815\) | 14919.6 | + | 25841.4i | 0.641239 | + | 1.11066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26187.0 | + | 45357.2i | −1.12138 | + | 1.94229i | ||||
\(818\) | −45663.9 | −1.95184 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 32328.5 | 1.37678 | ||||||||
\(821\) | −12798.3 | + | 22167.2i | −0.544047 | + | 0.942317i | 0.454619 | + | 0.890686i | \(0.349775\pi\) |
−0.998666 | + | 0.0516309i | \(0.983558\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21889.5 | − | 37913.6i | −0.927118 | − | 1.60582i | −0.788119 | − | 0.615524i | \(-0.788945\pi\) |
−0.139000 | − | 0.990292i | \(-0.544389\pi\) | |||||||
\(824\) | 443.047 | − | 767.380i | 0.0187309 | − | 0.0324429i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2735.78 | −0.115033 | −0.0575166 | − | 0.998345i | \(-0.518318\pi\) | ||||
−0.0575166 | + | 0.998345i | \(0.518318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15572.1 | − | 26971.7i | −0.652402 | − | 1.12999i | −0.982538 | − | 0.186060i | \(-0.940428\pi\) |
0.330137 | − | 0.943933i | \(-0.392905\pi\) | |||||||
\(830\) | 17895.5 | + | 30995.9i | 0.748387 | + | 1.29625i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 10528.1 | 0.438696 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11063.4 | + | 19162.3i | −0.458520 | + | 0.794179i | ||||
\(836\) | 7542.43 | + | 13063.9i | 0.312034 | + | 0.540458i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18698.3 | − | 32386.5i | 0.770792 | − | 1.33505i | ||||
\(839\) | −14977.3 | −0.616300 | −0.308150 | − | 0.951338i | \(-0.599710\pi\) | ||||
−0.308150 | + | 0.951338i | \(0.599710\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11089.6 | 0.454698 | ||||||||
\(842\) | 17276.5 | − | 29923.9i | 0.707113 | − | 1.22476i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −915.285 | − | 1585.32i | −0.0373287 | − | 0.0646552i | ||||
\(845\) | −9190.04 | + | 15917.6i | −0.374139 | + | 0.648027i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2228.53 | −0.0902452 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5051.72 | − | 8749.84i | −0.203850 | − | 0.353079i | ||||
\(851\) | −7946.55 | − | 13763.8i | −0.320099 | − | 0.554427i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42861.7 | −1.72047 | −0.860233 | − | 0.509901i | \(-0.829682\pi\) | ||||
−0.860233 | + | 0.509901i | \(0.829682\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 255.216 | − | 442.047i | 0.0101905 | − | 0.0176505i | ||||
\(857\) | 4695.00 | + | 8131.98i | 0.187139 | + | 0.324134i | 0.944295 | − | 0.329100i | \(-0.106745\pi\) |
−0.757156 | + | 0.653234i | \(0.773412\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16780.6 | − | 29064.8i | 0.666526 | − | 1.15446i | −0.312343 | − | 0.949969i | \(-0.601114\pi\) |
0.978869 | − | 0.204488i | \(-0.0655528\pi\) | |||||||
\(860\) | 33268.6 | 1.31913 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37155.9 | −1.46814 | ||||||||
\(863\) | 12845.8 | − | 22249.6i | 0.506693 | − | 0.877617i | −0.493277 | − | 0.869872i | \(-0.664201\pi\) |
0.999970 | − | 0.00774521i | \(-0.00246540\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2793.43 | − | 4838.37i | −0.109803 | − | 0.190184i | ||||
\(866\) | −22256.3 | + | 38549.1i | −0.873327 | + | 1.51265i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3977.14 | 0.155254 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3158.98 | + | 5471.52i | 0.122891 | + | 0.212853i | ||||
\(872\) | 259.888 | + | 450.138i | 0.0100928 | + | 0.0174812i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −106067. | −4.10500 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2675.76 | − | 4634.55i | 0.103026 | − | 0.178447i | −0.809904 | − | 0.586563i | \(-0.800481\pi\) |
0.912930 | + | 0.408116i | \(0.133814\pi\) | |||||||
\(878\) | 8076.69 | + | 13989.2i | 0.310450 | + | 0.537715i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4045.07 | + | 7006.26i | −0.154954 | + | 0.268388i | ||||
\(881\) | −34212.7 | −1.30835 | −0.654174 | − | 0.756344i | \(-0.726984\pi\) | ||||
−0.654174 | + | 0.756344i | \(0.726984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17149.2 | 0.653587 | 0.326794 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326794 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(884\) | −7342.64 | + | 12717.8i | −0.279366 | + | 0.483876i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9174.21 | + | 15890.2i | 0.347871 | + | 0.602530i | ||||
\(887\) | −2010.44 | + | 3482.18i | −0.0761035 | + | 0.131815i | −0.901566 | − | 0.432642i | \(-0.857581\pi\) |
0.825462 | + | 0.564458i | \(0.190915\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −46039.0 | −1.73397 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9522.53 | − | 16493.5i | −0.357442 | − | 0.619107i | ||||
\(893\) | 17957.8 | + | 31103.9i | 0.672941 | + | 1.16557i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18248.5 | 0.681544 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4210.50 | + | 7292.79i | −0.156466 | + | 0.271006i | ||||
\(899\) | 7903.91 | + | 13690.0i | 0.293226 | + | 0.507882i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1733.62 | − | 3002.72i | 0.0641013 | − | 0.111027i | ||||
\(902\) | −21185.2 | −0.782030 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3429.59 | −0.126180 | ||||||||
\(905\) | −11531.0 | + | 19972.3i | −0.423540 | + | 0.733593i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11483.6 | + | 19890.2i | 0.420405 | + | 0.728163i | 0.995979 | − | 0.0895869i | \(-0.0285547\pi\) |
−0.575574 | + | 0.817750i | \(0.695221\pi\) | |||||||
\(908\) | 14319.7 | − | 24802.5i | 0.523366 | − | 0.906497i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9860.77 | −0.358619 | −0.179309 | − | 0.983793i | \(-0.557386\pi\) | ||||
−0.179309 | + | 0.983793i | \(0.557386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6022.65 | − | 10431.5i | −0.218314 | − | 0.378131i | ||||
\(914\) | 3746.35 | + | 6488.87i | 0.135578 | + | 0.234828i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21857.5 | −0.788421 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2635.77 | − | 4565.30i | 0.0946096 | − | 0.163869i | −0.814836 | − | 0.579692i | \(-0.803173\pi\) |
0.909446 | + | 0.415823i | \(0.136506\pi\) | |||||||
\(920\) | 1779.75 | + | 3082.61i | 0.0637788 | + | 0.110468i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1778.18 | + | 3079.90i | −0.0635154 | + | 0.110012i | ||||
\(923\) | −3917.44 | −0.139701 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2131.00 | −0.0757478 | ||||||||
\(926\) | −32940.3 | + | 57054.3i | −1.16899 | + | 2.02475i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −24367.6 | − | 42206.0i | −0.861968 | − | 1.49297i | ||||
\(929\) | 7451.31 | − | 12906.0i | 0.263153 | − | 0.455795i | −0.703925 | − | 0.710274i | \(-0.748571\pi\) |
0.967078 | + | 0.254480i | \(0.0819042\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 8061.24 | 0.283321 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 38448.7 | + | 66595.1i | 1.34698 | + | 2.33304i | ||||
\(935\) | −6293.50 | − | 10900.7i | −0.220128 | − | 0.381272i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21934.8 | 0.764757 | 0.382378 | − | 0.924006i | \(-0.375105\pi\) | ||||
0.382378 | + | 0.924006i | \(0.375105\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 11407.0 | − | 19757.6i | 0.395805 | − | 0.685554i | ||||
\(941\) | −7260.76 | − | 12576.0i | −0.251535 | − | 0.435671i | 0.712414 | − | 0.701760i | \(-0.247602\pi\) |
−0.963949 | + | 0.266089i | \(0.914269\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38250.7 | − | 66252.1i | 1.32090 | − | 2.28787i | ||||
\(944\) | −23836.4 | −0.821831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −21801.3 | −0.749282 | ||||||||
\(947\) | 971.867 | − | 1683.32i | 0.0333489 | − | 0.0577621i | −0.848869 | − | 0.528603i | \(-0.822716\pi\) |
0.882218 | + | 0.470841i | \(0.156049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4509.71 | − | 7811.05i | −0.154259 | − | 0.267184i | ||||
\(950\) | −7110.91 | + | 12316.5i | −0.242851 | + | 0.420630i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16904.1 | 0.574583 | 0.287292 | − | 0.957843i | \(-0.407245\pi\) | ||||
0.287292 | + | 0.957843i | \(0.407245\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15511.9 | + | 26867.4i | 0.525606 | + | 0.910376i | ||||
\(956\) | 842.527 | + | 1459.30i | 0.0285034 | + | 0.0493694i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33975.1 | −1.14581 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11373.8 | − | 19700.1i | 0.381788 | − | 0.661276i | ||||
\(962\) | 3015.57 | + | 5223.12i | 0.101066 | + | 0.175052i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20247.4 | − | 35069.5i | 0.676478 | − | 1.17169i | ||||
\(965\) | 36797.6 | 1.22752 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26699.3 | 0.887891 | 0.443946 | − | 0.896054i | \(-0.353578\pi\) | ||||
0.443946 | + | 0.896054i | \(0.353578\pi\) | |||||||
\(968\) | 1038.42 | − | 1798.60i | 0.0344795 | − | 0.0597203i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27852.1 | − | 48241.3i | −0.921936 | − | 1.59684i | ||||
\(971\) | −5544.74 | + | 9603.77i | −0.183253 | + | 0.317404i | −0.942987 | − | 0.332831i | \(-0.891996\pi\) |
0.759733 | + | 0.650235i | \(0.225330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −18487.9 | −0.608205 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −405.771 | − | 702.815i | −0.0133078 | − | 0.0230498i | ||||
\(977\) | 25945.9 | + | 44939.7i | 0.849625 | + | 1.47159i | 0.881543 | + | 0.472103i | \(0.156505\pi\) |
−0.0319179 | + | 0.999490i | \(0.510162\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15494.2 | 0.505820 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32057.7 | − | 55525.6i | 1.04176 | − | 1.80437i | ||||
\(983\) | −12280.3 | − | 21270.2i | −0.398456 | − | 0.690145i | 0.595080 | − | 0.803666i | \(-0.297120\pi\) |
−0.993536 | + | 0.113521i | \(0.963787\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4221.87 | + | 7312.49i | −0.136569 | + | 0.236544i | ||||
\(986\) | 71582.0 | 2.31200 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20671.3 | 0.665629 | ||||||||
\(989\) | 39363.0 | − | 68178.7i | 1.26559 | − | 2.19207i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9253.76 | + | 16028.0i | 0.296625 | + | 0.513769i | 0.975362 | − | 0.220612i | \(-0.0708056\pi\) |
−0.678737 | + | 0.734382i | \(0.737472\pi\) | |||||||
\(992\) | 10857.2 | − | 18805.2i | 0.347497 | − | 0.601882i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33707.4 | 1.07397 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21483.1 | − | 37209.8i | −0.682424 | − | 1.18199i | −0.974239 | − | 0.225518i | \(-0.927593\pi\) |
0.291815 | − | 0.956475i | \(-0.405741\pi\) | |||||||
\(998\) | −27142.9 | − | 47012.9i | −0.860916 | − | 1.49115i | ||||
\(999\) | 0 | 0 |
(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 | 441.4.e.x.226.1 | 8 | ||
3.2 | odd | 2 | inner | 441.4.e.x.226.4 | 8 | ||
7.2 | even | 3 | 441.4.a.v.1.4 | 4 | |||
7.3 | odd | 6 | 63.4.e.d.46.1 | yes | 8 | ||
7.4 | even | 3 | inner | 441.4.e.x.361.1 | 8 | ||
7.5 | odd | 6 | 441.4.a.w.1.4 | 4 | |||
7.6 | odd | 2 | 63.4.e.d.37.1 | ✓ | 8 | ||
21.2 | odd | 6 | 441.4.a.v.1.1 | 4 | |||
21.5 | even | 6 | 441.4.a.w.1.1 | 4 | |||
21.11 | odd | 6 | inner | 441.4.e.x.361.4 | 8 | ||
21.17 | even | 6 | 63.4.e.d.46.4 | yes | 8 | ||
21.20 | even | 2 | 63.4.e.d.37.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.e.d.37.1 | ✓ | 8 | 7.6 | odd | 2 | ||
63.4.e.d.37.4 | yes | 8 | 21.20 | even | 2 | ||
63.4.e.d.46.1 | yes | 8 | 7.3 | odd | 6 | ||
63.4.e.d.46.4 | yes | 8 | 21.17 | even | 6 | ||
441.4.a.v.1.1 | 4 | 21.2 | odd | 6 | |||
441.4.a.v.1.4 | 4 | 7.2 | even | 3 | |||
441.4.a.w.1.1 | 4 | 21.5 | even | 6 | |||
441.4.a.w.1.4 | 4 | 7.5 | odd | 6 | |||
441.4.e.x.226.1 | 8 | 1.1 | even | 1 | trivial | ||
441.4.e.x.226.4 | 8 | 3.2 | odd | 2 | inner | ||
441.4.e.x.361.1 | 8 | 7.4 | even | 3 | inner | ||
441.4.e.x.361.4 | 8 | 21.11 | odd | 6 | inner |