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 | 361.4 | ||
Root | \(-2.02770 + 3.51207i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.361 |
Dual form | 441.4.e.x.226.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | 0.962222 | + | 0.272264i | \(0.0877726\pi\) |
−0.245323 | + | 0.969441i | \(0.578894\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.22311 | + | 7.31464i | −0.527889 | + | 0.914330i | ||||
\(5\) | −4.96020 | − | 8.59131i | −0.443654 | − | 0.768430i | 0.554304 | − | 0.832314i | \(-0.312985\pi\) |
−0.997957 | + | 0.0638840i | \(0.979651\pi\) | |||||||
\(6\) | 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 | \(-0.773923\pi\) |
0.943765 | + | 0.330616i | \(0.107256\pi\) | |||||||
\(12\) | 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 | 0.309858 | + | 0.950783i | \(0.399718\pi\) |
−0.978331 | + | 0.207046i | \(0.933615\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 65.9542 | + | 114.236i | 0.796365 | + | 1.37934i | 0.921969 | + | 0.387264i | \(0.126580\pi\) |
−0.125604 | + | 0.992080i | \(0.540087\pi\) | |||||||
\(20\) | 83.7899 | 0.936799 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 54.9084 | 0.532115 | ||||||||
\(23\) | 99.1391 | + | 171.714i | 0.898779 | + | 1.55673i | 0.829056 | + | 0.559165i | \(0.188878\pi\) |
0.0697230 | + | 0.997566i | \(0.477788\pi\) | |||||||
\(24\) | 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 | \(-0.293950\pi\) | ||||
0.603054 | + | 0.797700i | \(0.293950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −41.9622 | + | 72.6807i | −0.243117 | + | 0.421092i | −0.961601 | − | 0.274453i | \(-0.911503\pi\) |
0.718483 | + | 0.695544i | \(0.244837\pi\) | |||||||
\(32\) | −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 | 0.763147 | − | 0.646225i | \(-0.223653\pi\) |
−0.941221 | + | 0.337792i | \(0.890320\pi\) | |||||||
\(38\) | −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 | \(-0.237261\pi\) | ||||
0.734833 | + | 0.678249i | \(0.237261\pi\) | |||||||
\(42\) | 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 | \(-0.0278166\pi\) |
−0.573676 | + | 0.819082i | \(0.694483\pi\) | |||||||
\(48\) | 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 | \(-0.818066\pi\) |
0.889002 | + | 0.457902i | \(0.151399\pi\) | |||||||
\(54\) | 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 | \(-0.689506\pi\) |
0.997427 | + | 0.0716901i | \(0.0228393\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.73689 | + | 11.6686i | 0.0141405 | + | 0.0244921i | 0.873009 | − | 0.487704i | \(-0.162165\pi\) |
−0.858869 | + | 0.512196i | \(0.828832\pi\) | |||||||
\(62\) | −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 | −0.978462 | − | 0.206429i | \(-0.933816\pi\) |
0.668004 | + | 0.744158i | \(0.267149\pi\) | |||||||
\(68\) | −395.749 | − | 685.457i | −0.705759 | − | 1.22241i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −211.140 | −0.352925 | −0.176463 | − | 0.984307i | \(-0.556466\pi\) | ||||
−0.176463 | + | 0.984307i | \(0.556466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 243.062 | − | 420.995i | 0.389702 | − | 0.674983i | −0.602708 | − | 0.797962i | \(-0.705911\pi\) |
0.992409 | + | 0.122979i | \(0.0392448\pi\) | |||||||
\(74\) | 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 | 0.742285 | − | 0.670084i | \(-0.233742\pi\) |
−0.951453 | + | 0.307795i | \(0.900409\pi\) | |||||||
\(80\) | 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 | \(-0.700184\pi\) | ||||
−0.588253 | + | 0.808677i | \(0.700184\pi\) | |||||||
\(84\) | 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 | 0.974531 | + | 0.224252i | \(0.0719939\pi\) |
−0.293057 | + | 0.956095i | \(0.594673\pi\) | |||||||
\(90\) | 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 | 0.0281660 | − | 0.999603i | \(-0.491033\pi\) |
0.851599 | − | 0.524194i | \(-0.175633\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 244.831 | + | 424.059i | 0.234212 | + | 0.405668i | 0.959044 | − | 0.283259i | \(-0.0914155\pi\) |
−0.724831 | + | 0.688927i | \(0.758082\pi\) | |||||||
\(104\) | 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 | \(-0.207337\pi\) |
−0.922678 | + | 0.385573i | \(0.874004\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 143.616 | − | 248.749i | 0.126201 | − | 0.218586i | −0.796001 | − | 0.605295i | \(-0.793055\pi\) |
0.922202 | + | 0.386709i | \(0.126388\pi\) | |||||||
\(110\) | −272.357 | − | 471.736i | −0.236074 | − | 0.408893i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1895.21 | 1.57776 | 0.788879 | − | 0.614548i | \(-0.210662\pi\) | ||||
0.788879 | + | 0.614548i | \(0.210662\pi\) | |||||||
\(114\) | 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 | \(-0.0367051\pi\) |
−0.596322 | + | 0.802746i | \(0.703372\pi\) | |||||||
\(132\) | 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 | \(-0.843951\pi\) |
0.848868 | + | 0.528605i | \(0.177285\pi\) | |||||||
\(138\) | 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 | \(-0.229792\pi\) |
−0.947560 | + | 0.319578i | \(0.896459\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −77.1840 | + | 133.687i | −0.0415970 | + | 0.0720481i | −0.886074 | − | 0.463543i | \(-0.846578\pi\) |
0.844477 | + | 0.535591i | \(0.179911\pi\) | |||||||
\(152\) | −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 | 0.467132 | + | 0.884188i | \(0.345287\pi\) |
−0.999295 | + | 0.0375459i | \(0.988046\pi\) | |||||||
\(158\) | 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 | −0.959922 | − | 0.280268i | \(-0.909577\pi\) |
0.237242 | − | 0.971451i | \(-0.423757\pi\) | |||||||
\(164\) | −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 | \(-0.327140\pi\) | ||||
0.516754 | + | 0.856134i | \(0.327140\pi\) | |||||||
\(168\) | 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 | \(-0.206158\pi\) |
−0.921243 | + | 0.388987i | \(0.872825\pi\) | |||||||
\(174\) | 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 | \(-0.958805\pi\) |
0.607585 | + | 0.794254i | \(0.292138\pi\) | |||||||
\(180\) | 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 | 0.993914 | + | 0.110163i | \(0.0351372\pi\) |
−0.401553 | + | 0.915836i | \(0.631530\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1854.64 | − | 3212.34i | 0.691711 | − | 1.19808i | −0.279566 | − | 0.960126i | \(-0.590191\pi\) |
0.971277 | − | 0.237952i | \(-0.0764761\pi\) | |||||||
\(194\) | −2807.56 | − | 4862.84i | −1.03903 | − | 1.79965i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 851.150 | 0.307827 | 0.153913 | − | 0.988084i | \(-0.450812\pi\) | ||||
0.153913 | + | 0.988084i | \(0.450812\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1698.89 | − | 2942.57i | 0.605182 | − | 1.04821i | −0.386840 | − | 0.922147i | \(-0.626434\pi\) |
0.992023 | − | 0.126060i | \(-0.0402331\pi\) | |||||||
\(200\) | −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 | \(-0.998428\pi\) |
0.504271 | + | 0.863545i | \(0.331761\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1293.92 | + | 2241.14i | 0.373384 | + | 0.646720i | 0.990084 | − | 0.140479i | \(-0.0448641\pi\) |
−0.616700 | + | 0.787198i | \(0.711531\pi\) | |||||||
\(230\) | 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 | \(-0.123828\pi\) |
−0.791106 | + | 0.611679i | \(0.790495\pi\) | |||||||
\(234\) | 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 | \(-0.491405\pi\) | ||||
0.0269976 | + | 0.999635i | \(0.491405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2397.21 | − | 4152.10i | 0.640739 | − | 1.10979i | −0.344529 | − | 0.938776i | \(-0.611961\pi\) |
0.985268 | − | 0.171017i | \(-0.0547052\pi\) | |||||||
\(242\) | −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 | \(-0.787757\pi\) | ||||
−0.785816 | + | 0.618460i | \(0.787757\pi\) | |||||||
\(252\) | 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 | \(-0.320884\pi\) |
−0.999235 | + | 0.0390999i | \(0.987551\pi\) | |||||||
\(258\) | 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 | \(-0.841066\pi\) |
0.853625 | + | 0.520889i | \(0.174399\pi\) | |||||||
\(264\) | 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 | −0.454199 | − | 0.890900i | \(-0.650075\pi\) |
0.998642 | − | 0.0521018i | \(-0.0165920\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1607.88 | + | 2784.92i | 0.360411 | + | 0.624251i | 0.988029 | − | 0.154271i | \(-0.0493030\pi\) |
−0.627617 | + | 0.778522i | \(0.715970\pi\) | |||||||
\(272\) | −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 | −0.955660 | − | 0.294472i | \(-0.904856\pi\) |
0.732850 | + | 0.680390i | \(0.238190\pi\) | |||||||
\(278\) | 2223.93 | + | 3851.97i | 0.479794 | + | 0.831027i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1768.61 | 0.375468 | 0.187734 | − | 0.982220i | \(-0.439886\pi\) | ||||
0.187734 | + | 0.982220i | \(0.439886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1170.26 | − | 2026.96i | 0.245813 | − | 0.425760i | −0.716547 | − | 0.697539i | \(-0.754279\pi\) |
0.962360 | + | 0.271779i | \(0.0876119\pi\) | |||||||
\(284\) | 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 | \(-0.382014\pi\) | ||||
0.362235 | + | 0.932087i | \(0.382014\pi\) | |||||||
\(294\) | 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 | \(-0.799022\pi\) |
0.914791 | + | 0.403928i | \(0.132355\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4873.12 | − | 8440.50i | −0.880017 | − | 1.52423i | −0.851321 | − | 0.524646i | \(-0.824198\pi\) |
−0.0286960 | − | 0.999588i | \(-0.509135\pi\) | |||||||
\(314\) | −8490.97 | −1.52603 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2481.00 | 0.441669 | ||||||||
\(317\) | −4295.96 | − | 7440.81i | −0.761151 | − | 1.31835i | −0.942258 | − | 0.334889i | \(-0.891301\pi\) |
0.181106 | − | 0.983464i | \(-0.442032\pi\) | |||||||
\(318\) | 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 | 0.997377 | − | 0.0723864i | \(-0.0230615\pi\) |
−0.561377 | + | 0.827560i | \(0.689728\pi\) | |||||||
\(332\) | 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 | \(-0.684409\pi\) |
0.998447 | + | 0.0557090i | \(0.0177419\pi\) | |||||||
\(348\) | 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 | \(-0.752615\pi\) |
0.963767 | + | 0.266744i | \(0.0859479\pi\) | |||||||
\(354\) | 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 | \(-0.146276\pi\) |
−0.832242 | + | 0.554413i | \(0.812943\pi\) | |||||||
\(360\) | 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 | −0.821227 | − | 0.570601i | \(-0.806710\pi\) |
0.904769 | + | 0.425903i | \(0.140043\pi\) | |||||||
\(368\) | −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 | 0.712197 | − | 0.701980i | \(-0.247700\pi\) |
−0.964031 | + | 0.265791i | \(0.914367\pi\) | |||||||
\(374\) | −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 | \(-0.329898\pi\) |
−0.999942 | + | 0.0107937i | \(0.996564\pi\) | |||||||
\(384\) | 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 | 0.403025 | + | 0.915189i | \(0.367959\pi\) |
−0.994089 | + | 0.108564i | \(0.965375\pi\) | |||||||
\(390\) | 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 | 0.999259 | − | 0.0384997i | \(-0.0122579\pi\) |
−0.532971 | + | 0.846134i | \(0.678925\pi\) | |||||||
\(398\) | 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 | \(-0.109808\pi\) |
−0.763407 | + | 0.645918i | \(0.776475\pi\) | |||||||
\(402\) | 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 | −0.294130 | − | 0.955766i | \(-0.595030\pi\) |
0.974782 | − | 0.223159i | \(-0.0716369\pi\) | |||||||
\(410\) | 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 | \(-0.319336\pi\) | ||||
0.537587 | + | 0.843208i | \(0.319336\pi\) | |||||||
\(420\) | 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 | 0.487928 | + | 0.872884i | \(0.337753\pi\) |
−0.999904 | + | 0.0138840i | \(0.995580\pi\) | |||||||
\(432\) | 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 | 0.953743 | − | 0.300625i | \(-0.0971951\pi\) |
−0.737220 | + | 0.675653i | \(0.763862\pi\) | |||||||
\(440\) | 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 | \(-0.244674\pi\) |
−0.961460 | + | 0.274944i | \(0.911341\pi\) | |||||||
\(444\) | 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 | \(-0.534805\pi\) | ||||
−0.109127 | + | 0.994028i | \(0.534805\pi\) | |||||||
\(450\) | 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 | 0.909424 | − | 0.415869i | \(-0.136523\pi\) |
−0.814866 | + | 0.579650i | \(0.803189\pi\) | |||||||
\(458\) | −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 | \(-0.514105\pi\) | ||||
−0.0442987 | + | 0.999018i | \(0.514105\pi\) | |||||||
\(462\) | 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 | −0.766502 | − | 0.642242i | \(-0.778004\pi\) |
−0.172947 | − | 0.984931i | \(-0.555329\pi\) | |||||||
\(468\) | 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 | \(-0.964174\pi\) |
0.594101 | + | 0.804390i | \(0.297508\pi\) | |||||||
\(480\) | 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 | −0.740275 | − | 0.672305i | \(-0.765304\pi\) |
0.952370 | + | 0.304944i | \(0.0986378\pi\) | |||||||
\(488\) | −12.1911 | − | 21.1156i | −0.00113087 | − | 0.00195873i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15809.9 | 1.45314 | 0.726570 | − | 0.687092i | \(-0.241113\pi\) | ||||
0.726570 | + | 0.687092i | \(0.241113\pi\) | |||||||
\(492\) | 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 | −0.992754 | − | 0.120167i | \(-0.961657\pi\) |
0.392309 | − | 0.919833i | \(-0.371676\pi\) | |||||||
\(500\) | 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 | \(-0.581597\pi\) | ||||
−0.253545 | + | 0.967323i | \(0.581597\pi\) | |||||||
\(504\) | 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 | −0.979048 | − | 0.203630i | \(-0.934726\pi\) |
0.313175 | − | 0.949695i | \(-0.398607\pi\) | |||||||
\(510\) | 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 | \(-0.774532\pi\) |
0.943131 | + | 0.332420i | \(0.107865\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1211.08 | − | 2097.66i | −0.101256 | − | 0.175381i | 0.810946 | − | 0.585121i | \(-0.198953\pi\) |
−0.912202 | + | 0.409740i | \(0.865619\pi\) | |||||||
\(524\) | −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 | −0.999641 | − | 0.0267819i | \(-0.991474\pi\) |
0.476627 | − | 0.879106i | \(-0.341859\pi\) | |||||||
\(542\) | −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 | \(-0.730335\pi\) |
0.980063 | + | 0.198689i | \(0.0636682\pi\) | |||||||
\(558\) | 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 | −0.489455 | − | 0.872028i | \(-0.662804\pi\) |
0.999926 | − | 0.0121334i | \(-0.00386228\pi\) | |||||||
\(564\) | 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 | −0.996497 | − | 0.0836335i | \(-0.973348\pi\) |
0.425820 | − | 0.904808i | \(-0.359986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2324.08 | − | 4025.42i | 0.170332 | − | 0.295024i | −0.768204 | − | 0.640205i | \(-0.778849\pi\) |
0.938536 | + | 0.345182i | \(0.112183\pi\) | |||||||
\(572\) | −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 | −0.947768 | − | 0.318959i | \(-0.896667\pi\) |
0.750111 | + | 0.661312i | \(0.230000\pi\) | |||||||
\(578\) | 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 | \(-0.549531\pi\) | ||||
−0.154980 | + | 0.987918i | \(0.549531\pi\) | |||||||
\(588\) | 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 | \(-0.135589\pi\) |
−0.813162 | + | 0.582037i | \(0.802256\pi\) | |||||||
\(594\) | 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 | 0.304646 | + | 0.952466i | \(0.401462\pi\) |
−0.977182 | + | 0.212402i | \(0.931871\pi\) | |||||||
\(600\) | 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 | 0.998231 | − | 0.0594590i | \(-0.0189376\pi\) |
−0.550608 | + | 0.834764i | \(0.685604\pi\) | |||||||
\(608\) | −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 | 0.109535 | − | 0.993983i | \(-0.465064\pi\) |
0.806047 | − | 0.591852i | \(-0.201603\pi\) | |||||||
\(614\) | −12073.6 | − | 20912.0i | −0.793566 | − | 1.37450i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19107.2 | −1.24672 | −0.623361 | − | 0.781935i | \(-0.714233\pi\) | ||||
−0.623361 | + | 0.781935i | \(0.714233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 546.469 | − | 946.512i | 0.0354837 | − | 0.0614596i | −0.847738 | − | 0.530415i | \(-0.822036\pi\) |
0.883222 | + | 0.468955i | \(0.155369\pi\) | |||||||
\(620\) | −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 | −0.375776 | − | 0.926711i | \(-0.622624\pi\) |
0.990443 | − | 0.137924i | \(-0.0440430\pi\) | |||||||
\(642\) | 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 | \(-0.725214\pi\) |
0.983132 | + | 0.182897i | \(0.0585475\pi\) | |||||||
\(648\) | 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 | \(-0.0400788\pi\) |
−0.604796 | + | 0.796380i | \(0.706745\pi\) | |||||||
\(654\) | 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 | \(-0.613185\pi\) | ||||
−0.348137 | + | 0.937444i | \(0.613185\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12520.0 | + | 21685.3i | −0.736721 | + | 1.27604i | 0.217243 | + | 0.976118i | \(0.430294\pi\) |
−0.953964 | + | 0.299921i | \(0.903040\pi\) | |||||||
\(662\) | −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 | \(-0.0545549\pi\) |
−0.640376 | + | 0.768061i | \(0.721222\pi\) | |||||||
\(678\) | 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 | −0.424549 | − | 0.905405i | \(-0.639567\pi\) |
0.996378 | − | 0.0850328i | \(-0.0270995\pi\) | |||||||
\(684\) | 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 | 0.997911 | − | 0.0646110i | \(-0.0205807\pi\) |
−0.554910 | + | 0.831910i | \(0.687247\pi\) | |||||||
\(692\) | 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 | \(-0.310637\pi\) | ||||
0.560426 | + | 0.828204i | \(0.310637\pi\) | |||||||
\(702\) | 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 | 0.864146 | − | 0.503242i | \(-0.167860\pi\) |
−0.867893 | + | 0.496751i | \(0.834526\pi\) | |||||||
\(710\) | −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 | \(-0.221961\pi\) |
−0.939411 | + | 0.342792i | \(0.888627\pi\) | |||||||
\(720\) | 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 | −0.922059 | − | 0.387050i | \(-0.873494\pi\) |
0.125834 | − | 0.992051i | \(-0.459839\pi\) | |||||||
\(734\) | 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 | −0.745286 | − | 0.666744i | \(-0.767687\pi\) |
0.950061 | + | 0.312065i | \(0.101021\pi\) | |||||||
\(740\) | −3358.11 | − | 5816.42i | −0.166820 | − | 0.288940i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37020.3 | 1.82792 | 0.913959 | − | 0.405805i | \(-0.133009\pi\) | ||||
0.913959 | + | 0.405805i | \(0.133009\pi\) | |||||||
\(744\) | 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 | 0.991071 | + | 0.133336i | \(0.0425689\pi\) |
−0.380063 | + | 0.924960i | \(0.624098\pi\) | |||||||
\(752\) | −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 | 0.933177 | + | 0.359417i | \(0.117024\pi\) |
−0.155324 | + | 0.987864i | \(0.549642\pi\) | |||||||
\(762\) | 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 | \(-0.855851\pi\) |
0.828518 | + | 0.559963i | \(0.189185\pi\) | |||||||
\(774\) | 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 | −0.971064 | − | 0.238818i | \(-0.923240\pi\) |
0.692355 | + | 0.721557i | \(0.256573\pi\) | |||||||
\(788\) | −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 | \(-0.521286\pi\) | ||||
−0.0668228 | + | 0.997765i | \(0.521286\pi\) | |||||||
\(798\) | 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 | \(-0.759459\pi\) |
0.957809 | + | 0.287405i | \(0.0927926\pi\) | |||||||
\(810\) | 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 | 0.998666 | + | 0.0516309i | \(0.0164419\pi\) |
−0.454619 | + | 0.890686i | \(0.650225\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21889.5 | + | 37913.6i | −0.927118 | + | 1.60582i | −0.139000 | + | 0.990292i | \(0.544389\pi\) |
−0.788119 | + | 0.615524i | \(0.788945\pi\) | |||||||
\(824\) | −443.047 | − | 767.380i | −0.0187309 | − | 0.0324429i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2735.78 | 0.115033 | 0.0575166 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575166 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15572.1 | + | 26971.7i | −0.652402 | + | 1.12999i | 0.330137 | + | 0.943933i | \(0.392905\pi\) |
−0.982538 | + | 0.186060i | \(0.940428\pi\) | |||||||
\(830\) | −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 | \(-0.400290\pi\) | ||||
0.308150 | + | 0.951338i | \(0.400290\pi\) | |||||||
\(840\) | 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 | \(-0.893255\pi\) |
0.757156 | + | 0.653234i | \(0.226588\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16780.6 | + | 29064.8i | 0.666526 | + | 1.15446i | 0.978869 | + | 0.204488i | \(0.0655528\pi\) |
−0.312343 | + | 0.949969i | \(0.601114\pi\) | |||||||
\(860\) | −33268.6 | −1.31913 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −37155.9 | −1.46814 | ||||||||
\(863\) | −12845.8 | − | 22249.6i | −0.506693 | − | 0.877617i | −0.999970 | − | 0.00774521i | \(-0.997535\pi\) |
0.493277 | − | 0.869872i | \(-0.335799\pi\) | |||||||
\(864\) | 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 | 0.912930 | − | 0.408116i | \(-0.133814\pi\) |
−0.809904 | + | 0.586563i | \(0.800481\pi\) | |||||||
\(878\) | −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 | \(-0.273016\pi\) | ||||
0.654174 | + | 0.756344i | \(0.273016\pi\) | |||||||
\(882\) | 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 | \(-0.142419\pi\) |
−0.825462 | + | 0.564458i | \(0.809085\pi\) | |||||||
\(888\) | 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 | −0.575574 | − | 0.817750i | \(-0.695221\pi\) |
0.995979 | + | 0.0895869i | \(0.0285547\pi\) | |||||||
\(908\) | −14319.7 | − | 24802.5i | −0.523366 | − | 0.906497i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9860.77 | 0.358619 | 0.179309 | − | 0.983793i | \(-0.442614\pi\) | ||||
0.179309 | + | 0.983793i | \(0.442614\pi\) | |||||||
\(912\) | 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 | 0.909446 | − | 0.415823i | \(-0.136506\pi\) |
−0.814836 | + | 0.579692i | \(0.803173\pi\) | |||||||
\(920\) | −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 | \(-0.251429\pi\) |
−0.967078 | + | 0.254480i | \(0.918096\pi\) | |||||||
\(930\) | 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 | \(-0.752398\pi\) |
0.963949 | + | 0.266089i | \(0.0857314\pi\) | |||||||
\(942\) | 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 | \(-0.177284\pi\) |
−0.882218 | + | 0.470841i | \(0.843951\pi\) | |||||||
\(948\) | 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 | \(-0.592755\pi\) | ||||
−0.287292 | + | 0.957843i | \(0.592755\pi\) | |||||||
\(954\) | 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 | \(-0.108004\pi\) |
−0.759733 | + | 0.650235i | \(0.774670\pi\) | |||||||
\(972\) | 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 | 0.0319179 | + | 0.999490i | \(0.489838\pi\) |
−0.881543 | + | 0.472103i | \(0.843495\pi\) | |||||||
\(978\) | 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 | \(-0.702880\pi\) |
0.993536 | + | 0.113521i | \(0.0362130\pi\) | |||||||
\(984\) | 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 | −0.678737 | − | 0.734382i | \(-0.737472\pi\) |
0.975362 | + | 0.220612i | \(0.0708056\pi\) | |||||||
\(992\) | −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 | 0.291815 | + | 0.956475i | \(0.405741\pi\) |
−0.974239 | + | 0.225518i | \(0.927593\pi\) | |||||||
\(998\) | 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.361.4 | 8 | ||
3.2 | odd | 2 | inner | 441.4.e.x.361.1 | 8 | ||
7.2 | even | 3 | inner | 441.4.e.x.226.4 | 8 | ||
7.3 | odd | 6 | 441.4.a.w.1.1 | 4 | |||
7.4 | even | 3 | 441.4.a.v.1.1 | 4 | |||
7.5 | odd | 6 | 63.4.e.d.37.4 | yes | 8 | ||
7.6 | odd | 2 | 63.4.e.d.46.4 | yes | 8 | ||
21.2 | odd | 6 | inner | 441.4.e.x.226.1 | 8 | ||
21.5 | even | 6 | 63.4.e.d.37.1 | ✓ | 8 | ||
21.11 | odd | 6 | 441.4.a.v.1.4 | 4 | |||
21.17 | even | 6 | 441.4.a.w.1.4 | 4 | |||
21.20 | even | 2 | 63.4.e.d.46.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.e.d.37.1 | ✓ | 8 | 21.5 | even | 6 | ||
63.4.e.d.37.4 | yes | 8 | 7.5 | odd | 6 | ||
63.4.e.d.46.1 | yes | 8 | 21.20 | even | 2 | ||
63.4.e.d.46.4 | yes | 8 | 7.6 | odd | 2 | ||
441.4.a.v.1.1 | 4 | 7.4 | even | 3 | |||
441.4.a.v.1.4 | 4 | 21.11 | odd | 6 | |||
441.4.a.w.1.1 | 4 | 7.3 | odd | 6 | |||
441.4.a.w.1.4 | 4 | 21.17 | even | 6 | |||
441.4.e.x.226.1 | 8 | 21.2 | odd | 6 | inner | ||
441.4.e.x.226.4 | 8 | 7.2 | even | 3 | inner | ||
441.4.e.x.361.1 | 8 | 3.2 | odd | 2 | inner | ||
441.4.e.x.361.4 | 8 | 1.1 | even | 1 | trivial |