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 | 226.2 | ||
Root | \(0.799027 + 1.38396i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.226 |
Dual form | 441.4.e.x.361.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.799027 | + | 1.38396i | −0.282499 | + | 0.489302i | −0.972000 | − | 0.234983i | \(-0.924497\pi\) |
0.689501 | + | 0.724285i | \(0.257830\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.72311 | + | 4.71657i | 0.340389 | + | 0.589571i | ||||
\(5\) | −9.14584 | + | 15.8411i | −0.818029 | + | 1.41687i | 0.0891033 | + | 0.996022i | \(0.471600\pi\) |
−0.907132 | + | 0.420846i | \(0.861733\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −21.4878 | −0.949635 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.6156 | − | 25.3149i | −0.462184 | − | 0.800527i | ||||
\(11\) | 30.6336 | + | 53.0590i | 0.839672 | + | 1.45435i | 0.890169 | + | 0.455630i | \(0.150586\pi\) |
−0.0504975 | + | 0.998724i | \(0.516081\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.4462 | −0.692228 | −0.346114 | − | 0.938192i | \(-0.612499\pi\) | ||||
−0.346114 | + | 0.938192i | \(0.612499\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.61555 | + | 7.99438i | −0.0721180 | + | 0.124912i | ||||
\(17\) | 40.6644 | + | 70.4329i | 0.580152 | + | 1.00485i | 0.995461 | + | 0.0951718i | \(0.0303400\pi\) |
−0.415309 | + | 0.909680i | \(0.636327\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.4542 | + | 18.1072i | −0.126230 | + | 0.218636i | −0.922213 | − | 0.386682i | \(-0.873621\pi\) |
0.795983 | + | 0.605319i | \(0.206954\pi\) | |||||||
\(20\) | −99.6206 | −1.11379 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −97.9084 | −0.948825 | ||||||||
\(23\) | −16.8655 | + | 29.2119i | −0.152900 | + | 0.264831i | −0.932292 | − | 0.361705i | \(-0.882195\pi\) |
0.779392 | + | 0.626536i | \(0.215528\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −104.793 | − | 181.507i | −0.838343 | − | 1.45205i | ||||
\(26\) | 25.9254 | − | 44.9041i | 0.195554 | − | 0.338709i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −52.0227 | −0.333116 | −0.166558 | − | 0.986032i | \(-0.553265\pi\) | ||||
−0.166558 | + | 0.986032i | \(0.553265\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 96.9622 | + | 167.943i | 0.561772 | + | 0.973017i | 0.997342 | + | 0.0728626i | \(0.0232135\pi\) |
−0.435570 | + | 0.900155i | \(0.643453\pi\) | |||||||
\(32\) | −93.3271 | − | 161.647i | −0.515564 | − | 0.892983i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −129.968 | −0.655568 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 133.578 | − | 231.363i | 0.593515 | − | 1.02800i | −0.400240 | − | 0.916410i | \(-0.631073\pi\) |
0.993755 | − | 0.111587i | \(-0.0355935\pi\) | |||||||
\(38\) | −16.7064 | − | 28.9364i | −0.0713194 | − | 0.123529i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 196.524 | − | 340.390i | 0.776829 | − | 1.34551i | ||||
\(41\) | 203.176 | 0.773921 | 0.386960 | − | 0.922096i | \(-0.373525\pi\) | ||||
0.386960 | + | 0.922096i | \(0.373525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.9520 | −0.0778523 | −0.0389262 | − | 0.999242i | \(-0.512394\pi\) | ||||
−0.0389262 | + | 0.999242i | \(0.512394\pi\) | |||||||
\(44\) | −166.838 | + | 288.971i | −0.571630 | + | 0.990092i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.9520 | − | 46.6822i | −0.0863882 | − | 0.149629i | ||||
\(47\) | 123.961 | − | 214.706i | 0.384713 | − | 0.666343i | −0.607016 | − | 0.794690i | \(-0.707634\pi\) |
0.991729 | + | 0.128346i | \(0.0409669\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 334.929 | 0.947324 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −88.3547 | − | 153.035i | −0.235627 | − | 0.408117i | ||||
\(53\) | 70.4131 | + | 121.959i | 0.182490 | + | 0.316082i | 0.942728 | − | 0.333563i | \(-0.108251\pi\) |
−0.760238 | + | 0.649645i | \(0.774918\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1120.68 | −2.74750 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 41.5676 | − | 71.9971i | 0.0941050 | − | 0.162995i | ||||
\(59\) | 110.734 | + | 191.797i | 0.244344 | + | 0.423217i | 0.961947 | − | 0.273236i | \(-0.0880940\pi\) |
−0.717603 | + | 0.696453i | \(0.754761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 326.263 | − | 565.104i | 0.684815 | − | 1.18613i | −0.288680 | − | 0.957426i | \(-0.593216\pi\) |
0.973495 | − | 0.228709i | \(-0.0734503\pi\) | |||||||
\(62\) | −309.902 | −0.634800 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 224.435 | 0.438349 | ||||||||
\(65\) | 296.748 | − | 513.983i | 0.566263 | − | 0.980796i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −302.239 | − | 523.493i | −0.551110 | − | 0.954551i | −0.998195 | − | 0.0600592i | \(-0.980871\pi\) |
0.447085 | − | 0.894492i | \(-0.352462\pi\) | |||||||
\(68\) | −221.468 | + | 383.593i | −0.394954 | + | 0.684081i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −716.031 | −1.19686 | −0.598431 | − | 0.801174i | \(-0.704209\pi\) | ||||
−0.598431 | + | 0.801174i | \(0.704209\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 194.438 | + | 336.777i | 0.311743 | + | 0.539956i | 0.978740 | − | 0.205105i | \(-0.0657537\pi\) |
−0.666996 | + | 0.745061i | \(0.732420\pi\) | |||||||
\(74\) | 213.465 | + | 369.731i | 0.335334 | + | 0.580816i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −113.872 | −0.171869 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 144.871 | − | 250.923i | 0.206319 | − | 0.357355i | −0.744233 | − | 0.667920i | \(-0.767185\pi\) |
0.950552 | + | 0.310565i | \(0.100518\pi\) | |||||||
\(80\) | −84.4263 | − | 146.231i | −0.117989 | − | 0.204363i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −162.343 | + | 281.186i | −0.218632 | + | 0.378681i | ||||
\(83\) | −115.652 | −0.152946 | −0.0764728 | − | 0.997072i | \(-0.524366\pi\) | ||||
−0.0764728 | + | 0.997072i | \(0.524366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1487.64 | −1.89832 | ||||||||
\(86\) | 17.5403 | − | 30.3806i | 0.0219932 | − | 0.0380933i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −658.249 | − | 1140.12i | −0.797382 | − | 1.38111i | ||||
\(89\) | −469.682 | + | 813.513i | −0.559395 | + | 0.968901i | 0.438152 | + | 0.898901i | \(0.355633\pi\) |
−0.997547 | + | 0.0699997i | \(0.977700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −183.707 | −0.208182 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 198.096 | + | 343.112i | 0.217362 | + | 0.376482i | ||||
\(95\) | −191.225 | − | 331.212i | −0.206519 | − | 0.357701i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −120.394 | −0.126022 | −0.0630110 | − | 0.998013i | \(-0.520070\pi\) | ||||
−0.0630110 | + | 0.998013i | \(0.520070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 570.725 | − | 988.525i | 0.570725 | − | 0.988525i | ||||
\(101\) | −640.502 | − | 1109.38i | −0.631013 | − | 1.09295i | −0.987345 | − | 0.158587i | \(-0.949306\pi\) |
0.356332 | − | 0.934359i | \(-0.384027\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 265.669 | − | 460.153i | 0.254147 | − | 0.440196i | −0.710516 | − | 0.703681i | \(-0.751539\pi\) |
0.964664 | + | 0.263485i | \(0.0848718\pi\) | |||||||
\(104\) | 697.198 | 0.657364 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −225.048 | −0.206213 | ||||||||
\(107\) | 66.6758 | − | 115.486i | 0.0602411 | − | 0.104341i | −0.834332 | − | 0.551262i | \(-0.814146\pi\) |
0.894573 | + | 0.446922i | \(0.147480\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 108.884 | + | 188.593i | 0.0956811 | + | 0.165725i | 0.909893 | − | 0.414844i | \(-0.136164\pi\) |
−0.814212 | + | 0.580568i | \(0.802830\pi\) | |||||||
\(110\) | 895.455 | − | 1550.97i | 0.776166 | − | 1.34436i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2006.09 | 1.67006 | 0.835031 | − | 0.550204i | \(-0.185450\pi\) | ||||
0.835031 | + | 0.550204i | \(0.185450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −308.499 | − | 534.335i | −0.250153 | − | 0.433278i | ||||
\(116\) | −141.664 | − | 245.369i | −0.113389 | − | 0.196396i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −353.917 | −0.276108 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1211.34 | + | 2098.10i | −0.910097 | + | 1.57633i | ||||
\(122\) | 521.386 | + | 903.067i | 0.386919 | + | 0.670163i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −528.078 | + | 914.658i | −0.382442 | + | 0.662409i | ||||
\(125\) | 1547.22 | 1.10710 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1638.92 | 1.14512 | 0.572562 | − | 0.819861i | \(-0.305950\pi\) | ||||
0.572562 | + | 0.819861i | \(0.305950\pi\) | |||||||
\(128\) | 567.287 | − | 982.570i | 0.391731 | − | 0.678498i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 474.220 | + | 821.372i | 0.319937 | + | 0.554147i | ||||
\(131\) | −45.8755 | + | 79.4587i | −0.0305967 | + | 0.0529950i | −0.880918 | − | 0.473268i | \(-0.843074\pi\) |
0.850322 | + | 0.526263i | \(0.176407\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 965.989 | 0.622752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −873.789 | − | 1513.45i | −0.550932 | − | 0.954243i | ||||
\(137\) | −933.564 | − | 1616.98i | −0.582188 | − | 1.00838i | −0.995220 | − | 0.0976621i | \(-0.968864\pi\) |
0.413032 | − | 0.910717i | \(-0.364470\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −639.778 | −0.390397 | −0.195199 | − | 0.980764i | \(-0.562535\pi\) | ||||
−0.195199 | + | 0.980764i | \(0.562535\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 572.128 | − | 990.955i | 0.338112 | − | 0.585627i | ||||
\(143\) | −993.946 | − | 1721.56i | −0.581244 | − | 1.00674i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 475.792 | − | 824.095i | 0.272499 | − | 0.471982i | ||||
\(146\) | −621.446 | −0.352269 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1454.99 | 0.808103 | ||||||||
\(149\) | −1568.27 | + | 2716.32i | −0.862264 | + | 1.49348i | 0.00747495 | + | 0.999972i | \(0.497621\pi\) |
−0.869739 | + | 0.493513i | \(0.835713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1360.68 | + | 2356.77i | 0.733317 | + | 1.27014i | 0.955458 | + | 0.295128i | \(0.0953623\pi\) |
−0.222141 | + | 0.975015i | \(0.571304\pi\) | |||||||
\(152\) | 224.638 | − | 389.085i | 0.119872 | − | 0.207625i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3547.20 | −1.83818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1439.87 | + | 2493.93i | 0.731939 | + | 1.26776i | 0.956053 | + | 0.293193i | \(0.0947178\pi\) |
−0.224114 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(158\) | 231.511 | + | 400.989i | 0.116570 | + | 0.201905i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3414.22 | 1.68699 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −323.071 | + | 559.576i | −0.155245 | + | 0.268892i | −0.933148 | − | 0.359492i | \(-0.882950\pi\) |
0.777903 | + | 0.628384i | \(0.216283\pi\) | |||||||
\(164\) | 553.271 | + | 958.293i | 0.263434 | + | 0.456281i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 92.4093 | − | 160.058i | 0.0432069 | − | 0.0748366i | ||||
\(167\) | −3765.03 | −1.74459 | −0.872296 | − | 0.488979i | \(-0.837370\pi\) | ||||
−0.872296 | + | 0.488979i | \(0.837370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1144.24 | −0.520821 | ||||||||
\(170\) | 1188.67 | − | 2058.83i | 0.536274 | − | 0.928854i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −59.7777 | − | 103.538i | −0.0265001 | − | 0.0458995i | ||||
\(173\) | −1154.49 | + | 1999.64i | −0.507366 | + | 0.878783i | 0.492598 | + | 0.870257i | \(0.336047\pi\) |
−0.999964 | + | 0.00852600i | \(0.997286\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −565.565 | −0.242222 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −750.577 | − | 1300.04i | −0.316057 | − | 0.547427i | ||||
\(179\) | 1516.88 | + | 2627.31i | 0.633390 | + | 1.09706i | 0.986854 | + | 0.161616i | \(0.0516705\pi\) |
−0.353464 | + | 0.935448i | \(0.614996\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4079.71 | 1.67537 | 0.837686 | − | 0.546152i | \(-0.183908\pi\) | ||||
0.837686 | + | 0.546152i | \(0.183908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 362.403 | − | 627.700i | 0.145199 | − | 0.251493i | ||||
\(185\) | 2443.36 | + | 4232.03i | 0.971025 | + | 1.68186i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2491.40 | + | 4315.23i | −0.974274 | + | 1.68749i | ||||
\(188\) | 1350.24 | 0.523809 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 611.177 | 0.233365 | ||||||||
\(191\) | −438.554 | + | 759.599i | −0.166140 | + | 0.287762i | −0.937059 | − | 0.349170i | \(-0.886464\pi\) |
0.770920 | + | 0.636932i | \(0.219797\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 729.356 | + | 1263.28i | 0.272022 | + | 0.471155i | 0.969379 | − | 0.245568i | \(-0.0789744\pi\) |
−0.697358 | + | 0.716723i | \(0.745641\pi\) | |||||||
\(194\) | 96.1979 | − | 166.620i | 0.0356011 | − | 0.0616629i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 952.250 | 0.344391 | 0.172195 | − | 0.985063i | \(-0.444914\pi\) | ||||
0.172195 | + | 0.985063i | \(0.444914\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1671.11 | + | 2894.44i | 0.595285 | + | 1.03106i | 0.993507 | + | 0.113774i | \(0.0362941\pi\) |
−0.398222 | + | 0.917289i | \(0.630373\pi\) | |||||||
\(200\) | 2251.77 | + | 3900.18i | 0.796120 | + | 1.37892i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2047.11 | 0.713041 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1858.22 | + | 3218.52i | −0.633090 | + | 1.09654i | ||||
\(206\) | 424.554 | + | 735.349i | 0.143593 | + | 0.248710i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 149.757 | − | 259.387i | 0.0499221 | − | 0.0864677i | ||||
\(209\) | −1281.00 | −0.423966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1439.27 | 0.469589 | 0.234794 | − | 0.972045i | \(-0.424558\pi\) | ||||
0.234794 | + | 0.972045i | \(0.424558\pi\) | |||||||
\(212\) | −383.485 | + | 664.216i | −0.124235 | + | 0.215182i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 106.552 | + | 184.553i | 0.0340361 | + | 0.0589522i | ||||
\(215\) | 200.770 | − | 347.743i | 0.0636855 | − | 0.110306i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −348.007 | −0.108119 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3051.74 | − | 5285.77i | −0.935220 | − | 1.61985i | ||||
\(221\) | −1319.41 | − | 2285.28i | −0.401597 | − | 0.695587i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1009.86 | −0.303253 | −0.151626 | − | 0.988438i | \(-0.548451\pi\) | ||||
−0.151626 | + | 0.988438i | \(0.548451\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1602.92 | + | 2776.34i | −0.471790 | + | 0.817165i | ||||
\(227\) | −1474.30 | − | 2553.57i | −0.431070 | − | 0.746635i | 0.565896 | − | 0.824477i | \(-0.308530\pi\) |
−0.996966 | + | 0.0778419i | \(0.975197\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2019.42 | + | 3497.74i | −0.582739 | + | 1.00933i | 0.412414 | + | 0.910997i | \(0.364686\pi\) |
−0.995153 | + | 0.0983374i | \(0.968648\pi\) | |||||||
\(230\) | 985.995 | 0.282672 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1117.85 | 0.316339 | ||||||||
\(233\) | −1497.90 | + | 2594.44i | −0.421162 | + | 0.729473i | −0.996053 | − | 0.0887561i | \(-0.971711\pi\) |
0.574892 | + | 0.818230i | \(0.305044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2267.45 | + | 3927.34i | 0.629413 | + | 1.09018i | ||||
\(236\) | −603.081 | + | 1044.57i | −0.166344 | + | 0.288117i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1810.28 | −0.489948 | −0.244974 | − | 0.969530i | \(-0.578779\pi\) | ||||
−0.244974 | + | 0.969530i | \(0.578779\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1874.71 | − | 3247.10i | −0.501083 | − | 0.867900i | −0.999999 | − | 0.00125048i | \(-0.999602\pi\) |
0.498917 | − | 0.866650i | \(-0.333731\pi\) | |||||||
\(242\) | −1935.79 | − | 3352.88i | −0.514203 | − | 0.890625i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3553.80 | 0.932414 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 339.200 | − | 587.512i | 0.0873797 | − | 0.151346i | ||||
\(248\) | −2083.50 | − | 3608.74i | −0.533478 | − | 0.924012i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1236.27 | + | 2141.28i | −0.312754 | + | 0.541706i | ||||
\(251\) | 2706.96 | 0.680724 | 0.340362 | − | 0.940295i | \(-0.389450\pi\) | ||||
0.340362 | + | 0.940295i | \(0.389450\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2066.61 | −0.513544 | ||||||||
\(254\) | −1309.54 | + | 2268.20i | −0.323496 | + | 0.560312i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1804.29 | + | 3125.13i | 0.440502 | + | 0.762971i | ||||
\(257\) | 2687.64 | − | 4655.13i | 0.652337 | − | 1.12988i | −0.330218 | − | 0.943905i | \(-0.607122\pi\) |
0.982554 | − | 0.185975i | \(-0.0595445\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3232.31 | 0.770998 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −73.3116 | − | 126.979i | −0.0172870 | − | 0.0299420i | ||||
\(263\) | −2623.28 | − | 4543.66i | −0.615051 | − | 1.06530i | −0.990376 | − | 0.138406i | \(-0.955802\pi\) |
0.375324 | − | 0.926893i | \(-0.377531\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2575.95 | −0.597129 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1646.06 | − | 2851.06i | 0.375184 | − | 0.649837i | ||||
\(269\) | 1506.66 | + | 2609.61i | 0.341496 | + | 0.591489i | 0.984711 | − | 0.174197i | \(-0.0557329\pi\) |
−0.643214 | + | 0.765686i | \(0.722400\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3448.62 | − | 5973.19i | 0.773022 | − | 1.33891i | −0.162877 | − | 0.986646i | \(-0.552077\pi\) |
0.935899 | − | 0.352267i | \(-0.114589\pi\) | |||||||
\(272\) | −750.756 | −0.167358 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2983.77 | 0.657869 | ||||||||
\(275\) | 6420.37 | − | 11120.4i | 1.40787 | − | 2.43850i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1659.30 | − | 2874.00i | −0.359920 | − | 0.623400i | 0.628027 | − | 0.778191i | \(-0.283863\pi\) |
−0.987947 | + | 0.154792i | \(0.950529\pi\) | |||||||
\(278\) | 511.200 | − | 885.424i | 0.110287 | − | 0.191022i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6274.14 | 1.33197 | 0.665986 | − | 0.745964i | \(-0.268011\pi\) | ||||
0.665986 | + | 0.745964i | \(0.268011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3886.24 | + | 6731.16i | 0.816300 | + | 1.41387i | 0.908391 | + | 0.418122i | \(0.137311\pi\) |
−0.0920914 | + | 0.995751i | \(0.529355\pi\) | |||||||
\(284\) | −1949.83 | − | 3377.21i | −0.407399 | − | 0.705635i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3176.76 | 0.656803 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −850.695 | + | 1473.45i | −0.173152 | + | 0.299908i | ||||
\(290\) | 760.341 | + | 1316.95i | 0.153961 | + | 0.266669i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1058.95 | + | 1834.16i | −0.212228 | + | 0.367590i | ||||
\(293\) | 854.897 | 0.170456 | 0.0852280 | − | 0.996361i | \(-0.472838\pi\) | ||||
0.0852280 | + | 0.996361i | \(0.472838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4051.02 | −0.799523 | ||||||||
\(296\) | −2870.29 | + | 4971.49i | −0.563623 | + | 0.976223i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2506.17 | − | 4340.82i | −0.487177 | − | 0.843815i | ||||
\(299\) | 547.222 | − | 947.817i | 0.105842 | − | 0.183323i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4348.89 | −0.828645 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −96.5041 | − | 167.150i | −0.0182069 | − | 0.0315352i | ||||
\(305\) | 5967.90 | + | 10336.7i | 1.12040 | + | 1.94058i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2550.68 | −0.474185 | −0.237092 | − | 0.971487i | \(-0.576194\pi\) | ||||
−0.237092 | + | 0.971487i | \(0.576194\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2834.31 | − | 4909.17i | 0.519284 | − | 0.899427i | ||||
\(311\) | −3740.25 | − | 6478.31i | −0.681962 | − | 1.18119i | −0.974381 | − | 0.224903i | \(-0.927794\pi\) |
0.292419 | − | 0.956290i | \(-0.405540\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.12392 | − | 5.41079i | 0.000564135 | − | 0.000977111i | −0.865743 | − | 0.500488i | \(-0.833154\pi\) |
0.866307 | + | 0.499511i | \(0.166487\pi\) | |||||||
\(314\) | −4601.99 | −0.827088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1578.00 | 0.280915 | ||||||||
\(317\) | 482.902 | − | 836.410i | 0.0855598 | − | 0.148194i | −0.820070 | − | 0.572263i | \(-0.806065\pi\) |
0.905630 | + | 0.424070i | \(0.139399\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1593.64 | − | 2760.27i | −0.279708 | − | 0.484469i | ||||
\(320\) | −2052.64 | + | 3555.28i | −0.358582 | + | 0.621083i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1700.46 | −0.292929 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3400.13 | + | 5889.20i | 0.580324 | + | 1.00515i | ||||
\(326\) | −516.285 | − | 894.232i | −0.0877129 | − | 0.151923i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4365.80 | −0.734942 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3355.10 | + | 5811.20i | −0.557139 | + | 0.964992i | 0.440595 | + | 0.897706i | \(0.354767\pi\) |
−0.997734 | + | 0.0672865i | \(0.978566\pi\) | |||||||
\(332\) | −314.934 | − | 545.482i | −0.0520610 | − | 0.0901723i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3008.36 | − | 5210.64i | 0.492845 | − | 0.853633i | ||||
\(335\) | 11056.9 | 1.80330 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −605.546 | −0.0978819 | −0.0489409 | − | 0.998802i | \(-0.515585\pi\) | ||||
−0.0489409 | + | 0.998802i | \(0.515585\pi\) | |||||||
\(338\) | 914.281 | − | 1583.58i | 0.147131 | − | 0.254839i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4051.02 | − | 7016.57i | −0.646168 | − | 1.11920i | ||||
\(341\) | −5940.61 | + | 10289.4i | −0.943408 | + | 1.63403i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 471.700 | 0.0739313 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1844.94 | − | 3195.53i | −0.286660 | − | 0.496510i | ||||
\(347\) | 3469.08 | + | 6008.62i | 0.536686 | + | 0.929567i | 0.999080 | + | 0.0428923i | \(0.0136572\pi\) |
−0.462394 | + | 0.886675i | \(0.653009\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10368.9 | −1.59035 | −0.795176 | − | 0.606378i | \(-0.792622\pi\) | ||||
−0.795176 | + | 0.606378i | \(0.792622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5717.90 | − | 9903.69i | 0.865809 | − | 1.49963i | ||||
\(353\) | 2940.88 | + | 5093.75i | 0.443420 | + | 0.768026i | 0.997941 | − | 0.0641440i | \(-0.0204317\pi\) |
−0.554521 | + | 0.832170i | \(0.687098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6548.70 | − | 11342.7i | 0.979068 | − | 1.69580i | ||||
\(356\) | −5115.98 | −0.761647 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4848.11 | −0.715728 | ||||||||
\(359\) | 294.634 | − | 510.322i | 0.0433153 | − | 0.0750244i | −0.843555 | − | 0.537043i | \(-0.819541\pi\) |
0.886870 | + | 0.462019i | \(0.152875\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3210.92 | + | 5561.47i | 0.468132 | + | 0.810829i | ||||
\(362\) | −3259.80 | + | 5646.14i | −0.473291 | + | 0.819763i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7113.21 | −1.02006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1774.36 | − | 3073.28i | −0.252373 | − | 0.437122i | 0.711806 | − | 0.702376i | \(-0.247878\pi\) |
−0.964179 | + | 0.265254i | \(0.914544\pi\) | |||||||
\(368\) | −155.687 | − | 269.658i | −0.0220537 | − | 0.0381982i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7809.25 | −1.09725 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 790.667 | − | 1369.47i | 0.109756 | − | 0.190104i | −0.805915 | − | 0.592031i | \(-0.798326\pi\) |
0.915672 | + | 0.401927i | \(0.131660\pi\) | |||||||
\(374\) | −3981.39 | − | 6895.97i | −0.550462 | − | 0.953429i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2663.64 | + | 4613.56i | −0.365337 | + | 0.632783i | ||||
\(377\) | 1687.94 | 0.230592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3057.01 | 0.414322 | 0.207161 | − | 0.978307i | \(-0.433578\pi\) | ||||
0.207161 | + | 0.978307i | \(0.433578\pi\) | |||||||
\(380\) | 1041.46 | − | 1803.85i | 0.140594 | − | 0.243515i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −700.834 | − | 1213.88i | −0.0938685 | − | 0.162585i | ||||
\(383\) | 5289.87 | − | 9162.33i | 0.705744 | − | 1.22238i | −0.260678 | − | 0.965426i | \(-0.583946\pi\) |
0.966422 | − | 0.256959i | \(-0.0827204\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2331.10 | −0.307383 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −327.846 | − | 567.845i | −0.0428965 | − | 0.0742989i | ||||
\(389\) | −3696.65 | − | 6402.78i | −0.481819 | − | 0.834534i | 0.517964 | − | 0.855403i | \(-0.326690\pi\) |
−0.999782 | + | 0.0208684i | \(0.993357\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2743.31 | −0.354821 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −760.874 | + | 1317.87i | −0.0972900 | + | 0.168511i | ||||
\(395\) | 2649.93 | + | 4589.81i | 0.337550 | + | 0.584654i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 889.086 | − | 1539.94i | 0.112398 | − | 0.194679i | −0.804339 | − | 0.594171i | \(-0.797480\pi\) |
0.916737 | + | 0.399492i | \(0.130814\pi\) | |||||||
\(398\) | −5341.04 | −0.672669 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1934.71 | 0.241839 | ||||||||
\(401\) | −73.8031 | + | 127.831i | −0.00919090 | + | 0.0159191i | −0.870584 | − | 0.492019i | \(-0.836259\pi\) |
0.861393 | + | 0.507938i | \(0.169592\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3146.06 | − | 5449.13i | −0.388874 | − | 0.673550i | ||||
\(404\) | 3488.31 | − | 6041.94i | 0.429579 | − | 0.744053i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16367.9 | 1.99343 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1080.03 | − | 1870.66i | −0.130572 | − | 0.226157i | 0.793325 | − | 0.608798i | \(-0.208348\pi\) |
−0.923897 | + | 0.382641i | \(0.875015\pi\) | |||||||
\(410\) | −2969.53 | − | 5143.37i | −0.357694 | − | 0.619544i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2893.79 | 0.346036 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1057.74 | − | 1832.05i | 0.125114 | − | 0.216704i | ||||
\(416\) | 3028.11 | + | 5244.84i | 0.356888 | + | 0.618148i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1023.56 | − | 1772.85i | 0.119770 | − | 0.207447i | ||||
\(419\) | −13491.0 | −1.57298 | −0.786488 | − | 0.617605i | \(-0.788103\pi\) | ||||
−0.786488 | + | 0.617605i | \(0.788103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14146.7 | −1.63769 | −0.818847 | − | 0.574012i | \(-0.805386\pi\) | ||||
−0.818847 | + | 0.574012i | \(0.805386\pi\) | |||||||
\(422\) | −1150.01 | + | 1991.88i | −0.132658 | + | 0.229771i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1513.02 | − | 2620.63i | −0.173299 | − | 0.300163i | ||||
\(425\) | 8522.69 | − | 14761.7i | 0.972732 | − | 1.68482i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 726.262 | 0.0820215 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 320.841 | + | 555.712i | 0.0359821 | + | 0.0623229i | ||||
\(431\) | −4544.26 | − | 7870.89i | −0.507864 | − | 0.879646i | −0.999959 | − | 0.00910411i | \(-0.997102\pi\) |
0.492095 | − | 0.870542i | \(-0.336231\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15461.2 | −1.71597 | −0.857986 | − | 0.513673i | \(-0.828284\pi\) | ||||
−0.857986 | + | 0.513673i | \(0.828284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −593.009 | + | 1027.12i | −0.0651376 | + | 0.112822i | ||||
\(437\) | −352.632 | − | 610.776i | −0.0386010 | − | 0.0668590i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −891.091 | + | 1543.41i | −0.0968780 | + | 0.167798i | −0.910391 | − | 0.413749i | \(-0.864219\pi\) |
0.813513 | + | 0.581547i | \(0.197552\pi\) | |||||||
\(440\) | 24081.0 | 2.60913 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4216.97 | 0.453803 | ||||||||
\(443\) | −6712.36 | + | 11626.1i | −0.719896 | + | 1.24690i | 0.241145 | + | 0.970489i | \(0.422477\pi\) |
−0.961041 | + | 0.276407i | \(0.910856\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8591.27 | − | 14880.5i | −0.915203 | − | 1.58518i | ||||
\(446\) | 806.907 | − | 1397.60i | 0.0856685 | − | 0.148382i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 418.639 | 0.0440018 | 0.0220009 | − | 0.999758i | \(-0.492996\pi\) | ||||
0.0220009 | + | 0.999758i | \(0.492996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6224.02 | + | 10780.3i | 0.649839 | + | 1.12555i | ||||
\(452\) | 5462.80 | + | 9461.85i | 0.568470 | + | 0.984619i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4712.03 | 0.487107 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 354.205 | − | 613.501i | 0.0362560 | − | 0.0627973i | −0.847328 | − | 0.531070i | \(-0.821790\pi\) |
0.883584 | + | 0.468273i | \(0.155123\pi\) | |||||||
\(458\) | −3227.15 | − | 5589.59i | −0.329246 | − | 0.570271i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1680.15 | − | 2910.11i | 0.170299 | − | 0.294966i | ||||
\(461\) | −8223.97 | −0.830865 | −0.415432 | − | 0.909624i | \(-0.636370\pi\) | ||||
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9414.17 | −0.944954 | −0.472477 | − | 0.881343i | \(-0.656640\pi\) | ||||
−0.472477 | + | 0.881343i | \(0.656640\pi\) | |||||||
\(464\) | 240.114 | − | 415.889i | 0.0240237 | − | 0.0416103i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2393.73 | − | 4146.05i | −0.237955 | − | 0.412151i | ||||
\(467\) | −5410.76 | + | 9371.72i | −0.536146 | + | 0.928632i | 0.462961 | + | 0.886379i | \(0.346787\pi\) |
−0.999107 | + | 0.0422535i | \(0.986546\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −7247.02 | −0.711234 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2379.43 | − | 4121.29i | −0.232038 | − | 0.401902i | ||||
\(473\) | −672.470 | − | 1164.75i | −0.0653704 | − | 0.113225i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4382.11 | 0.423295 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1446.47 | − | 2505.35i | 0.138410 | − | 0.239733i | ||||
\(479\) | 4092.75 | + | 7088.85i | 0.390402 | + | 0.676196i | 0.992503 | − | 0.122224i | \(-0.0390026\pi\) |
−0.602100 | + | 0.798420i | \(0.705669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4334.09 | + | 7506.87i | −0.410848 | + | 0.711609i | ||||
\(482\) | 5991.79 | 0.566221 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13194.4 | −1.23915 | ||||||||
\(485\) | 1101.10 | − | 1907.17i | 0.103090 | − | 0.178557i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2001.58 | + | 3466.83i | 0.186242 | + | 0.322581i | 0.943994 | − | 0.329961i | \(-0.107036\pi\) |
−0.757752 | + | 0.652543i | \(0.773702\pi\) | |||||||
\(488\) | −7010.67 | + | 12142.8i | −0.650324 | + | 1.12639i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11180.8 | −1.02766 | −0.513831 | − | 0.857891i | \(-0.671774\pi\) | ||||
−0.513831 | + | 0.857891i | \(0.671774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2115.47 | − | 3664.11i | −0.193258 | − | 0.334733i | ||||
\(494\) | 542.060 | + | 938.876i | 0.0493693 | + | 0.0855101i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1790.14 | −0.162056 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1885.54 | − | 3265.85i | 0.169155 | − | 0.292985i | −0.768968 | − | 0.639287i | \(-0.779229\pi\) |
0.938123 | + | 0.346302i | \(0.112563\pi\) | |||||||
\(500\) | 4213.24 | + | 7297.55i | 0.376844 | + | 0.652713i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2162.93 | + | 3746.31i | −0.192304 | + | 0.333080i | ||||
\(503\) | −13597.2 | −1.20531 | −0.602654 | − | 0.798003i | \(-0.705890\pi\) | ||||
−0.602654 | + | 0.798003i | \(0.705890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23431.7 | 2.06475 | ||||||||
\(506\) | 1651.28 | − | 2860.09i | 0.145075 | − | 0.251278i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4462.97 | + | 7730.08i | 0.389788 | + | 0.675132i | ||||
\(509\) | −3680.38 | + | 6374.60i | −0.320491 | + | 0.555106i | −0.980589 | − | 0.196073i | \(-0.937181\pi\) |
0.660099 | + | 0.751179i | \(0.270515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3309.87 | 0.285698 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4295.00 | + | 7439.16i | 0.368569 | + | 0.638380i | ||||
\(515\) | 4859.54 | + | 8416.97i | 0.415800 | + | 0.720186i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15189.5 | 1.29213 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6376.46 | + | 11044.4i | −0.537743 | + | 0.931398i | ||||
\(521\) | −6899.40 | − | 11950.1i | −0.580169 | − | 1.00488i | −0.995459 | − | 0.0951930i | \(-0.969653\pi\) |
0.415290 | − | 0.909689i | \(-0.363680\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9423.58 | − | 16322.1i | 0.787886 | − | 1.36466i | −0.139373 | − | 0.990240i | \(-0.544509\pi\) |
0.927260 | − | 0.374419i | \(-0.122158\pi\) | |||||||
\(524\) | −499.697 | −0.0416591 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8384.29 | 0.695005 | ||||||||
\(527\) | −7885.83 | + | 13658.7i | −0.651826 | + | 1.12900i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5514.61 | + | 9551.58i | 0.453243 | + | 0.785040i | ||||
\(530\) | 2058.25 | − | 3565.00i | 0.168688 | − | 0.292177i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6592.29 | −0.535730 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1219.61 | + | 2112.43i | 0.0985579 | + | 0.170707i | ||||
\(536\) | 6494.45 | + | 11248.7i | 0.523354 | + | 0.906475i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4815.44 | −0.385889 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7234.77 | − | 12531.0i | 0.574948 | − | 0.995839i | −0.421099 | − | 0.907015i | \(-0.638356\pi\) |
0.996047 | − | 0.0888248i | \(-0.0283111\pi\) | |||||||
\(542\) | 5511.09 | + | 9545.49i | 0.436756 | + | 0.756483i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7590.19 | − | 13146.6i | 0.598211 | − | 1.03613i | ||||
\(545\) | −3983.36 | −0.313080 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5749.63 | 0.449427 | 0.224713 | − | 0.974425i | \(-0.427855\pi\) | ||||
0.224713 | + | 0.974425i | \(0.427855\pi\) | |||||||
\(548\) | 5084.39 | − | 8806.43i | 0.396340 | − | 0.686482i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 10260.1 | + | 17771.0i | 0.795441 | + | 1.37774i | ||||
\(551\) | 543.857 | − | 941.988i | 0.0420492 | − | 0.0728313i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5303.31 | 0.406708 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1742.19 | − | 3017.55i | −0.132887 | − | 0.230167i | ||||
\(557\) | 2715.39 | + | 4703.19i | 0.206561 | + | 0.357775i | 0.950629 | − | 0.310330i | \(-0.100439\pi\) |
−0.744068 | + | 0.668104i | \(0.767106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 712.260 | 0.0538915 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5013.21 | + | 8683.14i | −0.376280 | + | 0.651737i | ||||
\(563\) | 12065.3 | + | 20897.8i | 0.903185 | + | 1.56436i | 0.823335 | + | 0.567556i | \(0.192111\pi\) |
0.0798500 | + | 0.996807i | \(0.474556\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18347.4 | + | 31778.6i | −1.36616 | + | 2.36626i | ||||
\(566\) | −12420.8 | −0.922415 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15385.9 | 1.13658 | ||||||||
\(569\) | 9024.27 | − | 15630.5i | 0.664880 | − | 1.15161i | −0.314437 | − | 0.949278i | \(-0.601816\pi\) |
0.979318 | − | 0.202328i | \(-0.0648509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5637.42 | + | 9764.30i | 0.413168 | + | 0.715628i | 0.995234 | − | 0.0975136i | \(-0.0310889\pi\) |
−0.582066 | + | 0.813141i | \(0.697756\pi\) | |||||||
\(572\) | 5413.25 | − | 9376.02i | 0.395698 | − | 0.685369i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7069.54 | 0.512731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12047.5 | − | 20866.8i | −0.869225 | − | 1.50554i | −0.862790 | − | 0.505562i | \(-0.831285\pi\) |
−0.00643457 | − | 0.999979i | \(-0.502048\pi\) | |||||||
\(578\) | −1359.46 | − | 2354.65i | −0.0978303 | − | 0.169447i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5182.53 | 0.371022 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4314.02 | + | 7472.10i | −0.306464 | + | 0.530811i | ||||
\(584\) | −4178.05 | − | 7236.59i | −0.296043 | − | 0.512761i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −683.086 | + | 1183.14i | −0.0481536 | + | 0.0834045i | ||||
\(587\) | 11438.9 | 0.804315 | 0.402157 | − | 0.915571i | \(-0.368260\pi\) | ||||
0.402157 | + | 0.915571i | \(0.368260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4054.66 | −0.283649 | ||||||||
\(590\) | 3236.87 | − | 5606.43i | 0.225864 | − | 0.391208i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1233.07 | + | 2135.74i | 0.0856063 | + | 0.148274i | ||||
\(593\) | 2087.22 | − | 3615.17i | 0.144539 | − | 0.250349i | −0.784662 | − | 0.619924i | \(-0.787163\pi\) |
0.929201 | + | 0.369575i | \(0.120497\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17082.2 | −1.17402 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 874.491 | + | 1514.66i | 0.0598003 | + | 0.103577i | ||||
\(599\) | −5727.77 | − | 9920.79i | −0.390702 | − | 0.676715i | 0.601841 | − | 0.798616i | \(-0.294434\pi\) |
−0.992542 | + | 0.121901i | \(0.961101\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17539.2 | 1.19042 | 0.595208 | − | 0.803572i | \(-0.297070\pi\) | ||||
0.595208 | + | 0.803572i | \(0.297070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7410.59 | + | 12835.5i | −0.499226 | + | 0.864685i | ||||
\(605\) | −22157.4 | − | 38377.8i | −1.48897 | − | 2.57898i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1692.86 | − | 2932.12i | 0.113198 | − | 0.196064i | −0.803860 | − | 0.594818i | \(-0.797224\pi\) |
0.917058 | + | 0.398754i | \(0.130557\pi\) | |||||||
\(608\) | 3902.65 | 0.260318 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19074.1 | −1.26604 | ||||||||
\(611\) | −4022.06 | + | 6966.41i | −0.266309 | + | 0.461261i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2135.94 | − | 3699.56i | −0.140734 | − | 0.243758i | 0.787039 | − | 0.616903i | \(-0.211613\pi\) |
−0.927773 | + | 0.373145i | \(0.878279\pi\) | |||||||
\(614\) | 2038.06 | − | 3530.02i | 0.133957 | − | 0.232020i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13123.9 | 0.856321 | 0.428160 | − | 0.903703i | \(-0.359162\pi\) | ||||
0.428160 | + | 0.903703i | \(0.359162\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −946.969 | − | 1640.20i | −0.0614893 | − | 0.106503i | 0.833642 | − | 0.552305i | \(-0.186252\pi\) |
−0.895131 | + | 0.445803i | \(0.852918\pi\) | |||||||
\(620\) | −9659.43 | − | 16730.6i | −0.625697 | − | 1.08374i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11954.3 | 0.770614 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1051.49 | + | 1821.23i | −0.0672952 | + | 0.116559i | ||||
\(626\) | 4.99219 | + | 8.64673i | 0.000318735 | + | 0.000552066i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7841.87 | + | 13582.5i | −0.498288 | + | 0.863060i | ||||
\(629\) | 21727.5 | 1.37731 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20443.8 | 1.28979 | 0.644894 | − | 0.764272i | \(-0.276902\pi\) | ||||
0.644894 | + | 0.764272i | \(0.276902\pi\) | |||||||
\(632\) | −3112.95 | + | 5391.79i | −0.195928 | + | 0.339357i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 771.703 | + | 1336.63i | 0.0483411 | + | 0.0837292i | ||||
\(635\) | −14989.3 | + | 25962.3i | −0.936745 | + | 1.62249i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5093.46 | 0.316069 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 10376.6 | + | 17972.9i | 0.640895 | + | 1.11006i | ||||
\(641\) | −9614.27 | − | 16652.4i | −0.592419 | − | 1.02610i | −0.993906 | − | 0.110235i | \(-0.964840\pi\) |
0.401486 | − | 0.915865i | \(-0.368494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18525.1 | 1.13617 | 0.568087 | − | 0.822969i | \(-0.307684\pi\) | ||||
0.568087 | + | 0.822969i | \(0.307684\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1358.71 | − | 2353.36i | 0.0827522 | − | 0.143331i | ||||
\(647\) | 4011.20 | + | 6947.60i | 0.243735 | + | 0.422161i | 0.961775 | − | 0.273840i | \(-0.0882940\pi\) |
−0.718040 | + | 0.696001i | \(0.754961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6784.36 | + | 11750.9i | −0.410338 | + | 0.710726i | ||||
\(650\) | −10867.2 | −0.655764 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3519.03 | −0.211374 | ||||||||
\(653\) | −1025.85 | + | 1776.82i | −0.0614769 | + | 0.106481i | −0.895126 | − | 0.445814i | \(-0.852914\pi\) |
0.833649 | + | 0.552295i | \(0.186248\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −839.141 | − | 1453.43i | −0.0500579 | − | 0.0867029i | ||||
\(656\) | −937.770 | + | 1624.26i | −0.0558136 | + | 0.0966721i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14765.2 | 0.872792 | 0.436396 | − | 0.899755i | \(-0.356255\pi\) | ||||
0.436396 | + | 0.899755i | \(0.356255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 323.532 | + | 560.374i | 0.0190377 | + | 0.0329743i | 0.875387 | − | 0.483422i | \(-0.160606\pi\) |
−0.856350 | + | 0.516397i | \(0.827273\pi\) | |||||||
\(662\) | −5361.63 | − | 9286.62i | −0.314782 | − | 0.545218i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2485.11 | 0.145243 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 877.390 | − | 1519.68i | 0.0509335 | − | 0.0882195i | ||||
\(668\) | −10252.6 | − | 17758.0i | −0.593840 | − | 1.02856i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8834.78 | + | 15302.3i | −0.509429 | + | 0.882357i | ||||
\(671\) | 39978.5 | 2.30008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22596.6 | −1.29426 | −0.647130 | − | 0.762380i | \(-0.724031\pi\) | ||||
−0.647130 | + | 0.762380i | \(0.724031\pi\) | |||||||
\(674\) | 483.848 | − | 838.049i | 0.0276515 | − | 0.0478938i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3115.90 | − | 5396.90i | −0.177282 | − | 0.307061i | ||||
\(677\) | 12602.1 | − | 21827.5i | 0.715420 | − | 1.23914i | −0.247377 | − | 0.968919i | \(-0.579569\pi\) |
0.962797 | − | 0.270225i | \(-0.0870980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 31966.2 | 1.80272 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9493.42 | − | 16443.1i | −0.533023 | − | 0.923223i | ||||
\(683\) | 8510.27 | + | 14740.2i | 0.476774 | + | 0.825796i | 0.999646 | − | 0.0266151i | \(-0.00847285\pi\) |
−0.522872 | + | 0.852411i | \(0.675140\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34152.9 | 1.90499 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 101.321 | − | 175.493i | 0.00561456 | − | 0.00972470i | ||||
\(689\) | −2284.64 | − | 3957.11i | −0.126325 | − | 0.218801i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9645.26 | + | 16706.1i | −0.531003 | + | 0.919724i | 0.468342 | + | 0.883547i | \(0.344851\pi\) |
−0.999345 | + | 0.0361772i | \(0.988482\pi\) | |||||||
\(692\) | −12575.2 | −0.690806 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11087.6 | −0.606452 | ||||||||
\(695\) | 5851.31 | − | 10134.8i | 0.319356 | − | 0.553142i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8262.04 | + | 14310.3i | 0.448991 | + | 0.777676i | ||||
\(698\) | 8285.01 | − | 14350.1i | 0.449273 | − | 0.778163i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28511.4 | −1.53618 | −0.768088 | − | 0.640345i | \(-0.778792\pi\) | ||||
−0.768088 | + | 0.640345i | \(0.778792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2792.90 | + | 4837.45i | 0.149838 | + | 0.259528i | ||||
\(704\) | 6875.25 | + | 11908.3i | 0.368069 | + | 0.637515i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9399.37 | −0.501062 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14213.3 | + | 24618.1i | −0.752877 | + | 1.30402i | 0.193546 | + | 0.981091i | \(0.438001\pi\) |
−0.946423 | + | 0.322930i | \(0.895332\pi\) | |||||||
\(710\) | 10465.2 | + | 18126.2i | 0.553171 | + | 0.958120i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10092.4 | − | 17480.6i | 0.531221 | − | 0.920102i | ||||
\(713\) | −6541.27 | −0.343580 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36361.9 | 1.90190 | ||||||||
\(716\) | −8261.26 | + | 14308.9i | −0.431198 | + | 0.746857i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 470.842 | + | 815.522i | 0.0244731 | + | 0.0423886i | ||||
\(719\) | 10881.7 | − | 18847.6i | 0.564420 | − | 0.977603i | −0.432684 | − | 0.901546i | \(-0.642433\pi\) |
0.997103 | − | 0.0760577i | \(-0.0242333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10262.4 | −0.528987 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11109.5 | + | 19242.2i | 0.570278 | + | 0.987750i | ||||
\(725\) | 5451.61 | + | 9442.47i | 0.279266 | + | 0.483703i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13422.8 | 0.684763 | 0.342382 | − | 0.939561i | \(-0.388766\pi\) | ||||
0.342382 | + | 0.939561i | \(0.388766\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5683.65 | − | 9844.36i | 0.288166 | − | 0.499118i | ||||
\(731\) | −892.666 | − | 1546.14i | −0.0451661 | − | 0.0782301i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2279.76 | − | 3948.66i | 0.114877 | − | 0.198973i | −0.802854 | − | 0.596176i | \(-0.796686\pi\) |
0.917731 | + | 0.397204i | \(0.130019\pi\) | |||||||
\(734\) | 5671.04 | 0.285180 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6296.04 | 0.315319 | ||||||||
\(737\) | 18517.4 | − | 32073.0i | 0.925503 | − | 1.60302i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18332.7 | + | 31753.2i | 0.912557 | + | 1.58059i | 0.810439 | + | 0.585823i | \(0.199228\pi\) |
0.102118 | + | 0.994772i | \(0.467438\pi\) | |||||||
\(740\) | −13307.1 | + | 23048.6i | −0.661052 | + | 1.14498i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10321.3 | 0.509625 | 0.254813 | − | 0.966990i | \(-0.417986\pi\) | ||||
0.254813 | + | 0.966990i | \(0.417986\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28686.2 | − | 49686.0i | −1.41071 | − | 2.44343i | ||||
\(746\) | 1263.53 | + | 2188.50i | 0.0620121 | + | 0.107408i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27137.4 | −1.32653 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13339.0 | − | 23103.9i | 0.648134 | − | 1.12260i | −0.335434 | − | 0.942064i | \(-0.608883\pi\) |
0.983568 | − | 0.180537i | \(-0.0577836\pi\) | |||||||
\(752\) | 1144.30 | + | 1981.98i | 0.0554896 | + | 0.0961107i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1348.71 | + | 2336.03i | −0.0651421 | + | 0.112829i | ||||
\(755\) | −49778.4 | −2.39950 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11630.8 | −0.558425 | −0.279212 | − | 0.960229i | \(-0.590073\pi\) | ||||
−0.279212 | + | 0.960229i | \(0.590073\pi\) | |||||||
\(758\) | −2442.63 | + | 4230.77i | −0.117045 | + | 0.202729i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4109.01 | + | 7117.02i | 0.196118 | + | 0.339686i | ||||
\(761\) | −18045.8 | + | 31256.3i | −0.859607 | + | 1.48888i | 0.0126976 | + | 0.999919i | \(0.495958\pi\) |
−0.872304 | + | 0.488963i | \(0.837375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4776.93 | −0.226208 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8453.51 | + | 14641.9i | 0.398744 | + | 0.690644i | ||||
\(767\) | −3592.89 | − | 6223.07i | −0.169142 | − | 0.292962i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33089.3 | −1.55167 | −0.775833 | − | 0.630938i | \(-0.782670\pi\) | ||||
−0.775833 | + | 0.630938i | \(0.782670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3972.23 | + | 6880.11i | −0.185186 | + | 0.320752i | ||||
\(773\) | 15495.4 | + | 26838.8i | 0.720997 | + | 1.24880i | 0.960601 | + | 0.277933i | \(0.0896493\pi\) |
−0.239603 | + | 0.970871i | \(0.577017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20321.9 | − | 35198.6i | 0.941915 | − | 1.63144i | ||||
\(776\) | 2587.00 | 0.119675 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11814.9 | 0.544453 | ||||||||
\(779\) | −2124.05 | + | 3678.96i | −0.0976917 | + | 0.169207i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21934.6 | − | 37991.9i | −1.00497 | − | 1.74066i | ||||
\(782\) | 2191.98 | − | 3796.62i | 0.100236 | − | 0.173615i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −52675.4 | −2.39499 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12710.6 | − | 22015.4i | −0.575711 | − | 0.997161i | −0.995964 | − | 0.0897537i | \(-0.971392\pi\) |
0.420253 | − | 0.907407i | \(-0.361941\pi\) | |||||||
\(788\) | 2593.08 | + | 4491.35i | 0.117227 | + | 0.203043i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8469.46 | −0.381430 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10586.0 | + | 18335.5i | −0.474048 | + | 0.821075i | ||||
\(794\) | 1420.81 | + | 2460.91i | 0.0635045 | + | 0.109993i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9101.22 | + | 15763.8i | −0.405257 | + | 0.701925i | ||||
\(797\) | −20283.3 | −0.901470 | −0.450735 | − | 0.892658i | \(-0.648838\pi\) | ||||
−0.450735 | + | 0.892658i | \(0.648838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20163.2 | 0.892768 | ||||||||
\(800\) | −19560.0 | + | 33879.0i | −0.864439 | + | 1.49725i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −117.941 | − | 204.281i | −0.00519284 | − | 0.00899426i | ||||
\(803\) | −11912.7 | + | 20633.4i | −0.523524 | + | 0.906771i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10055.1 | 0.439426 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 13763.0 | + | 23838.2i | 0.599232 | + | 1.03790i | ||||
\(809\) | 8215.67 | + | 14230.0i | 0.357043 | + | 0.618416i | 0.987465 | − | 0.157836i | \(-0.0504517\pi\) |
−0.630423 | + | 0.776252i | \(0.717118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6371.81 | −0.275887 | −0.137944 | − | 0.990440i | \(-0.544049\pi\) | ||||
−0.137944 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13078.4 | + | 22652.4i | −0.563142 | + | 0.975390i | ||||
\(815\) | −5909.52 | − | 10235.6i | −0.253989 | − | 0.439922i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 229.491 | − | 397.490i | 0.00982727 | − | 0.0170213i | ||||
\(818\) | 3451.88 | 0.147545 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20240.5 | −0.861987 | ||||||||
\(821\) | −2612.24 | + | 4524.54i | −0.111045 | + | 0.192335i | −0.916192 | − | 0.400740i | \(-0.868753\pi\) |
0.805147 | + | 0.593075i | \(0.202086\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1856.55 | − | 3215.64i | −0.0786333 | − | 0.136197i | 0.824027 | − | 0.566550i | \(-0.191722\pi\) |
−0.902660 | + | 0.430353i | \(0.858389\pi\) | |||||||
\(824\) | −5708.65 | + | 9887.67i | −0.241347 | + | 0.418026i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10202.6 | −0.428996 | −0.214498 | − | 0.976724i | \(-0.568812\pi\) | ||||
−0.214498 | + | 0.976724i | \(0.568812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12497.6 | + | 21646.5i | 0.523594 | + | 0.906891i | 0.999623 | + | 0.0274616i | \(0.00874239\pi\) |
−0.476029 | + | 0.879430i | \(0.657924\pi\) | |||||||
\(830\) | 1690.32 | + | 2927.72i | 0.0706891 | + | 0.122437i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7282.06 | −0.303437 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34434.4 | − | 59642.1i | 1.42713 | − | 2.47186i | ||||
\(836\) | −3488.31 | − | 6041.94i | −0.144313 | − | 0.249958i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10779.7 | − | 18670.9i | 0.444364 | − | 0.769661i | ||||
\(839\) | 31173.6 | 1.28275 | 0.641377 | − | 0.767226i | \(-0.278363\pi\) | ||||
0.641377 | + | 0.767226i | \(0.278363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21682.6 | −0.889033 | ||||||||
\(842\) | 11303.6 | − | 19578.4i | 0.462646 | − | 0.801327i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3919.29 | + | 6788.40i | 0.159843 | + | 0.276856i | ||||
\(845\) | 10465.1 | − | 18126.0i | 0.426046 | − | 0.737934i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1299.98 | −0.0526434 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 13619.7 | + | 23590.1i | 0.549591 | + | 0.951920i | ||||
\(851\) | 4505.72 | + | 7804.13i | 0.181497 | + | 0.314362i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25280.7 | 1.01477 | 0.507383 | − | 0.861721i | \(-0.330613\pi\) | ||||
0.507383 | + | 0.861721i | \(0.330613\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1432.72 | + | 2481.54i | −0.0572070 | + | 0.0990855i | ||||
\(857\) | 13705.4 | + | 23738.4i | 0.546285 | + | 0.946194i | 0.998525 | + | 0.0542972i | \(0.0172918\pi\) |
−0.452240 | + | 0.891896i | \(0.649375\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12279.4 | − | 21268.6i | 0.487740 | − | 0.844790i | −0.512161 | − | 0.858890i | \(-0.671155\pi\) |
0.999901 | + | 0.0140994i | \(0.00448813\pi\) | |||||||
\(860\) | 2186.87 | 0.0867113 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14523.9 | 0.573883 | ||||||||
\(863\) | −3574.18 | + | 6190.66i | −0.140981 | + | 0.244186i | −0.927866 | − | 0.372913i | \(-0.878359\pi\) |
0.786885 | + | 0.617099i | \(0.211692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21117.6 | − | 36576.7i | −0.830080 | − | 1.43774i | ||||
\(866\) | 12353.9 | − | 21397.6i | 0.484760 | − | 0.839629i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17751.7 | 0.692962 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9806.52 | + | 16985.4i | 0.381494 | + | 0.660767i | ||||
\(872\) | −2339.69 | − | 4052.46i | −0.0908621 | − | 0.157378i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1127.05 | 0.0436190 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14109.2 | − | 24437.9i | 0.543256 | − | 0.940946i | −0.455459 | − | 0.890257i | \(-0.650525\pi\) |
0.998714 | − | 0.0506895i | \(-0.0161419\pi\) | |||||||
\(878\) | −1424.01 | − | 2466.46i | −0.0547359 | − | 0.0948053i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5172.57 | − | 8959.15i | 0.198145 | − | 0.343197i | ||||
\(881\) | 7431.50 | 0.284192 | 0.142096 | − | 0.989853i | \(-0.454616\pi\) | ||||
0.142096 | + | 0.989853i | \(0.454616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4937.77 | 0.188187 | 0.0940936 | − | 0.995563i | \(-0.470005\pi\) | ||||
0.0940936 | + | 0.995563i | \(0.470005\pi\) | |||||||
\(884\) | 7185.79 | − | 12446.1i | 0.273398 | − | 0.473540i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10726.7 | − | 18579.2i | −0.406739 | − | 0.704493i | ||||
\(887\) | 20986.8 | − | 36350.3i | 0.794441 | − | 1.37601i | −0.128753 | − | 0.991677i | \(-0.541097\pi\) |
0.923194 | − | 0.384335i | \(-0.125569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27458.6 | 1.03417 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2749.97 | − | 4763.08i | −0.103224 | − | 0.178789i | ||||
\(893\) | 2591.83 | + | 4489.17i | 0.0971245 | + | 0.168224i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55492.5 | −2.07253 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −334.504 | + | 579.378i | −0.0124305 | + | 0.0215302i | ||||
\(899\) | −5044.24 | − | 8736.88i | −0.187135 | − | 0.324128i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5726.62 | + | 9918.80i | −0.211744 | + | 0.366751i | ||||
\(902\) | −19892.6 | −0.734315 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43106.4 | −1.58595 | ||||||||
\(905\) | −37312.4 | + | 64626.9i | −1.37050 | + | 2.37378i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20712.1 | − | 35874.4i | −0.758252 | − | 1.31333i | −0.943741 | − | 0.330685i | \(-0.892720\pi\) |
0.185489 | − | 0.982646i | \(-0.440613\pi\) | |||||||
\(908\) | 8029.37 | − | 13907.3i | 0.293463 | − | 0.508292i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40072.0 | 1.45735 | 0.728675 | − | 0.684860i | \(-0.240136\pi\) | ||||
0.728675 | + | 0.684860i | \(0.240136\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3542.85 | − | 6136.40i | −0.128424 | − | 0.222437i | ||||
\(914\) | 566.039 | + | 980.408i | 0.0204846 | + | 0.0354803i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21996.5 | −0.793432 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10908.7 | − | 18894.5i | 0.391562 | − | 0.678206i | −0.601094 | − | 0.799179i | \(-0.705268\pi\) |
0.992656 | + | 0.120973i | \(0.0386015\pi\) | |||||||
\(920\) | 6628.96 | + | 11481.7i | 0.237555 | + | 0.411457i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6571.18 | − | 11381.6i | 0.234718 | − | 0.406544i | ||||
\(923\) | 23232.5 | 0.828501 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −55992.0 | −1.99028 | ||||||||
\(926\) | 7522.18 | − | 13028.8i | 0.266948 | − | 0.462368i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4855.13 | + | 8409.33i | 0.171743 | + | 0.297467i | ||||
\(929\) | −5988.52 | + | 10372.4i | −0.211493 | + | 0.366317i | −0.952182 | − | 0.305532i | \(-0.901166\pi\) |
0.740689 | + | 0.671848i | \(0.234499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16315.8 | −0.573435 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8646.69 | − | 14976.5i | −0.302921 | − | 0.524675i | ||||
\(935\) | −45571.9 | − | 78932.9i | −1.59397 | − | 2.76083i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15155.2 | 0.528389 | 0.264194 | − | 0.964469i | \(-0.414894\pi\) | ||||
0.264194 | + | 0.964469i | \(0.414894\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12349.0 | + | 21389.2i | −0.428491 | + | 0.742168i | ||||
\(941\) | 3477.20 | + | 6022.69i | 0.120461 | + | 0.208644i | 0.919949 | − | 0.392037i | \(-0.128229\pi\) |
−0.799489 | + | 0.600681i | \(0.794896\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3426.67 | + | 5935.16i | −0.118333 | + | 0.204958i | ||||
\(944\) | −2044.39 | −0.0704865 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2149.29 | 0.0738682 | ||||||||
\(947\) | 4778.75 | − | 8277.03i | 0.163979 | − | 0.284020i | −0.772313 | − | 0.635242i | \(-0.780900\pi\) |
0.936292 | + | 0.351222i | \(0.114234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6308.79 | − | 10927.1i | −0.215798 | − | 0.373772i | ||||
\(950\) | −3501.43 | + | 6064.65i | −0.119580 | + | 0.207119i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8437.24 | 0.286788 | 0.143394 | − | 0.989666i | \(-0.454198\pi\) | ||||
0.143394 | + | 0.989666i | \(0.454198\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8021.90 | − | 13894.3i | −0.271814 | − | 0.470796i | ||||
\(956\) | −4929.61 | − | 8538.33i | −0.166773 | − | 0.288859i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13080.9 | −0.441153 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3907.84 | + | 6768.58i | −0.131175 | + | 0.227202i | ||||
\(962\) | −6926.12 | − | 11996.4i | −0.232128 | − | 0.402057i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10210.1 | − | 17684.4i | 0.341126 | − | 0.590847i | ||||
\(965\) | −26682.3 | −0.890087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52344.7 | 1.74074 | 0.870369 | − | 0.492401i | \(-0.163881\pi\) | ||||
0.870369 | + | 0.492401i | \(0.163881\pi\) | |||||||
\(968\) | 26029.0 | − | 45083.6i | 0.864261 | − | 1.49694i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1759.62 | + | 3047.76i | 0.0582454 | + | 0.100884i | ||||
\(971\) | −18491.5 | + | 32028.2i | −0.611143 | + | 1.05853i | 0.379905 | + | 0.925026i | \(0.375957\pi\) |
−0.991048 | + | 0.133506i | \(0.957377\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −6397.25 | −0.210453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3011.77 | + | 5216.54i | 0.0987750 | + | 0.171083i | ||||
\(977\) | 8936.51 | + | 15478.5i | 0.292635 | + | 0.506859i | 0.974432 | − | 0.224683i | \(-0.0721346\pi\) |
−0.681797 | + | 0.731541i | \(0.738801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −57552.2 | −1.87883 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8933.76 | − | 15473.7i | 0.290313 | − | 0.502838i | ||||
\(983\) | −16872.0 | − | 29223.2i | −0.547440 | − | 0.948195i | −0.998449 | − | 0.0556750i | \(-0.982269\pi\) |
0.451009 | − | 0.892520i | \(-0.351064\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8709.13 | + | 15084.7i | −0.281722 | + | 0.487956i | ||||
\(986\) | 6761.29 | 0.218381 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3694.72 | 0.118972 | ||||||||
\(989\) | 370.232 | − | 641.260i | 0.0119036 | − | 0.0206177i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7253.24 | + | 12563.0i | 0.232499 | + | 0.402701i | 0.958543 | − | 0.284948i | \(-0.0919763\pi\) |
−0.726044 | + | 0.687649i | \(0.758643\pi\) | |||||||
\(992\) | 18098.4 | − | 31347.4i | 0.579259 | − | 1.00331i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −61134.7 | −1.94784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21184.4 | − | 36692.5i | −0.672936 | − | 1.16556i | −0.977068 | − | 0.212929i | \(-0.931700\pi\) |
0.304132 | − | 0.952630i | \(-0.401634\pi\) | |||||||
\(998\) | 3013.20 | + | 5219.01i | 0.0955723 | + | 0.165536i | ||||
\(999\) | 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.226.2 | 8 | ||
3.2 | odd | 2 | inner | 441.4.e.x.226.3 | 8 | ||
7.2 | even | 3 | 441.4.a.v.1.3 | 4 | |||
7.3 | odd | 6 | 63.4.e.d.46.2 | yes | 8 | ||
7.4 | even | 3 | inner | 441.4.e.x.361.2 | 8 | ||
7.5 | odd | 6 | 441.4.a.w.1.3 | 4 | |||
7.6 | odd | 2 | 63.4.e.d.37.2 | ✓ | 8 | ||
21.2 | odd | 6 | 441.4.a.v.1.2 | 4 | |||
21.5 | even | 6 | 441.4.a.w.1.2 | 4 | |||
21.11 | odd | 6 | inner | 441.4.e.x.361.3 | 8 | ||
21.17 | even | 6 | 63.4.e.d.46.3 | yes | 8 | ||
21.20 | even | 2 | 63.4.e.d.37.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.e.d.37.2 | ✓ | 8 | 7.6 | odd | 2 | ||
63.4.e.d.37.3 | yes | 8 | 21.20 | even | 2 | ||
63.4.e.d.46.2 | yes | 8 | 7.3 | odd | 6 | ||
63.4.e.d.46.3 | yes | 8 | 21.17 | even | 6 | ||
441.4.a.v.1.2 | 4 | 21.2 | odd | 6 | |||
441.4.a.v.1.3 | 4 | 7.2 | even | 3 | |||
441.4.a.w.1.2 | 4 | 21.5 | even | 6 | |||
441.4.a.w.1.3 | 4 | 7.5 | odd | 6 | |||
441.4.e.x.226.2 | 8 | 1.1 | even | 1 | trivial | ||
441.4.e.x.226.3 | 8 | 3.2 | odd | 2 | inner | ||
441.4.e.x.361.2 | 8 | 7.4 | even | 3 | inner | ||
441.4.e.x.361.3 | 8 | 21.11 | odd | 6 | inner |