Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1151,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.2 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1151 |
Dual form | 3150.2.bf.b.1601.2 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.63896 | − | 0.189469i | 0.997433 | − | 0.0716124i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.67303 | − | 2.69798i | −1.40897 | − | 0.813471i | −0.413683 | − | 0.910421i | \(-0.635758\pi\) |
−0.995289 | + | 0.0969504i | \(0.969091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51764i | 0.698267i | 0.937073 | + | 0.349134i | \(0.113524\pi\) | ||||
−0.937073 | + | 0.349134i | \(0.886476\pi\) | |||||||
\(14\) | −2.19067 | + | 1.48356i | −0.585481 | + | 0.396499i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.24969 | + | 3.89658i | −0.545630 | + | 0.945058i | 0.452937 | + | 0.891542i | \(0.350376\pi\) |
−0.998567 | + | 0.0535160i | \(0.982957\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.48004 | + | 1.43185i | −0.568960 | + | 0.328489i | −0.756734 | − | 0.653723i | \(-0.773206\pi\) |
0.187774 | + | 0.982212i | \(0.439873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.39595 | 1.15042 | ||||||||
\(23\) | −0.232051 | + | 0.133975i | −0.0483859 | + | 0.0279356i | −0.523998 | − | 0.851720i | \(-0.675560\pi\) |
0.475612 | + | 0.879655i | \(0.342227\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.25882 | − | 2.18034i | −0.246875 | − | 0.427600i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.15539 | − | 2.38014i | 0.218349 | − | 0.449804i | ||||
\(29\) | − | 8.89898i | − | 1.65250i | −0.563304 | − | 0.826250i | \(-0.690470\pi\) | ||
0.563304 | − | 0.826250i | \(-0.309530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.18154 | + | 2.41421i | 0.751027 | + | 0.433606i | 0.826065 | − | 0.563575i | \(-0.190574\pi\) |
−0.0750380 | + | 0.997181i | \(0.523908\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.49938i | − | 0.771637i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.25882 | − | 5.64444i | −0.535747 | − | 0.927940i | −0.999127 | − | 0.0417807i | \(-0.986697\pi\) |
0.463380 | − | 0.886160i | \(-0.346636\pi\) | |||||||
\(38\) | 1.43185 | − | 2.48004i | 0.232277 | − | 0.402316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.760279 | 0.118736 | 0.0593678 | − | 0.998236i | \(-0.481092\pi\) | ||||
0.0593678 | + | 0.998236i | \(0.481092\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.86370 | 0.894206 | 0.447103 | − | 0.894482i | \(-0.352456\pi\) | ||||
0.447103 | + | 0.894482i | \(0.352456\pi\) | |||||||
\(44\) | −4.67303 | + | 2.69798i | −0.704486 | + | 0.406735i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.133975 | − | 0.232051i | 0.0197535 | − | 0.0342140i | ||||
\(47\) | −3.99768 | − | 6.92418i | −0.583121 | − | 1.01000i | −0.995107 | − | 0.0988053i | \(-0.968498\pi\) |
0.411986 | − | 0.911190i | \(-0.364835\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | − | 1.00000i | 0.989743 | − | 0.142857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.18034 | + | 1.25882i | 0.302359 | + | 0.174567i | ||||
\(53\) | 7.27319 | + | 4.19918i | 0.999050 | + | 0.576802i | 0.907967 | − | 0.419042i | \(-0.137634\pi\) |
0.0910826 | + | 0.995843i | \(0.470967\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.189469 | + | 2.63896i | 0.0253188 | + | 0.352646i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.44949 | + | 7.70674i | 0.584247 | + | 1.01194i | ||||
\(59\) | 6.33573 | − | 10.9738i | 0.824842 | − | 1.42867i | −0.0771977 | − | 0.997016i | \(-0.524597\pi\) |
0.902040 | − | 0.431653i | \(-0.142069\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.27035 | + | 1.31079i | −0.290689 | + | 0.167829i | −0.638253 | − | 0.769827i | \(-0.720342\pi\) |
0.347564 | + | 0.937656i | \(0.387009\pi\) | |||||||
\(62\) | −4.82843 | −0.613211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.91119 | − | 8.50643i | 0.599997 | − | 1.03923i | −0.392824 | − | 0.919614i | \(-0.628502\pi\) |
0.992821 | − | 0.119612i | \(-0.0381649\pi\) | |||||||
\(68\) | 2.24969 | + | 3.89658i | 0.272815 | + | 0.472529i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.76268i | − | 0.565226i | −0.959234 | − | 0.282613i | \(-0.908799\pi\) | ||
0.959234 | − | 0.282613i | \(-0.0912013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0951 | − | 5.82843i | −1.18155 | − | 0.682166i | −0.225174 | − | 0.974319i | \(-0.572295\pi\) |
−0.956372 | + | 0.292153i | \(0.905628\pi\) | |||||||
\(74\) | 5.64444 | + | 3.25882i | 0.656153 | + | 0.378830i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.86370i | 0.328489i | ||||||||
\(77\) | −12.8431 | − | 6.23445i | −1.46361 | − | 0.710482i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.29618 | − | 7.44120i | −0.483358 | − | 0.837200i | 0.516460 | − | 0.856312i | \(-0.327250\pi\) |
−0.999817 | + | 0.0191114i | \(0.993916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.658421 | + | 0.380139i | −0.0727104 | + | 0.0419794i | ||||
\(83\) | −9.45001 | −1.03727 | −0.518636 | − | 0.854995i | \(-0.673560\pi\) | ||||
−0.518636 | + | 0.854995i | \(0.673560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.07812 | + | 2.93185i | −0.547587 | + | 0.316150i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.69798 | − | 4.67303i | 0.287605 | − | 0.498147i | ||||
\(89\) | −3.98502 | − | 6.90226i | −0.422412 | − | 0.731638i | 0.573763 | − | 0.819021i | \(-0.305483\pi\) |
−0.996175 | + | 0.0873828i | \(0.972150\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.477014 | + | 6.64394i | 0.0500046 | + | 0.696474i | ||||
\(92\) | 0.267949i | 0.0279356i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.92418 | + | 3.99768i | 0.714175 | + | 0.412329i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.16353i | 0.625812i | 0.949784 | + | 0.312906i | \(0.101302\pi\) | ||||
−0.949784 | + | 0.312906i | \(0.898698\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.02458 | + | 12.1669i | −0.698972 | + | 1.21065i | 0.269852 | + | 0.962902i | \(0.413025\pi\) |
−0.968823 | + | 0.247753i | \(0.920308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.2776 | + | 7.08845i | −1.20974 | + | 0.698446i | −0.962703 | − | 0.270560i | \(-0.912791\pi\) |
−0.247040 | + | 0.969005i | \(0.579458\pi\) | |||||||
\(104\) | −2.51764 | −0.246875 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.39836 | −0.815721 | ||||||||
\(107\) | 1.42178 | − | 0.820863i | 0.137448 | − | 0.0793559i | −0.429699 | − | 0.902972i | \(-0.641380\pi\) |
0.567147 | + | 0.823616i | \(0.308047\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.94887 | − | 17.2319i | 0.952929 | − | 1.65052i | 0.213890 | − | 0.976858i | \(-0.431387\pi\) |
0.739039 | − | 0.673663i | \(-0.235280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.48356 | − | 2.19067i | −0.140184 | − | 0.206999i | ||||
\(113\) | − | 5.95867i | − | 0.560545i | −0.959921 | − | 0.280272i | \(-0.909575\pi\) | ||
0.959921 | − | 0.280272i | \(-0.0904248\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.70674 | − | 4.44949i | −0.715553 | − | 0.413125i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.6715i | 1.16650i | ||||||||
\(119\) | −5.19856 | + | 10.7091i | −0.476551 | + | 0.981706i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.05816 | + | 15.6892i | 0.823469 | + | 1.42629i | ||||
\(122\) | 1.31079 | − | 2.27035i | 0.118673 | − | 0.205548i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.18154 | − | 2.41421i | 0.375513 | − | 0.216803i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.5103 | 1.28758 | 0.643792 | − | 0.765200i | \(-0.277360\pi\) | ||||
0.643792 | + | 0.765200i | \(0.277360\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.73325 | + | 13.3944i | 0.675657 | + | 1.17027i | 0.976276 | + | 0.216529i | \(0.0694735\pi\) |
−0.300619 | + | 0.953744i | \(0.597193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.27343 | + | 4.24849i | −0.543975 | + | 0.368391i | ||||
\(134\) | 9.82237i | 0.848524i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.89658 | − | 2.24969i | −0.334129 | − | 0.192909i | ||||
\(137\) | −7.46651 | − | 4.31079i | −0.637907 | − | 0.368296i | 0.145901 | − | 0.989299i | \(-0.453392\pi\) |
−0.783808 | + | 0.621004i | \(0.786725\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.2512i | − | 0.869495i | −0.900552 | − | 0.434748i | \(-0.856838\pi\) | ||
0.900552 | − | 0.434748i | \(-0.143162\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.38134 | + | 4.12460i | 0.199838 | + | 0.346129i | ||||
\(143\) | 6.79253 | − | 11.7650i | 0.568020 | − | 0.983839i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.6569 | 0.964728 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.51764 | −0.535747 | ||||||||
\(149\) | −7.96640 | + | 4.59940i | −0.652633 | + | 0.376798i | −0.789464 | − | 0.613797i | \(-0.789641\pi\) |
0.136831 | + | 0.990594i | \(0.456308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.37429 | − | 11.0406i | 0.518733 | − | 0.898471i | −0.481030 | − | 0.876704i | \(-0.659737\pi\) |
0.999763 | − | 0.0217674i | \(-0.00692931\pi\) | |||||||
\(152\) | −1.43185 | − | 2.48004i | −0.116139 | − | 0.201158i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.2397 | − | 1.02236i | 1.14747 | − | 0.0823845i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9899 | − | 6.92236i | −0.956896 | − | 0.552464i | −0.0616798 | − | 0.998096i | \(-0.519646\pi\) |
−0.895216 | + | 0.445632i | \(0.852979\pi\) | |||||||
\(158\) | 7.44120 | + | 4.29618i | 0.591990 | + | 0.341786i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.586988 | + | 0.397520i | −0.0462612 | + | 0.0313289i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.3025 | − | 17.8444i | −0.806954 | − | 1.39768i | −0.914964 | − | 0.403535i | \(-0.867781\pi\) |
0.108010 | − | 0.994150i | \(-0.465552\pi\) | |||||||
\(164\) | 0.380139 | − | 0.658421i | 0.0296839 | − | 0.0514140i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.18394 | − | 4.72500i | 0.635197 | − | 0.366731i | ||||
\(167\) | −6.84961 | −0.530038 | −0.265019 | − | 0.964243i | \(-0.585378\pi\) | ||||
−0.265019 | + | 0.964243i | \(0.585378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.66150 | 0.512423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.93185 | − | 5.07812i | 0.223552 | − | 0.387203i | ||||
\(173\) | 6.37902 | + | 11.0488i | 0.484988 | + | 0.840024i | 0.999851 | − | 0.0172486i | \(-0.00549068\pi\) |
−0.514863 | + | 0.857272i | \(0.672157\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.39595i | 0.406735i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.90226 | + | 3.98502i | 0.517347 | + | 0.298690i | ||||
\(179\) | −16.3390 | − | 9.43331i | −1.22123 | − | 0.705079i | −0.256052 | − | 0.966663i | \(-0.582422\pi\) |
−0.965181 | + | 0.261584i | \(0.915755\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 25.5498i | − | 1.89910i | −0.313615 | − | 0.949550i | \(-0.601540\pi\) | ||
0.313615 | − | 0.949550i | \(-0.398460\pi\) | |||||||
\(182\) | −3.73508 | − | 5.51532i | −0.276862 | − | 0.408822i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.133975 | − | 0.232051i | −0.00987674 | − | 0.0171070i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.0257 | − | 12.1392i | 1.53755 | − | 0.887707i | ||||
\(188\) | −7.99536 | −0.583121 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.00657 | + | 4.04524i | −0.506977 | + | 0.292704i | −0.731590 | − | 0.681745i | \(-0.761222\pi\) |
0.224613 | + | 0.974448i | \(0.427888\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.06350 | + | 12.2343i | −0.508442 | + | 0.880648i | 0.491510 | + | 0.870872i | \(0.336445\pi\) |
−0.999952 | + | 0.00977575i | \(0.996888\pi\) | |||||||
\(194\) | −3.08176 | − | 5.33777i | −0.221258 | − | 0.383230i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.59808 | − | 6.50000i | 0.185577 | − | 0.464286i | ||||
\(197\) | 14.2738i | 1.01697i | 0.861072 | + | 0.508483i | \(0.169793\pi\) | ||||
−0.861072 | + | 0.508483i | \(0.830207\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.06742 | + | 1.77098i | 0.217444 | + | 0.125541i | 0.604766 | − | 0.796403i | \(-0.293267\pi\) |
−0.387322 | + | 0.921944i | \(0.626600\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 14.0492i | − | 0.988495i | ||||||
\(203\) | −1.68608 | − | 23.4840i | −0.118339 | − | 1.64826i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.08845 | − | 12.2776i | 0.493876 | − | 0.855418i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.18034 | − | 1.25882i | 0.151179 | − | 0.0872834i | ||||
\(209\) | 15.4524 | 1.06887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.92340 | −0.270098 | −0.135049 | − | 0.990839i | \(-0.543119\pi\) | ||||
−0.135049 | + | 0.990839i | \(0.543119\pi\) | |||||||
\(212\) | 7.27319 | − | 4.19918i | 0.499525 | − | 0.288401i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.820863 | + | 1.42178i | −0.0561131 | + | 0.0971907i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4923 | + | 5.57874i | 0.780150 | + | 0.378709i | ||||
\(218\) | 19.8977i | 1.34764i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.81017 | − | 5.66390i | −0.659903 | − | 0.380995i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6904i | 0.983740i | 0.870669 | + | 0.491870i | \(0.163686\pi\) | ||||
−0.870669 | + | 0.491870i | \(0.836314\pi\) | |||||||
\(224\) | 2.38014 | + | 1.15539i | 0.159030 | + | 0.0771980i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.97934 | + | 5.16036i | 0.198182 | + | 0.343262i | ||||
\(227\) | 11.3913 | − | 19.7303i | 0.756068 | − | 1.30955i | −0.188774 | − | 0.982021i | \(-0.560451\pi\) |
0.944842 | − | 0.327527i | \(-0.106215\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5089 | + | 10.1087i | −1.15702 | + | 0.668005i | −0.950588 | − | 0.310456i | \(-0.899518\pi\) |
−0.206431 | + | 0.978461i | \(0.566185\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.89898 | 0.584247 | ||||||||
\(233\) | −2.27840 | + | 1.31543i | −0.149263 | + | 0.0861769i | −0.572771 | − | 0.819715i | \(-0.694132\pi\) |
0.423509 | + | 0.905892i | \(0.360798\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.33573 | − | 10.9738i | −0.412421 | − | 0.714334i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.852491 | − | 11.8737i | −0.0552588 | − | 0.769656i | ||||
\(239\) | − | 16.8766i | − | 1.09165i | −0.837898 | − | 0.545827i | \(-0.816216\pi\) | ||
0.837898 | − | 0.545827i | \(-0.183784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5793 | − | 7.26268i | −0.810306 | − | 0.467831i | 0.0367560 | − | 0.999324i | \(-0.488298\pi\) |
−0.847062 | + | 0.531494i | \(0.821631\pi\) | |||||||
\(242\) | −15.6892 | − | 9.05816i | −1.00854 | − | 0.582280i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.62158i | 0.167829i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.60488 | − | 6.24384i | −0.229373 | − | 0.397286i | ||||
\(248\) | −2.41421 | + | 4.18154i | −0.153303 | + | 0.265528i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.7243 | 0.992507 | 0.496254 | − | 0.868178i | \(-0.334709\pi\) | ||||
0.496254 | + | 0.868178i | \(0.334709\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.44584 | 0.0908993 | ||||||||
\(254\) | −12.5663 | + | 7.25517i | −0.788481 | + | 0.455230i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −9.83083 | − | 17.0275i | −0.613230 | − | 1.06215i | −0.990692 | − | 0.136121i | \(-0.956536\pi\) |
0.377462 | − | 0.926025i | \(-0.376797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.66933 | − | 14.2780i | −0.600823 | − | 0.887192i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.3944 | − | 7.73325i | −0.827508 | − | 0.477762i | ||||
\(263\) | 3.74275 | + | 2.16088i | 0.230788 | + | 0.133245i | 0.610935 | − | 0.791680i | \(-0.290794\pi\) |
−0.380148 | + | 0.924926i | \(0.624127\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.30871 | − | 6.81601i | 0.202870 | − | 0.417917i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.91119 | − | 8.50643i | −0.299999 | − | 0.519613i | ||||
\(269\) | 8.79895 | − | 15.2402i | 0.536482 | − | 0.929214i | −0.462608 | − | 0.886563i | \(-0.653086\pi\) |
0.999090 | − | 0.0426509i | \(-0.0135803\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.12436 | + | 5.26795i | −0.554265 | + | 0.320005i | −0.750840 | − | 0.660484i | \(-0.770351\pi\) |
0.196575 | + | 0.980489i | \(0.437018\pi\) | |||||||
\(272\) | 4.49938 | 0.272815 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.62158 | 0.520849 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.50971 | − | 2.61489i | 0.0907097 | − | 0.157114i | −0.817100 | − | 0.576496i | \(-0.804420\pi\) |
0.907810 | + | 0.419382i | \(0.137753\pi\) | |||||||
\(278\) | 5.12560 | + | 8.87780i | 0.307413 | + | 0.532455i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.6880i | − | 0.637591i | −0.947824 | − | 0.318795i | \(-0.896722\pi\) | ||
0.947824 | − | 0.318795i | \(-0.103278\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.2149 | + | 8.78434i | 0.904434 | + | 0.522175i | 0.878636 | − | 0.477492i | \(-0.158454\pi\) |
0.0257976 | + | 0.999667i | \(0.491787\pi\) | |||||||
\(284\) | −4.12460 | − | 2.38134i | −0.244750 | − | 0.141307i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.5851i | 0.803301i | ||||||||
\(287\) | 2.00634 | − | 0.144049i | 0.118431 | − | 0.00850295i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.62220 | − | 2.80973i | −0.0954235 | − | 0.165278i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.0951 | + | 5.82843i | −0.590773 | + | 0.341083i | ||||
\(293\) | 14.6710 | 0.857086 | 0.428543 | − | 0.903521i | \(-0.359027\pi\) | ||||
0.428543 | + | 0.903521i | \(0.359027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.64444 | − | 3.25882i | 0.328076 | − | 0.189415i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.59940 | − | 7.96640i | 0.266436 | − | 0.461481i | ||||
\(299\) | −0.337300 | − | 0.584220i | −0.0195065 | − | 0.0337863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4741 | − | 1.11099i | 0.891911 | − | 0.0640363i | ||||
\(302\) | 12.7486i | 0.733599i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.48004 | + | 1.43185i | 0.142240 | + | 0.0821223i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.2772i | − | 1.21435i | −0.794567 | − | 0.607177i | \(-0.792302\pi\) | ||
0.794567 | − | 0.607177i | \(-0.207698\pi\) | |||||||
\(308\) | −11.8208 | + | 8.00524i | −0.673550 | + | 0.456141i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.91724 | + | 10.2490i | −0.335536 | + | 0.581165i | −0.983588 | − | 0.180431i | \(-0.942251\pi\) |
0.648052 | + | 0.761596i | \(0.275584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.90551 | − | 2.25485i | 0.220753 | − | 0.127452i | −0.385546 | − | 0.922689i | \(-0.625987\pi\) |
0.606299 | + | 0.795237i | \(0.292654\pi\) | |||||||
\(314\) | 13.8447 | 0.781302 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.59235 | −0.483358 | ||||||||
\(317\) | 15.9202 | − | 9.19151i | 0.894165 | − | 0.516247i | 0.0188626 | − | 0.999822i | \(-0.493995\pi\) |
0.875303 | + | 0.483576i | \(0.160662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.0092 | + | 41.5852i | −1.34426 | + | 2.32833i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.309587 | − | 0.637756i | 0.0172526 | − | 0.0355408i | ||||
\(323\) | − | 12.8849i | − | 0.716934i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.8444 | + | 10.3025i | 0.988313 | + | 0.570603i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.760279i | 0.0419794i | ||||||||
\(329\) | −11.8616 | − | 17.5152i | −0.653952 | − | 0.965644i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.98066 | − | 6.89471i | −0.218797 | − | 0.378967i | 0.735643 | − | 0.677369i | \(-0.236880\pi\) |
−0.954440 | + | 0.298401i | \(0.903547\pi\) | |||||||
\(332\) | −4.72500 | + | 8.18394i | −0.259318 | + | 0.449152i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.93193 | − | 3.42480i | 0.324581 | − | 0.187397i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.89417 | 0.375549 | 0.187775 | − | 0.982212i | \(-0.439873\pi\) | ||||
0.187775 | + | 0.982212i | \(0.439873\pi\) | |||||||
\(338\) | −5.76903 | + | 3.33075i | −0.313794 | + | 0.181169i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.0270 | − | 22.5634i | −0.705451 | − | 1.22188i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.0938 | − | 3.95164i | 0.976972 | − | 0.213368i | ||||
\(344\) | 5.86370i | 0.316150i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0488 | − | 6.37902i | −0.593986 | − | 0.342938i | ||||
\(347\) | 14.1645 | + | 8.17789i | 0.760392 | + | 0.439012i | 0.829436 | − | 0.558601i | \(-0.188662\pi\) |
−0.0690448 | + | 0.997614i | \(0.521995\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 24.5851i | − | 1.31601i | −0.753014 | − | 0.658004i | \(-0.771401\pi\) | ||
0.753014 | − | 0.658004i | \(-0.228599\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.69798 | − | 4.67303i | −0.143803 | − | 0.249073i | ||||
\(353\) | −6.85906 | + | 11.8802i | −0.365071 | + | 0.632321i | −0.988788 | − | 0.149329i | \(-0.952289\pi\) |
0.623717 | + | 0.781651i | \(0.285622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.97005 | −0.422412 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.8666 | 0.997132 | ||||||||
\(359\) | −10.3059 | + | 5.95011i | −0.543924 | + | 0.314035i | −0.746668 | − | 0.665197i | \(-0.768348\pi\) |
0.202744 | + | 0.979232i | \(0.435014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.39960 | + | 9.35238i | −0.284190 | + | 0.492231i | ||||
\(362\) | 12.7749 | + | 22.1268i | 0.671433 | + | 1.16296i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.99233 | + | 2.90887i | 0.314083 | + | 0.152466i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9026 | + | 6.29461i | 0.569110 | + | 0.328576i | 0.756794 | − | 0.653654i | \(-0.226765\pi\) |
−0.187684 | + | 0.982230i | \(0.560098\pi\) | |||||||
\(368\) | 0.232051 | + | 0.133975i | 0.0120965 | + | 0.00698391i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.9893 | + | 9.70342i | 1.03779 | + | 0.503776i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.5868 | − | 23.5331i | −0.703499 | − | 1.21850i | −0.967230 | − | 0.253900i | \(-0.918286\pi\) |
0.263731 | − | 0.964596i | \(-0.415047\pi\) | |||||||
\(374\) | −12.1392 | + | 21.0257i | −0.627704 | + | 1.08722i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.92418 | − | 3.99768i | 0.357087 | − | 0.206164i | ||||
\(377\) | 22.4044 | 1.15389 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7335 | 0.808174 | 0.404087 | − | 0.914721i | \(-0.367589\pi\) | ||||
0.404087 | + | 0.914721i | \(0.367589\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.04524 | − | 7.00657i | 0.206973 | − | 0.358487i | ||||
\(383\) | 7.89060 | + | 13.6669i | 0.403191 | + | 0.698347i | 0.994109 | − | 0.108384i | \(-0.0345677\pi\) |
−0.590918 | + | 0.806732i | \(0.701234\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 14.1270i | − | 0.719046i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.33777 | + | 3.08176i | 0.270984 | + | 0.156453i | ||||
\(389\) | −13.7556 | − | 7.94182i | −0.697438 | − | 0.402666i | 0.108954 | − | 0.994047i | \(-0.465250\pi\) |
−0.806393 | + | 0.591381i | \(0.798583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.20560i | − | 0.0609700i | ||||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.13689 | − | 12.3615i | −0.359552 | − | 0.622762i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.3557 | + | 18.6806i | −1.62388 | + | 0.937550i | −0.638017 | + | 0.770022i | \(0.720245\pi\) |
−0.985867 | + | 0.167528i | \(0.946422\pi\) | |||||||
\(398\) | −3.54195 | −0.177542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.4856 | − | 14.1368i | 1.22275 | − | 0.705957i | 0.257249 | − | 0.966345i | \(-0.417184\pi\) |
0.965504 | + | 0.260389i | \(0.0838507\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.07812 | + | 10.5276i | −0.302773 | + | 0.524417i | ||||
\(404\) | 7.02458 | + | 12.1669i | 0.349486 | + | 0.605327i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.2022 | + | 19.4947i | 0.655214 | + | 0.967507i | ||||
\(407\) | 35.1689i | 1.74326i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.8647 | + | 8.00481i | 0.685567 | + | 0.395812i | 0.801949 | − | 0.597392i | \(-0.203796\pi\) |
−0.116382 | + | 0.993204i | \(0.537130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.1769i | 0.698446i | ||||||||
\(413\) | 14.6405 | − | 30.1599i | 0.720414 | − | 1.48407i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.25882 | + | 2.18034i | −0.0617187 | + | 0.106900i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −13.3822 | + | 7.72620i | −0.654544 | + | 0.377901i | ||||
\(419\) | 29.5137 | 1.44184 | 0.720919 | − | 0.693020i | \(-0.243720\pi\) | ||||
0.720919 | + | 0.693020i | \(0.243720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.309114 | 0.0150653 | 0.00753265 | − | 0.999972i | \(-0.497602\pi\) | ||||
0.00753265 | + | 0.999972i | \(0.497602\pi\) | |||||||
\(422\) | 3.39776 | − | 1.96170i | 0.165400 | − | 0.0954939i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.19918 | + | 7.27319i | −0.203930 | + | 0.353217i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.74301 | + | 3.88928i | −0.277924 | + | 0.188215i | ||||
\(428\) | − | 1.64173i | − | 0.0793559i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.63843 | + | 4.41005i | 0.367930 | + | 0.212425i | 0.672554 | − | 0.740048i | \(-0.265197\pi\) |
−0.304624 | + | 0.952473i | \(0.598531\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.56388i | − | 0.459611i | −0.973237 | − | 0.229805i | \(-0.926191\pi\) | ||
0.973237 | − | 0.229805i | \(-0.0738089\pi\) | |||||||
\(434\) | −12.7420 | + | 0.914836i | −0.611636 | + | 0.0439135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.94887 | − | 17.2319i | −0.476464 | − | 0.825260i | ||||
\(437\) | 0.383663 | − | 0.664525i | 0.0183531 | − | 0.0317885i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.3336 | + | 18.0905i | −1.49547 | + | 0.863412i | −0.999986 | − | 0.00520362i | \(-0.998344\pi\) |
−0.495487 | + | 0.868615i | \(0.665010\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.3278 | 0.538809 | ||||||||
\(443\) | 3.53830 | − | 2.04284i | 0.168110 | − | 0.0970582i | −0.413584 | − | 0.910466i | \(-0.635723\pi\) |
0.581694 | + | 0.813408i | \(0.302390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.34519 | − | 12.7222i | −0.347805 | − | 0.602415i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.63896 | + | 0.189469i | −0.124679 | + | 0.00895155i | ||||
\(449\) | 19.9377i | 0.940918i | 0.882422 | + | 0.470459i | \(0.155912\pi\) | ||||
−0.882422 | + | 0.470459i | \(0.844088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.55281 | − | 2.05121i | −0.167295 | − | 0.0965879i | ||||
\(452\) | −5.16036 | − | 2.97934i | −0.242723 | − | 0.140136i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.7826i | 1.06924i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0623 | − | 17.4283i | −0.470693 | − | 0.815264i | 0.528745 | − | 0.848780i | \(-0.322663\pi\) |
−0.999438 | + | 0.0335168i | \(0.989329\pi\) | |||||||
\(458\) | 10.1087 | − | 17.5089i | 0.472351 | − | 0.818136i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.909299 | −0.0423503 | −0.0211751 | − | 0.999776i | \(-0.506741\pi\) | ||||
−0.0211751 | + | 0.999776i | \(0.506741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.4280 | −0.995843 | −0.497922 | − | 0.867222i | \(-0.665903\pi\) | ||||
−0.497922 | + | 0.867222i | \(0.665903\pi\) | |||||||
\(464\) | −7.70674 | + | 4.44949i | −0.357777 | + | 0.206562i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.31543 | − | 2.27840i | 0.0609363 | − | 0.105545i | ||||
\(467\) | 6.34607 | + | 10.9917i | 0.293661 | + | 0.508636i | 0.974672 | − | 0.223637i | \(-0.0717930\pi\) |
−0.681012 | + | 0.732273i | \(0.738460\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3487 | − | 23.3786i | 0.524035 | − | 1.07952i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.9738 | + | 6.33573i | 0.505111 | + | 0.291626i | ||||
\(473\) | −27.4013 | − | 15.8201i | −1.25991 | − | 0.727411i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.67511 | + | 9.85666i | 0.305953 | + | 0.451779i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.43828 | + | 14.6155i | 0.385958 | + | 0.668499i | ||||
\(479\) | 6.43828 | − | 11.1514i | 0.294172 | − | 0.509522i | −0.680620 | − | 0.732637i | \(-0.738289\pi\) |
0.974792 | + | 0.223115i | \(0.0716227\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2107 | − | 8.20453i | 0.647950 | − | 0.374094i | ||||
\(482\) | 14.5254 | 0.661612 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.1163 | 0.823469 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.4097 | + | 18.0301i | −0.471708 | + | 0.817022i | −0.999476 | − | 0.0323665i | \(-0.989696\pi\) |
0.527768 | + | 0.849388i | \(0.323029\pi\) | |||||||
\(488\) | −1.31079 | − | 2.27035i | −0.0593366 | − | 0.102774i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.3271i | 1.23325i | 0.787256 | + | 0.616627i | \(0.211501\pi\) | ||||
−0.787256 | + | 0.616627i | \(0.788499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.6755 | + | 20.0199i | 1.56171 | + | 0.901653i | ||||
\(494\) | 6.24384 | + | 3.60488i | 0.280924 | + | 0.162191i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 4.82843i | − | 0.216803i | ||||||
\(497\) | −0.902379 | − | 12.5685i | −0.0404772 | − | 0.563775i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6802 | − | 28.8909i | −0.746708 | − | 1.29334i | −0.949393 | − | 0.314092i | \(-0.898300\pi\) |
0.202685 | − | 0.979244i | \(-0.435033\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.6176 | + | 7.86214i | −0.607784 | + | 0.350904i | ||||
\(503\) | 16.2936 | 0.726494 | 0.363247 | − | 0.931693i | \(-0.381668\pi\) | ||||
0.363247 | + | 0.931693i | \(0.381668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.25214 | + | 0.722921i | −0.0556642 | + | 0.0321377i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.25517 | − | 12.5663i | 0.321896 | − | 0.557540i | ||||
\(509\) | 12.3400 | + | 21.3735i | 0.546961 | + | 0.947365i | 0.998481 | + | 0.0551036i | \(0.0175489\pi\) |
−0.451519 | + | 0.892261i | \(0.649118\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.7449 | − | 13.4683i | −1.22736 | − | 0.595801i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.0275 | + | 9.83083i | 0.751051 | + | 0.433619i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.1426i | 1.89741i | ||||||||
\(518\) | 15.5129 | + | 7.53044i | 0.681597 | + | 0.330869i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.141663 | − | 0.245367i | 0.00620635 | − | 0.0107497i | −0.862906 | − | 0.505365i | \(-0.831358\pi\) |
0.869112 | + | 0.494616i | \(0.164691\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.77021 | − | 5.64083i | 0.427222 | − | 0.246656i | −0.270941 | − | 0.962596i | \(-0.587335\pi\) |
0.698162 | + | 0.715940i | \(0.254001\pi\) | |||||||
\(524\) | 15.4665 | 0.675657 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.32175 | −0.188437 | ||||||||
\(527\) | −18.8143 | + | 10.8625i | −0.819565 | + | 0.473176i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4641 | + | 19.8564i | −0.498439 | + | 0.863322i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.542582 | + | 7.55719i | 0.0235239 | + | 0.327646i | ||||
\(533\) | 1.91411i | 0.0829092i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.50643 | + | 4.91119i | 0.367422 | + | 0.212131i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.5979i | 0.758700i | ||||||||
\(539\) | −35.0737 | − | 14.0191i | −1.51073 | − | 0.603845i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.4125 | + | 30.1593i | 0.748621 | + | 1.29665i | 0.948484 | + | 0.316826i | \(0.102617\pi\) |
−0.199862 | + | 0.979824i | \(0.564049\pi\) | |||||||
\(542\) | 5.26795 | − | 9.12436i | 0.226278 | − | 0.391925i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.89658 | + | 2.24969i | −0.167064 | + | 0.0964546i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.4261 | −1.51471 | −0.757356 | − | 0.653002i | \(-0.773509\pi\) | ||||
−0.757356 | + | 0.653002i | \(0.773509\pi\) | |||||||
\(548\) | −7.46651 | + | 4.31079i | −0.318953 | + | 0.184148i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.7420 | + | 22.0698i | 0.542828 | + | 0.940206i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.7473 | − | 18.8230i | −0.542071 | − | 0.800436i | ||||
\(554\) | 3.01942i | 0.128283i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.87780 | − | 5.12560i | −0.376503 | − | 0.217374i | ||||
\(557\) | −7.05105 | − | 4.07093i | −0.298763 | − | 0.172491i | 0.343124 | − | 0.939290i | \(-0.388515\pi\) |
−0.641887 | + | 0.766799i | \(0.721848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.7627i | 0.624395i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.34398 | + | 9.25605i | 0.225422 | + | 0.390443i | ||||
\(563\) | −10.2088 | + | 17.6821i | −0.430248 | + | 0.745212i | −0.996894 | − | 0.0787491i | \(-0.974907\pi\) |
0.566646 | + | 0.823961i | \(0.308241\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.5687 | −0.738467 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.76268 | 0.199838 | ||||||||
\(569\) | 22.5542 | − | 13.0217i | 0.945520 | − | 0.545896i | 0.0538334 | − | 0.998550i | \(-0.482856\pi\) |
0.891686 | + | 0.452654i | \(0.149523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.18811 | − | 10.7181i | 0.258964 | − | 0.448539i | −0.707000 | − | 0.707213i | \(-0.749952\pi\) |
0.965965 | + | 0.258674i | \(0.0832855\pi\) | |||||||
\(572\) | −6.79253 | − | 11.7650i | −0.284010 | − | 0.491920i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.66552 | + | 1.12792i | −0.0695175 | + | 0.0470786i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.3399 | − | 13.4753i | −0.971654 | − | 0.560985i | −0.0719139 | − | 0.997411i | \(-0.522911\pi\) |
−0.899740 | + | 0.436426i | \(0.856244\pi\) | |||||||
\(578\) | 2.80973 | + | 1.62220i | 0.116869 | + | 0.0674746i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.9382 | + | 1.79048i | −1.03461 | + | 0.0742816i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.6586 | − | 39.2458i | −0.938422 | − | 1.62539i | ||||
\(584\) | 5.82843 | − | 10.0951i | 0.241182 | − | 0.417740i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.7054 | + | 7.33548i | −0.524856 | + | 0.303026i | ||||
\(587\) | 35.3511 | 1.45910 | 0.729548 | − | 0.683930i | \(-0.239731\pi\) | ||||
0.729548 | + | 0.683930i | \(0.239731\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.8272 | −0.569739 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.25882 | + | 5.64444i | −0.133937 | + | 0.231985i | ||||
\(593\) | −14.7057 | − | 25.4711i | −0.603893 | − | 1.04597i | −0.992225 | − | 0.124454i | \(-0.960282\pi\) |
0.388333 | − | 0.921519i | \(-0.373051\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.19881i | 0.376798i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.584220 | + | 0.337300i | 0.0238905 | + | 0.0137932i | ||||
\(599\) | 26.5494 | + | 15.3283i | 1.08478 | + | 0.626298i | 0.932182 | − | 0.361990i | \(-0.117903\pi\) |
0.152598 | + | 0.988288i | \(0.451236\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.3407i | 1.40078i | 0.713758 | + | 0.700392i | \(0.246992\pi\) | ||||
−0.713758 | + | 0.700392i | \(0.753008\pi\) | |||||||
\(602\) | −12.8454 | + | 8.69918i | −0.523541 | + | 0.354552i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.37429 | − | 11.0406i | −0.259366 | − | 0.449236i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.2475 | + | 16.3087i | −1.14653 | + | 0.661950i | −0.948040 | − | 0.318153i | \(-0.896938\pi\) |
−0.198492 | + | 0.980103i | \(0.563604\pi\) | |||||||
\(608\) | −2.86370 | −0.116139 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.4326 | − | 10.0647i | 0.705247 | − | 0.407174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.99843 | + | 13.8537i | −0.323054 | + | 0.559545i | −0.981117 | − | 0.193418i | \(-0.938043\pi\) |
0.658063 | + | 0.752963i | \(0.271376\pi\) | |||||||
\(614\) | 10.6386 | + | 18.4266i | 0.429339 | + | 0.743636i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.23445 | − | 12.8431i | 0.251193 | − | 0.517464i | ||||
\(617\) | − | 25.1429i | − | 1.01221i | −0.862471 | − | 0.506107i | \(-0.831084\pi\) | ||
0.862471 | − | 0.506107i | \(-0.168916\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.3379 | + | 18.6703i | 1.29977 | + | 0.750423i | 0.980364 | − | 0.197195i | \(-0.0631832\pi\) |
0.319406 | + | 0.947618i | \(0.396517\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 11.8345i | − | 0.474519i | ||||||
\(623\) | −11.8241 | − | 17.4597i | −0.473722 | − | 0.699510i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.25485 | + | 3.90551i | −0.0901219 | + | 0.156096i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.9899 | + | 6.92236i | −0.478448 | + | 0.276232i | ||||
\(629\) | 29.3253 | 1.16928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.5015 | 1.97062 | 0.985311 | − | 0.170767i | \(-0.0546245\pi\) | ||||
0.985311 | + | 0.170767i | \(0.0546245\pi\) | |||||||
\(632\) | 7.44120 | − | 4.29618i | 0.295995 | − | 0.170893i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.19151 | + | 15.9202i | −0.365041 | + | 0.632270i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.51764 | + | 17.4427i | 0.0997525 | + | 0.691105i | ||||
\(638\) | − | 48.0185i | − | 1.90107i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.4439 | − | 18.1542i | −1.24196 | − | 0.717046i | −0.272467 | − | 0.962165i | \(-0.587840\pi\) |
−0.969493 | + | 0.245119i | \(0.921173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.2653i | − | 0.404824i | −0.979300 | − | 0.202412i | \(-0.935122\pi\) | ||
0.979300 | − | 0.202412i | \(-0.0648780\pi\) | |||||||
\(644\) | 0.0507680 | + | 0.707107i | 0.00200054 | + | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.44244 | + | 11.1586i | 0.253474 | + | 0.439031i | ||||
\(647\) | 10.9108 | − | 18.8980i | 0.428946 | − | 0.742956i | −0.567834 | − | 0.823143i | \(-0.692218\pi\) |
0.996780 | + | 0.0801869i | \(0.0255517\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −59.2142 | + | 34.1873i | −2.32436 | + | 1.34197i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20.6050 | −0.806954 | ||||||||
\(653\) | −40.9556 | + | 23.6457i | −1.60272 | + | 0.925329i | −0.611775 | + | 0.791032i | \(0.709544\pi\) |
−0.990941 | + | 0.134297i | \(0.957122\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.380139 | − | 0.658421i | −0.0148419 | − | 0.0257070i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.0301 | + | 9.23779i | 0.741869 | + | 0.360127i | ||||
\(659\) | 3.58255i | 0.139556i | 0.997563 | + | 0.0697782i | \(0.0222291\pi\) | ||||
−0.997563 | + | 0.0697782i | \(0.977771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41761 | − | 0.818459i | −0.0551388 | − | 0.0318344i | 0.472177 | − | 0.881504i | \(-0.343468\pi\) |
−0.527316 | + | 0.849669i | \(0.676802\pi\) | |||||||
\(662\) | 6.89471 | + | 3.98066i | 0.267970 | + | 0.154713i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 9.45001i | − | 0.366731i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.19224 | + | 2.06502i | 0.0461636 | + | 0.0799577i | ||||
\(668\) | −3.42480 | + | 5.93193i | −0.132510 | + | 0.229513i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.1459 | 0.546097 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.02242 | 0.0779587 | 0.0389794 | − | 0.999240i | \(-0.487589\pi\) | ||||
0.0389794 | + | 0.999240i | \(0.487589\pi\) | |||||||
\(674\) | −5.97053 | + | 3.44709i | −0.229976 | + | 0.132777i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.33075 | − | 5.76903i | 0.128106 | − | 0.221886i | ||||
\(677\) | −11.4413 | − | 19.8169i | −0.439725 | − | 0.761626i | 0.557943 | − | 0.829879i | \(-0.311591\pi\) |
−0.997668 | + | 0.0682532i | \(0.978257\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.16780 | + | 16.2653i | 0.0448159 | + | 0.624205i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.5634 | + | 13.0270i | 0.863997 | + | 0.498829i | ||||
\(683\) | −27.1977 | − | 15.7026i | −1.04069 | − | 0.600844i | −0.120663 | − | 0.992694i | \(-0.538502\pi\) |
−0.920029 | + | 0.391850i | \(0.871835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.6938 | + | 12.4691i | −0.522834 | + | 0.476073i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.93185 | − | 5.07812i | −0.111776 | − | 0.193601i | ||||
\(689\) | −10.5720 | + | 18.3113i | −0.402762 | + | 0.697604i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.3677 | − | 16.9554i | 1.11720 | − | 0.645015i | 0.176515 | − | 0.984298i | \(-0.443518\pi\) |
0.940684 | + | 0.339283i | \(0.110184\pi\) | |||||||
\(692\) | 12.7580 | 0.484988 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.3558 | −0.620857 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.71039 | + | 2.96248i | −0.0647857 | + | 0.112212i | ||||
\(698\) | 12.2925 | + | 21.2913i | 0.465279 | + | 0.805887i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 10.5296i | − | 0.397699i | −0.980030 | − | 0.198849i | \(-0.936280\pi\) | ||
0.980030 | − | 0.198849i | \(-0.0637205\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.1640 | + | 9.33229i | 0.609637 | + | 0.351974i | ||||
\(704\) | 4.67303 | + | 2.69798i | 0.176122 | + | 0.101684i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 13.7181i | − | 0.516288i | ||||||
\(707\) | −16.2323 | + | 33.4390i | −0.610479 | + | 1.25760i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.52572 | − | 13.0349i | −0.282634 | − | 0.489537i | 0.689398 | − | 0.724382i | \(-0.257875\pi\) |
−0.972033 | + | 0.234845i | \(0.924542\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.90226 | − | 3.98502i | 0.258673 | − | 0.149345i | ||||
\(713\) | −1.29377 | −0.0484522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −16.3390 | + | 9.43331i | −0.610616 | + | 0.352539i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.95011 | − | 10.3059i | 0.222056 | − | 0.384613i | ||||
\(719\) | 12.2137 | + | 21.1547i | 0.455494 | + | 0.788938i | 0.998716 | − | 0.0506506i | \(-0.0161295\pi\) |
−0.543223 | + | 0.839589i | \(0.682796\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.0569 | + | 21.0323i | −1.15662 | + | 0.783285i | ||||
\(722\) | − | 10.7992i | − | 0.401905i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.1268 | − | 12.7749i | −0.822335 | − | 0.474775i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 43.7349i | − | 1.62204i | −0.585020 | − | 0.811019i | \(-0.698913\pi\) | ||
0.585020 | − | 0.811019i | \(-0.301087\pi\) | |||||||
\(728\) | −6.64394 | + | 0.477014i | −0.246241 | + | 0.0176793i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1915 | + | 22.8484i | −0.487906 | + | 0.845077i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.7280 | + | 22.3596i | −1.43045 | + | 0.825872i | −0.997155 | − | 0.0753789i | \(-0.975983\pi\) |
−0.433297 | + | 0.901251i | \(0.642650\pi\) | |||||||
\(734\) | −12.5892 | −0.464677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.267949 | −0.00987674 | ||||||||
\(737\) | −45.9003 | + | 26.5005i | −1.69076 | + | 0.976160i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7360 | − | 18.5954i | 0.394932 | − | 0.684042i | −0.598161 | − | 0.801376i | \(-0.704102\pi\) |
0.993092 | + | 0.117334i | \(0.0374348\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −22.1629 | + | 1.59123i | −0.813626 | + | 0.0584157i | ||||
\(743\) | 29.5637i | 1.08459i | 0.840190 | + | 0.542293i | \(0.182444\pi\) | ||||
−0.840190 | + | 0.542293i | \(0.817556\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.5331 | + | 13.5868i | 0.861607 | + | 0.497449i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 24.2784i | − | 0.887707i | ||||||
\(749\) | 3.59648 | − | 2.43561i | 0.131413 | − | 0.0889951i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.596750 | − | 1.03360i | −0.0217757 | − | 0.0377166i | 0.854932 | − | 0.518740i | \(-0.173599\pi\) |
−0.876708 | + | 0.481023i | \(0.840265\pi\) | |||||||
\(752\) | −3.99768 | + | 6.92418i | −0.145780 | + | 0.252499i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.4028 | + | 11.2022i | −0.706608 | + | 0.407960i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.8915 | 0.977386 | 0.488693 | − | 0.872456i | \(-0.337474\pi\) | ||||
0.488693 | + | 0.872456i | \(0.337474\pi\) | |||||||
\(758\) | −13.6256 | + | 7.86673i | −0.494903 | + | 0.285732i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.939574 | − | 1.62739i | −0.0340595 | − | 0.0589928i | 0.848493 | − | 0.529206i | \(-0.177510\pi\) |
−0.882553 | + | 0.470213i | \(0.844177\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.9897 | − | 47.3594i | 0.832284 | − | 1.71452i | ||||
\(764\) | 8.09049i | 0.292704i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.6669 | − | 7.89060i | −0.493806 | − | 0.285099i | ||||
\(767\) | 27.6281 | + | 15.9511i | 0.997592 | + | 0.575960i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.6544i | 1.82664i | 0.407239 | + | 0.913322i | \(0.366492\pi\) | ||||
−0.407239 | + | 0.913322i | \(0.633508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.06350 | + | 12.2343i | 0.254221 | + | 0.440324i | ||||
\(773\) | 24.3353 | − | 42.1499i | 0.875279 | − | 1.51603i | 0.0188128 | − | 0.999823i | \(-0.494011\pi\) |
0.856466 | − | 0.516204i | \(-0.172655\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.16353 | −0.221258 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.8836 | 0.569456 | ||||||||
\(779\) | −1.88552 | + | 1.08861i | −0.0675558 | + | 0.0390034i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8496 | + | 22.2562i | −0.459795 | + | 0.796388i | ||||
\(782\) | 0.602802 | + | 1.04408i | 0.0215562 | + | 0.0373364i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.33013 | − | 5.50000i | −0.154647 | − | 0.196429i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.9437 | + | 7.47307i | 0.461395 | + | 0.266386i | 0.712630 | − | 0.701540i | \(-0.247504\pi\) |
−0.251236 | + | 0.967926i | \(0.580837\pi\) | |||||||
\(788\) | 12.3615 | + | 7.13689i | 0.440359 | + | 0.254241i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.12898 | − | 15.7247i | −0.0401420 | − | 0.559105i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.30009 | − | 5.71593i | −0.117190 | − | 0.202979i | ||||
\(794\) | 18.6806 | − | 32.3557i | 0.662948 | − | 1.14826i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.06742 | − | 1.77098i | 0.108722 | − | 0.0627706i | ||||
\(797\) | 15.0557 | 0.533301 | 0.266650 | − | 0.963793i | \(-0.414083\pi\) | ||||
0.266650 | + | 0.963793i | \(0.414083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.9741 | 1.27267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.1368 | + | 24.4856i | −0.499187 | + | 0.864617i | ||||
\(803\) | 31.4499 | + | 54.4729i | 1.10984 | + | 1.92231i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 12.1562i | − | 0.428185i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.1669 | − | 7.02458i | −0.428031 | − | 0.247124i | ||||
\(809\) | 30.7426 | + | 17.7493i | 1.08085 | + | 0.624031i | 0.931127 | − | 0.364696i | \(-0.118827\pi\) |
0.149727 | + | 0.988727i | \(0.452160\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 24.5935i | − | 0.863594i | −0.901971 | − | 0.431797i | \(-0.857880\pi\) | ||
0.901971 | − | 0.431797i | \(-0.142120\pi\) | |||||||
\(812\) | −21.1808 | − | 10.2818i | −0.743301 | − | 0.360822i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.5844 | − | 30.4571i | −0.616334 | − | 1.06752i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.5422 | + | 8.39595i | −0.508768 | + | 0.293737i | ||||
\(818\) | −16.0096 | −0.559763 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.3035 | + | 7.10342i | −0.429395 | + | 0.247911i | −0.699089 | − | 0.715035i | \(-0.746411\pi\) |
0.269694 | + | 0.962946i | \(0.413077\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.945584 | − | 1.63780i | 0.0329610 | − | 0.0570901i | −0.849074 | − | 0.528273i | \(-0.822840\pi\) |
0.882035 | + | 0.471183i | \(0.156173\pi\) | |||||||
\(824\) | −7.08845 | − | 12.2776i | −0.246938 | − | 0.427709i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.40085 | + | 33.4395i | 0.0835361 | + | 1.16351i | ||||
\(827\) | 31.9280i | 1.11024i | 0.831769 | + | 0.555122i | \(0.187329\pi\) | ||||
−0.831769 | + | 0.555122i | \(0.812671\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.38864 | + | 1.95643i | 0.117692 | + | 0.0679497i | 0.557691 | − | 0.830049i | \(-0.311688\pi\) |
−0.439998 | + | 0.897999i | \(0.645021\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.51764i | − | 0.0872834i | ||||||
\(833\) | −11.6897 | + | 29.2460i | −0.405025 | + | 1.01331i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.72620 | − | 13.3822i | 0.267216 | − | 0.462832i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.5596 | + | 14.7568i | −0.882941 | + | 0.509766i | ||||
\(839\) | −15.3513 | −0.529984 | −0.264992 | − | 0.964251i | \(-0.585369\pi\) | ||||
−0.264992 | + | 0.964251i | \(0.585369\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.1918 | −1.73075 | ||||||||
\(842\) | −0.267701 | + | 0.154557i | −0.00922557 | + | 0.00532639i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.96170 | + | 3.39776i | −0.0675244 | + | 0.116956i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.8767 | + | 39.6869i | 0.923495 | + | 1.36366i | ||||
\(848\) | − | 8.39836i | − | 0.288401i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.51242 | + | 0.873198i | 0.0518452 | + | 0.0299328i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2302i | 0.761148i | 0.924750 | + | 0.380574i | \(0.124274\pi\) | ||||
−0.924750 | + | 0.380574i | \(0.875726\pi\) | |||||||
\(854\) | 3.02896 | − | 6.23972i | 0.103649 | − | 0.213519i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.820863 | + | 1.42178i | 0.0280565 | + | 0.0485953i | ||||
\(857\) | −26.4098 | + | 45.7432i | −0.902143 | + | 1.56256i | −0.0774356 | + | 0.996997i | \(0.524673\pi\) |
−0.824707 | + | 0.565560i | \(0.808660\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.2916 | + | 8.82859i | −0.521742 | + | 0.301228i | −0.737647 | − | 0.675187i | \(-0.764063\pi\) |
0.215905 | + | 0.976414i | \(0.430730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.82010 | −0.300414 | ||||||||
\(863\) | 14.2452 | − | 8.22446i | 0.484912 | − | 0.279964i | −0.237549 | − | 0.971375i | \(-0.576344\pi\) |
0.722461 | + | 0.691412i | \(0.243011\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.78194 | + | 8.28256i | 0.162497 | + | 0.281453i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.5775 | − | 7.16328i | 0.359024 | − | 0.243138i | ||||
\(869\) | 46.3639i | 1.57279i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.4161 | + | 12.3646i | 0.725657 | + | 0.418958i | ||||
\(872\) | 17.2319 | + | 9.94887i | 0.583547 | + | 0.336911i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.767327i | 0.0259552i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.1078 | + | 46.9521i | 0.915366 | + | 1.58546i | 0.806365 | + | 0.591418i | \(0.201432\pi\) |
0.109001 | + | 0.994042i | \(0.465235\pi\) | |||||||
\(878\) | 18.0905 | − | 31.3336i | 0.610524 | − | 1.05746i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.1647 | −1.69009 | −0.845046 | − | 0.534694i | \(-0.820427\pi\) | ||||
−0.845046 | + | 0.534694i | \(0.820427\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.841563 | 0.0283208 | 0.0141604 | − | 0.999900i | \(-0.495492\pi\) | ||||
0.0141604 | + | 0.999900i | \(0.495492\pi\) | |||||||
\(884\) | −9.81017 | + | 5.66390i | −0.329952 | + | 0.190498i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.04284 | + | 3.53830i | −0.0686305 | + | 0.118872i | ||||
\(887\) | 20.0492 | + | 34.7262i | 0.673185 | + | 1.16599i | 0.976996 | + | 0.213258i | \(0.0684075\pi\) |
−0.303811 | + | 0.952732i | \(0.598259\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.2922 | − | 2.74926i | 1.28428 | − | 0.0922071i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.7222 | + | 7.34519i | 0.425972 | + | 0.245935i | ||||
\(893\) | 19.8288 | + | 11.4482i | 0.663546 | + | 0.383098i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.19067 | − | 1.48356i | 0.0731852 | − | 0.0495624i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.96885 | − | 17.2665i | −0.332665 | − | 0.576192i | ||||
\(899\) | 21.4840 | − | 37.2114i | 0.716533 | − | 1.24107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.7248 | + | 18.8937i | −1.09022 | + | 0.629440i | ||||
\(902\) | 4.10243 | 0.136596 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.95867 | 0.198182 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.5945 | + | 39.1348i | −0.750238 | + | 1.29945i | 0.197469 | + | 0.980309i | \(0.436728\pi\) |
−0.947707 | + | 0.319142i | \(0.896605\pi\) | |||||||
\(908\) | −11.3913 | − | 19.7303i | −0.378034 | − | 0.654774i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 58.2281i | 1.92918i | 0.263746 | + | 0.964592i | \(0.415042\pi\) | ||||
−0.263746 | + | 0.964592i | \(0.584958\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.1602 | + | 25.4959i | 1.46149 | + | 0.843791i | ||||
\(914\) | 17.4283 | + | 10.0623i | 0.576478 | + | 0.332830i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 20.2175i | 0.668005i | ||||||||
\(917\) | 22.9455 | + | 33.8820i | 0.757729 | + | 1.11888i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.61745 | − | 11.4618i | −0.218290 | − | 0.378089i | 0.735996 | − | 0.676986i | \(-0.236714\pi\) |
−0.954285 | + | 0.298898i | \(0.903381\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.787476 | − | 0.454649i | 0.0259341 | − | 0.0149731i | ||||
\(923\) | 11.9907 | 0.394679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.5572 | − | 10.7140i | 0.609827 | − | 0.352084i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.44949 | − | 7.70674i | 0.146062 | − | 0.252986i | ||||
\(929\) | 10.4434 | + | 18.0885i | 0.342637 | + | 0.593464i | 0.984921 | − | 0.173002i | \(-0.0553467\pi\) |
−0.642285 | + | 0.766466i | \(0.722013\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7504 | + | 12.4002i | −0.516197 | + | 0.406400i | ||||
\(932\) | 2.63087i | 0.0861769i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.9917 | − | 6.34607i | −0.359660 | − | 0.207650i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.2465i | 0.759430i | 0.925103 | + | 0.379715i | \(0.123978\pi\) | ||||
−0.925103 | + | 0.379715i | \(0.876022\pi\) | |||||||
\(938\) | 1.86103 | + | 25.9208i | 0.0607649 | + | 0.846345i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.752551 | − | 1.30346i | 0.0245325 | − | 0.0424915i | −0.853499 | − | 0.521095i | \(-0.825524\pi\) |
0.878031 | + | 0.478604i | \(0.158857\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.176423 | + | 0.101858i | −0.00574513 | + | 0.00331695i | ||||
\(944\) | −12.6715 | −0.412421 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.6403 | 1.02871 | ||||||||
\(947\) | 21.0122 | − | 12.1314i | 0.682805 | − | 0.394218i | −0.118106 | − | 0.993001i | \(-0.537682\pi\) |
0.800911 | + | 0.598783i | \(0.204349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6739 | − | 25.4159i | 0.476334 | − | 0.825035i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −10.7091 | − | 5.19856i | −0.347085 | − | 0.168486i | ||||
\(953\) | − | 56.7061i | − | 1.83689i | −0.395547 | − | 0.918446i | \(-0.629445\pi\) | ||
0.395547 | − | 0.918446i | \(-0.370555\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.6155 | − | 8.43828i | −0.472700 | − | 0.272913i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.8766i | 0.416023i | ||||||||
\(959\) | −20.5206 | − | 9.96132i | −0.662643 | − | 0.321668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.84315 | − | 6.65652i | −0.123972 | − | 0.214727i | ||||
\(962\) | −8.20453 | + | 14.2107i | −0.264525 | + | 0.458170i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.5793 | + | 7.26268i | −0.405153 | + | 0.233915i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.23556 | −0.232680 | −0.116340 | − | 0.993209i | \(-0.537116\pi\) | ||||
−0.116340 | + | 0.993209i | \(0.537116\pi\) | |||||||
\(968\) | −15.6892 | + | 9.05816i | −0.504270 | + | 0.291140i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.3560 | − | 33.5256i | −0.621163 | − | 1.07589i | −0.989269 | − | 0.146103i | \(-0.953327\pi\) |
0.368106 | − | 0.929784i | \(-0.380006\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.94228 | − | 27.0525i | −0.0622667 | − | 0.867263i | ||||
\(974\) | − | 20.8194i | − | 0.667096i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.27035 | + | 1.31079i | 0.0726722 | + | 0.0419573i | ||||
\(977\) | −15.7279 | − | 9.08052i | −0.503181 | − | 0.290512i | 0.226845 | − | 0.973931i | \(-0.427159\pi\) |
−0.730026 | + | 0.683419i | \(0.760492\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.0060i | 1.37448i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −13.6635 | − | 23.6659i | −0.436021 | − | 0.755211i | ||||
\(983\) | −8.19988 | + | 14.2026i | −0.261536 | + | 0.452993i | −0.966650 | − | 0.256100i | \(-0.917562\pi\) |
0.705115 | + | 0.709093i | \(0.250896\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −40.0399 | −1.27513 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.20977 | −0.229373 | ||||||||
\(989\) | −1.36068 | + | 0.785587i | −0.0432670 | + | 0.0249802i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.44584 | − | 9.43247i | 0.172993 | − | 0.299632i | −0.766472 | − | 0.642278i | \(-0.777990\pi\) |
0.939465 | + | 0.342645i | \(0.111323\pi\) | |||||||
\(992\) | 2.41421 | + | 4.18154i | 0.0766514 | + | 0.132764i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.06574 | + | 10.4335i | 0.224112 | + | 0.330930i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.7856 | − | 17.7740i | −0.974988 | − | 0.562910i | −0.0742349 | − | 0.997241i | \(-0.523651\pi\) |
−0.900753 | + | 0.434331i | \(0.856985\pi\) | |||||||
\(998\) | 28.8909 | + | 16.6802i | 0.914527 | + | 0.528002i | ||||
\(999\) | 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 | 3150.2.bf.b.1151.2 | 8 | ||
3.2 | odd | 2 | 3150.2.bf.c.1151.4 | 8 | |||
5.2 | odd | 4 | 3150.2.bp.a.899.3 | 8 | |||
5.3 | odd | 4 | 3150.2.bp.d.899.2 | 8 | |||
5.4 | even | 2 | 630.2.be.a.521.3 | yes | 8 | ||
7.5 | odd | 6 | 3150.2.bf.c.1601.4 | 8 | |||
15.2 | even | 4 | 3150.2.bp.f.899.3 | 8 | |||
15.8 | even | 4 | 3150.2.bp.c.899.2 | 8 | |||
15.14 | odd | 2 | 630.2.be.b.521.1 | yes | 8 | ||
21.5 | even | 6 | inner | 3150.2.bf.b.1601.2 | 8 | ||
35.4 | even | 6 | 4410.2.b.e.881.8 | 8 | |||
35.12 | even | 12 | 3150.2.bp.c.1349.2 | 8 | |||
35.19 | odd | 6 | 630.2.be.b.341.1 | yes | 8 | ||
35.24 | odd | 6 | 4410.2.b.b.881.8 | 8 | |||
35.33 | even | 12 | 3150.2.bp.f.1349.3 | 8 | |||
105.47 | odd | 12 | 3150.2.bp.d.1349.2 | 8 | |||
105.59 | even | 6 | 4410.2.b.e.881.1 | 8 | |||
105.68 | odd | 12 | 3150.2.bp.a.1349.3 | 8 | |||
105.74 | odd | 6 | 4410.2.b.b.881.1 | 8 | |||
105.89 | even | 6 | 630.2.be.a.341.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.3 | ✓ | 8 | 105.89 | even | 6 | ||
630.2.be.a.521.3 | yes | 8 | 5.4 | even | 2 | ||
630.2.be.b.341.1 | yes | 8 | 35.19 | odd | 6 | ||
630.2.be.b.521.1 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.bf.b.1151.2 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.bf.b.1601.2 | 8 | 21.5 | even | 6 | inner | ||
3150.2.bf.c.1151.4 | 8 | 3.2 | odd | 2 | |||
3150.2.bf.c.1601.4 | 8 | 7.5 | odd | 6 | |||
3150.2.bp.a.899.3 | 8 | 5.2 | odd | 4 | |||
3150.2.bp.a.1349.3 | 8 | 105.68 | odd | 12 | |||
3150.2.bp.c.899.2 | 8 | 15.8 | even | 4 | |||
3150.2.bp.c.1349.2 | 8 | 35.12 | even | 12 | |||
3150.2.bp.d.899.2 | 8 | 5.3 | odd | 4 | |||
3150.2.bp.d.1349.2 | 8 | 105.47 | odd | 12 | |||
3150.2.bp.f.899.3 | 8 | 15.2 | even | 4 | |||
3150.2.bp.f.1349.3 | 8 | 35.33 | even | 12 | |||
4410.2.b.b.881.1 | 8 | 105.74 | odd | 6 | |||
4410.2.b.b.881.8 | 8 | 35.24 | odd | 6 | |||
4410.2.b.e.881.1 | 8 | 105.59 | even | 6 | |||
4410.2.b.e.881.8 | 8 | 35.4 | even | 6 |