Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(199,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.199");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.j (of order \(6\), 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: | \(10.7798042729\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 450) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.199 |
Dual form | 1350.2.j.g.1099.2 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.389270 | − | 0.224745i | 0.147130 | − | 0.0849456i | −0.424628 | − | 0.905368i | \(-0.639595\pi\) |
0.571758 | + | 0.820422i | \(0.306262\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | − | 4.24264i | −0.738549 | − | 1.27920i | −0.953149 | − | 0.302502i | \(-0.902178\pi\) |
0.214600 | − | 0.976702i | \(-0.431155\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.389270 | + | 0.224745i | 0.107964 | + | 0.0623330i | 0.553010 | − | 0.833175i | \(-0.313479\pi\) |
−0.445046 | + | 0.895508i | \(0.646813\pi\) | |||||||
\(14\) | −0.224745 | + | 0.389270i | −0.0600656 | + | 0.104037i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 4.89898i | 1.18818i | 0.804400 | + | 0.594089i | \(0.202487\pi\) | ||||
−0.804400 | + | 0.594089i | \(0.797513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.44949 | −1.70903 | −0.854515 | − | 0.519427i | \(-0.826146\pi\) | ||||
−0.854515 | + | 0.519427i | \(0.826146\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.24264 | + | 2.44949i | 0.904534 | + | 0.522233i | ||||
\(23\) | −2.12132 | − | 1.22474i | −0.442326 | − | 0.255377i | 0.262258 | − | 0.964998i | \(-0.415533\pi\) |
−0.704584 | + | 0.709621i | \(0.748866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.449490 | −0.0881522 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 0.449490i | − | 0.0849456i | ||||||
\(29\) | 1.22474 | + | 2.12132i | 0.227429 | + | 0.393919i | 0.957046 | − | 0.289938i | \(-0.0936346\pi\) |
−0.729616 | + | 0.683857i | \(0.760301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.22474 | + | 3.85337i | −0.399576 | + | 0.692086i | −0.993674 | − | 0.112307i | \(-0.964176\pi\) |
0.594098 | + | 0.804393i | \(0.297509\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.44949 | − | 4.24264i | −0.420084 | − | 0.727607i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.3485i | 1.86568i | 0.360295 | + | 0.932838i | \(0.382676\pi\) | ||||
−0.360295 | + | 0.932838i | \(0.617324\pi\) | |||||||
\(38\) | 6.45145 | − | 3.72474i | 1.04656 | − | 0.604233i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20881 | − | 1.27526i | 0.336840 | − | 0.194475i | −0.322034 | − | 0.946728i | \(-0.604366\pi\) |
0.658874 | + | 0.752254i | \(0.271033\pi\) | |||||||
\(44\) | −4.89898 | −0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.44949 | 0.361158 | ||||||||
\(47\) | −9.43879 | + | 5.44949i | −1.37679 | + | 0.794890i | −0.991772 | − | 0.128019i | \(-0.959138\pi\) |
−0.385018 | + | 0.922909i | \(0.625805\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.39898 | + | 5.88721i | −0.485568 | + | 0.841029i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.389270 | − | 0.224745i | 0.0539820 | − | 0.0311665i | ||||
\(53\) | 3.55051i | 0.487700i | 0.969813 | + | 0.243850i | \(0.0784105\pi\) | ||||
−0.969813 | + | 0.243850i | \(0.921590\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.224745 | + | 0.389270i | 0.0300328 | + | 0.0520183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.12132 | − | 1.22474i | −0.278543 | − | 0.160817i | ||||
\(59\) | 2.72474 | − | 4.71940i | 0.354732 | − | 0.614413i | −0.632340 | − | 0.774691i | \(-0.717906\pi\) |
0.987072 | + | 0.160278i | \(0.0512389\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | − | 4.44949i | − | 0.565086i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.301783 | + | 0.174235i | 0.0368687 | + | 0.0212861i | 0.518321 | − | 0.855186i | \(-0.326557\pi\) |
−0.481452 | + | 0.876472i | \(0.659891\pi\) | |||||||
\(68\) | 4.24264 | + | 2.44949i | 0.514496 | + | 0.297044i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.3485 | −1.58417 | −0.792086 | − | 0.610410i | \(-0.791005\pi\) | ||||
−0.792086 | + | 0.610410i | \(0.791005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.00000i | − | 0.117041i | −0.998286 | − | 0.0585206i | \(-0.981362\pi\) | ||
0.998286 | − | 0.0585206i | \(-0.0186383\pi\) | |||||||
\(74\) | −5.67423 | − | 9.82806i | −0.659616 | − | 1.14249i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.72474 | + | 6.45145i | −0.427258 | + | 0.740032i | ||||
\(77\) | −1.90702 | − | 1.10102i | −0.217325 | − | 0.125473i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.34847 | + | 14.4600i | 0.939276 | + | 1.62687i | 0.766825 | + | 0.641856i | \(0.221835\pi\) |
0.172451 | + | 0.985018i | \(0.444831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.00000i | 0.993884i | ||||||||
\(83\) | 4.71940 | − | 2.72474i | 0.518021 | − | 0.299080i | −0.218104 | − | 0.975926i | \(-0.569987\pi\) |
0.736125 | + | 0.676846i | \(0.236654\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.27526 | + | 2.20881i | −0.137514 | + | 0.238182i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264 | − | 2.44949i | 0.452267 | − | 0.261116i | ||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.202041 | 0.0211797 | ||||||||
\(92\) | −2.12132 | + | 1.22474i | −0.221163 | + | 0.127688i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.44949 | − | 9.43879i | 0.562072 | − | 0.973537i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.61926 | + | 4.39898i | −0.773618 | + | 0.446649i | −0.834164 | − | 0.551517i | \(-0.814049\pi\) |
0.0605456 | + | 0.998165i | \(0.480716\pi\) | |||||||
\(98\) | − | 6.79796i | − | 0.686698i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.22474 | + | 7.31747i | 0.420378 | + | 0.728116i | 0.995976 | − | 0.0896167i | \(-0.0285642\pi\) |
−0.575599 | + | 0.817732i | \(0.695231\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.4600 | − | 8.34847i | −1.42478 | − | 0.822599i | −0.428081 | − | 0.903740i | \(-0.640810\pi\) |
−0.996703 | + | 0.0811413i | \(0.974143\pi\) | |||||||
\(104\) | −0.224745 | + | 0.389270i | −0.0220380 | + | 0.0381710i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.77526 | − | 3.07483i | −0.172428 | − | 0.298654i | ||||
\(107\) | 9.24745i | 0.893985i | 0.894538 | + | 0.446992i | \(0.147505\pi\) | ||||
−0.894538 | + | 0.446992i | \(0.852495\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.55051 | −0.531642 | −0.265821 | − | 0.964022i | \(-0.585643\pi\) | ||||
−0.265821 | + | 0.964022i | \(0.585643\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.389270 | − | 0.224745i | −0.0367825 | − | 0.0212364i | ||||
\(113\) | −3.55159 | − | 2.05051i | −0.334105 | − | 0.192896i | 0.323557 | − | 0.946209i | \(-0.395121\pi\) |
−0.657662 | + | 0.753313i | \(0.728455\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.44949 | 0.227429 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.44949i | 0.501666i | ||||||||
\(119\) | 1.10102 | + | 1.90702i | 0.100930 | + | 0.174817i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50000 | + | 11.2583i | −0.590909 | + | 1.02348i | ||||
\(122\) | 6.92820 | + | 4.00000i | 0.627250 | + | 0.362143i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.22474 | + | 3.85337i | 0.199788 | + | 0.346043i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.34847i | − | 0.297129i | −0.988903 | − | 0.148564i | \(-0.952535\pi\) | ||
0.988903 | − | 0.148564i | \(-0.0474652\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.89898 | + | 3.28913i | −0.165915 | + | 0.287373i | −0.936980 | − | 0.349384i | \(-0.886391\pi\) |
0.771065 | + | 0.636756i | \(0.219724\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.89986 | + | 1.67423i | −0.251450 | + | 0.145175i | ||||
\(134\) | −0.348469 | −0.0301032 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.89898 | −0.420084 | ||||||||
\(137\) | 2.59808 | − | 1.50000i | 0.221969 | − | 0.128154i | −0.384893 | − | 0.922961i | \(-0.625762\pi\) |
0.606861 | + | 0.794808i | \(0.292428\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | + | 3.46410i | −0.169638 | + | 0.293821i | −0.938293 | − | 0.345843i | \(-0.887593\pi\) |
0.768655 | + | 0.639664i | \(0.220926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.5601 | − | 6.67423i | 0.970103 | − | 0.560089i | ||||
\(143\) | − | 2.20204i | − | 0.184144i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.500000 | + | 0.866025i | 0.0413803 | + | 0.0716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.82806 | + | 5.67423i | 0.807862 | + | 0.466419i | ||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | − | 17.3205i | −0.813788 | − | 1.40952i | −0.910195 | − | 0.414181i | \(-0.864068\pi\) |
0.0964061 | − | 0.995342i | \(-0.469265\pi\) | |||||||
\(152\) | − | 7.44949i | − | 0.604233i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.20204 | 0.177446 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.1455 | − | 9.89898i | −1.36836 | − | 0.790025i | −0.377644 | − | 0.925951i | \(-0.623266\pi\) |
−0.990719 | + | 0.135926i | \(0.956599\pi\) | |||||||
\(158\) | −14.4600 | − | 8.34847i | −1.15037 | − | 0.664169i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.10102 | −0.0867726 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.44949i | 0.583489i | 0.956496 | + | 0.291745i | \(0.0942357\pi\) | ||||
−0.956496 | + | 0.291745i | \(0.905764\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.72474 | + | 4.71940i | −0.211481 | + | 0.366296i | ||||
\(167\) | −16.9706 | − | 9.79796i | −1.31322 | − | 0.758189i | −0.330593 | − | 0.943773i | \(-0.607249\pi\) |
−0.982628 | + | 0.185584i | \(0.940582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.39898 | − | 11.0834i | −0.492229 | − | 0.852566i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 2.55051i | − | 0.194475i | ||||||
\(173\) | −8.48528 | + | 4.89898i | −0.645124 | + | 0.372463i | −0.786586 | − | 0.617481i | \(-0.788153\pi\) |
0.141462 | + | 0.989944i | \(0.454820\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.44949 | + | 4.24264i | −0.184637 | + | 0.319801i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.79423 | − | 4.50000i | 0.584202 | − | 0.337289i | ||||
\(179\) | 9.24745 | 0.691187 | 0.345593 | − | 0.938384i | \(-0.387678\pi\) | ||||
0.345593 | + | 0.938384i | \(0.387678\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.7980 | 1.32291 | 0.661456 | − | 0.749984i | \(-0.269939\pi\) | ||||
0.661456 | + | 0.749984i | \(0.269939\pi\) | |||||||
\(182\) | −0.174973 | + | 0.101021i | −0.0129698 | + | 0.00748814i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.22474 | − | 2.12132i | 0.0902894 | − | 0.156386i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.7846 | − | 12.0000i | 1.51992 | − | 0.877527i | ||||
\(188\) | 10.8990i | 0.794890i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.550510 | − | 0.953512i | −0.0398335 | − | 0.0689937i | 0.845421 | − | 0.534100i | \(-0.179349\pi\) |
−0.885255 | + | 0.465106i | \(0.846016\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.3205 | − | 10.0000i | −1.24676 | − | 0.719816i | −0.276296 | − | 0.961073i | \(-0.589107\pi\) |
−0.970461 | + | 0.241257i | \(0.922440\pi\) | |||||||
\(194\) | 4.39898 | − | 7.61926i | 0.315828 | − | 0.547031i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.39898 | + | 5.88721i | 0.242784 | + | 0.420515i | ||||
\(197\) | − | 0.247449i | − | 0.0176300i | −0.999961 | − | 0.00881500i | \(-0.997194\pi\) | ||
0.999961 | − | 0.00881500i | \(-0.00280594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7980 | 0.978111 | 0.489056 | − | 0.872253i | \(-0.337341\pi\) | ||||
0.489056 | + | 0.872253i | \(0.337341\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.31747 | − | 4.22474i | −0.514856 | − | 0.297252i | ||||
\(203\) | 0.953512 | + | 0.550510i | 0.0669234 | + | 0.0386382i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.6969 | 1.16333 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 0.449490i | − | 0.0311665i | ||||||
\(209\) | 18.2474 | + | 31.6055i | 1.26220 | + | 2.18620i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.72474 | − | 2.98735i | 0.118736 | − | 0.205657i | −0.800531 | − | 0.599292i | \(-0.795449\pi\) |
0.919267 | + | 0.393634i | \(0.128782\pi\) | |||||||
\(212\) | 3.07483 | + | 1.77526i | 0.211180 | + | 0.121925i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.62372 | − | 8.00853i | −0.316071 | − | 0.547452i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000i | 0.135769i | ||||||||
\(218\) | 4.80688 | − | 2.77526i | 0.325563 | − | 0.187964i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.10102 | + | 1.90702i | −0.0740627 | + | 0.128280i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.4135 | − | 8.89898i | 1.03216 | − | 0.595920i | 0.114560 | − | 0.993416i | \(-0.463454\pi\) |
0.917604 | + | 0.397497i | \(0.130121\pi\) | |||||||
\(224\) | 0.449490 | 0.0300328 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.10102 | 0.272796 | ||||||||
\(227\) | 11.8226 | − | 6.82577i | 0.784692 | − | 0.453042i | −0.0533987 | − | 0.998573i | \(-0.517005\pi\) |
0.838090 | + | 0.545531i | \(0.183672\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.57321 | − | 11.3851i | 0.434370 | − | 0.752351i | −0.562874 | − | 0.826543i | \(-0.690304\pi\) |
0.997244 | + | 0.0741916i | \(0.0236376\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.12132 | + | 1.22474i | −0.139272 | + | 0.0804084i | ||||
\(233\) | 23.6969i | 1.55244i | 0.630463 | + | 0.776219i | \(0.282865\pi\) | ||||
−0.630463 | + | 0.776219i | \(0.717135\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.72474 | − | 4.71940i | −0.177366 | − | 0.307207i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.90702 | − | 1.10102i | −0.123614 | − | 0.0713686i | ||||
\(239\) | −7.22474 | + | 12.5136i | −0.467330 | + | 0.809439i | −0.999303 | − | 0.0373219i | \(-0.988117\pi\) |
0.531973 | + | 0.846761i | \(0.321451\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.60102 | + | 2.77305i | 0.103131 | + | 0.178628i | 0.912973 | − | 0.408020i | \(-0.133781\pi\) |
−0.809842 | + | 0.586648i | \(0.800447\pi\) | |||||||
\(242\) | − | 13.0000i | − | 0.835672i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.89986 | − | 1.67423i | −0.184514 | − | 0.106529i | ||||
\(248\) | −3.85337 | − | 2.22474i | −0.244689 | − | 0.141271i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.550510 | 0.0347479 | 0.0173739 | − | 0.999849i | \(-0.494469\pi\) | ||||
0.0173739 | + | 0.999849i | \(0.494469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000i | 0.754434i | ||||||||
\(254\) | 1.67423 | + | 2.89986i | 0.105051 | + | 0.181953i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.0834 | + | 6.39898i | 0.691361 | + | 0.399157i | 0.804122 | − | 0.594465i | \(-0.202636\pi\) |
−0.112761 | + | 0.993622i | \(0.535969\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.55051 | + | 4.41761i | 0.158481 | + | 0.274497i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 3.79796i | − | 0.234639i | ||||||
\(263\) | −17.7098 | + | 10.2247i | −1.09203 | + | 0.630485i | −0.934117 | − | 0.356968i | \(-0.883811\pi\) |
−0.157915 | + | 0.987453i | \(0.550477\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.67423 | − | 2.89986i | 0.102654 | − | 0.177802i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.301783 | − | 0.174235i | 0.0184343 | − | 0.0106431i | ||||
\(269\) | 14.4495 | 0.881001 | 0.440500 | − | 0.897752i | \(-0.354801\pi\) | ||||
0.440500 | + | 0.897752i | \(0.354801\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3485 | 0.932353 | 0.466177 | − | 0.884692i | \(-0.345631\pi\) | ||||
0.466177 | + | 0.884692i | \(0.345631\pi\) | |||||||
\(272\) | 4.24264 | − | 2.44949i | 0.257248 | − | 0.148522i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.50000 | + | 2.59808i | −0.0906183 | + | 0.156956i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.34278 | − | 0.775255i | 0.0806799 | − | 0.0465806i | −0.459117 | − | 0.888376i | \(-0.651834\pi\) |
0.539797 | + | 0.841795i | \(0.318501\pi\) | |||||||
\(278\) | − | 4.00000i | − | 0.239904i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.55051 | + | 16.5420i | 0.569736 | + | 0.986811i | 0.996592 | + | 0.0824916i | \(0.0262878\pi\) |
−0.426856 | + | 0.904320i | \(0.640379\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.4726 | + | 6.62372i | 0.681977 | + | 0.393740i | 0.800599 | − | 0.599200i | \(-0.204515\pi\) |
−0.118623 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(284\) | −6.67423 | + | 11.5601i | −0.396043 | + | 0.685967i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.10102 | + | 1.90702i | 0.0651047 | + | 0.112765i | ||||
\(287\) | − | 4.04541i | − | 0.238793i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.866025 | − | 0.500000i | −0.0506803 | − | 0.0292603i | ||||
\(293\) | 13.8957 | + | 8.02270i | 0.811797 | + | 0.468691i | 0.847580 | − | 0.530668i | \(-0.178059\pi\) |
−0.0357824 | + | 0.999360i | \(0.511392\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.3485 | −0.659616 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | −0.550510 | − | 0.953512i | −0.0318368 | − | 0.0551430i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.573214 | − | 0.992836i | 0.0330395 | − | 0.0572261i | ||||
\(302\) | 17.3205 | + | 10.0000i | 0.996683 | + | 0.575435i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.72474 | + | 6.45145i | 0.213629 | + | 0.370016i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.6969i | − | 1.29538i | −0.761903 | − | 0.647691i | \(-0.775735\pi\) | ||
0.761903 | − | 0.647691i | \(-0.224265\pi\) | |||||||
\(308\) | −1.90702 | + | 1.10102i | −0.108663 | + | 0.0627365i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.550510 | + | 0.953512i | −0.0312166 | + | 0.0540687i | −0.881212 | − | 0.472722i | \(-0.843271\pi\) |
0.849995 | + | 0.526791i | \(0.176605\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.10867 | + | 2.94949i | −0.288759 | + | 0.166715i | −0.637382 | − | 0.770548i | \(-0.719983\pi\) |
0.348623 | + | 0.937263i | \(0.386649\pi\) | |||||||
\(314\) | 19.7980 | 1.11726 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.6969 | 0.939276 | ||||||||
\(317\) | 14.8492 | − | 8.57321i | 0.834017 | − | 0.481520i | −0.0212094 | − | 0.999775i | \(-0.506752\pi\) |
0.855226 | + | 0.518255i | \(0.173418\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | − | 10.3923i | 0.335936 | − | 0.581857i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.953512 | − | 0.550510i | 0.0531371 | − | 0.0306787i | ||||
\(323\) | − | 36.4949i | − | 2.03063i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.72474 | − | 6.45145i | −0.206295 | − | 0.357313i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.79423 | + | 4.50000i | 0.430364 | + | 0.248471i | ||||
\(329\) | −2.44949 | + | 4.24264i | −0.135045 | + | 0.233904i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.17423 | − | 5.49794i | −0.174472 | − | 0.302194i | 0.765507 | − | 0.643428i | \(-0.222488\pi\) |
−0.939978 | + | 0.341234i | \(0.889155\pi\) | |||||||
\(332\) | − | 5.44949i | − | 0.299080i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.5959 | 1.07224 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.0990 | − | 10.4495i | −0.985918 | − | 0.569220i | −0.0818663 | − | 0.996643i | \(-0.526088\pi\) |
−0.904052 | + | 0.427423i | \(0.859421\pi\) | |||||||
\(338\) | 11.0834 | + | 6.39898i | 0.602855 | + | 0.348059i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.7980 | 1.18043 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.20204i | 0.334879i | ||||||||
\(344\) | 1.27526 | + | 2.20881i | 0.0687571 | + | 0.119091i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.89898 | − | 8.48528i | 0.263371 | − | 0.456172i | ||||
\(347\) | −10.3923 | − | 6.00000i | −0.557888 | − | 0.322097i | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.00000 | + | 12.1244i | 0.374701 | + | 0.649002i | 0.990282 | − | 0.139072i | \(-0.0444119\pi\) |
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 4.89898i | − | 0.261116i | ||||||
\(353\) | 7.79423 | − | 4.50000i | 0.414845 | − | 0.239511i | −0.278024 | − | 0.960574i | \(-0.589680\pi\) |
0.692869 | + | 0.721063i | \(0.256346\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.50000 | + | 7.79423i | −0.238500 | + | 0.413093i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.00853 | + | 4.62372i | −0.423264 | + | 0.244371i | ||||
\(359\) | −14.2020 | −0.749555 | −0.374778 | − | 0.927115i | \(-0.622281\pi\) | ||||
−0.374778 | + | 0.927115i | \(0.622281\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.4949 | 1.92078 | ||||||||
\(362\) | −15.4135 | + | 8.89898i | −0.810115 | + | 0.467720i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.101021 | − | 0.174973i | 0.00529491 | − | 0.00917106i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9959 | − | 6.34847i | 0.573980 | − | 0.331387i | −0.184757 | − | 0.982784i | \(-0.559150\pi\) |
0.758737 | + | 0.651397i | \(0.225817\pi\) | |||||||
\(368\) | 2.44949i | 0.127688i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.797959 | + | 1.38211i | 0.0414280 | + | 0.0717553i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.4347 | + | 11.7980i | 1.05807 | + | 0.610875i | 0.924897 | − | 0.380218i | \(-0.124151\pi\) |
0.133170 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(374\) | −12.0000 | + | 20.7846i | −0.620505 | + | 1.07475i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.44949 | − | 9.43879i | −0.281036 | − | 0.486769i | ||||
\(377\) | 1.10102i | 0.0567054i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.89898 | 0.457110 | 0.228555 | − | 0.973531i | \(-0.426600\pi\) | ||||
0.228555 | + | 0.973531i | \(0.426600\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.953512 | + | 0.550510i | 0.0487859 | + | 0.0281666i | ||||
\(383\) | 18.6633 | + | 10.7753i | 0.953650 | + | 0.550590i | 0.894213 | − | 0.447642i | \(-0.147736\pi\) |
0.0594368 | + | 0.998232i | \(0.481070\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.0000 | 1.01797 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.79796i | 0.446649i | ||||||||
\(389\) | −12.7980 | − | 22.1667i | −0.648882 | − | 1.12390i | −0.983390 | − | 0.181504i | \(-0.941903\pi\) |
0.334508 | − | 0.942393i | \(-0.391430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.00000 | − | 10.3923i | 0.303433 | − | 0.525561i | ||||
\(392\) | −5.88721 | − | 3.39898i | −0.297349 | − | 0.171674i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.123724 | + | 0.214297i | 0.00623314 | + | 0.0107961i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.5959i | 0.883114i | 0.897233 | + | 0.441557i | \(0.145574\pi\) | ||||
−0.897233 | + | 0.441557i | \(0.854426\pi\) | |||||||
\(398\) | −11.9494 | + | 6.89898i | −0.598968 | + | 0.345815i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.3485 | − | 33.5125i | 0.966216 | − | 1.67354i | 0.259906 | − | 0.965634i | \(-0.416308\pi\) |
0.706311 | − | 0.707902i | \(-0.250358\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.73205 | + | 1.00000i | −0.0862796 | + | 0.0498135i | ||||
\(404\) | 8.44949 | 0.420378 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.10102 | −0.0546427 | ||||||||
\(407\) | 48.1475 | − | 27.7980i | 2.38658 | − | 1.37789i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0505103 | − | 0.0874863i | 0.00249757 | − | 0.00432592i | −0.864774 | − | 0.502161i | \(-0.832538\pi\) |
0.867271 | + | 0.497835i | \(0.165872\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.4600 | + | 8.34847i | −0.712392 | + | 0.411300i | ||||
\(413\) | − | 2.44949i | − | 0.120532i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.224745 | + | 0.389270i | 0.0110190 | + | 0.0190855i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −31.6055 | − | 18.2474i | −1.54588 | − | 0.892512i | ||||
\(419\) | 13.0732 | − | 22.6435i | 0.638668 | − | 1.10621i | −0.347057 | − | 0.937844i | \(-0.612819\pi\) |
0.985725 | − | 0.168362i | \(-0.0538477\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0227 | + | 22.5560i | 0.634688 | + | 1.09931i | 0.986581 | + | 0.163271i | \(0.0522046\pi\) |
−0.351893 | + | 0.936040i | \(0.614462\pi\) | |||||||
\(422\) | 3.44949i | 0.167919i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.55051 | −0.172428 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.11416 | − | 1.79796i | −0.150705 | − | 0.0870093i | ||||
\(428\) | 8.00853 | + | 4.62372i | 0.387107 | + | 0.223496i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.3485 | −1.22099 | −0.610496 | − | 0.792019i | \(-0.709030\pi\) | ||||
−0.610496 | + | 0.792019i | \(0.709030\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.59592i | 0.461150i | 0.973055 | + | 0.230575i | \(0.0740608\pi\) | ||||
−0.973055 | + | 0.230575i | \(0.925939\pi\) | |||||||
\(434\) | −1.00000 | − | 1.73205i | −0.0480015 | − | 0.0831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.77526 | + | 4.80688i | −0.132911 | + | 0.230208i | ||||
\(437\) | 15.8028 | + | 9.12372i | 0.755948 | + | 0.436447i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.67423 | + | 2.89986i | 0.0799069 | + | 0.138403i | 0.903210 | − | 0.429200i | \(-0.141204\pi\) |
−0.823303 | + | 0.567603i | \(0.807871\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.20204i | − | 0.104740i | ||||||
\(443\) | −7.10318 | + | 4.10102i | −0.337482 | + | 0.194845i | −0.659158 | − | 0.752004i | \(-0.729087\pi\) |
0.321676 | + | 0.946850i | \(0.395754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.89898 | + | 15.4135i | −0.421379 | + | 0.729850i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.389270 | + | 0.224745i | −0.0183913 | + | 0.0106182i | ||||
\(449\) | −28.5959 | −1.34952 | −0.674762 | − | 0.738035i | \(-0.735754\pi\) | ||||
−0.674762 | + | 0.738035i | \(0.735754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.0908 | −2.07616 | ||||||||
\(452\) | −3.55159 | + | 2.05051i | −0.167053 | + | 0.0964479i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.82577 | + | 11.8226i | −0.320349 | + | 0.554861i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.8619 | + | 6.84847i | −0.554876 | + | 0.320358i | −0.751086 | − | 0.660204i | \(-0.770470\pi\) |
0.196210 | + | 0.980562i | \(0.437136\pi\) | |||||||
\(458\) | 13.1464i | 0.614292i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.32577 | + | 4.02834i | 0.108322 | + | 0.187619i | 0.915090 | − | 0.403249i | \(-0.132119\pi\) |
−0.806769 | + | 0.590867i | \(0.798786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.63191 | + | 2.67423i | 0.215263 | + | 0.124282i | 0.603755 | − | 0.797170i | \(-0.293671\pi\) |
−0.388492 | + | 0.921452i | \(0.627004\pi\) | |||||||
\(464\) | 1.22474 | − | 2.12132i | 0.0568574 | − | 0.0984798i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.8485 | − | 20.5222i | −0.548870 | − | 0.950670i | ||||
\(467\) | − | 10.3485i | − | 0.478870i | −0.970912 | − | 0.239435i | \(-0.923038\pi\) | ||
0.970912 | − | 0.239435i | \(-0.0769622\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.156633 | 0.00723266 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.71940 | + | 2.72474i | 0.217228 | + | 0.125417i | ||||
\(473\) | −10.8209 | − | 6.24745i | −0.497545 | − | 0.287258i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.20204 | 0.100930 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 14.4495i | − | 0.660904i | ||||||
\(479\) | −0.123724 | − | 0.214297i | −0.00565311 | − | 0.00979147i | 0.863185 | − | 0.504888i | \(-0.168466\pi\) |
−0.868838 | + | 0.495096i | \(0.835133\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.55051 | + | 4.41761i | −0.116293 | + | 0.201426i | ||||
\(482\) | −2.77305 | − | 1.60102i | −0.126309 | − | 0.0729245i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.50000 | + | 11.2583i | 0.295455 | + | 0.511742i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.4495i | 1.10791i | 0.832546 | + | 0.553956i | \(0.186882\pi\) | ||||
−0.832546 | + | 0.553956i | \(0.813118\pi\) | |||||||
\(488\) | 6.92820 | − | 4.00000i | 0.313625 | − | 0.181071i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.6237 | + | 23.5970i | −0.614830 | + | 1.06492i | 0.375584 | + | 0.926788i | \(0.377442\pi\) |
−0.990414 | + | 0.138129i | \(0.955891\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3923 | + | 6.00000i | −0.468046 | + | 0.270226i | ||||
\(494\) | 3.34847 | 0.150655 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.44949 | 0.199788 | ||||||||
\(497\) | −5.19615 | + | 3.00000i | −0.233079 | + | 0.134568i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.17423 | + | 7.22999i | −0.186864 | + | 0.323659i | −0.944203 | − | 0.329364i | \(-0.893166\pi\) |
0.757339 | + | 0.653022i | \(0.226499\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.476756 | + | 0.275255i | −0.0212787 | + | 0.0122852i | ||||
\(503\) | − | 21.5505i | − | 0.960890i | −0.877025 | − | 0.480445i | \(-0.840475\pi\) | ||
0.877025 | − | 0.480445i | \(-0.159525\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.00000 | − | 10.3923i | −0.266733 | − | 0.461994i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.89986 | − | 1.67423i | −0.128660 | − | 0.0742821i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.224745 | − | 0.389270i | −0.00994213 | − | 0.0172203i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12.7980 | −0.564494 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 46.2405 | + | 26.6969i | 2.03365 | + | 1.17413i | ||||
\(518\) | −4.41761 | − | 2.55051i | −0.194099 | − | 0.112063i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.3939 | 1.28777 | 0.643885 | − | 0.765123i | \(-0.277322\pi\) | ||||
0.643885 | + | 0.765123i | \(0.277322\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.3485i | − | 0.889776i | −0.895586 | − | 0.444888i | \(-0.853243\pi\) | ||
0.895586 | − | 0.444888i | \(-0.146757\pi\) | |||||||
\(524\) | 1.89898 | + | 3.28913i | 0.0829573 | + | 0.143686i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.2247 | − | 17.7098i | 0.445820 | − | 0.772183i | ||||
\(527\) | −18.8776 | − | 10.8990i | −0.822321 | − | 0.474767i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.50000 | − | 14.7224i | −0.369565 | − | 0.640106i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.34847i | 0.145175i | ||||||||
\(533\) | 3.50343 | − | 2.02270i | 0.151750 | − | 0.0876130i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.174235 | + | 0.301783i | −0.00752579 | + | 0.0130350i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.5136 | + | 7.22474i | −0.539501 | + | 0.311481i | ||||
\(539\) | 33.3031 | 1.43446 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.7980 | −1.62506 | −0.812531 | − | 0.582919i | \(-0.801911\pi\) | ||||
−0.812531 | + | 0.582919i | \(0.801911\pi\) | |||||||
\(542\) | −13.2922 | + | 7.67423i | −0.570947 | + | 0.329637i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.44949 | + | 4.24264i | −0.105021 | + | 0.181902i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.5546 | + | 7.82577i | −0.579554 | + | 0.334606i | −0.760956 | − | 0.648803i | \(-0.775270\pi\) |
0.181402 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(548\) | − | 3.00000i | − | 0.128154i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.12372 | − | 15.8028i | −0.388684 | − | 0.673220i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.49961 | + | 3.75255i | 0.276392 | + | 0.159575i | ||||
\(554\) | −0.775255 | + | 1.34278i | −0.0329374 | + | 0.0570493i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 41.3939i | 1.75391i | 0.480568 | + | 0.876957i | \(0.340430\pi\) | ||||
−0.480568 | + | 0.876957i | \(0.659570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.14643 | 0.0484887 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.5420 | − | 9.55051i | −0.697781 | − | 0.402864i | ||||
\(563\) | −20.7364 | − | 11.9722i | −0.873937 | − | 0.504568i | −0.00528250 | − | 0.999986i | \(-0.501681\pi\) |
−0.868655 | + | 0.495418i | \(0.835015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.2474 | −0.556832 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 13.3485i | − | 0.560089i | ||||||
\(569\) | −16.8990 | − | 29.2699i | −0.708442 | − | 1.22706i | −0.965435 | − | 0.260644i | \(-0.916065\pi\) |
0.256993 | − | 0.966413i | \(-0.417268\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9722 | + | 22.4685i | −0.542869 | + | 0.940277i | 0.455868 | + | 0.890047i | \(0.349329\pi\) |
−0.998738 | + | 0.0502301i | \(0.984005\pi\) | |||||||
\(572\) | −1.90702 | − | 1.10102i | −0.0797367 | − | 0.0460360i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.02270 | + | 3.50343i | 0.0844260 | + | 0.146230i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 40.3939i | − | 1.68162i | −0.541331 | − | 0.840810i | \(-0.682079\pi\) | ||
0.541331 | − | 0.840810i | \(-0.317921\pi\) | |||||||
\(578\) | 6.06218 | − | 3.50000i | 0.252153 | − | 0.145581i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.22474 | − | 2.12132i | 0.0508110 | − | 0.0880072i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0635 | − | 8.69694i | 0.623868 | − | 0.360190i | ||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.0454 | −0.662830 | ||||||||
\(587\) | −23.1202 | + | 13.3485i | −0.954274 | + | 0.550950i | −0.894406 | − | 0.447256i | \(-0.852401\pi\) |
−0.0598679 | + | 0.998206i | \(0.519068\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5732 | − | 28.7056i | 0.682887 | − | 1.18280i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.82806 | − | 5.67423i | 0.403931 | − | 0.233210i | ||||
\(593\) | 7.89898i | 0.324372i | 0.986760 | + | 0.162186i | \(0.0518545\pi\) | ||||
−0.986760 | + | 0.162186i | \(0.948146\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.953512 | + | 0.550510i | 0.0389920 | + | 0.0225120i | ||||
\(599\) | 11.3258 | − | 19.6168i | 0.462758 | − | 0.801521i | −0.536339 | − | 0.844003i | \(-0.680193\pi\) |
0.999097 | + | 0.0424819i | \(0.0135265\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.24745 | + | 14.2850i | 0.336420 | + | 0.582697i | 0.983757 | − | 0.179507i | \(-0.0574503\pi\) |
−0.647336 | + | 0.762205i | \(0.724117\pi\) | |||||||
\(602\) | 1.14643i | 0.0467249i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.0000 | −0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.89986 | + | 1.67423i | 0.117702 | + | 0.0679551i | 0.557695 | − | 0.830046i | \(-0.311686\pi\) |
−0.439993 | + | 0.898001i | \(0.645019\pi\) | |||||||
\(608\) | −6.45145 | − | 3.72474i | −0.261641 | − | 0.151058i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.89898 | −0.198191 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0454i | 0.486509i | 0.969962 | + | 0.243255i | \(0.0782151\pi\) | ||||
−0.969962 | + | 0.243255i | \(0.921785\pi\) | |||||||
\(614\) | 11.3485 | + | 19.6561i | 0.457987 | + | 0.793257i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.10102 | − | 1.90702i | 0.0443614 | − | 0.0768362i | ||||
\(617\) | −38.4462 | − | 22.1969i | −1.54779 | − | 0.893615i | −0.998310 | − | 0.0581058i | \(-0.981494\pi\) |
−0.549476 | − | 0.835509i | \(-0.685173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.8712 | − | 27.4897i | −0.637916 | − | 1.10490i | −0.985889 | − | 0.167399i | \(-0.946463\pi\) |
0.347973 | − | 0.937505i | \(-0.386870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.10102i | − | 0.0441469i | ||||||
\(623\) | −3.50343 | + | 2.02270i | −0.140362 | + | 0.0810379i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.94949 | − | 5.10867i | 0.117885 | − | 0.204183i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.1455 | + | 9.89898i | −0.684181 | + | 0.395012i | ||||
\(629\) | −55.5959 | −2.21675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.20204 | −0.246899 | −0.123450 | − | 0.992351i | \(-0.539396\pi\) | ||||
−0.123450 | + | 0.992351i | \(0.539396\pi\) | |||||||
\(632\) | −14.4600 | + | 8.34847i | −0.575187 | + | 0.332084i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.57321 | + | 14.8492i | −0.340486 | + | 0.589739i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.64624 | + | 1.52781i | −0.104848 | + | 0.0605339i | ||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.19694 | − | 12.4655i | −0.284262 | − | 0.492356i | 0.688168 | − | 0.725551i | \(-0.258415\pi\) |
−0.972430 | + | 0.233195i | \(0.925082\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2867 | + | 8.82577i | 0.602848 | + | 0.348054i | 0.770161 | − | 0.637850i | \(-0.220176\pi\) |
−0.167313 | + | 0.985904i | \(0.553509\pi\) | |||||||
\(644\) | −0.550510 | + | 0.953512i | −0.0216931 | + | 0.0375736i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.2474 | + | 31.6055i | 0.717936 | + | 1.24350i | ||||
\(647\) | 24.2474i | 0.953266i | 0.879102 | + | 0.476633i | \(0.158143\pi\) | ||||
−0.879102 | + | 0.476633i | \(0.841857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26.6969 | −1.04795 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.45145 | + | 3.72474i | 0.252658 | + | 0.145872i | ||||
\(653\) | 15.8028 | + | 9.12372i | 0.618410 | + | 0.357039i | 0.776250 | − | 0.630426i | \(-0.217120\pi\) |
−0.157840 | + | 0.987465i | \(0.550453\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.00000 | −0.351391 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 4.89898i | − | 0.190982i | ||||||
\(659\) | −4.92679 | − | 8.53344i | −0.191920 | − | 0.332416i | 0.753966 | − | 0.656913i | \(-0.228138\pi\) |
−0.945887 | + | 0.324497i | \(0.894805\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.69694 | + | 6.40329i | −0.143794 | + | 0.249059i | −0.928922 | − | 0.370274i | \(-0.879264\pi\) |
0.785128 | + | 0.619333i | \(0.212597\pi\) | |||||||
\(662\) | 5.49794 | + | 3.17423i | 0.213683 | + | 0.123370i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.72474 | + | 4.71940i | 0.105741 | + | 0.183148i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 6.00000i | − | 0.232321i | ||||||
\(668\) | −16.9706 | + | 9.79796i | −0.656611 | + | 0.379094i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5959 | + | 33.9411i | −0.756492 | + | 1.31028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6561 | − | 11.3485i | 0.757688 | − | 0.437451i | −0.0707771 | − | 0.997492i | \(-0.522548\pi\) |
0.828465 | + | 0.560041i | \(0.189215\pi\) | |||||||
\(674\) | 20.8990 | 0.804999 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.7980 | −0.492229 | ||||||||
\(677\) | −22.3810 | + | 12.9217i | −0.860172 | + | 0.496621i | −0.864070 | − | 0.503372i | \(-0.832093\pi\) |
0.00389777 | + | 0.999992i | \(0.498759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.97730 | + | 3.42478i | −0.0758817 | + | 0.131431i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18.8776 | + | 10.8990i | −0.722860 | + | 0.417343i | ||||
\(683\) | − | 41.9444i | − | 1.60496i | −0.596681 | − | 0.802479i | \(-0.703514\pi\) | ||
0.596681 | − | 0.802479i | \(-0.296486\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.10102 | − | 5.37113i | −0.118398 | − | 0.205071i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.20881 | − | 1.27526i | −0.0842100 | − | 0.0486186i | ||||
\(689\) | −0.797959 | + | 1.38211i | −0.0303998 | + | 0.0526540i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.5227 | − | 33.8143i | −0.742679 | − | 1.28636i | −0.951271 | − | 0.308355i | \(-0.900222\pi\) |
0.208593 | − | 0.978003i | \(-0.433112\pi\) | |||||||
\(692\) | 9.79796i | 0.372463i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.1838 | + | 22.0454i | 1.44631 | + | 0.835029i | ||||
\(698\) | −12.1244 | − | 7.00000i | −0.458914 | − | 0.264954i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −33.7980 | −1.27653 | −0.638266 | − | 0.769816i | \(-0.720348\pi\) | ||||
−0.638266 | + | 0.769816i | \(0.720348\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 84.5403i | − | 3.18850i | ||||||
\(704\) | 2.44949 | + | 4.24264i | 0.0923186 | + | 0.159901i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.50000 | + | 7.79423i | −0.169360 | + | 0.293340i | ||||
\(707\) | 3.28913 | + | 1.89898i | 0.123700 | + | 0.0714185i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.22474 | + | 3.85337i | 0.0835520 | + | 0.144716i | 0.904773 | − | 0.425894i | \(-0.140040\pi\) |
−0.821221 | + | 0.570610i | \(0.806707\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 9.00000i | − | 0.337289i | ||||||
\(713\) | 9.43879 | − | 5.44949i | 0.353486 | − | 0.204085i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.62372 | − | 8.00853i | 0.172797 | − | 0.299293i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.2993 | − | 7.10102i | 0.459007 | − | 0.265008i | ||||
\(719\) | 7.95459 | 0.296656 | 0.148328 | − | 0.988938i | \(-0.452611\pi\) | ||||
0.148328 | + | 0.988938i | \(0.452611\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.50510 | −0.279505 | ||||||||
\(722\) | −31.6055 | + | 18.2474i | −1.17624 | + | 0.679100i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.89898 | − | 15.4135i | 0.330728 | − | 0.572838i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.8564 | − | 8.00000i | 0.513906 | − | 0.296704i | −0.220532 | − | 0.975380i | \(-0.570779\pi\) |
0.734438 | + | 0.678676i | \(0.237446\pi\) | |||||||
\(728\) | 0.202041i | 0.00748814i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.24745 | + | 10.8209i | 0.231070 | + | 0.400225i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.5167 | − | 13.0000i | −0.831672 | − | 0.480166i | 0.0227529 | − | 0.999741i | \(-0.492757\pi\) |
−0.854425 | + | 0.519575i | \(0.826090\pi\) | |||||||
\(734\) | −6.34847 | + | 10.9959i | −0.234326 | + | 0.405865i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.22474 | − | 2.12132i | −0.0451447 | − | 0.0781929i | ||||
\(737\) | − | 1.70714i | − | 0.0628834i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.04541 | −0.112027 | −0.0560136 | − | 0.998430i | \(-0.517839\pi\) | ||||
−0.0560136 | + | 0.998430i | \(0.517839\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.38211 | − | 0.797959i | −0.0507387 | − | 0.0292940i | ||||
\(743\) | 42.7370 | + | 24.6742i | 1.56787 | + | 0.905210i | 0.996417 | + | 0.0845746i | \(0.0269531\pi\) |
0.571452 | + | 0.820635i | \(0.306380\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.5959 | −0.863908 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 24.0000i | − | 0.877527i | ||||||
\(749\) | 2.07832 | + | 3.59975i | 0.0759400 | + | 0.131532i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.97730 | − | 5.15683i | 0.108643 | − | 0.188175i | −0.806578 | − | 0.591128i | \(-0.798683\pi\) |
0.915221 | + | 0.402953i | \(0.132016\pi\) | |||||||
\(752\) | 9.43879 | + | 5.44949i | 0.344197 | + | 0.198722i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.550510 | − | 0.953512i | −0.0200484 | − | 0.0347248i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.0454i | 1.38278i | 0.722480 | + | 0.691392i | \(0.243002\pi\) | ||||
−0.722480 | + | 0.691392i | \(0.756998\pi\) | |||||||
\(758\) | −7.70674 | + | 4.44949i | −0.279921 | + | 0.161613i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.94949 | − | 12.0369i | 0.251919 | − | 0.436336i | −0.712135 | − | 0.702042i | \(-0.752272\pi\) |
0.964054 | + | 0.265706i | \(0.0856051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.16064 | + | 1.24745i | −0.0782206 | + | 0.0451607i | ||||
\(764\) | −1.10102 | −0.0398335 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.5505 | −0.778652 | ||||||||
\(767\) | 2.12132 | − | 1.22474i | 0.0765964 | − | 0.0442230i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.0959 | + | 24.4148i | −0.508312 | + | 0.880422i | 0.491642 | + | 0.870797i | \(0.336397\pi\) |
−0.999954 | + | 0.00962438i | \(0.996936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.3205 | + | 10.0000i | −0.623379 | + | 0.359908i | ||||
\(773\) | 10.4041i | 0.374209i | 0.982340 | + | 0.187104i | \(0.0599103\pi\) | ||||
−0.982340 | + | 0.187104i | \(0.940090\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.39898 | − | 7.61926i | −0.157914 | − | 0.273515i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 22.1667 | + | 12.7980i | 0.794715 | + | 0.458829i | ||||
\(779\) | −33.5227 | + | 58.0630i | −1.20108 | + | 2.08032i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.6969 | + | 56.6328i | 1.16999 | + | 2.02648i | ||||
\(782\) | 12.0000i | 0.429119i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.79796 | 0.242784 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.0484 | + | 17.3485i | 1.07111 | + | 0.618406i | 0.928485 | − | 0.371370i | \(-0.121112\pi\) |
0.142626 | + | 0.989777i | \(0.454445\pi\) | |||||||
\(788\) | −0.214297 | − | 0.123724i | −0.00763401 | − | 0.00440750i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.84337 | −0.0655426 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.59592i | − | 0.127695i | ||||||
\(794\) | −8.79796 | − | 15.2385i | −0.312228 | − | 0.540795i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.89898 | − | 11.9494i | 0.244528 | − | 0.423535i | ||||
\(797\) | 26.1951 | + | 15.1237i | 0.927877 | + | 0.535710i | 0.886139 | − | 0.463419i | \(-0.153377\pi\) |
0.0417372 | + | 0.999129i | \(0.486711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26.6969 | − | 46.2405i | −0.944470 | − | 1.63587i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38.6969i | 1.36644i | ||||||||
\(803\) | −4.24264 | + | 2.44949i | −0.149720 | + | 0.0864406i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.00000 | − | 1.73205i | 0.0352235 | − | 0.0610089i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.31747 | + | 4.22474i | −0.257428 | + | 0.148626i | ||||
\(809\) | −6.30306 | −0.221604 | −0.110802 | − | 0.993843i | \(-0.535342\pi\) | ||||
−0.110802 | + | 0.993843i | \(0.535342\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.5505 | −1.00254 | −0.501272 | − | 0.865290i | \(-0.667134\pi\) | ||||
−0.501272 | + | 0.865290i | \(0.667134\pi\) | |||||||
\(812\) | 0.953512 | − | 0.550510i | 0.0334617 | − | 0.0193191i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.7980 | + | 48.1475i | −0.974318 | + | 1.68757i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.4545 | + | 9.50000i | −0.575669 | + | 0.332363i | ||||
\(818\) | 0.101021i | 0.00353210i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5959 | + | 23.5488i | 0.474501 | + | 0.821860i | 0.999574 | − | 0.0291978i | \(-0.00929526\pi\) |
−0.525073 | + | 0.851057i | \(0.675962\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.8099 | + | 8.55051i | 0.516241 | + | 0.298052i | 0.735395 | − | 0.677638i | \(-0.236996\pi\) |
−0.219154 | + | 0.975690i | \(0.570330\pi\) | |||||||
\(824\) | 8.34847 | − | 14.4600i | 0.290833 | − | 0.503737i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.22474 | + | 2.12132i | 0.0426143 | + | 0.0738102i | ||||
\(827\) | − | 35.9444i | − | 1.24991i | −0.780661 | − | 0.624954i | \(-0.785118\pi\) | ||
0.780661 | − | 0.624954i | \(-0.214882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.7423 | 1.62343 | 0.811714 | − | 0.584055i | \(-0.198535\pi\) | ||||
0.811714 | + | 0.584055i | \(0.198535\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.389270 | − | 0.224745i | −0.0134955 | − | 0.00779163i | ||||
\(833\) | −28.8413 | − | 16.6515i | −0.999292 | − | 0.576941i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 36.4949 | 1.26220 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.1464i | 0.903213i | ||||||||
\(839\) | −18.6742 | − | 32.3447i | −0.644706 | − | 1.11666i | −0.984369 | − | 0.176117i | \(-0.943646\pi\) |
0.339663 | − | 0.940547i | \(-0.389687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.5000 | − | 19.9186i | 0.396552 | − | 0.686848i | ||||
\(842\) | −22.5560 | − | 13.0227i | −0.777331 | − | 0.448792i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.72474 | − | 2.98735i | −0.0593682 | − | 0.102829i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.84337i | 0.200780i | ||||||||
\(848\) | 3.07483 | − | 1.77526i | 0.105590 | − | 0.0609625i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.8990 | − | 24.0737i | 0.476451 | − | 0.825237i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.8372 | + | 23.0000i | −1.36400 | + | 0.787505i | −0.990153 | − | 0.139986i | \(-0.955294\pi\) |
−0.373845 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(854\) | 3.59592 | 0.123050 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.24745 | −0.316071 | ||||||||
\(857\) | −43.2138 | + | 24.9495i | −1.47615 | + | 0.852258i | −0.999638 | − | 0.0269070i | \(-0.991434\pi\) |
−0.476517 | + | 0.879165i | \(0.658101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.1742 | + | 17.6223i | −0.347140 | + | 0.601265i | −0.985740 | − | 0.168274i | \(-0.946181\pi\) |
0.638600 | + | 0.769539i | \(0.279514\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.9524 | − | 12.6742i | 0.747702 | − | 0.431686i | ||||
\(863\) | 43.8434i | 1.49245i | 0.665696 | + | 0.746223i | \(0.268135\pi\) | ||||
−0.665696 | + | 0.746223i | \(0.731865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.79796 | − | 8.31031i | −0.163041 | − | 0.282396i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.73205 | + | 1.00000i | 0.0587896 | + | 0.0339422i | ||||
\(869\) | 40.8990 | − | 70.8391i | 1.38740 | − | 2.40305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0783167 | + | 0.135648i | 0.00265366 | + | 0.00459627i | ||||
\(872\) | − | 5.55051i | − | 0.187964i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.2474 | −0.617229 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.5378 | − | 15.8990i | −0.929887 | − | 0.536870i | −0.0431110 | − | 0.999070i | \(-0.513727\pi\) |
−0.886776 | + | 0.462200i | \(0.847060\pi\) | |||||||
\(878\) | −2.89986 | − | 1.67423i | −0.0978655 | − | 0.0565027i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.6969 | −1.30373 | −0.651866 | − | 0.758334i | \(-0.726014\pi\) | ||||
−0.651866 | + | 0.758334i | \(0.726014\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.7980i | 1.60853i | 0.594271 | + | 0.804265i | \(0.297441\pi\) | ||||
−0.594271 | + | 0.804265i | \(0.702559\pi\) | |||||||
\(884\) | 1.10102 | + | 1.90702i | 0.0370313 | + | 0.0641401i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.10102 | − | 7.10318i | 0.137776 | − | 0.238636i | ||||
\(887\) | −4.76756 | − | 2.75255i | −0.160079 | − | 0.0924216i | 0.417821 | − | 0.908530i | \(-0.362794\pi\) |
−0.577899 | + | 0.816108i | \(0.696127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.752551 | − | 1.30346i | −0.0252398 | − | 0.0437165i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 17.7980i | − | 0.595920i | ||||||
\(893\) | 70.3142 | − | 40.5959i | 2.35297 | − | 1.35849i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.224745 | − | 0.389270i | 0.00750820 | − | 0.0130046i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.7648 | − | 14.2980i | 0.826412 | − | 0.477129i | ||||
\(899\) | −10.8990 | −0.363501 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.3939 | −0.579474 | ||||||||
\(902\) | 38.1838 | − | 22.0454i | 1.27138 | − | 0.734032i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.05051 | − | 3.55159i | 0.0681990 | − | 0.118124i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.4787 | + | 18.1742i | −1.04523 | + | 0.603466i | −0.921311 | − | 0.388826i | \(-0.872881\pi\) |
−0.123922 | + | 0.992292i | \(0.539547\pi\) | |||||||
\(908\) | − | 13.6515i | − | 0.453042i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.67423 | − | 6.36396i | −0.121733 | − | 0.210847i | 0.798718 | − | 0.601705i | \(-0.205512\pi\) |
−0.920451 | + | 0.390858i | \(0.872178\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.1202 | − | 13.3485i | −0.765168 | − | 0.441770i | ||||
\(914\) | 6.84847 | − | 11.8619i | 0.226527 | − | 0.392357i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.57321 | − | 11.3851i | −0.217185 | − | 0.376176i | ||||
\(917\) | 1.70714i | 0.0563748i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.34847 | −0.110456 | −0.0552279 | − | 0.998474i | \(-0.517589\pi\) | ||||
−0.0552279 | + | 0.998474i | \(0.517589\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.02834 | − | 2.32577i | −0.132666 | − | 0.0765950i | ||||
\(923\) | −5.19615 | − | 3.00000i | −0.171033 | − | 0.0987462i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.34847 | −0.175762 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.44949i | 0.0804084i | ||||||||
\(929\) | 25.5959 | + | 44.3334i | 0.839775 | + | 1.45453i | 0.890083 | + | 0.455799i | \(0.150646\pi\) |
−0.0503079 | + | 0.998734i | \(0.516020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.3207 | − | 43.8567i | 0.829851 | − | 1.43734i | ||||
\(932\) | 20.5222 | + | 11.8485i | 0.672225 | + | 0.388110i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.17423 | + | 8.96204i | 0.169306 | + | 0.293247i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.20204i | − | 0.235280i | −0.993056 | − | 0.117640i | \(-0.962467\pi\) | ||
0.993056 | − | 0.117640i | \(-0.0375330\pi\) | |||||||
\(938\) | −0.135648 | + | 0.0783167i | −0.00442908 | + | 0.00255713i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.8207 | − | 46.4548i | 0.874329 | − | 1.51438i | 0.0168524 | − | 0.999858i | \(-0.494635\pi\) |
0.857476 | − | 0.514524i | \(-0.172031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.0919 | + | 11.0227i | −0.621717 | + | 0.358949i | ||||
\(944\) | −5.44949 | −0.177366 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.4949 | 0.406244 | ||||||||
\(947\) | 22.6435 | − | 13.0732i | 0.735814 | − | 0.424822i | −0.0847314 | − | 0.996404i | \(-0.527003\pi\) |
0.820545 | + | 0.571581i | \(0.193670\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.224745 | − | 0.389270i | 0.00729553 | − | 0.0126362i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.90702 | + | 1.10102i | −0.0618070 | + | 0.0356843i | ||||
\(953\) | − | 2.20204i | − | 0.0713311i | −0.999364 | − | 0.0356656i | \(-0.988645\pi\) | ||
0.999364 | − | 0.0356656i | \(-0.0113551\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.22474 | + | 12.5136i | 0.233665 | + | 0.404720i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.214297 | + | 0.123724i | 0.00692362 | + | 0.00399735i | ||||
\(959\) | 0.674235 | − | 1.16781i | 0.0217722 | − | 0.0377105i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.60102 | + | 9.70125i | 0.180678 | + | 0.312944i | ||||
\(962\) | − | 5.10102i | − | 0.164464i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.20204 | 0.103131 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.7128 | + | 16.0000i | 0.891184 | + | 0.514525i | 0.874330 | − | 0.485333i | \(-0.161301\pi\) |
0.0168544 | + | 0.999858i | \(0.494635\pi\) | |||||||
\(968\) | −11.2583 | − | 6.50000i | −0.361856 | − | 0.208918i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.8434 | 1.31073 | 0.655363 | − | 0.755314i | \(-0.272516\pi\) | ||||
0.655363 | + | 0.755314i | \(0.272516\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.79796i | 0.0576399i | ||||||||
\(974\) | −12.2247 | − | 21.1739i | −0.391706 | − | 0.678455i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | 7.79423 | + | 4.50000i | 0.249359 | + | 0.143968i | 0.619471 | − | 0.785020i | \(-0.287347\pi\) |
−0.370111 | + | 0.928987i | \(0.620681\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.0454 | + | 38.1838i | 0.704574 | + | 1.22036i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 27.2474i | − | 0.869501i | ||||||
\(983\) | 11.3458 | − | 6.55051i | 0.361875 | − | 0.208929i | −0.308028 | − | 0.951377i | \(-0.599669\pi\) |
0.669903 | + | 0.742449i | \(0.266336\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.00000 | − | 10.3923i | 0.191079 | − | 0.330958i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.89986 | + | 1.67423i | −0.0922568 | + | 0.0532645i | ||||
\(989\) | −6.24745 | −0.198657 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | −3.85337 | + | 2.22474i | −0.122345 | + | 0.0706357i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.00000 | − | 5.19615i | 0.0951542 | − | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.96753 | − | 4.02270i | 0.220664 | − | 0.127400i | −0.385594 | − | 0.922669i | \(-0.626003\pi\) |
0.606258 | + | 0.795268i | \(0.292670\pi\) | |||||||
\(998\) | − | 8.34847i | − | 0.264266i | ||||||
\(999\) | 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 | 1350.2.j.g.199.2 | 8 | ||
3.2 | odd | 2 | 450.2.j.f.49.4 | 8 | |||
5.2 | odd | 4 | 1350.2.e.k.901.2 | 4 | |||
5.3 | odd | 4 | 1350.2.e.n.901.1 | 4 | |||
5.4 | even | 2 | inner | 1350.2.j.g.199.3 | 8 | ||
9.2 | odd | 6 | 450.2.j.f.349.1 | 8 | |||
9.4 | even | 3 | 4050.2.c.w.649.2 | 4 | |||
9.5 | odd | 6 | 4050.2.c.y.649.4 | 4 | |||
9.7 | even | 3 | inner | 1350.2.j.g.1099.3 | 8 | ||
15.2 | even | 4 | 450.2.e.m.301.1 | yes | 4 | ||
15.8 | even | 4 | 450.2.e.l.301.2 | yes | 4 | ||
15.14 | odd | 2 | 450.2.j.f.49.1 | 8 | |||
45.2 | even | 12 | 450.2.e.m.151.2 | yes | 4 | ||
45.4 | even | 6 | 4050.2.c.w.649.3 | 4 | |||
45.7 | odd | 12 | 1350.2.e.k.451.2 | 4 | |||
45.13 | odd | 12 | 4050.2.a.bl.1.2 | 2 | |||
45.14 | odd | 6 | 4050.2.c.y.649.1 | 4 | |||
45.22 | odd | 12 | 4050.2.a.by.1.1 | 2 | |||
45.23 | even | 12 | 4050.2.a.bu.1.2 | 2 | |||
45.29 | odd | 6 | 450.2.j.f.349.4 | 8 | |||
45.32 | even | 12 | 4050.2.a.br.1.1 | 2 | |||
45.34 | even | 6 | inner | 1350.2.j.g.1099.2 | 8 | ||
45.38 | even | 12 | 450.2.e.l.151.1 | ✓ | 4 | ||
45.43 | odd | 12 | 1350.2.e.n.451.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.e.l.151.1 | ✓ | 4 | 45.38 | even | 12 | ||
450.2.e.l.301.2 | yes | 4 | 15.8 | even | 4 | ||
450.2.e.m.151.2 | yes | 4 | 45.2 | even | 12 | ||
450.2.e.m.301.1 | yes | 4 | 15.2 | even | 4 | ||
450.2.j.f.49.1 | 8 | 15.14 | odd | 2 | |||
450.2.j.f.49.4 | 8 | 3.2 | odd | 2 | |||
450.2.j.f.349.1 | 8 | 9.2 | odd | 6 | |||
450.2.j.f.349.4 | 8 | 45.29 | odd | 6 | |||
1350.2.e.k.451.2 | 4 | 45.7 | odd | 12 | |||
1350.2.e.k.901.2 | 4 | 5.2 | odd | 4 | |||
1350.2.e.n.451.1 | 4 | 45.43 | odd | 12 | |||
1350.2.e.n.901.1 | 4 | 5.3 | odd | 4 | |||
1350.2.j.g.199.2 | 8 | 1.1 | even | 1 | trivial | ||
1350.2.j.g.199.3 | 8 | 5.4 | even | 2 | inner | ||
1350.2.j.g.1099.2 | 8 | 45.34 | even | 6 | inner | ||
1350.2.j.g.1099.3 | 8 | 9.7 | even | 3 | inner | ||
4050.2.a.bl.1.2 | 2 | 45.13 | odd | 12 | |||
4050.2.a.br.1.1 | 2 | 45.32 | even | 12 | |||
4050.2.a.bu.1.2 | 2 | 45.23 | even | 12 | |||
4050.2.a.by.1.1 | 2 | 45.22 | odd | 12 | |||
4050.2.c.w.649.2 | 4 | 9.4 | even | 3 | |||
4050.2.c.w.649.3 | 4 | 45.4 | even | 6 | |||
4050.2.c.y.649.1 | 4 | 45.14 | odd | 6 | |||
4050.2.c.y.649.4 | 4 | 9.5 | odd | 6 |