Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.6879707136000000000000.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 11^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 215.1 | ||
Root | \(-1.83730 + 0.596975i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.215 |
Dual form | 363.2.f.g.233.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{9}{10}\right)\) |
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 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(3\) | −1.40126 | − | 1.01807i | −0.809017 | − | 0.587785i | ||||
\(4\) | 1.61803 | − | 1.17557i | 0.809017 | − | 0.587785i | ||||
\(5\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.79802 | − | 3.85115i | −1.05755 | − | 1.45560i | −0.882073 | − | 0.471114i | \(-0.843852\pi\) |
−0.175480 | − | 0.984483i | \(-0.556148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.927051 | + | 2.85317i | 0.309017 | + | 0.951057i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.46410 | −1.00000 | ||||||||
\(13\) | −3.31421 | + | 1.07685i | −0.919196 | + | 0.298665i | −0.730137 | − | 0.683301i | \(-0.760544\pi\) |
−0.189059 | + | 0.981966i | \(0.560544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.23607 | − | 3.80423i | 0.309017 | − | 0.951057i | ||||
\(17\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.749728 | + | 1.03191i | −0.171999 | + | 0.236737i | −0.886310 | − | 0.463091i | \(-0.846740\pi\) |
0.714311 | + | 0.699828i | \(0.246740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.24504i | 1.79922i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.04508 | − | 2.93893i | −0.809017 | − | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.60570 | − | 4.94183i | 0.309017 | − | 0.951057i | ||||
\(28\) | −9.05459 | − | 2.94201i | −1.71116 | − | 0.555988i | ||||
\(29\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.535233 | − | 1.64728i | −0.0961307 | − | 0.295860i | 0.891416 | − | 0.453186i | \(-0.149713\pi\) |
−0.987547 | + | 0.157326i | \(0.949713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.85410 | + | 3.52671i | 0.809017 | + | 0.587785i | ||||
\(37\) | 4.20378 | − | 3.05422i | 0.691096 | − | 0.502111i | −0.185924 | − | 0.982564i | \(-0.559528\pi\) |
0.877020 | + | 0.480453i | \(0.159528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.74038 | + | 1.86516i | 0.919196 | + | 0.298665i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 13.0053i | − | 1.98329i | −0.128984 | − | 0.991647i | \(-0.541172\pi\) | ||
0.128984 | − | 0.991647i | \(-0.458828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(48\) | −5.60503 | + | 4.07230i | −0.809017 | + | 0.587785i | ||||
\(49\) | −4.83928 | + | 14.8938i | −0.691326 | + | 2.12768i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.09659 | + | 5.63847i | −0.568095 | + | 0.781915i | ||||
\(53\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.10112 | − | 0.682697i | 0.278301 | − | 0.0904254i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1557 | + | 3.62471i | 1.42834 | + | 0.464097i | 0.918243 | − | 0.396018i | \(-0.129608\pi\) |
0.510100 | + | 0.860115i | \(0.329608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.39406 | − | 11.5534i | 1.05755 | − | 1.45560i | ||||
\(64\) | −2.47214 | − | 7.60845i | −0.309017 | − | 0.951057i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1244 | 1.48123 | 0.740613 | − | 0.671932i | \(-0.234535\pi\) | ||||
0.740613 | + | 0.671932i | \(0.234535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.34577 | + | 8.73420i | 0.742716 | + | 1.02226i | 0.998458 | + | 0.0555161i | \(0.0176804\pi\) |
−0.255741 | + | 0.966745i | \(0.582320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.67617 | + | 8.23639i | 0.309017 | + | 0.951057i | ||||
\(76\) | 2.55103i | 0.292623i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.8961 | − | 5.48987i | 1.90096 | − | 0.617659i | 0.939716 | − | 0.341956i | \(-0.111089\pi\) |
0.961243 | − | 0.275703i | \(-0.0889106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.28115 | + | 5.29007i | −0.809017 | + | 0.587785i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(84\) | 9.69263 | + | 13.3408i | 1.05755 | + | 1.45560i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.4203 | + | 9.75045i | 1.40683 | + | 1.02212i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.927051 | + | 2.85317i | −0.0961307 | + | 0.295860i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.54508 | − | 4.75528i | −0.156880 | − | 0.482826i | 0.841467 | − | 0.540309i | \(-0.181693\pi\) |
−0.998346 | + | 0.0574829i | \(0.981693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.66312 | + | 4.11450i | −0.558004 | + | 0.405413i | −0.830728 | − | 0.556679i | \(-0.812075\pi\) |
0.272724 | + | 0.962092i | \(0.412075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(108\) | −3.21140 | − | 9.88367i | −0.309017 | − | 0.951057i | ||||
\(109\) | − | 7.31130i | − | 0.700296i | −0.936694 | − | 0.350148i | \(-0.886131\pi\) | ||
0.936694 | − | 0.350148i | \(-0.113869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | −0.854242 | ||||||||
\(112\) | −18.1092 | + | 5.88403i | −1.71116 | + | 0.555988i | ||||
\(113\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.14488 | − | 8.45770i | −0.568095 | − | 0.781915i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.80252 | − | 2.03615i | −0.251673 | − | 0.182851i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4699 | − | 4.70156i | −1.28400 | − | 0.417196i | −0.414011 | − | 0.910272i | \(-0.635873\pi\) |
−0.869987 | + | 0.493075i | \(0.835873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.2404 | + | 18.2238i | −1.16575 | + | 1.60452i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07180 | 0.526492 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.548839 | + | 0.755412i | 0.0465519 | + | 0.0640732i | 0.831658 | − | 0.555288i | \(-0.187392\pi\) |
−0.785106 | + | 0.619361i | \(0.787392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.9441 | − | 15.9433i | 1.80992 | − | 1.31498i | ||||
\(148\) | 3.21140 | − | 9.88367i | 0.263975 | − | 0.812433i | ||||
\(149\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7409 | − | 16.1600i | 0.955463 | − | 1.31508i | 0.00640530 | − | 0.999979i | \(-0.497961\pi\) |
0.949058 | − | 0.315102i | \(-0.102039\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 11.4808 | − | 3.73032i | 0.919196 | − | 0.298665i | ||||
\(157\) | −18.2164 | − | 13.2350i | −1.45382 | − | 1.05626i | −0.984919 | − | 0.173016i | \(-0.944649\pi\) |
−0.468905 | − | 0.883249i | \(-0.655351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.25329 | + | 16.1680i | 0.411469 | + | 1.26637i | 0.915371 | + | 0.402611i | \(0.131897\pi\) |
−0.503902 | + | 0.863761i | \(0.668103\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.692847 | + | 0.503383i | −0.0532960 | + | 0.0387218i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.63925 | − | 1.18247i | −0.278301 | − | 0.0904254i | ||||
\(172\) | −15.2887 | − | 21.0431i | −1.16575 | − | 1.60452i | ||||
\(173\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 23.8014i | 1.79922i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.87132 | − | 18.0701i | 0.436412 | − | 1.34314i | −0.455221 | − | 0.890379i | \(-0.650440\pi\) |
0.891633 | − | 0.452759i | \(-0.149560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.9418 | − | 16.4365i | −0.882764 | − | 1.21502i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −23.5245 | + | 7.64358i | −1.71116 | + | 0.555988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(192\) | −4.28187 | + | 13.1782i | −0.309017 | + | 0.951057i | ||||
\(193\) | 25.9507 | + | 8.43189i | 1.86797 | + | 0.606941i | 0.992272 | + | 0.124083i | \(0.0395989\pi\) |
0.875699 | + | 0.482857i | \(0.160401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.67857 | + | 29.7876i | 0.691326 | + | 2.12768i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.9808 | −1.84173 | −0.920864 | − | 0.389885i | \(-0.872515\pi\) | ||||
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.9894 | − | 12.3435i | −1.19834 | − | 0.870643i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 13.9391i | 0.966500i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.72954 | + | 2.83640i | −0.600967 | + | 0.195266i | −0.593671 | − | 0.804708i | \(-0.702322\pi\) |
−0.00729508 | + | 0.999973i | \(0.502322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.84632 | + | 6.67038i | −0.328989 | + | 0.452815i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 18.6993i | − | 1.26358i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.6074 | + | 13.5191i | 1.24604 | + | 0.905303i | 0.997986 | − | 0.0634420i | \(-0.0202078\pi\) |
0.248058 | + | 0.968745i | \(0.420208\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.63525 | − | 14.2658i | 0.309017 | − | 0.951057i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(228\) | 2.59713 | − | 3.57465i | 0.171999 | − | 0.236737i | ||||
\(229\) | −6.42280 | − | 19.7673i | −0.424430 | − | 1.30626i | −0.903539 | − | 0.428507i | \(-0.859040\pi\) |
0.479108 | − | 0.877756i | \(-0.340960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.2649 | − | 9.50874i | −1.90096 | − | 0.617659i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.4954i | 1.89997i | 0.312301 | + | 0.949983i | \(0.398900\pi\) | ||||
−0.312301 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 1.00000 | ||||||||
\(244\) | 22.3114 | − | 7.24942i | 1.42834 | − | 0.464097i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.37354 | − | 4.22732i | 0.0873962 | − | 0.268978i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(252\) | − | 28.5617i | − | 1.79922i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.9443 | − | 9.40456i | −0.809017 | − | 0.587785i | ||||
\(257\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.5245 | − | 7.64358i | −1.46174 | − | 0.474949i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.6176 | − | 14.2530i | 1.19834 | − | 0.870643i | ||||
\(269\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.8364 | + | 25.9261i | 1.14423 | + | 1.57490i | 0.757673 | + | 0.652634i | \(0.226336\pi\) |
0.386558 | + | 0.922265i | \(0.373664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8.87869 | − | 27.3258i | −0.537363 | − | 1.65383i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.6938 | + | 4.12448i | −0.762699 | + | 0.247816i | −0.664437 | − | 0.747345i | \(-0.731328\pi\) |
−0.0982624 | + | 0.995161i | \(0.531328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.20378 | − | 3.05422i | 0.251673 | − | 0.182851i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5872 | + | 22.8304i | −0.986009 | + | 1.35713i | −0.0524806 | + | 0.998622i | \(0.516713\pi\) |
−0.933528 | + | 0.358503i | \(0.883287\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7533 | + | 9.99235i | 0.809017 | + | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.67617 | + | 8.23639i | −0.156880 | + | 0.482826i | ||||
\(292\) | 20.5353 | + | 6.67234i | 1.20174 | + | 0.390469i | ||||
\(293\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 14.0126 | + | 10.1807i | 0.809017 | + | 0.587785i | ||||
\(301\) | −50.0854 | + | 36.3892i | −2.88687 | + | 2.09744i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.99891 | + | 4.12765i | 0.171999 | + | 0.236737i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 34.2557i | − | 1.95508i | −0.210760 | − | 0.977538i | \(-0.567594\pi\) | ||
0.210760 | − | 0.977538i | \(-0.432406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.1244 | 0.689730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.56373 | + | 26.3565i | −0.484051 | + | 1.48975i | 0.349300 | + | 0.937011i | \(0.386419\pi\) |
−0.833351 | + | 0.552744i | \(0.813581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.8847 | − | 28.7453i | 1.17486 | − | 1.61705i | ||||
\(317\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −5.56231 | + | 17.1190i | −0.309017 | + | 0.951057i | ||||
\(325\) | 16.5710 | + | 5.38426i | 0.919196 | + | 0.298665i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.44345 | + | 10.2450i | −0.411624 | + | 0.566551i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.0000 | −1.70391 | −0.851957 | − | 0.523612i | \(-0.824584\pi\) | ||||
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.6113 | + | 9.16267i | 0.691096 | + | 0.502111i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 31.3660 | + | 10.1914i | 1.71116 | + | 0.555988i | ||||
\(337\) | 13.0395 | + | 17.9473i | 0.710306 | + | 0.977653i | 0.999790 | + | 0.0204700i | \(0.00651627\pi\) |
−0.289484 | + | 0.957183i | \(0.593484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.2075 | − | 12.7393i | 2.11701 | − | 0.687857i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.5379 | − | 24.1388i | 0.938780 | − | 1.29212i | −0.0175547 | − | 0.999846i | \(-0.505588\pi\) |
0.956335 | − | 0.292274i | \(-0.0944119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.1074i | 0.966500i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.36857 | + | 16.5228i | 0.282556 | + | 0.869619i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 33.1769 | 1.73894 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.23607 | − | 2.35114i | 0.168921 | − | 0.122729i | −0.500113 | − | 0.865960i | \(-0.666708\pi\) |
0.669034 | + | 0.743232i | \(0.266708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.85410 | + | 5.70634i | 0.0961307 | + | 0.295860i | ||||
\(373\) | − | 3.14299i | − | 0.162738i | −0.996684 | − | 0.0813690i | \(-0.974071\pi\) | ||
0.996684 | − | 0.0813690i | \(-0.0259292\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.47214 | − | 7.60845i | 0.126985 | − | 0.390820i | −0.867272 | − | 0.497834i | \(-0.834129\pi\) |
0.994258 | + | 0.107014i | \(0.0341289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.4896 | + | 21.3196i | 0.793554 | + | 1.09223i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 37.1064 | − | 12.0566i | 1.88622 | − | 0.612871i | ||||
\(388\) | −8.09017 | − | 5.87785i | −0.410716 | − | 0.298403i | ||||
\(389\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.0000 | 1.75660 | 0.878300 | − | 0.478110i | \(-0.158678\pi\) | ||||
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.50816 | − | 6.18154i | −0.425941 | − | 0.309464i | ||||
\(400\) | −16.1803 | + | 11.7557i | −0.809017 | + | 0.587785i | ||||
\(401\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.54775 | + | 4.88306i | 0.176726 | + | 0.243242i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.3195 | + | 12.4508i | −1.89478 | + | 0.615650i | −0.920273 | + | 0.391277i | \(0.872033\pi\) |
−0.974503 | + | 0.224373i | \(0.927967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.32624 | + | 13.3148i | −0.213138 | + | 0.655973i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.61729i | − | 0.0791988i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.0252 | + | 20.3615i | 1.36586 | + | 0.992358i | 0.998048 | + | 0.0624590i | \(0.0198943\pi\) |
0.367816 | + | 0.929899i | \(0.380106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.2546 | − | 53.1043i | −0.835010 | − | 2.56990i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(432\) | −16.8151 | − | 12.2169i | −0.809017 | − | 0.587785i | ||||
\(433\) | 29.9336 | − | 21.7481i | 1.43852 | − | 1.04514i | 0.450169 | − | 0.892943i | \(-0.351364\pi\) |
0.988350 | − | 0.152201i | \(-0.0486362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.59495 | − | 11.8299i | −0.411624 | − | 0.566551i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.8677i | − | 1.09141i | −0.837976 | − | 0.545707i | \(-0.816261\pi\) | ||
0.837976 | − | 0.545707i | \(-0.183739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.9808 | −2.23718 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(444\) | −14.5623 | + | 10.5801i | −0.691096 | + | 0.502111i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22.3842 | + | 30.8092i | −1.05755 | + | 1.45560i | ||||
\(449\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −32.9041 | + | 10.6912i | −1.54597 | + | 0.502317i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.6802 | − | 11.2683i | −1.62227 | − | 0.527108i | −0.649796 | − | 0.760109i | \(-0.725146\pi\) |
−0.972477 | + | 0.233001i | \(0.925146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(468\) | −19.8853 | − | 6.46111i | −0.919196 | − | 0.298665i | ||||
\(469\) | −33.9242 | − | 46.6927i | −1.56647 | − | 2.15607i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0517 | + | 37.0912i | 0.555311 | + | 1.70907i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.06542 | − | 1.97078i | 0.278301 | − | 0.0904254i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6432 | + | 14.6492i | −0.485290 | + | 0.667945i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.80252 | − | 2.03615i | −0.126994 | − | 0.0922667i | 0.522475 | − | 0.852655i | \(-0.325009\pi\) |
−0.649469 | + | 0.760388i | \(0.725009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.09896 | − | 28.0037i | 0.411469 | − | 1.26637i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.92820 | −0.311086 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.0315 | − | 25.4518i | 1.56822 | − | 1.13938i | 0.639391 | − | 0.768882i | \(-0.279187\pi\) |
0.928833 | − | 0.370499i | \(-0.120813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.48334 | 0.0658774 | ||||||||
\(508\) | −28.9398 | + | 9.40313i | −1.28400 | + | 0.417196i | ||||
\(509\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.8811 | − | 48.8770i | 0.702538 | − | 2.16219i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.89570 | + | 5.36197i | 0.171999 | + | 0.236737i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 45.0518i | 1.98329i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.4342 | − | 5.98964i | −0.806072 | − | 0.261909i | −0.123139 | − | 0.992389i | \(-0.539296\pi\) |
−0.682933 | + | 0.730481i | \(0.739296\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.2316 | − | 33.3519i | 1.05755 | − | 1.45560i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9.82437 | − | 7.13783i | 0.425941 | − | 0.309464i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.2757 | − | 8.53750i | 1.12968 | − | 0.367056i | 0.316227 | − | 0.948684i | \(-0.397584\pi\) |
0.813455 | + | 0.581628i | \(0.197584\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.6239 | + | 19.3434i | −1.14254 | + | 0.830105i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.54666 | + | 9.01070i | −0.279915 | + | 0.385270i | −0.925706 | − | 0.378245i | \(-0.876528\pi\) |
0.645791 | + | 0.763514i | \(0.276528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.1894i | 1.50185i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −68.4179 | − | 49.7085i | −2.90943 | − | 2.11382i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.77608 | + | 0.577083i | 0.0753225 | + | 0.0244738i | ||||
\(557\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.0048 | + | 43.1024i | 0.592340 | + | 1.82304i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 40.7456 | + | 13.2391i | 1.71116 | + | 0.555988i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.3577i | 1.64707i | 0.567265 | + | 0.823535i | \(0.308001\pi\) | ||||
−0.567265 | + | 0.823535i | \(0.691999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.4164 | − | 14.1068i | 0.809017 | − | 0.587785i | ||||
\(577\) | −14.4513 | + | 44.4765i | −0.601615 | + | 1.85158i | −0.0830461 | + | 0.996546i | \(0.526465\pi\) |
−0.518569 | + | 0.855036i | \(0.673535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.7793 | − | 38.2350i | −1.15447 | − | 1.58899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(588\) | 16.7638 | − | 51.5936i | 0.691326 | − | 2.12768i | ||||
\(589\) | 2.10112 | + | 0.682697i | 0.0865753 | + | 0.0281300i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.42280 | − | 19.7673i | −0.263975 | − | 0.812433i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.4058 | + | 26.4503i | 1.48999 | + | 1.08254i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.0856 | − | 29.0218i | −0.860100 | − | 1.18383i | −0.981546 | − | 0.191228i | \(-0.938753\pi\) |
0.121446 | − | 0.992598i | \(-0.461247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.2399 | + | 34.5928i | 0.457724 | + | 1.40873i | ||||
\(604\) | − | 39.9497i | − | 1.62553i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.7348 | + | 14.2103i | −1.77514 | + | 0.576778i | −0.998580 | − | 0.0532640i | \(-0.983038\pi\) |
−0.776561 | + | 0.630042i | \(0.783038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.70034 | − | 2.34032i | 0.0686763 | − | 0.0945248i | −0.773297 | − | 0.634044i | \(-0.781394\pi\) |
0.841973 | + | 0.539519i | \(0.181394\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.8885 | − | 18.8091i | −1.04055 | − | 0.756003i | −0.0701559 | − | 0.997536i | \(-0.522350\pi\) |
−0.970393 | + | 0.241533i | \(0.922350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 14.1910 | − | 19.5322i | 0.568095 | − | 0.781915i | ||||
\(625\) | 7.72542 | + | 23.7764i | 0.309017 | + | 0.951057i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −45.0333 | −1.79703 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.6176 | − | 14.2530i | 0.780965 | − | 0.567404i | −0.124303 | − | 0.992244i | \(-0.539670\pi\) |
0.905269 | + | 0.424840i | \(0.139670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.1200 | + | 4.91279i | 0.600967 | + | 0.195266i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 54.5723i | − | 2.16223i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5238 | + | 44.6997i | −0.572763 | + | 1.76278i | 0.0709114 | + | 0.997483i | \(0.477409\pi\) |
−0.643674 | + | 0.765300i | \(0.722591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.5819 | − | 4.41302i | 0.532316 | − | 0.172960i | ||||
\(652\) | 27.5066 | + | 19.9847i | 1.07724 | + | 0.782661i | ||||
\(653\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.0373 | + | 26.2026i | −0.742716 | + | 1.02226i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 50.2295 | 1.95370 | 0.976850 | − | 0.213925i | \(-0.0686249\pi\) | ||||
0.976850 | + | 0.213925i | \(0.0686249\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.3104 | − | 37.8874i | −0.475946 | − | 1.46481i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.5217 | − | 13.8161i | 1.63909 | − | 0.532573i | 0.662757 | − | 0.748835i | \(-0.269386\pi\) |
0.976335 | + | 0.216262i | \(0.0693864\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.0189 | + | 15.2711i | −0.809017 | + | 0.587785i | ||||
\(676\) | −0.529288 | + | 1.62898i | −0.0203572 | + | 0.0626531i | ||||
\(677\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.9901 | + | 19.2557i | −0.536891 | + | 0.738967i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −7.27851 | + | 2.36493i | −0.278301 | + | 0.0904254i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.1246 | + | 34.2380i | −0.424430 | + | 1.30626i | ||||
\(688\) | −49.4752 | − | 16.0755i | −1.88622 | − | 0.612871i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.1418 | − | 46.6018i | −0.576022 | − | 1.77281i | −0.632671 | − | 0.774421i | \(-0.718041\pi\) |
0.0566486 | − | 0.998394i | \(-0.481959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 27.9802 | + | 38.5115i | 1.05755 | + | 1.45560i | ||||
\(701\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.62776i | 0.249971i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.9865 | − | 46.1238i | 0.562831 | − | 1.73222i | −0.111479 | − | 0.993767i | \(-0.535559\pi\) |
0.674310 | − | 0.738448i | \(-0.264441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.3271 | + | 43.1180i | 1.17486 | + | 1.61705i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.6911 | + | 10.2970i | 1.18024 | + | 0.383482i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.0285 | − | 41.3307i | 1.11677 | − | 1.53711i | ||||
\(724\) | −11.7426 | − | 36.1401i | −0.436412 | − | 1.34314i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1769 | 1.15629 | 0.578144 | − | 0.815935i | \(-0.303777\pi\) | ||||
0.578144 | + | 0.815935i | \(0.303777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.8435 | − | 15.8702i | −0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −38.6445 | − | 12.5564i | −1.42834 | − | 0.464097i | ||||
\(733\) | 12.1427 | + | 16.7130i | 0.448501 | + | 0.617309i | 0.972075 | − | 0.234672i | \(-0.0754015\pi\) |
−0.523574 | + | 0.851980i | \(0.675402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.4888 | + | 8.93166i | −1.01119 | + | 0.328556i | −0.767329 | − | 0.641253i | \(-0.778415\pi\) |
−0.243863 | + | 0.969810i | \(0.578415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.22840 | + | 4.52520i | −0.228806 | + | 0.166237i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.4390 | + | 31.5603i | 1.58511 | + | 1.15165i | 0.910523 | + | 0.413458i | \(0.135679\pi\) |
0.674589 | + | 0.738194i | \(0.264321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −29.0779 | + | 40.0223i | −1.05755 | + | 1.45560i | ||||
\(757\) | −0.535233 | − | 1.64728i | −0.0194534 | − | 0.0598713i | 0.940859 | − | 0.338800i | \(-0.110021\pi\) |
−0.960312 | + | 0.278928i | \(0.910021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.1569 | + | 20.4572i | −1.01935 | + | 0.740600i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 8.56373 | + | 26.3565i | 0.309017 | + | 0.951057i | ||||
\(769\) | 12.4134i | 0.447637i | 0.974631 | + | 0.223819i | \(0.0718523\pi\) | ||||
−0.974631 | + | 0.223819i | \(0.928148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 51.9014 | − | 16.8638i | 1.86797 | − | 0.606941i | ||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.67617 | + | 8.23639i | −0.0961307 | + | 0.295860i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 25.1822 | + | 34.6603i | 0.903406 | + | 1.24343i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 50.6776 | + | 36.8195i | 1.80992 | + | 1.31498i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.3303 | + | 11.4795i | 1.25939 | + | 0.409201i | 0.861277 | − | 0.508136i | \(-0.169665\pi\) |
0.398113 | + | 0.917336i | \(0.369665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.8756 | −1.45154 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −42.0378 | + | 30.5422i | −1.48999 | + | 1.08254i | ||||
\(797\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −42.0000 | −1.48123 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.3754 | − | 45.9373i | 1.17197 | − | 1.61308i | 0.522695 | − | 0.852520i | \(-0.324927\pi\) |
0.649273 | − | 0.760555i | \(-0.275073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 55.5061i | − | 1.94668i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4203 | + | 9.75045i | 0.469518 | + | 0.341125i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.3783 | + | 47.3297i | −0.537363 | + | 1.65383i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.54508 | − | 4.75528i | −0.0538583 | − | 0.165759i | 0.920509 | − | 0.390721i | \(-0.127774\pi\) |
−0.974368 | + | 0.224962i | \(0.927774\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.66312 | + | 4.11450i | −0.196688 | + | 0.142902i | −0.681770 | − | 0.731566i | \(-0.738790\pi\) |
0.485082 | + | 0.874469i | \(0.338790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.9864 | + | 7.14381i | 0.762699 | + | 0.247816i | ||||
\(832\) | 16.3864 | + | 22.5539i | 0.568095 | + | 0.781915i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.00000 | −0.311086 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.96149 | + | 27.5806i | −0.309017 | + | 0.951057i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.7903 | + | 14.8516i | −0.371418 | + | 0.511213i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46.4860 | − | 15.1042i | 1.59540 | − | 0.518376i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.5763 | + | 16.7582i | 1.76594 | + | 0.573788i | 0.997788 | − | 0.0664795i | \(-0.0211767\pi\) |
0.768152 | + | 0.640268i | \(0.221177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0000 | 0.443554 | 0.221777 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.09896 | − | 28.0037i | −0.309017 | − | 0.951057i | ||||
\(868\) | 16.4901i | 0.559710i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.1827 | + | 13.0561i | −1.36154 | + | 0.442390i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.1353 | − | 8.81678i | 0.410716 | − | 0.298403i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.9824 | − | 30.2562i | −0.742716 | − | 1.02226i | ||||
\(877\) | 26.6817 | − | 36.7241i | 0.900975 | − | 1.24009i | −0.0691806 | − | 0.997604i | \(-0.522038\pi\) |
0.970156 | − | 0.242482i | \(-0.0779615\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.2164 | − | 13.2350i | −0.613029 | − | 0.445392i | 0.237450 | − | 0.971400i | \(-0.423688\pi\) |
−0.850480 | + | 0.526008i | \(0.823688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.3807 | + | 68.8809i | 0.750626 | + | 2.31019i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 46.0000 | 1.54019 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −9.27051 | − | 28.5317i | −0.309017 | − | 0.951057i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 107.229 | 3.56837 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.87132 | − | 18.0701i | 0.194954 | − | 0.600007i | −0.805023 | − | 0.593244i | \(-0.797847\pi\) |
0.999977 | − | 0.00676342i | \(-0.00215288\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | − | 8.83701i | − | 0.292623i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −33.6302 | − | 24.4338i | −1.11117 | − | 0.807315i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0956 | − | 13.0278i | −1.32263 | − | 0.429749i | −0.439233 | − | 0.898373i | \(-0.644750\pi\) |
−0.883397 | + | 0.468625i | \(0.844750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −34.8748 | + | 48.0011i | −1.14916 | + | 1.58169i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.9808 | −0.854242 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9894 | − | 12.3435i | −0.558004 | − | 0.405413i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.7409 | − | 16.1600i | −0.384793 | − | 0.529623i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.3167 | − | 18.6233i | 1.87245 | − | 0.608397i | 0.881871 | − | 0.471491i | \(-0.156284\pi\) |
0.990584 | − | 0.136906i | \(-0.0437159\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.8328 | − | 28.2137i | 1.26726 | − | 0.920719i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | −58.5298 | + | 19.0175i | −1.90096 | + | 0.617659i | ||||
\(949\) | −30.4367 | − | 22.1135i | −0.988016 | − | 0.717835i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6525 | − | 16.4580i | 0.730725 | − | 0.530903i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 34.6739 | + | 47.7246i | 1.11677 | + | 1.53711i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.07673i | 0.131099i | 0.997849 | + | 0.0655495i | \(0.0208800\pi\) | ||||
−0.997849 | + | 0.0655495i | \(0.979120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(972\) | 25.2227 | − | 18.3253i | 0.809017 | − | 0.587785i | ||||
\(973\) | 1.37354 | − | 4.22732i | 0.0440336 | − | 0.135522i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.7387 | − | 24.4153i | −0.568095 | − | 0.781915i | ||||
\(976\) | 27.5784 | − | 37.9585i | 0.882764 | − | 1.21502i | ||||
\(977\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.8604 | − | 6.77795i | 0.666021 | − | 0.216403i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.74708 | − | 8.45463i | −0.0873962 | − | 0.268978i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.0333 | −1.43053 | −0.715265 | − | 0.698853i | \(-0.753694\pi\) | ||||
−0.715265 | + | 0.698853i | \(0.753694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.4390 | + | 31.5603i | 1.37850 | + | 1.00154i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.9231 | − | 50.8203i | −1.16937 | − | 1.60950i | −0.667687 | − | 0.744442i | \(-0.732715\pi\) |
−0.501680 | − | 0.865053i | \(-0.667285\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.34346 | − | 25.6785i | −0.263975 | − | 0.812433i |
(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 | 363.2.f.g.215.1 | 16 | ||
3.2 | odd | 2 | CM | 363.2.f.g.215.1 | 16 | ||
11.2 | odd | 10 | inner | 363.2.f.g.233.1 | 16 | ||
11.3 | even | 5 | 363.2.d.d.362.4 | yes | 4 | ||
11.4 | even | 5 | inner | 363.2.f.g.239.4 | 16 | ||
11.5 | even | 5 | inner | 363.2.f.g.161.3 | 16 | ||
11.6 | odd | 10 | inner | 363.2.f.g.161.4 | 16 | ||
11.7 | odd | 10 | inner | 363.2.f.g.239.3 | 16 | ||
11.8 | odd | 10 | 363.2.d.d.362.3 | ✓ | 4 | ||
11.9 | even | 5 | inner | 363.2.f.g.233.2 | 16 | ||
11.10 | odd | 2 | inner | 363.2.f.g.215.2 | 16 | ||
33.2 | even | 10 | inner | 363.2.f.g.233.1 | 16 | ||
33.5 | odd | 10 | inner | 363.2.f.g.161.3 | 16 | ||
33.8 | even | 10 | 363.2.d.d.362.3 | ✓ | 4 | ||
33.14 | odd | 10 | 363.2.d.d.362.4 | yes | 4 | ||
33.17 | even | 10 | inner | 363.2.f.g.161.4 | 16 | ||
33.20 | odd | 10 | inner | 363.2.f.g.233.2 | 16 | ||
33.26 | odd | 10 | inner | 363.2.f.g.239.4 | 16 | ||
33.29 | even | 10 | inner | 363.2.f.g.239.3 | 16 | ||
33.32 | even | 2 | inner | 363.2.f.g.215.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.d.362.3 | ✓ | 4 | 11.8 | odd | 10 | ||
363.2.d.d.362.3 | ✓ | 4 | 33.8 | even | 10 | ||
363.2.d.d.362.4 | yes | 4 | 11.3 | even | 5 | ||
363.2.d.d.362.4 | yes | 4 | 33.14 | odd | 10 | ||
363.2.f.g.161.3 | 16 | 11.5 | even | 5 | inner | ||
363.2.f.g.161.3 | 16 | 33.5 | odd | 10 | inner | ||
363.2.f.g.161.4 | 16 | 11.6 | odd | 10 | inner | ||
363.2.f.g.161.4 | 16 | 33.17 | even | 10 | inner | ||
363.2.f.g.215.1 | 16 | 1.1 | even | 1 | trivial | ||
363.2.f.g.215.1 | 16 | 3.2 | odd | 2 | CM | ||
363.2.f.g.215.2 | 16 | 11.10 | odd | 2 | inner | ||
363.2.f.g.215.2 | 16 | 33.32 | even | 2 | inner | ||
363.2.f.g.233.1 | 16 | 11.2 | odd | 10 | inner | ||
363.2.f.g.233.1 | 16 | 33.2 | even | 10 | inner | ||
363.2.f.g.233.2 | 16 | 11.9 | even | 5 | inner | ||
363.2.f.g.233.2 | 16 | 33.20 | odd | 10 | inner | ||
363.2.f.g.239.3 | 16 | 11.7 | odd | 10 | inner | ||
363.2.f.g.239.3 | 16 | 33.29 | even | 10 | inner | ||
363.2.f.g.239.4 | 16 | 11.4 | even | 5 | inner | ||
363.2.f.g.239.4 | 16 | 33.26 | odd | 10 | inner |