Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(117,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.117");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 117.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.117 |
Dual form | 392.3.j.a.325.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(3\) | −1.41421 | − | 2.44949i | −0.471405 | − | 0.816497i | 0.528060 | − | 0.849207i | \(-0.322919\pi\) |
−0.999465 | + | 0.0327103i | \(0.989586\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(5\) | 4.24264 | − | 7.34847i | 0.848528 | − | 1.46969i | −0.0339935 | − | 0.999422i | \(-0.510823\pi\) |
0.882522 | − | 0.470272i | \(-0.155844\pi\) | |||||||
\(6\) | 5.65685 | 0.942809 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 1.00000 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(10\) | 8.48528 | + | 14.6969i | 0.848528 | + | 1.46969i | ||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | −5.65685 | + | 9.79796i | −0.471405 | + | 0.816497i | ||||
\(13\) | 25.4558 | 1.95814 | 0.979071 | − | 0.203519i | \(-0.0652380\pi\) | ||||
0.979071 | + | 0.203519i | \(0.0652380\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −24.0000 | −1.60000 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 1.00000 | + | 1.73205i | 0.0555556 | + | 0.0962250i | ||||
\(19\) | 4.24264 | − | 7.34847i | 0.223297 | − | 0.386762i | −0.732510 | − | 0.680756i | \(-0.761651\pi\) |
0.955807 | + | 0.293994i | \(0.0949847\pi\) | |||||||
\(20\) | −33.9411 | −1.69706 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.00000 | − | 8.66025i | 0.217391 | − | 0.376533i | −0.736618 | − | 0.676309i | \(-0.763579\pi\) |
0.954010 | + | 0.299776i | \(0.0969119\pi\) | |||||||
\(24\) | −11.3137 | − | 19.5959i | −0.471405 | − | 0.816497i | ||||
\(25\) | −23.5000 | − | 40.7032i | −0.940000 | − | 1.62813i | ||||
\(26\) | −25.4558 | + | 44.0908i | −0.979071 | + | 1.69580i | ||||
\(27\) | −28.2843 | −1.04757 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 24.0000 | − | 41.5692i | 0.800000 | − | 1.38564i | ||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.500000 | − | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.00000 | −0.111111 | ||||||||
\(37\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(38\) | 8.48528 | + | 14.6969i | 0.223297 | + | 0.386762i | ||||
\(39\) | −36.0000 | − | 62.3538i | −0.923077 | − | 1.59882i | ||||
\(40\) | 33.9411 | − | 58.7878i | 0.848528 | − | 1.46969i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.24264 | − | 7.34847i | −0.0942809 | − | 0.163299i | ||||
\(46\) | 10.0000 | + | 17.3205i | 0.217391 | + | 0.376533i | ||||
\(47\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(48\) | 45.2548 | 0.942809 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 94.0000 | 1.88000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −50.9117 | − | 88.1816i | −0.979071 | − | 1.69580i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 28.2843 | − | 48.9898i | 0.523783 | − | 0.907218i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24.0000 | −0.421053 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 38.1838 | + | 66.1362i | 0.647182 | + | 1.12095i | 0.983793 | + | 0.179309i | \(0.0573862\pi\) |
−0.336610 | + | 0.941644i | \(0.609281\pi\) | |||||||
\(60\) | 48.0000 | + | 83.1384i | 0.800000 | + | 1.38564i | ||||
\(61\) | 4.24264 | − | 7.34847i | 0.0695515 | − | 0.120467i | −0.829152 | − | 0.559023i | \(-0.811177\pi\) |
0.898704 | + | 0.438556i | \(0.144510\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 108.000 | − | 187.061i | 1.66154 | − | 2.87787i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −28.2843 | −0.409917 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −110.000 | −1.54930 | −0.774648 | − | 0.632393i | \(-0.782073\pi\) | ||||
−0.774648 | + | 0.632393i | \(0.782073\pi\) | |||||||
\(72\) | 4.00000 | − | 6.92820i | 0.0555556 | − | 0.0962250i | ||||
\(73\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −66.4680 | + | 115.126i | −0.886240 | + | 1.53501i | ||||
\(76\) | −33.9411 | −0.446594 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 144.000 | 1.84615 | ||||||||
\(79\) | −65.0000 | + | 112.583i | −0.822785 | + | 1.42511i | 0.0808157 | + | 0.996729i | \(0.474247\pi\) |
−0.903601 | + | 0.428376i | \(0.859086\pi\) | |||||||
\(80\) | 67.8823 | + | 117.576i | 0.848528 | + | 1.46969i | ||||
\(81\) | 35.5000 | + | 61.4878i | 0.438272 | + | 0.759109i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 25.4558 | 0.306697 | 0.153348 | − | 0.988172i | \(-0.450994\pi\) | ||||
0.153348 | + | 0.988172i | \(0.450994\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(90\) | 16.9706 | 0.188562 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −40.0000 | −0.434783 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −36.0000 | − | 62.3538i | −0.378947 | − | 0.656356i | ||||
\(96\) | −45.2548 | + | 78.3837i | −0.471405 | + | 0.816497i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −94.0000 | + | 162.813i | −0.940000 | + | 1.62813i | ||||
\(101\) | −80.6102 | − | 139.621i | −0.798121 | − | 1.38239i | −0.920839 | − | 0.389944i | \(-0.872494\pi\) |
0.122718 | − | 0.992442i | \(-0.460839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 203.647 | 1.95814 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 56.5685 | + | 97.9796i | 0.523783 | + | 0.907218i | ||||
\(109\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −26.0000 | −0.230088 | −0.115044 | − | 0.993360i | \(-0.536701\pi\) | ||||
−0.115044 | + | 0.993360i | \(0.536701\pi\) | |||||||
\(114\) | 24.0000 | − | 41.5692i | 0.210526 | − | 0.364642i | ||||
\(115\) | −42.4264 | − | 73.4847i | −0.368925 | − | 0.638997i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.7279 | − | 22.0454i | 0.108786 | − | 0.188422i | ||||
\(118\) | −152.735 | −1.29436 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −192.000 | −1.60000 | ||||||||
\(121\) | −60.5000 | + | 104.789i | −0.500000 | + | 0.866025i | ||||
\(122\) | 8.48528 | + | 14.6969i | 0.0695515 | + | 0.120467i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −186.676 | −1.49341 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −250.000 | −1.96850 | −0.984252 | − | 0.176771i | \(-0.943435\pi\) | ||||
−0.984252 | + | 0.176771i | \(0.943435\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.500000 | + | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 216.000 | + | 374.123i | 1.66154 | + | 2.87787i | ||||
\(131\) | 123.037 | − | 213.106i | 0.939211 | − | 1.62676i | 0.172263 | − | 0.985051i | \(-0.444892\pi\) |
0.766948 | − | 0.641709i | \(-0.221774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −120.000 | + | 207.846i | −0.888889 | + | 1.53960i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −25.0000 | − | 43.3013i | −0.182482 | − | 0.316068i | 0.760243 | − | 0.649638i | \(-0.225080\pi\) |
−0.942725 | + | 0.333571i | \(0.891746\pi\) | |||||||
\(138\) | 28.2843 | − | 48.9898i | 0.204958 | − | 0.354999i | ||||
\(139\) | 263.044 | 1.89240 | 0.946200 | − | 0.323581i | \(-0.104887\pi\) | ||||
0.946200 | + | 0.323581i | \(0.104887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 110.000 | − | 190.526i | 0.774648 | − | 1.34173i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.00000 | + | 13.8564i | 0.0555556 | + | 0.0962250i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | −132.936 | − | 230.252i | −0.886240 | − | 1.53501i | ||||
\(151\) | 101.000 | + | 174.937i | 0.668874 | + | 1.15852i | 0.978219 | + | 0.207574i | \(0.0665568\pi\) |
−0.309345 | + | 0.950950i | \(0.600110\pi\) | |||||||
\(152\) | 33.9411 | − | 58.7878i | 0.223297 | − | 0.386762i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −144.000 | + | 249.415i | −0.923077 | + | 1.59882i | ||||
\(157\) | 156.978 | + | 271.893i | 0.999858 | + | 1.73180i | 0.514523 | + | 0.857476i | \(0.327969\pi\) |
0.485335 | + | 0.874328i | \(0.338698\pi\) | |||||||
\(158\) | −130.000 | − | 225.167i | −0.822785 | − | 1.42511i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −271.529 | −1.69706 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −142.000 | −0.876543 | ||||||||
\(163\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.4558 | + | 44.0908i | −0.153348 | + | 0.265607i | ||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 479.000 | 2.83432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.24264 | − | 7.34847i | −0.0248108 | − | 0.0429735i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −114.551 | + | 198.409i | −0.662146 | + | 1.14687i | 0.317904 | + | 0.948123i | \(0.397021\pi\) |
−0.980051 | + | 0.198748i | \(0.936312\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 108.000 | − | 187.061i | 0.610169 | − | 1.05684i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | −16.9706 | + | 29.3939i | −0.0942809 | + | 0.163299i | ||||
\(181\) | 263.044 | 1.45328 | 0.726640 | − | 0.687018i | \(-0.241081\pi\) | ||||
0.726640 | + | 0.687018i | \(0.241081\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −24.0000 | −0.131148 | ||||||||
\(184\) | 40.0000 | − | 69.2820i | 0.217391 | − | 0.376533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 144.000 | 0.757895 | ||||||||
\(191\) | −65.0000 | + | 112.583i | −0.340314 | + | 0.589441i | −0.984491 | − | 0.175435i | \(-0.943867\pi\) |
0.644177 | + | 0.764877i | \(0.277200\pi\) | |||||||
\(192\) | −90.5097 | − | 156.767i | −0.471405 | − | 0.816497i | ||||
\(193\) | 157.000 | + | 271.932i | 0.813472 | + | 1.40897i | 0.910420 | + | 0.413685i | \(0.135758\pi\) |
−0.0969488 | + | 0.995289i | \(0.530908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −610.940 | −3.13303 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | −188.000 | − | 325.626i | −0.940000 | − | 1.62813i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 322.441 | 1.59624 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.00000 | − | 8.66025i | −0.0241546 | − | 0.0418370i | ||||
\(208\) | −203.647 | + | 352.727i | −0.979071 | + | 1.69580i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 155.563 | + | 269.444i | 0.730345 | + | 1.26499i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −226.274 | −1.04757 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −47.0000 | −0.208889 | ||||||||
\(226\) | 26.0000 | − | 45.0333i | 0.115044 | − | 0.199262i | ||||
\(227\) | −199.404 | − | 345.378i | −0.878432 | − | 1.52149i | −0.853061 | − | 0.521811i | \(-0.825257\pi\) |
−0.0253712 | − | 0.999678i | \(-0.508077\pi\) | |||||||
\(228\) | 48.0000 | + | 83.1384i | 0.210526 | + | 0.364642i | ||||
\(229\) | 123.037 | − | 213.106i | 0.537278 | − | 0.930592i | −0.461772 | − | 0.886999i | \(-0.652786\pi\) |
0.999049 | − | 0.0435934i | \(-0.0138806\pi\) | |||||||
\(230\) | 169.706 | 0.737851 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 215.000 | − | 372.391i | 0.922747 | − | 1.59824i | 0.127601 | − | 0.991826i | \(-0.459272\pi\) |
0.795145 | − | 0.606419i | \(-0.207394\pi\) | |||||||
\(234\) | 25.4558 | + | 44.0908i | 0.108786 | + | 0.188422i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 152.735 | − | 264.545i | 0.647182 | − | 1.12095i | ||||
\(237\) | 367.696 | 1.55146 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 422.000 | 1.76569 | 0.882845 | − | 0.469664i | \(-0.155625\pi\) | ||||
0.882845 | + | 0.469664i | \(0.155625\pi\) | |||||||
\(240\) | 192.000 | − | 332.554i | 0.800000 | − | 1.38564i | ||||
\(241\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(242\) | −121.000 | − | 209.578i | −0.500000 | − | 0.866025i | ||||
\(243\) | −26.8701 | + | 46.5403i | −0.110576 | + | 0.191524i | ||||
\(244\) | −33.9411 | −0.139103 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 108.000 | − | 187.061i | 0.437247 | − | 0.757334i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −36.0000 | − | 62.3538i | −0.144578 | − | 0.250417i | ||||
\(250\) | 186.676 | − | 323.333i | 0.746705 | − | 1.29333i | ||||
\(251\) | 500.632 | 1.99455 | 0.997274 | − | 0.0737859i | \(-0.0235081\pi\) | ||||
0.997274 | + | 0.0737859i | \(0.0235081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 250.000 | − | 433.013i | 0.984252 | − | 1.70477i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −864.000 | −3.32308 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 246.073 | + | 426.211i | 0.939211 | + | 1.62676i | ||||
\(263\) | −137.000 | − | 237.291i | −0.520913 | − | 0.902247i | −0.999704 | − | 0.0243185i | \(-0.992258\pi\) |
0.478792 | − | 0.877929i | \(-0.341075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −80.6102 | − | 139.621i | −0.299666 | − | 0.519037i | 0.676393 | − | 0.736541i | \(-0.263542\pi\) |
−0.976060 | + | 0.217504i | \(0.930209\pi\) | |||||||
\(270\) | −240.000 | − | 415.692i | −0.888889 | − | 1.53960i | ||||
\(271\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 100.000 | 0.364964 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 56.5685 | + | 97.9796i | 0.204958 | + | 0.354999i | ||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | −263.044 | + | 455.605i | −0.946200 | + | 1.63887i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 338.000 | 1.20285 | 0.601423 | − | 0.798930i | \(-0.294600\pi\) | ||||
0.601423 | + | 0.798930i | \(0.294600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 156.978 | + | 271.893i | 0.554692 | + | 0.960754i | 0.997927 | + | 0.0643489i | \(0.0204971\pi\) |
−0.443236 | + | 0.896405i | \(0.646170\pi\) | |||||||
\(284\) | 220.000 | + | 381.051i | 0.774648 | + | 1.34173i | ||||
\(285\) | −101.823 | + | 176.363i | −0.357275 | + | 0.618818i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −32.0000 | −0.111111 | ||||||||
\(289\) | −144.500 | + | 250.281i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −449.720 | −1.53488 | −0.767440 | − | 0.641121i | \(-0.778470\pi\) | ||||
−0.767440 | + | 0.641121i | \(0.778470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 648.000 | 2.19661 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 127.279 | − | 220.454i | 0.425683 | − | 0.737305i | ||||
\(300\) | 531.744 | 1.77248 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −404.000 | −1.33775 | ||||||||
\(303\) | −228.000 | + | 394.908i | −0.752475 | + | 1.30333i | ||||
\(304\) | 67.8823 | + | 117.576i | 0.223297 | + | 0.386762i | ||||
\(305\) | −36.0000 | − | 62.3538i | −0.118033 | − | 0.204439i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −449.720 | −1.46489 | −0.732443 | − | 0.680829i | \(-0.761620\pi\) | ||||
−0.732443 | + | 0.680829i | \(0.761620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(312\) | −288.000 | − | 498.831i | −0.923077 | − | 1.59882i | ||||
\(313\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(314\) | −627.911 | −1.99972 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 520.000 | 1.64557 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 271.529 | − | 470.302i | 0.848528 | − | 1.46969i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 142.000 | − | 245.951i | 0.438272 | − | 0.759109i | ||||
\(325\) | −598.212 | − | 1036.13i | −1.84065 | − | 3.18811i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(332\) | −50.9117 | − | 88.1816i | −0.153348 | − | 0.265607i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.0000 | −0.0771513 | −0.0385757 | − | 0.999256i | \(-0.512282\pi\) | ||||
−0.0385757 | + | 0.999256i | \(0.512282\pi\) | |||||||
\(338\) | −479.000 | + | 829.652i | −1.41716 | + | 2.45459i | ||||
\(339\) | 36.7696 | + | 63.6867i | 0.108465 | + | 0.187866i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 16.9706 | 0.0496215 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −120.000 | + | 207.846i | −0.347826 | + | 0.602452i | ||||
\(346\) | −229.103 | − | 396.817i | −0.662146 | − | 1.14687i | ||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −687.308 | −1.96936 | −0.984682 | − | 0.174362i | \(-0.944214\pi\) | ||||
−0.984682 | + | 0.174362i | \(0.944214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −720.000 | −2.05128 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 216.000 | + | 374.123i | 0.610169 | + | 1.05684i | ||||
\(355\) | −466.690 | + | 808.332i | −1.31462 | + | 2.27699i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 341.000 | − | 590.629i | 0.949861 | − | 1.64521i | 0.204147 | − | 0.978940i | \(-0.434558\pi\) |
0.745713 | − | 0.666267i | \(-0.232109\pi\) | |||||||
\(360\) | −33.9411 | − | 58.7878i | −0.0942809 | − | 0.163299i | ||||
\(361\) | 144.500 | + | 250.281i | 0.400277 | + | 0.693300i | ||||
\(362\) | −263.044 | + | 455.605i | −0.726640 | + | 1.25858i | ||||
\(363\) | 342.240 | 0.942809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 24.0000 | − | 41.5692i | 0.0655738 | − | 0.113577i | ||||
\(367\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(368\) | 80.0000 | + | 138.564i | 0.217391 | + | 0.376533i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 264.000 | + | 457.261i | 0.704000 | + | 1.21936i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | −144.000 | + | 249.415i | −0.378947 | + | 0.656356i | ||||
\(381\) | 353.553 | + | 612.372i | 0.927962 | + | 1.60728i | ||||
\(382\) | −130.000 | − | 225.167i | −0.340314 | − | 0.589441i | ||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 362.039 | 0.942809 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −628.000 | −1.62694 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 610.940 | − | 1058.18i | 1.56651 | − | 2.71328i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −696.000 | −1.77099 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 551.543 | + | 955.301i | 1.39631 | + | 2.41848i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 241.831 | − | 418.863i | 0.609145 | − | 1.05507i | −0.382237 | − | 0.924064i | \(-0.624846\pi\) |
0.991382 | − | 0.131005i | \(-0.0418205\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 752.000 | 1.88000 | ||||||||
\(401\) | −275.000 | + | 476.314i | −0.685786 | + | 1.18782i | 0.287404 | + | 0.957810i | \(0.407208\pi\) |
−0.973189 | + | 0.230006i | \(0.926125\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −322.441 | + | 558.484i | −0.798121 | + | 1.38239i | ||||
\(405\) | 602.455 | 1.48754 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −70.7107 | + | 122.474i | −0.172045 | + | 0.297991i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 20.0000 | 0.0483092 | ||||||||
\(415\) | 108.000 | − | 187.061i | 0.260241 | − | 0.450751i | ||||
\(416\) | −407.294 | − | 705.453i | −0.979071 | − | 1.69580i | ||||
\(417\) | −372.000 | − | 644.323i | −0.892086 | − | 1.54514i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 500.632 | 1.19482 | 0.597412 | − | 0.801934i | \(-0.296196\pi\) | ||||
0.597412 | + | 0.801934i | \(0.296196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −622.254 | −1.46069 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 269.000 | + | 465.922i | 0.624130 | + | 1.08102i | 0.988708 | + | 0.149852i | \(0.0478798\pi\) |
−0.364578 | + | 0.931173i | \(0.618787\pi\) | |||||||
\(432\) | 226.274 | − | 391.918i | 0.523783 | − | 0.907218i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −42.4264 | − | 73.4847i | −0.0970856 | − | 0.168157i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.00445434 | 0.00222717 | − | 0.999998i | \(-0.499291\pi\) | ||||
0.00222717 | + | 0.999998i | \(0.499291\pi\) | |||||||
\(450\) | 47.0000 | − | 81.4064i | 0.104444 | − | 0.180903i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 52.0000 | + | 90.0666i | 0.115044 | + | 0.199262i | ||||
\(453\) | 285.671 | − | 494.797i | 0.630621 | − | 1.09227i | ||||
\(454\) | 797.616 | 1.75686 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −192.000 | −0.421053 | ||||||||
\(457\) | −443.000 | + | 767.299i | −0.969365 | + | 1.67899i | −0.271967 | + | 0.962307i | \(0.587674\pi\) |
−0.697398 | + | 0.716684i | \(0.745659\pi\) | |||||||
\(458\) | 246.073 | + | 426.211i | 0.537278 | + | 0.930592i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −169.706 | + | 293.939i | −0.368925 | + | 0.638997i | ||||
\(461\) | 263.044 | 0.570594 | 0.285297 | − | 0.958439i | \(-0.407908\pi\) | ||||
0.285297 | + | 0.958439i | \(0.407908\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 226.000 | 0.488121 | 0.244060 | − | 0.969760i | \(-0.421520\pi\) | ||||
0.244060 | + | 0.969760i | \(0.421520\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 430.000 | + | 744.782i | 0.922747 | + | 1.59824i | ||||
\(467\) | 241.831 | − | 418.863i | 0.517838 | − | 0.896922i | −0.481947 | − | 0.876200i | \(-0.660070\pi\) |
0.999785 | − | 0.0207219i | \(-0.00659647\pi\) | |||||||
\(468\) | −101.823 | −0.217571 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 444.000 | − | 769.031i | 0.942675 | − | 1.63276i | ||||
\(472\) | 305.470 | + | 529.090i | 0.647182 | + | 1.12095i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −367.696 | + | 636.867i | −0.775729 | + | 1.34360i | ||||
\(475\) | −398.808 | −0.839596 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −422.000 | + | 730.925i | −0.882845 | + | 1.52913i | ||||
\(479\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 384.000 | + | 665.108i | 0.800000 | + | 1.38564i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 484.000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −53.7401 | − | 93.0806i | −0.110576 | − | 0.191524i | ||||
\(487\) | −235.000 | − | 407.032i | −0.482546 | − | 0.835795i | 0.517253 | − | 0.855833i | \(-0.326955\pi\) |
−0.999799 | + | 0.0200380i | \(0.993621\pi\) | |||||||
\(488\) | 33.9411 | − | 58.7878i | 0.0695515 | − | 0.120467i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 216.000 | + | 374.123i | 0.437247 | + | 0.757334i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 144.000 | 0.289157 | ||||||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 373.352 | + | 646.665i | 0.746705 | + | 1.29333i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −500.632 | + | 867.119i | −0.997274 | + | 1.72733i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1368.00 | −2.70891 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −677.408 | − | 1173.31i | −1.33611 | − | 2.31421i | ||||
\(508\) | 500.000 | + | 866.025i | 0.984252 | + | 1.70477i | ||||
\(509\) | −470.933 | + | 815.680i | −0.925212 | + | 1.60251i | −0.133993 | + | 0.990982i | \(0.542780\pi\) |
−0.791219 | + | 0.611533i | \(0.790553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 1.00000 | ||||||||
\(513\) | −120.000 | + | 207.846i | −0.233918 | + | 0.405158i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 648.000 | 1.24855 | ||||||||
\(520\) | 864.000 | − | 1496.49i | 1.66154 | − | 2.87787i | ||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 479.418 | − | 830.377i | 0.916670 | − | 1.58772i | 0.112232 | − | 0.993682i | \(-0.464200\pi\) |
0.804438 | − | 0.594037i | \(-0.202467\pi\) | |||||||
\(524\) | −984.293 | −1.87842 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 548.000 | 1.04183 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 214.500 | + | 371.525i | 0.405482 | + | 0.702315i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 76.3675 | 0.143818 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 322.441 | 0.599332 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 960.000 | 1.77778 | ||||||||
\(541\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −372.000 | − | 644.323i | −0.685083 | − | 1.18660i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | −100.000 | + | 173.205i | −0.182482 | + | 0.316068i | ||||
\(549\) | −4.24264 | − | 7.34847i | −0.00772794 | − | 0.0133852i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −226.274 | −0.409917 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −526.087 | − | 911.210i | −0.946200 | − | 1.63887i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −338.000 | + | 585.433i | −0.601423 | + | 1.04170i | ||||
\(563\) | −199.404 | − | 345.378i | −0.354181 | − | 0.613460i | 0.632796 | − | 0.774318i | \(-0.281907\pi\) |
−0.986978 | + | 0.160858i | \(0.948574\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −110.309 | + | 191.060i | −0.195237 | + | 0.338160i | ||||
\(566\) | −627.911 | −1.10938 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −880.000 | −1.54930 | ||||||||
\(569\) | 565.000 | − | 978.609i | 0.992970 | − | 1.71987i | 0.393978 | − | 0.919120i | \(-0.371099\pi\) |
0.598992 | − | 0.800755i | \(-0.295568\pi\) | |||||||
\(570\) | −203.647 | − | 352.727i | −0.357275 | − | 0.618818i | ||||
\(571\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 367.696 | 0.641702 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −470.000 | −0.817391 | ||||||||
\(576\) | 32.0000 | − | 55.4256i | 0.0555556 | − | 0.0962250i | ||||
\(577\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(578\) | −289.000 | − | 500.563i | −0.500000 | − | 0.866025i | ||||
\(579\) | 444.063 | − | 769.140i | 0.766948 | − | 1.32839i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −108.000 | − | 187.061i | −0.184615 | − | 0.319763i | ||||
\(586\) | 449.720 | − | 778.938i | 0.767440 | − | 1.32925i | ||||
\(587\) | −1162.48 | −1.98038 | −0.990190 | − | 0.139725i | \(-0.955378\pi\) | ||||
−0.990190 | + | 0.139725i | \(0.955378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −648.000 | + | 1122.37i | −1.09831 | + | 1.90232i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 254.558 | + | 440.908i | 0.425683 | + | 0.737305i | ||||
\(599\) | 535.000 | + | 926.647i | 0.893155 | + | 1.54699i | 0.836071 | + | 0.548621i | \(0.184847\pi\) |
0.0570840 | + | 0.998369i | \(0.481820\pi\) | |||||||
\(600\) | −531.744 | + | 921.008i | −0.886240 | + | 1.53501i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 404.000 | − | 699.749i | 0.668874 | − | 1.15852i | ||||
\(605\) | 513.360 | + | 889.165i | 0.848528 | + | 1.46969i | ||||
\(606\) | −456.000 | − | 789.815i | −0.752475 | − | 1.30333i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | −271.529 | −0.446594 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 144.000 | 0.236066 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(614\) | 449.720 | − | 778.938i | 0.732443 | − | 1.26863i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1034.00 | −1.67585 | −0.837925 | − | 0.545785i | \(-0.816232\pi\) | ||||
−0.837925 | + | 0.545785i | \(0.816232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −555.786 | − | 962.649i | −0.897877 | − | 1.55517i | −0.830203 | − | 0.557461i | \(-0.811775\pi\) |
−0.0676742 | − | 0.997707i | \(-0.521558\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −141.421 | + | 244.949i | −0.227732 | + | 0.394443i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1152.00 | 1.84615 | ||||||||
\(625\) | −204.500 | + | 354.204i | −0.327200 | + | 0.566727i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 627.911 | − | 1087.57i | 0.999858 | − | 1.73180i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −110.000 | −0.174326 | −0.0871632 | − | 0.996194i | \(-0.527780\pi\) | ||||
−0.0871632 | + | 0.996194i | \(0.527780\pi\) | |||||||
\(632\) | −520.000 | + | 900.666i | −0.822785 | + | 1.42511i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1060.66 | + | 1837.12i | −1.67033 | + | 2.89310i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −55.0000 | + | 95.2628i | −0.0860720 | + | 0.149081i | ||||
\(640\) | 543.058 | + | 940.604i | 0.848528 | + | 1.46969i | ||||
\(641\) | −515.000 | − | 892.006i | −0.803432 | − | 1.39159i | −0.917344 | − | 0.398094i | \(-0.869672\pi\) |
0.113912 | − | 0.993491i | \(-0.463662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 738.219 | 1.14809 | 0.574043 | − | 0.818825i | \(-0.305374\pi\) | ||||
0.574043 | + | 0.818825i | \(0.305374\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(648\) | 284.000 | + | 491.902i | 0.438272 | + | 0.759109i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2392.85 | 3.68131 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1044.00 | − | 1808.26i | −1.59389 | − | 2.76070i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 632.153 | + | 1094.92i | 0.956359 | + | 1.65646i | 0.731227 | + | 0.682135i | \(0.238948\pi\) |
0.225133 | + | 0.974328i | \(0.427718\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 203.647 | 0.306697 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −670.000 | −0.995542 | −0.497771 | − | 0.867308i | \(-0.665848\pi\) | ||||
−0.497771 | + | 0.867308i | \(0.665848\pi\) | |||||||
\(674\) | 26.0000 | − | 45.0333i | 0.0385757 | − | 0.0668150i | ||||
\(675\) | 664.680 | + | 1151.26i | 0.984712 | + | 1.70557i | ||||
\(676\) | −958.000 | − | 1659.30i | −1.41716 | − | 2.45459i | ||||
\(677\) | 241.831 | − | 418.863i | 0.357209 | − | 0.618704i | −0.630284 | − | 0.776364i | \(-0.717062\pi\) |
0.987493 | + | 0.157660i | \(0.0503950\pi\) | |||||||
\(678\) | −147.078 | −0.216930 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −564.000 | + | 976.877i | −0.828194 | + | 1.43447i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | −16.9706 | + | 29.3939i | −0.0248108 | + | 0.0429735i | ||||
\(685\) | −424.264 | −0.619364 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −696.000 | −1.01310 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −240.000 | − | 415.692i | −0.347826 | − | 0.602452i | ||||
\(691\) | 123.037 | − | 213.106i | 0.178056 | − | 0.308402i | −0.763159 | − | 0.646211i | \(-0.776353\pi\) |
0.941215 | + | 0.337809i | \(0.109686\pi\) | |||||||
\(692\) | 916.410 | 1.32429 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1116.00 | − | 1932.97i | 1.60576 | − | 2.78125i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 687.308 | − | 1190.45i | 0.984682 | − | 1.70552i | ||||
\(699\) | −1216.22 | −1.73995 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 720.000 | − | 1247.08i | 1.02564 | − | 1.77646i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −864.000 | −1.22034 | ||||||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | −933.381 | − | 1616.66i | −1.31462 | − | 2.27699i | ||||
\(711\) | 65.0000 | + | 112.583i | 0.0914205 | + | 0.158345i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −596.798 | − | 1033.68i | −0.832354 | − | 1.44168i | ||||
\(718\) | 682.000 | + | 1181.26i | 0.949861 | + | 1.64521i | ||||
\(719\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(720\) | 135.765 | 0.188562 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −578.000 | −0.800554 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −526.087 | − | 911.210i | −0.726640 | − | 1.25858i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −342.240 | + | 592.777i | −0.471405 | + | 0.816497i | ||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 791.000 | 1.08505 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 48.0000 | + | 83.1384i | 0.0655738 | + | 0.113577i | ||||
\(733\) | −708.521 | + | 1227.19i | −0.966604 | + | 1.67421i | −0.261363 | + | 0.965241i | \(0.584172\pi\) |
−0.705241 | + | 0.708967i | \(0.749161\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −320.000 | −0.434783 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −610.940 | −0.824481 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1430.00 | 1.92463 | 0.962315 | − | 0.271937i | \(-0.0876644\pi\) | ||||
0.962315 | + | 0.271937i | \(0.0876644\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.7279 | − | 22.0454i | 0.0170387 | − | 0.0295119i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1056.00 | −1.40800 | ||||||||
\(751\) | −499.000 | + | 864.293i | −0.664447 | + | 1.15086i | 0.314987 | + | 0.949096i | \(0.398000\pi\) |
−0.979435 | + | 0.201761i | \(0.935334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −708.000 | − | 1226.29i | −0.940239 | − | 1.62854i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1714.03 | 2.27023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −288.000 | − | 498.831i | −0.378947 | − | 0.656356i | ||||
\(761\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(762\) | −1414.21 | −1.85592 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 520.000 | 0.680628 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 972.000 | + | 1683.55i | 1.26728 | + | 2.19498i | ||||
\(768\) | −362.039 | + | 627.069i | −0.471405 | + | 0.816497i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 628.000 | − | 1087.73i | 0.813472 | − | 1.40897i | ||||
\(773\) | −436.992 | − | 756.892i | −0.565320 | − | 0.979162i | −0.997020 | − | 0.0771451i | \(-0.975420\pi\) |
0.431700 | − | 0.902017i | \(-0.357914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 1221.88 | + | 2116.36i | 1.56651 | + | 2.71328i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2664.00 | 3.39363 | ||||||||
\(786\) | 696.000 | − | 1205.51i | 0.885496 | − | 1.53372i | ||||
\(787\) | 750.947 | + | 1300.68i | 0.954190 | + | 1.65271i | 0.736211 | + | 0.676752i | \(0.236613\pi\) |
0.217979 | + | 0.975954i | \(0.430054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −387.495 | + | 671.160i | −0.491121 | + | 0.850647i | ||||
\(790\) | −2206.17 | −2.79262 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 108.000 | − | 187.061i | 0.136192 | − | 0.235891i | ||||
\(794\) | 483.661 | + | 837.725i | 0.609145 | + | 1.05507i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −449.720 | −0.564266 | −0.282133 | − | 0.959375i | \(-0.591042\pi\) | ||||
−0.282133 | + | 0.959375i | \(0.591042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −752.000 | + | 1302.50i | −0.940000 | + | 1.62813i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −550.000 | − | 952.628i | −0.685786 | − | 1.18782i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −228.000 | + | 394.908i | −0.282528 | + | 0.489353i | ||||
\(808\) | −644.881 | − | 1116.97i | −0.798121 | − | 1.38239i | ||||
\(809\) | 325.000 | + | 562.917i | 0.401731 | + | 0.695818i | 0.993935 | − | 0.109970i | \(-0.0350755\pi\) |
−0.592204 | + | 0.805788i | \(0.701742\pi\) | |||||||
\(810\) | −602.455 | + | 1043.48i | −0.743772 | + | 1.28825i | ||||
\(811\) | 1450.98 | 1.78913 | 0.894564 | − | 0.446939i | \(-0.147486\pi\) | ||||
0.894564 | + | 0.446939i | \(0.147486\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | −141.421 | − | 244.949i | −0.172045 | − | 0.297991i | ||||
\(823\) | −473.000 | − | 819.260i | −0.574727 | − | 0.995456i | −0.996071 | − | 0.0885551i | \(-0.971775\pi\) |
0.421345 | − | 0.906901i | \(-0.361558\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | −20.0000 | + | 34.6410i | −0.0241546 | + | 0.0418370i | ||||
\(829\) | 38.1838 | + | 66.1362i | 0.0460600 | + | 0.0797783i | 0.888136 | − | 0.459580i | \(-0.152000\pi\) |
−0.842076 | + | 0.539358i | \(0.818667\pi\) | |||||||
\(830\) | 216.000 | + | 374.123i | 0.260241 | + | 0.450751i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1629.17 | 1.95814 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1488.00 | 1.78417 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −500.632 | + | 867.119i | −0.597412 | + | 1.03475i | ||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −478.004 | − | 827.928i | −0.567028 | − | 0.982120i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2032.22 | − | 3519.92i | 2.40500 | − | 4.16558i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 444.000 | − | 769.031i | 0.522968 | − | 0.905807i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 622.254 | − | 1077.78i | 0.730345 | − | 1.26499i | ||||
\(853\) | −449.720 | −0.527221 | −0.263611 | − | 0.964629i | \(-0.584913\pi\) | ||||
−0.263611 | + | 0.964629i | \(0.584913\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −72.0000 | −0.0842105 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 598.212 | − | 1036.13i | 0.696406 | − | 1.20621i | −0.273299 | − | 0.961929i | \(-0.588115\pi\) |
0.969705 | − | 0.244281i | \(-0.0785518\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1076.00 | −1.24826 | ||||||||
\(863\) | −737.000 | + | 1276.52i | −0.853998 | + | 1.47917i | 0.0235741 | + | 0.999722i | \(0.492495\pi\) |
−0.877572 | + | 0.479445i | \(0.840838\pi\) | |||||||
\(864\) | 452.548 | + | 783.837i | 0.523783 | + | 0.907218i | ||||
\(865\) | 972.000 | + | 1683.55i | 1.12370 | + | 1.94630i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 817.415 | 0.942809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 169.706 | 0.194171 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 636.000 | + | 1101.58i | 0.723549 | + | 1.25322i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −916.410 | − | 1587.27i | −1.03549 | − | 1.79352i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −720.000 | −0.802676 | ||||||||
\(898\) | −2.00000 | + | 3.46410i | −0.00222717 | + | 0.00385757i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 94.0000 | + | 162.813i | 0.104444 | + | 0.180903i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −208.000 | −0.230088 | ||||||||
\(905\) | 1116.00 | − | 1932.97i | 1.23315 | − | 2.13588i | ||||
\(906\) | 571.342 | + | 989.594i | 0.630621 | + | 1.09227i | ||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | −797.616 | + | 1381.51i | −0.878432 | + | 1.52149i | ||||
\(909\) | −161.220 | −0.177360 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −922.000 | −1.01207 | −0.506037 | − | 0.862512i | \(-0.668890\pi\) | ||||
−0.506037 | + | 0.862512i | \(0.668890\pi\) | |||||||
\(912\) | 192.000 | − | 332.554i | 0.210526 | − | 0.364642i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −886.000 | − | 1534.60i | −0.969365 | − | 1.67899i | ||||
\(915\) | −101.823 | + | 176.363i | −0.111282 | + | 0.192747i | ||||
\(916\) | −984.293 | −1.07456 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 775.000 | − | 1342.34i | 0.843308 | − | 1.46065i | −0.0437746 | − | 0.999041i | \(-0.513938\pi\) |
0.887083 | − | 0.461611i | \(-0.152728\pi\) | |||||||
\(920\) | −339.411 | − | 587.878i | −0.368925 | − | 0.638997i | ||||
\(921\) | 636.000 | + | 1101.58i | 0.690554 | + | 1.19607i | ||||
\(922\) | −263.044 | + | 455.605i | −0.285297 | + | 0.494149i | ||||
\(923\) | −2800.14 | −3.03374 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −226.000 | + | 391.443i | −0.244060 | + | 0.422725i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1720.00 | −1.84549 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 483.661 | + | 837.725i | 0.517838 | + | 0.896922i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 101.823 | − | 176.363i | 0.108786 | − | 0.188422i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −555.786 | − | 962.649i | −0.590633 | − | 1.02301i | −0.994147 | − | 0.108033i | \(-0.965545\pi\) |
0.403514 | − | 0.914973i | \(-0.367789\pi\) | |||||||
\(942\) | 888.000 | + | 1538.06i | 0.942675 | + | 1.63276i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1221.88 | −1.29436 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | −735.391 | − | 1273.73i | −0.775729 | − | 1.34360i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 398.808 | − | 690.756i | 0.419798 | − | 0.727112i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1010.00 | 1.05981 | 0.529906 | − | 0.848057i | \(-0.322227\pi\) | ||||
0.529906 | + | 0.848057i | \(0.322227\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 551.543 | + | 955.301i | 0.577532 | + | 1.00032i | ||||
\(956\) | −844.000 | − | 1461.85i | −0.882845 | − | 1.52913i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1536.00 | −1.60000 | ||||||||
\(961\) | −480.500 | + | 832.250i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2664.38 | 2.76101 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1430.00 | 1.47880 | 0.739400 | − | 0.673266i | \(-0.235109\pi\) | ||||
0.739400 | + | 0.673266i | \(0.235109\pi\) | |||||||
\(968\) | −484.000 | + | 838.313i | −0.500000 | + | 0.866025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.24264 | − | 7.34847i | 0.00436935 | − | 0.00756794i | −0.863832 | − | 0.503779i | \(-0.831943\pi\) |
0.868202 | + | 0.496211i | \(0.165276\pi\) | |||||||
\(972\) | 214.960 | 0.221153 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 940.000 | 0.965092 | ||||||||
\(975\) | −1692.00 | + | 2930.63i | −1.73538 | + | 3.00577i | ||||
\(976\) | 67.8823 | + | 117.576i | 0.0695515 | + | 0.120467i | ||||
\(977\) | 815.000 | + | 1411.62i | 0.834186 | + | 1.44485i | 0.894691 | + | 0.446685i | \(0.147396\pi\) |
−0.0605049 | + | 0.998168i | \(0.519271\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −864.000 | −0.874494 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −305.000 | − | 528.275i | −0.307770 | − | 0.533073i | 0.670104 | − | 0.742267i | \(-0.266249\pi\) |
−0.977874 | + | 0.209194i | \(0.932916\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −144.000 | + | 249.415i | −0.144578 | + | 0.250417i | ||||
\(997\) | 988.535 | + | 1712.19i | 0.991510 | + | 1.71735i | 0.608366 | + | 0.793657i | \(0.291825\pi\) |
0.383144 | + | 0.923689i | \(0.374841\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 392.3.j.a.117.1 | 4 | ||
7.2 | even | 3 | 56.3.h.c.13.2 | yes | 2 | ||
7.3 | odd | 6 | inner | 392.3.j.a.325.2 | 4 | ||
7.4 | even | 3 | inner | 392.3.j.a.325.1 | 4 | ||
7.5 | odd | 6 | 56.3.h.c.13.1 | ✓ | 2 | ||
7.6 | odd | 2 | inner | 392.3.j.a.117.2 | 4 | ||
8.5 | even | 2 | inner | 392.3.j.a.117.2 | 4 | ||
21.2 | odd | 6 | 504.3.l.a.181.2 | 2 | |||
21.5 | even | 6 | 504.3.l.a.181.1 | 2 | |||
28.19 | even | 6 | 224.3.h.c.209.2 | 2 | |||
28.23 | odd | 6 | 224.3.h.c.209.1 | 2 | |||
56.5 | odd | 6 | 56.3.h.c.13.2 | yes | 2 | ||
56.13 | odd | 2 | CM | 392.3.j.a.117.1 | 4 | ||
56.19 | even | 6 | 224.3.h.c.209.1 | 2 | |||
56.37 | even | 6 | 56.3.h.c.13.1 | ✓ | 2 | ||
56.45 | odd | 6 | inner | 392.3.j.a.325.1 | 4 | ||
56.51 | odd | 6 | 224.3.h.c.209.2 | 2 | |||
56.53 | even | 6 | inner | 392.3.j.a.325.2 | 4 | ||
84.23 | even | 6 | 2016.3.l.c.433.2 | 2 | |||
84.47 | odd | 6 | 2016.3.l.c.433.1 | 2 | |||
168.5 | even | 6 | 504.3.l.a.181.2 | 2 | |||
168.107 | even | 6 | 2016.3.l.c.433.1 | 2 | |||
168.131 | odd | 6 | 2016.3.l.c.433.2 | 2 | |||
168.149 | odd | 6 | 504.3.l.a.181.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.h.c.13.1 | ✓ | 2 | 7.5 | odd | 6 | ||
56.3.h.c.13.1 | ✓ | 2 | 56.37 | even | 6 | ||
56.3.h.c.13.2 | yes | 2 | 7.2 | even | 3 | ||
56.3.h.c.13.2 | yes | 2 | 56.5 | odd | 6 | ||
224.3.h.c.209.1 | 2 | 28.23 | odd | 6 | |||
224.3.h.c.209.1 | 2 | 56.19 | even | 6 | |||
224.3.h.c.209.2 | 2 | 28.19 | even | 6 | |||
224.3.h.c.209.2 | 2 | 56.51 | odd | 6 | |||
392.3.j.a.117.1 | 4 | 1.1 | even | 1 | trivial | ||
392.3.j.a.117.1 | 4 | 56.13 | odd | 2 | CM | ||
392.3.j.a.117.2 | 4 | 7.6 | odd | 2 | inner | ||
392.3.j.a.117.2 | 4 | 8.5 | even | 2 | inner | ||
392.3.j.a.325.1 | 4 | 7.4 | even | 3 | inner | ||
392.3.j.a.325.1 | 4 | 56.45 | odd | 6 | inner | ||
392.3.j.a.325.2 | 4 | 7.3 | odd | 6 | inner | ||
392.3.j.a.325.2 | 4 | 56.53 | even | 6 | inner | ||
504.3.l.a.181.1 | 2 | 21.5 | even | 6 | |||
504.3.l.a.181.1 | 2 | 168.149 | odd | 6 | |||
504.3.l.a.181.2 | 2 | 21.2 | odd | 6 | |||
504.3.l.a.181.2 | 2 | 168.5 | even | 6 | |||
2016.3.l.c.433.1 | 2 | 84.47 | odd | 6 | |||
2016.3.l.c.433.1 | 2 | 168.107 | even | 6 | |||
2016.3.l.c.433.2 | 2 | 84.23 | even | 6 | |||
2016.3.l.c.433.2 | 2 | 168.131 | odd | 6 |