Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [979,1,Mod(10,979)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(979, base_ring=CyclotomicField(44))
chi = DirichletCharacter(H, H._module([22, 43]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("979.10");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 979 = 11 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 979.v (of order \(44\), degree \(20\), 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: | \(0.488584647368\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\Q(\zeta_{44})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{44}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{44} - \cdots)\) |
Embedding invariants
Embedding label | 780.1 | ||
Root | \(-0.540641 - 0.841254i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 979.780 |
Dual form | 979.1.v.a.428.1 |
$q$-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 \(\left(\mathbb{Z}/979\mathbb{Z}\right)^\times\).
\(n\) | \(90\) | \(804\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{19}{44}\right)\) |
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 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(3\) | −0.415415 | − | 1.90963i | −0.415415 | − | 1.90963i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(4\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(5\) | 1.27155 | + | 1.10181i | 1.27155 | + | 1.10181i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.997452 | − | 0.0713392i | \(-0.0227273\pi\) | ||||
−0.997452 | + | 0.0713392i | \(0.977273\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.56449 | + | 1.17116i | −2.56449 | + | 1.17116i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(12\) | −1.38189 | − | 1.38189i | −1.38189 | − | 1.38189i | ||||
\(13\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.57582 | − | 2.88591i | 1.57582 | − | 2.88591i | ||||
\(16\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(17\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(20\) | 1.66538 | + | 0.239446i | 1.66538 | + | 0.239446i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.0498610 | + | 0.133682i | −0.0498610 | + | 0.133682i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.260554 | + | 1.81219i | 0.260554 | + | 1.81219i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13066 | + | 2.84623i | 2.13066 | + | 2.84623i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) | ||||
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.613435 | − | 1.64468i | −0.613435 | − | 1.64468i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.17116 | + | 1.56449i | −1.17116 | + | 1.56449i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.52421 | + | 2.37172i | −1.52421 | + | 2.37172i | ||||
\(37\) | −0.300613 | + | 0.300613i | −0.300613 | + | 0.300613i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.977147 | − | 0.212565i | \(-0.931818\pi\) | ||||
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(44\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(45\) | −4.55129 | − | 1.33638i | −4.55129 | − | 1.33638i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.07028 | + | 1.66538i | 1.07028 | + | 1.66538i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(48\) | −1.90963 | − | 0.415415i | −1.90963 | − | 0.415415i | ||||
\(49\) | 0.989821 | − | 0.142315i | 0.989821 | − | 0.142315i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.708089 | + | 1.10181i | −0.708089 | + | 1.10181i | 0.281733 | + | 0.959493i | \(0.409091\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.68251i | − | 1.68251i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.148568 | + | 0.682956i | −0.148568 | + | 0.682956i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(60\) | −0.234571 | − | 3.27974i | −0.234571 | − | 3.27974i | ||||
\(61\) | 0 | 0 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.474017 | + | 0.304632i | 0.474017 | + | 0.304632i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.275997 | + | 0.0396824i | 0.275997 | + | 0.0396824i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.45027 | + | 1.25667i | −1.45027 | + | 1.25667i | −0.540641 | + | 0.841254i | \(0.681818\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.35239 | − | 1.25038i | 3.35239 | − | 1.25038i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(80\) | 1.53046 | − | 0.698939i | 1.53046 | − | 0.698939i | ||||
\(81\) | 2.70391 | − | 3.12048i | 2.70391 | − | 3.12048i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.479249 | − | 0.877679i | \(-0.659091\pi\) | ||||
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.0303285 | + | 0.139418i | 0.0303285 | + | 0.139418i | ||||
\(93\) | −2.88591 | + | 1.85466i | −2.88591 | + | 1.85466i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.989821 | + | 1.14231i | −0.989821 | + | 1.14231i | 1.00000i | \(0.5\pi\) | ||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.56449 | + | 1.17116i | 2.56449 | + | 1.17116i | ||||
\(100\) | 1.19894 | + | 1.38365i | 1.19894 | + | 1.38365i | ||||
\(101\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.64468 | + | 0.613435i | −1.64468 | + | 0.613435i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(108\) | 3.33121 | + | 1.24248i | 3.33121 | + | 1.24248i | ||||
\(109\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.125226 | + | 0.0683785i | 0.125226 | + | 0.0683785i | 0.540641 | − | 0.841254i | \(-0.318182\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.210693 | + | 0.115047i | −0.210693 | + | 0.115047i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.40524 | − | 1.05195i | −1.40524 | − | 1.05195i | ||||
\(125\) | −0.755750 | + | 1.17597i | −0.755750 | + | 1.17597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(132\) | −0.139418 | + | 1.94931i | −0.139418 | + | 1.94931i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.426747 | + | 5.96670i | −0.426747 | + | 5.96670i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.56449 | + | 0.340335i | 1.56449 | + | 0.340335i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.73566 | − | 2.73566i | 2.73566 | − | 2.73566i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.81926i | 2.81926i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.682956 | − | 1.83107i | −0.682956 | − | 1.83107i | ||||
\(148\) | −0.0903680 | + | 0.415415i | −0.0903680 | + | 0.415415i | ||||
\(149\) | 0 | 0 | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) | ||||
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.03211 | − | 2.76719i | 1.03211 | − | 2.76719i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.304632 | − | 1.03748i | −0.304632 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.39820 | + | 0.894482i | 2.39820 | + | 0.894482i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.677760 | − | 1.24123i | 0.677760 | − | 1.24123i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.21297 | + | 0.698939i | −3.21297 | + | 0.698939i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.909632 | − | 0.415415i | 0.909632 | − | 0.415415i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(177\) | 1.36591 | 1.36591 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.08128 | −1.08128 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(180\) | −4.55129 | + | 1.33638i | −4.55129 | + | 1.33638i | ||||
\(181\) | −0.424047 | − | 1.94931i | −0.424047 | − | 1.94931i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.713463 | + | 0.0510279i | −0.713463 | + | 0.0510279i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.80075 | + | 0.822373i | 1.80075 | + | 0.822373i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.17116 | − | 0.254771i | 1.17116 | − | 0.254771i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(192\) | −1.83107 | + | 0.682956i | −1.83107 | + | 0.682956i | ||||
\(193\) | 0 | 0 | 0.479249 | − | 0.877679i | \(-0.340909\pi\) | ||||
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.755750 | − | 0.654861i | 0.755750 | − | 0.654861i | ||||
\(197\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.234072 | + | 0.797176i | 0.234072 | + | 0.797176i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.384822 | − | 1.03175i | 0.384822 | − | 1.03175i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.0286960 | − | 0.401223i | −0.0286960 | − | 0.401223i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(212\) | 1.30972i | 1.30972i | ||||||||
\(213\) | 3.00224 | + | 2.24745i | 3.00224 | + | 2.24745i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.909632 | − | 1.41542i | −0.909632 | − | 1.41542i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.79057 | − | 4.34221i | −2.79057 | − | 4.34221i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.86912 | − | 0.133682i | −1.86912 | − | 0.133682i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.474017 | + | 3.29686i | −0.474017 | + | 3.29686i | ||||
\(236\) | 0.244250 | + | 0.654861i | 0.244250 | + | 0.654861i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.800541 | − | 0.599278i | \(-0.204545\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(240\) | −1.97049 | − | 2.63227i | −1.97049 | − | 2.63227i | ||||
\(241\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.96173 | − | 2.16327i | −3.96173 | − | 2.16327i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.133682 | − | 0.0498610i | 0.133682 | − | 0.0498610i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(257\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.11435 | + | 0.620830i | −2.11435 | + | 0.620830i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.71524 | − | 0.936593i | −1.71524 | − | 0.936593i | ||||
\(268\) | 0.563465 | 0.563465 | ||||||||
\(269\) | −1.25667 | + | 0.368991i | −1.25667 | + | 0.368991i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.19894 | − | 1.38365i | 1.19894 | − | 1.38365i | ||||
\(276\) | 0.253638 | − | 0.115832i | 0.253638 | − | 0.115832i | ||||
\(277\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.49934 | + | 3.49934i | 3.49934 | + | 3.49934i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.936950 | − | 0.349464i | \(-0.113636\pi\) | ||||
−0.936950 | + | 0.349464i | \(0.886364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(284\) | −0.540641 | + | 1.84125i | −0.540641 | + | 1.84125i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.59259 | + | 1.41566i | 2.59259 | + | 1.41566i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.941398 | + | 0.704722i | −0.941398 | + | 0.704722i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.755750 | − | 3.47412i | 0.755750 | − | 3.47412i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.14420 | − | 2.86432i | 2.14420 | − | 2.86432i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.85466 | + | 2.88591i | 1.85466 | + | 2.88591i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.45027 | − | 0.425839i | −1.45027 | − | 0.425839i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.142315 | − | 1.98982i | 0.142315 | − | 1.98982i | − | 1.00000i | \(-0.5\pi\) | |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.909632 | − | 1.41542i | 0.909632 | − | 1.41542i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.587616 | − | 4.08696i | 0.587616 | − | 4.08696i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0801894 | + | 0.557730i | 0.0801894 | + | 0.557730i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.418852 | − | 1.12299i | 0.418852 | − | 1.12299i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.267092 | + | 0.909632i | 0.267092 | + | 0.909632i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.936950 | − | 0.349464i | \(-0.886364\pi\) | ||||
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.0785570 | − | 0.267541i | 0.0785570 | − | 0.267541i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.841254 | + | 1.54064i | −0.841254 | + | 1.54064i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.307223 | + | 0.354554i | 0.307223 | + | 0.354554i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.997452 | − | 0.0713392i | \(-0.0227273\pi\) | ||||
−0.997452 | + | 0.0713392i | \(0.977273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.254771 | + | 1.17116i | 0.254771 | + | 1.17116i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.22871 | −3.22871 | ||||||||
\(356\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.212565 | − | 0.977147i | \(-0.568182\pi\) | ||||
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.755750 | + | 0.654861i | 0.755750 | + | 0.654861i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94931 | − | 0.139418i | 1.94931 | − | 0.139418i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(368\) | 0.100889 | + | 0.100889i | 0.100889 | + | 0.100889i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.42508 | + | 3.12048i | −1.42508 | + | 3.12048i | ||||
\(373\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.55962 | + | 0.954688i | 2.55962 | + | 0.954688i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.418852 | − | 1.12299i | 0.418852 | − | 1.12299i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.12299 | − | 1.50013i | −1.12299 | − | 1.50013i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
−0.281733 | − | 0.959493i | \(-0.590909\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.215109 | + | 1.49611i | −0.215109 | + | 1.49611i | ||||
\(389\) | 0.574406 | − | 0.767317i | 0.574406 | − | 0.767317i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.79057 | − | 0.401223i | 2.79057 | − | 0.401223i | ||||
\(397\) | −0.682956 | − | 0.148568i | −0.682956 | − | 0.148568i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.75667 | + | 0.515804i | 1.75667 | + | 0.515804i | ||||
\(401\) | 1.61435 | + | 0.474017i | 1.61435 | + | 0.474017i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.87634 | − | 0.988668i | 6.87634 | − | 0.988668i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.424047 | + | 0.0303285i | 0.424047 | + | 0.0303285i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 3.12899i | − | 3.12899i | ||||||
\(412\) | −1.05195 | + | 1.40524i | −1.05195 | + | 1.40524i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.75089 | + | 0.956056i | −1.75089 | + | 0.956056i | −0.841254 | + | 0.540641i | \(0.818182\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.841254 | + | 0.459359i | 0.841254 | + | 0.459359i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.69515 | − | 3.01739i | −4.69515 | − | 3.01739i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.936950 | − | 0.349464i | \(-0.113636\pi\) | ||||
−0.936950 | + | 0.349464i | \(0.886364\pi\) | |||||||
\(432\) | 3.47412 | − | 0.755750i | 3.47412 | − | 0.755750i | ||||
\(433\) | 0.494217 | + | 0.494217i | 0.494217 | + | 0.494217i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.479249 | − | 0.877679i | \(-0.659091\pi\) | ||||
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.37172 | + | 1.52421i | −2.37172 | + | 1.52421i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(444\) | 0.830830 | 0.830830 | ||||||||
\(445\) | 1.66538 | − | 0.239446i | 1.66538 | − | 0.239446i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.142315 | − | 0.0101786i | 0.142315 | − | 0.0101786i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.115047 | + | 0.210693i | −0.115047 | + | 0.210693i | ||||
\(461\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.989821 | + | 0.857685i | −0.989821 | + | 0.857685i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.71307 | − | 0.821415i | −5.71307 | − | 0.821415i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.474017 | − | 0.304632i | −0.474017 | − | 0.304632i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.85466 | + | 1.01272i | −1.85466 | + | 1.01272i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.525491 | − | 3.65487i | 0.525491 | − | 3.65487i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(485\) | −2.51722 | + | 0.361922i | −2.51722 | + | 0.361922i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.584585 | + | 0.909632i | 0.584585 | + | 0.909632i | 1.00000 | \(0\) | ||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.65184 | − | 0.778649i | −2.65184 | − | 0.778649i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) | ||||
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.97049 | + | 4.31478i | 1.97049 | + | 4.31478i | ||||
\(496\) | −1.75089 | − | 0.125226i | −1.75089 | − | 0.125226i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.559521 | − | 0.418852i | −0.559521 | − | 0.418852i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(500\) | 1.39788i | 1.39788i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.17116 | − | 1.56449i | −1.17116 | − | 1.56449i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.153882 | − | 1.07028i | −0.153882 | − | 1.07028i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.755750 | − | 0.654861i | \(-0.227273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.76719 | − | 1.03211i | −2.76719 | − | 1.03211i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.557730 | − | 1.89945i | 0.557730 | − | 1.89945i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.415415 | − | 0.0903680i | 0.415415 | − | 0.0903680i | − | 1.00000i | \(-0.5\pi\) | |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.936593 | + | 1.71524i | 0.936593 | + | 1.71524i | ||||
\(529\) | 0.740365 | + | 0.641530i | 0.740365 | + | 0.641530i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.418852 | − | 1.92543i | −0.418852 | − | 1.92543i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.449181 | + | 2.06485i | 0.449181 | + | 2.06485i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.755750 | − | 0.654861i | −0.755750 | − | 0.654861i | ||||
\(540\) | 2.86684 | + | 5.25023i | 2.86684 | + | 5.25023i | ||||
\(541\) | 0 | 0 | 0.997452 | − | 0.0713392i | \(-0.0227273\pi\) | ||||
−0.997452 | + | 0.0713392i | \(0.977273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.54632 | + | 1.61955i | −3.54632 | + | 1.61955i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(548\) | 1.50013 | − | 0.559521i | 1.50013 | − | 0.559521i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.393828 | + | 1.34125i | 0.393828 | + | 1.34125i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.349464 | − | 0.936950i | \(-0.386364\pi\) | ||||
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) | ||||
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(564\) | 0.822373 | − | 3.78039i | 0.822373 | − | 3.78039i | ||||
\(565\) | 0.0838914 | + | 0.224922i | 0.0838914 | + | 0.224922i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.973039 | − | 2.13066i | −0.973039 | − | 2.13066i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.255250 | − | 0.0555263i | −0.255250 | − | 0.0555263i | ||||
\(576\) | 1.52421 | + | 2.37172i | 1.52421 | + | 2.37172i | ||||
\(577\) | −0.0683785 | + | 0.956056i | −0.0683785 | + | 0.956056i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.29639 | − | 0.186393i | 1.29639 | − | 0.186393i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.817178 | − | 1.27155i | 0.817178 | − | 1.27155i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(588\) | −1.56449 | − | 1.17116i | −1.56449 | − | 1.17116i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.148568 | + | 0.398326i | 0.148568 | + | 0.398326i | ||||
\(593\) | 0 | 0 | 0.212565 | − | 0.977147i | \(-0.431818\pi\) | ||||
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.42508 | − | 0.778150i | 1.42508 | − | 0.778150i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.373128 | + | 0.203743i | 0.373128 | + | 0.203743i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.57239 | − | 0.226075i | −1.57239 | − | 0.226075i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.27155 | + | 1.10181i | −1.27155 | + | 1.10181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.574406 | − | 1.05195i | −0.574406 | − | 1.05195i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.66538 | − | 1.07028i | 1.66538 | − | 1.07028i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(620\) | −0.627791 | − | 2.88591i | −0.627791 | − | 2.88591i | ||||
\(621\) | −0.486727 | + | 0.142916i | −0.486727 | + | 0.142916i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.146813i | −0.500000 | + | 0.146813i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.817178 | − | 0.708089i | −0.817178 | − | 0.708089i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.50109 | − | 0.544078i | 2.50109 | − | 0.544078i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.24745 | − | 4.92123i | 2.24745 | − | 4.92123i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.14231 | + | 0.989821i | −1.14231 | + | 0.989821i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.89945 | + | 0.273100i | 1.89945 | + | 0.273100i | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.64468 | − | 0.898064i | −1.64468 | − | 0.898064i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.613435 | − | 0.334961i | 0.613435 | − | 0.334961i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.100889 | − | 1.41061i | −0.100889 | − | 1.41061i | ||||
\(653\) | −0.424047 | + | 1.94931i | −0.424047 | + | 1.94931i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(660\) | −2.32505 | + | 2.32505i | −2.32505 | + | 2.32505i | ||||
\(661\) | 1.94931 | + | 0.139418i | 1.94931 | + | 0.139418i | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.60276 | + | 4.60276i | −4.60276 | + | 4.60276i | ||||
\(676\) | 0.540641 | − | 0.841254i | 0.540641 | − | 0.841254i | ||||
\(677\) | 0 | 0 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.139418 | + | 1.94931i | 0.139418 | + | 1.94931i | 0.281733 | + | 0.959493i | \(0.409091\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.61435 | + | 2.15652i | 1.61435 | + | 2.15652i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.521178 | + | 3.62487i | 0.521178 | + | 3.62487i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.557730 | + | 1.89945i | 0.557730 | + | 1.89945i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(705\) | 6.49270 | − | 0.464367i | 6.49270 | − | 0.464367i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.14908 | − | 0.738467i | 1.14908 | − | 0.738467i | ||||
\(709\) | −0.340335 | − | 1.56449i | −0.340335 | − | 1.56449i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.250452 | 0.250452 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.909632 | + | 0.584585i | −0.909632 | + | 0.584585i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.75089 | + | 0.125226i | −1.75089 | + | 0.125226i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(720\) | −3.10629 | + | 3.58485i | −3.10629 | + | 3.58485i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.41061 | − | 1.41061i | −1.41061 | − | 1.41061i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.956056 | + | 1.75089i | −0.956056 | + | 1.75089i | −0.415415 | + | 0.909632i | \(0.636364\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.32202 | + | 4.50237i | −1.32202 | + | 4.50237i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.14908 | − | 3.08080i | 1.14908 | − | 3.08080i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0801894 | − | 0.557730i | −0.0801894 | − | 0.557730i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(740\) | −0.572615 | + | 0.428654i | −0.572615 | + | 0.428654i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.349464 | − | 0.936950i | \(-0.613636\pi\) | ||||
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.118239 | − | 0.258908i | −0.118239 | − | 0.258908i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(752\) | 1.95949 | − | 0.281733i | 1.95949 | − | 0.281733i | ||||
\(753\) | −3.66456 | − | 0.797176i | −3.66456 | − | 0.797176i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.540641 | + | 0.158746i | 0.540641 | + | 0.158746i | 0.540641 | − | 0.841254i | \(-0.318182\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.150750 | − | 0.234571i | −0.150750 | − | 0.234571i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.847507 | − | 0.847507i | 0.847507 | − | 0.847507i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.17116 | + | 1.56449i | −1.17116 | + | 1.56449i | ||||
\(769\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.755750 | + | 3.47412i | −0.755750 | + | 3.47412i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.767317 | + | 0.574406i | −0.767317 | + | 0.574406i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.82065 | − | 1.54019i | 2.82065 | − | 1.54019i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.89945 | + | 0.273100i | 1.89945 | + | 0.273100i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.281733 | − | 0.959493i | 0.281733 | − | 0.959493i | ||||
\(785\) | 0.755750 | − | 1.65486i | 0.755750 | − | 1.65486i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.936950 | − | 0.349464i | \(-0.113636\pi\) | ||||
−0.936950 | + | 0.349464i | \(0.886364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.06389 | + | 3.77974i | 2.06389 | + | 3.77974i | ||||
\(796\) | 0.627899 | + | 0.544078i | 0.627899 | + | 0.544078i | ||||
\(797\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
1.00000 | \(0\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.794278 | + | 2.70506i | −0.794278 | + | 2.70506i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.234072 | − | 1.07601i | −0.234072 | − | 1.07601i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.22668 | + | 2.24649i | 1.22668 | + | 2.24649i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.22940 | − | 0.831524i | 2.22940 | − | 0.831524i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.909632 | − | 0.584585i | −0.909632 | − | 0.584585i | − | 1.00000i | \(-0.5\pi\) | |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.14032 | − | 1.71474i | −3.14032 | − | 1.71474i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(828\) | −0.241058 | − | 0.322016i | −0.241058 | − | 0.322016i | ||||
\(829\) | 1.28173 | − | 0.959493i | 1.28173 | − | 0.959493i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
1.00000 | \(0\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.37412 | − | 5.25023i | 3.37412 | − | 5.25023i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.59700 | − | 0.114220i | −1.59700 | − | 0.114220i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.989821 | + | 0.142315i | −0.989821 | + | 0.142315i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.61435 | + | 0.474017i | 1.61435 | + | 0.474017i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0.708089 | + | 1.10181i | 0.708089 | + | 1.10181i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0251978 | − | 0.0551755i | −0.0251978 | − | 0.0551755i | ||||
\(852\) | 3.74071 | + | 0.267541i | 3.74071 | + | 0.267541i | ||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.599278 | − | 0.800541i | \(-0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.148568 | − | 0.398326i | −0.148568 | − | 0.398326i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.05195 | + | 1.40524i | 1.05195 | + | 1.40524i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.682956 | + | 1.83107i | −0.682956 | + | 1.83107i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.20055 | − | 4.08870i | 1.20055 | − | 4.08870i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) | ||||
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.53046 | − | 0.698939i | −1.53046 | − | 0.698939i | ||||
\(881\) | 0.258908 | − | 0.118239i | 0.258908 | − | 0.118239i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.86912 | − | 0.133682i | 1.86912 | − | 0.133682i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.73683 | + | 1.50497i | 1.73683 | + | 1.50497i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.212565 | − | 0.977147i | \(-0.568182\pi\) | ||||
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.12899 | −4.12899 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.37491 | − | 1.19136i | −1.37491 | − | 1.19136i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −4.69515 | − | 2.14420i | −4.69515 | − | 2.14420i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.60857 | − | 2.94588i | 1.60857 | − | 2.94588i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0801894 | − | 0.273100i | 0.0801894 | − | 0.273100i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.234072 | − | 0.797176i | −0.234072 | − | 0.797176i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.755750 | − | 0.654861i | \(-0.227273\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.64468 | + | 0.898064i | −1.64468 | + | 0.898064i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) | ||||
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.623095 | − | 0.466443i | −0.623095 | − | 0.466443i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.49934 | − | 3.49934i | 3.49934 | − | 3.49934i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.822373 | + | 1.80075i | 0.822373 | + | 1.80075i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.210730 | + | 2.94639i | −0.210730 | + | 2.94639i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.85895 | + | 0.554833i | −3.85895 | + | 0.554833i | ||||
\(940\) | 1.38365 | + | 3.02977i | 1.38365 | + | 3.02977i | ||||
\(941\) | 0 | 0 | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) | ||||
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.559521 | + | 0.418852i | 0.559521 | + | 0.418852i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.118239 | − | 0.822373i | 0.118239 | − | 0.822373i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.445301 | + | 0.333348i | −0.445301 | + | 0.333348i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.76991 | + | 0.966443i | 1.76991 | + | 0.966443i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.08080 | − | 1.14908i | −3.08080 | − | 1.14908i | ||||
\(961\) | −1.57293 | + | 1.36295i | −1.57293 | + | 1.36295i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.989821 | − | 1.14231i | 0.989821 | − | 1.14231i | − | 1.00000i | \(-0.5\pi\) | |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(972\) | −4.50237 | + | 0.322016i | −4.50237 | + | 0.322016i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.00000 | −1.00000 | ||||||||
\(980\) | 1.68251 | 1.68251 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.10181 | − | 0.708089i | 1.10181 | − | 0.708089i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.38189 | + | 1.38189i | 1.38189 | + | 1.38189i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.03175 | − | 0.384822i | 1.03175 | − | 0.384822i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.580699 | + | 1.27155i | −0.580699 | + | 1.27155i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.49611 | − | 0.215109i | −1.49611 | − | 0.215109i |
(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 | 979.1.v.a.780.1 | yes | 20 | |
11.10 | odd | 2 | CM | 979.1.v.a.780.1 | yes | 20 | |
89.72 | even | 44 | inner | 979.1.v.a.428.1 | ✓ | 20 | |
979.428 | odd | 44 | inner | 979.1.v.a.428.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
979.1.v.a.428.1 | ✓ | 20 | 89.72 | even | 44 | inner | |
979.1.v.a.428.1 | ✓ | 20 | 979.428 | odd | 44 | inner | |
979.1.v.a.780.1 | yes | 20 | 1.1 | even | 1 | trivial | |
979.1.v.a.780.1 | yes | 20 | 11.10 | odd | 2 | CM |