Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1564,1,Mod(271,1564)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1564, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 11, 12]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1564.271");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1564 = 2^{2} \cdot 17 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1564.w (of order \(22\), degree \(10\), 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: | \(0.780537679758\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
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: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{22}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{22} - \cdots)\) |
Embedding invariants
Embedding label | 883.2 | ||
Root | \(0.281733 - 0.959493i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1564.883 |
Dual form | 1564.1.w.c.271.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1564\mathbb{Z}\right)^\times\).
\(n\) | \(783\) | \(921\) | \(1293\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{11}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(3\) | 1.19136 | + | 1.37491i | 1.19136 | + | 1.37491i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(4\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(5\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(6\) | 1.53046 | + | 0.983568i | 1.53046 | + | 0.983568i | ||||
\(7\) | −0.449181 | + | 0.983568i | −0.449181 | + | 0.983568i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(8\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(9\) | −0.328708 | + | 2.28621i | −0.328708 | + | 2.28621i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.45027 | − | 0.425839i | −1.45027 | − | 0.425839i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(12\) | 1.74557 | + | 0.512546i | 1.74557 | + | 0.512546i | ||||
\(13\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(14\) | −0.153882 | + | 1.07028i | −0.153882 | + | 1.07028i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(17\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(18\) | 0.328708 | + | 2.28621i | 0.328708 | + | 2.28621i | ||||
\(19\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.88745 | + | 0.554206i | −1.88745 | + | 0.554206i | ||||
\(22\) | −1.51150 | −1.51150 | ||||||||
\(23\) | 0.540641 | − | 0.841254i | 0.540641 | − | 0.841254i | ||||
\(24\) | 1.81926 | 1.81926 | ||||||||
\(25\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(26\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(27\) | −2.00448 | + | 1.28820i | −2.00448 | + | 1.28820i | ||||
\(28\) | 0.153882 | + | 1.07028i | 0.153882 | + | 1.07028i | ||||
\(29\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.989821 | − | 1.14231i | 0.989821 | − | 1.14231i | − | 1.00000i | \(-0.5\pi\) | |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(32\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(33\) | −1.14231 | − | 2.50132i | −1.14231 | − | 2.50132i | ||||
\(34\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.959493 | + | 2.10100i | 0.959493 | + | 2.10100i | ||||
\(37\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.27155 | − | 2.78431i | 1.27155 | − | 2.78431i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(42\) | −1.65486 | + | 1.06351i | −1.65486 | + | 1.06351i | ||||
\(43\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(44\) | −1.45027 | + | 0.425839i | −1.45027 | + | 0.425839i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.281733 | − | 0.959493i | 0.281733 | − | 0.959493i | ||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 1.74557 | − | 0.512546i | 1.74557 | − | 0.512546i | ||||
\(49\) | −0.110783 | − | 0.127850i | −0.110783 | − | 0.127850i | ||||
\(50\) | −0.841254 | + | 0.540641i | −0.841254 | + | 0.540641i | ||||
\(51\) | 0.258908 | + | 1.80075i | 0.258908 | + | 1.80075i | ||||
\(52\) | −1.41542 | − | 0.909632i | −1.41542 | − | 0.909632i | ||||
\(53\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(54\) | −1.56036 | + | 1.80075i | −1.56036 | + | 1.80075i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.449181 | + | 0.983568i | 0.449181 | + | 0.983568i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(62\) | 0.627899 | − | 1.37491i | 0.627899 | − | 1.37491i | ||||
\(63\) | −2.10100 | − | 1.35023i | −2.10100 | − | 1.35023i | ||||
\(64\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.80075 | − | 2.07817i | −1.80075 | − | 2.07817i | ||||
\(67\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(68\) | 1.00000 | 1.00000 | ||||||||
\(69\) | 1.80075 | − | 0.258908i | 1.80075 | − | 0.258908i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(72\) | 1.51255 | + | 1.74557i | 1.51255 | + | 1.74557i | ||||
\(73\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.53046 | − | 0.983568i | −1.53046 | − | 0.983568i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.07028 | − | 1.23516i | 1.07028 | − | 1.23516i | ||||
\(78\) | 0.435615 | − | 3.02977i | 0.435615 | − | 3.02977i | ||||
\(79\) | −0.234072 | − | 0.512546i | −0.234072 | − | 0.512546i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.94306 | − | 0.570534i | −1.94306 | − | 0.570534i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(84\) | −1.28820 | + | 1.48666i | −1.28820 | + | 1.48666i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.27155 | + | 0.817178i | −1.27155 | + | 0.817178i | ||||
\(89\) | −0.857685 | − | 0.989821i | −0.857685 | − | 0.989821i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.81926 | 1.81926 | ||||||||
\(92\) | − | 1.00000i | − | 1.00000i | ||||||
\(93\) | 2.74982 | 2.74982 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.53046 | − | 0.983568i | 1.53046 | − | 0.983568i | ||||
\(97\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(98\) | −0.142315 | − | 0.0914602i | −0.142315 | − | 0.0914602i | ||||
\(99\) | 1.45027 | − | 3.17565i | 1.45027 | − | 3.17565i | ||||
\(100\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(101\) | −0.273100 | + | 1.89945i | −0.273100 | + | 1.89945i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(102\) | 0.755750 | + | 1.65486i | 0.755750 | + | 1.65486i | ||||
\(103\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(104\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.186393 | + | 1.29639i | −0.186393 | + | 1.29639i | ||||
\(107\) | −1.29639 | + | 1.49611i | −1.29639 | + | 1.49611i | −0.540641 | + | 0.841254i | \(0.681818\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(108\) | −0.989821 | + | 2.16741i | −0.989821 | + | 2.16741i | ||||
\(109\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.708089 | + | 0.817178i | 0.708089 | + | 0.817178i | ||||
\(113\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.72871 | − | 1.09485i | 3.72871 | − | 1.09485i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.909632 | + | 0.584585i | −0.909632 | + | 0.584585i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.08070 | + | 0.694523i | 1.08070 | + | 0.694523i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.215109 | − | 1.49611i | 0.215109 | − | 1.49611i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.39629 | − | 0.703616i | −2.39629 | − | 0.703616i | ||||
\(127\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(128\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.822373 | + | 1.80075i | −0.822373 | + | 1.80075i | −0.281733 | + | 0.959493i | \(0.590909\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(132\) | −2.31329 | − | 1.48666i | −2.31329 | − | 1.48666i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(137\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(138\) | 1.65486 | − | 0.755750i | 1.65486 | − | 0.755750i | ||||
\(139\) | −1.97964 | −1.97964 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.361922 | + | 2.51722i | 0.361922 | + | 2.51722i | ||||
\(144\) | 1.94306 | + | 1.24873i | 1.94306 | + | 1.24873i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.0437995 | − | 0.304632i | 0.0437995 | − | 0.304632i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(150\) | −1.74557 | − | 0.512546i | −1.74557 | − | 0.512546i | ||||
\(151\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.51255 | + | 1.74557i | −1.51255 | + | 1.74557i | ||||
\(154\) | 0.678936 | − | 1.48666i | 0.678936 | − | 1.48666i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.435615 | − | 3.02977i | −0.435615 | − | 3.02977i | ||||
\(157\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(158\) | −0.368991 | − | 0.425839i | −0.368991 | − | 0.425839i | ||||
\(159\) | −2.28621 | + | 0.671292i | −2.28621 | + | 0.671292i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.584585 | + | 0.909632i | 0.584585 | + | 0.909632i | ||||
\(162\) | −2.02509 | −2.02509 | ||||||||
\(163\) | 1.03748 | − | 0.304632i | 1.03748 | − | 0.304632i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.474017 | + | 0.304632i | 0.474017 | + | 0.304632i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(168\) | −0.817178 | + | 1.78937i | −0.817178 | + | 1.78937i | ||||
\(169\) | −1.19894 | + | 1.38365i | −1.19894 | + | 1.38365i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.153882 | − | 1.07028i | 0.153882 | − | 1.07028i | ||||
\(176\) | −0.989821 | + | 1.14231i | −0.989821 | + | 1.14231i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | ||||
\(179\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(182\) | 1.74557 | − | 0.512546i | 1.74557 | − | 0.512546i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.281733 | − | 0.959493i | −0.281733 | − | 0.959493i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.63843 | − | 0.774713i | 2.63843 | − | 0.774713i | ||||
\(187\) | −0.989821 | − | 1.14231i | −0.989821 | − | 1.14231i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.366660 | − | 2.55018i | −0.366660 | − | 2.55018i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(192\) | 1.19136 | − | 1.37491i | 1.19136 | − | 1.37491i | ||||
\(193\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.162317 | − | 0.0476607i | −0.162317 | − | 0.0476607i | ||||
\(197\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(198\) | 0.496841 | − | 3.45561i | 0.496841 | − | 3.45561i | ||||
\(199\) | 1.19136 | − | 1.37491i | 1.19136 | − | 1.37491i | 0.281733 | − | 0.959493i | \(-0.409091\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(200\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.19136 | + | 1.37491i | 1.19136 | + | 1.37491i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.74557 | + | 1.51255i | 1.74557 | + | 1.51255i | ||||
\(208\) | −1.68251 | −1.68251 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.474017 | − | 0.304632i | 0.474017 | − | 0.304632i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(212\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.822373 | + | 1.80075i | −0.822373 | + | 1.80075i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.339098 | + | 2.35848i | −0.339098 | + | 2.35848i | ||||
\(217\) | 0.678936 | + | 1.48666i | 0.678936 | + | 1.48666i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.239446 | − | 1.66538i | 0.239446 | − | 1.66538i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(224\) | 0.909632 | + | 0.584585i | 0.909632 | + | 0.584585i | ||||
\(225\) | −0.328708 | − | 2.28621i | −0.328708 | − | 2.28621i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.19136 | − | 1.37491i | −1.19136 | − | 1.37491i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.281733 | − | 0.959493i | \(-0.590909\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.97333 | 2.97333 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(234\) | 3.26921 | − | 2.10100i | 3.26921 | − | 2.10100i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.425839 | − | 0.932456i | 0.425839 | − | 0.932456i | ||||
\(238\) | −0.708089 | + | 0.817178i | −0.708089 | + | 0.817178i | ||||
\(239\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(242\) | 1.23259 | + | 0.361922i | 1.23259 | + | 0.361922i | ||||
\(243\) | −0.540641 | − | 1.18384i | −0.540641 | − | 1.18384i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.215109 | − | 1.49611i | −0.215109 | − | 1.49611i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(252\) | −2.49746 | −2.49746 | ||||||||
\(253\) | −1.14231 | + | 0.989821i | −1.14231 | + | 0.989821i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(257\) | −0.698939 | + | 0.449181i | −0.698939 | + | 0.449181i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.281733 | + | 1.95949i | −0.281733 | + | 1.95949i | ||||
\(263\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(264\) | −2.63843 | − | 0.774713i | −2.63843 | − | 0.774713i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.339098 | − | 2.35848i | 0.339098 | − | 2.35848i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(272\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(273\) | 2.16741 | + | 2.50132i | 2.16741 | + | 2.50132i | ||||
\(274\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(275\) | 1.51150 | 1.51150 | ||||||||
\(276\) | 1.37491 | − | 1.19136i | 1.37491 | − | 1.19136i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | −1.89945 | + | 0.557730i | −1.89945 | + | 0.557730i | ||||
\(279\) | 2.28621 | + | 2.63843i | 2.28621 | + | 2.63843i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | 1.00000 | \(0\) | ||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.234072 | − | 0.512546i | 0.234072 | − | 0.512546i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.05645 | + | 2.31329i | 1.05645 | + | 2.31329i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.21616 | + | 0.650724i | 2.21616 | + | 0.650724i | ||||
\(289\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.61435 | − | 1.03748i | −1.61435 | − | 1.03748i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.654861 | − | 0.755750i | \(-0.727273\pi\) | |||||||
\(294\) | −0.0437995 | − | 0.304632i | −0.0437995 | − | 0.304632i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.45561 | − | 1.01466i | 3.45561 | − | 1.01466i | ||||
\(298\) | −0.830830 | −0.830830 | ||||||||
\(299\) | −1.66538 | − | 0.239446i | −1.66538 | − | 0.239446i | ||||
\(300\) | −1.81926 | −1.81926 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.93694 | + | 1.88745i | −2.93694 | + | 1.88745i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.959493 | + | 2.10100i | −0.959493 | + | 2.10100i | ||||
\(307\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(308\) | 0.232593 | − | 1.61772i | 0.232593 | − | 1.61772i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.03748 | − | 0.304632i | −1.03748 | − | 0.304632i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(312\) | −1.27155 | − | 2.78431i | −1.27155 | − | 2.78431i | ||||
\(313\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(314\) | 0.544078 | − | 0.627899i | 0.544078 | − | 0.627899i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.474017 | − | 0.304632i | −0.474017 | − | 0.304632i | ||||
\(317\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(318\) | −2.00448 | + | 1.28820i | −2.00448 | + | 1.28820i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.60149 | −3.60149 | ||||||||
\(322\) | 0.817178 | + | 0.708089i | 0.817178 | + | 0.708089i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.94306 | + | 0.570534i | −1.94306 | + | 0.570534i | ||||
\(325\) | 1.10181 | + | 1.27155i | 1.10181 | + | 1.27155i | ||||
\(326\) | 0.909632 | − | 0.584585i | 0.909632 | − | 0.584585i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.540641 | + | 0.158746i | 0.540641 | + | 0.158746i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.279953 | + | 1.94711i | −0.279953 | + | 1.94711i | ||||
\(337\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(338\) | −0.760554 | + | 1.66538i | −0.760554 | + | 1.66538i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.92195 | + | 1.23516i | −1.92195 | + | 1.23516i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.861971 | + | 0.253098i | −0.861971 | + | 0.253098i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.45027 | − | 0.425839i | 1.45027 | − | 0.425839i | 0.540641 | − | 0.841254i | \(-0.318182\pi\) |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.41542 | − | 0.909632i | 1.41542 | − | 0.909632i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
1.00000 | \(0\) | |||||||||
\(350\) | −0.153882 | − | 1.07028i | −0.153882 | − | 1.07028i | ||||
\(351\) | 3.37255 | + | 2.16741i | 3.37255 | + | 2.16741i | ||||
\(352\) | −0.627899 | + | 1.37491i | −0.627899 | + | 1.37491i | ||||
\(353\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.25667 | − | 0.368991i | −1.25667 | − | 0.368991i | ||||
\(357\) | −1.88745 | − | 0.554206i | −1.88745 | − | 0.554206i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.332601 | + | 2.31329i | 0.332601 | + | 2.31329i | ||||
\(364\) | 1.53046 | − | 0.983568i | 1.53046 | − | 0.983568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.97964 | 1.97964 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(368\) | −0.540641 | − | 0.841254i | −0.540641 | − | 0.841254i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.927399 | − | 1.07028i | −0.927399 | − | 1.07028i | ||||
\(372\) | 2.31329 | − | 1.48666i | 2.31329 | − | 1.48666i | ||||
\(373\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(374\) | −1.27155 | − | 0.817178i | −1.27155 | − | 0.817178i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.07028 | − | 2.34358i | −1.07028 | − | 2.34358i | ||||
\(379\) | 1.89945 | + | 0.557730i | 1.89945 | + | 0.557730i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(384\) | 0.755750 | − | 1.65486i | 0.755750 | − | 1.65486i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.797176 | − | 0.234072i | 0.797176 | − | 0.234072i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.909632 | − | 0.415415i | 0.909632 | − | 0.415415i | ||||
\(392\) | −0.169170 | −0.169170 | ||||||||
\(393\) | −3.45561 | + | 1.01466i | −3.45561 | + | 1.01466i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.496841 | − | 3.45561i | −0.496841 | − | 3.45561i | ||||
\(397\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(398\) | 0.755750 | − | 1.65486i | 0.755750 | − | 1.65486i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(401\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.44009 | − | 0.716476i | −2.44009 | − | 0.716476i | ||||
\(404\) | 0.797176 | + | 1.74557i | 0.797176 | + | 1.74557i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.53046 | + | 0.983568i | 1.53046 | + | 0.983568i | ||||
\(409\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.28621 | + | 2.63843i | 2.28621 | + | 2.63843i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.10100 | + | 0.959493i | 2.10100 | + | 0.959493i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(417\) | −2.35848 | − | 2.72183i | −2.35848 | − | 2.72183i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.215109 | + | 1.49611i | 0.215109 | + | 1.49611i | 0.755750 | + | 0.654861i | \(0.227273\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.345139 | + | 0.755750i | −0.345139 | + | 0.755750i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0.368991 | − | 0.425839i | 0.368991 | − | 0.425839i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(425\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.281733 | + | 1.95949i | −0.281733 | + | 1.95949i | ||||
\(429\) | −3.02977 | + | 3.49654i | −3.02977 | + | 3.49654i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.53046 | + | 0.983568i | 1.53046 | + | 0.983568i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(432\) | 0.339098 | + | 2.35848i | 0.339098 | + | 2.35848i | ||||
\(433\) | 0.239446 | − | 0.153882i | 0.239446 | − | 0.153882i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(434\) | 1.07028 | + | 1.23516i | 1.07028 | + | 1.23516i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.45027 | + | 0.425839i | −1.45027 | + | 0.425839i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.328708 | − | 0.211248i | 0.328708 | − | 0.211248i | ||||
\(442\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(443\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.627899 | − | 1.37491i | −0.627899 | − | 1.37491i | ||||
\(448\) | 1.03748 | + | 0.304632i | 1.03748 | + | 0.304632i | ||||
\(449\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(450\) | −0.959493 | − | 2.10100i | −0.959493 | − | 2.10100i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.53046 | − | 0.983568i | −1.53046 | − | 0.983568i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.10181 | + | 1.27155i | 1.10181 | + | 1.27155i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(458\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(459\) | −2.38273 | −2.38273 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(462\) | 2.85288 | − | 0.837683i | 2.85288 | − | 0.837683i | ||||
\(463\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(468\) | 2.54487 | − | 2.93694i | 2.54487 | − | 2.93694i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.45027 | + | 0.425839i | 1.45027 | + | 0.425839i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.145886 | − | 1.01466i | 0.145886 | − | 1.01466i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −0.449181 | + | 0.983568i | −0.449181 | + | 0.983568i | ||||
\(477\) | −2.54487 | − | 1.63549i | −2.54487 | − | 1.63549i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.554206 | + | 1.88745i | −0.554206 | + | 1.88745i | ||||
\(484\) | 1.28463 | 1.28463 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.852267 | − | 0.983568i | −0.852267 | − | 0.983568i | ||||
\(487\) | 0.909632 | − | 0.584585i | 0.909632 | − | 0.584585i | − | 1.00000i | \(-0.5\pi\) | |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.65486 | + | 1.06351i | 1.65486 | + | 1.06351i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.627899 | − | 1.37491i | −0.627899 | − | 1.37491i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.449181 | + | 0.983568i | −0.449181 | + | 0.983568i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.145886 | + | 1.01466i | 0.145886 | + | 1.01466i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(504\) | −2.39629 | + | 0.703616i | −2.39629 | + | 0.703616i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.817178 | + | 1.27155i | −0.817178 | + | 1.27155i | ||||
\(507\) | −3.33076 | −3.33076 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | 1.00000 | \(0\) | ||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(524\) | 0.281733 | + | 1.95949i | 0.281733 | + | 1.95949i | ||||
\(525\) | 1.65486 | − | 1.06351i | 1.65486 | − | 1.06351i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.45027 | − | 0.425839i | 1.45027 | − | 0.425839i | ||||
\(528\) | −2.74982 | −2.74982 | ||||||||
\(529\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.339098 | − | 2.35848i | −0.339098 | − | 2.35848i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.106222 | + | 0.232593i | 0.106222 | + | 0.232593i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.78431 | + | 1.78937i | 2.78431 | + | 1.78937i | ||||
\(547\) | 0.0801894 | + | 0.557730i | 0.0801894 | + | 0.557730i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(548\) | 1.61435 | − | 1.03748i | 1.61435 | − | 1.03748i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.45027 | − | 0.425839i | 1.45027 | − | 0.425839i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.983568 | − | 1.53046i | 0.983568 | − | 1.53046i | ||||
\(553\) | 0.609264 | 0.609264 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.66538 | + | 1.07028i | −1.66538 | + | 1.07028i | ||||
\(557\) | −0.0405070 | − | 0.281733i | −0.0405070 | − | 0.281733i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(558\) | 2.93694 | + | 1.88745i | 2.93694 | + | 1.88745i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.391340 | − | 2.72183i | 0.391340 | − | 2.72183i | ||||
\(562\) | 0.118239 | + | 0.258908i | 0.118239 | + | 0.258908i | ||||
\(563\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.0801894 | − | 0.557730i | 0.0801894 | − | 0.557730i | ||||
\(567\) | 1.43394 | − | 1.65486i | 1.43394 | − | 1.65486i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.698939 | + | 0.449181i | 0.698939 | + | 0.449181i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.474017 | − | 0.304632i | 0.474017 | − | 0.304632i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(572\) | 1.66538 | + | 1.92195i | 1.66538 | + | 1.92195i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.281733 | + | 0.959493i | −0.281733 | + | 0.959493i | ||||
\(576\) | 2.30972 | 2.30972 | ||||||||
\(577\) | −1.84125 | + | 0.540641i | −1.84125 | + | 0.540641i | −0.841254 | + | 0.540641i | \(0.818182\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(578\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.29639 | − | 1.49611i | 1.29639 | − | 1.49611i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.84125 | − | 0.540641i | −1.84125 | − | 0.540641i | ||||
\(587\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(588\) | −0.127850 | − | 0.279953i | −0.127850 | − | 0.279953i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(594\) | 3.02977 | − | 1.94711i | 3.02977 | − | 1.94711i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.797176 | + | 0.234072i | −0.797176 | + | 0.234072i | ||||
\(597\) | 3.30972 | 3.30972 | ||||||||
\(598\) | −1.66538 | + | 0.239446i | −1.66538 | + | 0.239446i | ||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | −1.74557 | + | 0.512546i | −1.74557 | + | 0.512546i | ||||
\(601\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.28621 | + | 2.63843i | −2.28621 | + | 2.63843i | ||||
\(607\) | 0.0801894 | − | 0.557730i | 0.0801894 | − | 0.557730i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.328708 | + | 2.28621i | −0.328708 | + | 2.28621i | ||||
\(613\) | 1.25667 | − | 1.45027i | 1.25667 | − | 1.45027i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.232593 | − | 1.61772i | −0.232593 | − | 1.61772i | ||||
\(617\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.89945 | − | 0.557730i | 1.89945 | − | 0.557730i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.38273i | 2.38273i | ||||||||
\(622\) | −1.08128 | −1.08128 | ||||||||
\(623\) | 1.35881 | − | 0.398983i | 1.35881 | − | 0.398983i | ||||
\(624\) | −2.00448 | − | 2.31329i | −2.00448 | − | 2.31329i | ||||
\(625\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(632\) | −0.540641 | − | 0.158746i | −0.540641 | − | 0.158746i | ||||
\(633\) | 0.983568 | + | 0.288802i | 0.983568 | + | 0.288802i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.56036 | + | 1.80075i | −1.56036 | + | 1.80075i | ||||
\(637\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(642\) | −3.45561 | + | 1.01466i | −3.45561 | + | 1.01466i | ||||
\(643\) | 1.08128 | 1.08128 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(644\) | 0.983568 | + | 0.449181i | 0.983568 | + | 0.449181i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(648\) | −1.70362 | + | 1.09485i | −1.70362 | + | 1.09485i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(651\) | −1.23516 | + | 2.70463i | −1.23516 | + | 2.70463i | ||||
\(652\) | 0.708089 | − | 0.817178i | 0.708089 | − | 0.817178i | ||||
\(653\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.57501 | − | 1.65486i | 2.57501 | − | 1.65486i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.563465 | 0.563465 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0.279953 | + | 1.94711i | 0.279953 | + | 1.94711i | ||||
\(673\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.56036 | − | 1.80075i | 1.56036 | − | 1.80075i | ||||
\(676\) | −0.260554 | + | 1.81219i | −0.260554 | + | 1.81219i | ||||
\(677\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.471022 | − | 3.27603i | 0.471022 | − | 3.27603i | ||||
\(682\) | −1.49611 | + | 1.72661i | −1.49611 | + | 1.72661i | ||||
\(683\) | 0.234072 | − | 0.512546i | 0.234072 | − | 0.512546i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.755750 | + | 0.485691i | −0.755750 | + | 0.485691i | ||||
\(687\) | −2.00448 | − | 2.31329i | −2.00448 | − | 2.31329i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.20362 | 2.20362 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.08128 | 1.08128 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.47204 | + | 2.85288i | 2.47204 | + | 2.85288i | ||||
\(694\) | 1.27155 | − | 0.817178i | 1.27155 | − | 0.817178i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.10181 | − | 1.27155i | 1.10181 | − | 1.27155i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.449181 | − | 0.983568i | −0.449181 | − | 0.983568i | ||||
\(701\) | 1.61435 | + | 0.474017i | 1.61435 | + | 0.474017i | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(702\) | 3.84657 | + | 1.12945i | 3.84657 | + | 1.12945i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.215109 | + | 1.49611i | −0.215109 | + | 1.49611i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.118239 | − | 0.258908i | 0.118239 | − | 0.258908i | ||||
\(707\) | −1.74557 | − | 1.12181i | −1.74557 | − | 1.12181i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.24873 | − | 0.366660i | 1.24873 | − | 0.366660i | ||||
\(712\) | −1.30972 | −1.30972 | ||||||||
\(713\) | −0.425839 | − | 1.45027i | −0.425839 | − | 1.45027i | ||||
\(714\) | −1.96714 | −1.96714 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.909632 | − | 0.584585i | −0.909632 | − | 0.584585i | − | 1.00000i | \(-0.5\pi\) | |
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.970858 | + | 2.12588i | 0.970858 | + | 2.12588i | ||||
\(727\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(728\) | 1.19136 | − | 1.37491i | 1.19136 | − | 1.37491i | ||||
\(729\) | 0.142315 | − | 0.311626i | 0.142315 | − | 0.311626i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
−0.142315 | − | 0.989821i | \(-0.545455\pi\) | |||||||
\(734\) | 1.89945 | − | 0.557730i | 1.89945 | − | 0.557730i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.755750 | − | 0.654861i | −0.755750 | − | 0.654861i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.19136 | − | 0.765644i | −1.19136 | − | 0.765644i | ||||
\(743\) | −0.755750 | + | 1.65486i | −0.755750 | + | 1.65486i | 1.00000i | \(0.5\pi\) | ||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(744\) | 1.80075 | − | 2.07817i | 1.80075 | − | 2.07817i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.797176 | − | 1.74557i | −0.797176 | − | 1.74557i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.45027 | − | 0.425839i | −1.45027 | − | 0.425839i | ||||
\(749\) | −0.889217 | − | 1.94711i | −0.889217 | − | 1.94711i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.708089 | + | 0.817178i | −0.708089 | + | 0.817178i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.68718 | − | 1.94711i | −1.68718 | − | 1.94711i | ||||
\(757\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(758\) | 1.97964 | 1.97964 | ||||||||
\(759\) | −2.72183 | − | 0.391340i | −2.72183 | − | 0.391340i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.258908 | − | 1.80075i | 0.258908 | − | 1.80075i | ||||
\(769\) | −0.345139 | − | 0.755750i | −0.345139 | − | 0.755750i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.45027 | − | 0.425839i | −1.45027 | − | 0.425839i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.273100 | + | 1.89945i | −0.273100 | + | 1.89945i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.627899 | + | 1.37491i | −0.627899 | + | 1.37491i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.698939 | − | 0.449181i | 0.698939 | − | 0.449181i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.755750 | − | 0.654861i | 0.755750 | − | 0.654861i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.162317 | + | 0.0476607i | −0.162317 | + | 0.0476607i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.02977 | + | 1.94711i | −3.02977 | + | 1.94711i | ||||
\(787\) | −0.153882 | − | 1.07028i | −0.153882 | − | 1.07028i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
0.755750 | − | 0.654861i | \(-0.227273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.45027 | − | 3.17565i | −1.45027 | − | 3.17565i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.258908 | − | 1.80075i | 0.258908 | − | 1.80075i | ||||
\(797\) | −1.10181 | + | 1.27155i | −1.10181 | + | 1.27155i | −0.142315 | + | 0.989821i | \(0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(801\) | 2.54487 | − | 1.63549i | 2.54487 | − | 1.63549i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.54311 | −2.54311 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(809\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.74557 | + | 0.512546i | 1.74557 | + | 0.512546i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.797176 | + | 1.74557i | 0.797176 | + | 1.74557i | ||||
\(819\) | −0.598006 | + | 4.15922i | −0.598006 | + | 4.15922i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(822\) | 2.93694 | + | 1.88745i | 2.93694 | + | 1.88745i | ||||
\(823\) | −0.281733 | − | 1.95949i | −0.281733 | − | 1.95949i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.80075 | + | 2.07817i | 1.80075 | + | 2.07817i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.563465 | 0.563465 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(828\) | 2.28621 | + | 0.328708i | 2.28621 | + | 0.328708i | ||||
\(829\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(833\) | −0.0240754 | − | 0.167448i | −0.0240754 | − | 0.167448i | ||||
\(834\) | −3.02977 | − | 1.94711i | −3.02977 | − | 1.94711i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.512546 | + | 3.56484i | −0.512546 | + | 3.56484i | ||||
\(838\) | 0.627899 | + | 1.37491i | 0.627899 | + | 1.37491i | ||||
\(839\) | −1.89945 | − | 0.557730i | −1.89945 | − | 0.557730i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
−0.909632 | − | 0.415415i | \(-0.863636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(842\) | −0.118239 | + | 0.822373i | −0.118239 | + | 0.822373i | ||||
\(843\) | −0.339098 | + | 0.391340i | −0.339098 | + | 0.391340i | ||||
\(844\) | 0.234072 | − | 0.512546i | 0.234072 | − | 0.512546i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.16854 | + | 0.750975i | −1.16854 | + | 0.750975i | ||||
\(848\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(849\) | 0.983568 | − | 0.288802i | 0.983568 | − | 0.288802i | ||||
\(850\) | −1.00000 | −1.00000 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.281733 | + | 1.95949i | 0.281733 | + | 1.95949i | ||||
\(857\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(858\) | −1.92195 | + | 4.20849i | −1.92195 | + | 4.20849i | ||||
\(859\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.74557 | + | 0.512546i | 1.74557 | + | 0.512546i | ||||
\(863\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(864\) | 0.989821 | + | 2.16741i | 0.989821 | + | 2.16741i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(867\) | −0.755750 | + | 1.65486i | −0.755750 | + | 1.65486i | ||||
\(868\) | 1.37491 | + | 0.883600i | 1.37491 | + | 0.883600i | ||||
\(869\) | 0.121206 | + | 0.843008i | 0.121206 | + | 0.843008i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(878\) | −1.27155 | + | 0.817178i | −1.27155 | + | 0.817178i | ||||
\(879\) | −0.496841 | − | 3.45561i | −0.496841 | − | 3.45561i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(882\) | 0.255877 | − | 0.295298i | 0.255877 | − | 0.295298i | ||||
\(883\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(884\) | −0.698939 | − | 1.53046i | −0.698939 | − | 1.53046i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.822373 | + | 1.80075i | 0.822373 | + | 1.80075i | 0.540641 | + | 0.841254i | \(0.318182\pi\) |
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.57501 | + | 1.65486i | 2.57501 | + | 1.65486i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −0.989821 | − | 1.14231i | −0.989821 | − | 1.14231i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.08128 | 1.08128 | ||||||||
\(897\) | −1.65486 | − | 2.57501i | −1.65486 | − | 2.57501i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.51255 | − | 1.74557i | −1.51255 | − | 1.74557i | ||||
\(901\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.755750 | + | 1.65486i | 0.755750 | + | 1.65486i | 0.755750 | + | 0.654861i | \(0.227273\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | −1.74557 | − | 0.512546i | −1.74557 | − | 0.512546i | ||||
\(909\) | −4.25278 | − | 1.24873i | −4.25278 | − | 1.24873i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.0801894 | + | 0.557730i | −0.0801894 | + | 0.557730i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.41542 | + | 0.909632i | −1.41542 | + | 0.909632i | ||||
\(917\) | −1.40176 | − | 1.61772i | −1.40176 | − | 1.61772i | ||||
\(918\) | −2.28621 | + | 0.671292i | −2.28621 | + | 0.671292i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.50132 | − | 1.60750i | 2.50132 | − | 1.60750i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.817178 | − | 1.78937i | −0.817178 | − | 1.78937i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.61435 | − | 3.53494i | 1.61435 | − | 3.53494i | ||||
\(937\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(942\) | 1.51150 | 1.51150 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.66538 | − | 1.07028i | 1.66538 | − | 1.07028i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(948\) | −0.145886 | − | 1.01466i | −0.145886 | − | 1.01466i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.153882 | + | 1.07028i | −0.153882 | + | 1.07028i | ||||
\(953\) | −0.830830 | − | 1.81926i | −0.830830 | − | 1.81926i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(954\) | −2.90255 | − | 0.852267i | −2.90255 | − | 0.852267i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.861971 | + | 1.88745i | −0.861971 | + | 1.88745i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.182822 | − | 1.27155i | −0.182822 | − | 1.27155i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.99430 | − | 3.45561i | −2.99430 | − | 3.45561i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.96714i | 1.96714i | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 1.23259 | − | 0.361922i | 1.23259 | − | 0.361922i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(972\) | −1.09485 | − | 0.703616i | −1.09485 | − | 0.703616i | ||||
\(973\) | 0.889217 | − | 1.94711i | 0.889217 | − | 1.94711i | ||||
\(974\) | 0.708089 | − | 0.817178i | 0.708089 | − | 0.817178i | ||||
\(975\) | −0.435615 | + | 3.02977i | −0.435615 | + | 3.02977i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.273100 | + | 0.0801894i | 0.273100 | + | 0.0801894i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(978\) | 1.88745 | + | 0.554206i | 1.88745 | + | 0.554206i | ||||
\(979\) | 0.822373 | + | 1.80075i | 0.822373 | + | 1.80075i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.53046 | − | 0.983568i | −1.53046 | − | 0.983568i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
−0.540641 | − | 0.841254i | \(-0.681818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.540641 | + | 0.158746i | −0.540641 | + | 0.158746i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | −0.989821 | − | 1.14231i | −0.989821 | − | 1.14231i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(998\) | −0.153882 | + | 1.07028i | −0.153882 | + | 1.07028i | ||||
\(999\) | 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 | 1564.1.w.c.883.2 | yes | 20 | |
4.3 | odd | 2 | inner | 1564.1.w.c.883.1 | yes | 20 | |
17.16 | even | 2 | inner | 1564.1.w.c.883.1 | yes | 20 | |
23.18 | even | 11 | inner | 1564.1.w.c.271.2 | yes | 20 | |
68.67 | odd | 2 | CM | 1564.1.w.c.883.2 | yes | 20 | |
92.87 | odd | 22 | inner | 1564.1.w.c.271.1 | ✓ | 20 | |
391.271 | even | 22 | inner | 1564.1.w.c.271.1 | ✓ | 20 | |
1564.271 | odd | 22 | inner | 1564.1.w.c.271.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1564.1.w.c.271.1 | ✓ | 20 | 92.87 | odd | 22 | inner | |
1564.1.w.c.271.1 | ✓ | 20 | 391.271 | even | 22 | inner | |
1564.1.w.c.271.2 | yes | 20 | 23.18 | even | 11 | inner | |
1564.1.w.c.271.2 | yes | 20 | 1564.271 | odd | 22 | inner | |
1564.1.w.c.883.1 | yes | 20 | 4.3 | odd | 2 | inner | |
1564.1.w.c.883.1 | yes | 20 | 17.16 | even | 2 | inner | |
1564.1.w.c.883.2 | yes | 20 | 1.1 | even | 1 | trivial | |
1564.1.w.c.883.2 | yes | 20 | 68.67 | odd | 2 | CM |