Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1449,1,Mod(125,1449)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1449, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([11, 11, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1449.125");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1449 = 3^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1449.bu (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: | \(0.723145203305\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{88})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 125.3 | ||
Root | \(-0.599278 - 0.800541i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1449.125 |
Dual form | 1449.1.bu.a.881.3 |
$q$-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 \(\left(\mathbb{Z}/1449\mathbb{Z}\right)^\times\).
\(n\) | \(442\) | \(829\) | \(1289\) |
\(\chi(n)\) | \(e\left(\frac{3}{22}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.905808 | − | 0.784887i | 0.905808 | − | 0.784887i | −0.0713392 | − | 0.997452i | \(-0.522727\pi\) |
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0621254 | − | 0.432092i | 0.0621254 | − | 0.432092i | ||||
\(5\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.281733 | − | 0.959493i | 0.281733 | − | 0.959493i | ||||
\(8\) | 0.365119 | + | 0.568136i | 0.365119 | + | 0.568136i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.278401 | − | 0.321292i | 0.278401 | − | 0.321292i | −0.599278 | − | 0.800541i | \(-0.704545\pi\) |
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(14\) | −0.497898 | − | 1.09024i | −0.497898 | − | 1.09024i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.19550 | + | 0.351031i | 1.19550 | + | 0.351031i | ||||
\(17\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 0.509543i | − | 0.509543i | ||||||
\(23\) | 0.349464 | + | 0.936950i | 0.349464 | + | 0.936950i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.397086 | − | 0.181343i | −0.397086 | − | 0.181343i | ||||
\(29\) | −1.97460 | + | 0.283904i | −1.97460 | + | 0.283904i | −0.977147 | + | 0.212565i | \(0.931818\pi\) |
−0.997452 | + | 0.0713392i | \(0.977273\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(32\) | 0.744099 | − | 0.339819i | 0.744099 | − | 0.339819i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.74557 | − | 0.797176i | 1.74557 | − | 0.797176i | 0.755750 | − | 0.654861i | \(-0.227273\pi\) |
0.989821 | − | 0.142315i | \(-0.0454545\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.449181 | − | 0.698939i | 0.449181 | − | 0.698939i | −0.540641 | − | 0.841254i | \(-0.681818\pi\) |
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(44\) | −0.121532 | − | 0.140255i | −0.121532 | − | 0.140255i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.05195 | + | 0.574406i | 1.05195 | + | 0.574406i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(50\) | −1.18636 | − | 0.170572i | −1.18636 | − | 0.170572i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.136899 | − | 0.0401971i | −0.136899 | − | 0.0401971i | 0.212565 | − | 0.977147i | \(-0.431818\pi\) |
−0.349464 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.647988 | − | 0.190266i | 0.647988 | − | 0.190266i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.56577 | + | 1.80700i | −1.56577 | + | 1.80700i | ||||
\(59\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.110304 | + | 0.241532i | −0.110304 | + | 0.241532i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.49611 | + | 1.29639i | −1.49611 | + | 1.29639i | −0.654861 | + | 0.755750i | \(0.727273\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.47696 | + | 1.27979i | −1.47696 | + | 1.27979i | −0.599278 | + | 0.800541i | \(0.704545\pi\) |
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(74\) | 0.955459 | − | 2.09216i | 0.955459 | − | 2.09216i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.229843 | − | 0.357643i | −0.229843 | − | 0.357643i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.425839 | + | 1.45027i | 0.425839 | + | 1.45027i | 0.841254 | + | 0.540641i | \(0.181818\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.141717 | − | 0.985660i | −0.141717 | − | 0.985660i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.284187 | + | 0.0408599i | 0.284187 | + | 0.0408599i | ||||
\(89\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.426559 | − | 0.0927922i | 0.426559 | − | 0.0927922i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(98\) | −1.18636 | + | 0.170572i | −1.18636 | + | 0.170572i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.367237 | + | 0.236009i | −0.367237 | + | 0.236009i | ||||
\(101\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.155554 | + | 0.0710393i | −0.155554 | + | 0.0710393i | ||||
\(107\) | −0.806340 | + | 0.518203i | −0.806340 | + | 0.518203i | −0.877679 | − | 0.479249i | \(-0.840909\pi\) |
0.0713392 | + | 0.997452i | \(0.477273\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.281733 | + | 0.0405070i | −0.281733 | + | 0.0405070i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.673623 | − | 1.04818i | 0.673623 | − | 1.04818i | ||||
\(113\) | 0.457701 | + | 0.528215i | 0.457701 | + | 0.528215i | 0.936950 | − | 0.349464i | \(-0.113636\pi\) |
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.870845i | 0.870845i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.116593 | + | 0.810925i | 0.116593 | + | 0.810925i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.544078 | + | 0.627899i | −0.544078 | + | 0.627899i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) |
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(128\) | 0.320125 | + | 1.09024i | 0.320125 | + | 1.09024i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.337672 | + | 2.34856i | −0.337672 | + | 2.34856i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.60108 | −1.60108 | −0.800541 | − | 0.599278i | \(-0.795455\pi\) | ||||
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.333348 | + | 2.31849i | −0.333348 | + | 2.31849i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.236009 | − | 0.803771i | −0.236009 | − | 0.803771i | ||||
\(149\) | 1.22714 | − | 1.41620i | 1.22714 | − | 1.41620i | 0.349464 | − | 0.936950i | \(-0.386364\pi\) |
0.877679 | − | 0.479249i | \(-0.159091\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.45027 | + | 0.425839i | −1.45027 | + | 0.425839i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.488902 | − | 0.143555i | −0.488902 | − | 0.143555i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(158\) | 1.52403 | + | 0.979433i | 1.52403 | + | 0.979433i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.997452 | − | 0.0713392i | 0.997452 | − | 0.0713392i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.857685 | − | 0.989821i | −0.857685 | − | 0.989821i | 0.142315 | − | 0.989821i | \(-0.454545\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.274100 | − | 0.237509i | −0.274100 | − | 0.237509i | ||||
\(173\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.909632 | + | 0.415415i | −0.909632 | + | 0.415415i | ||||
\(176\) | 0.445613 | − | 0.286378i | 0.445613 | − | 0.286378i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.635768 | − | 0.290345i | −0.635768 | − | 0.290345i | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.404719 | + | 0.540641i | −0.404719 | + | 0.540641i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.68425 | + | 0.494541i | 1.68425 | + | 0.494541i | 0.977147 | − | 0.212565i | \(-0.0681818\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.449181 | − | 0.983568i | −0.449181 | − | 0.983568i | −0.989821 | − | 0.142315i | \(-0.954545\pi\) |
0.540641 | − | 0.841254i | \(-0.318182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.285870 | + | 0.329911i | −0.285870 | + | 0.329911i | ||||
\(197\) | −0.196911 | − | 0.670617i | −0.196911 | − | 0.670617i | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) |
0.800541 | − | 0.599278i | \(-0.204545\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(200\) | 0.190266 | − | 0.647988i | 0.190266 | − | 0.647988i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.283904 | + | 1.97460i | −0.283904 | + | 1.97460i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.153882 | − | 1.07028i | 0.153882 | − | 1.07028i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(212\) | −0.0258737 | + | 0.0566556i | −0.0258737 | + | 0.0566556i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.323658 | + | 1.10228i | −0.323658 | + | 1.10228i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.223402 | + | 0.257820i | −0.223402 | + | 0.257820i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(224\) | −0.116417 | − | 0.809696i | −0.116417 | − | 0.809696i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.829178 | + | 0.119218i | 0.829178 | + | 0.119218i | ||||
\(227\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.882259 | − | 1.01818i | −0.882259 | − | 1.01818i | ||||
\(233\) | −0.518203 | + | 0.806340i | −0.518203 | + | 0.806340i | −0.997452 | − | 0.0713392i | \(-0.977273\pi\) |
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.59673 | − | 0.729202i | 1.59673 | − | 0.729202i | 0.599278 | − | 0.800541i | \(-0.295455\pi\) |
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(242\) | 0.742096 | + | 0.643030i | 0.742096 | + | 0.643030i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.398326 | + | 0.148568i | 0.398326 | + | 0.148568i | ||||
\(254\) | 0.995796i | 0.995796i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.922314 | + | 0.592735i | 0.922314 | + | 0.592735i | ||||
\(257\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.53623 | − | 0.451077i | 1.53623 | − | 0.451077i | 0.599278 | − | 0.800541i | \(-0.295455\pi\) |
0.936950 | + | 0.349464i | \(0.113636\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.467213 | + | 0.726997i | 0.467213 | + | 0.726997i | ||||
\(269\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.45027 | + | 1.25667i | −1.45027 | + | 1.25667i | ||||
\(275\) | −0.425131 | −0.425131 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.828713 | − | 1.81463i | 0.828713 | − | 1.81463i | 0.349464 | − | 0.936950i | \(-0.386364\pi\) |
0.479249 | − | 0.877679i | \(-0.340909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(284\) | 0.461230 | + | 0.717688i | 0.461230 | + | 0.717688i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.09024 | + | 0.700657i | 1.09024 | + | 0.700657i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 2.24597i | − | 2.24597i | ||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(302\) | −0.979433 | + | 1.52403i | −0.979433 | + | 1.52403i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(308\) | −0.168813 | + | 0.0770945i | −0.168813 | + | 0.0770945i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.653106 | − | 0.0939025i | 0.653106 | − | 0.0939025i | ||||
\(317\) | 1.59673 | + | 0.729202i | 1.59673 | + | 0.729202i | 0.997452 | − | 0.0713392i | \(-0.0227273\pi\) |
0.599278 | + | 0.800541i | \(0.295455\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.458515 | + | 0.713463i | −0.458515 | + | 0.713463i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.847507 | − | 0.847507i | 0.847507 | − | 0.847507i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.55380 | − | 0.223402i | −1.55380 | − | 0.223402i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.755750 | − | 1.65486i | −0.755750 | − | 1.65486i | −0.755750 | − | 0.654861i | \(-0.772727\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.909632 | + | 1.41542i | 0.909632 | + | 1.41542i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0.337672 | − | 1.15001i | 0.337672 | − | 1.15001i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.755750 | + | 0.654861i | −0.755750 | + | 0.654861i | ||||
\(344\) | 0.561096 | 0.561096 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.724384 | + | 0.627683i | −0.724384 | + | 0.627683i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) |
0.212565 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(350\) | −0.497898 | + | 1.09024i | −0.497898 | + | 1.09024i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0979771 | − | 0.333679i | 0.0979771 | − | 0.333679i | ||||
\(353\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.803771 | + | 0.236009i | −0.803771 | + | 0.236009i | ||||
\(359\) | −0.778446 | − | 1.70456i | −0.778446 | − | 1.70456i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.0713392 | − | 0.997452i | \(-0.522727\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 0.0888866 | + | 1.24280i | 0.0888866 | + | 1.24280i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0771377 | + | 0.120029i | −0.0771377 | + | 0.120029i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.983568 | + | 0.449181i | 0.983568 | + | 0.449181i | 0.841254 | − | 0.540641i | \(-0.181818\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.989821 | − | 0.857685i | −0.989821 | − | 0.857685i | − | 1.00000i | \(-0.5\pi\) | |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.91377 | − | 0.873989i | 1.91377 | − | 0.873989i | ||||
\(383\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.17886 | − | 0.538368i | −1.17886 | − | 0.538368i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.27979 | − | 1.47696i | −1.27979 | − | 1.47696i | −0.800541 | − | 0.599278i | \(-0.795455\pi\) |
−0.479249 | − | 0.877679i | \(-0.659091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 0.675344i | − | 0.675344i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.704722 | − | 0.452897i | −0.704722 | − | 0.452897i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.517596 | − | 1.13338i | −0.517596 | − | 1.13338i | ||||
\(401\) | 1.68425 | − | 0.494541i | 1.68425 | − | 0.494541i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.977147 | + | 0.212565i | \(0.0681818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.29267 | + | 2.01144i | 1.29267 | + | 2.01144i | ||||
\(407\) | 0.229843 | − | 0.782773i | 0.229843 | − | 0.782773i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.512546 | − | 1.74557i | 0.512546 | − | 1.74557i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) |
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(422\) | −0.700657 | − | 1.09024i | −0.700657 | − | 1.09024i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.0271469 | − | 0.0924539i | −0.0271469 | − | 0.0924539i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.173817 | + | 0.380606i | 0.173817 | + | 0.380606i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.0994679 | + | 0.691814i | 0.0994679 | + | 0.691814i | 0.977147 | + | 0.212565i | \(0.0681818\pi\) |
−0.877679 | + | 0.479249i | \(0.840909\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.124251i | 0.124251i | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.420803 | + | 0.0605024i | −0.420803 | + | 0.0605024i | −0.349464 | − | 0.936950i | \(-0.613636\pi\) |
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.200672 | + | 0.173883i | 0.200672 | + | 0.173883i | ||||
\(449\) | −1.32661 | − | 1.14952i | −1.32661 | − | 1.14952i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.349464 | − | 0.936950i | \(-0.613636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.256672 | − | 0.164953i | 0.256672 | − | 0.164953i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.708089 | + | 1.10181i | −0.708089 | + | 1.10181i | 0.281733 | + | 0.959493i | \(0.409091\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.239446 | + | 0.153882i | 0.239446 | + | 0.153882i | 0.654861 | − | 0.755750i | \(-0.272727\pi\) |
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(464\) | −2.46030 | − | 0.353737i | −2.46030 | − | 0.353737i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.163493 | + | 1.13712i | 0.163493 | + | 1.13712i | ||||
\(467\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.822373 | + | 1.80075i | 0.822373 | + | 1.80075i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.0995111 | − | 0.338904i | −0.0995111 | − | 0.338904i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.873989 | − | 1.91377i | 0.873989 | − | 1.91377i | ||||
\(479\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.357637 | 0.357637 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.258908 | + | 1.80075i | −0.258908 | + | 1.80075i | 0.281733 | + | 0.959493i | \(0.409091\pi\) |
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.865611 | − | 1.34692i | −0.865611 | − | 1.34692i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) |
0.0713392 | − | 0.997452i | \(-0.477273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.811843 | + | 1.77769i | 0.811843 | + | 1.77769i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.89945 | + | 0.557730i | 1.89945 | + | 0.557730i | 0.989821 | + | 0.142315i | \(0.0454545\pi\) |
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.477416 | − | 0.178067i | 0.477416 | − | 0.178067i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.237509 | + | 0.274100i | 0.237509 | + | 0.274100i | ||||
\(509\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.175964 | − | 0.0252998i | 0.175964 | − | 0.0252998i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.73823 | − | 1.50619i | −1.73823 | − | 1.50619i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.03748 | − | 1.61435i | 1.03748 | − | 1.61435i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.755750 | + | 0.654861i | −0.755750 | + | 0.654861i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.28278 | − | 0.376660i | −1.28278 | − | 0.376660i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.407910 | + | 0.119773i | −0.407910 | + | 0.119773i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.186393 | + | 0.215109i | −0.186393 | + | 0.215109i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) |
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | 0.142315 | + | 0.989821i | \(0.454545\pi\) |
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(548\) | −0.0994679 | + | 0.691814i | −0.0994679 | + | 0.691814i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.385087 | + | 0.333679i | −0.385087 | + | 0.333679i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.51150 | 1.51150 | ||||||||
\(554\) | 1.73823 | − | 1.50619i | 1.73823 | − | 1.50619i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.587486 | − | 1.28641i | 0.587486 | − | 1.28641i | −0.349464 | − | 0.936950i | \(-0.613636\pi\) |
0.936950 | − | 0.349464i | \(-0.113636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.673623 | − | 2.29415i | −0.673623 | − | 2.29415i | ||||
\(563\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.26636 | − | 0.371836i | −1.26636 | − | 0.371836i | ||||
\(569\) | −0.136408 | − | 0.948742i | −0.136408 | − | 0.948742i | −0.936950 | − | 0.349464i | \(-0.886364\pi\) |
0.800541 | − | 0.599278i | \(-0.204545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.557730 | + | 0.0801894i | 0.557730 | + | 0.0801894i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.479249 | − | 0.877679i | 0.479249 | − | 0.877679i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(578\) | −0.647988 | + | 1.00829i | −0.647988 | + | 1.00829i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0510279 | + | 0.0327936i | −0.0510279 | + | 0.0327936i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.36667 | − | 0.340275i | 2.36667 | − | 0.340275i | ||||
\(593\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.535691 | − | 0.618220i | −0.535691 | − | 0.618220i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.60108i | 1.60108i | 0.599278 | + | 0.800541i | \(0.295455\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(602\) | −0.985660 | − | 0.141717i | −0.985660 | − | 0.141717i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.0939025 | + | 0.653106i | 0.0939025 | + | 0.653106i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.07028 | − | 1.66538i | −1.07028 | − | 1.66538i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) |
−0.415415 | − | 0.909632i | \(-0.636364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.119270 | − | 0.261164i | 0.119270 | − | 0.261164i | ||||
\(617\) | 0.170572 | − | 1.18636i | 0.170572 | − | 1.18636i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.877679 | − | 0.479249i | \(-0.159091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.512546 | + | 1.74557i | 0.512546 | + | 1.74557i | 0.654861 | + | 0.755750i | \(0.272727\pi\) |
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(632\) | −0.668470 | + | 0.771456i | −0.668470 | + | 0.771456i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.01867 | − | 0.592735i | 2.01867 | − | 0.592735i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.144661 | + | 1.00614i | 0.144661 | + | 1.00614i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.18971 | − | 0.764582i | −1.18971 | − | 0.764582i | −0.212565 | − | 0.977147i | \(-0.568182\pi\) |
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0.0311420 | − | 0.435423i | 0.0311420 | − | 0.435423i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.480978 | + | 0.309106i | −0.480978 | + | 0.309106i | ||||
\(653\) | −1.45640 | + | 0.665114i | −1.45640 | + | 0.665114i | −0.977147 | − | 0.212565i | \(-0.931818\pi\) |
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.120029 | + | 0.0771377i | −0.120029 | + | 0.0771377i | −0.599278 | − | 0.800541i | \(-0.704545\pi\) |
0.479249 | + | 0.877679i | \(0.340909\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(662\) | −1.98344 | − | 0.905808i | −1.98344 | − | 0.905808i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.956056 | − | 1.75089i | −0.956056 | − | 1.75089i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.281733 | − | 1.95949i | −0.281733 | − | 1.95949i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(674\) | 1.93489 | + | 0.568136i | 1.93489 | + | 0.568136i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.181343 | − | 0.397086i | −0.181343 | − | 0.397086i | ||||
\(677\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.494541 | + | 1.68425i | −0.494541 | + | 1.68425i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.170572 | + | 1.18636i | −0.170572 | + | 1.18636i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.782345 | − | 0.677906i | 0.782345 | − | 0.677906i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.163493 | + | 1.13712i | −0.163493 | + | 1.13712i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.122986 | + | 0.418852i | 0.122986 | + | 0.418852i | ||||
\(701\) | 0.784887 | − | 0.905808i | 0.784887 | − | 0.905808i | −0.212565 | − | 0.977147i | \(-0.568182\pi\) |
0.997452 | + | 0.0713392i | \(0.0227273\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.0468936 | + | 0.102683i | 0.0468936 | + | 0.102683i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.66538 | + | 0.239446i | 1.66538 | + | 0.239446i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.164953 | + | 0.256672i | −0.164953 | + | 0.256672i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.04301 | − | 0.933011i | −2.04301 | − | 0.933011i | ||||
\(719\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.09024 | − | 0.497898i | 1.09024 | − | 0.497898i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.50765 | + | 1.30638i | 1.50765 | + | 1.30638i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.578429 | + | 0.578429i | 0.578429 | + | 0.578429i | ||||
\(737\) | 0.841607i | 0.841607i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.239446 | − | 0.153882i | −0.239446 | − | 0.153882i | 0.415415 | − | 0.909632i | \(-0.363636\pi\) |
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0243370 | + | 0.169267i | 0.0243370 | + | 0.169267i | ||||
\(743\) | 1.15001 | + | 0.337672i | 1.15001 | + | 0.337672i | 0.800541 | − | 0.599278i | \(-0.204545\pi\) |
0.349464 | + | 0.936950i | \(0.386364\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.24348 | − | 0.365119i | 1.24348 | − | 0.365119i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.270040 | + | 0.919672i | 0.270040 | + | 0.919672i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.708089 | − | 1.10181i | −0.708089 | − | 1.10181i | −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 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.27155 | + | 1.10181i | −1.27155 | + | 1.10181i | −0.281733 | + | 0.959493i | \(0.590909\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(758\) | −1.56977 | −1.56977 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | ||||
\(764\) | 0.318322 | − | 0.697028i | 0.318322 | − | 0.697028i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.452897 | + | 0.132983i | −0.452897 | + | 0.132983i | ||||
\(773\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.31849 | − | 0.333348i | −2.31849 | − | 0.333348i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.830830i | 0.830830i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.815938 | − | 0.941643i | −0.815938 | − | 0.941643i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(788\) | −0.302001 | + | 0.0434212i | −0.302001 | + | 0.0434212i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.635768 | − | 0.290345i | 0.635768 | − | 0.290345i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.744099 | − | 0.339819i | −0.744099 | − | 0.339819i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.13745 | − | 1.76991i | 1.13745 | − | 1.76991i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.141226 | + | 0.0203052i | 0.141226 | + | 0.0203052i | 0.212565 | − | 0.977147i | \(-0.431818\pi\) |
−0.0713392 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(812\) | 0.835570 | + | 0.245345i | 0.835570 | + | 0.245345i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.406195 | − | 0.889443i | −0.406195 | − | 0.889443i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.550588 | − | 1.87513i | 0.550588 | − | 1.87513i | 0.0713392 | − | 0.997452i | \(-0.477273\pi\) |
0.479249 | − | 0.877679i | \(-0.340909\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | 0.415415 | + | 0.909632i | \(0.363636\pi\) |
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.75536 | 1.75536 | 0.877679 | − | 0.479249i | \(-0.159091\pi\) | ||||
0.877679 | + | 0.479249i | \(0.159091\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.85895 | − | 0.839462i | 2.85895 | − | 0.839462i | ||||
\(842\) | −0.905808 | − | 1.98344i | −0.905808 | − | 1.98344i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.452897 | − | 0.132983i | −0.452897 | − | 0.132983i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.810925 | + | 0.116593i | 0.810925 | + | 0.116593i | ||||
\(848\) | −0.149552 | − | 0.0961115i | −0.149552 | − | 0.0961115i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.35693 | + | 1.35693i | 1.35693 | + | 1.35693i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.588819 | − | 0.268905i | −0.588819 | − | 0.268905i | ||||
\(857\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.633095 | + | 0.548580i | 0.633095 | + | 0.548580i | ||||
\(863\) | −0.321292 | − | 0.278401i | −0.321292 | − | 0.278401i | 0.479249 | − | 0.877679i | \(-0.340909\pi\) |
−0.800541 | + | 0.599278i | \(0.795455\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.584515 | + | 0.266939i | 0.584515 | + | 0.266939i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.125879 | − | 0.145272i | −0.125879 | − | 0.145272i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.41542 | + | 0.909632i | 1.41542 | + | 0.909632i | 1.00000 | \(0\) | ||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.627899 | + | 1.37491i | 0.627899 | + | 1.37491i | 0.909632 | + | 0.415415i | \(0.136364\pi\) |
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.333679 | + | 0.385087i | −0.333679 | + | 0.385087i | ||||
\(887\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.449181 | + | 0.698939i | 0.449181 | + | 0.698939i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.13627 | 1.13627 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.10389 | −2.10389 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.132983 | + | 0.452897i | −0.132983 | + | 0.452897i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0801894 | − | 0.273100i | −0.0801894 | − | 0.273100i | 0.909632 | − | 0.415415i | \(-0.136364\pi\) |
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.497898 | + | 1.09024i | 0.497898 | + | 1.09024i | 0.977147 | + | 0.212565i | \(0.0681818\pi\) |
−0.479249 | + | 0.877679i | \(0.659091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.223402 | + | 1.55380i | 0.223402 | + | 1.55380i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.91899i | − | 1.91899i | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||
0.281733 | − | 0.959493i | \(-0.409091\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.74557 | − | 0.797176i | −1.74557 | − | 0.797176i | ||||
\(926\) | 0.337672 | − | 0.0485499i | 0.337672 | − | 0.0485499i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.37282 | + | 0.882259i | −1.37282 | + | 0.882259i | ||||
\(929\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.316219 | + | 0.274005i | 0.316219 | + | 0.274005i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(938\) | 2.15829 | + | 0.985660i | 2.15829 | + | 0.985660i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.356139 | − | 0.228877i | −0.356139 | − | 0.228877i | ||||
\(947\) | 1.73749 | + | 0.249813i | 1.73749 | + | 0.249813i | 0.936950 | − | 0.349464i | \(-0.113636\pi\) |
0.800541 | + | 0.599278i | \(0.204545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.919672 | − | 0.270040i | 0.919672 | − | 0.270040i | 0.212565 | − | 0.977147i | \(-0.431818\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.215885 | − | 0.735235i | −0.215885 | − | 0.735235i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.451077 | + | 1.53623i | −0.451077 | + | 1.53623i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(968\) | −0.418145 | + | 0.362325i | −0.418145 | + | 0.362325i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.17886 | + | 1.83434i | 1.17886 | + | 1.83434i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.926113 | + | 1.06879i | −0.926113 | + | 1.06879i | 0.0713392 | + | 0.997452i | \(0.477273\pi\) |
−0.997452 | + | 0.0713392i | \(0.977273\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.84125 | − | 0.540641i | −1.84125 | − | 0.540641i | ||||
\(983\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.811843 | + | 0.176606i | 0.811843 | + | 0.176606i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.29639 | + | 1.49611i | 1.29639 | + | 1.49611i | 0.755750 | + | 0.654861i | \(0.227273\pi\) |
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.13066 | + | 0.973039i | 2.13066 | + | 0.973039i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(998\) | 2.15829 | − | 0.985660i | 2.15829 | − | 0.985660i | ||||
\(999\) | 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 | 1449.1.bu.a.125.3 | yes | 40 | |
3.2 | odd | 2 | inner | 1449.1.bu.a.125.2 | ✓ | 40 | |
7.6 | odd | 2 | CM | 1449.1.bu.a.125.3 | yes | 40 | |
21.20 | even | 2 | inner | 1449.1.bu.a.125.2 | ✓ | 40 | |
23.7 | odd | 22 | inner | 1449.1.bu.a.881.2 | yes | 40 | |
69.53 | even | 22 | inner | 1449.1.bu.a.881.3 | yes | 40 | |
161.76 | even | 22 | inner | 1449.1.bu.a.881.2 | yes | 40 | |
483.398 | odd | 22 | inner | 1449.1.bu.a.881.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1449.1.bu.a.125.2 | ✓ | 40 | 3.2 | odd | 2 | inner | |
1449.1.bu.a.125.2 | ✓ | 40 | 21.20 | even | 2 | inner | |
1449.1.bu.a.125.3 | yes | 40 | 1.1 | even | 1 | trivial | |
1449.1.bu.a.125.3 | yes | 40 | 7.6 | odd | 2 | CM | |
1449.1.bu.a.881.2 | yes | 40 | 23.7 | odd | 22 | inner | |
1449.1.bu.a.881.2 | yes | 40 | 161.76 | even | 22 | inner | |
1449.1.bu.a.881.3 | yes | 40 | 69.53 | even | 22 | inner | |
1449.1.bu.a.881.3 | yes | 40 | 483.398 | odd | 22 | inner |