Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,1,Mod(107,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, base_ring=CyclotomicField(92))
chi = DirichletCharacter(H, H._module([46, 23, 22]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3525.107");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.bg (of order \(92\), degree \(44\), 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: | \(1.75920416953\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{92})\) |
Coefficient field: | \(\Q(\zeta_{184})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{88} - x^{84} + x^{80} - x^{76} + x^{72} - x^{68} + x^{64} - x^{60} + x^{56} - x^{52} + x^{48} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{46}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{46} - \cdots)\) |
Embedding invariants
Embedding label | 257.1 | ||
Root | \(-0.102264 + 0.994757i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.257 |
Dual form | 3525.1.bg.a.2318.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times\).
\(n\) | \(1552\) | \(2026\) | \(2351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.202623 | + | 1.97098i | −0.202623 | + | 1.97098i | 0.0341411 | + | 0.999417i | \(0.489130\pi\) |
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(3\) | 0.930278 | + | 0.366854i | 0.930278 | + | 0.366854i | ||||
\(4\) | −2.86464 | − | 0.595279i | −2.86464 | − | 0.595279i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.911560 | + | 1.75923i | −0.911560 | + | 1.75923i | ||||
\(7\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(8\) | 1.15433 | − | 3.63700i | 1.15433 | − | 3.63700i | ||||
\(9\) | 0.730836 | + | 0.682553i | 0.730836 | + | 0.682553i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.816970 | − | 0.576680i | \(-0.195652\pi\) | ||||
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(12\) | −2.44653 | − | 1.60468i | −2.44653 | − | 1.60468i | ||||
\(13\) | 0 | 0 | −0.753713 | − | 0.657204i | \(-0.771739\pi\) | ||||
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.25097 | + | 1.84646i | 4.25097 | + | 1.84646i | ||||
\(17\) | 0.113799 | + | 0.660021i | 0.113799 | + | 0.660021i | 0.985460 | + | 0.169910i | \(0.0543478\pi\) |
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(18\) | −1.49339 | + | 1.30216i | −1.49339 | + | 1.30216i | ||||
\(19\) | 1.93993 | − | 0.266637i | 1.93993 | − | 0.266637i | 0.942261 | − | 0.334880i | \(-0.108696\pi\) |
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.25556 | + | 0.129075i | −1.25556 | + | 0.129075i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(24\) | 2.40810 | − | 2.95995i | 2.40810 | − | 2.95995i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.429483 | + | 0.903075i | 0.429483 | + | 0.903075i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.650963 | + | 1.49867i | −0.650963 | + | 1.49867i | 0.203456 | + | 0.979084i | \(0.434783\pi\) |
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(32\) | −2.63053 | + | 4.67839i | −2.63053 | + | 4.67839i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.32395 | + | 0.0905606i | −1.32395 | + | 0.0905606i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.68727 | − | 2.39032i | −1.68727 | − | 2.39032i | ||||
\(37\) | 0 | 0 | 0.236764 | − | 0.971567i | \(-0.423913\pi\) | ||||
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(38\) | 0.132463 | + | 3.87760i | 0.132463 | + | 3.87760i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.548452 | − | 0.836182i | \(-0.684783\pi\) | ||||
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 2.50084i | − | 2.50084i | ||||||
\(47\) | 0.971567 | − | 0.236764i | 0.971567 | − | 0.236764i | ||||
\(48\) | 3.27721 | + | 3.27721i | 3.27721 | + | 3.27721i | ||||
\(49\) | 0.631088 | + | 0.775711i | 0.631088 | + | 0.775711i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.136267 | + | 0.655751i | −0.136267 | + | 0.655751i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.30114 | + | 0.412965i | −1.30114 | + | 0.412965i | −0.871660 | − | 0.490110i | \(-0.836957\pi\) |
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(54\) | −1.86697 | + | 0.663521i | −1.86697 | + | 0.663521i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.90249 | + | 0.463625i | 1.90249 | + | 0.463625i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) | ||||
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.116615 | + | 0.0709153i | 0.116615 | + | 0.0709153i | 0.576680 | − | 0.816970i | \(-0.304348\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(62\) | −2.82195 | − | 1.58670i | −2.82195 | − | 1.58670i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.90164 | − | 3.45995i | −4.90164 | − | 3.45995i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.903075 | − | 0.429483i | \(-0.141304\pi\) | ||||
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(68\) | 0.0669031 | − | 1.95846i | 0.0669031 | − | 1.95846i | ||||
\(69\) | −1.21537 | − | 0.340531i | −1.21537 | − | 0.340531i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(72\) | 3.32608 | − | 1.87016i | 3.32608 | − | 1.87016i | ||||
\(73\) | 0 | 0 | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) | ||||
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.71592 | − | 0.390980i | −5.71592 | − | 0.390980i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.311173 | − | 1.11059i | −0.311173 | − | 1.11059i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) |
0.631088 | − | 0.775711i | \(-0.282609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.0682424 | + | 0.997669i | 0.0682424 | + | 0.997669i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.156340 | + | 0.906751i | −0.156340 | + | 0.906751i | 0.796805 | + | 0.604236i | \(0.206522\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.136167 | − | 0.990686i | \(-0.456522\pi\) | ||||
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.67356 | + | 0.377653i | 3.67356 | + | 0.377653i | ||||
\(93\) | −1.15537 | + | 1.15537i | −1.15537 | + | 1.15537i | ||||
\(94\) | 0.269797 | + | 1.96292i | 0.269797 | + | 1.96292i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.16341 | + | 3.38719i | −4.16341 | + | 3.38719i | ||||
\(97\) | 0 | 0 | 0.366854 | − | 0.930278i | \(-0.380435\pi\) | ||||
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(98\) | −1.65679 | + | 1.08669i | −1.65679 | + | 1.08669i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(102\) | −1.26486 | − | 0.401450i | −1.26486 | − | 0.401450i | ||||
\(103\) | 0 | 0 | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | ||||
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.550304 | − | 2.64821i | −0.550304 | − | 2.64821i | ||||
\(107\) | 0.523661 | − | 0.600560i | 0.523661 | − | 0.600560i | −0.429483 | − | 0.903075i | \(-0.641304\pi\) |
0.953145 | + | 0.302515i | \(0.0978261\pi\) | |||||||
\(108\) | −0.692734 | − | 2.84264i | −0.692734 | − | 2.84264i | ||||
\(109\) | 1.70992 | − | 0.479097i | 1.70992 | − | 0.479097i | 0.730836 | − | 0.682553i | \(-0.239130\pi\) |
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.627903 | − | 0.828014i | 0.627903 | − | 0.828014i | −0.366854 | − | 0.930278i | \(-0.619565\pi\) |
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(114\) | −1.29929 | + | 3.65584i | −1.29929 | + | 3.65584i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.334880 | − | 0.942261i | 0.334880 | − | 0.942261i | ||||
\(122\) | −0.163402 | + | 0.215478i | −0.163402 | + | 0.215478i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.75690 | − | 3.90564i | 2.75690 | − | 3.90564i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.236764 | − | 0.971567i | \(-0.576087\pi\) | ||||
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(128\) | 4.28535 | − | 4.91464i | 4.28535 | − | 4.91464i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.53186 | + | 0.347996i | 2.53186 | + | 0.347996i | ||||
\(137\) | −1.48487 | + | 0.973925i | −1.48487 | + | 0.973925i | −0.490110 | + | 0.871660i | \(0.663043\pi\) |
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(138\) | 0.917444 | − | 2.32648i | 0.917444 | − | 2.32648i | ||||
\(139\) | −0.418569 | + | 0.340531i | −0.418569 | + | 0.340531i | −0.816970 | − | 0.576680i | \(-0.804348\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.990686 | + | 0.136167i | 0.990686 | + | 0.136167i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.84646 | + | 4.25097i | 1.84646 | + | 4.25097i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.302515 | + | 0.953145i | 0.302515 | + | 0.953145i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.03675 | − | 1.70486i | −1.03675 | − | 1.70486i | −0.576680 | − | 0.816970i | \(-0.695652\pi\) |
−0.460065 | − | 0.887885i | \(-0.652174\pi\) | |||||||
\(152\) | 1.26956 | − | 7.36332i | 1.26956 | − | 7.36332i | ||||
\(153\) | −0.367331 | + | 0.560041i | −0.367331 | + | 0.560041i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(158\) | 2.25201 | − | 0.388285i | 2.25201 | − | 0.388285i | ||||
\(159\) | −1.36192 | − | 0.0931581i | −1.36192 | − | 0.0931581i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.98022 | − | 0.0676462i | −1.98022 | − | 0.0676462i | ||||
\(163\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.75551 | − | 0.491872i | −1.75551 | − | 0.491872i | ||||
\(167\) | −0.0499031 | + | 1.46082i | −0.0499031 | + | 1.46082i | 0.657204 | + | 0.753713i | \(0.271739\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.136167 | + | 0.990686i | 0.136167 | + | 0.990686i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.59976 | + | 1.12924i | 1.59976 | + | 1.12924i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.48953 | − | 0.837519i | −1.48953 | − | 0.837519i | −0.490110 | − | 0.871660i | \(-0.663043\pi\) |
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.979167 | − | 0.347996i | 0.979167 | − | 0.347996i | 0.203456 | − | 0.979084i | \(-0.434783\pi\) |
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0824691 | + | 0.108752i | 0.0824691 | + | 0.108752i | ||||
\(184\) | −0.979886 | + | 4.71547i | −0.979886 | + | 4.71547i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.04311 | − | 2.51132i | −2.04311 | − | 2.51132i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2.92413 | + | 0.0998912i | −2.92413 | + | 0.0998912i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(192\) | −3.29059 | − | 5.01691i | −3.29059 | − | 5.01691i | ||||
\(193\) | 0 | 0 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.34607 | − | 2.59781i | −1.34607 | − | 2.59781i | ||||
\(197\) | −0.00465974 | − | 0.136405i | −0.00465974 | − | 0.136405i | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) |
0.994757 | − | 0.102264i | \(-0.0326087\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.842917 | − | 1.19414i | −0.842917 | − | 1.19414i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
0.136167 | − | 0.990686i | \(-0.456522\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.780709 | − | 1.79737i | 0.780709 | − | 1.79737i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00571 | − | 0.762653i | −1.00571 | − | 0.762653i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.502852 | + | 0.618088i | −0.502852 | + | 0.618088i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(212\) | 3.97314 | − | 0.408451i | 3.97314 | − | 0.408451i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.07759 | + | 1.15382i | 1.07759 | + | 1.15382i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.78025 | − | 0.519584i | 3.78025 | − | 0.519584i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.597823 | + | 3.46730i | 0.597823 | + | 3.46730i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.836182 | − | 0.548452i | \(-0.815217\pi\) | ||||
0.836182 | + | 0.548452i | \(0.184783\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.50478 | + | 1.40536i | 1.50478 | + | 1.40536i | ||||
\(227\) | 0.603619 | − | 1.90185i | 0.603619 | − | 1.90185i | 0.236764 | − | 0.971567i | \(-0.423913\pi\) |
0.366854 | − | 0.930278i | \(-0.380435\pi\) | |||||||
\(228\) | −5.17396 | − | 2.46063i | −5.17396 | − | 2.46063i | ||||
\(229\) | 0.917985 | − | 1.77163i | 0.917985 | − | 1.77163i | 0.398401 | − | 0.917211i | \(-0.369565\pi\) |
0.519584 | − | 0.854419i | \(-0.326087\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.149477 | − | 1.45401i | 0.149477 | − | 1.45401i | −0.604236 | − | 0.796805i | \(-0.706522\pi\) |
0.753713 | − | 0.657204i | \(-0.228261\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.117947 | − | 1.14731i | 0.117947 | − | 1.14731i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.628038 | + | 1.21206i | −0.628038 | + | 1.21206i | 0.334880 | + | 0.942261i | \(0.391304\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(242\) | 1.78933 | + | 0.850966i | 1.78933 | + | 0.850966i | ||||
\(243\) | −0.302515 | + | 0.953145i | −0.302515 | + | 0.953145i | ||||
\(244\) | −0.291846 | − | 0.272565i | −0.291846 | − | 0.272565i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.69923 | + | 4.09752i | 4.69923 | + | 4.09752i | ||||
\(249\) | −0.478085 | + | 0.786177i | −0.478085 | + | 0.786177i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.72321 | + | 5.05732i | 4.72321 | + | 5.05732i | ||||
\(257\) | 0.923623 | + | 1.64266i | 0.923623 | + | 1.64266i | 0.753713 | + | 0.657204i | \(0.228261\pi\) |
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.23618 | + | 0.937426i | 1.23618 | + | 0.937426i | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) |
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.234658 | + | 0.332435i | 0.234658 | + | 0.332435i | 0.917211 | − | 0.398401i | \(-0.130435\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(272\) | −0.734944 | + | 3.01586i | −0.734944 | + | 3.01586i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.61872 | − | 3.12399i | −1.61872 | − | 3.12399i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.27889 | + | 1.69898i | 3.27889 | + | 1.69898i | ||||
\(277\) | 0 | 0 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(278\) | −0.586369 | − | 0.893992i | −0.586369 | − | 0.893992i | ||||
\(279\) | −1.49867 | + | 0.650963i | −1.49867 | + | 0.650963i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −0.469118 | + | 1.92504i | −0.469118 | + | 1.92504i | ||||
\(283\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.11573 | + | 1.62366i | −5.11573 | + | 1.62366i | ||||
\(289\) | 0.519584 | − | 0.184660i | 0.519584 | − | 0.184660i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.268373 | + | 0.0462723i | 0.268373 | + | 0.0462723i | 0.302515 | − | 0.953145i | \(-0.402174\pi\) |
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(294\) | −1.93993 | + | 0.403122i | −1.93993 | + | 0.403122i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.57031 | − | 1.69797i | 3.57031 | − | 1.69797i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.73893 | + | 2.44853i | 8.73893 | + | 2.44853i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.02940 | − | 0.837480i | −1.02940 | − | 0.837480i | ||||
\(307\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.230287 | + | 3.36668i | 0.230287 | + | 3.36668i | ||||
\(317\) | −0.437008 | + | 0.666272i | −0.437008 | + | 0.666272i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(318\) | 0.459571 | − | 2.66545i | 0.459571 | − | 2.66545i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.707469 | − | 0.366581i | 0.707469 | − | 0.366581i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.396748 | + | 1.25005i | 0.396748 | + | 1.25005i | ||||
\(324\) | 0.398401 | − | 2.89858i | 0.398401 | − | 2.89858i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.76646 | + | 0.181598i | 1.76646 | + | 0.181598i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.713755 | − | 0.580683i | 0.713755 | − | 0.580683i | −0.203456 | − | 0.979084i | \(-0.565217\pi\) |
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(332\) | 0.987626 | − | 2.50445i | 0.987626 | − | 2.50445i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.86914 | − | 0.394354i | −2.86914 | − | 0.394354i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.953145 | − | 0.302515i | \(-0.902174\pi\) | ||||
0.953145 | + | 0.302515i | \(0.0978261\pi\) | |||||||
\(338\) | −1.98022 | + | 0.0676462i | −1.98022 | + | 0.0676462i | ||||
\(339\) | 0.887885 | − | 0.539935i | 0.887885 | − | 0.539935i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.54986 | + | 2.92430i | −2.54986 | + | 2.92430i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.95255 | − | 2.76613i | 1.95255 | − | 2.76613i | ||||
\(347\) | −1.12306 | − | 1.28797i | −1.12306 | − | 1.28797i | −0.953145 | − | 0.302515i | \(-0.902174\pi\) |
−0.169910 | − | 0.985460i | \(-0.554348\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.180699 | + | 0.508438i | −0.180699 | + | 0.508438i | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) |
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.0416125 | − | 0.404779i | −0.0416125 | − | 0.404779i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
0.953145 | − | 0.302515i | \(-0.0978261\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.72931 | − | 0.764718i | 2.72931 | − | 0.764718i | ||||
\(362\) | 0.487493 | + | 2.00044i | 0.487493 | + | 2.00044i | ||||
\(363\) | 0.657204 | − | 0.753713i | 0.657204 | − | 0.753713i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.231058 | + | 0.140510i | −0.231058 | + | 0.140510i | ||||
\(367\) | 0 | 0 | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | ||||
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(368\) | −5.57568 | − | 1.76964i | −5.57568 | − | 1.76964i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.99748 | − | 2.62195i | 3.99748 | − | 2.62195i | ||||
\(373\) | 0 | 0 | 0.366854 | − | 0.930278i | \(-0.380435\pi\) | ||||
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.260399 | − | 3.80690i | 0.260399 | − | 3.80690i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.730836 | − | 1.68255i | −0.730836 | − | 1.68255i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.733918 | + | 1.54321i | −0.733918 | + | 1.54321i | 0.102264 | + | 0.994757i | \(0.467391\pi\) |
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(384\) | 5.78952 | − | 2.99989i | 5.78952 | − | 2.99989i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.228074 | − | 0.814006i | −0.228074 | − | 0.814006i | ||||
\(392\) | 3.54975 | − | 1.39984i | 3.54975 | − | 1.39984i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.269797 | + | 0.0184546i | 0.269797 | + | 0.0184546i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) | ||||
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(398\) | 2.52443 | − | 1.41942i | 2.52443 | − | 1.41942i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.22767 | + | 1.25256i | 2.22767 | + | 1.25256i | ||||
\(409\) | 0.461039 | + | 0.280364i | 0.461039 | + | 0.280364i | 0.730836 | − | 0.682553i | \(-0.239130\pi\) |
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.73863 | + | 0.361291i | −1.73863 | + | 0.361291i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.70696 | − | 1.82770i | 1.70696 | − | 1.82770i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.514311 | + | 0.163235i | −0.514311 | + | 0.163235i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.502852 | − | 0.618088i | −0.502852 | − | 0.618088i | 0.460065 | − | 0.887885i | \(-0.347826\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(422\) | −1.11635 | − | 1.11635i | −1.11635 | − | 1.11635i | ||||
\(423\) | 0.871660 | + | 0.490110i | 0.871660 | + | 0.490110i | ||||
\(424\) | 5.20897i | 5.20897i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.85760 | + | 1.40866i | −1.85760 | + | 1.40866i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(432\) | 0.158233 | + | 4.63197i | 0.158233 | + | 4.63197i | ||||
\(433\) | 0 | 0 | 0.236764 | − | 0.971567i | \(-0.423913\pi\) | ||||
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.18350 | + | 0.354561i | −5.18350 | + | 0.354561i | ||||
\(437\) | −2.40128 | + | 0.585176i | −2.40128 | + | 0.585176i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.366581 | − | 0.843954i | 0.366581 | − | 0.843954i | −0.631088 | − | 0.775711i | \(-0.717391\pi\) |
0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0682424 | + | 0.997669i | −0.0682424 | + | 0.997669i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.762664 | − | 1.60365i | −0.762664 | − | 1.60365i | −0.796805 | − | 0.604236i | \(-0.793478\pi\) |
0.0341411 | − | 0.999417i | \(-0.489130\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −2.29161 | + | 1.99818i | −2.29161 | + | 1.99818i | ||||
\(453\) | −0.339029 | − | 1.96632i | −0.339029 | − | 1.96632i | ||||
\(454\) | 3.62620 | + | 1.57508i | 3.62620 | + | 1.57508i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.88231 | − | 6.38419i | 3.88231 | − | 6.38419i | ||||
\(457\) | 0 | 0 | −0.753713 | − | 0.657204i | \(-0.771739\pi\) | ||||
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(458\) | 3.30585 | + | 2.16831i | 3.30585 | + | 2.16831i | ||||
\(459\) | −0.547173 | + | 0.386237i | −0.547173 | + | 0.386237i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.83554 | + | 0.589232i | 2.83554 | + | 0.589232i | ||||
\(467\) | 0.501972 | + | 0.197952i | 0.501972 | + | 0.197952i | 0.604236 | − | 0.796805i | \(-0.293478\pi\) |
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.23744 | + | 0.464945i | 2.23744 | + | 0.464945i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.23279 | − | 0.586291i | −1.23279 | − | 0.586291i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −2.26169 | − | 1.48344i | −2.26169 | − | 1.48344i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.52022 | + | 2.49989i | −1.52022 | + | 2.49989i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.81734 | − | 0.789381i | −1.81734 | − | 0.789381i | ||||
\(487\) | 0 | 0 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(488\) | 0.392532 | − | 0.342270i | 0.392532 | − | 0.342270i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.53446 | + | 5.16882i | −5.53446 | + | 5.16882i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.45267 | − | 1.10160i | −1.45267 | − | 1.10160i | ||||
\(499\) | 0.0861339 | − | 1.25923i | 0.0861339 | − | 1.25923i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
0.816970 | − | 0.576680i | \(-0.195652\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.582332 | + | 1.34066i | −0.582332 | + | 1.34066i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.264590 | − | 0.0644788i | 0.264590 | − | 0.0644788i | −0.102264 | − | 0.994757i | \(-0.532609\pi\) |
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.236764 | + | 0.971567i | −0.236764 | + | 0.971567i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.72930 | + | 4.34466i | −5.72930 | + | 4.34466i | ||||
\(513\) | 1.07396 | + | 1.63739i | 1.07396 | + | 1.63739i | ||||
\(514\) | −3.42481 | + | 1.48761i | −3.42481 | + | 1.48761i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.07843 | − | 1.32557i | −1.07843 | − | 1.32557i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) | ||||
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.09813 | + | 2.24655i | −2.09813 | + | 2.24655i | ||||
\(527\) | −1.06323 | − | 0.259102i | −1.06323 | − | 0.259102i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.580683 | − | 0.120667i | 0.580683 | − | 0.120667i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.894675 | + | 0.727872i | 0.894675 | + | 0.727872i | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) |
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(542\) | −0.702771 | + | 0.395148i | −0.702771 | + | 0.395148i | ||||
\(543\) | 1.03856 | + | 0.0354783i | 1.03856 | + | 0.0354783i | ||||
\(544\) | −3.38719 | − | 1.20381i | −3.38719 | − | 1.20381i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) | ||||
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(548\) | 4.83336 | − | 1.90603i | 4.83336 | − | 1.90603i | ||||
\(549\) | 0.0368232 | + | 0.131424i | 0.0368232 | + | 0.131424i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −2.64146 | + | 4.02722i | −2.64146 | + | 4.02722i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.40176 | − | 0.726333i | 1.40176 | − | 0.726333i | ||||
\(557\) | 0.809371 | − | 1.70186i | 0.809371 | − | 1.70186i | 0.102264 | − | 0.994757i | \(-0.467391\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(558\) | −0.979373 | − | 3.08575i | −0.979373 | − | 3.08575i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.33256 | − | 1.33256i | 1.33256 | − | 1.33256i | 0.429483 | − | 0.903075i | \(-0.358696\pi\) |
0.903075 | − | 0.429483i | \(-0.141304\pi\) | |||||||
\(564\) | −2.75690 | − | 0.979802i | −2.75690 | − | 0.979802i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.136267 | − | 0.383417i | −0.136267 | − | 0.383417i | 0.854419 | − | 0.519584i | \(-0.173913\pi\) |
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.22069 | − | 5.87429i | −1.22069 | − | 5.87429i | ||||
\(577\) | 0 | 0 | 0.657204 | − | 0.753713i | \(-0.271739\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(578\) | 0.258682 | + | 1.06151i | 0.258682 | + | 1.06151i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.145581 | + | 0.519584i | −0.145581 | + | 0.519584i | ||||
\(587\) | −0.200250 | − | 1.94790i | −0.200250 | − | 1.94790i | −0.302515 | − | 0.953145i | \(-0.597826\pi\) |
0.102264 | − | 0.994757i | \(-0.467391\pi\) | |||||||
\(588\) | −0.299208 | − | 2.91050i | −0.299208 | − | 2.91050i | ||||
\(589\) | −0.863223 | + | 3.08088i | −0.863223 | + | 3.08088i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0457060 | − | 0.128604i | 0.0457060 | − | 0.128604i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.178978 | − | 0.205261i | −0.178978 | − | 0.205261i | 0.657204 | − | 0.753713i | \(-0.271739\pi\) |
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.346072 | − | 1.42011i | −0.346072 | − | 1.42011i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.46007 | + | 0.887885i | −1.46007 | + | 0.887885i | −0.460065 | + | 0.887885i | \(0.652174\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.95504 | + | 5.50095i | 1.95504 | + | 5.50095i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.836182 | − | 0.548452i | \(-0.184783\pi\) | ||||
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(608\) | −3.85561 | + | 9.77715i | −3.85561 | + | 9.77715i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.38565 | − | 1.38565i | 1.38565 | − | 1.38565i | ||||
\(613\) | 0 | 0 | −0.994757 | − | 0.102264i | \(-0.967391\pi\) | ||||
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.348908 | − | 1.09932i | −0.348908 | − | 1.09932i | −0.953145 | − | 0.302515i | \(-0.902174\pi\) |
0.604236 | − | 0.796805i | \(-0.293478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.121183 | + | 0.0627919i | −0.121183 | + | 0.0627919i | −0.519584 | − | 0.854419i | \(-0.673913\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.655806 | − | 1.07843i | −0.655806 | − | 1.07843i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.18930 | − | 0.422677i | −1.18930 | − | 0.422677i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(632\) | −4.39842 | − | 0.150255i | −4.39842 | − | 0.150255i | ||||
\(633\) | −0.694541 | + | 0.390521i | −0.694541 | + | 0.390521i | ||||
\(634\) | −1.22466 | − | 0.996337i | −1.22466 | − | 0.996337i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.84596 | + | 1.07759i | 3.84596 | + | 1.07759i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(642\) | 0.579175 | + | 1.46869i | 0.579175 | + | 1.46869i | ||||
\(643\) | 0 | 0 | −0.871660 | − | 0.490110i | \(-0.836957\pi\) | ||||
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.54422 | + | 0.528695i | −2.54422 | + | 0.528695i | ||||
\(647\) | −1.34526 | − | 0.231946i | −1.34526 | − | 0.231946i | −0.548452 | − | 0.836182i | \(-0.684783\pi\) |
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(648\) | 3.70730 | + | 0.903444i | 3.70730 | + | 0.903444i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.245871 | + | 0.324230i | 0.245871 | + | 0.324230i | 0.903075 | − | 0.429483i | \(-0.141304\pi\) |
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(654\) | −0.715852 | + | 3.44487i | −0.715852 | + | 3.44487i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.614311 | + | 0.266833i | −0.614311 | + | 0.266833i | −0.682553 | − | 0.730836i | \(-0.739130\pi\) |
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(662\) | 0.999894 | + | 1.52446i | 0.999894 | + | 1.52446i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.11739 | + | 1.61530i | 3.11739 | + | 1.61530i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.01255 | − | 4.15501i | 1.01255 | − | 4.15501i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.490110 | − | 0.871660i | \(-0.336957\pi\) | ||||
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.199666 | − | 2.91901i | 0.199666 | − | 2.91901i | ||||
\(677\) | 0.429951 | + | 0.326042i | 0.429951 | + | 0.326042i | 0.796805 | − | 0.604236i | \(-0.206522\pi\) |
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(678\) | 0.884297 | + | 1.85941i | 0.884297 | + | 1.85941i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.25923 | − | 1.54781i | 1.25923 | − | 1.54781i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.760368 | − | 1.35231i | −0.760368 | − | 1.35231i | −0.930278 | − | 0.366854i | \(-0.880435\pi\) |
0.169910 | − | 0.985460i | \(-0.445652\pi\) | |||||||
\(684\) | −3.91054 | − | 4.18716i | −3.91054 | − | 4.18716i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.50391 | − | 1.31134i | 1.50391 | − | 1.31134i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.979167 | + | 1.61017i | −0.979167 | + | 1.61017i | −0.203456 | + | 0.979084i | \(0.565217\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(692\) | 3.76840 | + | 3.28587i | 3.76840 | + | 3.28587i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.76613 | − | 1.95255i | 2.76613 | − | 1.95255i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.965509 | − | 0.459176i | −0.965509 | − | 0.459176i | ||||
\(699\) | 0.672464 | − | 1.29780i | 0.672464 | − | 1.29780i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.806244 | 0.806244 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.51897 | + | 0.315646i | 1.51897 | + | 0.315646i | 0.887885 | − | 0.460065i | \(-0.152174\pi\) |
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.530621 | − | 1.02405i | 0.530621 | − | 1.02405i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.623882 | − | 1.96569i | 0.623882 | − | 1.96569i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.954224 | + | 5.53439i | 0.954224 | + | 5.53439i | ||||
\(723\) | −1.02890 | + | 0.897153i | −1.02890 | + | 0.897153i | ||||
\(724\) | −3.01211 | + | 0.414006i | −3.01211 | + | 0.414006i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.35239 | + | 1.44806i | 1.35239 | + | 1.44806i | ||||
\(727\) | 0 | 0 | −0.490110 | − | 0.871660i | \(-0.663043\pi\) | ||||
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.631088 | + | 0.775711i | −0.631088 | + | 0.775711i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.171506 | − | 0.360627i | −0.171506 | − | 0.360627i | ||||
\(733\) | 0 | 0 | −0.796805 | − | 0.604236i | \(-0.793478\pi\) | ||||
0.796805 | + | 0.604236i | \(0.206522\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.69892 | − | 6.21353i | 2.69892 | − | 6.21353i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.70486 | − | 0.116615i | 1.70486 | − | 0.116615i | 0.816970 | − | 0.576680i | \(-0.195652\pi\) |
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.0668540 | − | 1.95703i | −0.0668540 | − | 1.95703i | −0.236764 | − | 0.971567i | \(-0.576087\pi\) |
0.169910 | − | 0.985460i | \(-0.445652\pi\) | |||||||
\(744\) | 2.86840 | + | 5.53577i | 2.86840 | + | 5.53577i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.733164 | + | 0.555976i | −0.733164 | + | 0.555976i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 0.796802i | − | 0.796802i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||
0.917211 | − | 0.398401i | \(-0.130435\pi\) | |||||||
\(752\) | 4.56728 | + | 0.787479i | 4.56728 | + | 0.787479i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(758\) | 3.46437 | − | 1.09954i | 3.46437 | − | 1.09954i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.89293 | − | 1.75923i | −2.89293 | − | 1.75923i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.53860 | + | 6.43744i | 2.53860 | + | 6.43744i | ||||
\(769\) | −0.547173 | − | 0.386237i | −0.547173 | − | 0.386237i | 0.269797 | − | 0.962917i | \(-0.413043\pi\) |
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.256609 | + | 1.86697i | 0.256609 | + | 1.86697i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.0657501 | + | 1.92471i | −0.0657501 | + | 1.92471i | 0.236764 | + | 0.971567i | \(0.423913\pi\) |
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.65061 | − | 0.284593i | 1.65061 | − | 0.284593i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.25042 | + | 4.46281i | 1.25042 | + | 4.46281i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.548452 | − | 0.836182i | \(-0.315217\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(788\) | −0.0678507 | + | 0.393526i | −0.0678507 | + | 0.393526i | ||||
\(789\) | 0.806094 | + | 1.32557i | 0.806094 | + | 1.32557i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.70381 | + | 3.92256i | 1.70381 | + | 3.92256i | ||||
\(797\) | −0.536765 | − | 0.0551811i | −0.536765 | − | 0.0551811i | −0.169910 | − | 0.985460i | \(-0.554348\pi\) |
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.266833 | + | 0.614311i | 0.266833 | + | 0.614311i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.347674 | + | 1.67310i | 0.347674 | + | 1.67310i | 0.682553 | + | 0.730836i | \(0.260870\pi\) |
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0963423 | + | 0.395342i | 0.0963423 | + | 0.395342i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.79008 | + | 2.53597i | −1.79008 | + | 2.53597i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.646011 | + | 0.851893i | −0.646011 | + | 0.851893i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(822\) | −0.359812 | − | 3.50002i | −0.359812 | − | 3.50002i | ||||
\(823\) | 0 | 0 | −0.102264 | − | 0.994757i | \(-0.532609\pi\) | ||||
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.16366 | + | 1.53451i | −1.16366 | + | 1.53451i | −0.366854 | + | 0.930278i | \(0.619565\pi\) |
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(828\) | 2.42700 | + | 2.78340i | 2.42700 | + | 2.78340i | ||||
\(829\) | −0.157049 | + | 0.222488i | −0.157049 | + | 0.222488i | −0.887885 | − | 0.460065i | \(-0.847826\pi\) |
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.440168 | + | 0.504806i | −0.440168 | + | 0.504806i | ||||
\(834\) | −0.217522 | − | 1.04677i | −0.217522 | − | 1.04677i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.63299 | + | 0.0557845i | −1.63299 | + | 0.0557845i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.990686 | − | 0.136167i | −0.990686 | − | 0.136167i | ||||
\(842\) | 1.32013 | − | 0.865875i | 1.32013 | − | 0.865875i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.80842 | − | 1.47126i | 1.80842 | − | 1.47126i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.14262 | + | 1.61872i | −1.14262 | + | 1.61872i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.29365 | − | 0.647007i | −6.29365 | − | 0.647007i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.429483 | − | 0.903075i | \(-0.358696\pi\) | ||||
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.57976 | − | 2.59781i | −1.57976 | − | 2.59781i | ||||
\(857\) | −0.135385 | + | 0.785216i | −0.135385 | + | 0.785216i | 0.836182 | + | 0.548452i | \(0.184783\pi\) |
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.0185847 | + | 0.271698i | 0.0185847 | + | 0.271698i | 0.997669 | + | 0.0682424i | \(0.0217391\pi\) |
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.13659 | − | 0.195968i | 1.13659 | − | 0.195968i | 0.429483 | − | 0.903075i | \(-0.358696\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | −5.35470 | − | 0.366272i | −5.35470 | − | 0.366272i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.551101 | + | 0.0188262i | 0.551101 | + | 0.0188262i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.231339 | − | 6.77202i | 0.231339 | − | 6.77202i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.666817 | − | 4.85145i | −0.666817 | − | 4.85145i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.366854 | − | 0.930278i | \(-0.619565\pi\) | ||||
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(878\) | 1.58914 | + | 0.893530i | 1.58914 | + | 0.893530i | ||||
\(879\) | 0.232687 | + | 0.141500i | 0.232687 | + | 0.141500i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) | ||||
−0.979084 | + | 0.203456i | \(0.934783\pi\) | |||||||
\(882\) | −1.95256 | − | 0.336656i | −1.95256 | − | 0.336656i | ||||
\(883\) | 0 | 0 | −0.971567 | − | 0.236764i | \(-0.923913\pi\) | ||||
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.31531 | − | 1.17826i | 3.31531 | − | 1.17826i | ||||
\(887\) | 1.86642 | − | 0.592374i | 1.86642 | − | 0.592374i | 0.871660 | − | 0.490110i | \(-0.163043\pi\) |
0.994757 | − | 0.102264i | \(-0.0326087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.82164 | − | 0.718362i | 1.82164 | − | 0.718362i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.420634 | − | 0.811787i | −0.420634 | − | 0.811787i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.28668 | − | 3.23949i | −2.28668 | − | 3.23949i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.94429 | − | 0.269797i | 3.94429 | − | 0.269797i | ||||
\(907\) | 0 | 0 | 0.971567 | − | 0.236764i | \(-0.0760870\pi\) | ||||
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(908\) | −2.86128 | + | 5.08878i | −2.86128 | + | 5.08878i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(912\) | 7.23138 | + | 5.48373i | 7.23138 | + | 5.48373i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.68431 | + | 4.52862i | −3.68431 | + | 4.52862i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.650397 | − | 1.15673i | −0.650397 | − | 1.15673i | ||||
\(919\) | −0.861502 | − | 0.922444i | −0.861502 | − | 0.922444i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.816970 | − | 0.576680i | \(-0.195652\pi\) | ||||
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.43110 | + | 1.33655i | 1.43110 | + | 1.33655i | ||||
\(932\) | −1.29374 | + | 4.07623i | −1.29374 | + | 4.07623i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.491872 | + | 0.949270i | −0.491872 | + | 0.949270i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.930278 | − | 0.366854i | \(-0.880435\pi\) | ||||
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.73917 | − | 0.827114i | −1.73917 | − | 0.827114i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
−0.753713 | − | 0.657204i | \(-0.771739\pi\) | |||||||
\(948\) | −1.02085 | + | 3.21643i | −1.02085 | + | 3.21643i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.650963 | + | 0.459500i | −0.650963 | + | 0.459500i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.205261 | − | 0.178978i | −0.205261 | − | 0.178978i | 0.548452 | − | 0.836182i | \(-0.315217\pi\) |
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(954\) | 1.40536 | − | 2.31102i | 1.40536 | − | 2.31102i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.13970 | − | 1.22032i | −1.13970 | − | 1.22032i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.792625 | − | 0.0814843i | 0.792625 | − | 0.0814843i | ||||
\(964\) | 2.52061 | − | 3.09825i | 2.52061 | − | 3.09825i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.429483 | − | 0.903075i | \(-0.641304\pi\) | ||||
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(968\) | −3.04044 | − | 2.30564i | −3.04044 | − | 2.30564i | ||||
\(969\) | −0.0895000 | + | 1.30844i | −0.0895000 | + | 1.30844i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.398401 | − | 0.917211i | \(-0.369565\pi\) | ||||
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(972\) | 1.43398 | − | 2.55033i | 1.43398 | − | 2.55033i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.364786 | + | 0.516785i | 0.364786 | + | 0.516785i | ||||
\(977\) | −0.404592 | + | 1.66025i | −0.404592 | + | 1.66025i | 0.302515 | + | 0.953145i | \(0.402174\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.57668 | + | 0.816970i | 1.57668 | + | 0.816970i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.09435 | − | 1.66847i | −1.09435 | − | 1.66847i | −0.604236 | − | 0.796805i | \(-0.706522\pi\) |
−0.490110 | − | 0.871660i | \(-0.663043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.373224 | + | 1.79605i | −0.373224 | + | 1.79605i | 0.203456 | + | 0.979084i | \(0.434783\pi\) |
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(992\) | −5.29898 | − | 6.98775i | −5.29898 | − | 6.98775i | ||||
\(993\) | 0.877017 | − | 0.278353i | 0.877017 | − | 0.278353i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.83753 | − | 1.96752i | 1.83753 | − | 1.96752i | ||||
\(997\) | 0 | 0 | −0.971567 | − | 0.236764i | \(-0.923913\pi\) | ||||
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(998\) | 2.46448 | + | 0.424919i | 2.46448 | + | 0.424919i | ||||
\(999\) | 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 | 3525.1.bg.a.257.1 | ✓ | 88 | |
3.2 | odd | 2 | inner | 3525.1.bg.a.257.2 | yes | 88 | |
5.2 | odd | 4 | inner | 3525.1.bg.a.3218.1 | yes | 88 | |
5.3 | odd | 4 | inner | 3525.1.bg.a.3218.2 | yes | 88 | |
5.4 | even | 2 | inner | 3525.1.bg.a.257.2 | yes | 88 | |
15.2 | even | 4 | inner | 3525.1.bg.a.3218.2 | yes | 88 | |
15.8 | even | 4 | inner | 3525.1.bg.a.3218.1 | yes | 88 | |
15.14 | odd | 2 | CM | 3525.1.bg.a.257.1 | ✓ | 88 | |
47.15 | odd | 46 | inner | 3525.1.bg.a.2882.1 | yes | 88 | |
141.62 | even | 46 | inner | 3525.1.bg.a.2882.2 | yes | 88 | |
235.62 | even | 92 | inner | 3525.1.bg.a.2318.1 | yes | 88 | |
235.109 | odd | 46 | inner | 3525.1.bg.a.2882.2 | yes | 88 | |
235.203 | even | 92 | inner | 3525.1.bg.a.2318.2 | yes | 88 | |
705.62 | odd | 92 | inner | 3525.1.bg.a.2318.2 | yes | 88 | |
705.203 | odd | 92 | inner | 3525.1.bg.a.2318.1 | yes | 88 | |
705.344 | even | 46 | inner | 3525.1.bg.a.2882.1 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.1.bg.a.257.1 | ✓ | 88 | 1.1 | even | 1 | trivial | |
3525.1.bg.a.257.1 | ✓ | 88 | 15.14 | odd | 2 | CM | |
3525.1.bg.a.257.2 | yes | 88 | 3.2 | odd | 2 | inner | |
3525.1.bg.a.257.2 | yes | 88 | 5.4 | even | 2 | inner | |
3525.1.bg.a.2318.1 | yes | 88 | 235.62 | even | 92 | inner | |
3525.1.bg.a.2318.1 | yes | 88 | 705.203 | odd | 92 | inner | |
3525.1.bg.a.2318.2 | yes | 88 | 235.203 | even | 92 | inner | |
3525.1.bg.a.2318.2 | yes | 88 | 705.62 | odd | 92 | inner | |
3525.1.bg.a.2882.1 | yes | 88 | 47.15 | odd | 46 | inner | |
3525.1.bg.a.2882.1 | yes | 88 | 705.344 | even | 46 | inner | |
3525.1.bg.a.2882.2 | yes | 88 | 141.62 | even | 46 | inner | |
3525.1.bg.a.2882.2 | yes | 88 | 235.109 | odd | 46 | inner | |
3525.1.bg.a.3218.1 | yes | 88 | 5.2 | odd | 4 | inner | |
3525.1.bg.a.3218.1 | yes | 88 | 15.8 | even | 4 | inner | |
3525.1.bg.a.3218.2 | yes | 88 | 5.3 | odd | 4 | inner | |
3525.1.bg.a.3218.2 | yes | 88 | 15.2 | even | 4 | inner |