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: | \( x^{88} - x^{84} + x^{80} - x^{76} + x^{72} - x^{68} + x^{64} - x^{60} + x^{56} - x^{52} + x^{48} - x^{44} + x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
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 | 368.1 | ||
Root | \(0.366854 + 0.930278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.368 |
Dual form | 3525.1.bg.a.182.1 |
$q$-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 \(\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times\).
\(n\) | \(1552\) | \(2026\) | \(2351\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.626895 | − | 1.58970i | −0.626895 | − | 1.58970i | −0.796805 | − | 0.604236i | \(-0.793478\pi\) |
0.169910 | − | 0.985460i | \(-0.445652\pi\) | |||||||
\(3\) | −0.753713 | − | 0.657204i | −0.753713 | − | 0.657204i | ||||
\(4\) | −1.40330 | + | 1.31059i | −1.40330 | + | 1.31059i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.572255 | + | 1.61017i | −0.572255 | + | 1.61017i | ||||
\(7\) | 0 | 0 | 0.836182 | − | 0.548452i | \(-0.184783\pi\) | ||||
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(8\) | 1.41995 | + | 0.675300i | 1.41995 | + | 0.675300i | ||||
\(9\) | 0.136167 | + | 0.990686i | 0.136167 | + | 0.990686i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(12\) | 1.91901 | − | 0.0655554i | 1.91901 | − | 0.0655554i | ||||
\(13\) | 0 | 0 | −0.871660 | − | 0.490110i | \(-0.836957\pi\) | ||||
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0523262 | − | 0.764982i | 0.0523262 | − | 0.764982i | ||||
\(17\) | −0.404779 | − | 0.0416125i | −0.404779 | − | 0.0416125i | −0.102264 | − | 0.994757i | \(-0.532609\pi\) |
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(18\) | 1.48953 | − | 0.837519i | 1.48953 | − | 0.837519i | ||||
\(19\) | −1.24888 | + | 0.759461i | −1.24888 | + | 0.759461i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.741248 | + | 0.292310i | 0.741248 | + | 0.292310i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(24\) | −0.626428 | − | 1.44218i | −0.626428 | − | 1.44218i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.548452 | − | 0.836182i | 0.548452 | − | 0.836182i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25923 | + | 0.0861339i | 1.25923 | + | 0.0861339i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(32\) | 0.249789 | − | 0.0792796i | 0.249789 | − | 0.0792796i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.187602 | + | 0.669562i | 0.187602 | + | 0.669562i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.48947 | − | 1.21177i | −1.48947 | − | 1.21177i | ||||
\(37\) | 0 | 0 | 0.169910 | − | 0.985460i | \(-0.445652\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(38\) | 1.99023 | + | 1.50924i | 1.99023 | + | 1.50924i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.0341411 | − | 0.999417i | \(-0.489130\pi\) | ||||
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 1.36161i | − | 1.36161i | ||||||
\(47\) | 0.985460 | − | 0.169910i | 0.985460 | − | 0.169910i | ||||
\(48\) | −0.542188 | + | 0.542188i | −0.542188 | + | 0.542188i | ||||
\(49\) | 0.398401 | − | 0.917211i | 0.398401 | − | 0.917211i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.277739 | + | 0.297386i | 0.277739 | + | 0.297386i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.850966 | − | 1.78933i | −0.850966 | − | 1.78933i | −0.548452 | − | 0.836182i | \(-0.684783\pi\) |
−0.302515 | − | 0.953145i | \(-0.597826\pi\) | |||||||
\(54\) | −1.67310 | − | 0.347674i | −1.67310 | − | 0.347674i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.44042 | + | 0.248353i | 1.44042 | + | 0.248353i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.11059 | − | 1.57335i | 1.11059 | − | 1.57335i | 0.334880 | − | 0.942261i | \(-0.391304\pi\) |
0.775711 | − | 0.631088i | \(-0.217391\pi\) | |||||||
\(62\) | −0.652480 | − | 2.05580i | −0.652480 | − | 2.05580i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.766521 | − | 0.942181i | −0.766521 | − | 0.942181i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.836182 | − | 0.548452i | \(-0.815217\pi\) | ||||
0.836182 | + | 0.548452i | \(0.184783\pi\) | |||||||
\(68\) | 0.622563 | − | 0.472104i | 0.622563 | − | 0.472104i | ||||
\(69\) | −0.366581 | − | 0.707469i | −0.366581 | − | 0.707469i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(72\) | −0.475660 | + | 1.49868i | −0.475660 | + | 1.49868i | ||||
\(73\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.757212 | − | 2.70252i | 0.757212 | − | 2.70252i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.37749 | + | 0.713755i | 1.37749 | + | 0.713755i | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.962917 | + | 0.269797i | −0.962917 | + | 0.269797i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.666248 | − | 0.0684924i | 0.666248 | − | 0.0684924i | 0.236764 | − | 0.971567i | \(-0.423913\pi\) |
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.42329 | + | 0.561274i | −1.42329 | + | 0.561274i | ||||
\(93\) | −0.892493 | − | 0.892493i | −0.892493 | − | 0.892493i | ||||
\(94\) | −0.887885 | − | 1.46007i | −0.887885 | − | 1.46007i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.240372 | − | 0.104408i | −0.240372 | − | 0.104408i | ||||
\(97\) | 0 | 0 | 0.657204 | − | 0.753713i | \(-0.271739\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(98\) | −1.70784 | − | 0.0583417i | −1.70784 | − | 0.0583417i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(102\) | 0.298640 | − | 0.627950i | 0.298640 | − | 0.627950i | ||||
\(103\) | 0 | 0 | 0.604236 | − | 0.796805i | \(-0.293478\pi\) | ||||
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.31102 | + | 2.47450i | −2.31102 | + | 2.47450i | ||||
\(107\) | −0.977935 | + | 1.73926i | −0.977935 | + | 1.73926i | −0.429483 | + | 0.903075i | \(0.641304\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(108\) | 0.326250 | + | 1.89221i | 0.326250 | + | 1.89221i | ||||
\(109\) | 0.867003 | − | 1.67324i | 0.867003 | − | 1.67324i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
0.730836 | − | 0.682553i | \(-0.239130\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.58748 | − | 0.386859i | −1.58748 | − | 0.386859i | −0.657204 | − | 0.753713i | \(-0.728261\pi\) |
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(114\) | −0.508185 | − | 2.44552i | −0.508185 | − | 2.44552i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.203456 | − | 0.979084i | −0.203456 | − | 0.979084i | ||||
\(122\) | −3.19737 | − | 0.779178i | −3.19737 | − | 0.779178i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.87997 | + | 1.52947i | −1.87997 | + | 1.52947i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(128\) | −0.888811 | + | 1.58075i | −0.888811 | + | 1.58075i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.546666 | − | 0.332435i | −0.546666 | − | 0.332435i | ||||
\(137\) | 1.88342 | + | 0.0643397i | 1.88342 | + | 0.0643397i | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) |
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(138\) | −0.894853 | + | 1.02626i | −0.894853 | + | 1.02626i | ||||
\(139\) | 1.62876 | + | 0.707469i | 1.62876 | + | 0.707469i | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) |
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.854419 | − | 0.519584i | −0.854419 | − | 0.519584i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.764982 | − | 0.0523262i | 0.764982 | − | 0.0523262i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.903075 | + | 0.429483i | −0.903075 | + | 0.429483i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.942261 | − | 0.334880i | \(-0.108696\pi\) | ||||
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.440832 | + | 0.311173i | −0.440832 | + | 0.311173i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) |
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(152\) | −2.28622 | + | 0.235030i | −2.28622 | + | 0.235030i | ||||
\(153\) | −0.0138924 | − | 0.406675i | −0.0138924 | − | 0.406675i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.753713 | − | 0.657204i | \(-0.228261\pi\) | ||||
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(158\) | 0.271116 | − | 2.63723i | 0.271116 | − | 2.63723i | ||||
\(159\) | −0.534568 | + | 1.90790i | −0.534568 | + | 1.90790i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.03254 | + | 1.36161i | 1.03254 | + | 1.36161i | ||||
\(163\) | 0 | 0 | 0.302515 | − | 0.953145i | \(-0.402174\pi\) | ||||
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.526549 | − | 1.01619i | −0.526549 | − | 1.01619i | ||||
\(167\) | 0.216997 | − | 0.164554i | 0.216997 | − | 0.164554i | −0.490110 | − | 0.871660i | \(-0.663043\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.519584 | + | 0.854419i | 0.519584 | + | 0.854419i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.922444 | − | 1.13384i | −0.922444 | − | 1.13384i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.348908 | + | 1.09932i | 0.348908 | + | 1.09932i | 0.953145 | + | 0.302515i | \(0.0978261\pi\) |
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.59976 | + | 0.332435i | 1.59976 | + | 0.332435i | 0.917211 | − | 0.398401i | \(-0.130435\pi\) |
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.87108 | + | 0.455969i | −1.87108 | + | 0.455969i | ||||
\(184\) | 0.855140 | + | 0.915632i | 0.855140 | + | 0.915632i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.859293 | + | 1.97829i | −0.859293 | + | 1.97829i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.16021 | + | 1.52997i | −1.16021 | + | 1.52997i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(192\) | −0.0414679 | + | 1.21389i | −0.0414679 | + | 1.21389i | ||||
\(193\) | 0 | 0 | −0.236764 | − | 0.971567i | \(-0.576087\pi\) | ||||
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.643012 | + | 1.80926i | 0.643012 | + | 1.80926i | ||||
\(197\) | −1.53451 | − | 1.16366i | −1.53451 | − | 1.16366i | −0.930278 | − | 0.366854i | \(-0.880435\pi\) |
−0.604236 | − | 0.796805i | \(-0.706522\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.211252 | − | 0.171866i | −0.211252 | − | 0.171866i | 0.519584 | − | 0.854419i | \(-0.326087\pi\) |
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.779503 | − | 0.0533194i | −0.779503 | − | 0.0533194i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.188654 | + | 0.774147i | −0.188654 | + | 0.774147i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.794945 | − | 1.83015i | −0.794945 | − | 1.83015i | −0.460065 | − | 0.887885i | \(-0.652174\pi\) |
−0.334880 | − | 0.942261i | \(-0.608696\pi\) | |||||||
\(212\) | 3.53924 | + | 1.39569i | 3.53924 | + | 1.39569i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.37795 | + | 0.464289i | 3.37795 | + | 0.464289i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.34345 | − | 0.816970i | 1.34345 | − | 0.816970i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −3.20346 | − | 0.329326i | −3.20346 | − | 0.329326i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | ||||
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.380196 | + | 2.76613i | 0.380196 | + | 2.76613i | ||||
\(227\) | 0.487293 | + | 0.231746i | 0.487293 | + | 0.231746i | 0.657204 | − | 0.753713i | \(-0.271739\pi\) |
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(228\) | −2.34683 | + | 1.53929i | −2.34683 | + | 1.53929i | ||||
\(229\) | 0.180699 | − | 0.508438i | 0.180699 | − | 0.508438i | −0.816970 | − | 0.576680i | \(-0.804348\pi\) |
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.0999066 | − | 0.253346i | −0.0999066 | − | 0.253346i | 0.871660 | − | 0.490110i | \(-0.163043\pi\) |
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.569146 | − | 1.44325i | −0.569146 | − | 1.44325i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.730836 | − | 0.682553i | \(-0.239130\pi\) | ||||
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.663521 | + | 1.86697i | −0.663521 | + | 1.86697i | −0.203456 | + | 0.979084i | \(0.565217\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(242\) | −1.42890 | + | 0.937216i | −1.42890 | + | 0.937216i | ||||
\(243\) | 0.903075 | + | 0.429483i | 0.903075 | + | 0.429483i | ||||
\(244\) | 0.503524 | + | 3.66341i | 0.503524 | + | 3.66341i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.72989 | + | 0.972667i | 1.72989 | + | 0.972667i | ||||
\(249\) | −0.547173 | − | 0.386237i | −0.547173 | − | 0.386237i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.86681 | + | 0.256587i | 1.86681 | + | 0.256587i | ||||
\(257\) | 1.86642 | + | 0.592374i | 1.86642 | + | 0.592374i | 0.994757 | + | 0.102264i | \(0.0326087\pi\) |
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.434326 | − | 1.78226i | 0.434326 | − | 1.78226i | −0.169910 | − | 0.985460i | \(-0.554348\pi\) |
0.604236 | − | 0.796805i | \(-0.293478\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.269797 | − | 0.962917i | \(-0.586957\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.05893 | + | 0.861502i | 1.05893 | + | 0.861502i | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) |
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(272\) | −0.0530133 | + | 0.307471i | −0.0530133 | + | 0.307471i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.07843 | − | 3.03440i | −1.07843 | − | 3.03440i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.44163 | + | 0.512354i | 1.44163 | + | 0.512354i | ||||
\(277\) | 0 | 0 | −0.236764 | − | 0.971567i | \(-0.576087\pi\) | ||||
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(278\) | 0.103601 | − | 3.03274i | 0.103601 | − | 3.03274i | ||||
\(279\) | 0.0861339 | + | 1.25923i | 0.0861339 | + | 1.25923i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −0.290349 | + | 1.68399i | −0.290349 | + | 1.68399i | ||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.112554 | + | 0.236668i | 0.112554 | + | 0.236668i | ||||
\(289\) | −0.816970 | − | 0.169768i | −0.816970 | − | 0.169768i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.106270 | − | 1.03372i | −0.106270 | − | 1.03372i | −0.903075 | − | 0.429483i | \(-0.858696\pi\) |
0.796805 | − | 0.604236i | \(-0.206522\pi\) | |||||||
\(294\) | 1.24888 | + | 1.16637i | 1.24888 | + | 1.16637i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.771025 | + | 0.505716i | 0.771025 | + | 0.505716i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.515625 | + | 0.995111i | 0.515625 | + | 0.995111i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.637780 | + | 0.277027i | −0.637780 | + | 0.277027i | ||||
\(307\) | 0 | 0 | 0.302515 | − | 0.953145i | \(-0.402174\pi\) | ||||
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.753713 | − | 0.657204i | \(-0.228261\pi\) | ||||
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.86847 | + | 0.803707i | −2.86847 | + | 0.803707i | ||||
\(317\) | 0.0681230 | + | 1.99417i | 0.0681230 | + | 1.99417i | 0.102264 | + | 0.994757i | \(0.467391\pi\) |
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(318\) | 3.36809 | − | 0.346251i | 3.36809 | − | 0.346251i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.88013 | − | 0.668198i | 1.88013 | − | 0.668198i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.537123 | − | 0.255445i | 0.537123 | − | 0.255445i | ||||
\(324\) | 0.997669 | − | 1.64060i | 0.997669 | − | 1.64060i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.75313 | + | 0.691345i | −1.75313 | + | 0.691345i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.614311 | − | 0.266833i | −0.614311 | − | 0.266833i | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(332\) | −0.845180 | + | 0.969294i | −0.845180 | + | 0.969294i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.397624 | − | 0.241801i | −0.397624 | − | 0.241801i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.429483 | − | 0.903075i | \(-0.358696\pi\) | ||||
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(338\) | 1.03254 | − | 1.36161i | 1.03254 | − | 1.36161i | ||||
\(339\) | 0.942261 | + | 1.33488i | 0.942261 | + | 1.33488i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.22418 | + | 2.17720i | −1.22418 | + | 2.17720i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.52886 | − | 1.24382i | 1.52886 | − | 1.24382i | ||||
\(347\) | −0.565274 | − | 1.00534i | −0.565274 | − | 1.00534i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
0.429483 | − | 0.903075i | \(-0.358696\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.361291 | − | 1.73863i | −0.361291 | − | 1.73863i | −0.631088 | − | 0.775711i | \(-0.717391\pi\) |
0.269797 | − | 0.962917i | \(-0.413043\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.500795 | − | 1.26993i | 0.500795 | − | 1.26993i | −0.429483 | − | 0.903075i | \(-0.641304\pi\) |
0.930278 | − | 0.366854i | \(-0.119565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.522857 | − | 1.00907i | 0.522857 | − | 1.00907i | ||||
\(362\) | −0.474414 | − | 2.75154i | −0.474414 | − | 2.75154i | ||||
\(363\) | −0.490110 | + | 0.871660i | −0.490110 | + | 0.871660i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.89782 | + | 2.68860i | 1.89782 | + | 2.68860i | ||||
\(367\) | 0 | 0 | 0.604236 | − | 0.796805i | \(-0.293478\pi\) | ||||
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(368\) | 0.262399 | − | 0.551746i | 0.262399 | − | 0.551746i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.42213 | + | 0.0827424i | 2.42213 | + | 0.0827424i | ||||
\(373\) | 0 | 0 | 0.657204 | − | 0.753713i | \(-0.271739\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.51405 | + | 0.424216i | 1.51405 | + | 0.424216i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.136167 | + | 0.00931405i | −0.136167 | + | 0.00931405i | −0.136167 | − | 0.990686i | \(-0.543478\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.632563 | + | 0.964420i | 0.632563 | + | 0.964420i | 0.999417 | + | 0.0341411i | \(0.0108696\pi\) |
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(384\) | 1.70878 | − | 0.607301i | 1.70878 | − | 0.607301i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.287878 | − | 0.149166i | −0.287878 | − | 0.149166i | ||||
\(392\) | 1.18510 | − | 1.03336i | 1.18510 | − | 1.03336i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.887885 | + | 3.16890i | −0.887885 | + | 3.16890i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(398\) | −0.140782 | + | 0.443569i | −0.140782 | + | 0.443569i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.193552 | + | 0.609831i | 0.193552 | + | 0.609831i | ||||
\(409\) | 1.02405 | − | 1.45075i | 1.02405 | − | 1.45075i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
0.887885 | − | 0.460065i | \(-0.152174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.37728 | − | 1.28629i | −1.37728 | − | 1.28629i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.34892 | − | 0.185405i | 1.34892 | − | 0.185405i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.762664 | − | 1.60365i | −0.762664 | − | 1.60365i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.794945 | + | 1.83015i | −0.794945 | + | 1.83015i | −0.334880 | + | 0.942261i | \(0.608696\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(422\) | −2.41103 | + | 2.41103i | −2.41103 | + | 2.41103i | ||||
\(423\) | 0.302515 | + | 0.953145i | 0.302515 | + | 0.953145i | ||||
\(424\) | − | 3.11542i | − | 3.11542i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.907117 | − | 3.72237i | −0.907117 | − | 3.72237i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(432\) | −0.610966 | − | 0.463310i | −0.610966 | − | 0.463310i | ||||
\(433\) | 0 | 0 | 0.169910 | − | 0.985460i | \(-0.445652\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.976267 | + | 3.48434i | 0.976267 | + | 3.48434i | ||||
\(437\) | −1.14773 | + | 0.197888i | −1.14773 | + | 0.197888i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.668198 | − | 0.0457060i | −0.668198 | − | 0.0457060i | −0.269797 | − | 0.962917i | \(-0.586957\pi\) |
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.962917 | + | 0.269797i | 0.962917 | + | 0.269797i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.03357 | + | 1.57580i | −1.03357 | + | 1.57580i | −0.236764 | + | 0.971567i | \(0.576087\pi\) |
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.73473 | − | 1.53766i | 2.73473 | − | 1.53766i | ||||
\(453\) | 0.536765 | + | 0.0551811i | 0.536765 | + | 0.0551811i | ||||
\(454\) | 0.0629249 | − | 0.919929i | 0.0629249 | − | 0.919929i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.87761 | + | 1.32536i | 1.87761 | + | 1.32536i | ||||
\(457\) | 0 | 0 | −0.871660 | − | 0.490110i | \(-0.836957\pi\) | ||||
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(458\) | −0.921541 | + | 0.0314808i | −0.921541 | + | 0.0314808i | ||||
\(459\) | −0.256797 | + | 0.315646i | −0.256797 | + | 0.315646i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.836182 | − | 0.548452i | \(-0.184783\pi\) | ||||
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.340112 | + | 0.317642i | −0.340112 | + | 0.317642i | ||||
\(467\) | 1.33842 | + | 1.16704i | 1.33842 | + | 1.16704i | 0.971567 | + | 0.236764i | \(0.0760870\pi\) |
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −1.93754 | + | 1.80954i | −1.93754 | + | 1.80954i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.65679 | − | 1.08669i | 1.65679 | − | 1.08669i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.38387 | − | 0.115597i | 3.38387 | − | 0.115597i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.56869 | + | 1.10730i | 1.56869 | + | 1.10730i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.116615 | − | 1.70486i | 0.116615 | − | 1.70486i | ||||
\(487\) | 0 | 0 | −0.994757 | − | 0.102264i | \(-0.967391\pi\) | ||||
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(488\) | 2.63947 | − | 1.48410i | 2.63947 | − | 1.48410i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.131782 | − | 0.958784i | 0.131782 | − | 0.958784i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.270979 | + | 1.11197i | −0.270979 | + | 1.11197i | ||||
\(499\) | −0.767255 | − | 0.214975i | −0.767255 | − | 0.214975i | −0.136167 | − | 0.990686i | \(-0.543478\pi\) |
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.271698 | − | 0.0185847i | −0.271698 | − | 0.0185847i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.02406 | − | 0.176565i | 1.02406 | − | 0.176565i | 0.366854 | − | 0.930278i | \(-0.380435\pi\) |
0.657204 | + | 0.753713i | \(0.271739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.169910 | − | 0.985460i | 0.169910 | − | 0.985460i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.333028 | − | 1.36659i | −0.333028 | − | 1.36659i | ||||
\(513\) | −0.0499031 | + | 1.46082i | −0.0499031 | + | 1.46082i | ||||
\(514\) | −0.228352 | − | 3.33839i | −0.228352 | − | 3.33839i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.459500 | − | 1.05788i | 0.459500 | − | 1.05788i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.682553 | − | 0.730836i | \(-0.739130\pi\) | ||||
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.429483 | − | 0.903075i | \(-0.641304\pi\) | ||||
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.10554 | + | 0.426846i | −3.10554 | + | 0.426846i | ||||
\(527\) | −0.506127 | − | 0.0872650i | −0.506127 | − | 0.0872650i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.266833 | − | 0.249204i | −0.266833 | − | 0.249204i | ||||
\(530\) | 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 | ||||||||
\(541\) | 1.42298 | − | 0.618088i | 1.42298 | − | 0.618088i | 0.460065 | − | 0.887885i | \(-0.347826\pi\) |
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(542\) | 0.705690 | − | 2.22345i | 0.705690 | − | 2.22345i | ||||
\(543\) | −0.987286 | − | 1.30193i | −0.987286 | − | 1.30193i | ||||
\(544\) | −0.104408 | + | 0.0216963i | −0.104408 | + | 0.0216963i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.102264 | − | 0.994757i | \(-0.467391\pi\) | ||||
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(548\) | −2.72733 | + | 2.37811i | −2.72733 | + | 2.37811i | ||||
\(549\) | 1.70992 | + | 0.886009i | 1.70992 | + | 0.886009i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.0427739 | − | 1.25212i | −0.0427739 | − | 1.25212i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.21284 | + | 1.14184i | −3.21284 | + | 1.14184i | ||||
\(557\) | −1.07396 | − | 1.63739i | −1.07396 | − | 1.63739i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.366854 | − | 0.930278i | \(-0.619565\pi\) | |||||||
\(558\) | 1.94780 | − | 0.926334i | 1.94780 | − | 0.926334i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.38463 | + | 1.38463i | 1.38463 | + | 1.38463i | 0.836182 | + | 0.548452i | \(0.184783\pi\) |
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(564\) | 1.87997 | − | 0.390662i | 1.87997 | − | 0.390662i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.854419 | − | 0.519584i | \(-0.826087\pi\) | ||||
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.277739 | − | 1.33655i | 0.277739 | − | 1.33655i | −0.576680 | − | 0.816970i | \(-0.695652\pi\) |
0.854419 | − | 0.519584i | \(-0.173913\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.829031 | − | 0.887675i | 0.829031 | − | 0.887675i | ||||
\(577\) | 0 | 0 | 0.490110 | − | 0.871660i | \(-0.336957\pi\) | ||||
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(578\) | 0.242274 | + | 1.40516i | 0.242274 | + | 1.40516i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.57668 | + | 0.816970i | −1.57668 | + | 0.816970i | ||||
\(587\) | 0.536221 | − | 1.35976i | 0.536221 | − | 1.35976i | −0.366854 | − | 0.930278i | \(-0.619565\pi\) |
0.903075 | − | 0.429483i | \(-0.141304\pi\) | |||||||
\(588\) | 0.704408 | − | 1.78626i | 0.704408 | − | 1.78626i | ||||
\(589\) | −1.63805 | + | 0.848768i | −1.63805 | + | 0.848768i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.391823 | + | 1.88555i | 0.391823 | + | 1.88555i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.509307 | + | 0.905802i | 0.509307 | + | 0.905802i | 0.999417 | + | 0.0341411i | \(0.0108696\pi\) |
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.0462723 | + | 0.268373i | 0.0462723 | + | 0.268373i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.665120 | − | 0.942261i | −0.665120 | − | 0.942261i | 0.334880 | − | 0.942261i | \(-0.391304\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.210799 | − | 1.01442i | 0.210799 | − | 1.01442i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) | ||||
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(608\) | −0.251747 | + | 0.288716i | −0.251747 | + | 0.288716i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.552480 | + | 0.552480i | 0.552480 | + | 0.552480i | ||||
\(613\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.40105 | − | 0.666310i | 1.40105 | − | 0.666310i | 0.429483 | − | 0.903075i | \(-0.358696\pi\) |
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.81464 | − | 0.644923i | 1.81464 | − | 0.644923i | 0.816970 | − | 0.576680i | \(-0.195652\pi\) |
0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.650963 | − | 0.459500i | 0.650963 | − | 0.459500i | ||||
\(622\) | 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 | ||||||||
\(631\) | 0.780136 | − | 0.162114i | 0.780136 | − | 0.162114i | 0.203456 | − | 0.979084i | \(-0.434783\pi\) |
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(632\) | 1.47397 | + | 1.94371i | 1.47397 | + | 1.94371i | ||||
\(633\) | −0.603619 | + | 1.90185i | −0.603619 | + | 1.90185i | ||||
\(634\) | 3.12742 | − | 1.35843i | 3.12742 | − | 1.35843i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.75031 | − | 3.37795i | −1.75031 | − | 3.37795i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.631088 | − | 0.775711i | \(-0.717391\pi\) | ||||
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(642\) | −2.24087 | − | 2.56994i | −2.24087 | − | 2.56994i | ||||
\(643\) | 0 | 0 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.742799 | − | 0.693726i | −0.742799 | − | 0.693726i | ||||
\(647\) | −0.202623 | − | 1.97098i | −0.202623 | − | 1.97098i | −0.236764 | − | 0.971567i | \(-0.576087\pi\) |
0.0341411 | − | 0.999417i | \(-0.489130\pi\) | |||||||
\(648\) | −1.54949 | − | 0.267159i | −1.54949 | − | 0.267159i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.32629 | − | 0.323209i | 1.32629 | − | 0.323209i | 0.490110 | − | 0.871660i | \(-0.336957\pi\) |
0.836182 | + | 0.548452i | \(0.184783\pi\) | |||||||
\(654\) | 2.19806 | + | 2.35354i | 2.19806 | + | 2.35354i | ||||
\(655\) | 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 | ||||||||
\(661\) | 0.0277687 | + | 0.405963i | 0.0277687 | + | 0.405963i | 0.990686 | + | 0.136167i | \(0.0434783\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(662\) | −0.0390749 | + | 1.14384i | −0.0390749 | + | 1.14384i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.992294 | + | 0.352661i | 0.992294 | + | 0.352661i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −0.0888487 | + | 0.515312i | −0.0888487 | + | 0.515312i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) | ||||
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.84893 | − | 0.518045i | −1.84893 | − | 0.518045i | ||||
\(677\) | −0.420439 | + | 1.72528i | −0.420439 | + | 1.72528i | 0.236764 | + | 0.971567i | \(0.423913\pi\) |
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(678\) | 1.53135 | − | 2.33474i | 1.53135 | − | 2.33474i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.214975 | − | 0.494921i | −0.214975 | − | 0.494921i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.74847 | + | 0.554940i | 1.74847 | + | 0.554940i | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) |
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(684\) | 2.78046 | + | 0.382165i | 2.78046 | + | 0.382165i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.470342 | + | 0.264460i | −0.470342 | + | 0.264460i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.59976 | − | 1.12924i | −1.59976 | − | 1.12924i | −0.917211 | − | 0.398401i | \(-0.869565\pi\) |
−0.682553 | − | 0.730836i | \(-0.739130\pi\) | |||||||
\(692\) | −1.93038 | − | 1.08540i | −1.93038 | − | 1.08540i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.24382 | + | 1.52886i | −1.24382 | + | 1.52886i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −2.53740 | + | 1.66428i | −2.53740 | + | 1.66428i | ||||
\(699\) | −0.0911989 | + | 0.256609i | −0.0911989 | + | 0.256609i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.730836 | − | 0.682553i | \(-0.239130\pi\) | ||||
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.33275 | −2.33275 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.34066 | − | 1.25209i | 1.34066 | − | 1.25209i | 0.398401 | − | 0.917211i | \(-0.369565\pi\) |
0.942261 | − | 0.334880i | \(-0.108696\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.519540 | + | 1.46184i | −0.519540 | + | 1.46184i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.908226 | + | 0.431933i | 0.908226 | + | 0.431933i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.93189 | − | 0.198604i | −1.93189 | − | 0.198604i | ||||
\(723\) | 1.72708 | − | 0.971091i | 1.72708 | − | 0.971091i | ||||
\(724\) | −2.68064 | + | 1.63013i | −2.68064 | + | 1.63013i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.69292 | + | 0.232687i | 1.69292 | + | 0.232687i | ||||
\(727\) | 0 | 0 | −0.953145 | − | 0.302515i | \(-0.902174\pi\) | ||||
0.953145 | + | 0.302515i | \(0.0978261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.398401 | − | 0.917211i | −0.398401 | − | 0.917211i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.02809 | − | 3.09208i | 2.02809 | − | 3.09208i | ||||
\(733\) | 0 | 0 | 0.236764 | − | 0.971567i | \(-0.423913\pi\) | ||||
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.208330 | + | 0.0142502i | 0.208330 | + | 0.0142502i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.311173 | + | 1.11059i | 0.311173 | + | 1.11059i | 0.942261 | + | 0.334880i | \(0.108696\pi\) |
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.16467 | + | 0.883195i | 1.16467 | + | 0.883195i | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) |
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(744\) | −0.664598 | − | 1.87000i | −0.664598 | − | 1.87000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.158575 | + | 0.650716i | 0.158575 | + | 0.650716i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.99534i | 1.99534i | 0.0682424 | + | 0.997669i | \(0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(752\) | −0.0784130 | − | 0.762749i | −0.0784130 | − | 0.762749i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.971567 | − | 0.236764i | \(-0.0760870\pi\) | ||||
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(758\) | 0.100169 | + | 0.210625i | 0.100169 | + | 0.210625i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.990686 | − | 0.136167i | \(-0.0434783\pi\) | ||||
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.13658 | − | 1.61017i | 1.13658 | − | 1.61017i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.23841 | − | 1.42027i | −1.23841 | − | 1.42027i | ||||
\(769\) | −0.256797 | − | 0.315646i | −0.256797 | − | 0.315646i | 0.631088 | − | 0.775711i | \(-0.282609\pi\) |
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.01743 | − | 1.67310i | −1.01743 | − | 1.67310i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.733164 | − | 0.555976i | 0.733164 | − | 0.555976i | −0.169910 | − | 0.985460i | \(-0.554348\pi\) |
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −0.0566599 | + | 0.551149i | −0.0566599 | + | 0.551149i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.680803 | − | 0.352764i | −0.680803 | − | 0.352764i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) | ||||
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(788\) | 3.67847 | − | 0.378158i | 3.67847 | − | 0.378158i | ||||
\(789\) | −1.49867 | + | 1.05788i | −1.49867 | + | 1.05788i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.521696 | − | 0.0356850i | 0.521696 | − | 0.0356850i | ||||
\(797\) | −1.65196 | + | 0.651449i | −1.65196 | + | 0.651449i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.405963 | + | 0.0277687i | −0.405963 | + | 0.0277687i | ||||
\(800\) | 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 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.787230 | + | 0.842917i | −0.787230 | + | 0.842917i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.231946 | − | 1.34526i | −0.231946 | − | 1.34526i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.242028 | − | 0.196904i | 0.242028 | − | 0.196904i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.94823 | − | 0.718463i | −2.94823 | − | 0.718463i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(822\) | −1.18140 | + | 2.99582i | −1.18140 | + | 2.99582i | ||||
\(823\) | 0 | 0 | 0.366854 | − | 0.930278i | \(-0.380435\pi\) | ||||
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.893968 | − | 0.217854i | −0.893968 | − | 0.217854i | −0.236764 | − | 0.971567i | \(-0.576087\pi\) |
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(828\) | −0.749851 | − | 1.33361i | −0.749851 | − | 1.33361i | ||||
\(829\) | −0.806094 | + | 0.655806i | −0.806094 | + | 0.655806i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) |
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.199432 | + | 0.354689i | −0.199432 | + | 0.354689i | ||||
\(834\) | −2.07121 | + | 2.21773i | −2.07121 | + | 2.21773i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.762653 | − | 1.00571i | 0.762653 | − | 1.00571i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.854419 | + | 0.519584i | 0.854419 | + | 0.519584i | ||||
\(842\) | 3.40772 | + | 0.116411i | 3.40772 | + | 0.116411i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.51412 | + | 1.52640i | 3.51412 | + | 1.52640i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.32557 | − | 1.07843i | 1.32557 | − | 1.07843i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.41333 | + | 0.557345i | −1.41333 | + | 0.557345i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.548452 | − | 0.836182i | \(-0.684783\pi\) | ||||
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.56314 | + | 1.80926i | −2.56314 | + | 1.80926i | ||||
\(857\) | −1.98488 | + | 0.204051i | −1.98488 | + | 0.204051i | −0.985460 | + | 0.169910i | \(0.945652\pi\) |
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.00063 | + | 0.280364i | −1.00063 | + | 0.280364i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.158655 | + | 1.54329i | −0.158655 | + | 1.54329i | 0.548452 | + | 0.836182i | \(0.315217\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0.0707053 | − | 0.252350i | 0.0707053 | − | 0.252350i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.504189 | + | 0.664872i | 0.504189 | + | 0.664872i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.36104 | − | 1.79043i | 2.36104 | − | 1.79043i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.03409 | + | 1.70048i | 1.03409 | + | 1.70048i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.657204 | − | 0.753713i | \(-0.728261\pi\) | ||||
0.657204 | + | 0.753713i | \(0.271739\pi\) | |||||||
\(878\) | 0.346231 | + | 1.09088i | 0.346231 | + | 1.09088i | ||||
\(879\) | −0.599268 | + | 0.848969i | −0.599268 | + | 0.848969i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(882\) | −0.174753 | − | 1.69988i | −0.174753 | − | 1.69988i | ||||
\(883\) | 0 | 0 | −0.985460 | − | 0.169910i | \(-0.945652\pi\) | ||||
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.15299 | + | 0.655198i | 3.15299 | + | 0.655198i | ||||
\(887\) | −0.627764 | − | 1.32000i | −0.627764 | − | 1.32000i | −0.930278 | − | 0.366854i | \(-0.880435\pi\) |
0.302515 | − | 0.953145i | \(-0.402174\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.10168 | + | 0.960616i | −1.10168 | + | 0.960616i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.269995 | + | 0.759692i | 0.269995 | + | 0.759692i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.99290 | − | 1.62135i | −1.99290 | − | 1.62135i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.248774 | − | 0.887885i | −0.248774 | − | 0.887885i | ||||
\(907\) | 0 | 0 | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) | ||||
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(908\) | −0.987544 | + | 0.313432i | −0.987544 | + | 0.313432i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(912\) | 0.265357 | − | 1.08890i | 0.265357 | − | 1.08890i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.412779 | + | 0.950313i | 0.412779 | + | 0.950313i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.662766 | + | 0.210353i | 0.662766 | + | 0.210353i | ||||
\(919\) | 0.789381 | + | 0.108498i | 0.789381 | + | 0.108498i | 0.519584 | − | 0.854419i | \(-0.326087\pi\) |
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(920\) | 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 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.199031 | + | 1.44806i | 0.199031 | + | 1.44806i | ||||
\(932\) | 0.472232 | + | 0.224583i | 0.472232 | + | 0.224583i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.01619 | − | 2.85930i | 1.01619 | − | 2.85930i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.753713 | − | 0.657204i | \(-0.771739\pi\) | ||||
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(938\) | 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 | ||||||||
\(947\) | −0.769396 | + | 0.504647i | −0.769396 | + | 0.504647i | −0.871660 | − | 0.490110i | \(-0.836957\pi\) |
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(948\) | 2.69020 | + | 1.27940i | 2.69020 | + | 1.27940i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.25923 | − | 1.54781i | 1.25923 | − | 1.54781i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.905802 | − | 0.509307i | −0.905802 | − | 0.509307i | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) |
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(954\) | −2.76613 | − | 1.95255i | −2.76613 | − | 1.95255i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.587564 | + | 0.0807588i | 0.587564 | + | 0.0807588i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.85622 | − | 0.731998i | −1.85622 | − | 0.731998i | ||||
\(964\) | −1.51571 | − | 3.48952i | −1.51571 | − | 3.48952i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.548452 | − | 0.836182i | \(-0.315217\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(968\) | 0.372277 | − | 1.52765i | 0.372277 | − | 1.52765i | ||||
\(969\) | −0.572716 | − | 0.160468i | −0.572716 | − | 0.160468i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(972\) | −1.83016 | + | 0.580867i | −1.83016 | + | 0.580867i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.14547 | − | 0.931909i | −1.14547 | − | 0.931909i | ||||
\(977\) | −0.195968 | + | 1.13659i | −0.195968 | + | 1.13659i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.77571 | + | 0.631088i | 1.77571 | + | 0.631088i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.0184223 | + | 0.539279i | −0.0184223 | + | 0.539279i | 0.953145 | + | 0.302515i | \(0.0978261\pi\) |
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.0931581 | − | 0.0997480i | −0.0931581 | − | 0.0997480i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(992\) | 0.321372 | − | 0.0783162i | 0.321372 | − | 0.0783162i | ||||
\(993\) | 0.287650 | + | 0.604843i | 0.287650 | + | 0.604843i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.27405 | − | 0.175114i | 1.27405 | − | 0.175114i | ||||
\(997\) | 0 | 0 | −0.985460 | − | 0.169910i | \(-0.945652\pi\) | ||||
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(998\) | 0.139244 | + | 1.35447i | 0.139244 | + | 1.35447i | ||||
\(999\) | 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.368.1 | yes | 88 | |
3.2 | odd | 2 | inner | 3525.1.bg.a.368.2 | yes | 88 | |
5.2 | odd | 4 | inner | 3525.1.bg.a.932.2 | yes | 88 | |
5.3 | odd | 4 | inner | 3525.1.bg.a.932.1 | yes | 88 | |
5.4 | even | 2 | inner | 3525.1.bg.a.368.2 | yes | 88 | |
15.2 | even | 4 | inner | 3525.1.bg.a.932.1 | yes | 88 | |
15.8 | even | 4 | inner | 3525.1.bg.a.932.2 | yes | 88 | |
15.14 | odd | 2 | CM | 3525.1.bg.a.368.1 | yes | 88 | |
47.41 | odd | 46 | inner | 3525.1.bg.a.3143.1 | yes | 88 | |
141.41 | even | 46 | inner | 3525.1.bg.a.3143.2 | yes | 88 | |
235.88 | even | 92 | inner | 3525.1.bg.a.182.1 | ✓ | 88 | |
235.182 | even | 92 | inner | 3525.1.bg.a.182.2 | yes | 88 | |
235.229 | odd | 46 | inner | 3525.1.bg.a.3143.2 | yes | 88 | |
705.182 | odd | 92 | inner | 3525.1.bg.a.182.1 | ✓ | 88 | |
705.323 | odd | 92 | inner | 3525.1.bg.a.182.2 | yes | 88 | |
705.464 | even | 46 | inner | 3525.1.bg.a.3143.1 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.1.bg.a.182.1 | ✓ | 88 | 235.88 | even | 92 | inner | |
3525.1.bg.a.182.1 | ✓ | 88 | 705.182 | odd | 92 | inner | |
3525.1.bg.a.182.2 | yes | 88 | 235.182 | even | 92 | inner | |
3525.1.bg.a.182.2 | yes | 88 | 705.323 | odd | 92 | inner | |
3525.1.bg.a.368.1 | yes | 88 | 1.1 | even | 1 | trivial | |
3525.1.bg.a.368.1 | yes | 88 | 15.14 | odd | 2 | CM | |
3525.1.bg.a.368.2 | yes | 88 | 3.2 | odd | 2 | inner | |
3525.1.bg.a.368.2 | yes | 88 | 5.4 | even | 2 | inner | |
3525.1.bg.a.932.1 | yes | 88 | 5.3 | odd | 4 | inner | |
3525.1.bg.a.932.1 | yes | 88 | 15.2 | even | 4 | inner | |
3525.1.bg.a.932.2 | yes | 88 | 5.2 | odd | 4 | inner | |
3525.1.bg.a.932.2 | yes | 88 | 15.8 | even | 4 | inner | |
3525.1.bg.a.3143.1 | yes | 88 | 47.41 | odd | 46 | inner | |
3525.1.bg.a.3143.1 | yes | 88 | 705.464 | even | 46 | inner | |
3525.1.bg.a.3143.2 | yes | 88 | 141.41 | even | 46 | inner | |
3525.1.bg.a.3143.2 | yes | 88 | 235.229 | odd | 46 | inner |