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 | 107.2 | ||
Root | \(-0.985460 - 0.169910i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.107 |
Dual form | 3525.1.bg.a.593.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times\).
\(n\) | \(1552\) | \(2026\) | \(2351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{11}{46}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34526 | + | 0.231946i | 1.34526 | + | 0.231946i | 0.796805 | − | 0.604236i | \(-0.206522\pi\) |
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(3\) | 0.994757 | + | 0.102264i | 0.994757 | + | 0.102264i | ||||
\(4\) | 0.813657 | + | 0.289174i | 0.813657 | + | 0.289174i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.31448 | + | 0.368301i | 1.31448 | + | 0.368301i | ||||
\(7\) | 0 | 0 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(8\) | −0.162405 | − | 0.0913155i | −0.162405 | − | 0.0913155i | ||||
\(9\) | 0.979084 | + | 0.203456i | 0.979084 | + | 0.203456i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(12\) | 0.779819 | + | 0.370865i | 0.779819 | + | 0.370865i | ||||
\(13\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.867134 | − | 0.705466i | −0.867134 | − | 0.705466i | ||||
\(17\) | −0.217854 | + | 0.893968i | −0.217854 | + | 0.893968i | 0.753713 | + | 0.657204i | \(0.228261\pi\) |
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(18\) | 1.26993 | + | 0.500795i | 1.26993 | + | 0.500795i | ||||
\(19\) | 1.28629 | + | 1.37728i | 1.28629 | + | 1.37728i | 0.887885 | + | 0.460065i | \(0.152174\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.277623 | − | 1.61018i | −0.277623 | − | 1.61018i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.429483 | − | 0.903075i | \(-0.358696\pi\) | |||||||
\(24\) | −0.152215 | − | 0.107445i | −0.152215 | − | 0.107445i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.953145 | + | 0.302515i | 0.953145 | + | 0.302515i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.655806 | − | 0.806094i | 0.655806 | − | 0.806094i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(32\) | −0.880441 | − | 1.00973i | −0.880441 | − | 1.00973i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.500422 | + | 1.15209i | −0.500422 | + | 1.15209i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.737804 | + | 0.448669i | 0.737804 | + | 0.448669i | ||||
\(37\) | 0 | 0 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(38\) | 1.41093 | + | 2.15114i | 1.41093 | + | 2.15114i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.269797 | − | 0.962917i | \(-0.413043\pi\) | ||||
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.429483 | − | 0.903075i | \(-0.641304\pi\) | ||||
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 2.23050i | − | 2.23050i | ||||||
\(47\) | −0.604236 | + | 0.796805i | −0.604236 | + | 0.796805i | ||||
\(48\) | −0.790444 | − | 0.790444i | −0.790444 | − | 0.790444i | ||||
\(49\) | −0.816970 | + | 0.576680i | −0.816970 | + | 0.576680i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.308133 | + | 0.867003i | −0.308133 | + | 0.867003i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.199432 | − | 0.354689i | −0.199432 | − | 0.354689i | 0.753713 | − | 0.657204i | \(-0.228261\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(54\) | 1.21206 | + | 0.628038i | 1.21206 | + | 0.628038i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.13870 | + | 1.50160i | 1.13870 | + | 1.50160i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.942261 | − | 0.334880i | \(-0.108696\pi\) | ||||
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.81734 | + | 0.249787i | −1.81734 | + | 0.249787i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(62\) | 1.06920 | − | 0.932292i | 1.06920 | − | 0.932292i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.369395 | − | 0.607445i | −0.369395 | − | 0.607445i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.302515 | − | 0.953145i | \(-0.402174\pi\) | ||||
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(68\) | −0.435770 | + | 0.664385i | −0.435770 | + | 0.664385i | ||||
\(69\) | −0.111504 | − | 1.63013i | −0.111504 | − | 1.63013i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(72\) | −0.140429 | − | 0.122448i | −0.140429 | − | 0.122448i | ||||
\(73\) | 0 | 0 | −0.836182 | − | 0.548452i | \(-0.815217\pi\) | ||||
0.836182 | + | 0.548452i | \(0.184783\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.648323 | + | 1.49259i | 0.648323 | + | 1.49259i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.70486 | − | 0.116615i | −1.70486 | − | 0.116615i | −0.816970 | − | 0.576680i | \(-0.804348\pi\) |
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.917211 | + | 0.398401i | 0.917211 | + | 0.398401i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.455969 | − | 1.87108i | −0.455969 | − | 1.87108i | −0.490110 | − | 0.871660i | \(-0.663043\pi\) |
0.0341411 | − | 0.999417i | \(-0.489130\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.730836 | − | 0.682553i | \(-0.760870\pi\) | ||||
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.239732 | − | 1.39042i | 0.239732 | − | 1.39042i | ||||
\(93\) | 0.734803 | − | 0.734803i | 0.734803 | − | 0.734803i | ||||
\(94\) | −0.997669 | + | 0.931758i | −0.997669 | + | 0.931758i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.772565 | − | 1.09448i | −0.772565 | − | 1.09448i | ||||
\(97\) | 0 | 0 | 0.102264 | − | 0.994757i | \(-0.467391\pi\) | ||||
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(98\) | −1.23279 | + | 0.586291i | −1.23279 | + | 0.586291i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(102\) | −0.615615 | + | 1.09487i | −0.615615 | + | 1.09487i | ||||
\(103\) | 0 | 0 | 0.836182 | − | 0.548452i | \(-0.184783\pi\) | ||||
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.186018 | − | 0.523405i | −0.186018 | − | 0.523405i | ||||
\(107\) | −0.463035 | − | 1.17418i | −0.463035 | − | 1.17418i | −0.953145 | − | 0.302515i | \(-0.902174\pi\) |
0.490110 | − | 0.871660i | \(-0.336957\pi\) | |||||||
\(108\) | 0.688053 | + | 0.521767i | 0.688053 | + | 0.521767i | ||||
\(109\) | 0.0368232 | − | 0.538336i | 0.0368232 | − | 0.538336i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) |
0.979084 | − | 0.203456i | \(-0.0652174\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.272175 | − | 0.00929776i | −0.272175 | − | 0.00929776i | −0.102264 | − | 0.994757i | \(-0.532609\pi\) |
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(114\) | 1.18355 | + | 2.28415i | 1.18355 | + | 2.28415i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.460065 | − | 0.887885i | −0.460065 | − | 0.887885i | ||||
\(122\) | −2.50272 | − | 0.0854955i | −2.50272 | − | 0.0854955i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.766702 | − | 0.466242i | 0.766702 | − | 0.466242i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.796805 | − | 0.604236i | \(-0.793478\pi\) | ||||
0.796805 | + | 0.604236i | \(0.206522\pi\) | |||||||
\(128\) | 0.135429 | + | 0.343423i | 0.135429 | + | 0.343423i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.117014 | − | 0.125291i | 0.117014 | − | 0.125291i | ||||
\(137\) | −0.487293 | + | 0.231746i | −0.487293 | + | 0.231746i | −0.657204 | − | 0.753713i | \(-0.728261\pi\) |
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(138\) | 0.228100 | − | 2.21881i | 0.228100 | − | 2.21881i | ||||
\(139\) | 1.15067 | + | 1.63013i | 1.15067 | + | 1.63013i | 0.631088 | + | 0.775711i | \(0.282609\pi\) |
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.682553 | + | 0.730836i | −0.682553 | + | 0.730836i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.705466 | − | 0.867134i | −0.705466 | − | 0.867134i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.871660 | + | 0.490110i | −0.871660 | + | 0.490110i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.269797 | − | 0.962917i | \(-0.586957\pi\) | ||||
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.108498 | + | 0.789381i | −0.108498 | + | 0.789381i | 0.854419 | + | 0.519584i | \(0.173913\pi\) |
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(152\) | −0.0831320 | − | 0.341134i | −0.0831320 | − | 0.341134i | ||||
\(153\) | −0.395181 | + | 0.830946i | −0.395181 | + | 0.830946i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(158\) | −2.26642 | − | 0.552311i | −2.26642 | − | 0.552311i | ||||
\(159\) | −0.162114 | − | 0.373224i | −0.162114 | − | 0.373224i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.14148 | + | 0.748695i | 1.14148 | + | 0.748695i | ||||
\(163\) | 0 | 0 | −0.753713 | − | 0.657204i | \(-0.771739\pi\) | ||||
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.179407 | − | 2.62284i | −0.179407 | − | 2.62284i | ||||
\(167\) | −1.07396 | + | 1.63739i | −1.07396 | + | 1.63739i | −0.366854 | + | 0.930278i | \(0.619565\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.730836 | − | 0.682553i | 0.730836 | − | 0.682553i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.979167 | + | 1.61017i | 0.979167 | + | 1.61017i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.49339 | + | 1.30216i | −1.49339 | + | 1.30216i | −0.657204 | + | 0.753713i | \(0.728261\pi\) |
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.241801 | + | 0.125291i | 0.241801 | + | 0.125291i | 0.576680 | − | 0.816970i | \(-0.304348\pi\) |
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.83335 | + | 0.0626292i | −1.83335 | + | 0.0626292i | ||||
\(184\) | −0.101947 | + | 0.286852i | −0.101947 | + | 0.286852i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.15893 | − | 0.818064i | 1.15893 | − | 0.818064i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.722056 | + | 0.473597i | −0.722056 | + | 0.473597i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(192\) | −0.305339 | − | 0.642036i | −0.305339 | − | 0.642036i | ||||
\(193\) | 0 | 0 | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) | ||||
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.831494 | + | 0.232974i | −0.831494 | + | 0.232974i | ||||
\(197\) | −1.00609 | − | 1.53391i | −1.00609 | − | 1.53391i | −0.836182 | − | 0.548452i | \(-0.815217\pi\) |
−0.169910 | − | 0.985460i | \(-0.554348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.67310 | + | 1.01743i | 1.67310 | + | 1.01743i | 0.942261 | + | 0.334880i | \(0.108696\pi\) |
0.730836 | + | 0.682553i | \(0.239130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.501429 | + | 0.616339i | −0.501429 | + | 0.616339i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.0557845 | − | 1.63299i | 0.0557845 | − | 1.63299i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03116 | + | 0.727872i | 1.03116 | + | 0.727872i | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) |
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(212\) | −0.0597022 | − | 0.346266i | −0.0597022 | − | 0.346266i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.350556 | − | 1.68697i | −0.350556 | − | 1.68697i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.127171 | − | 0.136167i | −0.127171 | − | 0.136167i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.174401 | − | 0.715659i | 0.174401 | − | 0.715659i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.363988 | − | 0.0756376i | −0.363988 | − | 0.0756376i | ||||
\(227\) | −0.694541 | − | 0.390521i | −0.694541 | − | 0.390521i | 0.102264 | − | 0.994757i | \(-0.467391\pi\) |
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(228\) | 0.492286 | + | 1.55107i | 0.492286 | + | 1.55107i | ||||
\(229\) | 0.767255 | + | 0.214975i | 0.767255 | + | 0.214975i | 0.631088 | − | 0.775711i | \(-0.282609\pi\) |
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.92970 | + | 0.332713i | 1.92970 | + | 0.332713i | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) |
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.68399 | − | 0.290349i | −1.68399 | − | 0.290349i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.391823 | − | 0.109784i | −0.391823 | − | 0.109784i | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(242\) | −0.412965 | − | 1.30114i | −0.412965 | − | 1.30114i | ||||
\(243\) | 0.871660 | + | 0.490110i | 0.871660 | + | 0.490110i | ||||
\(244\) | −1.55092 | − | 0.322285i | −1.55092 | − | 0.322285i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.180115 | + | 0.0710281i | −0.180115 | + | 0.0710281i | ||||
\(249\) | −0.262234 | − | 1.90790i | −0.262234 | − | 1.90790i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.247177 | + | 1.18948i | 0.247177 | + | 1.18948i | ||||
\(257\) | 1.16704 | − | 1.33842i | 1.16704 | − | 1.33842i | 0.236764 | − | 0.971567i | \(-0.423913\pi\) |
0.930278 | − | 0.366854i | \(-0.119565\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0393770 | − | 1.15269i | 0.0393770 | − | 1.15269i | −0.796805 | − | 0.604236i | \(-0.793478\pi\) |
0.836182 | − | 0.548452i | \(-0.184783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.398401 | − | 0.917211i | \(-0.369565\pi\) | ||||
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.572255 | + | 0.347996i | 0.572255 | + | 0.347996i | 0.775711 | − | 0.631088i | \(-0.217391\pi\) |
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(272\) | 0.819573 | − | 0.621502i | 0.819573 | − | 0.621502i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.709287 | + | 0.198733i | −0.709287 | + | 0.198733i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.380665 | − | 1.35861i | 0.380665 | − | 1.35861i | ||||
\(277\) | 0 | 0 | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) | ||||
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(278\) | 1.16985 | + | 2.45984i | 1.16985 | + | 2.45984i | ||||
\(279\) | 0.806094 | − | 0.655806i | 0.806094 | − | 0.655806i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −1.08772 | + | 0.824847i | −1.08772 | + | 0.824847i | ||||
\(283\) | 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 | ||||||||
\(288\) | −0.656589 | − | 1.16774i | −0.656589 | − | 1.16774i | ||||
\(289\) | 0.136167 | + | 0.0705559i | 0.136167 | + | 0.0705559i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.42011 | + | 0.346072i | −1.42011 | + | 0.346072i | −0.871660 | − | 0.490110i | \(-0.836957\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(294\) | −1.28629 | + | 0.457146i | −1.28629 | + | 0.457146i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.329051 | + | 1.03675i | −0.329051 | + | 1.03675i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.143761 | − | 2.10171i | −0.143761 | − | 2.10171i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.724354 | + | 1.02618i | −0.724354 | + | 1.02618i | ||||
\(307\) | 0 | 0 | −0.753713 | − | 0.657204i | \(-0.771739\pi\) | ||||
0.753713 | + | 0.657204i | \(0.228261\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.398401 | − | 0.917211i | \(-0.630435\pi\) | ||||
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.35344 | − | 0.587884i | −1.35344 | − | 0.587884i | ||||
\(317\) | 0.542084 | − | 1.13984i | 0.542084 | − | 1.13984i | −0.429483 | − | 0.903075i | \(-0.641304\pi\) |
0.971567 | − | 0.236764i | \(-0.0760870\pi\) | |||||||
\(318\) | −0.131517 | − | 0.539684i | −0.131517 | − | 0.539684i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.340531 | − | 1.21537i | −0.340531 | − | 1.21537i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.51146 | + | 0.849854i | −1.51146 | + | 0.849854i | ||||
\(324\) | 0.631088 | + | 0.589395i | 0.631088 | + | 0.589395i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0916825 | − | 0.531748i | 0.0916825 | − | 0.531748i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.11059 | + | 1.57335i | 1.11059 | + | 1.57335i | 0.775711 | + | 0.631088i | \(0.217391\pi\) |
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(332\) | 0.170064 | − | 1.65427i | 0.170064 | − | 1.65427i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.82454 | + | 1.95360i | −1.82454 | + | 1.95360i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.490110 | − | 0.871660i | \(-0.336957\pi\) | ||||
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(338\) | 1.14148 | − | 0.748695i | 1.14148 | − | 0.748695i | ||||
\(339\) | −0.269797 | − | 0.0370827i | −0.269797 | − | 0.0370827i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.943759 | + | 2.39321i | 0.943759 | + | 2.39321i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.31102 | + | 1.40536i | −2.31102 | + | 1.40536i | ||||
\(347\) | −0.726875 | + | 1.84323i | −0.726875 | + | 1.84323i | −0.236764 | + | 0.971567i | \(0.576087\pi\) |
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.917985 | − | 1.77163i | −0.917985 | − | 1.77163i | −0.519584 | − | 0.854419i | \(-0.673913\pi\) |
−0.398401 | − | 0.917211i | \(-0.630435\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.660021 | − | 0.113799i | 0.660021 | − | 0.113799i | 0.169910 | − | 0.985460i | \(-0.445652\pi\) |
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.174115 | + | 2.54547i | −0.174115 | + | 2.54547i | ||||
\(362\) | 0.296223 | + | 0.224633i | 0.296223 | + | 0.224633i | ||||
\(363\) | −0.366854 | − | 0.930278i | −0.366854 | − | 0.930278i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.48086 | − | 0.340986i | −2.48086 | − | 0.340986i | ||||
\(367\) | 0 | 0 | 0.836182 | − | 0.548452i | \(-0.184783\pi\) | ||||
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(368\) | −0.895191 | + | 1.59210i | −0.895191 | + | 1.59210i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.810363 | − | 0.385391i | 0.810363 | − | 0.385391i | ||||
\(373\) | 0 | 0 | 0.102264 | − | 0.994757i | \(-0.467391\pi\) | ||||
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.170891 | − | 0.0742286i | 0.170891 | − | 0.0742286i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.979084 | − | 1.20346i | −0.979084 | − | 1.20346i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.88853 | − | 0.599394i | 1.88853 | − | 0.599394i | 0.903075 | − | 0.429483i | \(-0.141304\pi\) |
0.985460 | − | 0.169910i | \(-0.0543478\pi\) | |||||||
\(384\) | 0.0995987 | + | 0.355472i | 0.0995987 | + | 0.355472i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.49993 | + | 0.102598i | 1.49993 | + | 0.102598i | ||||
\(392\) | 0.185339 | − | 0.0190535i | 0.185339 | − | 0.0190535i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.997669 | − | 2.29686i | −0.997669 | − | 2.29686i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.836182 | − | 0.548452i | \(-0.815217\pi\) | ||||
0.836182 | + | 0.548452i | \(0.184783\pi\) | |||||||
\(398\) | 2.01476 | + | 1.75678i | 2.01476 | + | 1.75678i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) | ||||
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.129213 | − | 0.112668i | 0.129213 | − | 0.112668i | ||||
\(409\) | 1.97675 | − | 0.271698i | 1.97675 | − | 0.271698i | 0.979084 | − | 0.203456i | \(-0.0652174\pi\) |
0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.508438 | + | 0.180699i | −0.508438 | + | 0.180699i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.453809 | − | 2.18385i | 0.453809 | − | 2.18385i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.977935 | + | 1.73926i | 0.977935 | + | 1.73926i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.03116 | − | 0.727872i | 1.03116 | − | 0.727872i | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) |
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(422\) | 1.21835 | + | 1.21835i | 1.21835 | + | 1.21835i | ||||
\(423\) | −0.753713 | + | 0.657204i | −0.753713 | + | 0.657204i | ||||
\(424\) | 0.0758143i | 0.0758143i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.0372107 | − | 1.08927i | −0.0372107 | − | 1.08927i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(432\) | −0.613091 | − | 0.934732i | −0.613091 | − | 0.934732i | ||||
\(433\) | 0 | 0 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.185634 | − | 0.427372i | 0.185634 | − | 0.427372i | ||||
\(437\) | 1.86056 | − | 2.45352i | 1.86056 | − | 2.45352i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.21537 | − | 1.49389i | 1.21537 | − | 1.49389i | 0.398401 | − | 0.917211i | \(-0.369565\pi\) |
0.816970 | − | 0.576680i | \(-0.195652\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.917211 | + | 0.398401i | −0.917211 | + | 0.398401i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.514311 | + | 0.163235i | 0.514311 | + | 0.163235i | 0.548452 | − | 0.836182i | \(-0.315217\pi\) |
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.218768 | − | 0.0862709i | −0.218768 | − | 0.0862709i | ||||
\(453\) | −0.188654 | + | 0.774147i | −0.188654 | + | 0.774147i | ||||
\(454\) | −0.843756 | − | 0.686447i | −0.843756 | − | 0.686447i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.0478104 | − | 0.347847i | −0.0478104 | − | 0.347847i | ||||
\(457\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(458\) | 0.982292 | + | 0.467158i | 0.982292 | + | 0.467158i | ||||
\(459\) | −0.478085 | + | 0.786177i | −0.478085 | + | 0.786177i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.51876 | + | 0.895169i | 2.51876 | + | 0.895169i | ||||
\(467\) | −1.98488 | − | 0.204051i | −1.98488 | − | 0.204051i | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) |
−0.985460 | − | 0.169910i | \(-0.945652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2.19806 | − | 0.781189i | −2.19806 | − | 0.781189i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.123097 | − | 0.387846i | −0.123097 | − | 0.387846i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.501638 | − | 0.238569i | −0.501638 | − | 0.238569i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.117582 | − | 0.855472i | −0.117582 | − | 0.855472i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.05893 | + | 0.861502i | 1.05893 | + | 0.861502i | ||||
\(487\) | 0 | 0 | 0.236764 | − | 0.971567i | \(-0.423913\pi\) | ||||
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(488\) | 0.317953 | + | 0.125384i | 0.317953 | + | 0.125384i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.203456 | − | 0.979084i | \(-0.565217\pi\) | ||||
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.13734 | + | 0.236343i | −1.13734 | + | 0.236343i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.0897559 | − | 2.62744i | 0.0897559 | − | 2.62744i | ||||
\(499\) | −1.49867 | + | 0.650963i | −1.49867 | + | 0.650963i | −0.979084 | − | 0.203456i | \(-0.934783\pi\) |
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.23578 | + | 1.51897i | −1.23578 | + | 1.51897i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.883195 | + | 1.16467i | −0.883195 | + | 1.16467i | 0.102264 | + | 0.994757i | \(0.467391\pi\) |
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.796805 | − | 0.604236i | 0.796805 | − | 0.604236i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.962917 | − | 0.269797i | \(-0.0869565\pi\) | ||||
−0.962917 | + | 0.269797i | \(0.913043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.0440179 | + | 1.28854i | 0.0440179 | + | 1.28854i | ||||
\(513\) | 0.809371 | + | 1.70186i | 0.809371 | + | 1.70186i | ||||
\(514\) | 1.88041 | − | 1.52983i | 1.88041 | − | 1.52983i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.61872 | + | 1.14262i | −1.61872 | + | 1.14262i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.490110 | − | 0.871660i | \(-0.663043\pi\) | ||||
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.320333 | − | 1.54153i | 0.320333 | − | 1.54153i | ||||
\(527\) | 0.577752 | + | 0.761881i | 0.577752 | + | 0.761881i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.57335 | + | 0.559168i | −1.57335 | + | 0.559168i | ||||
\(530\) | 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 | ||||||||
\(541\) | −0.985454 | + | 1.39607i | −0.985454 | + | 1.39607i | −0.0682424 | + | 0.997669i | \(0.521739\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(542\) | 0.689114 | + | 0.600876i | 0.689114 | + | 0.600876i | ||||
\(543\) | 0.227720 | + | 0.149362i | 0.227720 | + | 0.149362i | ||||
\(544\) | 1.09448 | − | 0.567112i | 1.09448 | − | 0.567112i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.971567 | − | 0.236764i | \(-0.923913\pi\) | ||||
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(548\) | −0.463504 | + | 0.0476497i | −0.463504 | + | 0.0476497i | ||||
\(549\) | −1.83015 | − | 0.125185i | −1.83015 | − | 0.125185i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.130747 | + | 0.274923i | −0.130747 | + | 0.274923i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.464861 | + | 1.65911i | 0.464861 | + | 1.65911i | ||||
\(557\) | 1.69257 | − | 0.537196i | 1.69257 | − | 0.537196i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(558\) | 1.23652 | − | 0.695258i | 1.23652 | − | 0.695258i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.25566 | − | 1.25566i | 1.25566 | − | 1.25566i | 0.302515 | − | 0.953145i | \(-0.402174\pi\) |
0.953145 | − | 0.302515i | \(-0.0978261\pi\) | |||||||
\(564\) | −0.766702 | + | 0.397273i | −0.766702 | + | 0.397273i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.308133 | + | 0.594669i | −0.308133 | + | 0.594669i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
0.682553 | + | 0.730836i | \(0.260870\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.238081 | − | 0.669895i | −0.238081 | − | 0.669895i | ||||
\(577\) | 0 | 0 | −0.366854 | − | 0.930278i | \(-0.619565\pi\) | ||||
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(578\) | 0.166814 | + | 0.126499i | 0.166814 | + | 0.126499i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.99069 | + | 0.136167i | −1.99069 | + | 0.136167i | ||||
\(587\) | 1.85712 | − | 0.320200i | 1.85712 | − | 0.320200i | 0.871660 | − | 0.490110i | \(-0.163043\pi\) |
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(588\) | −0.850959 | + | 0.146720i | −0.850959 | + | 0.146720i | ||||
\(589\) | 1.95377 | − | 0.133641i | 1.95377 | − | 0.133641i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.843954 | − | 1.62876i | −0.843954 | − | 1.62876i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.536221 | − | 1.35976i | 0.536221 | − | 1.35976i | −0.366854 | − | 0.930278i | \(-0.619565\pi\) |
0.903075 | − | 0.429483i | \(-0.141304\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.56028 | + | 1.18320i | 1.56028 | + | 1.18320i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.96292 | − | 0.269797i | −1.96292 | − | 0.269797i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.316548 | + | 0.610910i | −0.316548 | + | 0.610910i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.903075 | − | 0.429483i | \(-0.141304\pi\) | ||||
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(608\) | 0.258181 | − | 2.51141i | 0.258181 | − | 2.51141i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.561829 | + | 0.561829i | −0.561829 | + | 0.561829i | ||||
\(613\) | 0 | 0 | 0.169910 | − | 0.985460i | \(-0.445652\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.48953 | + | 0.837519i | −1.48953 | + | 0.837519i | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) |
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.494921 | + | 1.76640i | 0.494921 | + | 1.76640i | 0.631088 | + | 0.775711i | \(0.282609\pi\) |
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.222488 | − | 1.61872i | 0.222488 | − | 1.61872i | ||||
\(622\) | 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 | ||||||||
\(631\) | 1.45075 | − | 0.751719i | 1.45075 | − | 0.751719i | 0.460065 | − | 0.887885i | \(-0.347826\pi\) |
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(632\) | 0.266227 | + | 0.174619i | 0.266227 | + | 0.174619i | ||||
\(633\) | 0.951318 | + | 0.829507i | 0.951318 | + | 0.829507i | ||||
\(634\) | 0.993623 | − | 1.40764i | 0.993623 | − | 1.40764i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.0239787 | − | 0.350556i | −0.0239787 | − | 0.350556i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.519584 | − | 0.854419i | \(-0.673913\pi\) | ||||
0.519584 | + | 0.854419i | \(0.326087\pi\) | |||||||
\(642\) | −0.176202 | − | 1.71397i | −0.176202 | − | 1.71397i | ||||
\(643\) | 0 | 0 | 0.753713 | − | 0.657204i | \(-0.228261\pi\) | ||||
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.23043 | + | 0.792694i | −2.23043 | + | 0.792694i | ||||
\(647\) | 0.395342 | − | 0.0963423i | 0.395342 | − | 0.0963423i | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) |
0.429483 | + | 0.903075i | \(0.358696\pi\) | |||||||
\(648\) | −0.112579 | − | 0.148458i | −0.112579 | − | 0.148458i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.669369 | − | 0.0228663i | 0.669369 | − | 0.0228663i | 0.302515 | − | 0.953145i | \(-0.402174\pi\) |
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(654\) | 0.246673 | − | 0.694072i | 0.246673 | − | 0.694072i | ||||
\(655\) | 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 | ||||||||
\(661\) | 0.713755 | − | 0.580683i | 0.713755 | − | 0.580683i | −0.203456 | − | 0.979084i | \(-0.565217\pi\) |
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(662\) | 1.12910 | + | 2.37416i | 1.12910 | + | 2.37416i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.0968070 | + | 0.345509i | −0.0968070 | + | 0.345509i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −1.34732 | + | 1.02171i | −1.34732 | + | 1.02171i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.657204 | − | 0.753713i | \(-0.728261\pi\) | ||||
0.657204 | + | 0.753713i | \(0.271739\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.792026 | − | 0.344025i | 0.792026 | − | 0.344025i | ||||
\(677\) | −0.0681230 | + | 1.99417i | −0.0681230 | + | 1.99417i | 0.0341411 | + | 0.999417i | \(0.489130\pi\) |
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(678\) | −0.354345 | − | 0.112464i | −0.354345 | − | 0.112464i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.650963 | − | 0.459500i | −0.650963 | − | 0.459500i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.757993 | + | 0.869303i | −0.757993 | + | 0.869303i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(684\) | 0.331087 | + | 1.59328i | 0.331087 | + | 1.59328i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.741248 | + | 0.292310i | 0.741248 | + | 0.292310i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.241801 | − | 1.75923i | −0.241801 | − | 1.75923i | −0.576680 | − | 0.816970i | \(-0.695652\pi\) |
0.334880 | − | 0.942261i | \(-0.391304\pi\) | |||||||
\(692\) | −1.59165 | + | 0.627667i | −1.59165 | + | 0.627667i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.40536 | + | 2.31102i | −1.40536 | + | 2.31102i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.824004 | − | 2.59622i | −0.824004 | − | 2.59622i | ||||
\(699\) | 1.88555 | + | 0.528307i | 1.88555 | + | 0.528307i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.914293 | 0.914293 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.08677 | − | 0.386237i | −1.08677 | − | 0.386237i | −0.269797 | − | 0.962917i | \(-0.586957\pi\) |
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.64547 | − | 0.461039i | −1.64547 | − | 0.461039i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.48003 | − | 0.832177i | −1.48003 | − | 0.832177i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.824642 | + | 3.38393i | −0.824642 | + | 3.38393i | ||||
\(723\) | −0.378541 | − | 0.149277i | −0.378541 | − | 0.149277i | ||||
\(724\) | 0.160512 | + | 0.171866i | 0.160512 | + | 0.171866i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.277739 | − | 1.33655i | −0.277739 | − | 1.33655i | ||||
\(727\) | 0 | 0 | 0.657204 | − | 0.753713i | \(-0.271739\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.816970 | + | 0.576680i | 0.816970 | + | 0.576680i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.50983 | − | 0.479199i | −1.50983 | − | 0.479199i | ||||
\(733\) | 0 | 0 | 0.0341411 | − | 0.999417i | \(-0.489130\pi\) | ||||
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.38142 | + | 1.69799i | −1.38142 | + | 1.69799i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.789381 | + | 1.81734i | −0.789381 | + | 1.81734i | −0.269797 | + | 0.962917i | \(0.586957\pi\) |
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.03357 | + | 1.57580i | 1.03357 | + | 1.57580i | 0.796805 | + | 0.604236i | \(0.206522\pi\) |
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(744\) | −0.186434 | + | 0.0522364i | −0.186434 | + | 0.0522364i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0657501 | − | 1.92471i | −0.0657501 | − | 1.92471i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.26218i | − | 1.26218i | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||
0.775711 | − | 0.631088i | \(-0.217391\pi\) | |||||||
\(752\) | 1.08607 | − | 0.264669i | 1.08607 | − | 0.264669i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | ||||
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(758\) | −1.03798 | − | 1.84605i | −1.03798 | − | 1.84605i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.67959 | − | 0.368301i | 2.67959 | − | 0.368301i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.124240 | + | 1.20852i | 0.124240 | + | 1.20852i | ||||
\(769\) | −0.478085 | − | 0.786177i | −0.478085 | − | 0.786177i | 0.519584 | − | 0.854419i | \(-0.326087\pi\) |
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.29780 | − | 1.21206i | 1.29780 | − | 1.21206i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.0748554 | − | 0.114126i | 0.0748554 | − | 0.114126i | −0.796805 | − | 0.604236i | \(-0.793478\pi\) |
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.99400 | + | 0.485924i | 1.99400 | + | 0.485924i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.11525 | + | 0.0762852i | 1.11525 | + | 0.0762852i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.429483 | − | 0.903075i | \(-0.358696\pi\) | ||||
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(788\) | −0.375047 | − | 1.53901i | −0.375047 | − | 1.53901i | ||||
\(789\) | 0.157049 | − | 1.14262i | 0.157049 | − | 1.14262i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.06711 | + | 1.31166i | 1.06711 | + | 1.31166i | ||||
\(797\) | −0.339029 | + | 1.96632i | −0.339029 | + | 1.96632i | −0.102264 | + | 0.994757i | \(0.532609\pi\) |
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.580683 | − | 0.713755i | −0.580683 | − | 0.713755i | ||||
\(800\) | 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 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.663521 | + | 1.86697i | 0.663521 | + | 1.86697i | 0.460065 | + | 0.887885i | \(0.347826\pi\) |
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.533668 | + | 0.404693i | 0.533668 | + | 0.404693i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.878833 | − | 0.534430i | 0.878833 | − | 0.534430i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.72226 | + | 0.0929952i | 2.72226 | + | 0.0929952i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(822\) | −0.725892 | + | 0.125156i | −0.725892 | + | 0.125156i | ||||
\(823\) | 0 | 0 | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) | ||||
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.136405 | − | 0.00465974i | −0.136405 | − | 0.00465974i | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) |
−0.102264 | + | 0.994757i | \(0.532609\pi\) | |||||||
\(828\) | 0.517606 | − | 1.31256i | 0.517606 | − | 1.31256i | ||||
\(829\) | 1.24888 | − | 0.759461i | 1.24888 | − | 0.759461i | 0.269797 | − | 0.962917i | \(-0.413043\pi\) |
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.337554 | − | 0.855977i | −0.337554 | − | 0.855977i | ||||
\(834\) | 0.912161 | + | 2.56658i | 0.912161 | + | 2.56658i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.868934 | − | 0.569934i | 0.868934 | − | 0.569934i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.682553 | − | 0.730836i | 0.682553 | − | 0.730836i | ||||
\(842\) | 1.55600 | − | 0.740002i | 1.55600 | − | 0.740002i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.628529 | + | 0.890422i | 0.628529 | + | 0.890422i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.16637 | + | 0.709287i | −1.16637 | + | 0.709287i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.0772870 | + | 0.448255i | −0.0772870 | + | 0.448255i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) | ||||
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.0320215 | + | 0.232974i | −0.0320215 | + | 0.232974i | ||||
\(857\) | −0.298838 | − | 1.22629i | −0.298838 | − | 1.22629i | −0.903075 | − | 0.429483i | \(-0.858696\pi\) |
0.604236 | − | 0.796805i | \(-0.293478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.34066 | + | 0.582332i | 1.34066 | + | 0.582332i | 0.942261 | − | 0.334880i | \(-0.108696\pi\) |
0.398401 | + | 0.917211i | \(0.369565\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.66025 | + | 0.404592i | 1.66025 | + | 0.404592i | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | −0.533729 | − | 1.22877i | −0.533729 | − | 1.22877i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.128237 | + | 0.0841109i | 0.128237 | + | 0.0841109i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.0551386 | + | 0.0840656i | −0.0551386 | + | 0.0840656i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.07202 | − | 2.86906i | 3.07202 | − | 2.86906i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.102264 | − | 0.994757i | \(-0.532609\pi\) | ||||
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(878\) | 1.98149 | − | 1.72777i | 1.98149 | − | 1.72777i | ||||
\(879\) | −1.44806 | + | 0.199031i | −1.44806 | + | 0.199031i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.942261 | − | 0.334880i | \(-0.108696\pi\) | ||||
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(882\) | −1.32629 | + | 0.323209i | −1.32629 | + | 0.323209i | ||||
\(883\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.654019 | + | 0.338885i | 0.654019 | + | 0.338885i | ||||
\(887\) | −0.923623 | − | 1.64266i | −0.923623 | − | 1.64266i | −0.753713 | − | 0.657204i | \(-0.771739\pi\) |
−0.169910 | − | 0.985460i | \(-0.554348\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.87464 | + | 0.192719i | −1.87464 | + | 0.192719i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.360528 | − | 0.101015i | 0.360528 | − | 0.101015i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.0433534 | + | 0.0263638i | 0.0433534 | + | 0.0263638i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.433349 | + | 0.997669i | −0.433349 | + | 0.997669i | ||||
\(907\) | 0 | 0 | 0.604236 | − | 0.796805i | \(-0.293478\pi\) | ||||
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(908\) | −0.452189 | − | 0.518593i | −0.452189 | − | 0.518593i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.917211 | − | 0.398401i | \(-0.130435\pi\) | ||||
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(912\) | 0.0719225 | − | 2.10540i | 0.0719225 | − | 2.10540i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.562117 | + | 0.396785i | 0.562117 | + | 0.396785i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.825497 | + | 0.946720i | −0.825497 | + | 0.946720i | ||||
\(919\) | 0.332435 | + | 1.59976i | 0.332435 | + | 1.59976i | 0.730836 | + | 0.682553i | \(0.239130\pi\) |
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(920\) | 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 | 0.519584 | − | 0.854419i | \(-0.326087\pi\) | ||||
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.84511 | − | 0.383417i | −1.84511 | − | 0.383417i | ||||
\(932\) | 1.47390 | + | 0.828731i | 1.47390 | + | 0.828731i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.62284 | − | 0.734885i | −2.62284 | − | 0.734885i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.994757 | − | 0.102264i | \(-0.967391\pi\) | ||||
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(938\) | 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 | ||||||||
\(947\) | 0.0412886 | + | 0.130090i | 0.0412886 | + | 0.130090i | 0.971567 | − | 0.236764i | \(-0.0760870\pi\) |
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(948\) | −1.28623 | − | 0.723211i | −1.28623 | − | 0.723211i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.655806 | − | 1.07843i | 0.655806 | − | 1.07843i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.35976 | + | 0.536221i | −1.35976 | + | 0.536221i | −0.930278 | − | 0.366854i | \(-0.880435\pi\) |
−0.429483 | + | 0.903075i | \(0.641304\pi\) | |||||||
\(954\) | −0.0756376 | − | 0.550304i | −0.0756376 | − | 0.550304i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.0162500 | − | 0.0781994i | −0.0162500 | − | 0.0781994i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.214457 | − | 1.24382i | −0.214457 | − | 1.24382i | ||||
\(964\) | −0.287063 | − | 0.202631i | −0.287063 | − | 0.202631i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.953145 | − | 0.302515i | \(-0.902174\pi\) | ||||
0.953145 | + | 0.302515i | \(0.0978261\pi\) | |||||||
\(968\) | −0.00636105 | + | 0.186208i | −0.00636105 | + | 0.186208i | ||||
\(969\) | −1.59045 | + | 0.690830i | −1.59045 | + | 0.690830i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(972\) | 0.567505 | + | 0.650843i | 0.567505 | + | 0.650843i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.75209 | + | 1.06547i | 1.75209 | + | 1.06547i | ||||
\(977\) | −1.57877 | + | 1.19722i | −1.57877 | + | 1.19722i | −0.707107 | + | 0.707107i | \(0.750000\pi\) |
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.145581 | − | 0.519584i | 0.145581 | − | 0.519584i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.342213 | + | 0.719572i | 0.342213 | + | 0.719572i | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) |
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.519540 | − | 1.46184i | 0.519540 | − | 1.46184i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
0.854419 | − | 0.519584i | \(-0.173913\pi\) | |||||||
\(992\) | −1.39134 | + | 0.0475295i | −1.39134 | + | 0.0475295i | ||||
\(993\) | 0.943871 | + | 1.67867i | 0.943871 | + | 1.67867i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.338345 | − | 1.62820i | 0.338345 | − | 1.62820i | ||||
\(997\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(998\) | −2.16708 | + | 0.528103i | −2.16708 | + | 0.528103i | ||||
\(999\) | 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.107.2 | yes | 88 | |
3.2 | odd | 2 | inner | 3525.1.bg.a.107.1 | ✓ | 88 | |
5.2 | odd | 4 | inner | 3525.1.bg.a.3068.1 | yes | 88 | |
5.3 | odd | 4 | inner | 3525.1.bg.a.3068.2 | yes | 88 | |
5.4 | even | 2 | inner | 3525.1.bg.a.107.1 | ✓ | 88 | |
15.2 | even | 4 | inner | 3525.1.bg.a.3068.2 | yes | 88 | |
15.8 | even | 4 | inner | 3525.1.bg.a.3068.1 | yes | 88 | |
15.14 | odd | 2 | CM | 3525.1.bg.a.107.2 | yes | 88 | |
47.29 | odd | 46 | inner | 3525.1.bg.a.1157.1 | yes | 88 | |
141.29 | even | 46 | inner | 3525.1.bg.a.1157.2 | yes | 88 | |
235.29 | odd | 46 | inner | 3525.1.bg.a.1157.2 | yes | 88 | |
235.123 | even | 92 | inner | 3525.1.bg.a.593.1 | yes | 88 | |
235.217 | even | 92 | inner | 3525.1.bg.a.593.2 | yes | 88 | |
705.29 | even | 46 | inner | 3525.1.bg.a.1157.1 | yes | 88 | |
705.452 | odd | 92 | inner | 3525.1.bg.a.593.1 | yes | 88 | |
705.593 | odd | 92 | inner | 3525.1.bg.a.593.2 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.1.bg.a.107.1 | ✓ | 88 | 3.2 | odd | 2 | inner | |
3525.1.bg.a.107.1 | ✓ | 88 | 5.4 | even | 2 | inner | |
3525.1.bg.a.107.2 | yes | 88 | 1.1 | even | 1 | trivial | |
3525.1.bg.a.107.2 | yes | 88 | 15.14 | odd | 2 | CM | |
3525.1.bg.a.593.1 | yes | 88 | 235.123 | even | 92 | inner | |
3525.1.bg.a.593.1 | yes | 88 | 705.452 | odd | 92 | inner | |
3525.1.bg.a.593.2 | yes | 88 | 235.217 | even | 92 | inner | |
3525.1.bg.a.593.2 | yes | 88 | 705.593 | odd | 92 | inner | |
3525.1.bg.a.1157.1 | yes | 88 | 47.29 | odd | 46 | inner | |
3525.1.bg.a.1157.1 | yes | 88 | 705.29 | even | 46 | inner | |
3525.1.bg.a.1157.2 | yes | 88 | 141.29 | even | 46 | inner | |
3525.1.bg.a.1157.2 | yes | 88 | 235.29 | odd | 46 | inner | |
3525.1.bg.a.3068.1 | yes | 88 | 5.2 | odd | 4 | inner | |
3525.1.bg.a.3068.1 | yes | 88 | 15.8 | even | 4 | inner | |
3525.1.bg.a.3068.2 | yes | 88 | 5.3 | odd | 4 | inner | |
3525.1.bg.a.3068.2 | yes | 88 | 15.2 | even | 4 | inner |