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 | 407.1 | ||
Root | \(0.971567 - 0.236764i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.407 |
Dual form | 3525.1.bg.a.2018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3525\mathbb{Z}\right)^\times\).
\(n\) | \(1552\) | \(2026\) | \(2351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{46}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.395342 | + | 0.0963423i | −0.395342 | + | 0.0963423i | −0.429483 | − | 0.903075i | \(-0.641304\pi\) |
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(3\) | −0.169910 | + | 0.985460i | −0.169910 | + | 0.985460i | ||||
\(4\) | −0.740871 | + | 0.383889i | −0.740871 | + | 0.383889i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.0277687 | − | 0.405963i | −0.0277687 | − | 0.405963i | ||||
\(7\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(8\) | 0.562608 | − | 0.490569i | 0.562608 | − | 0.490569i | ||||
\(9\) | −0.942261 | − | 0.334880i | −0.942261 | − | 0.334880i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(12\) | −0.252425 | − | 0.795326i | −0.252425 | − | 0.795326i | ||||
\(13\) | 0 | 0 | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.306035 | − | 0.433553i | 0.306035 | − | 0.433553i | ||||
\(17\) | 1.53451 | − | 1.16366i | 1.53451 | − | 1.16366i | 0.604236 | − | 0.796805i | \(-0.293478\pi\) |
0.930278 | − | 0.366854i | \(-0.119565\pi\) | |||||||
\(18\) | 0.404779 | + | 0.0416125i | 0.404779 | + | 0.0416125i | ||||
\(19\) | 0.361291 | + | 1.73863i | 0.361291 | + | 1.73863i | 0.631088 | + | 0.775711i | \(0.282609\pi\) |
−0.269797 | + | 0.962917i | \(0.586957\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.246038 | − | 1.00962i | 0.246038 | − | 1.00962i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.953145 | − | 0.302515i | \(-0.0978261\pi\) | |||||||
\(24\) | 0.387843 | + | 0.637780i | 0.387843 | + | 0.637780i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.490110 | − | 0.871660i | 0.490110 | − | 0.871660i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.222488 | − | 0.157049i | −0.222488 | − | 0.157049i | 0.460065 | − | 0.887885i | \(-0.347826\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(32\) | −0.353057 | + | 0.895291i | −0.353057 | + | 0.895291i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.494549 | + | 0.607882i | −0.494549 | + | 0.607882i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.826651 | − | 0.113621i | 0.826651 | − | 0.113621i | ||||
\(37\) | 0 | 0 | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) | ||||
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(38\) | −0.310337 | − | 0.652546i | −0.310337 | − | 0.652546i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | ||||
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.953145 | − | 0.302515i | \(-0.902174\pi\) | ||||
0.953145 | + | 0.302515i | \(0.0978261\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.422850i | 0.422850i | ||||||||
\(47\) | 0.999417 | + | 0.0341411i | 0.999417 | + | 0.0341411i | ||||
\(48\) | 0.375250 | + | 0.375250i | 0.375250 | + | 0.375250i | ||||
\(49\) | 0.519584 | − | 0.854419i | 0.519584 | − | 0.854419i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.886009 | + | 1.70992i | 0.886009 | + | 1.70992i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.440168 | − | 0.504806i | 0.440168 | − | 0.504806i | −0.490110 | − | 0.871660i | \(-0.663043\pi\) |
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(54\) | −0.109784 | + | 0.391823i | −0.109784 | + | 0.391823i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.77474 | + | 0.0606268i | −1.77474 | + | 0.0606268i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.05893 | + | 1.13384i | 1.05893 | + | 1.13384i | 0.990686 | + | 0.136167i | \(0.0434783\pi\) |
0.0682424 | + | 0.997669i | \(0.478261\pi\) | |||||||
\(62\) | 0.103089 | + | 0.0406532i | 0.103089 | + | 0.0406532i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.0189375 | + | 0.137780i | −0.0189375 | + | 0.137780i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.871660 | − | 0.490110i | \(-0.836957\pi\) | ||||
0.871660 | + | 0.490110i | \(0.163043\pi\) | |||||||
\(68\) | −0.690163 | + | 1.45120i | −0.690163 | + | 1.45120i | ||||
\(69\) | 0.953137 | + | 0.414006i | 0.953137 | + | 0.414006i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.854419 | − | 0.519584i | \(-0.173913\pi\) | ||||
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(72\) | −0.694405 | + | 0.273838i | −0.694405 | + | 0.273838i | ||||
\(73\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.935110 | − | 1.14940i | −0.935110 | − | 1.14940i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.789381 | + | 1.81734i | 0.789381 | + | 1.81734i | 0.519584 | + | 0.854419i | \(0.326087\pi\) |
0.269797 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.775711 | + | 0.631088i | 0.775711 | + | 0.631088i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.108752 | − | 0.0824691i | −0.108752 | − | 0.0824691i | 0.548452 | − | 0.836182i | \(-0.315217\pi\) |
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.979084 | − | 0.203456i | \(-0.934783\pi\) | ||||
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.205300 | + | 0.842451i | 0.205300 | + | 0.842451i | ||||
\(93\) | 0.192569 | − | 0.192569i | 0.192569 | − | 0.192569i | ||||
\(94\) | −0.398401 | + | 0.0827887i | −0.398401 | + | 0.0827887i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.822285 | − | 0.500042i | −0.822285 | − | 0.500042i | ||||
\(97\) | 0 | 0 | −0.985460 | − | 0.169910i | \(-0.945652\pi\) | ||||
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(98\) | −0.123097 | + | 0.387846i | −0.123097 | + | 0.387846i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(102\) | −0.515015 | − | 0.590644i | −0.515015 | − | 0.590644i | ||||
\(103\) | 0 | 0 | 0.903075 | − | 0.429483i | \(-0.141304\pi\) | ||||
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.125383 | + | 0.241978i | −0.125383 | + | 0.241978i | ||||
\(107\) | 0.167093 | + | 1.62537i | 0.167093 | + | 1.62537i | 0.657204 | + | 0.753713i | \(0.271739\pi\) |
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(108\) | −0.0284881 | + | 0.833936i | −0.0284881 | + | 0.833936i | ||||
\(109\) | −1.83015 | + | 0.794945i | −1.83015 | + | 0.794945i | −0.887885 | + | 0.460065i | \(0.847826\pi\) |
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.22222 | − | 0.801657i | −1.22222 | − | 0.801657i | −0.236764 | − | 0.971567i | \(-0.576087\pi\) |
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(114\) | 0.695787 | − | 0.194950i | 0.695787 | − | 0.194950i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.962917 | + | 0.269797i | −0.962917 | + | 0.269797i | ||||
\(122\) | −0.527876 | − | 0.346234i | −0.527876 | − | 0.346234i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.225125 | + | 0.0309427i | 0.225125 | + | 0.0309427i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.0341411 | − | 0.999417i | \(-0.489130\pi\) | ||||
−0.0341411 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(128\) | −0.104205 | − | 1.01364i | −0.104205 | − | 1.01364i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.292475 | − | 1.40747i | 0.292475 | − | 1.40747i | ||||
\(137\) | 0.603619 | − | 1.90185i | 0.603619 | − | 1.90185i | 0.236764 | − | 0.971567i | \(-0.423913\pi\) |
0.366854 | − | 0.930278i | \(-0.380435\pi\) | |||||||
\(138\) | −0.416701 | − | 0.0718466i | −0.416701 | − | 0.0718466i | ||||
\(139\) | −0.680803 | − | 0.414006i | −0.680803 | − | 0.414006i | 0.136167 | − | 0.990686i | \(-0.456522\pi\) |
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.203456 | + | 0.979084i | −0.203456 | + | 0.979084i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.433553 | + | 0.306035i | −0.433553 | + | 0.306035i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.753713 | + | 0.657204i | 0.753713 | + | 0.657204i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.997669 | − | 0.0682424i | \(-0.978261\pi\) | ||||
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.922444 | − | 0.861502i | −0.922444 | − | 0.861502i | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) |
−0.990686 | + | 0.136167i | \(0.956522\pi\) | |||||||
\(152\) | 1.05618 | + | 0.800928i | 1.05618 | + | 0.800928i | ||||
\(153\) | −1.83560 | + | 0.582593i | −1.83560 | + | 0.582593i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(158\) | −0.487162 | − | 0.642419i | −0.487162 | − | 0.642419i | ||||
\(159\) | 0.422677 | + | 0.519540i | 0.422677 | + | 0.519540i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.367472 | − | 0.174762i | −0.367472 | − | 0.174762i | ||||
\(163\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0509395 | + | 0.0221261i | 0.0509395 | + | 0.0221261i | ||||
\(167\) | −0.809371 | + | 1.70186i | −0.809371 | + | 1.70186i | −0.102264 | + | 0.994757i | \(0.532609\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.979084 | − | 0.203456i | 0.979084 | − | 0.203456i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.241801 | − | 1.75923i | 0.241801 | − | 1.75923i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.26993 | + | 0.500795i | 1.26993 | + | 0.500795i | 0.903075 | − | 0.429483i | \(-0.141304\pi\) |
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.394354 | + | 1.40747i | −0.394354 | + | 1.40747i | 0.460065 | + | 0.887885i | \(0.347826\pi\) |
−0.854419 | + | 0.519584i | \(0.826087\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.29727 | + | 0.850881i | −1.29727 | + | 0.850881i | ||||
\(184\) | −0.356866 | − | 0.688720i | −0.356866 | − | 0.688720i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.0575781 | + | 0.0946831i | −0.0575781 | + | 0.0946831i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −0.753546 | + | 0.358371i | −0.753546 | + | 0.358371i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.576680 | − | 0.816970i | \(-0.695652\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(192\) | −0.132559 | − | 0.0420724i | −0.132559 | − | 0.0420724i | ||||
\(193\) | 0 | 0 | −0.548452 | − | 0.836182i | \(-0.684783\pi\) | ||||
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0569430 | + | 0.832477i | −0.0569430 | + | 0.832477i | ||||
\(197\) | 0.666310 | + | 1.40105i | 0.666310 | + | 1.40105i | 0.903075 | + | 0.429483i | \(0.141304\pi\) |
−0.236764 | + | 0.971567i | \(0.576087\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.86697 | − | 0.256609i | 1.86697 | − | 0.256609i | 0.887885 | − | 0.460065i | \(-0.152174\pi\) |
0.979084 | + | 0.203456i | \(0.0652174\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.31284 | − | 0.926702i | −1.31284 | − | 0.926702i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.569934 | + | 0.868934i | −0.569934 | + | 0.868934i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.848969 | + | 1.39607i | 0.848969 | + | 1.39607i | 0.917211 | + | 0.398401i | \(0.130435\pi\) |
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(212\) | −0.132319 | + | 0.542972i | −0.132319 | + | 0.542972i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.222651 | − | 0.626481i | −0.222651 | − | 0.626481i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.151869 | − | 0.730836i | −0.151869 | − | 0.730836i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.646947 | − | 0.490596i | 0.646947 | − | 0.490596i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.302515 | − | 0.953145i | \(-0.597826\pi\) | ||||
0.302515 | + | 0.953145i | \(0.402174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.560430 | + | 0.199177i | 0.560430 | + | 0.199177i | ||||
\(227\) | 0.951318 | − | 0.829507i | 0.951318 | − | 0.829507i | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) |
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(228\) | 1.29158 | − | 0.726217i | 1.29158 | − | 0.726217i | ||||
\(229\) | −0.0861339 | − | 1.25923i | −0.0861339 | − | 1.25923i | −0.816970 | − | 0.576680i | \(-0.804348\pi\) |
0.730836 | − | 0.682553i | \(-0.239130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.83094 | − | 0.446188i | 1.83094 | − | 0.446188i | 0.836182 | − | 0.548452i | \(-0.184783\pi\) |
0.994757 | + | 0.102264i | \(0.0326087\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.92504 | + | 0.469118i | −1.92504 | + | 0.469118i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0457060 | − | 0.668198i | −0.0457060 | − | 0.668198i | −0.962917 | − | 0.269797i | \(-0.913043\pi\) |
0.917211 | − | 0.398401i | \(-0.130435\pi\) | |||||||
\(242\) | 0.354689 | − | 0.199432i | 0.354689 | − | 0.199432i | ||||
\(243\) | −0.753713 | + | 0.657204i | −0.753713 | + | 0.657204i | ||||
\(244\) | −1.21980 | − | 0.433516i | −1.21980 | − | 0.433516i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.202217 | + | 0.0207885i | −0.202217 | + | 0.0207885i | ||||
\(249\) | 0.0997480 | − | 0.0931581i | 0.0997480 | − | 0.0931581i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0922795 | + | 0.259650i | 0.0922795 | + | 0.259650i | ||||
\(257\) | 0.197952 | + | 0.501972i | 0.197952 | + | 0.501972i | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) |
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.937216 | + | 1.42890i | −0.937216 | + | 1.42890i | −0.0341411 | + | 0.999417i | \(0.510870\pi\) |
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.631088 | − | 0.775711i | \(-0.282609\pi\) | ||||
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.911560 | − | 0.125291i | 0.911560 | − | 0.125291i | 0.334880 | − | 0.942261i | \(-0.391304\pi\) |
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(272\) | −0.0348925 | − | 1.02141i | −0.0348925 | − | 1.02141i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0554078 | + | 0.810034i | −0.0554078 | + | 0.810034i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.865084 | + | 0.0591734i | −0.865084 | + | 0.0591734i | ||||
\(277\) | 0 | 0 | −0.548452 | − | 0.836182i | \(-0.684783\pi\) | ||||
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(278\) | 0.309037 | + | 0.0980838i | 0.309037 | + | 0.0980838i | ||||
\(279\) | 0.157049 | + | 0.222488i | 0.157049 | + | 0.222488i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | −0.0138924 | − | 0.406675i | −0.0138924 | − | 0.406675i | ||||
\(283\) | 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 | ||||||||
\(288\) | 0.632486 | − | 0.725366i | 0.632486 | − | 0.725366i | ||||
\(289\) | 0.730836 | − | 2.60839i | 0.730836 | − | 2.60839i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.18320 | − | 1.56028i | 1.18320 | − | 1.56028i | 0.429483 | − | 0.903075i | \(-0.358696\pi\) |
0.753713 | − | 0.657204i | \(-0.228261\pi\) | |||||||
\(294\) | −0.361291 | − | 0.187206i | −0.361291 | − | 0.187206i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.447680 | + | 0.251718i | 0.447680 | + | 0.251718i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.864355 | + | 0.375442i | 0.864355 | + | 0.375442i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.669562 | − | 0.407169i | 0.669562 | − | 0.407169i | ||||
\(307\) | 0 | 0 | 0.930278 | − | 0.366854i | \(-0.119565\pi\) | ||||
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.631088 | − | 0.775711i | \(-0.717391\pi\) | ||||
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
0.169910 | + | 0.985460i | \(0.445652\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.28248 | − | 1.04338i | −1.28248 | − | 1.04338i | ||||
\(317\) | −1.55738 | + | 0.494291i | −1.55738 | + | 0.494291i | −0.953145 | − | 0.302515i | \(-0.902174\pi\) |
−0.604236 | + | 0.796805i | \(0.706522\pi\) | |||||||
\(318\) | −0.217156 | − | 0.164674i | −0.217156 | − | 0.164674i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.63013 | − | 0.111504i | −1.63013 | − | 0.111504i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.57758 | + | 2.24753i | 2.57758 | + | 2.24753i | ||||
\(324\) | −0.816970 | − | 0.169768i | −0.816970 | − | 0.169768i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.472425 | − | 1.93860i | −0.472425 | − | 1.93860i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.116615 | + | 0.0709153i | 0.116615 | + | 0.0709153i | 0.576680 | − | 0.816970i | \(-0.304348\pi\) |
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(332\) | 0.112230 | + | 0.0193504i | 0.112230 | + | 0.0193504i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.156017 | − | 0.750796i | 0.156017 | − | 0.750796i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.657204 | − | 0.753713i | \(-0.728261\pi\) | ||||
0.657204 | + | 0.753713i | \(0.271739\pi\) | |||||||
\(338\) | −0.367472 | + | 0.174762i | −0.367472 | + | 0.174762i | ||||
\(339\) | 0.997669 | − | 1.06824i | 0.997669 | − | 1.06824i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.0738943 | + | 0.718794i | 0.0738943 | + | 0.718794i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.550304 | − | 0.0756376i | −0.550304 | − | 0.0756376i | ||||
\(347\) | 0.139601 | − | 1.35795i | 0.139601 | − | 1.35795i | −0.657204 | − | 0.753713i | \(-0.728261\pi\) |
0.796805 | − | 0.604236i | \(-0.206522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.767255 | + | 0.214975i | −0.767255 | + | 0.214975i | −0.631088 | − | 0.775711i | \(-0.717391\pi\) |
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.893968 | + | 0.217854i | 0.893968 | + | 0.217854i | 0.657204 | − | 0.753713i | \(-0.271739\pi\) |
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.990686 | − | 0.136167i | \(-0.956522\pi\) | ||||
0.990686 | + | 0.136167i | \(0.0434783\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.97509 | + | 0.857901i | −1.97509 | + | 0.857901i | ||||
\(362\) | 0.0203062 | − | 0.594425i | 0.0203062 | − | 0.594425i | ||||
\(363\) | −0.102264 | − | 0.994757i | −0.102264 | − | 0.994757i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.430891 | − | 0.461371i | 0.430891 | − | 0.461371i | ||||
\(367\) | 0 | 0 | 0.903075 | − | 0.429483i | \(-0.141304\pi\) | ||||
−0.903075 | + | 0.429483i | \(0.858696\pi\) | |||||||
\(368\) | −0.362428 | − | 0.415650i | −0.362428 | − | 0.415650i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0687437 | + | 0.216594i | −0.0687437 | + | 0.216594i | ||||
\(373\) | 0 | 0 | −0.985460 | − | 0.169910i | \(-0.945652\pi\) | ||||
0.985460 | + | 0.169910i | \(0.0543478\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.579029 | − | 0.471075i | 0.579029 | − | 0.471075i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.942261 | − | 0.665120i | 0.942261 | − | 0.665120i | − | 1.00000i | \(-0.5\pi\) | |
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.669053 | − | 1.18991i | −0.669053 | − | 1.18991i | −0.971567 | − | 0.236764i | \(-0.923913\pi\) |
0.302515 | − | 0.953145i | \(-0.402174\pi\) | |||||||
\(384\) | 1.01661 | + | 0.0695378i | 1.01661 | + | 0.0695378i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.775711 | − | 0.631088i | \(-0.782609\pi\) | ||||
0.775711 | + | 0.631088i | \(0.217391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.797306 | − | 1.83558i | −0.797306 | − | 1.83558i | ||||
\(392\) | −0.126829 | − | 0.735595i | −0.126829 | − | 0.735595i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.398401 | − | 0.489701i | −0.398401 | − | 0.489701i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.903075 | − | 0.429483i | \(-0.858696\pi\) | ||||
0.903075 | + | 0.429483i | \(0.141304\pi\) | |||||||
\(398\) | −0.713370 | + | 0.281317i | −0.713370 | + | 0.281317i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.917211 | − | 0.398401i | \(-0.869565\pi\) | ||||
0.917211 | + | 0.398401i | \(0.130435\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.33731 | + | 0.527366i | 1.33731 | + | 0.527366i | ||||
\(409\) | −0.543860 | − | 0.582332i | −0.543860 | − | 0.582332i | 0.398401 | − | 0.917211i | \(-0.369565\pi\) |
−0.942261 | + | 0.334880i | \(0.891304\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.77163 | + | 0.917985i | 1.77163 | + | 0.917985i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.141604 | − | 0.398435i | 0.141604 | − | 0.398435i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.523661 | − | 0.600560i | 0.523661 | − | 0.600560i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.848969 | − | 1.39607i | 0.848969 | − | 1.39607i | −0.0682424 | − | 0.997669i | \(-0.521739\pi\) |
0.917211 | − | 0.398401i | \(-0.130435\pi\) | |||||||
\(422\) | −0.470134 | − | 0.470134i | −0.470134 | − | 0.470134i | ||||
\(423\) | −0.930278 | − | 0.366854i | −0.930278 | − | 0.366854i | ||||
\(424\) | − | 0.499941i | − | 0.499941i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.747757 | − | 1.14005i | −0.747757 | − | 1.14005i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(432\) | −0.227920 | − | 0.479247i | −0.227920 | − | 0.479247i | ||||
\(433\) | 0 | 0 | −0.0341411 | − | 0.999417i | \(-0.510870\pi\) | ||||
0.0341411 | + | 0.999417i | \(0.489130\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.05073 | − | 1.29152i | 1.05073 | − | 1.29152i | ||||
\(437\) | 1.84425 | + | 0.0630014i | 1.84425 | + | 0.0630014i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.111504 | + | 0.0787081i | 0.111504 | + | 0.0787081i | 0.631088 | − | 0.775711i | \(-0.282609\pi\) |
−0.519584 | + | 0.854419i | \(0.673913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.775711 | + | 0.631088i | −0.775711 | + | 0.631088i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.977935 | + | 1.73926i | −0.977935 | + | 1.73926i | −0.429483 | + | 0.903075i | \(0.641304\pi\) |
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.21326 | + | 0.124727i | 1.21326 | + | 0.124727i | ||||
\(453\) | 1.00571 | − | 0.762653i | 1.00571 | − | 0.762653i | ||||
\(454\) | −0.296180 | + | 0.419591i | −0.296180 | + | 0.419591i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.968739 | + | 0.904739i | −0.968739 | + | 0.904739i | ||||
\(457\) | 0 | 0 | 0.994757 | − | 0.102264i | \(-0.0326087\pi\) | ||||
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(458\) | 0.155370 | + | 0.489530i | 0.155370 | + | 0.489530i | ||||
\(459\) | −0.262234 | − | 1.90790i | −0.262234 | − | 1.90790i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.871660 | − | 0.490110i | \(-0.163043\pi\) | ||||
−0.871660 | + | 0.490110i | \(0.836957\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.680861 | + | 0.352794i | −0.680861 | + | 0.352794i | ||||
\(467\) | 0.135385 | − | 0.785216i | 0.135385 | − | 0.785216i | −0.836182 | − | 0.548452i | \(-0.815217\pi\) |
0.971567 | − | 0.236764i | \(-0.0760870\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.715852 | − | 0.370925i | 0.715852 | − | 0.370925i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.583803 | + | 0.328256i | −0.583803 | + | 0.328256i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.942261 | − | 0.334880i | \(-0.891304\pi\) | ||||
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.0824452 | + | 0.259763i | 0.0824452 | + | 0.259763i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.609826 | − | 0.569538i | 0.609826 | − | 0.569538i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.234658 | − | 0.332435i | 0.234658 | − | 0.332435i | ||||
\(487\) | 0 | 0 | 0.796805 | − | 0.604236i | \(-0.206522\pi\) | ||||
−0.796805 | + | 0.604236i | \(0.793478\pi\) | |||||||
\(488\) | 1.15199 | + | 0.118428i | 1.15199 | + | 0.118428i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.334880 | − | 0.942261i | \(-0.608696\pi\) | ||||
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.136178 | + | 0.0483978i | −0.136178 | + | 0.0483978i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.0304595 | + | 0.0464393i | −0.0304595 | + | 0.0464393i | ||||
\(499\) | 0.806094 | − | 0.655806i | 0.806094 | − | 0.655806i | −0.136167 | − | 0.990686i | \(-0.543478\pi\) |
0.942261 | + | 0.334880i | \(0.108696\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.53960 | − | 1.08677i | −1.53960 | − | 1.08677i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.95703 | + | 0.0668540i | 1.95703 | + | 0.0668540i | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) |
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.0341411 | + | 0.999417i | 0.0341411 | + | 0.999417i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.0682424 | − | 0.997669i | \(-0.478261\pi\) | ||||
−0.0682424 | + | 0.997669i | \(0.521739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.497365 | + | 0.758294i | 0.497365 | + | 0.758294i | ||||
\(513\) | 1.69257 | + | 0.537196i | 1.69257 | + | 0.537196i | ||||
\(514\) | −0.126620 | − | 0.179380i | −0.126620 | − | 0.179380i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.709287 | + | 1.16637i | −0.709287 | + | 1.16637i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.460065 | − | 0.887885i | \(-0.652174\pi\) | ||||
0.460065 | + | 0.887885i | \(0.347826\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.657204 | − | 0.753713i | \(-0.271739\pi\) | ||||
−0.657204 | + | 0.753713i | \(0.728261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.232858 | − | 0.655198i | 0.232858 | − | 0.655198i | ||||
\(527\) | −0.524163 | + | 0.0179059i | −0.524163 | + | 0.0179059i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0709153 | − | 0.0367454i | −0.0709153 | − | 0.0367454i | ||||
\(530\) | 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 | ||||||||
\(541\) | −1.69292 | + | 1.02949i | −1.69292 | + | 1.02949i | −0.775711 | + | 0.631088i | \(0.782609\pi\) |
−0.917211 | + | 0.398401i | \(0.869565\pi\) | |||||||
\(542\) | −0.348307 | + | 0.137355i | −0.348307 | + | 0.137355i | ||||
\(543\) | −1.32000 | − | 0.627764i | −1.32000 | − | 0.627764i | ||||
\(544\) | 0.500042 | + | 1.78468i | 0.500042 | + | 1.78468i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.604236 | − | 0.796805i | \(-0.706522\pi\) | ||||
0.604236 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(548\) | 0.282893 | + | 1.64075i | 0.282893 | + | 1.64075i | ||||
\(549\) | −0.618088 | − | 1.42298i | −0.618088 | − | 1.42298i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0.739341 | − | 0.234656i | 0.739341 | − | 0.234656i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.663320 | + | 0.0453723i | 0.663320 | + | 0.0453723i | ||||
\(557\) | −0.264460 | − | 0.470342i | −0.264460 | − | 0.470342i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(558\) | −0.0835232 | − | 0.0728285i | −0.0835232 | − | 0.0728285i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.381550 | + | 0.381550i | −0.381550 | + | 0.381550i | −0.871660 | − | 0.490110i | \(-0.836957\pi\) |
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(564\) | −0.225125 | − | 0.803480i | −0.225125 | − | 0.803480i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.203456 | − | 0.979084i | \(-0.434783\pi\) | ||||
−0.203456 | + | 0.979084i | \(0.565217\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.886009 | + | 0.248248i | 0.886009 | + | 0.248248i | 0.682553 | − | 0.730836i | \(-0.260870\pi\) |
0.203456 | + | 0.979084i | \(0.434783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0639838 | − | 0.123483i | 0.0639838 | − | 0.123483i | ||||
\(577\) | 0 | 0 | −0.102264 | − | 0.994757i | \(-0.532609\pi\) | ||||
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(578\) | −0.0376323 | + | 1.10162i | −0.0376323 | + | 1.10162i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.317447 | + | 0.730836i | −0.317447 | + | 0.730836i | ||||
\(587\) | −1.72528 | − | 0.420439i | −1.72528 | − | 0.420439i | −0.753713 | − | 0.657204i | \(-0.771739\pi\) |
−0.971567 | + | 0.236764i | \(0.923913\pi\) | |||||||
\(588\) | −0.810698 | − | 0.197562i | −0.810698 | − | 0.197562i | ||||
\(589\) | 0.192667 | − | 0.443565i | 0.192667 | − | 0.443565i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.49389 | + | 0.418569i | −1.49389 | + | 0.418569i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.200250 | − | 1.94790i | 0.200250 | − | 1.94790i | −0.102264 | − | 0.994757i | \(-0.532609\pi\) |
0.302515 | − | 0.953145i | \(-0.402174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.0643397 | + | 1.88342i | −0.0643397 | + | 1.88342i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.460065 | − | 0.887885i | \(-0.347826\pi\) | ||||
−0.460065 | + | 0.887885i | \(0.652174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.931758 | + | 0.997669i | −0.931758 | + | 0.997669i | 0.0682424 | + | 0.997669i | \(0.478261\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.01413 | + | 0.284147i | 1.01413 | + | 0.284147i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.302515 | − | 0.953145i | \(-0.402174\pi\) | ||||
−0.302515 | + | 0.953145i | \(0.597826\pi\) | |||||||
\(608\) | −1.68413 | − | 0.290374i | −1.68413 | − | 0.290374i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.13629 | − | 1.13629i | 1.13629 | − | 1.13629i | ||||
\(613\) | 0 | 0 | −0.236764 | − | 0.971567i | \(-0.576087\pi\) | ||||
0.236764 | + | 0.971567i | \(0.423913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.49339 | − | 1.30216i | −1.49339 | − | 1.30216i | −0.836182 | − | 0.548452i | \(-0.815217\pi\) |
−0.657204 | − | 0.753713i | \(-0.728261\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.54781 | − | 0.105873i | −1.54781 | − | 0.105873i | −0.730836 | − | 0.682553i | \(-0.760870\pi\) |
−0.816970 | + | 0.576680i | \(0.804348\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.759461 | − | 0.709287i | −0.759461 | − | 0.709287i | ||||
\(622\) | 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 | ||||||||
\(631\) | 0.280364 | + | 1.00063i | 0.280364 | + | 1.00063i | 0.962917 | + | 0.269797i | \(0.0869565\pi\) |
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(632\) | 1.33564 | + | 0.635203i | 1.33564 | + | 0.635203i | ||||
\(633\) | −1.52002 | + | 0.599418i | −1.52002 | + | 0.599418i | ||||
\(634\) | 0.568078 | − | 0.345456i | 0.568078 | − | 0.345456i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.512595 | − | 0.222651i | −0.512595 | − | 0.222651i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.136167 | − | 0.990686i | \(-0.456522\pi\) | ||||
−0.136167 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(642\) | 0.655202 | − | 0.112968i | 0.655202 | − | 0.112968i | ||||
\(643\) | 0 | 0 | −0.930278 | − | 0.366854i | \(-0.880435\pi\) | ||||
0.930278 | + | 0.366854i | \(0.119565\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.23556 | − | 0.640215i | −1.23556 | − | 0.640215i | ||||
\(647\) | 0.404693 | − | 0.533668i | 0.404693 | − | 0.533668i | −0.548452 | − | 0.836182i | \(-0.684783\pi\) |
0.953145 | + | 0.302515i | \(0.0978261\pi\) | |||||||
\(648\) | 0.746013 | − | 0.0254846i | 0.746013 | − | 0.0254846i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.769396 | + | 0.504647i | −0.769396 | + | 0.504647i | −0.871660 | − | 0.490110i | \(-0.836957\pi\) |
0.102264 | + | 0.994757i | \(0.467391\pi\) | |||||||
\(654\) | 0.373539 | + | 0.720898i | 0.373539 | + | 0.720898i | ||||
\(655\) | 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 | ||||||||
\(661\) | 1.11059 | + | 1.57335i | 1.11059 | + | 1.57335i | 0.775711 | + | 0.631088i | \(0.217391\pi\) |
0.334880 | + | 0.942261i | \(0.391304\pi\) | |||||||
\(662\) | −0.0529351 | − | 0.0168008i | −0.0529351 | − | 0.0168008i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.101641 | + | 0.00695246i | −0.101641 | + | 0.00695246i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −0.0536865 | − | 1.57157i | −0.0536865 | − | 1.57157i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.366854 | − | 0.930278i | \(-0.380435\pi\) | ||||
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.647271 | + | 0.526594i | −0.647271 | + | 0.526594i | ||||
\(677\) | −0.437008 | + | 0.666272i | −0.437008 | + | 0.666272i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(678\) | −0.291504 | + | 0.518439i | −0.291504 | + | 0.518439i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.655806 | + | 1.07843i | 0.655806 | + | 1.07843i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.626895 | − | 1.58970i | −0.626895 | − | 1.58970i | −0.796805 | − | 0.604236i | \(-0.793478\pi\) |
0.169910 | − | 0.985460i | \(-0.445652\pi\) | |||||||
\(684\) | 0.496206 | + | 1.39619i | 0.496206 | + | 1.39619i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.25556 | + | 0.129075i | 1.25556 | + | 0.129075i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.394354 | − | 0.368301i | 0.394354 | − | 0.368301i | −0.460065 | − | 0.887885i | \(-0.652174\pi\) |
0.854419 | + | 0.519584i | \(0.173913\pi\) | |||||||
\(692\) | −1.13310 | + | 0.116487i | −1.13310 | + | 0.116487i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.0756376 | + | 0.550304i | 0.0756376 | + | 0.550304i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0.282617 | − | 0.158908i | 0.282617 | − | 0.158908i | ||||
\(699\) | 0.128604 | + | 1.88013i | 0.128604 | + | 1.88013i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.887885 | − | 0.460065i | \(-0.152174\pi\) | ||||
−0.887885 | + | 0.460065i | \(0.847826\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.374412 | −0.374412 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.51725 | − | 0.786177i | 1.51725 | − | 0.786177i | 0.519584 | − | 0.854419i | \(-0.326087\pi\) |
0.997669 | + | 0.0682424i | \(0.0217391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.135214 | − | 1.97675i | −0.135214 | − | 1.97675i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.213301 | + | 0.185989i | −0.213301 | + | 0.185989i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.730836 | − | 0.682553i | \(-0.239130\pi\) | ||||
−0.730836 | + | 0.682553i | \(0.760870\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.698183 | − | 0.529449i | 0.698183 | − | 0.529449i | ||||
\(723\) | 0.666248 | + | 0.0684924i | 0.666248 | + | 0.0684924i | ||||
\(724\) | −0.248146 | − | 1.19414i | −0.248146 | − | 1.19414i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.136267 | + | 0.383417i | 0.136267 | + | 0.383417i | ||||
\(727\) | 0 | 0 | −0.366854 | − | 0.930278i | \(-0.619565\pi\) | ||||
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.519584 | − | 0.854419i | −0.519584 | − | 0.854419i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.634468 | − | 1.12840i | 0.634468 | − | 1.12840i | ||||
\(733\) | 0 | 0 | 0.548452 | − | 0.836182i | \(-0.315217\pi\) | ||||
−0.548452 | + | 0.836182i | \(0.684783\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.817039 | + | 0.576729i | 0.817039 | + | 0.576729i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.861502 | − | 1.05893i | 0.861502 | − | 1.05893i | −0.136167 | − | 0.990686i | \(-0.543478\pi\) |
0.997669 | − | 0.0682424i | \(-0.0217391\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.762664 | − | 1.60365i | −0.762664 | − | 1.60365i | −0.796805 | − | 0.604236i | \(-0.793478\pi\) |
0.0341411 | − | 0.999417i | \(-0.489130\pi\) | |||||||
\(744\) | 0.0138725 | − | 0.202809i | 0.0138725 | − | 0.202809i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0748554 | + | 0.114126i | 0.0748554 | + | 0.114126i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.63394i | 1.63394i | 0.576680 | + | 0.816970i | \(0.304348\pi\) | ||||
−0.576680 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(752\) | 0.320658 | − | 0.422851i | 0.320658 | − | 0.422851i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.836182 | − | 0.548452i | \(-0.184783\pi\) | ||||
−0.836182 | + | 0.548452i | \(0.815217\pi\) | |||||||
\(758\) | −0.308436 | + | 0.353730i | −0.308436 | + | 0.353730i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.334880 | − | 0.942261i | \(-0.391304\pi\) | ||||
−0.334880 | + | 0.942261i | \(0.608696\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.379143 | + | 0.405963i | 0.379143 | + | 0.405963i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.271554 | + | 0.0468206i | −0.271554 | + | 0.0468206i | ||||
\(769\) | −0.262234 | + | 1.90790i | −0.262234 | + | 1.90790i | 0.136167 | + | 0.990686i | \(0.456522\pi\) |
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.528307 | + | 0.109784i | −0.528307 | + | 0.109784i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.787854 | + | 1.65662i | −0.787854 | + | 1.65662i | −0.0341411 | + | 0.999417i | \(0.510870\pi\) |
−0.753713 | + | 0.657204i | \(0.771739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.492053 | + | 0.648869i | 0.492053 | + | 0.648869i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.211425 | − | 0.486749i | −0.211425 | − | 0.486749i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.953145 | − | 0.302515i | \(-0.0978261\pi\) | ||||
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(788\) | −1.03150 | − | 0.782209i | −1.03150 | − | 0.782209i | ||||
\(789\) | −1.24888 | − | 1.16637i | −1.24888 | − | 1.16637i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.28468 | + | 0.906823i | −1.28468 | + | 0.906823i | ||||
\(797\) | −0.188654 | − | 0.774147i | −0.188654 | − | 0.774147i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
0.796805 | − | 0.604236i | \(-0.206522\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.57335 | − | 1.11059i | 1.57335 | − | 1.11059i | ||||
\(800\) | 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 | 0.682553 | − | 0.730836i | \(-0.260870\pi\) | ||||
−0.682553 | + | 0.730836i | \(0.739130\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.628038 | − | 1.21206i | 0.628038 | − | 1.21206i | −0.334880 | − | 0.942261i | \(-0.608696\pi\) |
0.962917 | − | 0.269797i | \(-0.0869565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0314143 | + | 0.919594i | −0.0314143 | + | 0.919594i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.01249 | + | 0.139164i | 1.01249 | + | 0.139164i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.271114 | + | 0.177824i | 0.271114 | + | 0.177824i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.398401 | − | 0.917211i | \(-0.369565\pi\) | ||||
−0.398401 | + | 0.917211i | \(0.630435\pi\) | |||||||
\(822\) | −0.788841 | − | 0.192235i | −0.788841 | − | 0.192235i | ||||
\(823\) | 0 | 0 | −0.971567 | − | 0.236764i | \(-0.923913\pi\) | ||||
0.971567 | + | 0.236764i | \(0.0760870\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.53391 | − | 1.00609i | −1.53391 | − | 1.00609i | −0.985460 | − | 0.169910i | \(-0.945652\pi\) |
−0.548452 | − | 0.836182i | \(-0.684783\pi\) | |||||||
\(828\) | 0.0886738 | − | 0.862559i | 0.0886738 | − | 0.862559i | ||||
\(829\) | −1.93993 | − | 0.266637i | −1.93993 | − | 0.266637i | −0.942261 | − | 0.334880i | \(-0.891304\pi\) |
−0.997669 | + | 0.0682424i | \(0.978261\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.196944 | − | 1.91574i | −0.196944 | − | 1.91574i | ||||
\(834\) | −0.149166 | + | 0.287878i | −0.149166 | + | 0.287878i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.245937 | + | 0.116963i | −0.245937 | + | 0.116963i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.962917 | − | 0.269797i | \(-0.913043\pi\) | ||||
0.962917 | + | 0.269797i | \(0.0869565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.203456 | − | 0.979084i | 0.203456 | − | 0.979084i | ||||
\(842\) | −0.201133 | + | 0.633717i | −0.201133 | + | 0.633717i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.16491 | − | 0.708399i | −1.16491 | − | 0.708399i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.403122 | + | 0.0554078i | 0.403122 | + | 0.0554078i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.0841532 | − | 0.345324i | −0.0841532 | − | 0.345324i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.490110 | − | 0.871660i | \(-0.663043\pi\) | ||||
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.891366 | + | 0.832477i | 0.891366 | + | 0.832477i | ||||
\(857\) | −1.30193 | − | 0.987286i | −1.30193 | − | 0.987286i | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) |
−0.302515 | − | 0.953145i | \(-0.597826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.51897 | + | 1.23578i | 1.51897 | + | 1.23578i | 0.887885 | + | 0.460065i | \(0.152174\pi\) |
0.631088 | + | 0.775711i | \(0.282609\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.19722 | + | 1.57877i | 1.19722 | + | 1.57877i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
0.490110 | + | 0.871660i | \(0.336957\pi\) | |||||||
\(864\) | 0.607353 | + | 0.746537i | 0.607353 | + | 0.746537i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.44628 | + | 1.16340i | 2.44628 | + | 1.16340i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.639680 | + | 1.34505i | −0.639680 | + | 1.34505i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.735179 | + | 0.152772i | −0.735179 | + | 0.152772i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.985460 | − | 0.169910i | \(-0.0543478\pi\) | ||||
−0.985460 | + | 0.169910i | \(0.945652\pi\) | |||||||
\(878\) | −0.0516652 | − | 0.0203741i | −0.0516652 | − | 0.0203741i | ||||
\(879\) | 1.33655 | + | 1.43110i | 1.33655 | + | 1.43110i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.887885 | − | 0.460065i | \(-0.847826\pi\) | ||||
0.887885 | + | 0.460065i | \(0.152174\pi\) | |||||||
\(882\) | 0.245871 | − | 0.324230i | 0.245871 | − | 0.324230i | ||||
\(883\) | 0 | 0 | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | ||||
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.219055 | − | 0.781818i | 0.219055 | − | 0.781818i | ||||
\(887\) | −1.16704 | + | 1.33842i | −1.16704 | + | 1.33842i | −0.236764 | + | 0.971567i | \(0.576087\pi\) |
−0.930278 | + | 0.366854i | \(0.880435\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.301722 | + | 1.74995i | 0.301722 | + | 1.74995i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0880222 | − | 1.28684i | 0.0880222 | − | 1.28684i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.08090 | + | 0.148566i | −1.08090 | + | 0.148566i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.324123 | + | 0.398401i | −0.324123 | + | 0.398401i | ||||
\(907\) | 0 | 0 | −0.999417 | − | 0.0341411i | \(-0.989130\pi\) | ||||
0.999417 | + | 0.0341411i | \(0.0108696\pi\) | |||||||
\(908\) | −0.386366 | + | 0.979758i | −0.386366 | + | 0.979758i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.775711 | − | 0.631088i | \(-0.217391\pi\) | ||||
−0.775711 | + | 0.631088i | \(0.782609\pi\) | |||||||
\(912\) | −0.516846 | + | 0.787995i | −0.516846 | + | 0.787995i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.547220 | + | 0.899864i | 0.547220 | + | 0.899864i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.287484 | + | 0.729008i | 0.287484 | + | 0.729008i | ||||
\(919\) | 0.347996 | + | 0.979167i | 0.347996 | + | 0.979167i | 0.979084 | + | 0.203456i | \(0.0652174\pi\) |
−0.631088 | + | 0.775711i | \(0.717391\pi\) | |||||||
\(920\) | 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 | −0.136167 | − | 0.990686i | \(-0.543478\pi\) | ||||
0.136167 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.67324 | + | 0.594669i | 1.67324 | + | 0.594669i | ||||
\(932\) | −1.18520 | + | 1.03344i | −1.18520 | + | 1.03344i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.0221261 | + | 0.323473i | 0.0221261 | + | 0.323473i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.169910 | − | 0.985460i | \(-0.445652\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.59899 | + | 0.899069i | −1.59899 | + | 0.899069i | −0.604236 | + | 0.796805i | \(0.706522\pi\) |
−0.994757 | + | 0.102264i | \(0.967391\pi\) | |||||||
\(948\) | 1.24611 | − | 1.08656i | 1.24611 | − | 1.08656i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.222488 | − | 1.61872i | −0.222488 | − | 1.61872i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.94790 | + | 0.200250i | −1.94790 | + | 0.200250i | −0.994757 | − | 0.102264i | \(-0.967391\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(954\) | 0.199177 | − | 0.186018i | 0.199177 | − | 0.186018i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.310043 | − | 0.872378i | −0.310043 | − | 0.872378i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.386859 | − | 1.58748i | 0.386859 | − | 1.58748i | ||||
\(964\) | 0.290376 | + | 0.477503i | 0.290376 | + | 0.477503i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.490110 | − | 0.871660i | \(-0.336957\pi\) | ||||
−0.490110 | + | 0.871660i | \(0.663043\pi\) | |||||||
\(968\) | −0.409391 | + | 0.624167i | −0.409391 | + | 0.624167i | ||||
\(969\) | −2.65281 | + | 2.15822i | −2.65281 | + | 2.15822i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.816970 | − | 0.576680i | \(-0.804348\pi\) | ||||
0.816970 | + | 0.576680i | \(0.195652\pi\) | |||||||
\(972\) | 0.306111 | − | 0.776245i | 0.306111 | − | 0.776245i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.815646 | − | 0.112108i | 0.815646 | − | 0.112108i | ||||
\(977\) | 0.0466062 | + | 1.36431i | 0.0466062 | + | 1.36431i | 0.753713 | + | 0.657204i | \(0.228261\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.99069 | − | 0.136167i | 1.99069 | − | 0.136167i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.20304 | + | 0.381827i | 1.20304 | + | 0.381827i | 0.836182 | − | 0.548452i | \(-0.184783\pi\) |
0.366854 | + | 0.930278i | \(0.380435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.530621 | − | 1.02405i | −0.530621 | − | 1.02405i | −0.990686 | − | 0.136167i | \(-0.956522\pi\) |
0.460065 | − | 0.887885i | \(-0.347826\pi\) | |||||||
\(992\) | 0.219156 | − | 0.143744i | 0.219156 | − | 0.143744i | ||||
\(993\) | −0.0896983 | + | 0.102870i | −0.0896983 | + | 0.102870i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0381381 | + | 0.107310i | −0.0381381 | + | 0.107310i | ||||
\(997\) | 0 | 0 | 0.999417 | − | 0.0341411i | \(-0.0108696\pi\) | ||||
−0.999417 | + | 0.0341411i | \(0.989130\pi\) | |||||||
\(998\) | −0.255501 | + | 0.336929i | −0.255501 | + | 0.336929i | ||||
\(999\) | 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.407.1 | ✓ | 88 | |
3.2 | odd | 2 | inner | 3525.1.bg.a.407.2 | yes | 88 | |
5.2 | odd | 4 | inner | 3525.1.bg.a.3368.1 | yes | 88 | |
5.3 | odd | 4 | inner | 3525.1.bg.a.3368.2 | yes | 88 | |
5.4 | even | 2 | inner | 3525.1.bg.a.407.2 | yes | 88 | |
15.2 | even | 4 | inner | 3525.1.bg.a.3368.2 | yes | 88 | |
15.8 | even | 4 | inner | 3525.1.bg.a.3368.1 | yes | 88 | |
15.14 | odd | 2 | CM | 3525.1.bg.a.407.1 | ✓ | 88 | |
47.44 | odd | 46 | inner | 3525.1.bg.a.2582.1 | yes | 88 | |
141.44 | even | 46 | inner | 3525.1.bg.a.2582.2 | yes | 88 | |
235.44 | odd | 46 | inner | 3525.1.bg.a.2582.2 | yes | 88 | |
235.138 | even | 92 | inner | 3525.1.bg.a.2018.2 | yes | 88 | |
235.232 | even | 92 | inner | 3525.1.bg.a.2018.1 | yes | 88 | |
705.44 | even | 46 | inner | 3525.1.bg.a.2582.1 | yes | 88 | |
705.467 | odd | 92 | inner | 3525.1.bg.a.2018.2 | yes | 88 | |
705.608 | odd | 92 | inner | 3525.1.bg.a.2018.1 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3525.1.bg.a.407.1 | ✓ | 88 | 1.1 | even | 1 | trivial | |
3525.1.bg.a.407.1 | ✓ | 88 | 15.14 | odd | 2 | CM | |
3525.1.bg.a.407.2 | yes | 88 | 3.2 | odd | 2 | inner | |
3525.1.bg.a.407.2 | yes | 88 | 5.4 | even | 2 | inner | |
3525.1.bg.a.2018.1 | yes | 88 | 235.232 | even | 92 | inner | |
3525.1.bg.a.2018.1 | yes | 88 | 705.608 | odd | 92 | inner | |
3525.1.bg.a.2018.2 | yes | 88 | 235.138 | even | 92 | inner | |
3525.1.bg.a.2018.2 | yes | 88 | 705.467 | odd | 92 | inner | |
3525.1.bg.a.2582.1 | yes | 88 | 47.44 | odd | 46 | inner | |
3525.1.bg.a.2582.1 | yes | 88 | 705.44 | even | 46 | inner | |
3525.1.bg.a.2582.2 | yes | 88 | 141.44 | even | 46 | inner | |
3525.1.bg.a.2582.2 | yes | 88 | 235.44 | odd | 46 | inner | |
3525.1.bg.a.3368.1 | yes | 88 | 5.2 | odd | 4 | inner | |
3525.1.bg.a.3368.1 | yes | 88 | 15.8 | even | 4 | inner | |
3525.1.bg.a.3368.2 | yes | 88 | 5.3 | odd | 4 | inner | |
3525.1.bg.a.3368.2 | yes | 88 | 15.2 | even | 4 | inner |