Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3997,1,Mod(258,3997)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3997, base_ring=CyclotomicField(114))
chi = DirichletCharacter(H, H._module([57, 86]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3997.258");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3997 = 7 \cdot 571 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3997.ce (of order \(114\), degree \(36\), 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: | \(1.99476285549\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Coefficient field: | \(\Q(\zeta_{57})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{36} - x^{35} + x^{33} - x^{32} + x^{30} - x^{29} + x^{27} - x^{26} + x^{24} - x^{23} + x^{21} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{57}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{57} - \cdots)\) |
Embedding invariants
Embedding label | 1224.1 | ||
Root | \(-0.592235 - 0.805765i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3997.1224 |
Dual form | 3997.1.ce.a.1525.1 |
$q$-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 \(\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times\).
\(n\) | \(1716\) | \(2285\) |
\(\chi(n)\) | \(e\left(\frac{34}{57}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.87796 | − | 0.531035i | −1.87796 | − | 0.531035i | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) |
−0.879474 | − | 0.475947i | \(-0.842105\pi\) | |||||||
\(3\) | 0 | 0 | 0.298515 | − | 0.954405i | \(-0.403509\pi\) | ||||
−0.298515 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(4\) | 2.39280 | + | 1.47085i | 2.39280 | + | 1.47085i | ||||
\(5\) | 0 | 0 | 0.635724 | − | 0.771917i | \(-0.280702\pi\) | ||||
−0.635724 | + | 0.771917i | \(0.719298\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.789141 | − | 0.614213i | 0.789141 | − | 0.614213i | ||||
\(8\) | −2.39072 | − | 2.59701i | −2.39072 | − | 2.59701i | ||||
\(9\) | −0.821778 | − | 0.569808i | −0.821778 | − | 0.569808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.248433 | − | 0.117239i | 0.248433 | − | 0.117239i | −0.298515 | − | 0.954405i | \(-0.596491\pi\) |
0.546948 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.993931 | − | 0.110008i | \(-0.0350877\pi\) | ||||
−0.993931 | + | 0.110008i | \(0.964912\pi\) | |||||||
\(14\) | −1.80814 | + | 0.734403i | −1.80814 | + | 0.734403i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.84233 | + | 3.64054i | 1.84233 | + | 3.64054i | ||||
\(17\) | 0 | 0 | −0.451533 | − | 0.892254i | \(-0.649123\pi\) | ||||
0.451533 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(18\) | 1.24067 | + | 1.50647i | 1.24067 | + | 1.50647i | ||||
\(19\) | 0 | 0 | 0.298515 | − | 0.954405i | \(-0.403509\pi\) | ||||
−0.298515 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.528804 | + | 0.0882419i | −0.528804 | + | 0.0882419i | ||||
\(23\) | −0.970927 | + | 1.05471i | −0.970927 | + | 1.05471i | 0.0275543 | + | 0.999620i | \(0.491228\pi\) |
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.191711 | − | 0.981451i | −0.191711 | − | 0.981451i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.79167 | − | 0.308982i | 2.79167 | − | 0.308982i | ||||
\(29\) | −0.849008 | − | 1.15512i | −0.849008 | − | 1.15512i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) |
0.137354 | − | 0.990522i | \(-0.456140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.546948 | − | 0.837166i | \(-0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(32\) | −0.849842 | − | 4.35072i | −0.849842 | − | 4.35072i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.12825 | − | 2.57215i | −1.12825 | − | 2.57215i | ||||
\(37\) | −1.96075 | − | 0.217016i | −1.96075 | − | 0.217016i | −0.962268 | − | 0.272103i | \(-0.912281\pi\) |
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.635724 | − | 0.771917i | \(-0.280702\pi\) | ||||
−0.635724 | + | 0.771917i | \(0.719298\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.58154 | − | 1.09662i | 1.58154 | − | 1.09662i | 0.635724 | − | 0.771917i | \(-0.280702\pi\) |
0.945817 | − | 0.324699i | \(-0.105263\pi\) | |||||||
\(44\) | 0.766891 | + | 0.0848795i | 0.766891 | + | 0.0848795i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.38344 | − | 1.46510i | 2.38344 | − | 1.46510i | ||||
\(47\) | 0 | 0 | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) | ||||
0.998482 | + | 0.0550878i | \(0.0175439\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.245485 | − | 0.969400i | 0.245485 | − | 0.969400i | ||||
\(50\) | −0.161161 | + | 1.94493i | −0.161161 | + | 1.94493i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.74047 | + | 0.492157i | −1.74047 | + | 0.492157i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) |
−0.754107 | + | 0.656752i | \(0.771930\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.48173 | − | 0.580998i | −3.48173 | − | 0.580998i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.980991 | + | 2.62011i | 0.980991 | + | 2.62011i | ||||
\(59\) | 0 | 0 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.716783 | − | 0.697297i | \(-0.245614\pi\) | ||||
−0.716783 | + | 0.697297i | \(0.754386\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.998482 | + | 0.0550878i | −0.998482 | + | 0.0550878i | ||||
\(64\) | −0.377481 | + | 4.55552i | −0.377481 | + | 4.55552i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.37947 | − | 1.34197i | −1.37947 | − | 1.34197i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0825793 | + | 0.143032i | 0.0825793 | + | 0.143032i | 0.904357 | − | 0.426776i | \(-0.140351\pi\) |
−0.821778 | + | 0.569808i | \(0.807018\pi\) | |||||||
\(72\) | 0.484841 | + | 3.49642i | 0.484841 | + | 3.49642i | ||||
\(73\) | 0 | 0 | 0.592235 | − | 0.805765i | \(-0.298246\pi\) | ||||
−0.592235 | + | 0.805765i | \(0.701754\pi\) | |||||||
\(74\) | 3.56696 | + | 1.44877i | 3.56696 | + | 1.44877i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.124039 | − | 0.245109i | 0.124039 | − | 0.245109i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.0537749 | + | 1.95085i | 0.0537749 | + | 1.95085i | 0.245485 | + | 0.969400i | \(0.421053\pi\) |
−0.191711 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.350638 | + | 0.936511i | 0.350638 | + | 0.936511i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) | ||||
0.998482 | + | 0.0550878i | \(0.0175439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.55240 | + | 1.21954i | −3.55240 | + | 1.21954i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.898404 | − | 0.364900i | −0.898404 | − | 0.364900i | ||||
\(89\) | 0 | 0 | −0.451533 | − | 0.892254i | \(-0.649123\pi\) | ||||
0.451533 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.87455 | + | 1.09562i | −3.87455 | + | 1.09562i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.851919 | − | 0.523673i | \(-0.824561\pi\) | ||||
0.851919 | + | 0.523673i | \(0.175439\pi\) | |||||||
\(98\) | −0.975796 | + | 1.69013i | −0.975796 | + | 1.69013i | ||||
\(99\) | −0.270960 | − | 0.0452153i | −0.270960 | − | 0.0452153i | ||||
\(100\) | 0.984841 | − | 2.63039i | 0.984841 | − | 2.63039i | ||||
\(101\) | 0 | 0 | 0.851919 | − | 0.523673i | \(-0.175439\pi\) | ||||
−0.851919 | + | 0.523673i | \(0.824561\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.52987 | 3.52987 | ||||||||
\(107\) | 0.712647 | − | 1.40823i | 0.712647 | − | 1.40823i | −0.191711 | − | 0.981451i | \(-0.561404\pi\) |
0.904357 | − | 0.426776i | \(-0.140351\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.245485 | − | 0.425193i | −0.245485 | − | 0.425193i | 0.716783 | − | 0.697297i | \(-0.245614\pi\) |
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.68992 | + | 1.74132i | 3.68992 | + | 1.74132i | ||||
\(113\) | 0.897586 | − | 0.0993448i | 0.897586 | − | 0.0993448i | 0.350638 | − | 0.936511i | \(-0.385965\pi\) |
0.546948 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.332504 | − | 4.01272i | −0.332504 | − | 4.01272i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.587749 | + | 0.713665i | −0.587749 | + | 0.713665i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.90436 | + | 0.426776i | 1.90436 | + | 0.426776i | ||||
\(127\) | −1.55450 | + | 1.07787i | −1.55450 | + | 1.07787i | −0.592235 | + | 0.805765i | \(0.701754\pi\) |
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(128\) | 1.57368 | − | 4.20311i | 1.57368 | − | 4.20311i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.879474 | − | 0.475947i | \(-0.157895\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.87796 | + | 3.25271i | 1.87796 | + | 3.25271i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.355238 | − | 1.81862i | 0.355238 | − | 1.81862i | −0.191711 | − | 0.981451i | \(-0.561404\pi\) |
0.546948 | − | 0.837166i | \(-0.315789\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.904357 | − | 0.426776i | \(-0.859649\pi\) | ||||
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.0791255 | − | 0.312460i | −0.0791255 | − | 0.312460i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.560425 | − | 4.04149i | 0.560425 | − | 4.04149i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.37248 | − | 3.40324i | −4.37248 | − | 3.40324i | ||||
\(149\) | 1.35251 | + | 1.46921i | 1.35251 | + | 1.46921i | 0.716783 | + | 0.697297i | \(0.245614\pi\) |
0.635724 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.635724 | − | 0.771917i | −0.635724 | − | 0.771917i | 0.350638 | − | 0.936511i | \(-0.385965\pi\) |
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.363102 | + | 0.394434i | −0.363102 | + | 0.394434i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) | ||||
0.998482 | + | 0.0550878i | \(0.0175439\pi\) | |||||||
\(158\) | 0.934984 | − | 3.69217i | 0.934984 | − | 3.69217i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.118383 | + | 1.42867i | −0.118383 | + | 1.42867i | ||||
\(162\) | −0.161161 | − | 1.94493i | −0.161161 | − | 1.94493i | ||||
\(163\) | −0.130333 | − | 0.101443i | −0.130333 | − | 0.101443i | 0.546948 | − | 0.837166i | \(-0.315789\pi\) |
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.975796 | − | 0.218681i | 0.975796 | − | 0.218681i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.39726 | − | 0.297775i | 5.39726 | − | 0.297775i | ||||
\(173\) | 0 | 0 | 0.137354 | − | 0.990522i | \(-0.456140\pi\) | ||||
−0.137354 | + | 0.990522i | \(0.543860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.754107 | − | 0.656752i | −0.754107 | − | 0.656752i | ||||
\(176\) | 0.884508 | + | 0.688440i | 0.884508 | + | 0.688440i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.04171 | − | 0.563746i | 1.04171 | − | 0.563746i | 0.137354 | − | 0.990522i | \(-0.456140\pi\) |
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.06030 | 5.06030 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.0415578 | − | 1.50764i | −0.0415578 | − | 1.50764i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) |
0.635724 | − | 0.771917i | \(-0.280702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.451533 | + | 0.782079i | −0.451533 | + | 0.782079i | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) |
0.546948 | + | 0.837166i | \(0.315789\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.01324 | − | 1.95851i | 2.01324 | − | 1.95851i | ||||
\(197\) | −0.849008 | − | 1.15512i | −0.849008 | − | 1.15512i | −0.986361 | − | 0.164595i | \(-0.947368\pi\) |
0.137354 | − | 0.990522i | \(-0.456140\pi\) | |||||||
\(198\) | 0.484841 | + | 0.228802i | 0.484841 | + | 0.228802i | ||||
\(199\) | 0 | 0 | −0.137354 | − | 0.990522i | \(-0.543860\pi\) | ||||
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(200\) | −2.09052 | + | 2.84425i | −2.09052 | + | 2.84425i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.37947 | − | 0.390078i | −1.37947 | − | 0.390078i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.39887 | − | 0.313494i | 1.39887 | − | 0.313494i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0469482 | + | 0.0288589i | 0.0469482 | + | 0.0288589i | 0.546948 | − | 0.837166i | \(-0.315789\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | −4.88848 | − | 1.38233i | −4.88848 | − | 1.38233i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.08614 | + | 2.26615i | −2.08614 | + | 2.26615i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.235218 | + | 0.928855i | 0.235218 | + | 0.928855i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.975796 | − | 0.218681i | \(-0.929825\pi\) | ||||
0.975796 | + | 0.218681i | \(0.0701754\pi\) | |||||||
\(224\) | −3.34291 | − | 2.91134i | −3.34291 | − | 2.91134i | ||||
\(225\) | −0.401695 | + | 0.915773i | −0.401695 | + | 0.915773i | ||||
\(226\) | −1.73838 | − | 0.290085i | −1.73838 | − | 0.290085i | ||||
\(227\) | 0 | 0 | −0.975796 | − | 0.218681i | \(-0.929825\pi\) | ||||
0.975796 | + | 0.218681i | \(0.0701754\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.926494 | − | 0.376309i | \(-0.122807\pi\) | ||||
−0.926494 | + | 0.376309i | \(0.877193\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.970114 | + | 4.96644i | −0.970114 | + | 4.96644i | ||||
\(233\) | −1.88876 | − | 0.104206i | −1.88876 | − | 0.104206i | −0.926494 | − | 0.376309i | \(-0.877193\pi\) |
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.63358 | − | 1.13270i | −1.63358 | − | 1.13270i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) |
−0.754107 | − | 0.656752i | \(-0.771930\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(242\) | 1.48275 | − | 1.02811i | 1.48275 | − | 1.02811i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.716783 | − | 0.697297i | \(-0.754386\pi\) | ||||
0.716783 | + | 0.697297i | \(0.245614\pi\) | |||||||
\(252\) | −2.47019 | − | 1.33680i | −2.47019 | − | 1.33680i | ||||
\(253\) | −0.117558 | + | 0.375855i | −0.117558 | + | 0.375855i | ||||
\(254\) | 3.49167 | − | 1.19869i | 3.49167 | − | 1.19869i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.48011 | + | 3.37431i | −2.48011 | + | 3.37431i | ||||
\(257\) | 0 | 0 | −0.945817 | − | 0.324699i | \(-0.894737\pi\) | ||||
0.945817 | + | 0.324699i | \(0.105263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.68060 | + | 1.03306i | −1.68060 | + | 1.03306i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0395009 | + | 1.43302i | 0.0395009 | + | 1.43302i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.684424 | + | 0.420714i | −0.684424 | + | 0.420714i | −0.821778 | − | 0.569808i | \(-0.807018\pi\) |
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.32696 | − | 5.24007i | −1.32696 | − | 5.24007i | ||||
\(269\) | 0 | 0 | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.63287 | + | 3.22664i | −1.63287 | + | 3.22664i | ||||
\(275\) | −0.162691 | − | 0.221349i | −0.162691 | − | 0.221349i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.917421 | + | 0.996584i | 0.917421 | + | 0.996584i | 1.00000 | \(0\) | ||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.61152 | + | 0.553236i | 1.61152 | + | 0.553236i | 0.975796 | − | 0.218681i | \(-0.0701754\pi\) |
0.635724 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(284\) | −0.0127820 | + | 0.463707i | −0.0127820 | + | 0.463707i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.78069 | + | 4.05957i | −1.78069 | + | 4.05957i | ||||
\(289\) | −0.592235 | + | 0.805765i | −0.592235 | + | 0.805765i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.754107 | − | 0.656752i | \(-0.771930\pi\) | ||||
0.754107 | + | 0.656752i | \(0.228070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.12401 | + | 5.61091i | 4.12401 | + | 5.61091i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.75974 | − | 3.47735i | −1.75974 | − | 3.47735i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.574503 | − | 1.83679i | 0.574503 | − | 1.83679i | ||||
\(302\) | 0.783946 | + | 1.78722i | 0.783946 | + | 1.78722i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.635724 | − | 0.771917i | \(-0.280702\pi\) | ||||
−0.635724 | + | 0.771917i | \(0.719298\pi\) | |||||||
\(308\) | 0.657319 | − | 0.404052i | 0.657319 | − | 0.404052i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.904357 | − | 0.426776i | \(-0.140351\pi\) | ||||
−0.904357 | + | 0.426776i | \(0.859649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.0275543 | − | 0.999620i | \(-0.508772\pi\) | ||||
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.74073 | + | 4.74709i | −2.74073 | + | 4.74709i | ||||
\(317\) | 1.35589 | − | 0.465478i | 1.35589 | − | 0.465478i | 0.451533 | − | 0.892254i | \(-0.350877\pi\) |
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.346346 | − | 0.187433i | −0.346346 | − | 0.187433i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.980991 | − | 2.62011i | 0.980991 | − | 2.62011i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.538460 | + | 2.75662i | −0.538460 | + | 2.75662i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.190891 | + | 0.259716i | 0.190891 | + | 0.259716i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.677282 | − | 1.17309i | 0.677282 | − | 1.17309i | −0.298515 | − | 0.954405i | \(-0.596491\pi\) |
0.975796 | − | 0.218681i | \(-0.0701754\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.48764 | + | 1.29559i | 1.48764 | + | 1.29559i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.43139 | − | 1.39248i | −1.43139 | − | 1.39248i | −0.754107 | − | 0.656752i | \(-0.771930\pi\) |
−0.677282 | − | 0.735724i | \(-0.736842\pi\) | |||||||
\(338\) | −1.94863 | − | 0.107509i | −1.94863 | − | 0.107509i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.401695 | − | 0.915773i | −0.401695 | − | 0.915773i | ||||
\(344\) | −6.62895 | − | 1.48558i | −6.62895 | − | 1.48558i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.02149 | + | 0.889612i | 1.02149 | + | 0.889612i | 0.993931 | − | 0.110008i | \(-0.0350877\pi\) |
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.635724 | − | 0.771917i | \(-0.280702\pi\) | ||||
−0.635724 | + | 0.771917i | \(0.719298\pi\) | |||||||
\(350\) | 1.06742 | + | 1.63381i | 1.06742 | + | 1.63381i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.721201 | − | 0.981229i | −0.721201 | − | 0.981229i | ||||
\(353\) | 0 | 0 | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||||
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.25565 | + | 0.505504i | −2.25565 | + | 0.505504i | ||||
\(359\) | −0.472446 | − | 0.133595i | −0.472446 | − | 0.133595i | 0.0275543 | − | 0.999620i | \(-0.491228\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.821778 | − | 0.569808i | −0.821778 | − | 0.569808i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.926494 | − | 0.376309i | \(-0.877193\pi\) | ||||
0.926494 | + | 0.376309i | \(0.122807\pi\) | |||||||
\(368\) | −5.62848 | − | 1.59158i | −5.62848 | − | 1.59158i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.07118 | + | 1.45740i | −1.07118 | + | 1.45740i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.22501 | − | 0.578096i | −1.22501 | − | 0.578096i | −0.298515 | − | 0.954405i | \(-0.596491\pi\) |
−0.926494 | + | 0.376309i | \(0.877193\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.254515 | − | 0.103375i | −0.254515 | − | 0.103375i | 0.245485 | − | 0.969400i | \(-0.421053\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.722566 | + | 2.85335i | −0.722566 | + | 2.85335i | ||||
\(383\) | 0 | 0 | −0.821778 | − | 0.569808i | \(-0.807018\pi\) | ||||
0.821778 | + | 0.569808i | \(0.192982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.26327 | − | 1.22893i | 1.26327 | − | 1.22893i | ||||
\(387\) | −1.92454 | −1.92454 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.32643 | − | 0.717830i | 1.32643 | − | 0.717830i | 0.350638 | − | 0.936511i | \(-0.385965\pi\) |
0.975796 | + | 0.218681i | \(0.0701754\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.10443 | + | 1.68003i | −3.10443 | + | 1.68003i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.980991 | + | 2.62011i | 0.980991 | + | 2.62011i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.581849 | − | 0.506733i | −0.581849 | − | 0.506733i | ||||
\(397\) | 0 | 0 | 0.998482 | − | 0.0550878i | \(-0.0175439\pi\) | ||||
−0.998482 | + | 0.0550878i | \(0.982456\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.21982 | − | 2.50609i | 3.21982 | − | 2.50609i | ||||
\(401\) | −0.0484666 | − | 0.0262288i | −0.0484666 | − | 0.0262288i | 0.451533 | − | 0.892254i | \(-0.350877\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.38344 | + | 1.46510i | 2.38344 | + | 1.46510i | ||||
\(407\) | −0.512558 | + | 0.175961i | −0.512558 | + | 0.175961i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||||
0.0825793 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.79349 | − | 0.154121i | −2.79349 | − | 0.154121i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.904357 | − | 0.426776i | \(-0.140351\pi\) | ||||
−0.904357 | + | 0.426776i | \(0.859649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.09740 | + | 0.445727i | 1.09740 | + | 0.445727i | 0.851919 | − | 0.523673i | \(-0.175439\pi\) |
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(422\) | −0.0728414 | − | 0.0791269i | −0.0728414 | − | 0.0791269i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.43911 | + | 3.34341i | 5.43911 | + | 3.34341i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.77651 | − | 2.32141i | 3.77651 | − | 2.32141i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.326544 | + | 0.499813i | −0.326544 | + | 0.499813i | −0.962268 | − | 0.272103i | \(-0.912281\pi\) |
0.635724 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||||
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.0379974 | − | 1.37847i | 0.0379974 | − | 1.37847i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.754107 | + | 0.656752i | −0.754107 | + | 0.656752i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.0963226 | − | 0.257266i | 0.0963226 | − | 0.257266i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) |
0.975796 | + | 0.218681i | \(0.0701754\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50017 | + | 3.82680i | 2.50017 | + | 3.82680i | ||||
\(449\) | −0.794223 | + | 0.429812i | −0.794223 | + | 0.429812i | −0.821778 | − | 0.569808i | \(-0.807018\pi\) |
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(450\) | 1.24067 | − | 1.50647i | 1.24067 | − | 1.50647i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.29386 | + | 1.08250i | 2.29386 | + | 1.08250i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.25411 | − | 1.52278i | −1.25411 | − | 1.52278i | −0.754107 | − | 0.656752i | \(-0.771930\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.697019 | − | 0.0771460i | 0.697019 | − | 0.0771460i | 0.245485 | − | 0.969400i | \(-0.421053\pi\) |
0.451533 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(464\) | 2.64110 | − | 5.21895i | 2.64110 | − | 5.21895i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.49167 | + | 1.19869i | 3.49167 | + | 1.19869i | ||||
\(467\) | 0 | 0 | −0.754107 | − | 0.656752i | \(-0.771930\pi\) | ||||
0.754107 | + | 0.656752i | \(0.228070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.91286 | − | 0.211715i | −1.91286 | − | 0.211715i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.264342 | − | 0.457854i | 0.264342 | − | 0.457854i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.71071 | + | 0.587289i | 1.71071 | + | 0.587289i | ||||
\(478\) | 2.46629 | + | 2.99465i | 2.46629 | + | 2.99465i | ||||
\(479\) | 0 | 0 | 0.962268 | − | 0.272103i | \(-0.0877193\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.45606 | + | 0.843166i | −2.45606 | + | 0.843166i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.259684 | − | 1.32944i | 0.259684 | − | 1.32944i | −0.592235 | − | 0.805765i | \(-0.701754\pi\) |
0.851919 | − | 0.523673i | \(-0.175439\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.92498 | − | 0.431397i | −1.92498 | − | 0.431397i | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) |
−0.926494 | − | 0.376309i | \(-0.877193\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.153019 | + | 0.0621508i | 0.153019 | + | 0.0621508i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.254515 | − | 1.83543i | −0.254515 | − | 1.83543i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.245485 | − | 0.969400i | \(-0.421053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(504\) | 2.53015 | + | 2.46137i | 2.53015 | + | 2.46137i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.420361 | − | 0.643411i | 0.420361 | − | 0.643411i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.30499 | + | 0.292685i | −5.30499 | + | 0.292685i | ||||
\(509\) | 0 | 0 | 0.754107 | − | 0.656752i | \(-0.228070\pi\) | ||||
−0.754107 | + | 0.656752i | \(0.771930\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.90771 | − | 2.26316i | 2.90771 | − | 2.26316i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.70468 | − | 1.04759i | 3.70468 | − | 1.04759i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.0825793 | − | 0.996584i | \(-0.473684\pi\) | ||||
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(522\) | 0.686803 | − | 2.71213i | 0.686803 | − | 2.71213i | ||||
\(523\) | 0 | 0 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.50873 | − | 0.426629i | 1.50873 | − | 0.426629i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.0871302 | − | 1.05150i | −0.0871302 | − | 1.05150i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.187187 | + | 6.79079i | −0.187187 | + | 6.79079i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0526643 | − | 0.269612i | −0.0526643 | − | 0.269612i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.114457 | + | 0.365939i | 0.114457 | + | 0.365939i | 0.993931 | − | 0.110008i | \(-0.0350877\pi\) |
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.80871 | − | 0.853553i | 1.80871 | − | 0.853553i | 0.904357 | − | 0.426776i | \(-0.140351\pi\) |
0.904357 | − | 0.426776i | \(-0.140351\pi\) | |||||||
\(548\) | 3.52492 | − | 3.82909i | 3.52492 | − | 3.82909i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.187983 | + | 0.502079i | 0.187983 | + | 0.502079i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.24067 | + | 1.50647i | 1.24067 | + | 1.50647i | ||||
\(554\) | −1.19365 | − | 2.35872i | −1.19365 | − | 2.35872i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.78307 | − | 0.724221i | 1.78307 | − | 0.724221i | 0.789141 | − | 0.614213i | \(-0.210526\pi\) |
0.993931 | − | 0.110008i | \(-0.0350877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.73258 | − | 1.89473i | −2.73258 | − | 1.89473i | ||||
\(563\) | 0 | 0 | −0.677282 | − | 0.735724i | \(-0.736842\pi\) | ||||
0.677282 | + | 0.735724i | \(0.263158\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.851919 | + | 0.523673i | 0.851919 | + | 0.523673i | ||||
\(568\) | 0.174031 | − | 0.556408i | 0.174031 | − | 0.556408i | ||||
\(569\) | 0.368954 | + | 0.104330i | 0.368954 | + | 0.104330i | 0.451533 | − | 0.892254i | \(-0.350877\pi\) |
−0.0825793 | + | 0.996584i | \(0.526316\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.451533 | + | 0.892254i | 0.451533 | + | 0.892254i | ||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.22128 | + | 0.750719i | 1.22128 | + | 0.750719i | ||||
\(576\) | 2.90598 | − | 3.52853i | 2.90598 | − | 3.52853i | ||||
\(577\) | 0 | 0 | 0.546948 | − | 0.837166i | \(-0.315789\pi\) | ||||
−0.546948 | + | 0.837166i | \(0.684211\pi\) | |||||||
\(578\) | 1.54008 | − | 1.19869i | 1.54008 | − | 1.19869i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.374690 | + | 0.326318i | −0.374690 | + | 0.326318i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.451533 | − | 0.892254i | \(-0.649123\pi\) | ||||
0.451533 | + | 0.892254i | \(0.350877\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.82229 | − | 7.53800i | −2.82229 | − | 7.53800i | ||||
\(593\) | 0 | 0 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.07529 | + | 5.50486i | 1.07529 | + | 5.50486i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.63358 | + | 0.180805i | −1.63358 | + | 0.180805i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) |
−0.754107 | + | 0.656752i | \(0.771930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.298515 | − | 0.954405i | \(-0.596491\pi\) | ||||
0.298515 | + | 0.954405i | \(0.403509\pi\) | |||||||
\(602\) | −2.05429 | + | 3.14432i | −2.05429 | + | 3.14432i | ||||
\(603\) | 0.368954 | + | 1.88884i | 0.368954 | + | 1.88884i | ||||
\(604\) | −0.385787 | − | 2.78209i | −0.385787 | − | 2.78209i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.401695 | − | 0.915773i | \(-0.631579\pi\) | ||||
0.401695 | + | 0.915773i | \(0.368421\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.145253 | + | 1.75294i | 0.145253 | + | 1.75294i | 0.546948 | + | 0.837166i | \(0.315789\pi\) |
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.933093 | + | 0.263854i | −0.933093 | + | 0.263854i | ||||
\(617\) | −0.326644 | + | 0.200787i | −0.326644 | + | 0.200787i | −0.677282 | − | 0.735724i | \(-0.736842\pi\) |
0.350638 | + | 0.936511i | \(0.385965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.986361 | − | 0.164595i | \(-0.0526316\pi\) | ||||
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.926494 | + | 0.376309i | −0.926494 | + | 0.376309i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.0510579 | − | 1.85228i | −0.0510579 | − | 1.85228i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) |
0.350638 | − | 0.936511i | \(-0.385965\pi\) | |||||||
\(632\) | 4.93783 | − | 4.80359i | 4.93783 | − | 4.80359i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.79349 | + | 0.154121i | −2.79349 | + | 0.154121i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.550889 | + | 0.535913i | 0.550889 | + | 0.535913i | ||||
\(639\) | 0.0136387 | − | 0.164595i | 0.0136387 | − | 0.164595i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.582579 | + | 1.86261i | −0.582579 | + | 1.86261i | −0.0825793 | + | 0.996584i | \(0.526316\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.137354 | − | 0.990522i | \(-0.543860\pi\) | ||||
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(644\) | −2.38462 | + | 3.24439i | −2.38462 | + | 3.24439i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.754107 | − | 0.656752i | \(-0.228070\pi\) | ||||
−0.754107 | + | 0.656752i | \(0.771930\pi\) | |||||||
\(648\) | 1.59386 | − | 3.14954i | 1.59386 | − | 3.14954i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.162655 | − | 0.434432i | −0.162655 | − | 0.434432i | ||||
\(653\) | 0.315087 | − | 0.218477i | 0.315087 | − | 0.218477i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) |
0.716783 | + | 0.697297i | \(0.245614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.71678 | + | 0.697297i | 1.71678 | + | 0.697297i | 1.00000 | \(0\) | ||
0.716783 | + | 0.697297i | \(0.245614\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | −1.89485 | + | 1.84334i | −1.89485 | + | 1.84334i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.10572 | − | 3.22305i | −2.10572 | − | 3.22305i | ||||
\(667\) | 2.04264 | + | 0.226079i | 2.04264 | + | 0.226079i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.79774 | + | 0.198973i | 1.79774 | + | 0.198973i | 0.945817 | − | 0.324699i | \(-0.105263\pi\) |
0.851919 | + | 0.523673i | \(0.175439\pi\) | |||||||
\(674\) | 1.94863 | + | 3.37512i | 1.94863 | + | 3.37512i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.65653 | + | 0.911988i | 2.65653 | + | 0.911988i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.539928 | − | 0.254798i | −0.539928 | − | 0.254798i | 0.137354 | − | 0.990522i | \(-0.456140\pi\) |
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.268058 | + | 1.93310i | 0.268058 | + | 1.93310i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.90600 | + | 3.73734i | 6.90600 | + | 3.73734i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.245485 | − | 0.969400i | \(-0.421053\pi\) | ||||
−0.245485 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.241598 | + | 0.130746i | −0.241598 | + | 0.130746i | ||||
\(694\) | −1.44589 | − | 2.21310i | −1.44589 | − | 2.21310i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.838443 | − | 2.68065i | −0.838443 | − | 2.68065i | ||||
\(701\) | 0.289141 | − | 0.251813i | 0.289141 | − | 0.251813i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.440304 | + | 1.17600i | 0.440304 | + | 1.17600i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.370244 | − | 1.46206i | −0.370244 | − | 1.46206i | −0.821778 | − | 0.569808i | \(-0.807018\pi\) |
0.451533 | − | 0.892254i | \(-0.350877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.06742 | − | 1.63381i | 1.06742 | − | 1.63381i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.32179 | + | 0.183268i | 3.32179 | + | 0.183268i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.816288 | + | 0.501771i | 0.816288 | + | 0.501771i | ||||
\(719\) | 0 | 0 | −0.789141 | − | 0.614213i | \(-0.789474\pi\) | ||||
0.789141 | + | 0.614213i | \(0.210526\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.24067 | + | 1.50647i | 1.24067 | + | 1.50647i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.970927 | + | 1.05471i | −0.970927 | + | 1.05471i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.677282 | − | 0.735724i | \(-0.263158\pi\) | ||||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.245485 | − | 0.969400i | 0.245485 | − | 0.969400i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) | ||||
0.0825793 | + | 0.996584i | \(0.473684\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.41387 | + | 3.32789i | 5.41387 | + | 3.32789i | ||||
\(737\) | −0.500038 | − | 0.171663i | −0.500038 | − | 0.171663i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.534828 | + | 1.05685i | −0.534828 | + | 1.05685i | 0.451533 | + | 0.892254i | \(0.350877\pi\) |
−0.986361 | + | 0.164595i | \(0.947368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.78557 | − | 2.16809i | 2.78557 | − | 2.16809i | ||||
\(743\) | 1.75628 | − | 0.0968965i | 1.75628 | − | 0.0968965i | 0.851919 | − | 0.523673i | \(-0.175439\pi\) |
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.99352 | + | 1.73616i | 1.99352 | + | 1.73616i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.302573 | − | 1.54901i | −0.302573 | − | 1.54901i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.773077 | + | 0.218605i | 0.773077 | + | 0.218605i | 0.635724 | − | 0.771917i | \(-0.280702\pi\) |
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.322718 | + | 0.735724i | 0.322718 | + | 0.735724i | 1.00000 | \(0\) | ||
−0.677282 | + | 0.735724i | \(0.736842\pi\) | |||||||
\(758\) | 0.423071 | + | 0.329290i | 0.423071 | + | 0.329290i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.298515 | − | 0.954405i | \(-0.596491\pi\) | ||||
0.298515 | + | 0.954405i | \(0.403509\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.454882 | − | 0.184757i | −0.454882 | − | 0.184757i | ||||
\(764\) | 2.11807 | − | 3.66860i | 2.11807 | − | 3.66860i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.904357 | − | 0.426776i | \(-0.859649\pi\) | ||||
0.904357 | + | 0.426776i | \(0.140351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.23075 | + | 1.20722i | −2.23075 | + | 1.20722i | ||||
\(773\) | 0 | 0 | 0.962268 | − | 0.272103i | \(-0.0877193\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(774\) | 3.61419 | + | 1.02200i | 3.61419 | + | 1.02200i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.87218 | + | 0.643670i | −2.87218 | + | 0.643670i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0372843 | + | 0.0258523i | 0.0372843 | + | 0.0258523i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.98141 | − | 0.892254i | 3.98141 | − | 0.892254i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(788\) | −0.332504 | − | 4.01272i | −0.332504 | − | 4.01272i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.647302 | − | 0.629706i | 0.647302 | − | 0.629706i | ||||
\(792\) | 0.530365 | + | 0.811785i | 0.530365 | + | 0.811785i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.986361 | − | 0.164595i | \(-0.947368\pi\) | ||||
0.986361 | + | 0.164595i | \(0.0526316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.10709 | + | 1.66816i | −4.10709 | + | 1.66816i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.0770898 | + | 0.0749941i | 0.0770898 | + | 0.0749941i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.23942 | + | 1.07941i | 1.23942 | + | 1.07941i | 0.993931 | + | 0.110008i | \(0.0350877\pi\) |
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(812\) | −2.72706 | − | 2.96237i | −2.72706 | − | 2.96237i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.05600 | − | 0.0582613i | 1.05600 | − | 0.0582613i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.647302 | + | 0.629706i | 0.647302 | + | 0.629706i | 0.945817 | − | 0.324699i | \(-0.105263\pi\) |
−0.298515 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.525072 | + | 0.284155i | 0.525072 | + | 0.284155i | 0.716783 | − | 0.697297i | \(-0.245614\pi\) |
−0.191711 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.13978 | − | 1.55072i | 1.13978 | − | 1.55072i | 0.350638 | − | 0.936511i | \(-0.385965\pi\) |
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(828\) | 3.80831 | + | 1.30739i | 3.80831 | + | 1.30739i | ||||
\(829\) | 0 | 0 | −0.0275543 | − | 0.999620i | \(-0.508772\pi\) | ||||
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.245485 | − | 0.969400i | \(-0.578947\pi\) | ||||
0.245485 | + | 0.969400i | \(0.421053\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.314966 | + | 1.00700i | −0.314966 | + | 1.00700i | ||||
\(842\) | −1.82418 | − | 1.41982i | −1.82418 | − | 1.41982i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.0698904 | + | 0.138107i | 0.0698904 | + | 0.138107i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0254750 | + | 0.924185i | −0.0254750 | + | 0.924185i | ||||
\(848\) | −4.99823 | − | 5.42953i | −4.99823 | − | 5.42953i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.13263 | − | 1.85731i | 2.13263 | − | 1.85731i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.592235 | − | 0.805765i | \(-0.298246\pi\) | ||||
−0.592235 | + | 0.805765i | \(0.701754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.36092 | + | 1.51592i | −5.36092 | + | 1.51592i | ||||
\(857\) | 0 | 0 | 0.962268 | − | 0.272103i | \(-0.0877193\pi\) | ||||
−0.962268 | + | 0.272103i | \(0.912281\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.401695 | − | 0.915773i | \(-0.368421\pi\) | ||||
−0.401695 | + | 0.915773i | \(0.631579\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.878654 | − | 0.765220i | 0.878654 | − | 0.765220i | ||||
\(863\) | −0.0510579 | + | 0.0207379i | −0.0510579 | + | 0.0207379i | −0.401695 | − | 0.915773i | \(-0.631579\pi\) |
0.350638 | + | 0.936511i | \(0.385965\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.242074 | + | 0.478352i | 0.242074 | + | 0.478352i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.517346 | + | 1.65405i | −0.517346 | + | 1.65405i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.706561 | − | 1.61080i | 0.706561 | − | 1.61080i | −0.0825793 | − | 0.996584i | \(-0.526316\pi\) |
0.789141 | − | 0.614213i | \(-0.210526\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.0275543 | − | 0.999620i | \(-0.508772\pi\) | ||||
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(882\) | 1.76494 | − | 0.832894i | 1.76494 | − | 0.832894i | ||||
\(883\) | −0.851919 | + | 0.523673i | −0.851919 | + | 0.523673i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) |
0.0275543 | + | 0.999620i | \(0.491228\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.317507 | + | 0.431984i | −0.317507 | + | 0.431984i | ||||
\(887\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.564681 | + | 1.80539i | −0.564681 | + | 1.80539i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.196905 | + | 0.191552i | 0.196905 | + | 0.191552i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.33975 | − | 4.28342i | −1.33975 | − | 4.28342i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.71976 | − | 0.385408i | 1.71976 | − | 0.385408i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.30814 | + | 1.60043i | −2.30814 | + | 1.60043i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.40387 | − | 2.09354i | −2.40387 | − | 2.09354i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.861128 | + | 0.935434i | −0.861128 | + | 0.935434i | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) |
0.137354 | + | 0.990522i | \(0.456140\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.351919 | + | 0.342352i | 0.351919 | + | 0.342352i | 0.851919 | − | 0.523673i | \(-0.175439\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.54651 | + | 3.52568i | 1.54651 | + | 3.52568i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.783946 | − | 0.175686i | −0.783946 | − | 0.175686i | −0.191711 | − | 0.981451i | \(-0.561404\pi\) |
−0.592235 | + | 0.805765i | \(0.701754\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.162906 | + | 1.96598i | 0.162906 | + | 1.96598i | ||||
\(926\) | −1.34994 | − | 0.225265i | −1.34994 | − | 0.225265i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.30406 | + | 4.67546i | −4.30406 | + | 4.67546i | ||||
\(929\) | 0 | 0 | 0.975796 | − | 0.218681i | \(-0.0701754\pi\) | ||||
−0.975796 | + | 0.218681i | \(0.929825\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.36616 | − | 3.02742i | −4.36616 | − | 3.02742i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.191711 | − | 0.981451i | \(-0.561404\pi\) | ||||
0.191711 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(938\) | 3.47983 | + | 1.41338i | 3.47983 | + | 1.41338i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.879474 | − | 0.475947i | \(-0.157895\pi\) | ||||
−0.879474 | + | 0.475947i | \(0.842105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.739559 | + | 0.719454i | −0.739559 | + | 0.719454i | ||||
\(947\) | 0.445817 | + | 0.541326i | 0.445817 | + | 0.541326i | 0.945817 | − | 0.324699i | \(-0.105263\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.370244 | + | 1.46206i | −0.370244 | + | 1.46206i | 0.451533 | + | 0.892254i | \(0.350877\pi\) |
−0.821778 | + | 0.569808i | \(0.807018\pi\) | |||||||
\(954\) | −2.90077 | − | 2.01135i | −2.90077 | − | 2.01135i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.24280 | − | 5.11307i | −2.24280 | − | 5.11307i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.836686 | − | 1.65334i | −0.836686 | − | 1.65334i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.401695 | − | 0.915773i | −0.401695 | − | 0.915773i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.38806 | + | 0.751179i | −1.38806 | + | 0.751179i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.754107 | + | 0.656752i | 0.754107 | + | 0.656752i | 0.945817 | − | 0.324699i | \(-0.105263\pi\) |
−0.191711 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(968\) | 3.25854 | − | 0.179779i | 3.25854 | − | 0.179779i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.789141 | − | 0.614213i | \(-0.210526\pi\) | ||||
−0.789141 | + | 0.614213i | \(0.789474\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.19365 | + | 2.35872i | −1.19365 | + | 2.35872i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.418268 | + | 0.257108i | 0.418268 | + | 0.257108i | 0.716783 | − | 0.697297i | \(-0.245614\pi\) |
−0.298515 | + | 0.954405i | \(0.596491\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.0405441 | + | 0.489294i | −0.0405441 | + | 0.489294i | ||||
\(982\) | 3.38593 | + | 1.83237i | 3.38593 | + | 1.83237i | ||||
\(983\) | 0 | 0 | 0.0275543 | − | 0.999620i | \(-0.491228\pi\) | ||||
−0.0275543 | + | 0.999620i | \(0.508772\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.378951 | + | 2.73280i | −0.378951 | + | 2.73280i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.17799 | − | 1.43035i | −1.17799 | − | 1.43035i | −0.879474 | − | 0.475947i | \(-0.842105\pi\) |
−0.298515 | − | 0.954405i | \(-0.596491\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.254358 | − | 0.197975i | −0.254358 | − | 0.197975i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.998482 | − | 0.0550878i | \(-0.982456\pi\) | ||||
0.998482 | + | 0.0550878i | \(0.0175439\pi\) | |||||||
\(998\) | −0.496709 | + | 3.58200i | −0.496709 | + | 3.58200i | ||||
\(999\) | 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 | 3997.1.ce.a.1224.1 | ✓ | 36 | |
7.6 | odd | 2 | CM | 3997.1.ce.a.1224.1 | ✓ | 36 | |
571.383 | even | 57 | inner | 3997.1.ce.a.1525.1 | yes | 36 | |
3997.1525 | odd | 114 | inner | 3997.1.ce.a.1525.1 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3997.1.ce.a.1224.1 | ✓ | 36 | 1.1 | even | 1 | trivial | |
3997.1.ce.a.1224.1 | ✓ | 36 | 7.6 | odd | 2 | CM | |
3997.1.ce.a.1525.1 | yes | 36 | 571.383 | even | 57 | inner | |
3997.1.ce.a.1525.1 | yes | 36 | 3997.1525 | odd | 114 | inner |