Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1029,1,Mod(8,1029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1029, base_ring=CyclotomicField(98))
chi = DirichletCharacter(H, H._module([49, 96]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1029.8");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1029 = 3 \cdot 7^{3} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1029.t (of order \(98\), degree \(42\), 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: | \(0.513537897999\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Coefficient field: | \(\Q(\zeta_{98})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{42} - x^{35} + x^{28} - x^{21} + x^{14} - x^{7} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{49}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{49} + \cdots)\) |
Embedding invariants
Embedding label | 575.1 | ||
Root | \(-0.871319 - 0.490718i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1029.575 |
Dual form | 1029.1.t.a.995.1 |
$q$-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 \(\left(\mathbb{Z}/1029\mathbb{Z}\right)^\times\).
\(n\) | \(344\) | \(346\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{37}{49}\right)\) |
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 | 0 | −0.0320516 | − | 0.999486i | \(-0.510204\pi\) | ||||
0.0320516 | + | 0.999486i | \(0.489796\pi\) | |||||||
\(3\) | 0.718349 | − | 0.695683i | 0.718349 | − | 0.695683i | ||||
\(4\) | −0.997945 | + | 0.0640702i | −0.997945 | + | 0.0640702i | ||||
\(5\) | 0 | 0 | 0.949056 | − | 0.315108i | \(-0.102041\pi\) | ||||
−0.949056 | + | 0.315108i | \(0.897959\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.967295 | − | 0.253655i | 0.967295 | − | 0.253655i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0320516 | − | 0.999486i | 0.0320516 | − | 0.999486i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.981559 | − | 0.191159i | \(-0.938776\pi\) | ||||
0.981559 | + | 0.191159i | \(0.0612245\pi\) | |||||||
\(12\) | −0.672301 | + | 0.740278i | −0.672301 | + | 0.740278i | ||||
\(13\) | −1.52117 | − | 1.13528i | −1.52117 | − | 1.13528i | −0.949056 | − | 0.315108i | \(-0.897959\pi\) |
−0.572117 | − | 0.820172i | \(-0.693878\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.991790 | − | 0.127877i | 0.991790 | − | 0.127877i | ||||
\(17\) | 0 | 0 | 0.926917 | − | 0.375267i | \(-0.122449\pi\) | ||||
−0.926917 | + | 0.375267i | \(0.877551\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.809567 | 0.809567 | 0.404783 | − | 0.914413i | \(-0.367347\pi\) | ||||
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.518393 | − | 0.855143i | 0.518393 | − | 0.855143i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.871319 | − | 0.490718i | \(-0.163265\pi\) | ||||
−0.871319 | + | 0.490718i | \(0.836735\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.801414 | − | 0.598111i | 0.801414 | − | 0.598111i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.672301 | − | 0.740278i | −0.672301 | − | 0.740278i | ||||
\(28\) | −0.949056 | + | 0.315108i | −0.949056 | + | 0.315108i | ||||
\(29\) | 0 | 0 | −0.871319 | − | 0.490718i | \(-0.836735\pi\) | ||||
0.871319 | + | 0.490718i | \(0.163265\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.444127 | + | 1.94585i | 0.444127 | + | 1.94585i | 0.284528 | + | 0.958668i | \(0.408163\pi\) |
0.159600 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0320516 | + | 0.999486i | 0.0320516 | + | 0.999486i | ||||
\(37\) | −1.06061 | + | 0.429393i | −1.06061 | + | 0.429393i | −0.838088 | − | 0.545535i | \(-0.816327\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.88253 | + | 0.242725i | −1.88253 | + | 0.242725i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.838088 | − | 0.545535i | \(-0.816327\pi\) | ||||
0.838088 | + | 0.545535i | \(0.183673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.188505 | − | 1.95405i | 0.188505 | − | 1.95405i | −0.0960230 | − | 0.995379i | \(-0.530612\pi\) |
0.284528 | − | 0.958668i | \(-0.408163\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.462538 | − | 0.886599i | \(-0.653061\pi\) | ||||
0.462538 | + | 0.886599i | \(0.346939\pi\) | |||||||
\(48\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(49\) | 0.871319 | − | 0.490718i | 0.871319 | − | 0.490718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.59078 | + | 1.03549i | 1.59078 | + | 1.03549i | ||||
\(53\) | 0 | 0 | 0.159600 | − | 0.987182i | \(-0.448980\pi\) | ||||
−0.159600 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.581552 | − | 0.563201i | 0.581552 | − | 0.563201i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.838088 | − | 0.545535i | \(-0.183673\pi\) | ||||
−0.838088 | + | 0.545535i | \(0.816327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0908211 | − | 0.306007i | 0.0908211 | − | 0.306007i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.991790 | + | 0.127877i | \(0.0408163\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(64\) | −0.981559 | + | 0.191159i | −0.981559 | + | 0.191159i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.319696 | + | 1.40068i | −0.319696 | + | 1.40068i | 0.518393 | + | 0.855143i | \(0.326531\pi\) |
−0.838088 | + | 0.545535i | \(0.816327\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.871319 | − | 0.490718i | \(-0.163265\pi\) | ||||
−0.871319 | + | 0.490718i | \(0.836735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.857469 | + | 1.64361i | −0.857469 | + | 1.64361i | −0.0960230 | + | 0.995379i | \(0.530612\pi\) |
−0.761446 | + | 0.648228i | \(0.775510\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.159600 | − | 0.987182i | 0.159600 | − | 0.987182i | ||||
\(76\) | −0.807903 | + | 0.0518691i | −0.807903 | + | 0.0518691i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.354800 | + | 0.444905i | 0.354800 | + | 0.444905i | 0.926917 | − | 0.375267i | \(-0.122449\pi\) |
−0.572117 | + | 0.820172i | \(0.693878\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.997945 | − | 0.0640702i | −0.997945 | − | 0.0640702i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.967295 | − | 0.253655i | \(-0.918367\pi\) | ||||
0.967295 | + | 0.253655i | \(0.0816327\pi\) | |||||||
\(84\) | −0.462538 | + | 0.886599i | −0.462538 | + | 0.886599i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.761446 | − | 0.648228i | \(-0.775510\pi\) | ||||
0.761446 | + | 0.648228i | \(0.224490\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.75939 | − | 0.712299i | −1.75939 | − | 0.712299i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.67273 | + | 1.08883i | 1.67273 | + | 1.08883i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.338875 | + | 1.48471i | 0.338875 | + | 1.48471i | 0.801414 | + | 0.598111i | \(0.204082\pi\) |
−0.462538 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.761446 | + | 0.648228i | −0.761446 | + | 0.648228i | ||||
\(101\) | 0 | 0 | 0.345365 | − | 0.938468i | \(-0.387755\pi\) | ||||
−0.345365 | + | 0.938468i | \(0.612245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.668140 | + | 1.81555i | −0.668140 | + | 1.81555i | −0.0960230 | + | 0.995379i | \(0.530612\pi\) |
−0.572117 | + | 0.820172i | \(0.693878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.801414 | − | 0.598111i | \(-0.204082\pi\) | ||||
−0.801414 | + | 0.598111i | \(0.795918\pi\) | |||||||
\(108\) | 0.718349 | + | 0.695683i | 0.718349 | + | 0.695683i | ||||
\(109\) | 1.58967 | + | 1.18640i | 1.58967 | + | 1.18640i | 0.871319 | + | 0.490718i | \(0.163265\pi\) |
0.718349 | + | 0.695683i | \(0.244898\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.463167 | + | 1.04630i | −0.463167 | + | 1.04630i | ||||
\(112\) | 0.926917 | − | 0.375267i | 0.926917 | − | 0.375267i | ||||
\(113\) | 0 | 0 | −0.761446 | − | 0.648228i | \(-0.775510\pi\) | ||||
0.761446 | + | 0.648228i | \(0.224490\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.18345 | + | 1.48400i | −1.18345 | + | 1.48400i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.926917 | + | 0.375267i | 0.926917 | + | 0.375267i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.567886 | − | 1.91340i | −0.567886 | − | 1.91340i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0430966 | + | 0.0474542i | −0.0430966 | + | 0.0474542i | −0.761446 | − | 0.648228i | \(-0.775510\pi\) |
0.718349 | + | 0.695683i | \(0.244898\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.22398 | − | 1.53483i | −1.22398 | − | 1.53483i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.0960230 | − | 0.995379i | \(-0.469388\pi\) | ||||
−0.0960230 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.783090 | − | 0.205350i | 0.783090 | − | 0.205350i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.949056 | − | 0.315108i | \(-0.897959\pi\) | ||||
0.949056 | + | 0.315108i | \(0.102041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0663260 | − | 0.180229i | 0.0663260 | − | 0.180229i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.967295 | + | 0.253655i | \(0.0816327\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.0960230 | − | 0.995379i | −0.0960230 | − | 0.995379i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.284528 | − | 0.958668i | 0.284528 | − | 0.958668i | ||||
\(148\) | 1.03092 | − | 0.496464i | 1.03092 | − | 0.496464i | ||||
\(149\) | 0 | 0 | 0.967295 | − | 0.253655i | \(-0.0816327\pi\) | ||||
−0.967295 | + | 0.253655i | \(0.918367\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.529252 | − | 0.758722i | 0.529252 | − | 0.758722i | −0.462538 | − | 0.886599i | \(-0.653061\pi\) |
0.991790 | + | 0.127877i | \(0.0408163\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.86311 | − | 0.362840i | 1.86311 | − | 0.362840i | ||||
\(157\) | −0.868917 | + | 1.43337i | −0.868917 | + | 1.43337i | 0.0320516 | + | 0.999486i | \(0.489796\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.358069 | − | 0.972990i | −0.358069 | − | 0.972990i | −0.981559 | − | 0.191159i | \(-0.938776\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.997945 | − | 0.0640702i | \(-0.979592\pi\) | ||||
0.997945 | + | 0.0640702i | \(0.0204082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.740576 | + | 2.49525i | 0.740576 | + | 2.49525i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0259479 | − | 0.809151i | 0.0259479 | − | 0.809151i | ||||
\(172\) | −0.0629210 | + | 1.96211i | −0.0629210 | + | 1.96211i | ||||
\(173\) | 0 | 0 | −0.672301 | − | 0.740278i | \(-0.734694\pi\) | ||||
0.672301 | + | 0.740278i | \(0.265306\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.871319 | − | 0.490718i | \(-0.836735\pi\) | ||||
0.871319 | + | 0.490718i | \(0.163265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.0332306 | − | 1.03625i | 0.0332306 | − | 1.03625i | −0.838088 | − | 0.545535i | \(-0.816327\pi\) |
0.871319 | − | 0.490718i | \(-0.163265\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.147642 | − | 0.283002i | −0.147642 | − | 0.283002i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.838088 | − | 0.545535i | −0.838088 | − | 0.545535i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.0960230 | − | 0.995379i | \(-0.530612\pi\) | ||||
0.0960230 | + | 0.995379i | \(0.469388\pi\) | |||||||
\(192\) | −0.572117 | + | 0.820172i | −0.572117 | + | 0.820172i | ||||
\(193\) | −0.685059 | − | 0.0883286i | −0.685059 | − | 0.0883286i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.462538 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.838088 | + | 0.545535i | −0.838088 | + | 0.545535i | ||||
\(197\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.153908 | − | 1.59542i | −0.153908 | − | 1.59542i | −0.672301 | − | 0.740278i | \(-0.734694\pi\) |
0.518393 | − | 0.855143i | \(-0.326531\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.744774 | + | 1.22858i | 0.744774 | + | 1.22858i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.65386 | − | 0.931437i | −1.65386 | − | 0.931437i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.39657 | − | 1.04229i | 1.39657 | − | 1.04229i | 0.404783 | − | 0.914413i | \(-0.367347\pi\) |
0.991790 | − | 0.127877i | \(-0.0408163\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.923176 | + | 1.76956i | 0.923176 | + | 1.76956i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.527467 | + | 1.77721i | 0.527467 | + | 1.77721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.24633 | − | 0.504585i | −1.24633 | − | 0.504585i | −0.345365 | − | 0.938468i | \(-0.612245\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.572117 | − | 0.820172i | −0.572117 | − | 0.820172i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(228\) | −0.544272 | + | 0.599304i | −0.544272 | + | 0.599304i | ||||
\(229\) | −0.664528 | − | 0.643560i | −0.664528 | − | 0.643560i | 0.284528 | − | 0.958668i | \(-0.408163\pi\) |
−0.949056 | + | 0.315108i | \(0.897959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.159600 | − | 0.987182i | \(-0.551020\pi\) | ||||
0.159600 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.564383 | + | 0.0727692i | 0.564383 | + | 0.0727692i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.518393 | − | 0.855143i | \(-0.326531\pi\) | ||||
−0.518393 | + | 0.855143i | \(0.673469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.640249 | − | 0.259208i | −0.640249 | − | 0.259208i | 0.0320516 | − | 0.999486i | \(-0.489796\pi\) |
−0.672301 | + | 0.740278i | \(0.734694\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.761446 | + | 0.648228i | −0.761446 | + | 0.648228i | ||||
\(244\) | −0.0710286 | + | 0.311197i | −0.0710286 | + | 0.311197i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.23149 | − | 0.919085i | −1.23149 | − | 0.919085i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.838088 | − | 0.545535i | \(-0.183673\pi\) | ||||
−0.838088 | + | 0.545535i | \(0.816327\pi\) | |||||||
\(252\) | 0.284528 | + | 0.958668i | 0.284528 | + | 0.958668i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.967295 | − | 0.253655i | 0.967295 | − | 0.253655i | ||||
\(257\) | 0 | 0 | −0.997945 | − | 0.0640702i | \(-0.979592\pi\) | ||||
0.997945 | + | 0.0640702i | \(0.0204082\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.917004 | + | 0.684378i | −0.917004 | + | 0.684378i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.229297 | − | 1.41828i | 0.229297 | − | 1.41828i | ||||
\(269\) | 0 | 0 | −0.404783 | − | 0.914413i | \(-0.632653\pi\) | ||||
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.97950 | + | 0.127088i | −1.97950 | + | 0.127088i | −0.997945 | − | 0.0640702i | \(-0.979592\pi\) |
−0.981559 | + | 0.191159i | \(0.938776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.75939 | + | 0.712299i | −1.75939 | + | 0.712299i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.958968 | + | 1.37475i | 0.958968 | + | 1.37475i | 0.926917 | + | 0.375267i | \(0.122449\pi\) |
0.0320516 | + | 0.999486i | \(0.489796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.95908 | − | 0.381532i | 1.95908 | − | 0.381532i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.967295 | − | 0.253655i | \(-0.0816327\pi\) | ||||
−0.967295 | + | 0.253655i | \(0.918367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.705391 | − | 1.59349i | 0.705391 | − | 1.59349i | −0.0960230 | − | 0.995379i | \(-0.530612\pi\) |
0.801414 | − | 0.598111i | \(-0.204082\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.718349 | − | 0.695683i | 0.718349 | − | 0.695683i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.27632 | + | 0.830791i | 1.27632 | + | 0.830791i | ||||
\(292\) | 0.750401 | − | 1.69517i | 0.750401 | − | 1.69517i | ||||
\(293\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.0960230 | + | 0.995379i | −0.0960230 | + | 0.995379i | ||||
\(301\) | −0.313313 | − | 1.93795i | −0.313313 | − | 1.93795i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.802920 | − | 0.103525i | 0.802920 | − | 0.103525i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.00205461 | + | 0.0640702i | 0.00205461 | + | 0.0640702i | 1.00000 | \(0\) | ||
−0.997945 | + | 0.0640702i | \(0.979592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.783090 | + | 1.76901i | 0.783090 | + | 1.76901i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.159600 | − | 0.987182i | \(-0.551020\pi\) | ||||
0.159600 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.57006 | − | 0.756102i | −1.57006 | − | 0.756102i | −0.572117 | − | 0.820172i | \(-0.693878\pi\) |
−0.997945 | + | 0.0640702i | \(0.979592\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.382576 | − | 0.421259i | −0.382576 | − | 0.421259i | ||||
\(317\) | 0 | 0 | 0.572117 | − | 0.820172i | \(-0.306122\pi\) | ||||
−0.572117 | + | 0.820172i | \(0.693878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 1.00000 | ||||||||
\(325\) | −1.89811 | −1.89811 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.96729 | − | 0.253655i | 1.96729 | − | 0.253655i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.30063 | + | 1.43213i | −1.30063 | + | 1.43213i | −0.462538 | + | 0.886599i | \(0.653061\pi\) |
−0.838088 | + | 0.545535i | \(0.816327\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.395178 | + | 1.07383i | 0.395178 | + | 1.07383i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.404783 | − | 0.914413i | 0.404783 | − | 0.914413i | ||||
\(337\) | −1.20408 | − | 1.16609i | −1.20408 | − | 1.16609i | −0.981559 | − | 0.191159i | \(-0.938776\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.718349 | − | 0.695683i | 0.718349 | − | 0.695683i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.997945 | − | 0.0640702i | \(-0.0204082\pi\) | ||||
−0.997945 | + | 0.0640702i | \(0.979592\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0460485 | + | 0.0445954i | 0.0460485 | + | 0.0445954i | 0.718349 | − | 0.695683i | \(-0.244898\pi\) |
−0.672301 | + | 0.740278i | \(0.734694\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.182262 | + | 1.88934i | 0.182262 | + | 1.88934i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.345365 | − | 0.938468i | \(-0.612245\pi\) | ||||
0.345365 | + | 0.938468i | \(0.387755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.991790 | − | 0.127877i | \(-0.0408163\pi\) | ||||
−0.991790 | + | 0.127877i | \(0.959184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.344602 | −0.344602 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.926917 | − | 0.375267i | 0.926917 | − | 0.375267i | ||||
\(364\) | 1.80141 | + | 0.598111i | 1.80141 | + | 0.598111i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.525954 | + | 0.447751i | 0.525954 | + | 0.447751i | 0.871319 | − | 0.490718i | \(-0.163265\pi\) |
−0.345365 | + | 0.938468i | \(0.612245\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.73906 | − | 0.979419i | −1.73906 | − | 0.979419i | ||||
\(373\) | 1.37208 | + | 0.660758i | 1.37208 | + | 0.660758i | 0.967295 | − | 0.253655i | \(-0.0816327\pi\) |
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0488111 | − | 1.52211i | −0.0488111 | − | 1.52211i | −0.672301 | − | 0.740278i | \(-0.734694\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.00205461 | + | 0.0640702i | 0.00205461 | + | 0.0640702i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.404783 | − | 0.914413i | \(-0.632653\pi\) | ||||
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.94700 | − | 0.251038i | −1.94700 | − | 0.251038i | ||||
\(388\) | −0.433305 | − | 1.45995i | −0.433305 | − | 1.45995i | ||||
\(389\) | 0 | 0 | −0.518393 | − | 0.855143i | \(-0.673469\pi\) | ||||
0.518393 | + | 0.855143i | \(0.326531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.408780 | − | 0.395882i | 0.408780 | − | 0.395882i | −0.462538 | − | 0.886599i | \(-0.653061\pi\) |
0.871319 | + | 0.490718i | \(0.163265\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.419673 | − | 0.692295i | 0.419673 | − | 0.692295i | ||||
\(400\) | 0.718349 | − | 0.695683i | 0.718349 | − | 0.695683i | ||||
\(401\) | 0 | 0 | 0.462538 | − | 0.886599i | \(-0.346939\pi\) | ||||
−0.462538 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.53349 | − | 3.46418i | 1.53349 | − | 3.46418i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.769269 | + | 1.10281i | 0.769269 | + | 1.10281i | 0.991790 | + | 0.127877i | \(0.0408163\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.550444 | − | 1.85463i | 0.550444 | − | 1.85463i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0777370 | − | 0.175609i | −0.0777370 | − | 0.175609i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.997945 | − | 0.0640702i | \(-0.0204082\pi\) | ||||
−0.997945 | + | 0.0640702i | \(0.979592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0306505 | − | 0.189584i | −0.0306505 | − | 0.189584i | 0.967295 | − | 0.253655i | \(-0.0816327\pi\) |
−0.997945 | + | 0.0640702i | \(0.979592\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0102309 | − | 0.319036i | 0.0102309 | − | 0.319036i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.0960230 | − | 0.995379i | \(-0.469388\pi\) | ||||
−0.0960230 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(432\) | −0.761446 | − | 0.648228i | −0.761446 | − | 0.648228i | ||||
\(433\) | 0.877949 | − | 0.291499i | 0.877949 | − | 0.291499i | 0.159600 | − | 0.987182i | \(-0.448980\pi\) |
0.718349 | + | 0.695683i | \(0.244898\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.66241 | − | 1.08211i | −1.66241 | − | 1.08211i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.15139 | + | 0.859305i | 1.15139 | + | 0.859305i | 0.991790 | − | 0.127877i | \(-0.0408163\pi\) |
0.159600 | + | 0.987182i | \(0.448980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.462538 | − | 0.886599i | −0.462538 | − | 0.886599i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.761446 | − | 0.648228i | \(-0.224490\pi\) | ||||
−0.761446 | + | 0.648228i | \(0.775510\pi\) | |||||||
\(444\) | 0.395178 | − | 1.07383i | 0.395178 | − | 1.07383i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(449\) | 0 | 0 | −0.991790 | − | 0.127877i | \(-0.959184\pi\) | ||||
0.991790 | + | 0.127877i | \(0.0408163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.147642 | − | 0.913219i | −0.147642 | − | 0.913219i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.25182 | + | 1.21232i | 1.25182 | + | 1.21232i | 0.967295 | + | 0.253655i | \(0.0816327\pi\) |
0.284528 | + | 0.958668i | \(0.408163\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.572117 | − | 0.820172i | \(-0.693878\pi\) | ||||
0.572117 | + | 0.820172i | \(0.306122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.640249 | − | 0.259208i | −0.640249 | − | 0.259208i | 0.0320516 | − | 0.999486i | \(-0.489796\pi\) |
−0.672301 | + | 0.740278i | \(0.734694\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.284528 | − | 0.958668i | \(-0.591837\pi\) | ||||
0.284528 | + | 0.958668i | \(0.408163\pi\) | |||||||
\(468\) | 1.08594 | − | 1.55678i | 1.08594 | − | 1.55678i | ||||
\(469\) | 0.0460485 | + | 1.43596i | 0.0460485 | + | 1.43596i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.372984 | + | 1.63415i | 0.372984 | + | 1.63415i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.648798 | − | 0.484210i | 0.648798 | − | 0.484210i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.462538 | − | 0.886599i | \(-0.653061\pi\) | ||||
0.462538 | + | 0.886599i | \(0.346939\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.10085 | + | 0.550908i | 2.10085 | + | 0.550908i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.949056 | − | 0.315108i | −0.949056 | − | 0.315108i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.167333 | − | 1.73458i | −0.167333 | − | 1.73458i | −0.572117 | − | 0.820172i | \(-0.693878\pi\) |
0.404783 | − | 0.914413i | \(-0.367347\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.934111 | − | 0.449844i | −0.934111 | − | 0.449844i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.689311 | + | 1.87308i | 0.689311 | + | 1.87308i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.313313 | + | 0.0610178i | −0.313313 | + | 0.0610178i | −0.345365 | − | 0.938468i | \(-0.612245\pi\) |
0.0320516 | + | 0.999486i | \(0.489796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.462538 | − | 0.886599i | \(-0.653061\pi\) | ||||
0.462538 | + | 0.886599i | \(0.346939\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.26789 | + | 1.27725i | 2.26789 | + | 1.27725i | ||||
\(508\) | 0.0399677 | − | 0.0501179i | 0.0399677 | − | 0.0501179i | ||||
\(509\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.412517 | + | 1.80735i | −0.412517 | + | 1.80735i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.544272 | − | 0.599304i | −0.544272 | − | 0.599304i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.31981 | + | 1.45325i | 1.31981 | + | 1.45325i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.464378 | + | 1.26187i | 0.464378 | + | 1.26187i | 0.926917 | + | 0.375267i | \(0.122449\pi\) |
−0.462538 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0960230 | − | 0.995379i | −0.0960230 | − | 0.995379i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.518393 | − | 0.855143i | 0.518393 | − | 0.855143i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.768324 | + | 0.255101i | −0.768324 | + | 0.255101i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.57327 | − | 0.306394i | −1.57327 | − | 0.306394i | −0.672301 | − | 0.740278i | \(-0.734694\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.697032 | − | 0.767509i | −0.697032 | − | 0.767509i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.464378 | − | 1.26187i | 0.464378 | − | 1.26187i | −0.462538 | − | 0.886599i | \(-0.653061\pi\) |
0.926917 | − | 0.375267i | \(-0.122449\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.302938 | − | 0.100582i | −0.302938 | − | 0.100582i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.456049 | + | 0.340358i | 0.456049 | + | 0.340358i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0546424 | + | 0.184108i | −0.0546424 | + | 0.184108i | ||||
\(557\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.50514 | + | 2.75844i | −2.50514 | + | 2.75844i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.981559 | − | 0.191159i | \(-0.0612245\pi\) | ||||
−0.981559 | + | 0.191159i | \(0.938776\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.981559 | + | 0.191159i | −0.981559 | + | 0.191159i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.214598 | + | 0.236297i | −0.214598 | + | 0.236297i | −0.838088 | − | 0.545535i | \(-0.816327\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.159600 | + | 0.987182i | 0.159600 | + | 0.987182i | ||||
\(577\) | −1.34331 | − | 1.00254i | −1.34331 | − | 1.00254i | −0.997945 | − | 0.0640702i | \(-0.979592\pi\) |
−0.345365 | − | 0.938468i | \(-0.612245\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.553561 | + | 0.413133i | −0.553561 | + | 0.413133i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(588\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(589\) | 0.359551 | + | 1.57530i | 0.359551 | + | 1.57530i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.996992 | + | 0.561495i | −0.996992 | + | 0.561495i | ||||
\(593\) | 0 | 0 | −0.838088 | − | 0.545535i | \(-0.816327\pi\) | ||||
0.838088 | + | 0.545535i | \(0.183673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.22047 | − | 1.03900i | −1.22047 | − | 1.03900i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.967295 | − | 0.253655i | \(-0.0816327\pi\) | ||||
−0.967295 | + | 0.253655i | \(0.918367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.949508 | + | 0.808328i | −0.949508 | + | 0.808328i | −0.981559 | − | 0.191159i | \(-0.938776\pi\) |
0.0320516 | + | 0.999486i | \(0.489796\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.38971 | + | 0.364425i | 1.38971 | + | 0.364425i | ||||
\(604\) | −0.479553 | + | 0.791073i | −0.479553 | + | 0.791073i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.277479 | − | 0.347948i | −0.277479 | − | 0.347948i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.857469 | + | 1.64361i | −0.857469 | + | 1.64361i | −0.0960230 | + | 0.995379i | \(0.530612\pi\) |
−0.761446 | + | 0.648228i | \(0.775510\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.284528 | − | 0.958668i | \(-0.408163\pi\) | ||||
−0.284528 | + | 0.958668i | \(0.591837\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.400969 | − | 1.75676i | 0.400969 | − | 1.75676i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.83603 | + | 0.481465i | −1.83603 | + | 0.481465i | ||||
\(625\) | 0.284528 | − | 0.958668i | 0.284528 | − | 0.958668i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.775296 | − | 1.48610i | 0.775296 | − | 1.48610i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.83861 | − | 0.237063i | 1.83861 | − | 0.237063i | 0.871319 | − | 0.490718i | \(-0.163265\pi\) |
0.967295 | + | 0.253655i | \(0.0816327\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.278125 | − | 1.72030i | 0.278125 | − | 1.72030i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.88253 | − | 0.242725i | −1.88253 | − | 0.242725i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.284528 | − | 0.958668i | \(-0.591837\pi\) | ||||
0.284528 | + | 0.958668i | \(0.408163\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.137956 | + | 1.43006i | −0.137956 | + | 1.43006i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.761446 | + | 0.648228i | \(0.775510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.991790 | − | 0.127877i | \(-0.0408163\pi\) | ||||
−0.991790 | + | 0.127877i | \(0.959184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.89421 | + | 0.628922i | 1.89421 | + | 0.628922i | ||||
\(652\) | 0.419673 | + | 0.948049i | 0.419673 | + | 0.948049i | ||||
\(653\) | 0 | 0 | 0.838088 | − | 0.545535i | \(-0.183673\pi\) | ||||
−0.838088 | + | 0.545535i | \(0.816327\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.61528 | + | 0.909709i | 1.61528 | + | 0.909709i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.672301 | − | 0.740278i | \(-0.734694\pi\) | ||||
0.672301 | + | 0.740278i | \(0.265306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.44410 | + | 1.07776i | −1.44410 | + | 1.07776i | −0.462538 | + | 0.886599i | \(0.653061\pi\) |
−0.981559 | + | 0.191159i | \(0.938776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.24633 | + | 0.504585i | −1.24633 | + | 0.504585i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.830894 | + | 0.620112i | 0.830894 | + | 0.620112i | 0.926917 | − | 0.375267i | \(-0.122449\pi\) |
−0.0960230 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.981559 | − | 0.191159i | −0.981559 | − | 0.191159i | ||||
\(676\) | −0.898926 | − | 2.44267i | −0.898926 | − | 2.44267i | ||||
\(677\) | 0 | 0 | 0.0320516 | − | 0.999486i | \(-0.489796\pi\) | ||||
−0.0320516 | + | 0.999486i | \(0.510204\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.704396 | + | 1.35019i | 0.704396 | + | 1.35019i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.718349 | − | 0.695683i | \(-0.244898\pi\) | ||||
−0.718349 | + | 0.695683i | \(0.755102\pi\) | |||||||
\(684\) | 0.0259479 | + | 0.809151i | 0.0259479 | + | 0.809151i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.925077 | −0.925077 | ||||||||
\(688\) | −0.0629210 | − | 1.96211i | −0.0629210 | − | 1.96211i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.422370 | − | 0.140236i | 0.422370 | − | 0.140236i | −0.0960230 | − | 0.995379i | \(-0.530612\pi\) |
0.518393 | + | 0.855143i | \(0.326531\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.572117 | + | 0.820172i | −0.572117 | + | 0.820172i | ||||
\(701\) | 0 | 0 | 0.462538 | − | 0.886599i | \(-0.346939\pi\) | ||||
−0.462538 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.858634 | + | 0.347622i | −0.858634 | + | 0.347622i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0558543 | − | 0.0314565i | 0.0558543 | − | 0.0314565i | −0.462538 | − | 0.886599i | \(-0.653061\pi\) |
0.518393 | + | 0.855143i | \(0.326531\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.456049 | − | 0.340358i | 0.456049 | − | 0.340358i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.838088 | − | 0.545535i | \(-0.183673\pi\) | ||||
−0.838088 | + | 0.545535i | \(0.816327\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.185765 | + | 1.92565i | −0.185765 | + | 1.92565i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.640249 | + | 0.259208i | −0.640249 | + | 0.259208i | ||||
\(724\) | 0.0332306 | + | 1.03625i | 0.0332306 | + | 1.03625i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.04508 | − | 0.680271i | −1.04508 | − | 0.680271i | −0.0960230 | − | 0.995379i | \(-0.530612\pi\) |
−0.949056 | + | 0.315108i | \(0.897959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.0960230 | + | 0.995379i | −0.0960230 | + | 0.995379i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.165471 | + | 0.272961i | 0.165471 | + | 0.272961i | ||||
\(733\) | 0.908017 | + | 1.74050i | 0.908017 | + | 1.74050i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
0.284528 | + | 0.958668i | \(0.408163\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.165471 | − | 1.02350i | 0.165471 | − | 1.02350i | −0.761446 | − | 0.648228i | \(-0.775510\pi\) |
0.926917 | − | 0.375267i | \(-0.122449\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.52403 | + | 0.196502i | −1.52403 | + | 0.196502i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.718349 | − | 0.695683i | \(-0.244898\pi\) | ||||
−0.718349 | + | 0.695683i | \(0.755102\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0608375 | − | 0.0201994i | −0.0608375 | − | 0.0201994i | 0.284528 | − | 0.958668i | \(-0.408163\pi\) |
−0.345365 | + | 0.938468i | \(0.612245\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.871319 | + | 0.490718i | 0.871319 | + | 0.490718i | ||||
\(757\) | −1.46048 | + | 0.822529i | −1.46048 | + | 0.822529i | −0.997945 | − | 0.0640702i | \(-0.979592\pi\) |
−0.462538 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.159600 | − | 0.987182i | \(-0.448980\pi\) | ||||
−0.159600 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.83861 | + | 0.744372i | 1.83861 | + | 0.744372i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.518393 | − | 0.855143i | 0.518393 | − | 0.855143i | ||||
\(769\) | 1.20620 | + | 0.316302i | 1.20620 | + | 0.316302i | 0.801414 | − | 0.598111i | \(-0.204082\pi\) |
0.404783 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.689311 | + | 0.0442552i | 0.689311 | + | 0.0442552i | ||||
\(773\) | 0 | 0 | 0.967295 | − | 0.253655i | \(-0.0816327\pi\) | ||||
−0.967295 | + | 0.253655i | \(0.918367\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.51976 | + | 1.29379i | 1.51976 | + | 1.29379i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.182620 | + | 1.12957i | −0.182620 | + | 1.12957i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.801414 | − | 0.598111i | 0.801414 | − | 0.598111i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.196532 | + | 0.534040i | −0.196532 | + | 0.534040i | −0.997945 | − | 0.0640702i | \(-0.979592\pi\) |
0.801414 | + | 0.598111i | \(0.204082\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.485558 | + | 0.362381i | −0.485558 | + | 0.362381i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.255811 | + | 1.58228i | 0.255811 | + | 1.58228i | ||||
\(797\) | 0 | 0 | 0.404783 | − | 0.914413i | \(-0.367347\pi\) | ||||
−0.404783 | + | 0.914413i | \(0.632653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.821959 | − | 1.17834i | −0.821959 | − | 1.17834i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.981559 | − | 0.191159i | \(-0.0612245\pi\) | ||||
−0.981559 | + | 0.191159i | \(0.938776\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.109873 | − | 0.157511i | 0.109873 | − | 0.157511i | −0.761446 | − | 0.648228i | \(-0.775510\pi\) |
0.871319 | + | 0.490718i | \(0.163265\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.33356 | + | 1.46840i | −1.33356 | + | 1.46840i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.152607 | − | 1.58193i | 0.152607 | − | 1.58193i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.768324 | + | 1.73566i | −0.768324 | + | 1.73566i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.871319 | − | 0.490718i | \(-0.836735\pi\) | ||||
0.871319 | + | 0.490718i | \(0.163265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.52117 | − | 0.505064i | −1.52117 | − | 0.505064i | −0.572117 | − | 0.820172i | \(-0.693878\pi\) |
−0.949056 | + | 0.315108i | \(0.897959\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.949056 | − | 0.315108i | \(-0.897959\pi\) | ||||
0.949056 | + | 0.315108i | \(0.102041\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.769269 | + | 0.847051i | 0.769269 | + | 0.847051i | 0.991790 | − | 0.127877i | \(-0.0408163\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.64527 | + | 0.320416i | 1.64527 | + | 0.320416i | ||||
\(832\) | 1.71014 | + | 0.823560i | 1.71014 | + | 0.823560i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.14188 | − | 1.63697i | 1.14188 | − | 1.63697i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.345365 | − | 0.938468i | \(-0.612245\pi\) | ||||
0.345365 | + | 0.938468i | \(0.387755\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.518393 | + | 0.855143i | 0.518393 | + | 0.855143i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.32692 | + | 1.12963i | −1.32692 | + | 1.12963i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.991790 | + | 0.127877i | 0.991790 | + | 0.127877i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.601846 | − | 1.63541i | −0.601846 | − | 1.63541i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.59953 | − | 0.102693i | −1.59953 | − | 0.102693i | −0.761446 | − | 0.648228i | \(-0.775510\pi\) |
−0.838088 | + | 0.545535i | \(0.816327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.0320516 | − | 0.999486i | \(-0.489796\pi\) | ||||
−0.0320516 | + | 0.999486i | \(0.510204\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.30063 | − | 1.43213i | −1.30063 | − | 1.43213i | −0.838088 | − | 0.545535i | \(-0.816327\pi\) |
−0.462538 | − | 0.886599i | \(-0.653061\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.0320516 | − | 0.999486i | 0.0320516 | − | 0.999486i | ||||
\(868\) | −1.03465 | − | 1.70677i | −1.03465 | − | 1.70677i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.07647 | − | 1.76773i | 2.07647 | − | 1.76773i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.49481 | − | 0.291114i | 1.49481 | − | 0.291114i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.640249 | − | 1.73976i | −0.640249 | − | 1.73976i | ||||
\(877\) | −0.185765 | − | 1.92565i | −0.185765 | − | 1.92565i | −0.345365 | − | 0.938468i | \(-0.612245\pi\) |
0.159600 | − | 0.987182i | \(-0.448980\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.78714 | − | 0.860643i | −1.78714 | − | 0.860643i | −0.949056 | − | 0.315108i | \(-0.897959\pi\) |
−0.838088 | − | 0.545535i | \(-0.816327\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.518393 | − | 0.855143i | \(-0.673469\pi\) | ||||
0.518393 | + | 0.855143i | \(0.326531\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0296502 | + | 0.0568338i | −0.0296502 | + | 0.0568338i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.27610 | + | 0.423695i | 1.27610 | + | 0.423695i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.57327 | − | 1.17416i | −1.57327 | − | 1.17416i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.185765 | − | 0.0487134i | −0.185765 | − | 0.0487134i | 0.159600 | − | 0.987182i | \(-0.448980\pi\) |
−0.345365 | + | 0.938468i | \(0.612245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.572117 | − | 0.820172i | \(-0.693878\pi\) | ||||
0.572117 | + | 0.820172i | \(0.306122\pi\) | |||||||
\(912\) | 0.504757 | − | 0.632945i | 0.504757 | − | 0.632945i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.704396 | + | 0.599661i | 0.704396 | + | 0.599661i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.0306505 | − | 0.189584i | −0.0306505 | − | 0.189584i | 0.967295 | − | 0.253655i | \(-0.0816327\pi\) |
−0.997945 | + | 0.0640702i | \(0.979592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.0460485 | + | 0.0445954i | 0.0460485 | + | 0.0445954i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.593162 | + | 0.978483i | −0.593162 | + | 0.978483i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.79320 | + | 0.725988i | 1.79320 | + | 0.725988i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.761446 | − | 0.648228i | \(-0.224490\pi\) | ||||
−0.761446 | + | 0.648228i | \(0.775510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.705391 | − | 0.397269i | 0.705391 | − | 0.397269i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.27632 | − | 0.830791i | 1.27632 | − | 0.830791i | 0.284528 | − | 0.958668i | \(-0.408163\pi\) |
0.991790 | + | 0.127877i | \(0.0408163\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.65386 | + | 0.549119i | −1.65386 | + | 0.549119i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.0960230 | − | 0.995379i | \(-0.469388\pi\) | ||||
−0.0960230 | + | 0.995379i | \(0.530612\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.518393 | − | 0.855143i | \(-0.326531\pi\) | ||||
−0.518393 | + | 0.855143i | \(0.673469\pi\) | |||||||
\(948\) | −0.567886 | − | 0.0364595i | −0.567886 | − | 0.0364595i | ||||
\(949\) | 3.17031 | − | 1.52674i | 3.17031 | − | 1.52674i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.997945 | − | 0.0640702i | \(-0.0204082\pi\) | ||||
−0.997945 | + | 0.0640702i | \(0.979592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.68811 | + | 1.29453i | −2.68811 | + | 1.29453i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.655541 | + | 0.217655i | 0.655541 | + | 0.217655i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.47309 | + | 0.386289i | −1.47309 | + | 0.386289i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
−0.572117 | + | 0.820172i | \(0.693878\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.462538 | − | 0.886599i | \(-0.346939\pi\) | ||||
−0.462538 | + | 0.886599i | \(0.653061\pi\) | |||||||
\(972\) | 0.718349 | − | 0.695683i | 0.718349 | − | 0.695683i | ||||
\(973\) | 0.0184408 | − | 0.191159i | 0.0184408 | − | 0.191159i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.36351 | + | 1.32048i | −1.36351 | + | 1.32048i | ||||
\(976\) | 0.0509443 | − | 0.315108i | 0.0509443 | − | 0.315108i | ||||
\(977\) | 0 | 0 | −0.838088 | − | 0.545535i | \(-0.816327\pi\) | ||||
0.838088 | + | 0.545535i | \(0.183673\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.23674 | − | 1.55083i | 1.23674 | − | 1.55083i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.518393 | − | 0.855143i | \(-0.673469\pi\) | ||||
0.518393 | + | 0.855143i | \(0.326531\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.28785 | + | 0.838295i | 1.28785 | + | 0.838295i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0513731 | + | 1.60200i | 0.0513731 | + | 1.60200i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.572117 | + | 0.820172i | \(0.693878\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.0620067 | + | 1.93360i | 0.0620067 | + | 1.93360i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.287589 | − | 1.77884i | −0.287589 | − | 1.77884i | −0.572117 | − | 0.820172i | \(-0.693878\pi\) |
0.284528 | − | 0.958668i | \(-0.408163\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.03092 | + | 0.496464i | 1.03092 | + | 0.496464i |
(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 | 1029.1.t.a.575.1 | ✓ | 42 | |
3.2 | odd | 2 | CM | 1029.1.t.a.575.1 | ✓ | 42 | |
343.309 | even | 49 | inner | 1029.1.t.a.995.1 | yes | 42 | |
1029.995 | odd | 98 | inner | 1029.1.t.a.995.1 | yes | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1029.1.t.a.575.1 | ✓ | 42 | 1.1 | even | 1 | trivial | |
1029.1.t.a.575.1 | ✓ | 42 | 3.2 | odd | 2 | CM | |
1029.1.t.a.995.1 | yes | 42 | 343.309 | even | 49 | inner | |
1029.1.t.a.995.1 | yes | 42 | 1029.995 | odd | 98 | inner |