Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,1,Mod(238,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.238");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.f (of order \(6\), degree \(2\), 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: | \(1.07348884217\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{45})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - x^{21} + x^{15} - x^{12} + x^{9} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{45}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{45} - \cdots)\) |
Embedding invariants
Embedding label | 238.4 | ||
Root | \(-0.615661 - 0.788011i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.238 |
Dual form | 2151.1.f.b.1672.4 |
$q$-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 \(\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times\).
\(n\) | \(479\) | \(1441\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(3\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(4\) | −0.125393 | + | 0.217188i | −0.125393 | + | 0.217188i | ||||
\(5\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(6\) | −0.904793 | − | 0.657371i | −0.904793 | − | 0.657371i | ||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | −0.837909 | −0.837909 | ||||||||
\(9\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(10\) | −1.60900 | −1.60900 | ||||||||
\(11\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(12\) | −0.0262144 | + | 0.249413i | −0.0262144 | + | 0.249413i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.150383 | − | 1.43080i | 0.150383 | − | 1.43080i | ||||
\(16\) | 0.593946 | + | 1.02875i | 0.593946 | + | 1.02875i | ||||
\(17\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(18\) | −1.09395 | − | 0.232525i | −1.09395 | − | 0.232525i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0.180401 | + | 0.312464i | 0.180401 | + | 0.312464i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.987476 | − | 1.71036i | 0.987476 | − | 1.71036i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | −0.765468 | + | 0.340808i | −0.765468 | + | 0.340808i | ||||
\(25\) | −0.534899 | − | 0.926473i | −0.534899 | − | 0.926473i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(30\) | −1.46989 | + | 0.654439i | −1.46989 | + | 0.654439i | ||||
\(31\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.559193 | − | 0.829038i | \(-0.311111\pi\) | |||||||
\(32\) | 0.245307 | − | 0.424883i | 0.245307 | − | 0.424883i | ||||
\(33\) | 1.42864 | + | 1.03797i | 1.42864 | + | 1.03797i | ||||
\(34\) | 1.05094 | + | 1.82028i | 1.05094 | + | 1.82028i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0774974 | + | 0.238512i | 0.0774974 | + | 0.238512i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.602742 | + | 1.04398i | −0.602742 | + | 1.04398i | ||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | −0.442863 | −0.442863 | ||||||||
\(45\) | −0.444576 | − | 1.36827i | −0.444576 | − | 1.36827i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0.961025 | + | 0.698226i | 0.961025 | + | 0.698226i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(50\) | −0.598224 | + | 1.03615i | −0.598224 | + | 1.03615i | ||||
\(51\) | −1.71690 | + | 0.764415i | −1.71690 | + | 0.764415i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −1.09395 | + | 0.232525i | −1.09395 | + | 0.232525i | ||||
\(55\) | 2.54056 | 2.54056 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.10750 | + | 1.91825i | −1.10750 | + | 1.91825i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0.291895 | + | 0.212074i | 0.291895 | + | 0.212074i | ||||
\(61\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(62\) | −2.23132 | −2.23132 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.639198 | 0.639198 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.206439 | − | 1.96413i | 0.206439 | − | 1.96413i | ||||
\(67\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(68\) | 0.235663 | − | 0.408179i | 0.235663 | − | 0.408179i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(72\) | −0.560671 | + | 0.622688i | −0.560671 | + | 0.622688i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.865486 | − | 0.628812i | −0.865486 | − | 0.628812i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 1.70900 | 1.70900 | ||||||||
\(81\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.35192 | + | 2.34159i | −1.35192 | + | 2.34159i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.60229 | − | 1.16413i | −1.60229 | − | 1.16413i | ||||
\(88\) | −0.739830 | − | 1.28142i | −0.739830 | − | 1.28142i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −1.07663 | + | 1.19572i | −1.07663 | + | 1.19572i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.208548 | − | 1.98420i | 0.208548 | − | 1.98420i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.0512830 | − | 0.487925i | 0.0512830 | − | 0.487925i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | 1.11839 | 1.11839 | ||||||||
\(99\) | 1.72731 | + | 0.367150i | 1.72731 | + | 0.367150i | ||||
\(100\) | 0.268291 | 0.268291 | ||||||||
\(101\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(102\) | 1.70045 | + | 1.23545i | 1.70045 | + | 1.23545i | ||||
\(103\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0.167809 | + | 0.186371i | 0.167809 | + | 0.186371i | ||||
\(109\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(110\) | −1.42066 | − | 2.46066i | −1.42066 | − | 2.46066i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.496692 | 0.496692 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.126007 | + | 1.19888i | −0.126007 | + | 1.19888i | ||||
\(121\) | −1.05919 | + | 1.83458i | −1.05919 | + | 1.83458i | ||||
\(122\) | 1.05094 | − | 1.82028i | 1.05094 | − | 1.82028i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.250176 | + | 0.433317i | 0.250176 | + | 0.433317i | ||||
\(125\) | −0.100418 | −0.100418 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(128\) | −0.602742 | − | 1.04398i | −0.602742 | − | 1.04398i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | −0.404576 | + | 0.180129i | −0.404576 | + | 0.180129i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.71347 | 1.71347 | ||||||||
\(135\) | −0.962665 | − | 1.06915i | −0.962665 | − | 1.06915i | ||||
\(136\) | 1.57475 | 1.57475 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.345600 | − | 0.598597i | −0.345600 | − | 0.598597i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.16193 | + | 0.246977i | 1.16193 | + | 0.246977i | ||||
\(145\) | −2.84936 | −2.84936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | −0.125063 | + | 1.18989i | −0.125063 | + | 1.18989i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.25755 | + | 1.39666i | −1.25755 | + | 1.39666i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.43518 | − | 2.48580i | −1.43518 | − | 2.48580i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.352917 | − | 0.611271i | −0.352917 | − | 0.611271i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.904793 | + | 0.657371i | −0.904793 | + | 0.657371i | ||||
\(163\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.32091 | − | 1.03334i | 2.32091 | − | 1.03334i | ||||
\(166\) | 0.688547 | − | 1.19260i | 0.688547 | − | 1.19260i | ||||
\(167\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(170\) | 3.02393 | 3.02393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | −0.231531 | + | 2.20287i | −0.231531 | + | 2.20287i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.04885 | + | 1.81666i | −1.04885 | + | 1.81666i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 0.352917 | + | 0.0750149i | 0.352917 | + | 0.0750149i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.52045 | + | 1.10467i | 1.52045 | + | 1.10467i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.03841 | + | 0.907561i | −2.03841 | + | 0.907561i | ||||
\(187\) | −1.65940 | − | 2.87416i | −1.65940 | − | 2.87416i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0.583937 | − | 0.259985i | 0.583937 | − | 0.259985i | ||||
\(193\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.125393 | − | 0.217188i | −0.125393 | − | 0.217188i | ||||
\(197\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(198\) | −0.610294 | − | 1.87829i | −0.610294 | − | 1.87829i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0.448197 | + | 0.776301i | 0.448197 | + | 0.776301i | ||||
\(201\) | −0.160147 | + | 1.52370i | −0.160147 | + | 1.52370i | ||||
\(202\) | 0.904793 | − | 1.56715i | 0.904793 | − | 1.56715i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.0492669 | − | 0.468743i | 0.0492669 | − | 0.468743i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.258928 | + | 0.796899i | −0.258928 | + | 0.796899i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.748346 | − | 1.29617i | −0.748346 | − | 1.29617i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.318569 | + | 0.551778i | −0.318569 | + | 0.551778i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.04642 | − | 0.222424i | −1.04642 | − | 0.222424i | ||||
\(226\) | −0.233806 | −0.233806 | ||||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.829755 | + | 1.43718i | 0.829755 | + | 1.43718i | ||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(240\) | 1.56125 | − | 0.695112i | 1.56125 | − | 0.695112i | ||||
\(241\) | 0.104528 | + | 0.181049i | 0.104528 | + | 0.181049i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(242\) | 2.36917 | 2.36917 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(244\) | −0.471325 | −0.471325 | ||||||||
\(245\) | 0.719340 | + | 1.24593i | 0.719340 | + | 1.24593i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.835868 | + | 1.44777i | −0.835868 | + | 1.44777i | ||||
\(249\) | 0.996161 | + | 0.723753i | 0.996161 | + | 0.723753i | ||||
\(250\) | 0.0561532 | + | 0.0972603i | 0.0561532 | + | 0.0972603i | ||||
\(251\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.948445 | − | 1.64275i | −0.948445 | − | 1.64275i | ||||
\(255\) | −0.282628 | + | 2.68902i | −0.282628 | + | 2.68902i | ||||
\(256\) | −0.354499 | + | 0.614010i | −0.354499 | + | 0.614010i | ||||
\(257\) | −0.848048 | + | 1.46886i | −0.848048 | + | 1.46886i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.93726 | − | 0.411777i | −1.93726 | − | 0.411777i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(264\) | −1.19707 | − | 0.869722i | −1.19707 | − | 0.869722i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.192114 | − | 0.332751i | −0.192114 | − | 0.332751i | ||||
\(269\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(270\) | −0.497208 | + | 1.53025i | −0.497208 | + | 1.53025i | ||||
\(271\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(272\) | −1.11625 | − | 1.93341i | −1.11625 | − | 1.93341i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.944576 | − | 1.63605i | 0.944576 | − | 1.63605i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.616528 | − | 1.89748i | −0.616528 | − | 1.89748i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(284\) | −0.0774974 | + | 0.134229i | −0.0774974 | + | 0.134229i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.151608 | − | 0.466601i | −0.151608 | − | 0.466601i | ||||
\(289\) | 2.53209 | 2.53209 | ||||||||
\(290\) | 1.59334 | + | 2.75975i | 1.59334 | + | 2.75975i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(294\) | 1.02170 | − | 0.454888i | 1.02170 | − | 0.454888i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.72731 | − | 0.367150i | 1.72731 | − | 0.367150i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.245096 | − | 0.109124i | 0.245096 | − | 0.109124i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.70383 | 2.70383 | ||||||||
\(306\) | 2.05595 | + | 0.437005i | 2.05595 | + | 0.437005i | ||||
\(307\) | −1.43868 | −1.43868 | −0.719340 | − | 0.694658i | \(-0.755556\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.60508 | + | 2.78008i | −1.60508 | + | 2.78008i | ||||
\(311\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | 2.21500 | 2.21500 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.74871 | − | 3.02885i | 1.74871 | − | 3.02885i | ||||
\(320\) | 0.459801 | − | 0.796398i | 0.459801 | − | 0.796398i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.229105 | + | 0.102004i | 0.229105 | + | 0.102004i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.270562 | + | 0.468627i | 0.270562 | + | 0.468627i | ||||
\(327\) | 1.22256 | − | 0.544320i | 1.22256 | − | 0.544320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.29868 | − | 1.67009i | −2.29868 | − | 1.67009i | ||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −0.308800 | −0.308800 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.10209 | + | 1.90888i | 1.10209 | + | 1.90888i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(338\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | ||||
\(339\) | 0.0218524 | − | 0.207912i | 0.0218524 | − | 0.207912i | ||||
\(340\) | −0.339043 | − | 0.587239i | −0.339043 | − | 0.587239i | ||||
\(341\) | 3.52319 | 3.52319 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.559193 | − | 0.829038i | \(-0.311111\pi\) | |||||||
\(348\) | 0.453751 | − | 0.202023i | 0.453751 | − | 0.202023i | ||||
\(349\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.866371 | 0.866371 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.444576 | − | 0.770029i | 0.444576 | − | 0.770029i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(360\) | 0.372515 | + | 1.14648i | 0.372515 | + | 1.14648i | ||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.221432 | + | 2.10678i | −0.221432 | + | 2.10678i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.219706 | − | 2.09036i | 0.219706 | − | 2.09036i | ||||
\(367\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.404793 | + | 0.294099i | 0.404793 | + | 0.294099i | ||||
\(373\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(374\) | −1.85585 | + | 3.21442i | −1.85585 | + | 3.21442i | ||||
\(375\) | −0.0917368 | + | 0.0408438i | −0.0917368 | + | 0.0408438i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.54946 | − | 0.689864i | 1.54946 | − | 0.689864i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(384\) | −0.975256 | − | 0.708565i | −0.975256 | − | 0.708565i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.541124 | −0.541124 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.418955 | − | 0.725651i | 0.418955 | − | 0.725651i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.0390311 | − | 0.0676039i | −0.0390311 | − | 0.0676039i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.296333 | + | 0.329112i | −0.296333 | + | 0.329112i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.635403 | − | 1.10055i | 0.635403 | − | 1.10055i | ||||
\(401\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(402\) | 1.56533 | − | 0.696930i | 1.56533 | − | 0.696930i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.405782 | −0.405782 | ||||||||
\(405\) | −1.31430 | − | 0.585164i | −1.31430 | − | 0.585164i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.43861 | − | 0.640510i | 1.43861 | − | 0.640510i | ||||
\(409\) | −0.961262 | + | 1.66495i | −0.961262 | + | 1.66495i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.77148 | 1.77148 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.104528 | + | 0.181049i | 0.104528 | + | 0.181049i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(422\) | −1.37709 | −1.37709 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00528 | + | 1.74120i | 1.00528 | + | 1.74120i | ||||
\(426\) | −0.559193 | − | 0.406277i | −0.559193 | − | 0.406277i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(432\) | 1.16193 | − | 0.246977i | 1.16193 | − | 0.246977i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.60302 | + | 1.15894i | −2.60302 | + | 1.15894i | ||||
\(436\) | −0.167809 | + | 0.290654i | −0.167809 | + | 0.290654i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.913545 | − | 1.58231i | −0.913545 | − | 1.58231i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(440\) | −2.12876 | −2.12876 | ||||||||
\(441\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.961262 | − | 1.66495i | −0.961262 | − | 1.66495i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
−0.241922 | − | 0.970296i | \(-0.577778\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0.369723 | + | 1.13789i | 0.369723 | + | 1.13789i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.0262144 | + | 0.0454046i | 0.0262144 | + | 0.0454046i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.580762 | + | 1.78740i | −0.580762 | + | 1.78740i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 1.17633 | − | 2.03747i | 1.17633 | − | 2.03747i | ||||
\(465\) | −2.32216 | − | 1.68715i | −2.32216 | − | 1.68715i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.207022 | + | 1.96969i | −0.207022 | + | 1.96969i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.11839 | 1.11839 | ||||||||
\(479\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(480\) | −0.571032 | − | 0.414879i | −0.571032 | − | 0.414879i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.116903 | − | 0.202482i | 0.116903 | − | 0.202482i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.265632 | − | 0.460087i | −0.265632 | − | 0.460087i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | ||||
\(487\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(488\) | −0.787377 | − | 1.36378i | −0.787377 | − | 1.36378i | ||||
\(489\) | −0.442013 | + | 0.196797i | −0.442013 | + | 0.196797i | ||||
\(490\) | 0.804499 | − | 1.39343i | 0.804499 | − | 1.39343i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.86110 | + | 3.22351i | 1.86110 | + | 3.22351i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.69996 | − | 1.88800i | 1.69996 | − | 1.88800i | ||||
\(496\) | 2.37000 | 2.37000 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.143946 | − | 1.36955i | 0.143946 | − | 1.36955i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0.0125918 | − | 0.0218096i | 0.0125918 | − | 0.0218096i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.194206 | − | 0.336374i | −0.194206 | − | 0.336374i | ||||
\(503\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.32783 | 2.32783 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(508\) | −0.212679 | + | 0.368371i | −0.212679 | + | 0.368371i | ||||
\(509\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(510\) | 2.76250 | − | 1.22994i | 2.76250 | − | 1.22994i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.412551 | −0.412551 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.89689 | 1.89689 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0.684474 | + | 2.10659i | 0.684474 | + | 2.10659i | ||||
\(523\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.418955 | − | 0.725651i | 0.418955 | − | 0.725651i | ||||
\(527\) | −1.87481 | + | 3.24726i | −1.87481 | + | 3.24726i | ||||
\(528\) | −0.219269 | + | 2.08620i | −0.219269 | + | 2.08620i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.641876 | − | 1.11176i | 0.641876 | − | 1.11176i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.11566 | + | 1.93238i | 1.11566 | + | 1.93238i | ||||
\(539\) | −1.76590 | −1.76590 | ||||||||
\(540\) | 0.352917 | − | 0.0750149i | 0.352917 | − | 0.0750149i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0.987476 | + | 1.71036i | 0.987476 | + | 1.71036i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.461025 | + | 0.798520i | −0.461025 | + | 0.798520i | ||||
\(545\) | 0.962665 | − | 1.66738i | 0.962665 | − | 1.66738i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.83832 | + | 0.390746i | 1.83832 | + | 0.390746i | ||||
\(550\) | −2.11280 | −2.11280 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | −1.49305 | + | 1.65820i | −1.49305 | + | 1.65820i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.68496 | − | 1.95074i | −2.68496 | − | 1.95074i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.00000 | + | 1.73205i | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.150383 | − | 0.260471i | −0.150383 | − | 0.260471i | ||||
\(566\) | 1.25079 | 1.25079 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.517856 | −0.517856 | ||||||||
\(569\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.427707 | − | 0.475017i | 0.427707 | − | 0.475017i | ||||
\(577\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(578\) | −1.41593 | − | 2.45246i | −1.41593 | − | 2.45246i | ||||
\(579\) | 0.0505754 | − | 0.481193i | 0.0505754 | − | 0.481193i | ||||
\(580\) | 0.357291 | − | 0.618845i | 0.357291 | − | 0.618845i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.691200 | 0.691200 | ||||||||
\(587\) | 0.241922 | + | 0.419021i | 0.241922 | + | 0.419021i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(588\) | −0.202891 | − | 0.147409i | −0.202891 | − | 0.147409i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.0637646 | − | 0.0283898i | 0.0637646 | − | 0.0283898i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −1.32150 | − | 1.46768i | −1.32150 | − | 1.46768i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(600\) | 0.725198 | + | 0.526888i | 0.725198 | + | 0.526888i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.473442 | + | 1.45710i | 0.473442 | + | 1.45710i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.52384 | + | 2.63937i | 1.52384 | + | 2.63937i | ||||
\(606\) | 0.189153 | − | 1.79967i | 0.189153 | − | 1.79967i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.51196 | − | 2.61880i | −1.51196 | − | 2.61880i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.145647 | − | 0.448257i | −0.145647 | − | 0.448257i | ||||
\(613\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(614\) | 0.804499 | + | 1.39343i | 0.804499 | + | 1.39343i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(620\) | 0.719846 | 0.719846 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.388411 | 0.388411 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.462665 | − | 0.801359i | 0.462665 | − | 0.801359i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.248346 | − | 0.430148i | −0.248346 | − | 0.430148i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.43868 | −1.43868 | −0.719340 | − | 0.694658i | \(-0.755556\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.128708 | − | 1.22458i | 0.128708 | − | 1.22458i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.22007 | − | 2.11322i | 1.22007 | − | 2.11322i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3.91146 | −3.91146 | ||||||||
\(639\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | ||||
\(640\) | −1.73430 | −1.73430 | ||||||||
\(641\) | −0.0348995 | − | 0.0604477i | −0.0348995 | − | 0.0604477i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.848048 | + | 1.46886i | −0.848048 | + | 1.46886i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.876742 | 0.876742 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(648\) | 0.0875854 | + | 0.833319i | 0.0875854 | + | 0.833319i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.0606708 | − | 0.105085i | 0.0606708 | − | 0.105085i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | −1.21085 | − | 0.879734i | −1.21085 | − | 0.879734i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | −0.0665991 | + | 0.633648i | −0.0665991 | + | 0.633648i | ||||
\(661\) | 0.882948 | − | 1.52931i | 0.882948 | − | 1.52931i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.515869 | − | 0.893511i | −0.515869 | − | 0.893511i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.23256 | − | 2.13486i | 1.23256 | − | 2.13486i | ||||
\(671\) | −1.65940 | + | 2.87416i | −1.65940 | + | 2.87416i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −1.60900 | −1.60900 | ||||||||
\(675\) | −1.04642 | + | 0.222424i | −1.04642 | + | 0.222424i | ||||
\(676\) | 0.250787 | 0.250787 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | −0.213593 | + | 0.0950976i | −0.213593 | + | 0.0950976i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.13278 | − | 1.96204i | 1.13278 | − | 1.96204i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.97014 | − | 3.41238i | −1.97014 | − | 3.41238i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.23132 | −2.23132 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.34257 | + | 0.975435i | 1.34257 | + | 0.975435i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.948445 | + | 1.64275i | −0.948445 | + | 1.64275i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.564378 | + | 0.977532i | 0.564378 | + | 0.977532i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(710\) | −0.994416 | −0.994416 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(718\) | 0.904793 | + | 1.56715i | 0.904793 | + | 1.56715i | ||||
\(719\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(720\) | 1.14354 | − | 1.27003i | 1.14354 | − | 1.27003i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | ||||
\(723\) | 0.169131 | + | 0.122881i | 0.169131 | + | 0.122881i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.05939 | + | 1.83491i | −1.05939 | + | 1.83491i | ||||
\(726\) | 2.16435 | − | 0.963629i | 2.16435 | − | 0.963629i | ||||
\(727\) | −0.913545 | − | 1.58231i | −0.913545 | − | 1.58231i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.430577 | + | 0.191705i | −0.430577 | + | 0.191705i | ||||
\(733\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.559193 | − | 0.829038i | \(-0.311111\pi\) | |||||||
\(734\) | 0.688547 | − | 1.19260i | 0.688547 | − | 1.19260i | ||||
\(735\) | 1.16392 | + | 0.845635i | 1.16392 | + | 0.845635i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.70551 | −2.70551 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | −0.174744 | + | 1.66258i | −0.174744 | + | 1.66258i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.691200 | 0.691200 | ||||||||
\(747\) | 1.20442 | + | 0.256006i | 1.20442 | + | 0.256006i | ||||
\(748\) | 0.832311 | 0.832311 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.0908579 | + | 0.0660121i | 0.0908579 | + | 0.0660121i | ||||
\(751\) | −0.669131 | + | 1.15897i | −0.669131 | + | 1.15897i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.317271 | − | 0.141258i | 0.317271 | − | 0.141258i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.669131 | + | 1.15897i | −0.669131 | + | 1.15897i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(762\) | −1.53462 | − | 1.11496i | −1.53462 | − | 1.11496i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.835530 | + | 2.57150i | 0.835530 | + | 2.57150i | ||||
\(766\) | −1.11839 | −1.11839 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.0741104 | + | 0.705113i | −0.0741104 | + | 0.705113i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.177290 | + | 1.68680i | −0.177290 | + | 1.68680i | ||||
\(772\) | 0.0606708 | + | 0.105085i | 0.0606708 | + | 0.105085i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.13439 | −2.13439 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.490268 | + | 0.849169i | −0.490268 | + | 0.849169i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.545692 | + | 0.945166i | 0.545692 | + | 0.945166i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.93726 | + | 0.411777i | −1.93726 | + | 0.411777i | ||||
\(784\) | −1.18789 | −1.18789 | ||||||||
\(785\) | 1.42468 | + | 2.46762i | 1.42468 | + | 2.46762i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | −0.00875233 | + | 0.0151595i | −0.00875233 | + | 0.0151595i | ||||
\(789\) | 0.606126 | + | 0.440376i | 0.606126 | + | 0.440376i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.44733 | − | 0.307639i | −1.44733 | − | 0.307639i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.524857 | −0.524857 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.37709 | −1.37709 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.310847 | − | 0.225843i | −0.310847 | − | 0.225843i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.82264 | + | 0.811492i | −1.82264 | + | 0.811492i | ||||
\(808\) | −0.677883 | − | 1.17413i | −0.677883 | − | 1.17413i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0.168186 | + | 1.60018i | 0.168186 | + | 1.60018i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.61323 | + | 0.718254i | −1.61323 | + | 0.718254i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.348048 | + | 0.602837i | −0.348048 | + | 0.602837i | ||||
\(816\) | −1.80614 | − | 1.31224i | −1.80614 | − | 1.31224i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 2.15012 | 2.15012 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.197470 | − | 1.87880i | 0.197470 | − | 1.87880i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.98054 | 1.98054 | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) | ||||
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | −0.990599 | − | 1.71577i | −0.990599 | − | 1.71577i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.33500 | − | 1.48267i | −1.33500 | − | 1.48267i | ||||
\(838\) | −0.837909 | −0.837909 | ||||||||
\(839\) | −0.0348995 | − | 0.0604477i | −0.0348995 | − | 0.0604477i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.46126 | + | 2.53098i | −1.46126 | + | 2.53098i | ||||
\(842\) | 0.116903 | − | 0.202482i | 0.116903 | − | 0.202482i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.154400 | + | 0.267428i | 0.154400 | + | 0.267428i | ||||
\(845\) | −1.43868 | −1.43868 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.116903 | + | 1.11226i | −0.116903 | + | 1.11226i | ||||
\(850\) | 1.12429 | − | 1.94733i | 1.12429 | − | 1.94733i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.0162014 | + | 0.154146i | −0.0162014 | + | 0.154146i | ||||
\(853\) | −0.961262 | − | 1.66495i | −0.961262 | − | 1.66495i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
−0.241922 | − | 0.970296i | \(-0.577778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0348995 | + | 0.0604477i | −0.0348995 | + | 0.0604477i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.270562 | + | 0.468627i | 0.270562 | + | 0.468627i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −0.328284 | − | 0.364597i | −0.328284 | − | 0.364597i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.31318 | − | 1.02989i | 2.31318 | − | 1.02989i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2.57808 | + | 1.87308i | 2.57808 | + | 1.87308i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.12134 | −1.12134 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(878\) | −1.02170 | + | 1.76963i | −1.02170 | + | 1.76963i | ||||
\(879\) | −0.0646021 | + | 0.614648i | −0.0646021 | + | 0.614648i | ||||
\(880\) | 1.50895 | + | 2.61359i | 1.50895 | + | 2.61359i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0.748346 | − | 0.831123i | 0.748346 | − | 0.831123i | ||||
\(883\) | 0.876742 | 0.876742 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.07506 | + | 1.86206i | −1.07506 | + | 1.86206i | ||||
\(887\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.42864 | − | 1.03797i | 1.42864 | − | 1.03797i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.95142 | −3.95142 | ||||||||
\(900\) | 0.179522 | − | 0.199379i | 0.179522 | − | 0.199379i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0875854 | + | 0.151702i | −0.0875854 | + | 0.151702i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.58268 | + | 0.336408i | 1.58268 | + | 0.336408i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.08719 | + | 1.88307i | −1.08719 | + | 1.88307i | ||||
\(914\) | −0.345600 | + | 0.598597i | −0.345600 | + | 0.598597i | ||||
\(915\) | 2.47007 | − | 1.09975i | 2.47007 | − | 1.09975i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.05595 | − | 0.437005i | 2.05595 | − | 0.437005i | ||||
\(919\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.31430 | + | 0.585164i | −1.31430 | + | 0.585164i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.971677 | −0.971677 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | −0.335553 | + | 3.19257i | −0.335553 | + | 3.19257i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.0363024 | + | 0.345394i | −0.0363024 | + | 0.345394i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.77469 | −4.77469 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.876742 | 0.876742 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 2.02351 | − | 0.900923i | 2.02351 | − | 0.900923i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.125393 | − | 0.217188i | −0.125393 | − | 0.217188i | ||||
\(957\) | 0.365580 | − | 3.47826i | 0.365580 | − | 3.47826i | ||||
\(958\) | −0.490268 | + | 0.849169i | −0.490268 | + | 0.849169i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0961245 | − | 0.914564i | 0.0961245 | − | 0.914564i | ||||
\(961\) | −1.49027 | − | 2.58122i | −1.49027 | − | 2.58122i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.0524287 | −0.0524287 | ||||||||
\(965\) | −0.348048 | − | 0.602837i | −0.348048 | − | 0.602837i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(968\) | 0.887508 | − | 1.53721i | 0.887508 | − | 1.53721i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(972\) | 0.250787 | 0.250787 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.194206 | − | 0.336374i | −0.194206 | − | 0.336374i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.11625 | + | 1.93341i | −1.11625 | + | 1.93341i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0.437779 | + | 0.318065i | 0.437779 | + | 0.318065i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.360802 | −0.360802 | ||||||||
\(981\) | 0.895472 | − | 0.994522i | 0.895472 | − | 0.994522i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.0502092 | − | 0.0869649i | 0.0502092 | − | 0.0869649i | ||||
\(986\) | 2.08142 | − | 3.60513i | 2.08142 | − | 3.60513i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −2.77923 | − | 0.590744i | −2.77923 | − | 0.590744i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −0.489418 | − | 0.847697i | −0.489418 | − | 0.847697i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.282102 | + | 0.125600i | −0.282102 | + | 0.125600i | ||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2151.1.f.b.238.4 | ✓ | 24 | |
9.7 | even | 3 | inner | 2151.1.f.b.1672.4 | yes | 24 | |
239.238 | odd | 2 | CM | 2151.1.f.b.238.4 | ✓ | 24 | |
2151.1672 | odd | 6 | inner | 2151.1.f.b.1672.4 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.1.f.b.238.4 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2151.1.f.b.238.4 | ✓ | 24 | 239.238 | odd | 2 | CM | |
2151.1.f.b.1672.4 | yes | 24 | 9.7 | even | 3 | inner | |
2151.1.f.b.1672.4 | yes | 24 | 2151.1672 | odd | 6 | inner |