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 | 238.12 | ||
Root | \(-0.374607 + 0.927184i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.238 |
Dual form | 2151.1.f.b.1672.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(3\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(4\) | −1.49027 | + | 2.58122i | −1.49027 | + | 2.58122i | ||||
\(5\) | −0.961262 | + | 1.66495i | −0.961262 | + | 1.66495i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(6\) | 1.61409 | + | 1.17271i | 1.61409 | + | 1.17271i | ||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | −3.95142 | −3.95142 | ||||||||
\(9\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(10\) | −3.83568 | −3.83568 | ||||||||
\(11\) | −0.0348995 | − | 0.0604477i | −0.0348995 | − | 0.0604477i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(12\) | −0.311551 | + | 2.96421i | −0.311551 | + | 2.96421i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.200958 | + | 1.91199i | −0.200958 | + | 1.91199i | ||||
\(16\) | −2.45153 | − | 4.24617i | −2.45153 | − | 4.24617i | ||||
\(17\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(18\) | 1.95153 | + | 0.414810i | 1.95153 | + | 0.414810i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −2.86508 | − | 4.96246i | −2.86508 | − | 4.96246i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0696290 | − | 0.120601i | 0.0696290 | − | 0.120601i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | −3.60980 | + | 1.60719i | −3.60980 | + | 1.60719i | ||||
\(25\) | −1.34805 | − | 2.33489i | −1.34805 | − | 2.33489i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(30\) | −3.50407 | + | 1.56011i | −3.50407 | + | 1.56011i | ||||
\(31\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(32\) | 2.91540 | − | 5.04963i | 2.91540 | − | 5.04963i | ||||
\(33\) | −0.0564686 | − | 0.0410268i | −0.0564686 | − | 0.0410268i | ||||
\(34\) | 1.52836 | + | 2.64719i | 1.52836 | + | 2.64719i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.921036 | + | 2.83466i | 0.921036 | + | 2.83466i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.79835 | − | 6.57894i | 3.79835 | − | 6.57894i | ||||
\(41\) | 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 | \(0.333333\pi\) | |||||||
\(44\) | 0.208038 | 0.208038 | ||||||||
\(45\) | 0.594092 | + | 1.82843i | 0.594092 | + | 1.82843i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −3.96666 | − | 2.88195i | −3.96666 | − | 2.88195i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(50\) | 2.68953 | − | 4.65840i | 2.68953 | − | 4.65840i | ||||
\(51\) | 1.39963 | − | 0.623157i | 1.39963 | − | 0.623157i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 1.95153 | − | 0.414810i | 1.95153 | − | 0.414810i | ||||
\(55\) | 0.134190 | 0.134190 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.22832 | + | 2.12752i | −1.22832 | + | 2.12752i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | −4.63579 | − | 3.36810i | −4.63579 | − | 3.36810i | ||||
\(61\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(62\) | −1.74921 | −1.74921 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.73015 | 6.73015 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0145564 | − | 0.138495i | 0.0145564 | − | 0.138495i | ||||
\(67\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(68\) | −2.28322 | + | 3.95466i | −2.28322 | + | 3.95466i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(72\) | −2.64402 | + | 2.93648i | −2.64402 | + | 2.93648i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.18119 | − | 1.58473i | −2.18119 | − | 1.58473i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 9.42625 | 9.42625 | ||||||||
\(81\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.47274 | + | 2.55086i | −1.47274 | + | 2.55086i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.996161 | + | 0.723753i | 0.996161 | + | 0.723753i | ||||
\(88\) | 0.137903 | + | 0.238854i | 0.137903 | + | 0.238854i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −2.56657 | + | 2.85047i | −2.56657 | + | 2.85047i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.0916445 | + | 0.871939i | −0.0916445 | + | 0.871939i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.609485 | − | 5.79887i | 0.609485 | − | 5.79887i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | −1.99513 | −1.99513 | ||||||||
\(99\) | −0.0682737 | − | 0.0145120i | −0.0682737 | − | 0.0145120i | ||||
\(100\) | 8.03581 | 8.03581 | ||||||||
\(101\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(102\) | 2.47293 | + | 1.79669i | 2.47293 | + | 1.79669i | ||||
\(103\) | 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 | \(\pi\) | |||||||||
\(108\) | 1.99437 | + | 2.21497i | 1.99437 | + | 2.21497i | ||||
\(109\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(110\) | 0.133863 | + | 0.231858i | 0.133863 | + | 0.231858i | ||||
\(111\) | 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 | ||||||||
\(116\) | −3.67000 | −3.67000 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.794072 | − | 7.55509i | 0.794072 | − | 7.55509i | ||||
\(121\) | 0.497564 | − | 0.861806i | 0.497564 | − | 0.861806i | ||||
\(122\) | 1.52836 | − | 2.64719i | 1.52836 | − | 2.64719i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.30658 | − | 2.26306i | −1.30658 | − | 2.26306i | ||||
\(125\) | 3.26078 | 3.26078 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(128\) | 3.79835 | + | 6.57894i | 3.79835 | + | 6.57894i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | 0.190053 | − | 0.0846168i | 0.190053 | − | 0.0846168i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.692901 | −0.692901 | ||||||||
\(135\) | 1.28642 | + | 1.42871i | 1.28642 | + | 1.42871i | ||||
\(136\) | −6.05393 | −6.05393 | ||||||||
\(137\) | 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 | ||||||||
\(142\) | 0.616528 | + | 1.06786i | 0.616528 | + | 1.06786i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.79592 | − | 1.01940i | −4.79592 | − | 1.01940i | ||||
\(145\) | −2.36725 | −2.36725 | ||||||||
\(146\) | 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 | \(0.666667\pi\) | |||||||
\(150\) | 0.562265 | − | 5.34959i | 0.562265 | − | 5.34959i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.02517 | − | 1.13856i | 1.02517 | − | 1.13856i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.842779 | − | 1.45974i | −0.842779 | − | 1.45974i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.60493 | + | 9.70803i | 5.60493 | + | 9.70803i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.61409 | − | 1.17271i | 1.61409 | − | 1.17271i | ||||
\(163\) | −1.43868 | −1.43868 | −0.719340 | − | 0.694658i | \(-0.755556\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.122589 | − | 0.0545801i | 0.122589 | − | 0.0545801i | ||||
\(166\) | −0.747388 | + | 1.29451i | −0.747388 | + | 1.29451i | ||||
\(167\) | 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 | ||||
\(170\) | −5.87660 | −5.87660 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | −0.256790 | + | 2.44319i | −0.256790 | + | 2.44319i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.171114 | + | 0.296379i | −0.171114 | + | 0.296379i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | −5.60493 | − | 1.19137i | −5.60493 | − | 1.19137i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.23949 | − | 0.900539i | −1.23949 | − | 0.900539i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.59799 | + | 0.711469i | −1.59799 | + | 0.711469i | ||||
\(187\) | −0.0534691 | − | 0.0926113i | −0.0534691 | − | 0.0926113i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 6.14830 | − | 2.73740i | 6.14830 | − | 2.73740i | ||||
\(193\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.49027 | − | 2.58122i | −1.49027 | − | 2.58122i | ||||
\(197\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(198\) | −0.0430331 | − | 0.132442i | −0.0430331 | − | 0.132442i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 5.32671 | + | 9.22613i | 5.32671 | + | 9.22613i | ||||
\(201\) | −0.0363024 | + | 0.345394i | −0.0363024 | + | 0.345394i | ||||
\(202\) | −1.61409 | + | 2.79569i | −1.61409 | + | 2.79569i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.477324 | + | 4.54143i | −0.477324 | + | 4.54143i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
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 | ||||||||
\(216\) | −1.22106 | + | 3.75803i | −1.22106 | + | 3.75803i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.33500 | + | 2.31229i | 1.33500 | + | 2.31229i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.199979 | + | 0.346374i | −0.199979 | + | 0.346374i | ||||
\(221\) | 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 | ||||||||
\(225\) | −2.63718 | − | 0.560550i | −2.63718 | − | 0.560550i | ||||
\(226\) | 0.417095 | 0.417095 | ||||||||
\(227\) | 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 | ||||||||
\(232\) | −2.43274 | − | 4.21363i | −2.43274 | − | 4.21363i | ||||
\(233\) | 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 | ||||
\(240\) | 8.61130 | − | 3.83400i | 8.61130 | − | 3.83400i | ||||
\(241\) | 0.104528 | + | 0.181049i | 0.104528 | + | 0.181049i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(242\) | 1.98541 | 1.98541 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(244\) | 4.56645 | 4.56645 | ||||||||
\(245\) | −0.961262 | − | 1.66495i | −0.961262 | − | 1.66495i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.73219 | − | 3.00024i | 1.73219 | − | 3.00024i | ||||
\(249\) | 0.606126 | + | 0.440376i | 0.606126 | + | 0.440376i | ||||
\(250\) | 3.25284 | + | 5.63409i | 3.25284 | + | 5.63409i | ||||
\(251\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.76159 | − | 3.05117i | −1.76159 | − | 3.05117i | ||||
\(255\) | −0.307886 | + | 2.92934i | −0.307886 | + | 2.92934i | ||||
\(256\) | −4.21312 | + | 7.29734i | −4.21312 | + | 7.29734i | ||||
\(257\) | 0.882948 | − | 1.52931i | 0.882948 | − | 1.52931i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.20442 | + | 0.256006i | 1.20442 | + | 0.256006i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(264\) | 0.223131 | + | 0.162114i | 0.223131 | + | 0.162114i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.517565 | − | 0.896448i | −0.517565 | − | 0.896448i | ||||
\(269\) | 0.876742 | 0.876742 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(270\) | −1.18529 | + | 3.64795i | −1.18529 | + | 3.64795i | ||||
\(271\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(272\) | −3.75596 | − | 6.50552i | −3.75596 | − | 6.50552i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0940924 | + | 0.162973i | −0.0940924 | + | 0.162973i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.270928 | + | 0.833831i | 0.270928 | + | 0.833831i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.559193 | − | 0.829038i | \(-0.311111\pi\) | |||||||
\(284\) | −0.921036 | + | 1.59528i | −0.921036 | + | 1.59528i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.80182 | − | 5.54543i | −1.80182 | − | 5.54543i | ||||
\(289\) | 1.34730 | 1.34730 | ||||||||
\(290\) | −2.36148 | − | 4.09020i | −2.36148 | − | 4.09020i | ||||
\(291\) | 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 | \(0.266667\pi\) | |||||||
\(294\) | −1.82264 | + | 0.811492i | −1.82264 | + | 0.811492i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.0682737 | + | 0.0145120i | −0.0682737 | + | 0.0145120i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 7.34108 | − | 3.26846i | 7.34108 | − | 3.26846i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.94548 | 2.94548 | ||||||||
\(306\) | 2.98992 | + | 0.635526i | 2.98992 | + | 0.635526i | ||||
\(307\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.68145 | − | 2.91236i | 1.68145 | − | 2.91236i | ||||
\(311\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | 2.45665 | 2.45665 | ||||||||
\(315\) | 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 | ||||||||
\(319\) | 0.0429726 | − | 0.0744306i | 0.0429726 | − | 0.0744306i | ||||
\(320\) | −6.46944 | + | 11.2054i | −6.46944 | + | 11.2054i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 2.72286 | + | 1.21229i | 2.72286 | + | 1.21229i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.43518 | − | 2.48580i | −1.43518 | − | 2.48580i | ||||
\(327\) | 1.22256 | − | 0.544320i | 1.22256 | − | 0.544320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.216595 | + | 0.157366i | 0.216595 | + | 0.157366i | ||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −2.23306 | −2.23306 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.333843 | − | 0.578232i | −0.333843 | − | 0.578232i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.961262 | + | 1.66495i | −0.961262 | + | 1.66495i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(338\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | ||||
\(339\) | 0.0218524 | − | 0.207912i | 0.0218524 | − | 0.207912i | ||||
\(340\) | −4.38955 | − | 7.60292i | −4.38955 | − | 7.60292i | ||||
\(341\) | 0.0611957 | 0.0611957 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(348\) | −3.35271 | + | 1.49272i | −3.35271 | + | 1.49272i | ||||
\(349\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.406985 | −0.406985 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.594092 | + | 1.02900i | −0.594092 | + | 1.02900i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(360\) | −2.34751 | − | 7.22489i | −2.34751 | − | 7.22489i | ||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.104019 | − | 0.989677i | 0.104019 | − | 0.989677i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.319514 | − | 3.03997i | 0.319514 | − | 3.03997i | ||||
\(367\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.11409 | − | 1.53598i | −2.11409 | − | 1.53598i | ||||
\(373\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(374\) | 0.106678 | − | 0.184771i | 0.106678 | − | 0.184771i | ||||
\(375\) | 2.97887 | − | 1.32628i | 2.97887 | − | 1.32628i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.61323 | + | 0.718254i | −1.61323 | + | 0.718254i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(384\) | 6.14586 | + | 4.46523i | 6.14586 | + | 4.46523i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.87035 | 2.87035 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.97571 | − | 3.42203i | 1.97571 | − | 3.42203i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.69196 | + | 2.93057i | 1.69196 | + | 2.93057i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.139205 | − | 0.154603i | 0.139205 | − | 0.154603i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.60956 | + | 11.4481i | −6.60956 | + | 11.4481i | ||||
\(401\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(402\) | −0.632996 | + | 0.281828i | −0.632996 | + | 0.281828i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −4.82261 | −4.82261 | ||||||||
\(405\) | 1.75631 | + | 0.781961i | 1.75631 | + | 0.781961i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −5.53054 | + | 2.46236i | −5.53054 | + | 2.46236i | ||||
\(409\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.44038 | −1.44038 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.104528 | + | 0.181049i | 0.104528 | + | 0.181049i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(422\) | 1.49478 | 1.49478 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.06533 | − | 3.57726i | −2.06533 | − | 3.57726i | ||||
\(426\) | 0.997564 | + | 0.724773i | 0.997564 | + | 0.724773i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.43868 | −1.43868 | −0.719340 | − | 0.694658i | \(-0.755556\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(432\) | −4.79592 | + | 1.01940i | −4.79592 | + | 1.01940i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.16259 | + | 0.962846i | −2.16259 | + | 0.962846i | ||||
\(436\) | −1.99437 | + | 3.45435i | −1.99437 | + | 3.45435i | ||||
\(437\) | 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 | \(-0.533333\pi\) | |||||||
\(440\) | −0.530242 | −0.530242 | ||||||||
\(441\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.241922 | + | 0.419021i | 0.241922 | + | 0.419021i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −1.66222 | − | 5.11579i | −1.66222 | − | 5.11579i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.311551 | + | 0.539622i | 0.311551 | + | 0.539622i | ||||
\(453\) | 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 | ||||||||
\(459\) | 0.473442 | − | 1.45710i | 0.473442 | − | 1.45710i | ||||
\(460\) | 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 | \(0.666667\pi\) | |||||||
\(464\) | 3.01862 | − | 5.22841i | 3.01862 | − | 5.22841i | ||||
\(465\) | −1.36364 | − | 0.990746i | −1.36364 | − | 0.990746i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.128708 | − | 1.22458i | 0.128708 | − | 1.22458i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.99513 | −1.99513 | ||||||||
\(479\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(480\) | 9.06897 | + | 6.58899i | 9.06897 | + | 6.58899i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.208548 | + | 0.361215i | −0.208548 | + | 0.361215i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.48301 | + | 2.56864i | 1.48301 | + | 2.56864i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | ||||
\(487\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(488\) | 3.02697 | + | 5.24286i | 3.02697 | + | 5.24286i | ||||
\(489\) | −1.31430 | + | 0.585164i | −1.31430 | + | 0.585164i | ||||
\(490\) | 1.91784 | − | 3.32180i | 1.91784 | − | 3.32180i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.943248 | + | 1.63375i | 0.943248 | + | 1.63375i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.0897908 | − | 0.0997228i | 0.0897908 | − | 0.0997228i | ||||
\(496\) | 4.29872 | 4.29872 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.156247 | + | 1.48659i | −0.156247 | + | 1.48659i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −4.85944 | + | 8.41680i | −4.85944 | + | 8.41680i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.87481 | − | 3.24726i | −1.87481 | − | 3.24726i | ||||
\(503\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.11071 | −3.11071 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(508\) | 2.63166 | − | 4.55816i | 2.63166 | − | 4.55816i | ||||
\(509\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(510\) | −5.36854 | + | 2.39023i | −5.36854 | + | 2.39023i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −9.21474 | −9.21474 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.52319 | 3.52319 | ||||||||
\(515\) | 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 | \(\pi\) | |||||||||
\(522\) | 0.759146 | + | 2.33641i | 0.759146 | + | 2.33641i | ||||
\(523\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.97571 | − | 3.42203i | 1.97571 | − | 3.42203i | ||||
\(527\) | −0.671624 | + | 1.16329i | −0.671624 | + | 1.16329i | ||||
\(528\) | −0.0357726 | + | 0.340354i | −0.0357726 | + | 0.340354i | ||||
\(529\) | −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 | ||||||||
\(536\) | 0.686157 | − | 1.18846i | 0.686157 | − | 1.18846i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.874607 | + | 1.51486i | 0.874607 | + | 1.51486i | ||||
\(539\) | 0.0697990 | 0.0697990 | ||||||||
\(540\) | −5.60493 | + | 1.19137i | −5.60493 | + | 1.19137i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0.0696290 | + | 0.120601i | 0.0696290 | + | 0.120601i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.46666 | − | 7.73648i | 4.46666 | − | 7.73648i | ||||
\(545\) | −1.28642 | + | 2.22814i | −1.28642 | + | 2.22814i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.49861 | − | 0.318539i | −1.49861 | − | 0.318539i | ||||
\(550\) | −0.375453 | −0.375453 | ||||||||
\(551\) | 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 | \(\pi\) | |||||||||
\(558\) | −1.17045 | + | 1.29992i | −1.17045 | + | 1.29992i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0865149 | − | 0.0628567i | −0.0865149 | − | 0.0628567i | ||||
\(562\) | 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 | ||||||||
\(565\) | 0.200958 | + | 0.348070i | 0.200958 | + | 0.348070i | ||||
\(566\) | 3.98054 | 3.98054 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.44211 | −2.44211 | ||||||||
\(569\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(570\) | 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 | ||||||||
\(576\) | 4.50335 | − | 5.00148i | 4.50335 | − | 5.00148i | ||||
\(577\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(578\) | 1.34401 | + | 2.32790i | 1.34401 | + | 2.32790i | ||||
\(579\) | 0.150383 | − | 1.43080i | 0.150383 | − | 1.43080i | ||||
\(580\) | 3.52783 | − | 6.11039i | 3.52783 | − | 6.11039i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.23306 | −1.23306 | ||||||||
\(587\) | 0.719340 | + | 1.24593i | 0.719340 | + | 1.24593i | 0.961262 | + | 0.275637i | \(0.0888889\pi\) |
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(588\) | −2.41130 | − | 1.75192i | −2.41130 | − | 1.75192i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.54946 | − | 0.689864i | 1.54946 | − | 0.689864i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −0.0931817 | − | 0.103489i | −0.0931817 | − | 0.103489i | ||||
\(595\) | 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 | \(0.800000\pi\) | |||||||
\(600\) | 8.61880 | + | 6.26192i | 8.61880 | + | 6.26192i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.107320 | + | 0.330298i | 0.107320 | + | 0.330298i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.956579 | + | 1.65684i | 0.956579 | + | 1.65684i | ||||
\(606\) | −0.337437 | + | 3.21050i | −0.337437 | + | 3.21050i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.93830 | + | 5.08929i | 2.93830 | + | 5.08929i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.41111 | + | 4.34295i | 1.41111 | + | 4.34295i | ||||
\(613\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(614\) | 1.91784 | + | 3.32180i | 1.91784 | + | 3.32180i | ||||
\(615\) | 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 | \(0.333333\pi\) | |||||||
\(620\) | 5.02387 | 5.02387 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.74961 | 3.74961 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.78642 | + | 3.09417i | −1.78642 | + | 3.09417i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.83500 | + | 3.17832i | 1.83500 | + | 3.17832i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.0783141 | − | 0.745109i | 0.0783141 | − | 0.745109i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.69749 | − | 2.94013i | 1.69749 | − | 2.94013i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.171471 | 0.171471 | ||||||||
\(639\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | ||||
\(640\) | −14.6048 | −14.6048 | ||||||||
\(641\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.882948 | − | 1.52931i | 0.882948 | − | 1.52931i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(648\) | 0.413036 | + | 3.92978i | 0.413036 | + | 3.92978i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.14402 | − | 3.71355i | 2.14402 | − | 3.71355i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 2.16008 | + | 1.56939i | 2.16008 | + | 1.56939i | ||||
\(655\) | 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 | \(0.333333\pi\) | |||||||
\(660\) | −0.0418071 | + | 0.397768i | −0.0418071 | + | 0.397768i | ||||
\(661\) | −0.0348995 | + | 0.0604477i | −0.0348995 | + | 0.0604477i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.48023 | − | 2.56383i | −1.48023 | − | 2.56383i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.666059 | − | 1.15365i | 0.666059 | − | 1.15365i | ||||
\(671\) | −0.0534691 | + | 0.0926113i | −0.0534691 | + | 0.0926113i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −3.83568 | −3.83568 | ||||||||
\(675\) | −2.63718 | + | 0.560550i | −2.63718 | + | 0.560550i | ||||
\(676\) | 2.98054 | 2.98054 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0.381036 | − | 0.169648i | 0.381036 | − | 0.169648i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.81941 | − | 10.0795i | 5.81941 | − | 10.0795i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.0610467 | + | 0.105736i | 0.0610467 | + | 0.105736i | ||||
\(683\) | 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 | ||||||||
\(691\) | 0.939693 | + | 1.62760i | 0.939693 | + | 1.62760i | 0.766044 | + | 0.642788i | \(0.222222\pi\) |
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.74921 | −1.74921 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.93625 | − | 2.85986i | −3.93625 | − | 2.85986i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.76159 | + | 3.05117i | −1.76159 | + | 3.05117i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.234879 | − | 0.406822i | −0.234879 | − | 0.406822i | ||||
\(705\) | 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 | \(0.333333\pi\) | |||||||
\(710\) | −2.37058 | −2.37058 | ||||||||
\(711\) | 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 | ||||
\(718\) | −1.61409 | − | 2.79569i | −1.61409 | − | 2.79569i | ||||
\(719\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(720\) | 6.30739 | − | 7.00507i | 6.30739 | − | 7.00507i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | ||||
\(723\) | 0.169131 | + | 0.122881i | 0.169131 | + | 0.122881i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.65988 | − | 2.87500i | 1.65988 | − | 2.87500i | ||||
\(726\) | 1.81376 | − | 0.807538i | 1.81376 | − | 0.807538i | ||||
\(727\) | −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 | ||||||||
\(732\) | 4.17166 | − | 1.85734i | 4.17166 | − | 1.85734i | ||||
\(733\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(734\) | −0.747388 | + | 1.29451i | −0.747388 | + | 1.29451i | ||||
\(735\) | −1.55535 | − | 1.13003i | −1.55535 | − | 1.13003i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.0242409 | 0.0242409 | ||||||||
\(738\) | 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 | \(0.666667\pi\) | |||||||
\(744\) | 0.362126 | − | 3.44540i | 0.362126 | − | 3.44540i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.23306 | −1.23306 | ||||||||
\(747\) | 0.732841 | + | 0.155770i | 0.732841 | + | 0.155770i | ||||
\(748\) | 0.318733 | 0.318733 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.26321 | + | 3.82394i | 5.26321 | + | 3.82394i | ||||
\(751\) | −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 | ||||||||
\(753\) | −1.71690 | + | 0.764415i | −1.71690 | + | 0.764415i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(758\) | 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 | \(0.933333\pi\) | |||||||
\(762\) | −2.85032 | − | 2.07088i | −2.85032 | − | 2.07088i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.910202 | + | 2.80131i | 0.910202 | + | 2.80131i | ||||
\(766\) | 1.99513 | 1.99513 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.880783 | + | 8.38009i | −0.880783 | + | 8.38009i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.184586 | − | 1.75622i | 0.184586 | − | 1.75622i | ||||
\(772\) | 2.14402 | + | 3.71355i | 2.14402 | + | 3.71355i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.36378 | 2.36378 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.11566 | − | 1.93238i | 1.11566 | − | 1.93238i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0215691 | − | 0.0373587i | −0.0215691 | − | 0.0373587i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.20442 | − | 0.256006i | 1.20442 | − | 0.256006i | ||||
\(784\) | 4.90306 | 4.90306 | ||||||||
\(785\) | 1.18362 | + | 2.05010i | 1.18362 | + | 2.05010i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | −2.52764 | + | 4.37800i | −2.52764 | + | 4.37800i | ||||
\(789\) | −1.60229 | − | 1.16413i | −1.60229 | − | 1.16413i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.269778 | + | 0.0573432i | 0.269778 | + | 0.0573432i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −15.7204 | −15.7204 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.49478 | 1.49478 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.837437 | − | 0.608434i | −0.837437 | − | 0.608434i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.800944 | − | 0.356603i | 0.800944 | − | 0.356603i | ||||
\(808\) | −3.19677 | − | 5.53697i | −3.19677 | − | 5.53697i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0.400938 | + | 3.81467i | 0.400938 | + | 3.81467i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0637646 | − | 0.0283898i | 0.0637646 | − | 0.0283898i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.38295 | − | 2.39534i | 1.38295 | − | 2.39534i | ||||
\(816\) | −6.07727 | − | 4.41540i | −6.07727 | − | 4.41540i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0.965330 | 0.965330 | ||||||||
\(819\) | 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 | ||||||||
\(825\) | −0.0196707 | + | 0.187154i | −0.0196707 | + | 0.187154i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.23132 | −1.23132 | −0.615661 | − | 0.788011i | \(-0.711111\pi\) | ||||
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | −1.43687 | − | 2.48873i | −1.43687 | − | 2.48873i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.586655 | + | 0.651546i | 0.586655 | + | 0.651546i | ||||
\(838\) | −3.95142 | −3.95142 | ||||||||
\(839\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.258078 | + | 0.447004i | −0.258078 | + | 0.447004i | ||||
\(842\) | −0.208548 | + | 0.361215i | −0.208548 | + | 0.361215i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.11653 | + | 1.93388i | 1.11653 | + | 1.93388i | ||||
\(845\) | 1.92252 | 1.92252 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.208548 | − | 1.98420i | 0.208548 | − | 1.98420i | ||||
\(850\) | 4.12060 | − | 7.13708i | 4.12060 | − | 7.13708i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.192549 | + | 1.83198i | −0.192549 | + | 1.83198i | ||||
\(853\) | 0.241922 | + | 0.419021i | 0.241922 | + | 0.419021i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −0.848048 | + | 1.46886i | −0.848048 | + | 1.46886i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.43518 | − | 2.48580i | −1.43518 | − | 2.48580i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −3.90157 | − | 4.33314i | −3.90157 | − | 4.33314i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.23082 | − | 0.547995i | 1.23082 | − | 0.547995i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −3.82096 | − | 2.77609i | −3.82096 | − | 2.77609i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −5.28804 | −5.28804 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(878\) | 1.82264 | − | 3.15691i | 1.82264 | − | 3.15691i | ||||
\(879\) | −0.0646021 | + | 0.614648i | −0.0646021 | + | 0.614648i | ||||
\(880\) | −0.328971 | − | 0.569795i | −0.328971 | − | 0.569795i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −1.33500 | + | 1.48267i | −1.33500 | + | 1.48267i | ||||
\(883\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.482665 | + | 0.836001i | −0.482665 | + | 0.836001i | ||||
\(887\) | 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 | ||||||||
\(891\) | −0.0564686 | + | 0.0410268i | −0.0564686 | + | 0.0410268i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.07955 | −1.07955 | ||||||||
\(900\) | 5.37701 | − | 5.97177i | 5.37701 | − | 5.97177i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.413036 | + | 0.715400i | −0.413036 | + | 0.715400i | ||||
\(905\) | 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 | ||||||||
\(913\) | 0.0261472 | − | 0.0452882i | 0.0261472 | − | 0.0452882i | ||||
\(914\) | 0.616528 | − | 1.06786i | 0.616528 | − | 1.06786i | ||||
\(915\) | 2.69083 | − | 1.19803i | 2.69083 | − | 1.19803i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2.98992 | − | 0.635526i | 2.98992 | − | 0.635526i | ||||
\(919\) | −1.43868 | −1.43868 | −0.719340 | − | 0.694658i | \(-0.755556\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.75631 | − | 0.781961i | 1.75631 | − | 0.781961i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.17961 | 7.17961 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0.351519 | − | 3.34448i | 0.351519 | − | 3.34448i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.196449 | − | 1.86909i | 0.196449 | − | 1.86909i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.205591 | 0.205591 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 2.24426 | − | 0.999208i | 2.24426 | − | 0.999208i | ||||
\(943\) | 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 | ||||||||
\(956\) | −1.49027 | − | 2.58122i | −1.49027 | − | 2.58122i | ||||
\(957\) | 0.00898371 | − | 0.0854743i | 0.00898371 | − | 0.0854743i | ||||
\(958\) | 1.11566 | − | 1.93238i | 1.11566 | − | 1.93238i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.35248 | + | 12.8680i | −1.35248 | + | 12.8680i | ||||
\(961\) | 0.115661 | + | 0.200332i | 0.115661 | + | 0.200332i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.623102 | −0.623102 | ||||||||
\(965\) | 1.38295 | + | 2.39534i | 1.38295 | + | 2.39534i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(968\) | −1.96609 | + | 3.40536i | −1.96609 | + | 3.40536i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(972\) | 2.98054 | 2.98054 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.87481 | − | 3.24726i | −1.87481 | − | 3.24726i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.75596 | + | 6.50552i | −3.75596 | + | 6.50552i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | −2.32216 | − | 1.68715i | −2.32216 | − | 1.68715i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 5.73015 | 5.73015 | ||||||||
\(981\) | 0.895472 | − | 0.994522i | 0.895472 | − | 0.994522i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.63039 | + | 2.82392i | −1.63039 | + | 2.82392i | ||||
\(986\) | −1.88190 | + | 3.25955i | −1.88190 | + | 3.25955i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.261876 | + | 0.0556635i | 0.261876 | + | 0.0556635i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 2.55606 | + | 4.42722i | 2.55606 | + | 4.42722i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.04000 | + | 0.908266i | −2.04000 | + | 0.908266i | ||||
\(997\) | 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.238.12 | ✓ | 24 | |
9.7 | even | 3 | inner | 2151.1.f.b.1672.12 | yes | 24 | |
239.238 | odd | 2 | CM | 2151.1.f.b.238.12 | ✓ | 24 | |
2151.1672 | odd | 6 | inner | 2151.1.f.b.1672.12 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.1.f.b.238.12 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2151.1.f.b.238.12 | ✓ | 24 | 239.238 | odd | 2 | CM | |
2151.1.f.b.1672.12 | yes | 24 | 9.7 | even | 3 | inner | |
2151.1.f.b.1672.12 | yes | 24 | 2151.1672 | odd | 6 | inner |