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 | 238.5 | ||
Root | \(0.990268 - 0.139173i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.238 |
Dual form | 2151.1.f.b.1672.5 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(3\) | 0.913545 | − | 0.406737i | 0.913545 | − | 0.406737i | ||||
\(4\) | 0.115661 | − | 0.200332i | 0.115661 | − | 0.200332i | ||||
\(5\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(6\) | −0.709299 | − | 0.515336i | −0.709299 | − | 0.515336i | ||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | −1.07955 | −1.07955 | ||||||||
\(9\) | 0.669131 | − | 0.743145i | 0.669131 | − | 0.743145i | ||||
\(10\) | −0.424206 | −0.424206 | ||||||||
\(11\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.0348995 | − | 0.999391i | \(-0.488889\pi\) | |||||||
\(12\) | 0.0241798 | − | 0.230056i | 0.0241798 | − | 0.230056i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0505754 | − | 0.481193i | 0.0505754 | − | 0.481193i | ||||
\(16\) | 0.357583 | + | 0.619353i | 0.357583 | + | 0.619353i | ||||
\(17\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(18\) | −0.857583 | − | 0.182285i | −0.857583 | − | 0.182285i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −0.0559621 | − | 0.0969292i | −0.0559621 | − | 0.0969292i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.743520 | + | 1.28781i | −0.743520 | + | 1.28781i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | −0.986221 | + | 0.439094i | −0.986221 | + | 0.439094i | ||||
\(25\) | 0.382948 | + | 0.663285i | 0.382948 | + | 0.663285i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(30\) | −0.387532 | + | 0.172540i | −0.387532 | + | 0.172540i | ||||
\(31\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(32\) | −0.226268 | + | 0.391908i | −0.226268 | + | 0.391908i | ||||
\(33\) | −1.37217 | − | 0.996940i | −1.37217 | − | 0.996940i | ||||
\(34\) | −0.152245 | − | 0.263696i | −0.152245 | − | 0.263696i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0714827 | − | 0.220001i | −0.0714827 | − | 0.220001i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.261167 | + | 0.452355i | −0.261167 | + | 0.452355i | ||||
\(41\) | 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 | \(0.333333\pi\) | |||||||
\(44\) | −0.392346 | −0.392346 | ||||||||
\(45\) | −0.149516 | − | 0.460163i | −0.149516 | − | 0.460163i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 0.578582 | + | 0.420364i | 0.578582 | + | 0.420364i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0.335746 | − | 0.581530i | 0.335746 | − | 0.581530i | ||||
\(51\) | 0.317271 | − | 0.141258i | 0.317271 | − | 0.141258i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −0.857583 | + | 0.182285i | −0.857583 | + | 0.182285i | ||||
\(55\) | −0.820646 | −0.820646 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.328433 | − | 0.568863i | 0.328433 | − | 0.568863i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | −0.0905486 | − | 0.0657874i | −0.0905486 | − | 0.0657874i | ||||
\(61\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(62\) | 0.980536 | 0.980536 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.11192 | 1.11192 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.155438 | + | 1.47889i | −0.155438 | + | 1.47889i | ||||
\(67\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(68\) | 0.0401688 | − | 0.0695744i | 0.0401688 | − | 0.0695744i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(72\) | −0.722362 | + | 0.802264i | −0.722362 | + | 0.802264i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.619622 | + | 0.450182i | 0.619622 | + | 0.450182i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0.346029 | 0.346029 | ||||||||
\(81\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0840186 | − | 0.145524i | 0.0840186 | − | 0.145524i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.606126 | + | 0.440376i | 0.606126 | + | 0.440376i | ||||
\(88\) | 0.915513 | + | 1.58571i | 0.915513 | + | 1.58571i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −0.283849 | + | 0.315247i | −0.283849 | + | 0.315247i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.116903 | + | 1.11226i | −0.116903 | + | 1.11226i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.0473029 | + | 0.450057i | −0.0473029 | + | 0.450057i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | 0.876742 | 0.876742 | ||||||||
\(99\) | −1.65903 | − | 0.352638i | −1.65903 | − | 0.352638i | ||||
\(100\) | 0.177169 | 0.177169 | ||||||||
\(101\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(102\) | −0.246337 | − | 0.178974i | −0.246337 | − | 0.178974i | ||||
\(103\) | 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 | \(\pi\) | |||||||||
\(108\) | −0.154785 | − | 0.171906i | −0.154785 | − | 0.171906i | ||||
\(109\) | 1.33826 | 1.33826 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(110\) | 0.359747 | + | 0.623101i | 0.359747 | + | 0.623101i | ||||
\(111\) | 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 | ||||||||
\(116\) | 0.173310 | 0.173310 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.0545989 | + | 0.519474i | −0.0545989 | + | 0.519474i | ||||
\(121\) | −0.938371 | + | 1.62531i | −0.938371 | + | 1.62531i | ||||
\(122\) | −0.152245 | + | 0.263696i | −0.152245 | + | 0.263696i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.129354 | + | 0.224048i | 0.129354 | + | 0.224048i | ||||
\(125\) | 0.854417 | 0.854417 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(128\) | −0.261167 | − | 0.452355i | −0.261167 | − | 0.452355i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | −0.358426 | + | 0.159581i | −0.358426 | + | 0.159581i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.64774 | −1.64774 | ||||||||
\(135\) | −0.323755 | − | 0.359566i | −0.323755 | − | 0.359566i | ||||
\(136\) | −0.374925 | −0.374925 | ||||||||
\(137\) | 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 | ||||||||
\(142\) | −0.270928 | − | 0.469262i | −0.270928 | − | 0.469262i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.699539 | + | 0.148692i | 0.699539 | + | 0.148692i | ||||
\(145\) | 0.362502 | 0.362502 | ||||||||
\(146\) | 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 | \(0.666667\pi\) | |||||||
\(150\) | 0.0701901 | − | 0.667814i | 0.0701901 | − | 0.667814i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.232387 | − | 0.258091i | 0.232387 | − | 0.258091i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.270562 | + | 0.468627i | 0.270562 | + | 0.468627i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.109478 | + | 0.189622i | 0.109478 | + | 0.189622i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.709299 | + | 0.515336i | −0.709299 | + | 0.515336i | ||||
\(163\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.749697 | + | 0.333787i | −0.749697 | + | 0.333787i | ||||
\(166\) | −0.868210 | + | 1.50378i | −0.868210 | + | 1.50378i | ||||
\(167\) | 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 | ||||
\(170\) | −0.147325 | −0.147325 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0.0686613 | − | 0.653269i | 0.0686613 | − | 0.653269i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.606496 | − | 1.05048i | 0.606496 | − | 1.05048i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | −0.109478 | − | 0.0232703i | −0.109478 | − | 0.0232703i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.280969 | − | 0.204136i | −0.280969 | − | 0.204136i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.895764 | − | 0.398820i | 0.895764 | − | 0.398820i | ||||
\(187\) | −0.294524 | − | 0.510131i | −0.294524 | − | 0.510131i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 1.01579 | − | 0.452260i | 1.01579 | − | 0.452260i | ||||
\(193\) | −0.961262 | + | 1.66495i | −0.961262 | + | 1.66495i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.115661 | + | 0.200332i | 0.115661 | + | 0.200332i | ||||
\(197\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(198\) | 0.459520 | + | 1.41426i | 0.459520 | + | 1.41426i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −0.413412 | − | 0.716051i | −0.413412 | − | 0.716051i | ||||
\(201\) | 0.196449 | − | 1.86909i | 0.196449 | − | 1.86909i | ||||
\(202\) | 0.709299 | − | 1.22854i | 0.709299 | − | 1.22854i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.00839757 | − | 0.0798975i | 0.00839757 | − | 0.0798975i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.333600 | + | 1.02672i | −0.333600 | + | 1.02672i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.586655 | − | 1.01612i | −0.586655 | − | 1.01612i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0949171 | + | 0.164401i | −0.0949171 | + | 0.164401i | ||||
\(221\) | 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 | ||||||||
\(225\) | 0.749159 | + | 0.159239i | 0.749159 | + | 0.159239i | ||||
\(226\) | −0.183289 | −0.183289 | ||||||||
\(227\) | 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 | ||||||||
\(232\) | −0.404408 | − | 0.700455i | −0.404408 | − | 0.700455i | ||||
\(233\) | 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 | ||||
\(240\) | 0.316113 | − | 0.140743i | 0.316113 | − | 0.140743i | ||||
\(241\) | 0.104528 | + | 0.181049i | 0.104528 | + | 0.181049i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(242\) | 1.64542 | 1.64542 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(244\) | −0.0803376 | −0.0803376 | ||||||||
\(245\) | 0.241922 | + | 0.419021i | 0.241922 | + | 0.419021i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.603678 | − | 1.04560i | 0.603678 | − | 1.04560i | ||||
\(249\) | −1.60229 | − | 1.16413i | −1.60229 | − | 1.16413i | ||||
\(250\) | −0.374552 | − | 0.648743i | −0.374552 | − | 0.648743i | ||||
\(251\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.0305979 | − | 0.0529971i | −0.0305979 | − | 0.0529971i | ||||
\(255\) | 0.0175647 | − | 0.167117i | 0.0175647 | − | 0.167117i | ||||
\(256\) | 0.326986 | − | 0.566356i | 0.326986 | − | 0.566356i | ||||
\(257\) | −0.0348995 | + | 0.0604477i | −0.0348995 | + | 0.0604477i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.732841 | + | 0.155770i | 0.732841 | + | 0.155770i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(264\) | 1.48133 | + | 1.07625i | 1.48133 | + | 1.07625i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.217372 | − | 0.376500i | −0.217372 | − | 0.376500i | ||||
\(269\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(270\) | −0.131087 | + | 0.403444i | −0.131087 | + | 0.403444i | ||||
\(271\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(272\) | 0.124187 | + | 0.215099i | 0.124187 | + | 0.215099i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.649516 | − | 1.12499i | 0.649516 | − | 1.12499i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.345600 | + | 1.06365i | 0.345600 | + | 1.06365i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(284\) | 0.0714827 | − | 0.123812i | 0.0714827 | − | 0.123812i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.139841 | + | 0.430387i | 0.139841 | + | 0.430387i | ||||
\(289\) | −0.879385 | −0.879385 | ||||||||
\(290\) | −0.158910 | − | 0.275241i | −0.158910 | − | 0.275241i | ||||
\(291\) | 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 | \(0.266667\pi\) | |||||||
\(294\) | 0.800944 | − | 0.356603i | 0.800944 | − | 0.356603i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.65903 | + | 0.352638i | −1.65903 | + | 0.352638i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.161852 | − | 0.0720612i | 0.161852 | − | 0.0720612i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.168037 | −0.168037 | ||||||||
\(306\) | −0.297836 | − | 0.0633069i | −0.297836 | − | 0.0633069i | ||||
\(307\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.237213 | − | 0.410865i | 0.237213 | − | 0.410865i | ||||
\(311\) | −0.766044 | + | 1.32683i | −0.766044 | + | 1.32683i | 0.173648 | + | 0.984808i | \(0.444444\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | −0.656867 | −0.656867 | ||||||||
\(315\) | 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 | ||||||||
\(319\) | 0.635369 | − | 1.10049i | 0.635369 | − | 1.10049i | ||||
\(320\) | 0.268999 | − | 0.465920i | 0.268999 | − | 0.465920i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.211324 | − | 0.0940875i | −0.211324 | − | 0.0940875i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.842779 | − | 1.45974i | −0.842779 | − | 1.45974i | ||||
\(327\) | 1.22256 | − | 0.544320i | 1.22256 | − | 0.544320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.582083 | + | 0.422908i | 0.582083 | + | 0.422908i | ||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −0.458143 | −0.458143 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.454664 | − | 0.787502i | −0.454664 | − | 0.787502i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(338\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | ||||
\(339\) | 0.0218524 | − | 0.207912i | 0.0218524 | − | 0.207912i | ||||
\(340\) | −0.0194354 | − | 0.0336632i | −0.0194354 | − | 0.0336632i | ||||
\(341\) | 1.89689 | 1.89689 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(348\) | 0.158327 | − | 0.0704916i | 0.158327 | − | 0.0704916i | ||||
\(349\) | −0.0348995 | − | 0.0604477i | −0.0348995 | − | 0.0604477i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.767545 | 0.767545 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.149516 | − | 0.258969i | 0.149516 | − | 0.258969i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(360\) | 0.161410 | + | 0.496770i | 0.161410 | + | 0.496770i | ||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.196173 | + | 1.86646i | −0.196173 | + | 1.86646i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.0318278 | + | 0.302821i | −0.0318278 | + | 0.302821i | ||||
\(367\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.209299 | + | 0.152065i | 0.209299 | + | 0.152065i | ||||
\(373\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(374\) | −0.258222 | + | 0.447253i | −0.258222 | + | 0.447253i | ||||
\(375\) | 0.780549 | − | 0.347523i | 0.780549 | − | 0.347523i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0637646 | − | 0.0283898i | 0.0637646 | − | 0.0283898i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(384\) | −0.422578 | − | 0.307021i | −0.422578 | − | 0.307021i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.68556 | 1.68556 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.539776 | − | 0.934920i | 0.539776 | − | 0.934920i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.774117 | + | 1.34081i | 0.774117 | + | 1.34081i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.262531 | + | 0.291570i | −0.262531 | + | 0.291570i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.273871 | + | 0.474359i | −0.273871 | + | 0.474359i | ||||
\(401\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(402\) | −1.50528 | + | 0.670195i | −1.50528 | + | 0.670195i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.374288 | 0.374288 | ||||||||
\(405\) | −0.442013 | − | 0.196797i | −0.442013 | − | 0.196797i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.342511 | + | 0.152496i | −0.342511 | + | 0.152496i | ||||
\(409\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.958270 | −0.958270 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
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 | \(0.800000\pi\) | |||||||
\(422\) | 1.73642 | 1.73642 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.132996 | + | 0.230356i | 0.132996 | + | 0.230356i | ||||
\(426\) | −0.438371 | − | 0.318495i | −0.438371 | − | 0.318495i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(432\) | 0.699539 | − | 0.148692i | 0.699539 | − | 0.148692i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.331162 | − | 0.147443i | 0.331162 | − | 0.147443i | ||||
\(436\) | 0.154785 | − | 0.268096i | 0.154785 | − | 0.268096i | ||||
\(437\) | 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 | \(-0.533333\pi\) | |||||||
\(440\) | 0.885930 | 0.885930 | ||||||||
\(441\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.719340 | + | 1.24593i | 0.719340 | + | 1.24593i | 0.961262 | + | 0.275637i | \(0.0888889\pi\) |
−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 | \(\pi\) | |||||||||
\(450\) | −0.207503 | − | 0.638628i | −0.207503 | − | 0.638628i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.0241798 | − | 0.0418807i | −0.0241798 | − | 0.0418807i | ||||
\(453\) | 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 | ||||||||
\(459\) | 0.107320 | − | 0.330298i | 0.107320 | − | 0.330298i | ||||
\(460\) | 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 | \(0.666667\pi\) | |||||||
\(464\) | −0.267906 | + | 0.464027i | −0.267906 | + | 0.464027i | ||||
\(465\) | 0.437779 | + | 0.318065i | 0.437779 | + | 0.318065i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0783141 | − | 0.745109i | 0.0783141 | − | 0.745109i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.876742 | 0.876742 | ||||||||
\(479\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(480\) | 0.177140 | + | 0.128700i | 0.177140 | + | 0.128700i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.0916445 | − | 0.158733i | 0.0916445 | − | 0.158733i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.217067 | + | 0.375971i | 0.217067 | + | 0.375971i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | ||||
\(487\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(488\) | 0.187462 | + | 0.324694i | 0.187462 | + | 0.324694i | ||||
\(489\) | 1.75631 | − | 0.781961i | 1.75631 | − | 0.781961i | ||||
\(490\) | 0.212103 | − | 0.367373i | 0.212103 | − | 0.367373i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.130100 | + | 0.225339i | 0.130100 | + | 0.225339i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.549119 | + | 0.609859i | −0.549119 | + | 0.609859i | ||||
\(496\) | −0.799832 | −0.799832 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.181505 | + | 1.72691i | −0.181505 | + | 1.72691i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | 0.0988232 | − | 0.171167i | 0.0988232 | − | 0.171167i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.671624 | − | 1.16329i | −0.671624 | − | 1.16329i | ||||
\(503\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.782876 | 0.782876 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(508\) | 0.00807305 | − | 0.0139829i | 0.00807305 | − | 0.0139829i | ||||
\(509\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(510\) | −0.134588 | + | 0.0599226i | −0.134588 | + | 0.0599226i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.09570 | −1.09570 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.0611957 | 0.0611957 | ||||||||
\(515\) | 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 | \(\pi\) | |||||||||
\(522\) | −0.202983 | − | 0.624718i | −0.202983 | − | 0.624718i | ||||
\(523\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.539776 | − | 0.934920i | 0.539776 | − | 0.934920i | ||||
\(527\) | −0.194206 | + | 0.336374i | −0.194206 | + | 0.336374i | ||||
\(528\) | 0.126792 | − | 1.20635i | 0.126792 | − | 1.20635i | ||||
\(529\) | −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 | ||||||||
\(536\) | −1.01445 | + | 1.75708i | −1.01445 | + | 1.75708i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.490268 | − | 0.849169i | −0.490268 | − | 0.849169i | ||||
\(539\) | 1.69610 | 1.69610 | ||||||||
\(540\) | −0.109478 | + | 0.0232703i | −0.109478 | + | 0.0232703i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | −0.743520 | − | 1.28781i | −0.743520 | − | 1.28781i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.0785820 | + | 0.136108i | −0.0785820 | + | 0.136108i | ||||
\(545\) | 0.323755 | − | 0.560760i | 0.323755 | − | 0.560760i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.339707 | − | 0.0722070i | −0.339707 | − | 0.0722070i | ||||
\(550\) | −1.13892 | −1.13892 | ||||||||
\(551\) | 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 | \(\pi\) | |||||||||
\(558\) | 0.656107 | − | 0.728680i | 0.656107 | − | 0.728680i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.476550 | − | 0.346234i | −0.476550 | − | 0.346234i | ||||
\(562\) | 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 | ||||||||
\(565\) | −0.0505754 | − | 0.0875992i | −0.0505754 | − | 0.0875992i | ||||
\(566\) | 0.768677 | 0.768677 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.667200 | −0.667200 | ||||||||
\(569\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
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 | ||||||||
\(576\) | 0.744022 | − | 0.826321i | 0.744022 | − | 0.826321i | ||||
\(577\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(578\) | 0.385497 | + | 0.667701i | 0.385497 | + | 0.667701i | ||||
\(579\) | −0.200958 | + | 1.91199i | −0.200958 | + | 1.91199i | ||||
\(580\) | 0.0419275 | − | 0.0726206i | 0.0419275 | − | 0.0726206i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.541857 | 0.541857 | ||||||||
\(587\) | −0.961262 | − | 1.66495i | −0.961262 | − | 1.66495i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
−0.241922 | − | 0.970296i | \(-0.577778\pi\) | |||||||
\(588\) | 0.187144 | + | 0.135968i | 0.187144 | + | 0.135968i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.61323 | + | 0.718254i | −1.61323 | + | 0.718254i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.995023 | + | 1.10509i | 0.995023 | + | 1.10509i | ||||
\(595\) | 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 | \(0.800000\pi\) | |||||||
\(600\) | −0.668915 | − | 0.485995i | −0.668915 | − | 0.485995i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.580762 | − | 1.78740i | −0.580762 | − | 1.78740i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.454025 | + | 0.786394i | 0.454025 | + | 0.786394i | ||||
\(606\) | 0.148284 | − | 1.41083i | 0.148284 | − | 1.41083i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.0736627 | + | 0.127587i | 0.0736627 | + | 0.127587i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.0248257 | − | 0.0764056i | −0.0248257 | − | 0.0764056i | ||||
\(613\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(614\) | 0.212103 | + | 0.367373i | 0.212103 | + | 0.367373i | ||||
\(615\) | 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 | \(0.333333\pi\) | |||||||
\(620\) | 0.125174 | 0.125174 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.34325 | 1.34325 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.176245 | + | 0.305266i | −0.176245 | + | 0.305266i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.0866551 | − | 0.150091i | −0.0866551 | − | 0.150091i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.207022 | + | 1.96969i | −0.207022 | + | 1.96969i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0168859 | − | 0.0292472i | 0.0168859 | − | 0.0292472i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.11411 | −1.11411 | ||||||||
\(639\) | 0.413545 | − | 0.459289i | 0.413545 | − | 0.459289i | ||||
\(640\) | −0.252729 | −0.252729 | ||||||||
\(641\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.0348995 | + | 0.0604477i | −0.0348995 | + | 0.0604477i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(648\) | 0.112844 | + | 1.07364i | 0.112844 | + | 1.07364i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.222362 | − | 0.385142i | 0.222362 | − | 0.385142i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | −0.949228 | − | 0.689654i | −0.949228 | − | 0.689654i | ||||
\(655\) | 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 | \(0.333333\pi\) | |||||||
\(660\) | −0.0198431 | + | 0.188794i | −0.0198431 | + | 0.188794i | ||||
\(661\) | −0.848048 | + | 1.46886i | −0.848048 | + | 1.46886i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.06905 | + | 1.85164i | 1.06905 | + | 1.85164i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.398624 | + | 0.690436i | −0.398624 | + | 0.690436i | ||||
\(671\) | −0.294524 | + | 0.510131i | −0.294524 | + | 0.510131i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | −0.424206 | −0.424206 | ||||||||
\(675\) | 0.749159 | − | 0.159239i | 0.749159 | − | 0.159239i | ||||
\(676\) | −0.231323 | −0.231323 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | −0.167443 | + | 0.0745504i | −0.167443 | + | 0.0745504i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.0907025 | + | 0.157101i | −0.0907025 | + | 0.157101i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.831542 | − | 1.44027i | −0.831542 | − | 1.44027i | ||||
\(683\) | 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 | ||||||||
\(691\) | −0.766044 | − | 1.32683i | −0.766044 | − | 1.32683i | −0.939693 | − | 0.342020i | \(-0.888889\pi\) |
0.173648 | − | 0.984808i | \(-0.444444\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.980536 | 0.980536 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.654345 | − | 0.475410i | −0.654345 | − | 0.475410i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −0.0305979 | + | 0.0529971i | −0.0305979 | + | 0.0529971i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.942965 | − | 1.63326i | −0.942965 | − | 1.63326i | ||||
\(705\) | 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 | \(0.333333\pi\) | |||||||
\(710\) | −0.262174 | −0.262174 | ||||||||
\(711\) | 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 | ||||
\(718\) | 0.709299 | + | 1.22854i | 0.709299 | + | 1.22854i | ||||
\(719\) | −1.43868 | −1.43868 | −0.719340 | − | 0.694658i | \(-0.755556\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(720\) | 0.231539 | − | 0.257150i | 0.231539 | − | 0.257150i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | ||||
\(723\) | 0.169131 | + | 0.122881i | 0.169131 | + | 0.122881i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.286909 | + | 0.496942i | −0.286909 | + | 0.496942i | ||||
\(726\) | 1.50317 | − | 0.669252i | 1.50317 | − | 0.669252i | ||||
\(727\) | −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 | ||||||||
\(732\) | −0.0733921 | + | 0.0326763i | −0.0733921 | + | 0.0326763i | ||||
\(733\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(734\) | −0.868210 | + | 1.50378i | −0.868210 | + | 1.50378i | ||||
\(735\) | 0.391438 | + | 0.284396i | 0.391438 | + | 0.284396i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.18762 | −3.18762 | ||||||||
\(738\) | 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 | \(0.666667\pi\) | |||||||
\(744\) | 0.126203 | − | 1.20074i | 0.126203 | − | 1.20074i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.541857 | 0.541857 | ||||||||
\(747\) | −1.93726 | − | 0.411777i | −1.93726 | − | 0.411777i | ||||
\(748\) | −0.136260 | −0.136260 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.606038 | − | 0.440312i | −0.606038 | − | 0.440312i | ||||
\(751\) | −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 | ||||||||
\(753\) | 1.39963 | − | 0.623157i | 1.39963 | − | 0.623157i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.876742 | 0.876742 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(758\) | 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 | \(0.933333\pi\) | |||||||
\(762\) | −0.0495084 | − | 0.0359699i | −0.0495084 | − | 0.0359699i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0519263 | − | 0.159813i | −0.0519263 | − | 0.159813i | ||||
\(766\) | −0.876742 | −0.876742 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.0683586 | − | 0.650388i | 0.0683586 | − | 0.650388i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.00729598 | + | 0.0694166i | −0.00729598 | + | 0.0694166i | ||||
\(772\) | 0.222362 | + | 0.385142i | 0.222362 | + | 0.385142i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.856566 | −0.856566 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.874607 | − | 1.51486i | 0.874607 | − | 1.51486i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.524123 | − | 0.907807i | −0.524123 | − | 0.907807i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.732841 | − | 0.155770i | 0.732841 | − | 0.155770i | ||||
\(784\) | −0.715167 | −0.715167 | ||||||||
\(785\) | −0.181251 | − | 0.313936i | −0.181251 | − | 0.313936i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | −0.204246 | + | 0.353765i | −0.204246 | + | 0.353765i | ||||
\(789\) | 0.996161 | + | 0.723753i | 0.996161 | + | 0.723753i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.79101 | + | 0.380692i | 1.79101 | + | 0.380692i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.559193 | − | 0.829038i | \(-0.311111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.346595 | −0.346595 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.73642 | 1.73642 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.351716 | − | 0.255537i | −0.351716 | − | 0.255537i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.02170 | − | 0.454888i | 1.02170 | − | 0.454888i | ||||
\(808\) | −0.873377 | − | 1.51273i | −0.873377 | − | 1.51273i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | 0.0443416 | + | 0.421882i | 0.0443416 | + | 0.421882i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.54946 | − | 0.689864i | 1.54946 | − | 0.689864i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.465101 | − | 0.805578i | 0.465101 | − | 0.805578i | ||||
\(816\) | 0.200939 | + | 0.145991i | 0.200939 | + | 0.145991i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.26135 | −1.26135 | ||||||||
\(819\) | 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 | ||||||||
\(825\) | 0.135786 | − | 1.29192i | 0.135786 | − | 1.29192i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.749213 | −0.749213 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0.420078 | + | 0.727596i | 0.420078 | + | 0.727596i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.748346 | + | 0.831123i | 0.748346 | + | 0.831123i | ||||
\(838\) | −1.07955 | −1.07955 | ||||||||
\(839\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.219340 | − | 0.379908i | 0.219340 | − | 0.379908i | ||||
\(842\) | 0.0916445 | − | 0.158733i | 0.0916445 | − | 0.158733i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.229072 | + | 0.396764i | 0.229072 | + | 0.396764i | ||||
\(845\) | −0.483844 | −0.483844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.0916445 | + | 0.871939i | −0.0916445 | + | 0.871939i | ||||
\(850\) | 0.116603 | − | 0.201963i | 0.116603 | − | 0.201963i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0.0149440 | − | 0.142182i | 0.0149440 | − | 0.142182i | ||||
\(853\) | 0.719340 | + | 1.24593i | 0.719340 | + | 1.24593i | 0.961262 | + | 0.275637i | \(0.0888889\pi\) |
−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 | ||||||||
\(859\) | 0.882948 | − | 1.52931i | 0.882948 | − | 1.52931i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.842779 | − | 1.45974i | −0.842779 | − | 1.45974i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0.302806 | + | 0.336300i | 0.302806 | + | 0.336300i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.803358 | + | 0.357678i | −0.803358 | + | 0.357678i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.257123 | − | 0.186810i | −0.257123 | − | 0.186810i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.44472 | −1.44472 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(878\) | −0.800944 | + | 1.38728i | −0.800944 | + | 1.38728i | ||||
\(879\) | −0.0646021 | + | 0.614648i | −0.0646021 | + | 0.614648i | ||||
\(880\) | −0.293449 | − | 0.508269i | −0.293449 | − | 0.508269i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0.586655 | − | 0.651546i | 0.586655 | − | 0.651546i | ||||
\(883\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.630676 | − | 1.09236i | 0.630676 | − | 1.09236i | ||||
\(887\) | 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 | ||||||||
\(891\) | −1.37217 | + | 0.996940i | −1.37217 | + | 0.996940i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.837909 | −0.837909 | ||||||||
\(900\) | 0.118549 | − | 0.131662i | 0.118549 | − | 0.131662i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.112844 | + | 0.195452i | −0.112844 | + | 0.195452i | ||||
\(905\) | 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 | ||||||||
\(913\) | −1.67959 | + | 2.90914i | −1.67959 | + | 2.90914i | ||||
\(914\) | −0.270928 | + | 0.469262i | −0.270928 | + | 0.469262i | ||||
\(915\) | −0.153510 | + | 0.0683469i | −0.153510 | + | 0.0683469i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.297836 | + | 0.0633069i | −0.297836 | + | 0.0633069i | ||||
\(919\) | 1.92252 | 1.92252 | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) | ||||
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.442013 | + | 0.196797i | −0.442013 | + | 0.196797i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.339046 | −0.339046 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0.0495911 | − | 0.471827i | 0.0495911 | − | 0.471827i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.160147 | + | 1.52370i | −0.160147 | + | 1.52370i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.285007 | −0.285007 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | −0.600078 | + | 0.267172i | −0.600078 | + | 0.267172i | ||||
\(943\) | 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 | ||||||||
\(956\) | 0.115661 | + | 0.200332i | 0.115661 | + | 0.200332i | ||||
\(957\) | 0.132828 | − | 1.26378i | 0.132828 | − | 1.26378i | ||||
\(958\) | 0.874607 | − | 1.51486i | 0.874607 | − | 1.51486i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0562361 | − | 0.535050i | 0.0562361 | − | 0.535050i | ||||
\(961\) | −0.125393 | − | 0.217188i | −0.125393 | − | 0.217188i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.0483597 | 0.0483597 | ||||||||
\(965\) | 0.465101 | + | 0.805578i | 0.465101 | + | 0.805578i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(968\) | 1.01302 | − | 1.75460i | 1.01302 | − | 1.75460i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.43868 | −1.43868 | −0.719340 | − | 0.694658i | \(-0.755556\pi\) | ||||
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(972\) | −0.231323 | −0.231323 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.671624 | − | 1.16329i | −0.671624 | − | 1.16329i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.124187 | − | 0.215099i | 0.124187 | − | 0.215099i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | −1.36364 | − | 0.990746i | −1.36364 | − | 0.990746i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.111924 | 0.111924 | ||||||||
\(981\) | 0.895472 | − | 0.994522i | 0.895472 | − | 0.994522i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.0348995 | − | 0.0604477i | −0.0348995 | − | 0.0604477i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.427209 | + | 0.739947i | −0.427209 | + | 0.739947i | ||||
\(986\) | 0.114064 | − | 0.197564i | 0.114064 | − | 0.197564i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.703772 | + | 0.149591i | 0.703772 | + | 0.149591i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −0.253055 | − | 0.438304i | −0.253055 | − | 0.438304i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.418535 | + | 0.186344i | −0.418535 | + | 0.186344i | ||||
\(997\) | 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.238.5 | ✓ | 24 | |
9.7 | even | 3 | inner | 2151.1.f.b.1672.5 | yes | 24 | |
239.238 | odd | 2 | CM | 2151.1.f.b.238.5 | ✓ | 24 | |
2151.1672 | odd | 6 | inner | 2151.1.f.b.1672.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.1.f.b.238.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2151.1.f.b.238.5 | ✓ | 24 | 239.238 | odd | 2 | CM | |
2151.1.f.b.1672.5 | yes | 24 | 9.7 | even | 3 | inner | |
2151.1.f.b.1672.5 | yes | 24 | 2151.1672 | odd | 6 | inner |