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 | 238.1 | ||
Root | \(-0.719340 + 0.694658i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.238 |
Dual form | 2151.1.f.b.1672.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times\).
\(n\) | \(479\) | \(1441\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
−0.374607 | − | 0.927184i | \(-0.622222\pi\) | |||||||
\(3\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(4\) | −1.46126 | + | 2.53098i | −1.46126 | + | 2.53098i | ||||
\(5\) | −0.848048 | + | 1.46886i | −0.848048 | + | 1.46886i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(6\) | 0.612019 | − | 1.88360i | 0.612019 | − | 1.88360i | ||||
\(7\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | 3.80763 | 3.80763 | ||||||||
\(9\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(10\) | 3.35918 | 3.35918 | ||||||||
\(11\) | 0.997564 | + | 1.72783i | 0.997564 | + | 1.72783i | 0.559193 | + | 0.829038i | \(0.311111\pi\) |
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(12\) | −2.85866 | + | 0.607627i | −2.85866 | + | 0.607627i | ||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.65903 | + | 0.352638i | −1.65903 | + | 0.352638i | ||||
\(16\) | −2.30931 | − | 3.99984i | −2.30931 | − | 3.99984i | ||||
\(17\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(18\) | 1.80931 | − | 0.805557i | 1.80931 | − | 0.805557i | ||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | −2.47844 | − | 4.29278i | −2.47844 | − | 4.29278i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.97571 | − | 3.42203i | 1.97571 | − | 3.42203i | ||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 2.54780 | + | 2.82962i | 2.54780 | + | 2.82962i | ||||
\(25\) | −0.938371 | − | 1.62531i | −0.938371 | − | 1.62531i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.241922 | + | 0.419021i | 0.241922 | + | 0.419021i | 0.961262 | − | 0.275637i | \(-0.0888889\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(30\) | 2.24773 | + | 2.49636i | 2.24773 | + | 2.49636i | ||||
\(31\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(32\) | −2.66986 | + | 4.62433i | −2.66986 | + | 4.62433i | ||||
\(33\) | −0.616528 | + | 1.89748i | −0.616528 | + | 1.89748i | ||||
\(34\) | −0.343916 | − | 0.595681i | −0.343916 | − | 0.595681i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.36437 | − | 1.71782i | −2.36437 | − | 1.71782i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.22905 | + | 5.59288i | −3.22905 | + | 5.59288i | ||||
\(41\) | 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 | \(0.333333\pi\) | |||||||
\(44\) | −5.83081 | −5.83081 | ||||||||
\(45\) | −1.37217 | − | 0.996940i | −1.37217 | − | 0.996940i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | 1.42723 | − | 4.39257i | 1.42723 | − | 4.39257i | ||||
\(49\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(50\) | −1.85848 | + | 3.21898i | −1.85848 | + | 3.21898i | ||||
\(51\) | 0.232387 | + | 0.258091i | 0.232387 | + | 0.258091i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 1.80931 | + | 0.805557i | 1.80931 | + | 0.805557i | ||||
\(55\) | −3.38393 | −3.38393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.479135 | − | 0.829886i | 0.479135 | − | 0.829886i | ||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 1.53176 | − | 4.71427i | 1.53176 | − | 4.71427i | ||||
\(61\) | −0.173648 | − | 0.300767i | −0.173648 | − | 0.300767i | 0.766044 | − | 0.642788i | \(-0.222222\pi\) |
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(62\) | −2.43868 | −2.43868 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.95688 | 5.95688 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.86508 | − | 0.821547i | 3.86508 | − | 0.821547i | ||||
\(67\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(68\) | −0.507491 | + | 0.879000i | −0.507491 | + | 0.879000i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(72\) | −0.398005 | + | 3.78677i | −0.398005 | + | 3.78677i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.579945 | − | 1.78489i | 0.579945 | − | 1.78489i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 7.83362 | 7.83362 | ||||||||
\(81\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.719340 | + | 1.24593i | 0.719340 | + | 1.24593i | 0.961262 | + | 0.275637i | \(0.0888889\pi\) |
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.294524 | + | 0.510131i | −0.294524 | + | 0.510131i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.149516 | + | 0.460163i | −0.149516 | + | 0.460163i | ||||
\(88\) | 3.79835 | + | 6.57894i | 3.79835 | + | 6.57894i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | −0.351130 | + | 3.34078i | −0.351130 | + | 3.34078i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.20442 | − | 0.256006i | 1.20442 | − | 0.256006i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.22303 | + | 1.11019i | −5.22303 | + | 1.11019i | ||||
\(97\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(98\) | 1.98054 | 1.98054 | ||||||||
\(99\) | −1.82264 | + | 0.811492i | −1.82264 | + | 0.811492i | ||||
\(100\) | 5.48482 | 5.48482 | ||||||||
\(101\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(102\) | 0.212552 | − | 0.654168i | 0.212552 | − | 0.654168i | ||||
\(103\) | 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 | \(\pi\) | |||||||||
\(108\) | −0.305487 | − | 2.90651i | −0.305487 | − | 2.90651i | ||||
\(109\) | −0.209057 | −0.209057 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(110\) | 3.35100 | + | 5.80410i | 3.35100 | + | 5.80410i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.41404 | −1.41404 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −6.31698 | + | 1.34271i | −6.31698 | + | 1.34271i | ||||
\(121\) | −1.49027 | + | 2.58122i | −1.49027 | + | 2.58122i | ||||
\(122\) | −0.343916 | + | 0.595681i | −0.343916 | + | 0.595681i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.79929 | + | 3.11645i | 1.79929 | + | 3.11645i | ||||
\(125\) | 1.48704 | 1.48704 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.11839 | 1.11839 | 0.559193 | − | 0.829038i | \(-0.311111\pi\) | ||||
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(128\) | −3.22905 | − | 5.59288i | −3.22905 | − | 5.59288i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(132\) | −3.90157 | − | 4.33314i | −3.90157 | − | 4.33314i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.72219 | −3.72219 | ||||||||
\(135\) | −0.177290 | − | 1.68680i | −0.177290 | − | 1.68680i | ||||
\(136\) | 1.32237 | 1.32237 | ||||||||
\(137\) | 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 | ||||||||
\(142\) | 1.60229 | + | 2.77524i | 1.60229 | + | 2.77524i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.21932 | − | 1.87856i | 4.21932 | − | 1.87856i | ||||
\(145\) | −0.820646 | −0.820646 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | −3.63573 | + | 0.772799i | −3.63573 | + | 0.772799i | ||||
\(151\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0363024 | + | 0.345394i | −0.0363024 | + | 0.345394i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.04422 | + | 1.80864i | 1.04422 | + | 1.80864i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.241922 | − | 0.419021i | 0.241922 | − | 0.419021i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
0.961262 | + | 0.275637i | \(0.0888889\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.52834 | − | 7.84331i | −4.52834 | − | 7.84331i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.612019 | + | 1.88360i | 0.612019 | + | 1.88360i | ||||
\(163\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.26429 | − | 2.51475i | −2.26429 | − | 2.51475i | ||||
\(166\) | 1.42468 | − | 2.46762i | 1.42468 | − | 2.46762i | ||||
\(167\) | 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 | ||||
\(170\) | 1.16663 | 1.16663 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0.937330 | − | 0.199236i | 0.937330 | − | 0.199236i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.60737 | − | 7.98020i | 4.60737 | − | 7.98020i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 4.52834 | − | 2.01615i | 4.52834 | − | 2.01615i | ||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.107320 | − | 0.330298i | 0.107320 | − | 0.330298i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.63180 | − | 1.81229i | −1.63180 | − | 1.81229i | ||||
\(187\) | 0.346450 | + | 0.600070i | 0.346450 | + | 0.600070i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 3.98593 | + | 4.42683i | 3.98593 | + | 4.42683i | ||||
\(193\) | −0.0348995 | + | 0.0604477i | −0.0348995 | + | 0.0604477i | −0.882948 | − | 0.469472i | \(-0.844444\pi\) |
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.46126 | − | 2.53098i | −1.46126 | − | 2.53098i | ||||
\(197\) | 0.876742 | 0.876742 | 0.438371 | − | 0.898794i | \(-0.355556\pi\) | ||||
0.438371 | + | 0.898794i | \(0.355556\pi\) | |||||||
\(198\) | 3.19677 | + | 2.32259i | 3.19677 | + | 2.32259i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −3.57297 | − | 6.18856i | −3.57297 | − | 6.18856i | ||||
\(201\) | 1.83832 | − | 0.390746i | 1.83832 | − | 0.390746i | ||||
\(202\) | −0.612019 | + | 1.06005i | −0.612019 | + | 1.06005i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.992802 | + | 0.211027i | −0.992802 | + | 0.211027i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.08268 | − | 1.20243i | −1.08268 | − | 1.20243i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.08043 | + | 2.23807i | −3.08043 | + | 2.23807i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.207022 | + | 0.358573i | 0.207022 | + | 0.358573i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.94481 | − | 8.56466i | 4.94481 | − | 8.56466i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.71449 | − | 0.763340i | 1.71449 | − | 0.763340i | ||||
\(226\) | −3.87451 | −3.87451 | ||||||||
\(227\) | 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 | ||||||||
\(232\) | 0.921148 | + | 1.59548i | 0.921148 | + | 1.59548i | ||||
\(233\) | 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 | ||||
\(240\) | 5.24172 | + | 5.82152i | 5.24172 | + | 5.82152i | ||||
\(241\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(242\) | 5.90306 | 5.90306 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(244\) | 1.01498 | 1.01498 | ||||||||
\(245\) | −0.848048 | − | 1.46886i | −0.848048 | − | 1.46886i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.34421 | − | 4.06029i | 2.34421 | − | 4.06029i | ||||
\(249\) | −0.444576 | + | 1.36827i | −0.444576 | + | 1.36827i | ||||
\(250\) | −1.47257 | − | 2.55056i | −1.47257 | − | 2.55056i | ||||
\(251\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.10750 | − | 1.91825i | −1.10750 | − | 1.91825i | ||||
\(255\) | −0.576176 | + | 0.122470i | −0.576176 | + | 0.122470i | ||||
\(256\) | −3.41681 | + | 5.91809i | −3.41681 | + | 5.91809i | ||||
\(257\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.442013 | + | 0.196797i | −0.442013 | + | 0.196797i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.961262 | − | 1.66495i | −0.961262 | − | 1.66495i | −0.719340 | − | 0.694658i | \(-0.755556\pi\) |
−0.241922 | − | 0.970296i | \(-0.577778\pi\) | |||||||
\(264\) | −2.34751 | + | 7.22489i | −2.34751 | + | 7.22489i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.74627 | + | 4.75669i | 2.74627 | + | 4.75669i | ||||
\(269\) | −1.23132 | −1.23132 | −0.615661 | − | 0.788011i | \(-0.711111\pi\) | ||||
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(270\) | −2.71763 | + | 1.97448i | −2.71763 | + | 1.97448i | ||||
\(271\) | −1.99513 | −1.99513 | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) | ||||
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(272\) | −0.802015 | − | 1.38913i | −0.802015 | − | 1.38913i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.87217 | − | 3.24269i | 1.87217 | − | 3.24269i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.996161 | + | 0.723753i | 0.996161 | + | 0.723753i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | −0.374607 | + | 0.927184i | \(0.622222\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(284\) | 2.36437 | − | 4.09521i | 2.36437 | − | 4.09521i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.31992 | − | 3.13861i | −4.31992 | − | 3.13861i | ||||
\(289\) | −0.879385 | −0.879385 | ||||||||
\(290\) | 0.812659 | + | 1.40757i | 0.812659 | + | 1.40757i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(294\) | 1.32524 | + | 1.47183i | 1.32524 | + | 1.47183i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.82264 | − | 0.811492i | −1.82264 | − | 0.811492i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 3.67006 | + | 4.07602i | 3.67006 | + | 4.07602i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.589048 | 0.589048 | ||||||||
\(306\) | 0.628367 | − | 0.279767i | 0.628367 | − | 0.279767i | ||||
\(307\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.06812 | − | 3.58208i | 2.06812 | − | 3.58208i | ||||
\(311\) | −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 | \(0.333333\pi\) | |||||||
\(314\) | −0.958270 | −0.958270 | ||||||||
\(315\) | 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 | ||||||||
\(319\) | −0.482665 | + | 0.836001i | −0.482665 | + | 0.836001i | ||||
\(320\) | −5.05172 | + | 8.74984i | −5.05172 | + | 8.74984i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.95555 | − | 2.17186i | 1.95555 | − | 2.17186i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0691197 | − | 0.119719i | −0.0691197 | − | 0.119719i | ||||
\(327\) | −0.139886 | − | 0.155360i | −0.139886 | − | 0.155360i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.07103 | + | 6.37398i | −2.07103 | + | 6.37398i | ||||
\(331\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(332\) | −4.20457 | −4.20457 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.59381 | + | 2.76056i | 1.59381 | + | 2.76056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.848048 | + | 1.46886i | −0.848048 | + | 1.46886i | 0.0348995 | + | 0.999391i | \(0.488889\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(338\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | ||||
\(339\) | 1.91355 | − | 0.406737i | 1.91355 | − | 0.406737i | ||||
\(340\) | −0.860753 | − | 1.49087i | −0.860753 | − | 1.49087i | ||||
\(341\) | 2.45665 | 2.45665 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(348\) | −0.946181 | − | 1.05084i | −0.946181 | − | 1.05084i | ||||
\(349\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.6534 | −10.6534 | ||||||||
\(353\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.37217 | − | 2.37667i | 1.37217 | − | 2.37667i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(360\) | −5.22471 | − | 3.79598i | −5.22471 | − | 3.79598i | ||||
\(361\) | 1.00000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.91540 | + | 0.619688i | −2.91540 | + | 0.619688i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.672802 | + | 0.143009i | −0.672802 | + | 0.143009i | ||||
\(367\) | 0.719340 | + | 1.24593i | 0.719340 | + | 1.24593i | 0.961262 | + | 0.275637i | \(0.0888889\pi\) |
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.11202 | + | 3.42244i | −1.11202 | + | 3.42244i | ||||
\(373\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(374\) | 0.686157 | − | 1.18846i | 0.686157 | − | 1.18846i | ||||
\(375\) | 0.995023 | + | 1.10509i | 0.995023 | + | 1.10509i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.748346 | + | 0.831123i | 0.748346 | + | 0.831123i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(384\) | 1.99566 | − | 6.14202i | 1.99566 | − | 6.14202i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.138239 | 0.138239 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −1.90381 | + | 3.29750i | −1.90381 | + | 3.29750i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.868210 | − | 1.50378i | −0.868210 | − | 1.50378i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.609485 | − | 5.79887i | 0.609485 | − | 5.79887i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.33398 | + | 7.50667i | −4.33398 | + | 7.50667i | ||||
\(401\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(402\) | −2.49063 | − | 2.76613i | −2.49063 | − | 2.76613i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.80622 | 1.80622 | ||||||||
\(405\) | 1.13491 | − | 1.26045i | 1.13491 | − | 1.26045i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.884842 | + | 0.982716i | 0.884842 | + | 0.982716i | ||||
\(409\) | 0.882948 | − | 1.52931i | 0.882948 | − | 1.52931i | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) |
0.848048 | − | 0.529919i | \(-0.177778\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.44014 | −2.44014 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.961262 | + | 1.66495i | −0.961262 | + | 1.66495i | −0.241922 | + | 0.970296i | \(0.577778\pi\) |
−0.719340 | + | 0.694658i | \(0.755556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(422\) | −2.84936 | −2.84936 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.325893 | − | 0.564463i | −0.325893 | − | 0.564463i | ||||
\(426\) | −0.990268 | + | 3.04773i | −0.990268 | + | 3.04773i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(432\) | 4.21932 | + | 1.87856i | 4.21932 | + | 1.87856i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.549119 | − | 0.609859i | −0.549119 | − | 0.609859i | ||||
\(436\) | 0.305487 | − | 0.529119i | 0.305487 | − | 0.529119i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.669131 | − | 1.15897i | −0.669131 | − | 1.15897i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(440\) | −12.8847 | −12.8847 | ||||||||
\(441\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | −3.00708 | − | 2.18477i | −3.00708 | − | 2.18477i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 2.85866 | + | 4.95134i | 2.85866 | + | 4.95134i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.280969 | + | 0.204136i | −0.280969 | + | 0.204136i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(464\) | 1.11735 | − | 1.93530i | 1.11735 | − | 1.93530i | ||||
\(465\) | −0.645364 | + | 1.98623i | −0.645364 | + | 1.98623i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.473271 | − | 0.100597i | 0.473271 | − | 0.100597i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.98054 | 1.98054 | ||||||||
\(479\) | 0.374607 | + | 0.648838i | 0.374607 | + | 0.648838i | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) |
−0.615661 | + | 0.788011i | \(0.711111\pi\) | |||||||
\(480\) | 2.79867 | − | 8.61341i | 2.79867 | − | 8.61341i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.93726 | − | 3.35543i | 1.93726 | − | 3.35543i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.35534 | − | 7.54368i | −4.35534 | − | 7.54368i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.990268 | + | 1.71519i | −0.990268 | + | 1.71519i | ||||
\(487\) | 1.53209 | 1.53209 | 0.766044 | − | 0.642788i | \(-0.222222\pi\) | ||||
0.766044 | + | 0.642788i | \(0.222222\pi\) | |||||||
\(488\) | −0.661187 | − | 1.14521i | −0.661187 | − | 1.14521i | ||||
\(489\) | 0.0467046 | + | 0.0518708i | 0.0467046 | + | 0.0518708i | ||||
\(490\) | −1.67959 | + | 2.90914i | −1.67959 | + | 2.90914i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0840186 | + | 0.145524i | 0.0840186 | + | 0.145524i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.353717 | − | 3.36539i | 0.353717 | − | 3.36539i | ||||
\(496\) | −5.68701 | −5.68701 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.78709 | − | 0.592415i | 2.78709 | − | 0.592415i | ||||
\(499\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(500\) | −2.17295 | + | 3.76367i | −2.17295 | + | 3.76367i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.51718 | − | 2.62783i | −1.51718 | − | 2.62783i | ||||
\(503\) | −1.87939 | −1.87939 | −0.939693 | − | 0.342020i | \(-0.888889\pi\) | ||||
−0.939693 | + | 0.342020i | \(0.888889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.04825 | 1.04825 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(508\) | −1.63425 | + | 2.83061i | −1.63425 | + | 2.83061i | ||||
\(509\) | 0.939693 | − | 1.62760i | 0.939693 | − | 1.62760i | 0.173648 | − | 0.984808i | \(-0.444444\pi\) |
0.766044 | − | 0.642788i | \(-0.222222\pi\) | |||||||
\(510\) | 0.780628 | + | 0.866976i | 0.780628 | + | 0.866976i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 7.07614 | 7.07614 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.21500 | 2.21500 | ||||||||
\(515\) | 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 | \(\pi\) | |||||||||
\(522\) | 0.775257 | + | 0.563257i | 0.775257 | + | 0.563257i | ||||
\(523\) | 0.347296 | 0.347296 | 0.173648 | − | 0.984808i | \(-0.444444\pi\) | ||||
0.173648 | + | 0.984808i | \(0.444444\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.90381 | + | 3.29750i | −1.90381 | + | 3.29750i | ||||
\(527\) | 0.213817 | − | 0.370342i | 0.213817 | − | 0.370342i | ||||
\(528\) | 9.01337 | − | 1.91585i | 9.01337 | − | 1.91585i | ||||
\(529\) | −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 | ||||||||
\(536\) | 3.57800 | − | 6.19728i | 3.57800 | − | 6.19728i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.21934 | + | 2.11196i | 1.21934 | + | 2.11196i | ||||
\(539\) | −1.99513 | −1.99513 | ||||||||
\(540\) | 4.52834 | + | 2.01615i | 4.52834 | + | 2.01615i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 1.97571 | + | 3.42203i | 1.97571 | + | 3.42203i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.927232 | + | 1.60601i | −0.927232 | + | 1.60601i | ||||
\(545\) | 0.177290 | − | 0.307076i | 0.177290 | − | 0.307076i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.317271 | − | 0.141258i | 0.317271 | − | 0.141258i | ||||
\(550\) | −7.41580 | −7.41580 | ||||||||
\(551\) | 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 | \(\pi\) | |||||||||
\(558\) | 0.254911 | − | 2.42532i | 0.254911 | − | 2.42532i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.214118 | + | 0.658988i | −0.214118 | + | 0.658988i | ||||
\(562\) | 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 | ||||||||
\(565\) | 1.65903 | + | 2.87353i | 1.65903 | + | 2.87353i | ||||
\(566\) | 3.92252 | 3.92252 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.16087 | −6.16087 | ||||||||
\(569\) | 0.615661 | + | 1.06636i | 0.615661 | + | 1.06636i | 0.990268 | + | 0.139173i | \(0.0444444\pi\) |
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.622664 | + | 5.92425i | −0.622664 | + | 5.92425i | ||||
\(577\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(578\) | 0.870827 | + | 1.50832i | 0.870827 | + | 1.50832i | ||||
\(579\) | −0.0682737 | + | 0.0145120i | −0.0682737 | + | 0.0145120i | ||||
\(580\) | 1.19918 | − | 2.07704i | 1.19918 | − | 2.07704i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.20457 | −3.20457 | ||||||||
\(587\) | −0.0348995 | − | 0.0604477i | −0.0348995 | − | 0.0604477i | 0.848048 | − | 0.529919i | \(-0.177778\pi\) |
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(588\) | 0.903109 | − | 2.77948i | 0.903109 | − | 2.77948i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.586655 | + | 0.651546i | 0.586655 | + | 0.651546i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0.413036 | + | 3.92978i | 0.413036 | + | 3.92978i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.669131 | + | 1.15897i | −0.669131 | + | 1.15897i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(600\) | 2.20822 | − | 6.79619i | 2.20822 | − | 6.79619i | ||||
\(601\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.52045 | + | 1.10467i | 1.52045 | + | 1.10467i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.52764 | − | 4.37800i | −2.52764 | − | 4.37800i | ||||
\(606\) | −1.19729 | + | 0.254492i | −1.19729 | + | 0.254492i | ||||
\(607\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.583315 | − | 1.01033i | −0.583315 | − | 1.01033i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.821137 | − | 0.596591i | −0.821137 | − | 0.596591i | ||||
\(613\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(614\) | −1.67959 | − | 2.90914i | −1.67959 | − | 2.90914i | ||||
\(615\) | 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 | \(0.333333\pi\) | |||||||
\(620\) | −6.10352 | −6.10352 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.03436 | 3.03436 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.322710 | + | 0.558950i | −0.322710 | + | 0.558950i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.707022 | + | 1.22460i | 0.707022 | + | 1.22460i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.69610 | 1.69610 | 0.848048 | − | 0.529919i | \(-0.177778\pi\) | ||||
0.848048 | + | 0.529919i | \(0.177778\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.40724 | − | 0.299118i | 1.40724 | − | 0.299118i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.948445 | + | 1.64275i | −0.948445 | + | 1.64275i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.91187 | 1.91187 | ||||||||
\(639\) | 0.169131 | − | 1.60917i | 0.169131 | − | 1.60917i | ||||
\(640\) | 10.9536 | 10.9536 | ||||||||
\(641\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.559193 | + | 0.968551i | −0.559193 | + | 0.968551i | 0.438371 | + | 0.898794i | \(0.355556\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.749213 | −0.749213 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(648\) | −3.72442 | − | 0.791650i | −3.72442 | − | 0.791650i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.101995 | + | 0.176660i | −0.101995 | + | 0.176660i | ||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | −0.127947 | + | 0.393780i | −0.127947 | + | 0.393780i | ||||
\(655\) | 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 | \(0.333333\pi\) | |||||||
\(660\) | 9.67350 | − | 2.05617i | 9.67350 | − | 2.05617i | ||||
\(661\) | 0.997564 | − | 1.72783i | 0.997564 | − | 1.72783i | 0.438371 | − | 0.898794i | \(-0.355556\pi\) |
0.559193 | − | 0.829038i | \(-0.311111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.73898 | + | 4.74405i | 2.73898 | + | 4.74405i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.15660 | − | 5.46739i | 3.15660 | − | 5.46739i | ||||
\(671\) | 0.346450 | − | 0.600070i | 0.346450 | − | 0.600070i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(674\) | 3.35918 | 3.35918 | ||||||||
\(675\) | 1.71449 | + | 0.763340i | 1.71449 | + | 0.763340i | ||||
\(676\) | 2.92252 | 2.92252 | ||||||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | −2.59256 | − | 2.87932i | −2.59256 | − | 2.87932i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.12144 | + | 1.94239i | −1.12144 | + | 1.94239i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.43274 | − | 4.21363i | −2.43274 | − | 4.21363i | ||||
\(683\) | 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 | ||||||||
\(694\) | −2.43868 | −2.43868 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.569301 | + | 1.75213i | −0.569301 | + | 1.75213i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −1.10750 | + | 1.91825i | −1.10750 | + | 1.91825i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 5.94237 | + | 10.2925i | 5.94237 | + | 10.2925i | ||||
\(705\) | 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 | \(0.333333\pi\) | |||||||
\(710\) | −5.43527 | −5.43527 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.978148 | + | 0.207912i | −0.978148 | + | 0.207912i | ||||
\(718\) | −0.612019 | − | 1.06005i | −0.612019 | − | 1.06005i | ||||
\(719\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(720\) | −0.818837 | + | 7.79071i | −0.818837 | + | 7.79071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.990268 | − | 1.71519i | −0.990268 | − | 1.71519i | ||||
\(723\) | −0.604528 | + | 1.86055i | −0.604528 | + | 1.86055i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.454025 | − | 0.786394i | 0.454025 | − | 0.786394i | ||||
\(726\) | 3.94992 | + | 4.38683i | 3.94992 | + | 4.38683i | ||||
\(727\) | −0.669131 | − | 1.15897i | −0.669131 | − | 1.15897i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.679155 | + | 0.754278i | 0.679155 | + | 0.754278i | ||||
\(733\) | 0.615661 | − | 1.06636i | 0.615661 | − | 1.06636i | −0.374607 | − | 0.927184i | \(-0.622222\pi\) |
0.990268 | − | 0.139173i | \(-0.0444444\pi\) | |||||||
\(734\) | 1.42468 | − | 2.46762i | 1.42468 | − | 2.46762i | ||||
\(735\) | 0.524123 | − | 1.61308i | 0.524123 | − | 1.61308i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.74961 | 3.74961 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.82709 | 1.82709 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | 4.58597 | − | 0.974777i | 4.58597 | − | 0.974777i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.20457 | −3.20457 | ||||||||
\(747\) | −1.31430 | + | 0.585164i | −1.31430 | + | 0.585164i | ||||
\(748\) | −2.02502 | −2.02502 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.910097 | − | 2.80099i | 0.910097 | − | 2.80099i | ||||
\(751\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.02517 | + | 1.13856i | 1.02517 | + | 1.13856i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.98054 | 1.98054 | 0.990268 | − | 0.139173i | \(-0.0444444\pi\) | ||||
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(762\) | 0.684474 | − | 2.10659i | 0.684474 | − | 2.10659i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.476550 | − | 0.346234i | −0.476550 | − | 0.346234i | ||||
\(766\) | −1.98054 | −1.98054 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −6.68429 | + | 1.42079i | −6.68429 | + | 1.42079i | ||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.09395 | + | 0.232525i | −1.09395 | + | 0.232525i | ||||
\(772\) | −0.101995 | − | 0.176660i | −0.101995 | − | 0.176660i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.31088 | −2.31088 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.741922 | − | 1.28505i | 0.741922 | − | 1.28505i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.61409 | − | 2.79569i | −1.61409 | − | 2.79569i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.442013 | − | 0.196797i | −0.442013 | − | 0.196797i | ||||
\(784\) | 4.61862 | 4.61862 | ||||||||
\(785\) | 0.410323 | + | 0.710700i | 0.410323 | + | 0.710700i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(788\) | −1.28115 | + | 2.21902i | −1.28115 | + | 2.21902i | ||||
\(789\) | 0.594092 | − | 1.82843i | 0.594092 | − | 1.82843i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.93993 | + | 3.08986i | −6.93993 | + | 3.08986i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.374607 | − | 0.648838i | 0.374607 | − | 0.648838i | −0.615661 | − | 0.788011i | \(-0.711111\pi\) |
0.990268 | + | 0.139173i | \(0.0444444\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 10.0213 | 10.0213 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.84936 | −2.84936 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.69729 | + | 5.22372i | −1.69729 | + | 5.22372i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.823916 | − | 0.915051i | −0.823916 | − | 0.915051i | ||||
\(808\) | −1.17662 | − | 2.03797i | −1.17662 | − | 2.03797i | ||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | −3.28577 | − | 0.698413i | −3.28577 | − | 0.698413i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.33500 | − | 1.48267i | −1.33500 | − | 1.48267i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.0591929 | + | 0.102525i | −0.0591929 | + | 0.102525i | ||||
\(816\) | 0.495672 | − | 1.52552i | 0.495672 | − | 1.52552i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −3.49742 | −3.49742 | ||||||||
\(819\) | 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 | ||||||||
\(825\) | 3.66252 | − | 0.778492i | 3.66252 | − | 0.778492i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.483844 | −0.483844 | −0.241922 | − | 0.970296i | \(-0.577778\pi\) | ||||
−0.241922 | + | 0.970296i | \(0.577778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 2.41639 | + | 4.18531i | 2.41639 | + | 4.18531i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.173648 | + | 0.300767i | −0.173648 | + | 0.300767i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.128708 | + | 1.22458i | 0.128708 | + | 1.22458i | ||||
\(838\) | 3.80763 | 3.80763 | ||||||||
\(839\) | −0.438371 | − | 0.759281i | −0.438371 | − | 0.759281i | 0.559193 | − | 0.829038i | \(-0.311111\pi\) |
−0.997564 | + | 0.0697565i | \(0.977778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.382948 | − | 0.663285i | 0.382948 | − | 0.663285i | ||||
\(842\) | 1.93726 | − | 3.35543i | 1.93726 | − | 3.35543i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.10229 | + | 3.64127i | 2.10229 | + | 3.64127i | ||||
\(845\) | 1.69610 | 1.69610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.93726 | + | 0.411777i | −1.93726 | + | 0.411777i | ||||
\(850\) | −0.645443 | + | 1.11794i | −0.645443 | + | 1.11794i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 4.62541 | − | 0.983161i | 4.62541 | − | 0.983161i | ||||
\(853\) | 0.882948 | + | 1.52931i | 0.882948 | + | 1.52931i | 0.848048 | + | 0.529919i | \(0.177778\pi\) |
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | −0.438371 | + | 0.759281i | −0.438371 | + | 0.759281i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.559193 | + | 0.829038i | \(0.311111\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.0691197 | − | 0.119719i | −0.0691197 | − | 0.119719i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −0.558152 | − | 5.31046i | −0.558152 | − | 5.31046i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.588424 | − | 0.653511i | −0.588424 | − | 0.653511i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.502251 | + | 1.54577i | −0.502251 | + | 1.54577i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −0.796011 | −0.796011 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.719340 | − | 1.24593i | 0.719340 | − | 1.24593i | −0.241922 | − | 0.970296i | \(-0.577778\pi\) |
0.961262 | − | 0.275637i | \(-0.0888889\pi\) | |||||||
\(878\) | −1.32524 | + | 2.29538i | −1.32524 | + | 2.29538i | ||||
\(879\) | 1.58268 | − | 0.336408i | 1.58268 | − | 0.336408i | ||||
\(880\) | 7.81454 | + | 13.5352i | 7.81454 | + | 13.5352i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −0.207022 | + | 1.96969i | −0.207022 | + | 1.96969i | ||||
\(883\) | −0.749213 | −0.749213 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.74871 | − | 3.02885i | 1.74871 | − | 3.02885i | ||||
\(887\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.616528 | − | 1.89748i | −0.616528 | − | 1.89748i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.595768 | 0.595768 | ||||||||
\(900\) | −0.573320 | + | 5.45478i | −0.573320 | + | 5.45478i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.72442 | − | 6.45089i | 3.72442 | − | 6.45089i | ||||
\(905\) | 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 | ||||||||
\(909\) | 0.564602 | − | 0.251377i | 0.564602 | − | 0.251377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.43518 | + | 2.48580i | −1.43518 | + | 2.48580i | ||||
\(914\) | 1.60229 | − | 2.77524i | 1.60229 | − | 2.77524i | ||||
\(915\) | 0.394150 | + | 0.437748i | 0.394150 | + | 0.437748i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.628367 | + | 0.279767i | 0.628367 | + | 0.279767i | ||||
\(919\) | 0.0697990 | 0.0697990 | 0.0348995 | − | 0.999391i | \(-0.488889\pi\) | ||||
0.0348995 | + | 0.999391i | \(0.488889\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.13491 | + | 1.26045i | 1.13491 | + | 1.26045i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.58359 | −2.58359 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 4.04585 | − | 0.859972i | 4.04585 | − | 0.859972i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.49861 | + | 0.318539i | −1.49861 | + | 0.318539i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.17523 | −1.17523 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.749213 | −0.749213 | −0.374607 | − | 0.927184i | \(-0.622222\pi\) | ||||
−0.374607 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | −0.641208 | − | 0.712133i | −0.641208 | − | 0.712133i | ||||
\(943\) | 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 | ||||||||
\(956\) | −1.46126 | − | 2.53098i | −1.46126 | − | 2.53098i | ||||
\(957\) | −0.944236 | + | 0.200703i | −0.944236 | + | 0.200703i | ||||
\(958\) | 0.741922 | − | 1.28505i | 0.741922 | − | 1.28505i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −9.88266 | + | 2.10062i | −9.88266 | + | 2.10062i | ||||
\(961\) | −0.258078 | − | 0.447004i | −0.258078 | − | 0.447004i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.71732 | −5.71732 | ||||||||
\(965\) | −0.0591929 | − | 0.102525i | −0.0591929 | − | 0.102525i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(968\) | −5.67439 | + | 9.82832i | −5.67439 | + | 9.82832i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.76590 | −1.76590 | −0.882948 | − | 0.469472i | \(-0.844444\pi\) | ||||
−0.882948 | + | 0.469472i | \(0.844444\pi\) | |||||||
\(972\) | 2.92252 | 2.92252 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.51718 | − | 2.62783i | −1.51718 | − | 2.62783i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.802015 | + | 1.38913i | −0.802015 | + | 1.38913i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0.0427183 | − | 0.131474i | 0.0427183 | − | 0.131474i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.95688 | 4.95688 | ||||||||
\(981\) | 0.0218524 | − | 0.207912i | 0.0218524 | − | 0.207912i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.559193 | − | 0.968551i | −0.559193 | − | 0.968551i | −0.997564 | − | 0.0697565i | \(-0.977778\pi\) |
0.438371 | − | 0.898794i | \(-0.355556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.743520 | + | 1.28781i | −0.743520 | + | 1.28781i | ||||
\(986\) | 0.166402 | − | 0.288216i | 0.166402 | − | 0.288216i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −6.12258 | + | 2.72595i | −6.12258 | + | 2.72595i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 3.28746 | + | 5.69404i | 3.28746 | + | 5.69404i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.81341 | − | 3.12461i | −2.81341 | − | 3.12461i | ||||
\(997\) | 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.238.1 | ✓ | 24 | |
9.7 | even | 3 | inner | 2151.1.f.b.1672.1 | yes | 24 | |
239.238 | odd | 2 | CM | 2151.1.f.b.238.1 | ✓ | 24 | |
2151.1672 | odd | 6 | inner | 2151.1.f.b.1672.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.1.f.b.238.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2151.1.f.b.238.1 | ✓ | 24 | 239.238 | odd | 2 | CM | |
2151.1.f.b.1672.1 | yes | 24 | 9.7 | even | 3 | inner | |
2151.1.f.b.1672.1 | yes | 24 | 2151.1672 | odd | 6 | inner |