Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1027,1,Mod(394,1027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1027, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1027.394");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1027 = 13 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1027.s (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: | \(0.512539767974\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{15})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{30}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{30} - \cdots)\) |
Embedding invariants
Embedding label | 394.1 | ||
Root | \(0.669131 + 0.743145i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1027.394 |
Dual form | 1027.1.s.b.868.1 |
$q$-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 \(\left(\mathbb{Z}/1027\mathbb{Z}\right)^\times\).
\(n\) | \(80\) | \(872\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.72256 | − | 0.994522i | −1.72256 | − | 0.994522i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.809017 | − | 0.587785i | \(-0.800000\pi\) | |||||||
\(3\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(4\) | 1.47815 | + | 2.56023i | 1.47815 | + | 2.56023i | ||||
\(5\) | 0.415823i | 0.415823i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(8\) | − | 3.89116i | − | 3.89116i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0.413545 | − | 0.716282i | 0.413545 | − | 0.716282i | ||||
\(11\) | −0.704489 | − | 0.406737i | −0.704489 | − | 0.406737i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.39169 | + | 4.14253i | −2.39169 | + | 4.14253i | ||||
\(17\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 1.98904i | 1.98904i | ||||||||
\(19\) | −1.28716 | + | 0.743145i | −1.28716 | + | 0.743145i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(20\) | −1.06460 | + | 0.614648i | −1.06460 | + | 0.614648i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | ||||
\(23\) | 0.669131 | − | 1.15897i | 0.669131 | − | 1.15897i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.827091 | 0.827091 | ||||||||
\(26\) | −1.97815 | + | 0.207912i | −1.97815 | + | 0.207912i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 1.98904i | − | 1.98904i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(32\) | 4.86984 | − | 2.81160i | 4.86984 | − | 2.81160i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.47815 | − | 2.56023i | 1.47815 | − | 2.56023i | ||||
\(37\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(38\) | 2.95630 | 2.95630 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.61803 | 1.61803 | ||||||||
\(41\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(44\) | − | 2.40487i | − | 2.40487i | ||||||
\(45\) | 0.360114 | − | 0.207912i | 0.360114 | − | 0.207912i | ||||
\(46\) | −2.30524 | + | 1.33093i | −2.30524 | + | 1.33093i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(50\) | −1.42472 | − | 0.822560i | −1.42472 | − | 0.822560i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.70071 | + | 1.20243i | 2.70071 | + | 1.20243i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.169131 | − | 0.292943i | 0.169131 | − | 0.292943i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(62\) | −1.97815 | + | 3.42625i | −1.97815 | + | 3.42625i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.40142 | −6.40142 | ||||||||
\(65\) | 0.244415 | + | 0.336408i | 0.244415 | + | 0.336408i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.64728 | + | 0.951057i | 1.64728 | + | 0.951057i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | −3.36984 | + | 1.94558i | −3.36984 | + | 1.94558i | ||||
\(73\) | − | 1.48629i | − | 1.48629i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.80524 | − | 2.19696i | −3.80524 | − | 2.19696i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −1.00000 | ||||||||
\(80\) | −1.72256 | − | 0.994522i | −1.72256 | − | 0.994522i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.58268 | + | 2.74128i | −1.58268 | + | 2.74128i | ||||
\(89\) | 1.01807 | + | 0.587785i | 1.01807 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(90\) | −0.827091 | −0.827091 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.95630 | 3.95630 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.360114 | + | 0.207912i | −0.360114 | + | 0.207912i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(98\) | −1.72256 | + | 0.994522i | −1.72256 | + | 0.994522i | ||||
\(99\) | 0.813473i | 0.813473i | ||||||||
\(100\) | 1.22256 | + | 2.11754i | 1.22256 | + | 2.11754i | ||||
\(101\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | −2.28716 | − | 3.14801i | −2.28716 | − | 3.14801i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | −0.582676 | + | 0.336408i | −0.582676 | + | 0.336408i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.481926 | + | 0.278240i | 0.481926 | + | 0.278240i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.913545 | − | 0.406737i | −0.913545 | − | 0.406737i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.169131 | − | 0.292943i | −0.169131 | − | 0.292943i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.09240 | − | 2.94010i | 5.09240 | − | 2.94010i | ||||
\(125\) | 0.759747i | 0.759747i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(128\) | 6.15701 | + | 3.55475i | 6.15701 | + | 3.55475i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0864545 | − | 0.822560i | −0.0864545 | − | 0.822560i | ||||
\(131\) | −1.33826 | −1.33826 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.89169 | − | 3.27651i | −1.89169 | − | 3.27651i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.809017 | + | 0.0850311i | −0.809017 | + | 0.0850311i | ||||
\(144\) | 4.78339 | 4.78339 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.47815 | + | 2.56023i | −1.47815 | + | 2.56023i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.415823i | 0.415823i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(152\) | 2.89169 | + | 5.00856i | 2.89169 | + | 5.00856i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.827091 | 0.827091 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 1.72256 | + | 0.994522i | 1.72256 | + | 0.994522i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.16913 | + | 2.02499i | 1.16913 | + | 2.02499i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.72256 | − | 0.994522i | 1.72256 | − | 0.994522i | ||||
\(163\) | −1.01807 | + | 0.587785i | −1.01807 | + | 0.587785i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.72256 | + | 2.98357i | −1.72256 | + | 2.98357i | ||||
\(167\) | 0.704489 | + | 0.406737i | 0.704489 | + | 0.406737i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.28716 | + | 0.743145i | 1.28716 | + | 0.743145i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.36984 | − | 1.94558i | 3.36984 | − | 1.94558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.16913 | − | 2.02499i | −1.16913 | − | 2.02499i | ||||
\(179\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(180\) | 1.06460 | + | 0.614648i | 1.06460 | + | 0.614648i | ||||
\(181\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.50973 | − | 2.60369i | −4.50973 | − | 2.60369i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.22930i | 1.22930i | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(194\) | 0.827091 | 0.827091 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.95630 | 2.95630 | ||||||||
\(197\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(198\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | ||||
\(199\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | − | 3.21834i | − | 3.21834i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.360114 | − | 0.207912i | 0.360114 | − | 0.207912i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.33826 | −1.33826 | ||||||||
\(208\) | 0.500000 | + | 4.75718i | 0.500000 | + | 4.75718i | ||||
\(209\) | 1.20906 | 1.20906 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.00000 | 1.00000 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.413545 | − | 0.716282i | −0.413545 | − | 0.716282i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | −0.553432 | − | 0.958572i | −0.553432 | − | 0.958572i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 1.16913 | + | 1.60917i | 1.16913 | + | 1.60917i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.48629i | 1.48629i | 0.669131 | + | 0.743145i | \(0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.704489 | + | 0.406737i | −0.704489 | + | 0.406737i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(242\) | 0.672816i | 0.672816i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.360114 | + | 0.207912i | 0.360114 | + | 0.207912i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.604528 | + | 1.35779i | −0.604528 | + | 1.35779i | ||||
\(248\) | −7.73968 | −7.73968 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.755585 | − | 1.30871i | 0.755585 | − | 1.30871i | ||||
\(251\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.942790 | + | 0.544320i | −0.942790 | + | 0.544320i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.86984 | − | 6.70276i | −3.86984 | − | 6.70276i | ||||
\(257\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.500000 | + | 1.12302i | −0.500000 | + | 1.12302i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.30524 | + | 1.33093i | 2.30524 | + | 1.33093i | ||||
\(263\) | −0.913545 | + | 1.58231i | −0.913545 | + | 1.58231i | −0.104528 | + | 0.994522i | \(0.533333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.62321i | 5.62321i | ||||||||
\(269\) | 0.978148 | + | 1.69420i | 0.978148 | + | 1.69420i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.582676 | − | 0.336408i | −0.582676 | − | 0.336408i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.72256 | + | 0.994522i | −1.72256 | + | 0.994522i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.90211i | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.913545 | − | 1.58231i | 0.913545 | − | 1.58231i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.47815 | + | 0.658114i | 1.47815 | + | 0.658114i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.86984 | − | 2.81160i | −4.86984 | − | 2.81160i | ||||
\(289\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.80524 | − | 2.19696i | 3.80524 | − | 2.19696i | ||||
\(293\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.139886 | − | 1.33093i | −0.139886 | − | 1.33093i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0.413545 | − | 0.716282i | 0.413545 | − | 0.716282i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 7.10950i | − | 7.10950i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.42472 | − | 0.822560i | −1.42472 | − | 0.822560i | ||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.47815 | − | 2.56023i | −1.47815 | − | 2.56023i | ||||
\(317\) | 1.73205i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 2.66186i | − | 2.66186i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.95630 | −2.95630 | ||||||||
\(325\) | 0.669131 | − | 0.486152i | 0.669131 | − | 0.486152i | ||||
\(326\) | 2.33826 | 2.33826 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(332\) | 4.43444 | − | 2.56023i | 4.43444 | − | 2.56023i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.809017 | − | 1.40126i | −0.809017 | − | 1.40126i | ||||
\(335\) | −0.395472 | + | 0.684977i | −0.395472 | + | 0.684977i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.95630 | 1.95630 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(338\) | −1.47815 | + | 1.33093i | −1.47815 | + | 1.33093i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.809017 | + | 1.40126i | −0.809017 | + | 1.40126i | ||||
\(342\) | −1.47815 | − | 2.56023i | −1.47815 | − | 2.56023i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.309017 | − | 0.535233i | −0.309017 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.57433 | −4.57433 | ||||||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.47533i | 3.47533i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.72256 | − | 0.994522i | 1.72256 | − | 0.994522i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | −0.809017 | − | 1.40126i | −0.809017 | − | 1.40126i | ||||
\(361\) | 0.604528 | − | 1.04707i | 0.604528 | − | 1.04707i | ||||
\(362\) | −2.78716 | − | 1.60917i | −2.78716 | − | 1.60917i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.618034 | 0.618034 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.104528 | − | 0.181049i | 0.104528 | − | 0.181049i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(368\) | 3.20071 | + | 5.54379i | 3.20071 | + | 5.54379i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(380\) | 0.913545 | − | 1.58231i | 0.913545 | − | 1.58231i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.01807 | − | 0.587785i | 1.01807 | − | 0.587785i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.06460 | − | 0.614648i | −1.06460 | − | 0.614648i | ||||
\(389\) | −0.209057 | −0.209057 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.36984 | − | 1.94558i | −3.36984 | − | 1.94558i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 0.415823i | − | 0.415823i | ||||||
\(396\) | −2.08268 | + | 1.20243i | −2.08268 | + | 1.20243i | ||||
\(397\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.97815 | + | 3.42625i | −1.97815 | + | 3.42625i | ||||
\(401\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.16913 | − | 1.60917i | −1.16913 | − | 1.60917i | ||||
\(404\) | −0.618034 | −0.618034 | ||||||||
\(405\) | −0.360114 | − | 0.207912i | −0.360114 | − | 0.207912i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.30524 | + | 1.33093i | 2.30524 | + | 1.33093i | ||||
\(415\) | 0.720227 | 0.720227 | ||||||||
\(416\) | 2.28716 | − | 5.13706i | 2.28716 | − | 5.13706i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.08268 | − | 1.20243i | −2.08268 | − | 1.20243i | ||||
\(419\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.90211i | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.64728 | − | 0.951057i | −1.64728 | − | 0.951057i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.669131 | − | 0.743145i | \(-0.733333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.309017 | + | 0.535233i | 0.309017 | + | 0.535233i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.98904i | 1.98904i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(440\) | −1.13989 | − | 0.658114i | −1.13989 | − | 0.658114i | ||||
\(441\) | −1.00000 | −1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.244415 | + | 0.423339i | −0.244415 | + | 0.423339i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(450\) | 1.64512i | 1.64512i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.01807 | + | 0.587785i | 1.01807 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.64512i | 1.64512i | ||||||||
\(461\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.209057 | −0.209057 | −0.104528 | − | 0.994522i | \(-0.533333\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(468\) | −0.309017 | − | 2.94010i | −0.309017 | − | 2.94010i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.06460 | + | 0.614648i | −1.06460 | + | 0.614648i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.47815 | − | 2.56023i | 1.47815 | − | 2.56023i | ||||
\(479\) | 1.50000 | + | 0.866025i | 1.50000 | + | 0.866025i | 1.00000 | \(0\) | ||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.61803 | 1.61803 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(485\) | −0.0864545 | − | 0.149744i | −0.0864545 | − | 0.149744i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.01807 | + | 0.587785i | −1.01807 | + | 0.587785i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.413545 | − | 0.716282i | −0.413545 | − | 0.716282i | ||||
\(491\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.39169 | − | 1.73767i | 2.39169 | − | 1.73767i | ||||
\(495\) | −0.338261 | −0.338261 | ||||||||
\(496\) | 8.23968 | + | 4.75718i | 8.23968 | + | 4.75718i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.813473i | 0.813473i | 0.913545 | + | 0.406737i | \(0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(500\) | −1.94512 | + | 1.12302i | −1.94512 | + | 1.12302i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.0752842 | − | 0.0434654i | −0.0752842 | − | 0.0434654i | ||||
\(506\) | 2.16535 | 2.16535 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.28507i | 8.28507i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.78716 | + | 1.60917i | −2.78716 | + | 1.60917i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(524\) | −1.97815 | − | 3.42625i | −1.97815 | − | 3.42625i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.14728 | − | 1.81708i | 3.14728 | − | 1.81708i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.395472 | − | 0.684977i | −0.395472 | − | 0.684977i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.70071 | − | 6.40982i | 3.70071 | − | 6.40982i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.89116i | − | 3.89116i | ||||||
\(539\) | −0.704489 | + | 0.406737i | −0.704489 | + | 0.406737i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.82709 | −1.82709 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.669131 | + | 1.15897i | 0.669131 | + | 1.15897i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.22930i | 1.22930i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.360114 | − | 0.207912i | −0.360114 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(558\) | 3.95630 | 3.95630 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.89169 | − | 3.27651i | 1.89169 | − | 3.27651i | ||||
\(563\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.14728 | + | 1.81708i | −3.14728 | + | 1.81708i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.309017 | − | 0.535233i | 0.309017 | − | 0.535233i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(572\) | −1.41355 | − | 1.94558i | −1.41355 | − | 1.94558i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.553432 | − | 0.958572i | 0.553432 | − | 0.958572i | ||||
\(576\) | 3.20071 | + | 5.54379i | 3.20071 | + | 5.54379i | ||||
\(577\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(578\) | 1.72256 | − | 0.994522i | 1.72256 | − | 0.994522i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −5.78339 | −5.78339 | ||||||||
\(585\) | 0.169131 | − | 0.379874i | 0.169131 | − | 0.379874i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.47815 | + | 2.56023i | 1.47815 | + | 2.56023i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.90211i | − | 1.90211i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.08268 | + | 2.43173i | −1.08268 | + | 2.43173i | ||||
\(599\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.90211i | − | 1.90211i | ||||||
\(604\) | −1.06460 | + | 0.614648i | −1.06460 | + | 0.614648i | ||||
\(605\) | 0.121812 | − | 0.0703285i | 0.121812 | − | 0.0703285i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | −4.17886 | + | 7.23799i | −4.17886 | + | 7.23799i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.72256 | + | 0.994522i | −1.72256 | + | 0.994522i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 1.22256 | + | 2.11754i | 1.22256 | + | 2.11754i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.511170 | 0.511170 | ||||||||
\(626\) | 2.78716 | + | 1.60917i | 2.78716 | + | 1.60917i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(632\) | 3.89116i | 3.89116i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.72256 | − | 2.98357i | 1.72256 | − | 2.98357i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.104528 | − | 0.994522i | −0.104528 | − | 0.994522i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.47815 | + | 2.56023i | −1.47815 | + | 2.56023i | ||||
\(641\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.64728 | − | 0.951057i | 1.64728 | − | 0.951057i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 3.36984 | + | 1.94558i | 3.36984 | + | 1.94558i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.63611 | + | 0.171962i | −1.63611 | + | 0.171962i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.00973 | − | 1.73767i | −3.00973 | − | 1.73767i | ||||
\(653\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 0.556480i | − | 0.556480i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.28716 | + | 0.743145i | −1.28716 | + | 0.743145i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.73968 | −6.73968 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 2.40487i | 2.40487i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.36245 | − | 0.786610i | 1.36245 | − | 0.786610i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(674\) | −3.36984 | − | 1.94558i | −3.36984 | − | 1.94558i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.89169 | − | 0.614648i | 2.89169 | − | 0.614648i | ||||
\(677\) | −1.00000 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.78716 | − | 1.60917i | 2.78716 | − | 1.60917i | ||||
\(683\) | 0.360114 | − | 0.207912i | 0.360114 | − | 0.207912i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(684\) | 4.39391i | 4.39391i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.22930i | 1.22930i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.50973 | + | 2.60369i | 4.50973 | + | 2.60369i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(712\) | 2.28716 | − | 3.96149i | 2.28716 | − | 3.96149i | ||||
\(713\) | −2.30524 | − | 1.33093i | −2.30524 | − | 1.33093i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0353579 | − | 0.336408i | −0.0353579 | − | 0.336408i | ||||
\(716\) | −2.95630 | −2.95630 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.913545 | − | 1.58231i | −0.913545 | − | 1.58231i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(720\) | 1.98904i | 1.98904i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.08268 | + | 1.20243i | −2.08268 | + | 1.20243i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.39169 | + | 4.14253i | 2.39169 | + | 4.14253i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 1.00000 | ||||||||
\(730\) | −1.06460 | − | 0.614648i | −1.06460 | − | 0.614648i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.48629i | − | 1.48629i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||
0.669131 | − | 0.743145i | \(-0.266667\pi\) | |||||||
\(734\) | −0.360114 | + | 0.207912i | −0.360114 | + | 0.207912i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 7.52532i | − | 7.52532i | ||||||
\(737\) | −0.773659 | − | 1.34002i | −0.773659 | − | 1.34002i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.01807 | + | 0.587785i | 1.01807 | + | 0.587785i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.50000 | + | 0.866025i | −1.50000 | + | 0.866025i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.104528 | + | 0.181049i | −0.104528 | + | 0.181049i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.172909 | −0.172909 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | \(0.333333\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.08268 | + | 1.20243i | −2.08268 | + | 1.20243i | ||||
\(761\) | 1.64728 | − | 0.951057i | 1.64728 | − | 0.951057i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.33826 | −2.33826 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.28716 | − | 0.743145i | 1.28716 | − | 0.743145i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.64512i | − | 1.64512i | ||||||
\(776\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.360114 | + | 0.207912i | 0.360114 | + | 0.207912i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.39169 | + | 4.14253i | 2.39169 | + | 4.14253i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.28716 | + | 0.743145i | −1.28716 | + | 0.743145i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.413545 | + | 0.716282i | −0.413545 | + | 0.716282i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.16535 | 3.16535 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −3.44512 | −3.44512 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.02780 | − | 2.32545i | 4.02780 | − | 2.32545i | ||||
\(801\) | − | 1.17557i | − | 1.17557i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.604528 | + | 1.04707i | −0.604528 | + | 1.04707i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.413545 | + | 3.93462i | 0.413545 | + | 3.93462i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.704489 | + | 0.406737i | 0.704489 | + | 0.406737i | ||||
\(809\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(810\) | 0.413545 | + | 0.716282i | 0.413545 | + | 0.716282i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.244415 | − | 0.423339i | −0.244415 | − | 0.423339i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.72256 | + | 0.994522i | 1.72256 | + | 0.994522i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | −1.97815 | − | 3.42625i | −1.97815 | − | 3.42625i | ||||
\(829\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(830\) | −1.24064 | − | 0.716282i | −1.24064 | − | 0.716282i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.17886 | + | 3.76266i | −5.17886 | + | 3.76266i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.169131 | + | 0.292943i | −0.169131 | + | 0.292943i | ||||
\(836\) | 1.78716 | + | 3.09546i | 1.78716 | + | 3.09546i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.64728 | − | 0.951057i | 1.64728 | − | 0.951057i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.978148 | − | 0.207912i | \(-0.0666667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(842\) | 1.89169 | − | 3.27651i | 1.89169 | − | 3.27651i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.395472 | + | 0.128496i | 0.395472 | + | 0.128496i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.309017 | + | 0.535233i | −0.309017 | + | 0.535233i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.95630 | −1.95630 | −0.978148 | − | 0.207912i | \(-0.933333\pi\) | ||||
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.89169 | + | 3.27651i | 1.89169 | + | 3.27651i | ||||
\(863\) | − | 1.73205i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1.22930i | − | 1.22930i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.704489 | + | 0.406737i | 0.704489 | + | 0.406737i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.89169 | − | 0.198825i | 1.89169 | − | 0.198825i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.360114 | + | 0.207912i | 0.360114 | + | 0.207912i | ||||
\(874\) | 1.97815 | − | 3.42625i | 1.97815 | − | 3.42625i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.01807 | − | 0.587785i | 1.01807 | − | 0.587785i | 0.104528 | − | 0.994522i | \(-0.466667\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(878\) | 1.06460 | − | 0.614648i | 1.06460 | − | 0.614648i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.809017 | + | 1.40126i | 0.809017 | + | 1.40126i | ||||
\(881\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(882\) | 1.72256 | + | 0.994522i | 1.72256 | + | 0.994522i | ||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.842040 | − | 0.486152i | 0.842040 | − | 0.486152i | ||||
\(891\) | 0.704489 | − | 0.406737i | 0.704489 | − | 0.406737i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.360114 | − | 0.207912i | −0.360114 | − | 0.207912i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 1.22256 | − | 2.11754i | 1.22256 | − | 2.11754i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.672816i | 0.672816i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.209057 | 0.209057 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.95630 | 1.95630 | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) | ||||
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.704489 | + | 1.22021i | −0.704489 | + | 1.22021i | ||||
\(914\) | −1.16913 | − | 2.02499i | −1.16913 | − | 2.02499i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.104528 | − | 0.181049i | −0.104528 | − | 0.181049i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(920\) | 1.08268 | − | 1.87525i | 1.08268 | − | 1.87525i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.48629i | 1.48629i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.360114 | + | 0.207912i | 0.360114 | + | 0.207912i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.58268 | + | 3.55475i | −1.58268 | + | 3.55475i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.73205i | 1.73205i | 0.500000 | + | 0.866025i | \(0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.873619 | − | 1.20243i | −0.873619 | − | 1.20243i | ||||
\(950\) | 2.44512 | 2.44512 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.104528 | − | 0.181049i | −0.104528 | − | 0.181049i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.80524 | + | 2.19696i | −3.80524 | + | 2.19696i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.72256 | − | 2.98357i | −1.72256 | − | 2.98357i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.95630 | −2.95630 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.08268 | − | 1.20243i | −2.08268 | − | 1.20243i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | −1.13989 | + | 0.658114i | −1.13989 | + | 0.658114i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.343924i | 0.343924i | ||||||||
\(971\) | −0.809017 | − | 1.40126i | −0.809017 | − | 1.40126i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.33826 | 2.33826 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.478148 | − | 0.828176i | −0.478148 | − | 0.828176i | ||||
\(980\) | 1.22930i | 1.22930i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.36984 | + | 0.459289i | −4.36984 | + | 0.459289i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.582676 | + | 0.336408i | 0.582676 | + | 0.336408i | ||||
\(991\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(992\) | −5.59240 | − | 9.68633i | −5.59240 | − | 9.68633i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(998\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | ||||
\(999\) | 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 | 1027.1.s.b.394.1 | ✓ | 8 | |
13.10 | even | 6 | inner | 1027.1.s.b.868.1 | yes | 8 | |
79.78 | odd | 2 | CM | 1027.1.s.b.394.1 | ✓ | 8 | |
1027.868 | odd | 6 | inner | 1027.1.s.b.868.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1027.1.s.b.394.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
1027.1.s.b.394.1 | ✓ | 8 | 79.78 | odd | 2 | CM | |
1027.1.s.b.868.1 | yes | 8 | 13.10 | even | 6 | inner | |
1027.1.s.b.868.1 | yes | 8 | 1027.868 | odd | 6 | inner |