Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [964,1,Mod(83,964)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(964, base_ring=CyclotomicField(60))
chi = DirichletCharacter(H, H._module([30, 37]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("964.83");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 964 = 2^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 964.bh (of order \(60\), degree \(16\), 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: | \(0.481098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{60})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - x^{10} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{60}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{60} - \cdots)\) |
Embedding invariants
Embedding label | 159.1 | ||
Root | \(0.207912 + 0.978148i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 964.159 |
Dual form | 964.1.bh.a.867.1 |
$q$-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 \(\left(\mathbb{Z}/964\mathbb{Z}\right)^\times\).
\(n\) | \(483\) | \(489\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{19}{60}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0.786610 | − | 1.08268i | 0.786610 | − | 1.08268i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.544639 | − | 0.838671i | \(-0.683333\pi\) | ||||
0.544639 | + | 0.838671i | \(0.316667\pi\) | |||||||
\(8\) | − | 1.00000i | − | 1.00000i | ||||||
\(9\) | −0.669131 | − | 0.743145i | −0.669131 | − | 0.743145i | ||||
\(10\) | −1.22256 | + | 0.544320i | −1.22256 | + | 0.544320i | ||||
\(11\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.01693 | − | 0.390362i | 1.01693 | − | 0.390362i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(17\) | −1.49452 | − | 0.761497i | −1.49452 | − | 0.761497i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(18\) | 0.207912 | + | 0.978148i | 0.207912 | + | 0.978148i | ||||
\(19\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(20\) | 1.33093 | + | 0.139886i | 1.33093 | + | 0.139886i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.244415 | − | 0.752232i | −0.244415 | − | 0.752232i | ||||
\(26\) | −1.07587 | − | 0.170401i | −1.07587 | − | 0.170401i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.873619 | + | 0.786610i | −0.873619 | + | 0.786610i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
0.104528 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.838671 | − | 0.544639i | \(-0.183333\pi\) | ||||
−0.838671 | + | 0.544639i | \(0.816667\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.913545 | + | 1.40674i | 0.913545 | + | 1.40674i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(37\) | 1.32028 | + | 0.506809i | 1.32028 | + | 0.506809i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.08268 | − | 0.786610i | −1.08268 | − | 0.786610i | ||||
\(41\) | 1.64728 | − | 0.535233i | 1.64728 | − | 0.535233i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.978148 | + | 0.207912i | \(0.0666667\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.33093 | + | 0.139886i | −1.33093 | + | 0.139886i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.406737 | + | 0.913545i | −0.406737 | + | 0.913545i | ||||
\(50\) | −0.164446 | + | 0.773659i | −0.164446 | + | 0.773659i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.846528 | + | 0.685505i | 0.846528 | + | 0.685505i | ||||
\(53\) | −0.309017 | − | 1.45381i | −0.309017 | − | 1.45381i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.14988 | − | 0.244415i | 1.14988 | − | 0.244415i | ||||
\(59\) | 0 | 0 | −0.406737 | − | 0.913545i | \(-0.633333\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.363271 | − | 0.500000i | −0.363271 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −1.00000 | ||||||||
\(65\) | 0.377291 | − | 1.40807i | 0.377291 | − | 1.40807i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(68\) | −0.0877853 | − | 1.67504i | −0.0877853 | − | 1.67504i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.998630 | − | 0.0523360i | \(-0.983333\pi\) | ||||
0.998630 | + | 0.0523360i | \(0.0166667\pi\) | |||||||
\(72\) | −0.743145 | + | 0.669131i | −0.743145 | + | 0.669131i | ||||
\(73\) | −0.142040 | − | 0.896802i | −0.142040 | − | 0.896802i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(74\) | −0.889993 | − | 1.09905i | −0.889993 | − | 1.09905i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(80\) | 0.544320 | + | 1.22256i | 0.544320 | + | 1.22256i | ||||
\(81\) | −0.104528 | + | 0.994522i | −0.104528 | + | 0.994522i | ||||
\(82\) | −1.69420 | − | 0.360114i | −1.69420 | − | 0.360114i | ||||
\(83\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00006 | + | 1.01908i | −2.00006 | + | 1.01908i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.185505 | + | 0.692314i | 0.185505 | + | 0.692314i | 0.994522 | + | 0.104528i | \(0.0333333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(90\) | 1.22256 | + | 0.544320i | 1.22256 | + | 0.544320i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(98\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.529244 | − | 0.587785i | 0.529244 | − | 0.587785i | ||||
\(101\) | 0.705634 | + | 1.38488i | 0.705634 | + | 1.38488i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(104\) | −0.390362 | − | 1.01693i | −0.390362 | − | 1.01693i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.459289 | + | 1.41355i | −0.459289 | + | 1.41355i | ||||
\(107\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.66365 | + | 0.638616i | −1.66365 | + | 0.638616i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.69420 | + | 0.978148i | 1.69420 | + | 0.978148i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.11803 | − | 0.363271i | −1.11803 | − | 0.363271i | ||||
\(117\) | −0.970554 | − | 0.494522i | −0.970554 | − | 0.494522i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(122\) | 0.0646021 | + | 0.614648i | 0.0646021 | + | 0.614648i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.266080 | + | 0.0864545i | 0.266080 | + | 0.0864545i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.629320 | − | 0.777146i | \(-0.283333\pi\) | ||||
−0.629320 | + | 0.777146i | \(0.716667\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.03078 | + | 1.03078i | −1.03078 | + | 1.03078i | ||||
\(131\) | 0 | 0 | 0.777146 | − | 0.629320i | \(-0.216667\pi\) | ||||
−0.777146 | + | 0.629320i | \(0.783333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.761497 | + | 1.49452i | −0.761497 | + | 1.49452i | ||||
\(137\) | 0.451057 | + | 1.17504i | 0.451057 | + | 1.17504i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.978148 | − | 0.207912i | 0.978148 | − | 0.207912i | ||||
\(145\) | 0.164446 | + | 1.56460i | 0.164446 | + | 1.56460i | ||||
\(146\) | −0.325391 | + | 0.847673i | −0.325391 | + | 0.847673i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.221232 | + | 1.39680i | 0.221232 | + | 1.39680i | ||||
\(149\) | 0.669131 | + | 1.74314i | 0.669131 | + | 1.74314i | 0.669131 | + | 0.743145i | \(0.266667\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.434128 | + | 1.62019i | 0.434128 | + | 1.62019i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0658722 | − | 0.0813454i | −0.0658722 | − | 0.0813454i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.139886 | − | 1.33093i | 0.139886 | − | 1.33093i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(163\) | 0 | 0 | 0.544639 | − | 0.838671i | \(-0.316667\pi\) | ||||
−0.544639 | + | 0.838671i | \(0.683333\pi\) | |||||||
\(164\) | 1.28716 | + | 1.15897i | 1.28716 | + | 1.15897i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.629320 | − | 0.777146i | \(-0.716667\pi\) | ||||
0.629320 | + | 0.777146i | \(0.283333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.138616 | − | 0.124811i | 0.138616 | − | 0.124811i | ||||
\(170\) | 2.24164 | + | 0.117480i | 2.24164 | + | 0.117480i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.104528 | − | 1.99452i | −0.104528 | − | 1.99452i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.185505 | − | 0.692314i | 0.185505 | − | 0.692314i | ||||
\(179\) | 0 | 0 | 0.998630 | − | 0.0523360i | \(-0.0166667\pi\) | ||||
−0.998630 | + | 0.0523360i | \(0.983333\pi\) | |||||||
\(180\) | −0.786610 | − | 1.08268i | −0.786610 | − | 1.08268i | ||||
\(181\) | −0.951057 | + | 1.64728i | −0.951057 | + | 1.64728i | −0.207912 | + | 0.978148i | \(0.566667\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.58726 | − | 1.03078i | 1.58726 | − | 1.03078i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.207912 | − | 0.978148i | \(-0.433333\pi\) | ||||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.07394 | + | 1.47815i | 1.07394 | + | 1.47815i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(194\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.994522 | + | 0.104528i | −0.994522 | + | 0.104528i | ||||
\(197\) | −1.32028 | − | 1.32028i | −1.32028 | − | 1.32028i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
−0.406737 | − | 0.913545i | \(-0.633333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.933580 | − | 0.358368i | \(-0.883333\pi\) | ||||
0.933580 | + | 0.358368i | \(0.116667\pi\) | |||||||
\(200\) | −0.752232 | + | 0.244415i | −0.752232 | + | 0.244415i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0813454 | − | 1.55216i | 0.0813454 | − | 1.55216i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.716282 | − | 2.20449i | 0.716282 | − | 2.20449i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.170401 | + | 1.07587i | −0.170401 | + | 1.07587i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(212\) | 1.10453 | − | 0.994522i | 1.10453 | − | 0.994522i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.76007 | + | 0.278768i | 1.76007 | + | 0.278768i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.81708 | − | 0.190983i | −1.81708 | − | 0.190983i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.395472 | + | 0.684977i | −0.395472 | + | 0.684977i | ||||
\(226\) | −0.978148 | − | 1.69420i | −0.978148 | − | 1.69420i | ||||
\(227\) | 0 | 0 | −0.0523360 | − | 0.998630i | \(-0.516667\pi\) | ||||
0.0523360 | + | 0.998630i | \(0.483333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.809017 | − | 0.0850311i | 0.809017 | − | 0.0850311i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.786610 | + | 0.873619i | 0.786610 | + | 0.873619i | ||||
\(233\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(234\) | 0.593263 | + | 0.913545i | 0.593263 | + | 0.913545i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −1.00000 | ||||||||
\(242\) | −1.00000 | −1.00000 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.251377 | − | 0.564602i | 0.251377 | − | 0.564602i | ||||
\(245\) | 0.669131 | + | 1.15897i | 0.669131 | + | 1.15897i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.187205 | − | 0.207912i | −0.187205 | − | 0.207912i | ||||
\(251\) | 0 | 0 | 0.913545 | − | 0.406737i | \(-0.133333\pi\) | ||||
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(257\) | −0.978148 | + | 1.69420i | −0.978148 | + | 1.69420i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.40807 | − | 0.377291i | 1.40807 | − | 0.377291i | ||||
\(261\) | 1.16913 | + | 0.122881i | 1.16913 | + | 0.122881i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.81708 | − | 0.809017i | −1.81708 | − | 0.809017i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.571411 | + | 1.12146i | −0.571411 | + | 1.12146i | 0.406737 | + | 0.913545i | \(0.366667\pi\) |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 1.40674 | − | 0.913545i | 1.40674 | − | 0.913545i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.196895 | − | 1.24314i | 0.196895 | − | 1.24314i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.564602 | + | 1.73767i | −0.564602 | + | 1.73767i | 0.104528 | + | 0.994522i | \(0.466667\pi\) |
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.60917 | − | 1.16913i | −1.60917 | − | 1.16913i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.743145 | − | 0.669131i | \(-0.766667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.933580 | − | 0.358368i | \(-0.883333\pi\) | ||||
0.933580 | + | 0.358368i | \(0.116667\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(289\) | 1.06593 | + | 1.46713i | 1.06593 | + | 1.46713i | ||||
\(290\) | 0.639886 | − | 1.43721i | 0.639886 | − | 1.43721i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.705634 | − | 0.571411i | 0.705634 | − | 0.571411i | ||||
\(293\) | −0.978148 | − | 0.792088i | −0.978148 | − | 0.792088i | − | 1.00000i | \(-0.5\pi\) | |
−0.978148 | + | 0.207912i | \(0.933333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.506809 | − | 1.32028i | 0.506809 | − | 1.32028i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.292088 | − | 1.84417i | 0.292088 | − | 1.84417i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.827091 | −0.827091 | ||||||||
\(306\) | 0.434128 | − | 1.62019i | 0.434128 | − | 1.62019i | ||||
\(307\) | 0 | 0 | 0.629320 | − | 0.777146i | \(-0.283333\pi\) | ||||
−0.629320 | + | 0.777146i | \(0.716667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.838671 | − | 0.544639i | \(-0.816667\pi\) | ||||
0.838671 | + | 0.544639i | \(0.183333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.41355 | − | 1.27276i | 1.41355 | − | 1.27276i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.913545 | − | 0.406737i | \(-0.133333\pi\) | |||||||
\(314\) | 0.0163743 | + | 0.103383i | 0.0163743 | + | 0.103383i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.786610 | + | 1.08268i | −0.786610 | + | 1.08268i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.913545 | + | 0.406737i | −0.913545 | + | 0.406737i | ||||
\(325\) | −0.542195 | − | 0.669556i | −0.542195 | − | 0.669556i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.535233 | − | 1.64728i | −0.535233 | − | 1.64728i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.913545 | − | 0.406737i | \(-0.866667\pi\) | ||||
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.506809 | − | 1.32028i | −0.506809 | − | 1.32028i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.198825 | − | 1.89169i | −0.198825 | − | 1.89169i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.207912 | − | 0.978148i | \(-0.433333\pi\) | |||||||
\(338\) | −0.182451 | + | 0.0387811i | −0.182451 | + | 0.0387811i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.88258 | − | 1.22256i | −1.88258 | − | 1.22256i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.906737 | + | 1.77957i | −0.906737 | + | 1.77957i | ||||
\(347\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.604528 | + | 0.544320i | 0.604528 | + | 0.544320i | 0.913545 | − | 0.406737i | \(-0.133333\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.55216 | − | 0.0813454i | 1.55216 | − | 0.0813454i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.506809 | + | 0.506809i | −0.506809 | + | 0.506809i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(360\) | 0.139886 | + | 1.33093i | 0.139886 | + | 1.33093i | ||||
\(361\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(362\) | 1.64728 | − | 0.951057i | 1.64728 | − | 0.951057i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.08268 | − | 0.551651i | −1.08268 | − | 0.551651i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.50000 | − | 0.866025i | −1.50000 | − | 0.866025i | ||||
\(370\) | −1.88999 | + | 0.0990504i | −1.88999 | + | 0.0990504i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.292088 | + | 0.112122i | −0.292088 | + | 0.112122i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.581345 | + | 1.14095i | −0.581345 | + | 1.14095i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.838671 | − | 0.544639i | \(-0.816667\pi\) | ||||
0.838671 | + | 0.544639i | \(0.183333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.190983 | − | 1.81708i | −0.190983 | − | 1.81708i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(389\) | −0.312440 | − | 1.97267i | −0.312440 | − | 1.97267i | −0.207912 | − | 0.978148i | \(-0.566667\pi\) |
−0.104528 | − | 0.994522i | \(-0.533333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.913545 | + | 0.406737i | 0.913545 | + | 0.406737i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.483257 | + | 1.80354i | 0.483257 | + | 1.80354i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.278768 | − | 0.142040i | 0.278768 | − | 0.142040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.773659 | + | 0.164446i | 0.773659 | + | 0.164446i | ||||
\(401\) | −0.207912 | + | 1.97815i | −0.207912 | + | 1.97815i | 1.00000i | \(0.5\pi\) | ||
−0.207912 | + | 0.978148i | \(0.566667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.846528 | + | 1.30354i | −0.846528 | + | 1.30354i | ||||
\(405\) | 0.994522 | + | 0.895472i | 0.994522 | + | 0.895472i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.302208 | − | 1.90807i | −0.302208 | − | 1.90807i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
0.104528 | − | 0.994522i | \(-0.466667\pi\) | |||||||
\(410\) | −1.72256 | + | 1.55100i | −1.72256 | + | 1.55100i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.685505 | − | 0.846528i | 0.685505 | − | 0.846528i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.244415 | − | 0.336408i | −0.244415 | − | 0.336408i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.45381 | + | 0.309017i | −1.45381 | + | 0.309017i | ||||
\(425\) | −0.207539 | + | 1.31035i | −0.207539 | + | 1.31035i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.777146 | − | 0.629320i | \(-0.216667\pi\) | ||||
−0.777146 | + | 0.629320i | \(0.783333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.38488 | − | 1.12146i | −1.38488 | − | 1.12146i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(442\) | 1.47815 | + | 1.07394i | 1.47815 | + | 1.07394i | ||||
\(443\) | 0 | 0 | 0.0523360 | − | 0.998630i | \(-0.483333\pi\) | ||||
−0.0523360 | + | 0.998630i | \(0.516667\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.895472 | + | 0.343739i | 0.895472 | + | 0.343739i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.0809764 | + | 0.511265i | −0.0809764 | + | 0.511265i | 0.913545 | + | 0.406737i | \(0.133333\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(450\) | 0.684977 | − | 0.395472i | 0.684977 | − | 0.395472i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1.95630i | 1.95630i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(458\) | −0.743145 | − | 0.330869i | −0.743145 | − | 0.330869i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.95106 | − | 0.309017i | 1.95106 | − | 0.309017i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
1.00000 | \(0\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(464\) | −0.244415 | − | 1.14988i | −0.244415 | − | 1.14988i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.809017 | − | 1.40126i | 0.809017 | − | 1.40126i | ||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | −0.0570084 | − | 1.08779i | −0.0570084 | − | 1.08779i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.873619 | + | 1.20243i | −0.873619 | + | 1.20243i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.54047 | 1.54047 | ||||||||
\(482\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(485\) | 0.544320 | − | 1.22256i | 0.544320 | − | 1.22256i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(488\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 1.33826i | − | 1.33826i | ||||||
\(491\) | 0 | 0 | −0.669131 | − | 0.743145i | \(-0.733333\pi\) | ||||
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.90464 | − | 0.510348i | 1.90464 | − | 0.510348i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(500\) | 0.0581680 | + | 0.273659i | 0.0581680 | + | 0.273659i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) | ||||
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.05444 | + | 0.325391i | 2.05444 | + | 0.325391i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.53884 | + | 0.500000i | −1.53884 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.69420 | − | 0.978148i | 1.69420 | − | 0.978148i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.40807 | − | 0.377291i | −1.40807 | − | 0.377291i | ||||
\(521\) | 0.00547810 | − | 0.104528i | 0.00547810 | − | 0.104528i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
1.00000 | \(0\) | |||||||||
\(522\) | −0.951057 | − | 0.690983i | −0.951057 | − | 0.690983i | ||||
\(523\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(530\) | 1.16913 | + | 1.60917i | 1.16913 | + | 1.60917i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.46623 | − | 1.18733i | 1.46623 | − | 1.18733i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.05558 | − | 0.685505i | 1.05558 | − | 0.685505i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.251377 | + | 0.564602i | 0.251377 | + | 0.564602i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.67504 | + | 0.0877853i | −1.67504 | + | 0.0877853i | ||||
\(545\) | −0.617231 | + | 2.30354i | −0.617231 | + | 2.30354i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(548\) | −0.792088 | + | 0.978148i | −0.792088 | + | 0.978148i | ||||
\(549\) | −0.128496 | + | 0.604528i | −0.128496 | + | 0.604528i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.35779 | − | 1.22256i | 1.35779 | − | 1.22256i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.47815 | − | 0.155360i | −1.47815 | − | 0.155360i | −0.669131 | − | 0.743145i | \(-0.733333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.809017 | + | 1.81708i | 0.809017 | + | 1.81708i | ||||
\(563\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.39169 | − | 1.06485i | 2.39169 | − | 1.06485i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.128496 | + | 0.395472i | 0.128496 | + | 0.395472i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.669131 | + | 0.743145i | 0.669131 | + | 0.743145i | ||||
\(577\) | −0.557008 | + | 1.45106i | −0.557008 | + | 1.45106i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(578\) | −0.189560 | − | 1.80354i | −0.189560 | − | 1.80354i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.27276 | + | 0.924716i | −1.27276 | + | 0.924716i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.896802 | + | 0.142040i | −0.896802 | + | 0.142040i | ||||
\(585\) | −1.29885 | + | 0.661799i | −1.29885 | + | 0.661799i | ||||
\(586\) | 0.451057 | + | 1.17504i | 0.451057 | + | 1.17504i | ||||
\(587\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.09905 | + | 0.889993i | −1.09905 | + | 0.889993i | ||||
\(593\) | −1.32028 | + | 1.32028i | −1.32028 | + | 1.32028i | −0.406737 | + | 0.913545i | \(0.633333\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.17504 | + | 1.45106i | −1.17504 | + | 1.45106i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.155360 | − | 1.47815i | −0.155360 | − | 1.47815i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.139886 | − | 1.33093i | 0.139886 | − | 1.33093i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.716282 | + | 0.413545i | 0.716282 | + | 0.413545i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.18606 | + | 1.18606i | −1.18606 | + | 1.18606i | ||||
\(613\) | −0.402280 | + | 0.325760i | −0.402280 | + | 0.325760i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.358368 | − | 0.933580i | \(-0.616667\pi\) | ||||
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.942790 | − | 0.684977i | 0.942790 | − | 0.684977i | ||||
\(626\) | −1.86055 | + | 0.395472i | −1.86055 | + | 0.395472i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.0375111 | − | 0.0977196i | 0.0375111 | − | 0.0977196i | ||||
\(629\) | −1.58726 | − | 1.76283i | −1.58726 | − | 1.76283i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.358368 | − | 0.933580i | \(-0.616667\pi\) | ||||
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.461219 | + | 1.72129i | 0.461219 | + | 1.72129i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.0570084 | + | 1.08779i | −0.0570084 | + | 1.08779i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.22256 | − | 0.544320i | 1.22256 | − | 0.544320i | ||||
\(641\) | 0.978148 | + | 0.207912i | 0.978148 | + | 0.207912i | 0.669131 | − | 0.743145i | \(-0.266667\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.406737 | − | 0.913545i | \(-0.633333\pi\) | ||||
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 0.994522 | + | 0.104528i | 0.994522 | + | 0.104528i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.134777 | + | 0.850950i | 0.134777 | + | 0.850950i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.601105 | − | 0.390362i | −0.601105 | − | 0.390362i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.360114 | + | 1.69420i | −0.360114 | + | 1.69420i | ||||
\(657\) | −0.571411 | + | 0.705634i | −0.571411 | + | 0.705634i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.92920 | + | 0.101105i | −1.92920 | + | 0.101105i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.221232 | + | 1.39680i | −0.221232 | + | 1.39680i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.128496 | + | 0.604528i | −0.128496 | + | 0.604528i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(674\) | −0.773659 | + | 1.73767i | −0.773659 | + | 1.73767i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.177397 | + | 0.0576399i | 0.177397 | + | 0.0576399i | ||||
\(677\) | 1.53516 | + | 1.24314i | 1.53516 | + | 1.24314i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
0.669131 | + | 0.743145i | \(0.266667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.01908 | + | 2.00006i | 1.01908 | + | 2.00006i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.62700 | + | 0.435952i | 1.62700 | + | 0.435952i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.881761 | − | 1.35779i | −0.881761 | − | 1.35779i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(692\) | 1.67504 | − | 1.08779i | 1.67504 | − | 1.08779i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.86947 | − | 0.454480i | −2.86947 | − | 0.454480i | ||||
\(698\) | −0.251377 | − | 0.773659i | −0.251377 | − | 0.773659i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.50133 | − | 0.402280i | −1.50133 | − | 0.402280i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.38488 | − | 0.705634i | −1.38488 | − | 0.705634i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0375111 | + | 0.715754i | 0.0375111 | + | 0.715754i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
−0.913545 | + | 0.406737i | \(0.866667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.692314 | − | 0.185505i | 0.692314 | − | 0.185505i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0.544320 | − | 1.22256i | 0.544320 | − | 1.22256i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.00000 | −1.00000 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.90211 | −1.90211 | ||||||||
\(725\) | 0.805239 | + | 0.464905i | 0.805239 | + | 0.464905i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(730\) | 0.661799 | + | 1.01908i | 0.661799 | + | 1.01908i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.58231 | + | 0.704489i | −1.58231 | + | 0.704489i | −0.994522 | − | 0.104528i | \(-0.966667\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.866025 | + | 1.50000i | 0.866025 | + | 1.50000i | ||||
\(739\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(740\) | 1.68631 | + | 0.859217i | 1.68631 | + | 0.859217i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.994522 | − | 0.104528i | \(-0.966667\pi\) | ||||
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.41361 | + | 0.646724i | 2.41361 | + | 0.646724i | ||||
\(746\) | 0.309017 | + | 0.0489435i | 0.309017 | + | 0.0489435i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.07394 | − | 0.697423i | 1.07394 | − | 0.697423i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.494522 | − | 0.761497i | −0.494522 | − | 0.761497i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.302208 | + | 0.0809764i | 0.302208 | + | 0.0809764i | 0.406737 | − | 0.913545i | \(-0.366667\pi\) |
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.09563 | + | 0.804436i | 2.09563 | + | 0.804436i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.38488 | + | 1.12146i | 1.38488 | + | 1.12146i | 0.978148 | + | 0.207912i | \(0.0666667\pi\) |
0.406737 | + | 0.913545i | \(0.366667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.743145 | + | 1.66913i | −0.743145 | + | 1.66913i | ||||
\(773\) | 0.207912 | − | 0.978148i | 0.207912 | − | 0.978148i | −0.743145 | − | 0.669131i | \(-0.766667\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.207912 | − | 0.978148i | −0.207912 | − | 0.978148i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.715754 | + | 1.86460i | −0.715754 | + | 1.86460i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(785\) | −0.139886 | + | 0.00733113i | −0.139886 | + | 0.00733113i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | 0.483257 | − | 1.80354i | 0.483257 | − | 1.80354i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.564602 | − | 0.366657i | −0.564602 | − | 0.366657i | ||||
\(794\) | −0.312440 | − | 0.0163743i | −0.312440 | − | 0.0163743i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.571411 | + | 0.705634i | 0.571411 | + | 0.705634i | 0.978148 | − | 0.207912i | \(-0.0666667\pi\) |
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.587785 | − | 0.529244i | −0.587785 | − | 0.529244i | ||||
\(801\) | 0.390362 | − | 0.601105i | 0.390362 | − | 0.601105i | ||||
\(802\) | 1.16913 | − | 1.60917i | 1.16913 | − | 1.60917i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.38488 | − | 0.705634i | 1.38488 | − | 0.705634i | ||||
\(809\) | 0.103383 | − | 1.97267i | 0.103383 | − | 1.97267i | −0.104528 | − | 0.994522i | \(-0.533333\pi\) |
0.207912 | − | 0.978148i | \(-0.433333\pi\) | |||||||
\(810\) | −0.413545 | − | 1.27276i | −0.413545 | − | 1.27276i | ||||
\(811\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.692314 | + | 1.80354i | −0.692314 | + | 1.80354i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.26728 | − | 0.481926i | 2.26728 | − | 0.481926i | ||||
\(821\) | −1.53884 | + | 1.11803i | −1.53884 | + | 1.11803i | −0.587785 | + | 0.809017i | \(0.700000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.669131 | − | 0.743145i | \(-0.266667\pi\) | ||||
−0.669131 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.358368 | − | 0.933580i | \(-0.616667\pi\) | ||||
0.358368 | + | 0.933580i | \(0.383333\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.614648 | − | 1.89169i | 0.614648 | − | 1.89169i | 0.207912 | − | 0.978148i | \(-0.433333\pi\) |
0.406737 | − | 0.913545i | \(-0.366667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.01693 | + | 0.390362i | −1.01693 | + | 0.390362i | ||||
\(833\) | 1.30354 | − | 1.05558i | 1.30354 | − | 1.05558i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.0399263 | − | 0.379874i | 0.0399263 | − | 0.379874i | ||||
\(842\) | 0.0434654 | + | 0.413545i | 0.0434654 | + | 0.413545i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0260925 | − | 0.248254i | −0.0260925 | − | 0.248254i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.41355 | + | 0.459289i | 1.41355 | + | 0.459289i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.834908 | − | 1.03103i | 0.834908 | − | 1.03103i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.994522 | + | 1.10453i | −0.994522 | + | 1.10453i | 1.00000i | \(0.5\pi\) | ||
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.24164 | − | 1.45574i | −2.24164 | − | 1.45574i | ||||
\(866\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.638616 | + | 1.66365i | 0.638616 | + | 1.66365i | ||||
\(873\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.614648 | − | 1.89169i | −0.614648 | − | 1.89169i | −0.406737 | − | 0.913545i | \(-0.633333\pi\) |
−0.207912 | − | 0.978148i | \(-0.566667\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.58231 | − | 0.704489i | 1.58231 | − | 0.704489i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(882\) | −0.978148 | − | 0.207912i | −0.978148 | − | 0.207912i | ||||
\(883\) | 0 | 0 | 0.104528 | − | 0.994522i | \(-0.466667\pi\) | ||||
−0.104528 | + | 0.994522i | \(0.533333\pi\) | |||||||
\(884\) | −0.743145 | − | 1.66913i | −0.743145 | − | 1.66913i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.743145 | − | 0.669131i | \(-0.766667\pi\) | ||||
0.743145 | + | 0.669131i | \(0.233333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.603631 | − | 0.745423i | −0.603631 | − | 0.745423i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.325760 | − | 0.402280i | 0.325760 | − | 0.402280i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.790943 | −0.790943 | ||||||||
\(901\) | −0.645240 | + | 2.40807i | −0.645240 | + | 2.40807i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.978148 | − | 1.69420i | 0.978148 | − | 1.69420i | ||||
\(905\) | 1.03536 | + | 2.32545i | 1.03536 | + | 2.32545i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.557008 | − | 1.45106i | 0.557008 | − | 1.45106i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.207912 | − | 0.978148i | \(-0.566667\pi\) | ||||
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.336408 | + | 1.58268i | −0.336408 | + | 1.58268i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.478148 | + | 0.658114i | 0.478148 | + | 0.658114i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) | ||||
−0.994522 | + | 0.104528i | \(0.966667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.84417 | − | 0.707912i | −1.84417 | − | 0.707912i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0585410 | − | 1.11703i | 0.0585410 | − | 1.11703i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.363271 | + | 1.11803i | −0.363271 | + | 1.11803i | ||||
\(929\) | 0.516929 | + | 0.0270911i | 0.516929 | + | 0.0270911i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.40126 | + | 0.809017i | −1.40126 | + | 0.809017i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.494522 | + | 0.970554i | −0.494522 | + | 0.970554i | ||||
\(937\) | 1.73767 | − | 0.564602i | 1.73767 | − | 0.564602i | 0.743145 | − | 0.669131i | \(-0.233333\pi\) |
0.994522 | + | 0.104528i | \(0.0333333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.90807 | + | 0.302208i | 1.90807 | + | 0.302208i | 0.994522 | − | 0.104528i | \(-0.0333333\pi\) |
0.913545 | + | 0.406737i | \(0.133333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.494522 | − | 0.856537i | −0.494522 | − | 0.856537i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.72129 | + | 0.461219i | −1.72129 | + | 0.461219i | −0.978148 | − | 0.207912i | \(-0.933333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(954\) | 1.35779 | − | 0.604528i | 1.35779 | − | 0.604528i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.406737 | − | 0.913545i | 0.406737 | − | 0.913545i | ||||
\(962\) | −1.33409 | − | 0.770236i | −1.33409 | − | 0.770236i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(965\) | 2.44512 | 2.44512 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.406737 | − | 0.913545i | \(-0.366667\pi\) | ||||
−0.406737 | + | 0.913545i | \(0.633333\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.08268 | + | 0.786610i | −1.08268 | + | 0.786610i | ||||
\(971\) | 0 | 0 | −0.544639 | − | 0.838671i | \(-0.683333\pi\) | ||||
0.544639 | + | 0.838671i | \(0.316667\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.614648 | − | 0.0646021i | 0.614648 | − | 0.0646021i | ||||
\(977\) | −0.292088 | + | 0.112122i | −0.292088 | + | 0.112122i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.207912 | + | 0.978148i | \(0.433333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.669131 | + | 1.15897i | −0.669131 | + | 1.15897i | ||||
\(981\) | 1.58779 | + | 0.809017i | 1.58779 | + | 0.809017i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.46799 | + | 0.390890i | −2.46799 | + | 0.390890i | ||||
\(986\) | −1.90464 | − | 0.510348i | −1.90464 | − | 0.510348i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.0809764 | − | 0.511265i | 0.0809764 | − | 0.511265i | −0.913545 | − | 0.406737i | \(-0.866667\pi\) |
0.994522 | − | 0.104528i | \(-0.0333333\pi\) | |||||||
\(998\) | 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 | 964.1.bh.a.159.1 | ✓ | 16 | |
4.3 | odd | 2 | CM | 964.1.bh.a.159.1 | ✓ | 16 | |
241.144 | even | 60 | inner | 964.1.bh.a.867.1 | yes | 16 | |
964.867 | odd | 60 | inner | 964.1.bh.a.867.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
964.1.bh.a.159.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
964.1.bh.a.159.1 | ✓ | 16 | 4.3 | odd | 2 | CM | |
964.1.bh.a.867.1 | yes | 16 | 241.144 | even | 60 | inner | |
964.1.bh.a.867.1 | yes | 16 | 964.867 | odd | 60 | inner |