Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2359,1,Mod(6,2359)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2359, base_ring=CyclotomicField(56))
chi = DirichletCharacter(H, H._module([28, 47]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2359.6");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2359 = 7 \cdot 337 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2359.cv (of order \(56\), degree \(24\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.17729436480\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Coefficient field: | \(\Q(\zeta_{56})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{56}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{56} - \cdots)\) |
Embedding invariants
Embedding label | 1301.1 | ||
Root | \(-0.846724 + 0.532032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2359.1301 |
Dual form | 2359.1.cv.a.1728.1 |
$q$-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 \(\left(\mathbb{Z}/2359\mathbb{Z}\right)^\times\).
\(n\) | \(675\) | \(1695\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{43}{56}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.146988 | + | 0.643997i | 0.146988 | + | 0.643997i | 0.993712 | + | 0.111964i | \(0.0357143\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(3\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(4\) | 0.507843 | − | 0.244564i | 0.507843 | − | 0.244564i | ||||
\(5\) | 0 | 0 | −0.483719 | − | 0.875223i | \(-0.660714\pi\) | ||||
0.483719 | + | 0.875223i | \(0.339286\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.846724 | − | 0.532032i | −0.846724 | − | 0.532032i | ||||
\(8\) | 0.643997 | + | 0.807546i | 0.643997 | + | 0.807546i | ||||
\(9\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.559828 | + | 0.789004i | 0.559828 | + | 0.789004i | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(14\) | 0.218169 | − | 0.623490i | 0.218169 | − | 0.623490i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.0739590 | + | 0.0927417i | −0.0739590 | + | 0.0927417i | ||||
\(17\) | 0 | 0 | 0.960917 | − | 0.276836i | \(-0.0892857\pi\) | ||||
−0.960917 | + | 0.276836i | \(0.910714\pi\) | |||||||
\(18\) | −0.286605 | + | 0.595142i | −0.286605 | + | 0.595142i | ||||
\(19\) | 0 | 0 | 0.578671 | − | 0.815561i | \(-0.303571\pi\) | ||||
−0.578671 | + | 0.815561i | \(0.696429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.425828 | + | 0.476502i | −0.425828 | + | 0.476502i | ||||
\(23\) | 0.293211 | − | 0.162052i | 0.293211 | − | 0.162052i | −0.330279 | − | 0.943883i | \(-0.607143\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.532032 | + | 0.846724i | −0.532032 | + | 0.846724i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.560119 | − | 0.0631102i | −0.560119 | − | 0.0631102i | ||||
\(29\) | −0.370222 | − | 0.669867i | −0.370222 | − | 0.669867i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.167506 | − | 0.985871i | \(-0.446429\pi\) | ||||
−0.167506 | + | 0.985871i | \(0.553571\pi\) | |||||||
\(32\) | 0.860006 | + | 0.414157i | 0.860006 | + | 0.414157i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.549531 | + | 0.125427i | 0.549531 | + | 0.125427i | ||||
\(37\) | 0.846011 | − | 1.75676i | 0.846011 | − | 1.75676i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.59842 | + | 0.559311i | −1.59842 | + | 0.559311i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(44\) | 0.477267 | + | 0.263776i | 0.477267 | + | 0.263776i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.147459 | + | 0.165007i | 0.147459 | + | 0.165007i | ||||
\(47\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | ||||
\(50\) | −0.623490 | − | 0.218169i | −0.623490 | − | 0.218169i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.846724 | + | 0.467968i | 0.846724 | + | 0.467968i | 0.846724 | − | 0.532032i | \(-0.178571\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.115647 | − | 1.02640i | −0.115647 | − | 1.02640i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.376974 | − | 0.336884i | 0.376974 | − | 0.336884i | ||||
\(59\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.815561 | − | 0.578671i | \(-0.196429\pi\) | ||||
−0.815561 | + | 0.578671i | \(0.803571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.330279 | − | 0.943883i | −0.330279 | − | 0.943883i | ||||
\(64\) | −0.166701 | + | 0.730364i | −0.166701 | + | 0.730364i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.107758 | − | 0.0310446i | −0.107758 | − | 0.0310446i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.943883 | + | 1.33028i | 0.943883 | + | 1.33028i | 0.943883 | + | 0.330279i | \(0.107143\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(72\) | 1.03289i | 1.03289i | ||||||||
\(73\) | 0 | 0 | 0.578671 | − | 0.815561i | \(-0.303571\pi\) | ||||
−0.578671 | + | 0.815561i | \(0.696429\pi\) | |||||||
\(74\) | 1.25570 | + | 0.286605i | 1.25570 | + | 0.286605i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0542447 | − | 0.965916i | −0.0542447 | − | 0.965916i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0498289 | − | 0.218315i | −0.0498289 | − | 0.218315i | 0.943883 | − | 0.330279i | \(-0.107143\pi\) |
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.0560704 | − | 0.998427i | \(-0.517857\pi\) | ||||
0.0560704 | + | 0.998427i | \(0.482143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.595142 | − | 0.947164i | −0.595142 | − | 0.947164i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.276630 | + | 0.960203i | −0.276630 | + | 0.960203i | ||||
\(89\) | 0 | 0 | 0.875223 | − | 0.483719i | \(-0.160714\pi\) | ||||
−0.875223 | + | 0.483719i | \(0.839286\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.109273 | − | 0.154006i | 0.109273 | − | 0.154006i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.875223 | − | 0.483719i | \(-0.839286\pi\) | ||||
0.875223 | + | 0.483719i | \(0.160714\pi\) | |||||||
\(98\) | −0.516445 | + | 0.411851i | −0.516445 | + | 0.411851i | ||||
\(99\) | −0.0542447 | + | 0.965916i | −0.0542447 | + | 0.965916i | ||||
\(100\) | −0.0631102 | + | 0.560119i | −0.0631102 | + | 0.560119i | ||||
\(101\) | 0 | 0 | −0.745642 | − | 0.666347i | \(-0.767857\pi\) | ||||
0.745642 | + | 0.666347i | \(0.232143\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.176911 | + | 0.614073i | −0.176911 | + | 0.614073i | ||||
\(107\) | 0.656405 | − | 1.87590i | 0.656405 | − | 1.87590i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.433884 | − | 0.900969i | \(-0.357143\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.559828 | − | 1.01293i | 0.559828 | − | 1.01293i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.993712 | − | 0.111964i | \(-0.0357143\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.111964 | − | 0.0391781i | 0.111964 | − | 0.0391781i | ||||
\(113\) | −1.00435 | − | 1.59842i | −1.00435 | − | 1.59842i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.351840 | − | 0.249644i | −0.351840 | − | 0.249644i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0211590 | − | 0.0604691i | 0.0211590 | − | 0.0604691i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.559311 | − | 0.351438i | 0.559311 | − | 0.351438i | ||||
\(127\) | −1.60808 | − | 0.273223i | −1.60808 | − | 0.273223i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(128\) | 0.459679 | 0.459679 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.00415345 | − | 0.0739590i | 0.00415345 | − | 0.0739590i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.442244 | − | 0.0498289i | 0.442244 | − | 0.0498289i | 0.111964 | − | 0.993712i | \(-0.464286\pi\) |
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.985871 | − | 0.167506i | \(-0.0535714\pi\) | ||||
−0.985871 | + | 0.167506i | \(0.946429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.717956 | + | 0.803393i | −0.717956 | + | 0.803393i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.115647 | + | 0.0263957i | −0.115647 | + | 0.0263957i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.09906i | − | 1.09906i | ||||||
\(149\) | 0.222521 | − | 0.0250721i | 0.222521 | − | 0.0250721i | − | 1.00000i | \(-0.5\pi\) | |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.91881 | − | 0.552800i | −1.91881 | − | 0.552800i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.943883 | − | 0.330279i | \(-0.892857\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.614073 | − | 0.176911i | 0.614073 | − | 0.176911i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.276836 | − | 0.960917i | \(-0.589286\pi\) | ||||
0.276836 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(158\) | 0.133270 | − | 0.0641793i | 0.133270 | − | 0.0641793i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.334485 | − | 0.0187843i | −0.334485 | − | 0.0187843i | ||||
\(162\) | −0.595142 | + | 0.286605i | −0.595142 | + | 0.286605i | ||||
\(163\) | −1.77554 | + | 0.735454i | −1.77554 | + | 0.735454i | −0.781831 | + | 0.623490i | \(0.785714\pi\) |
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.674958 | + | 0.674958i | −0.674958 | + | 0.674958i | ||||
\(173\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(176\) | −0.114578 | − | 0.00643456i | −0.114578 | − | 0.00643456i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.595142 | + | 0.286605i | −0.595142 | + | 0.286605i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.319691 | + | 0.132420i | 0.319691 | + | 0.132420i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.77554 | − | 0.735454i | −1.77554 | − | 0.735454i | −0.993712 | − | 0.111964i | \(-0.964286\pi\) |
−0.781831 | − | 0.623490i | \(-0.785714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.75676 | + | 0.400969i | −1.75676 | + | 0.400969i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.440689 | + | 0.351438i | 0.440689 | + | 0.351438i | ||||
\(197\) | −0.292893 | − | 0.707107i | −0.292893 | − | 0.707107i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(198\) | −0.630020 | + | 0.107045i | −0.630020 | + | 0.107045i | ||||
\(199\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(200\) | −1.02640 | + | 0.115647i | −1.02640 | + | 0.115647i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0429145 | + | 0.764163i | −0.0429145 | + | 0.764163i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.330279 | + | 0.0561167i | 0.330279 | + | 0.0561167i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(212\) | 0.544451 | + | 0.0305757i | 0.544451 | + | 0.0305757i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.30455 | + | 0.146988i | 1.30455 | + | 0.146988i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.734614 | + | 0.211639i | 0.734614 | + | 0.211639i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.745642 | − | 0.666347i | \(-0.767857\pi\) | ||||
0.745642 | + | 0.666347i | \(0.232143\pi\) | |||||||
\(224\) | −0.507843 | − | 0.808227i | −0.507843 | − | 0.808227i | ||||
\(225\) | −0.943883 | + | 0.330279i | −0.943883 | + | 0.330279i | ||||
\(226\) | 0.881748 | − | 0.881748i | 0.881748 | − | 0.881748i | ||||
\(227\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.302527 | − | 0.730364i | 0.302527 | − | 0.730364i | ||||
\(233\) | 0.400969 | − | 1.75676i | 0.400969 | − | 1.75676i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.974928 | − | 0.777479i | 0.974928 | − | 0.777479i | − | 1.00000i | \(-0.5\pi\) | |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(242\) | 0.0420520 | + | 0.00473812i | 0.0420520 | + | 0.00473812i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(252\) | −0.398570 | − | 0.398570i | −0.398570 | − | 0.398570i | ||||
\(253\) | 0.292007 | + | 0.140623i | 0.292007 | + | 0.140623i | ||||
\(254\) | −0.0604131 | − | 1.07576i | −0.0604131 | − | 1.07576i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.234268 | + | 1.02640i | 0.234268 | + | 1.02640i | ||||
\(257\) | 0 | 0 | −0.985871 | − | 0.167506i | \(-0.946429\pi\) | ||||
0.985871 | + | 0.167506i | \(0.0535714\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.65099 | + | 1.03739i | −1.65099 | + | 1.03739i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.128204 | − | 0.754553i | 0.128204 | − | 0.754553i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.90097 | − | 0.433884i | −1.90097 | − | 0.433884i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.0623166 | + | 0.0105880i | −0.0623166 | + | 0.0105880i | ||||
\(269\) | 0 | 0 | 0.745642 | − | 0.666347i | \(-0.232143\pi\) | ||||
−0.745642 | + | 0.666347i | \(0.767857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.875223 | − | 0.483719i | \(-0.160714\pi\) | ||||
−0.875223 | + | 0.483719i | \(0.839286\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0970941 | + | 0.277479i | 0.0970941 | + | 0.277479i | ||||
\(275\) | −0.965916 | + | 0.0542447i | −0.965916 | + | 0.0542447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.06925 | + | 1.50696i | 1.06925 | + | 1.50696i | 0.846724 | + | 0.532032i | \(0.178571\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0739590 | + | 0.656405i | 0.0739590 | + | 0.656405i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0.804683 | + | 0.444733i | 0.804683 | + | 0.444733i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.414157 | + | 0.860006i | 0.414157 | + | 0.860006i | ||||
\(289\) | 0.846724 | − | 0.532032i | 0.846724 | − | 0.532032i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.875223 | − | 0.483719i | \(-0.839286\pi\) | ||||
0.875223 | + | 0.483719i | \(0.160714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.96349 | − | 0.448154i | 1.96349 | − | 0.448154i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.0488542 | + | 0.139617i | 0.0488542 | + | 0.139617i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.65099 | + | 0.376828i | 1.65099 | + | 0.376828i | ||||
\(302\) | 0.0739590 | − | 1.31696i | 0.0739590 | − | 1.31696i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(308\) | −0.263776 | − | 0.477267i | −0.263776 | − | 0.477267i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.0786972 | − | 0.0986831i | −0.0786972 | − | 0.0986831i | ||||
\(317\) | 0.789004 | + | 0.559828i | 0.789004 | + | 0.559828i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.321267 | − | 0.667118i | 0.321267 | − | 0.667118i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0370683 | − | 0.218169i | −0.0370683 | − | 0.218169i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.351438 | + | 0.440689i | 0.351438 | + | 0.440689i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.734614 | − | 1.03534i | −0.734614 | − | 1.03534i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0971591 | − | 0.862311i | 0.0971591 | − | 0.862311i | −0.846724 | − | 0.532032i | \(-0.821429\pi\) |
0.943883 | − | 0.330279i | \(-0.107143\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.75676 | − | 0.846011i | 1.75676 | − | 0.846011i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(338\) | −0.660558 | −0.660558 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.111964 | − | 0.993712i | 0.111964 | − | 0.993712i | ||||
\(344\) | −1.48104 | − | 0.930602i | −1.48104 | − | 0.930602i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.30521 | + | 1.16640i | −1.30521 | + | 1.16640i | −0.330279 | + | 0.943883i | \(0.607143\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(350\) | 0.411851 | + | 0.516445i | 0.411851 | + | 0.516445i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.154684 | + | 0.910405i | 0.154684 | + | 0.910405i | ||||
\(353\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.272052 | − | 0.341142i | −0.272052 | − | 0.341142i | ||||
\(359\) | 0.993712 | − | 1.11196i | 0.993712 | − | 1.11196i | − | 1.00000i | \(-0.5\pi\) | |
0.993712 | − | 0.111964i | \(-0.0357143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.330279 | − | 0.943883i | −0.330279 | − | 0.943883i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(368\) | −0.00665662 | + | 0.0391781i | −0.00665662 | + | 0.0391781i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.467968 | − | 0.846724i | −0.467968 | − | 0.846724i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.37876 | − | 0.314692i | −1.37876 | − | 0.314692i | −0.532032 | − | 0.846724i | \(-0.678571\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.277479 | + | 0.347948i | −0.277479 | + | 0.347948i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.212646 | − | 1.25155i | 0.212646 | − | 1.25155i | ||||
\(383\) | 0 | 0 | −0.666347 | − | 0.745642i | \(-0.732143\pi\) | ||||
0.666347 | + | 0.745642i | \(0.267857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.516445 | − | 1.07241i | −0.516445 | − | 1.07241i | ||||
\(387\) | −1.59842 | − | 0.559311i | −1.59842 | − | 0.559311i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.958689 | − | 0.461680i | −0.958689 | − | 0.461680i | −0.111964 | − | 0.993712i | \(-0.535714\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.448154 | + | 0.930602i | −0.448154 | + | 0.930602i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.412323 | − | 0.292558i | 0.412323 | − | 0.292558i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.208681 | + | 0.503800i | 0.208681 | + | 0.503800i | ||||
\(397\) | 0 | 0 | −0.578671 | − | 0.815561i | \(-0.696429\pi\) | ||||
0.578671 | + | 0.815561i | \(0.303571\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0391781 | − | 0.111964i | −0.0391781 | − | 0.111964i | ||||
\(401\) | −0.277479 | + | 1.21572i | −0.277479 | + | 1.21572i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.498426 | + | 0.0846860i | −0.498426 | + | 0.0846860i | ||||
\(407\) | 1.85971 | − | 0.315978i | 1.85971 | − | 0.315978i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.0124081 | + | 0.220947i | 0.0124081 | + | 0.220947i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.595142 | + | 0.286605i | 0.595142 | + | 0.286605i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.167382 | + | 0.985139i | 0.167382 | + | 0.985139i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.125427 | − | 1.11319i | −0.125427 | − | 1.11319i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.0971591 | + | 0.862311i | −0.0971591 | + | 0.862311i | 0.846724 | + | 0.532032i | \(0.178571\pi\) |
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.0365776 | − | 0.651325i | 0.0365776 | − | 0.651325i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.167506 | − | 0.985871i | \(-0.553571\pi\) | ||||
0.167506 | + | 0.985871i | \(0.446429\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.545848 | − | 1.89468i | 0.545848 | − | 1.89468i | 0.111964 | − | 0.993712i | \(-0.464286\pi\) |
0.433884 | − | 0.900969i | \(-0.357143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.529726 | − | 0.529726i | 0.529726 | − | 0.529726i | ||||
\(449\) | −1.47592 | + | 0.516445i | −1.47592 | + | 0.516445i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) |
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(450\) | −0.351438 | − | 0.559311i | −0.351438 | − | 0.559311i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.900969 | − | 0.566116i | −0.900969 | − | 0.566116i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.28061 | + | 1.43300i | −1.28061 | + | 1.43300i | −0.433884 | + | 0.900969i | \(0.642857\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.276836 | − | 0.960917i | \(-0.589286\pi\) | ||||
0.276836 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(464\) | 0.0895059 | + | 0.0152077i | 0.0895059 | + | 0.0152077i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.19028 | 1.19028 | ||||||||
\(467\) | 0 | 0 | −0.985871 | − | 0.167506i | \(-0.946429\pi\) | ||||
0.985871 | + | 0.167506i | \(0.0535714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.0747247 | + | 0.0836170i | 0.0747247 | + | 0.0836170i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.33614 | − | 0.948041i | −1.33614 | − | 0.948041i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.370222 | + | 0.893796i | 0.370222 | + | 0.893796i | ||||
\(478\) | 0.643997 | + | 0.513570i | 0.643997 | + | 0.513570i | ||||
\(479\) | 0 | 0 | 0.666347 | − | 0.745642i | \(-0.267857\pi\) | ||||
−0.666347 | + | 0.745642i | \(0.732143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.00404310 | − | 0.0358835i | −0.00404310 | − | 0.0358835i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.831919 | + | 0.663433i | 0.831919 | + | 0.663433i | 0.943883 | − | 0.330279i | \(-0.107143\pi\) |
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.43300 | − | 0.412840i | 1.43300 | − | 0.412840i | 0.532032 | − | 0.846724i | \(-0.321429\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.0914577 | − | 1.62856i | −0.0914577 | − | 1.62856i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.781831 | + | 0.376510i | −0.781831 | + | 0.376510i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.960917 | − | 0.276836i | \(-0.0892857\pi\) | ||||
−0.960917 | + | 0.276836i | \(0.910714\pi\) | |||||||
\(504\) | 0.549531 | − | 0.874573i | 0.549531 | − | 0.874573i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.0476394 | + | 0.208722i | −0.0476394 | + | 0.208722i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.883470 | + | 0.254523i | −0.883470 | + | 0.254523i | ||||
\(509\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.212404 | + | 0.102288i | −0.212404 | + | 0.102288i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.910749 | − | 0.910749i | −0.910749 | − | 0.910749i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(522\) | 0.504774 | − | 0.0283475i | 0.504774 | − | 0.0283475i | ||||
\(523\) | 0 | 0 | −0.960917 | − | 0.276836i | \(-0.910714\pi\) | ||||
0.960917 | + | 0.276836i | \(0.0892857\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 1.28799i | − | 1.28799i | ||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.472320 | + | 0.751694i | −0.472320 | + | 0.751694i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.0443259 | − | 0.107012i | −0.0443259 | − | 0.107012i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.467968 | + | 0.846724i | −0.467968 | + | 0.846724i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.70711 | − | 0.707107i | 1.70711 | − | 0.707107i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
1.00000 | \(0\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.96864 | + | 0.334485i | 1.96864 | + | 0.334485i | 0.993712 | + | 0.111964i | \(0.0357143\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(548\) | 0.212404 | − | 0.133462i | 0.212404 | − | 0.133462i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.176911 | − | 0.614073i | −0.176911 | − | 0.614073i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.0739590 | + | 0.211363i | −0.0739590 | + | 0.211363i | ||||
\(554\) | −0.813311 | + | 0.910095i | −0.813311 | + | 0.910095i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.411851 | + | 0.144113i | −0.411851 | + | 0.144113i | ||||
\(563\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.330279 | − | 0.943883i | 0.330279 | − | 0.943883i | ||||
\(568\) | −0.466404 | + | 1.61892i | −0.466404 | + | 1.61892i | ||||
\(569\) | 0.570690 | − | 1.37777i | 0.570690 | − | 1.37777i | −0.330279 | − | 0.943883i | \(-0.607143\pi\) |
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.218315 | − | 0.0498289i | 0.218315 | − | 0.0498289i | −0.111964 | − | 0.993712i | \(-0.535714\pi\) |
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.0187843 | + | 0.334485i | −0.0187843 | + | 0.334485i | ||||
\(576\) | −0.585706 | + | 0.467085i | −0.585706 | + | 0.467085i | ||||
\(577\) | 0 | 0 | −0.875223 | − | 0.483719i | \(-0.839286\pi\) | ||||
0.875223 | + | 0.483719i | \(0.160714\pi\) | |||||||
\(578\) | 0.467085 | + | 0.467085i | 0.467085 | + | 0.467085i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.104792 | + | 0.930051i | 0.104792 | + | 0.930051i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.167506 | − | 0.985871i | \(-0.553571\pi\) | ||||
0.167506 | + | 0.985871i | \(0.446429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.100355 | + | 0.208389i | 0.100355 | + | 0.208389i | ||||
\(593\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.106874 | − | 0.0671533i | 0.106874 | − | 0.0671533i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.678448 | − | 0.541044i | 0.678448 | − | 0.541044i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.578671 | − | 0.815561i | \(-0.303571\pi\) | ||||
−0.578671 | + | 0.815561i | \(0.696429\pi\) | |||||||
\(602\) | 1.11862i | 1.11862i | ||||||||
\(603\) | −0.0648927 | − | 0.0914577i | −0.0648927 | − | 0.0914577i | ||||
\(604\) | −1.10965 | + | 0.188537i | −1.10965 | + | 0.188537i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.960917 | − | 0.276836i | \(-0.910714\pi\) | ||||
0.960917 | + | 0.276836i | \(0.0892857\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.943883 | − | 0.669721i | 0.943883 | − | 0.669721i | − | 1.00000i | \(-0.5\pi\) | |
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.745088 | − | 0.665852i | 0.745088 | − | 0.665852i | ||||
\(617\) | 1.62856 | − | 1.15552i | 1.62856 | − | 1.15552i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
0.846724 | − | 0.532032i | \(-0.178571\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.433884 | − | 0.900969i | −0.433884 | − | 0.900969i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.33485 | − | 0.467085i | 1.33485 | − | 0.467085i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(632\) | 0.144209 | − | 0.180833i | 0.144209 | − | 0.180833i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.244553 | + | 0.590404i | −0.244553 | + | 0.590404i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.476844 | + | 0.108837i | 0.476844 | + | 0.108837i | ||||
\(639\) | −0.0914577 | + | 1.62856i | −0.0914577 | + | 1.62856i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.484586 | + | 1.68203i | 0.484586 | + | 1.68203i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.167506 | − | 0.985871i | \(-0.446429\pi\) | ||||
−0.167506 | + | 0.985871i | \(0.553571\pi\) | |||||||
\(644\) | −0.174460 | + | 0.0722637i | −0.174460 | + | 0.0722637i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(648\) | −0.643997 | + | 0.807546i | −0.643997 | + | 0.807546i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.721831 | + | 0.807730i | −0.721831 | + | 0.807730i | ||||
\(653\) | 1.17700 | + | 1.47592i | 1.17700 | + | 1.47592i | 0.846724 | + | 0.532032i | \(0.178571\pi\) |
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0927433 | + | 0.545848i | 0.0927433 | + | 0.545848i | 0.993712 | + | 0.111964i | \(0.0357143\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(662\) | 0.569607 | − | 0.0641793i | 0.569607 | − | 0.0641793i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.803051 | + | 1.00699i | 0.803051 | + | 1.00699i | ||||
\(667\) | −0.217106 | − | 0.136417i | −0.217106 | − | 0.136417i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.88777 | −1.88777 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(674\) | 0.559311 | + | 0.351438i | 0.559311 | + | 0.351438i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.125427 | + | 0.549531i | 0.125427 | + | 0.549531i | ||||
\(677\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.10568 | + | 0.881748i | 1.10568 | + | 0.881748i | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) |
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.656405 | − | 0.0739590i | 0.656405 | − | 0.0739590i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0663460 | − | 0.189606i | 0.0663460 | − | 0.189606i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.960917 | − | 0.276836i | \(-0.0892857\pi\) | ||||
−0.960917 | + | 0.276836i | \(0.910714\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.559828 | − | 0.789004i | 0.559828 | − | 0.789004i | ||||
\(694\) | −0.943010 | − | 0.669101i | −0.943010 | − | 0.669101i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.351438 | − | 0.440689i | 0.351438 | − | 0.440689i | ||||
\(701\) | 0.831919 | + | 1.32399i | 0.831919 | + | 1.32399i | 0.943883 | + | 0.330279i | \(0.107143\pi\) |
−0.111964 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.669584 | + | 0.277351i | −0.669584 | + | 0.277351i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.00628779 | − | 0.111964i | 0.00628779 | − | 0.111964i | −0.993712 | − | 0.111964i | \(-0.964286\pi\) |
1.00000 | \(0\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0971591 | − | 0.201753i | 0.0971591 | − | 0.201753i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.232145 | + | 0.291101i | −0.232145 | + | 0.291101i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.862165 | + | 0.476502i | 0.862165 | + | 0.476502i | ||||
\(719\) | 0 | 0 | 0.167506 | − | 0.985871i | \(-0.446429\pi\) | ||||
−0.167506 | + | 0.985871i | \(0.553571\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.559311 | − | 0.351438i | 0.559311 | − | 0.351438i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.764163 | + | 0.0429145i | 0.764163 | + | 0.0429145i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.875223 | − | 0.483719i | \(-0.839286\pi\) | ||||
0.875223 | + | 0.483719i | \(0.160714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.433884 | + | 0.900969i | −0.433884 | + | 0.900969i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.319278 | − | 0.0179303i | 0.319278 | − | 0.0179303i | ||||
\(737\) | −0.0358318 | − | 0.102401i | −0.0358318 | − | 0.102401i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.211881 | + | 0.511525i | −0.211881 | + | 0.511525i | −0.993712 | − | 0.111964i | \(-0.964286\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.476502 | − | 0.425828i | 0.476502 | − | 0.425828i | ||||
\(743\) | 1.14099 | − | 0.193862i | 1.14099 | − | 0.193862i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 0.934170i | − | 0.934170i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.55383 | + | 1.23914i | −1.55383 | + | 1.23914i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0429145 | + | 0.764163i | 0.0429145 | + | 0.764163i | 0.943883 | + | 0.330279i | \(0.107143\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.0187843 | − | 0.334485i | −0.0187843 | − | 0.334485i | −0.993712 | − | 0.111964i | \(-0.964286\pi\) |
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(758\) | −0.264863 | − | 0.127551i | −0.264863 | − | 0.127551i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.167506 | − | 0.985871i | \(-0.553571\pi\) | ||||
0.167506 | + | 0.985871i | \(0.446429\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.01293 | + | 0.559828i | −1.01293 | + | 0.559828i | ||||
\(764\) | −1.08156 | + | 0.0607393i | −1.08156 | + | 0.0607393i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.794095 | + | 0.633270i | −0.794095 | + | 0.633270i | ||||
\(773\) | 0 | 0 | 0.0560704 | − | 0.998427i | \(-0.482143\pi\) | ||||
−0.0560704 | + | 0.998427i | \(0.517857\pi\) | |||||||
\(774\) | 0.125246 | − | 1.11159i | 0.125246 | − | 1.11159i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.156405 | − | 0.685254i | 0.156405 | − | 0.685254i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.521183 | + | 1.48946i | −0.521183 | + | 1.48946i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.115647 | − | 0.0263957i | −0.115647 | − | 0.0263957i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.532032 | − | 0.846724i | \(-0.678571\pi\) | ||||
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(788\) | −0.321677 | − | 0.287468i | −0.321677 | − | 0.287468i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.88777i | 1.88777i | ||||||||
\(792\) | −0.814955 | + | 0.578241i | −0.814955 | + | 0.578241i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.808227 | + | 0.507843i | −0.808227 | + | 0.507843i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.823703 | −0.823703 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.953769 | + | 1.72571i | −0.953769 | + | 1.72571i | −0.330279 | + | 0.943883i | \(0.607143\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.993712 | − | 0.111964i | \(-0.0357143\pi\) | ||||
−0.993712 | + | 0.111964i | \(0.964286\pi\) | |||||||
\(812\) | 0.165093 | + | 0.398570i | 0.165093 | + | 0.398570i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.476844 | + | 1.15120i | 0.476844 | + | 1.15120i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.223929 | − | 1.98742i | −0.223929 | − | 1.98742i | −0.111964 | − | 0.993712i | \(-0.535714\pi\) |
−0.111964 | − | 0.993712i | \(-0.535714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.93760 | + | 0.218315i | −1.93760 | + | 0.218315i | −0.993712 | − | 0.111964i | \(-0.964286\pi\) |
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.84485 | + | 0.764163i | 1.84485 | + | 0.764163i | 0.943883 | + | 0.330279i | \(0.107143\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(828\) | 0.181454 | − | 0.0522760i | 0.181454 | − | 0.0522760i | ||||
\(829\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.220375 | − | 0.350725i | 0.220375 | − | 0.350725i | ||||
\(842\) | −0.0970941 | + | 0.425397i | −0.0970941 | + | 0.425397i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0500874 | + | 0.0399433i | −0.0500874 | + | 0.0399433i | ||||
\(848\) | −0.106023 | + | 0.0439162i | −0.106023 | + | 0.0439162i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.0366267 | − | 0.652198i | −0.0366267 | − | 0.652198i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.93760 | − | 0.677994i | 1.93760 | − | 0.677994i | ||||
\(857\) | 0 | 0 | 0.960917 | − | 0.276836i | \(-0.0892857\pi\) | ||||
−0.960917 | + | 0.276836i | \(0.910714\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.998427 | − | 0.0560704i | \(-0.0178571\pi\) | ||||
−0.998427 | + | 0.0560704i | \(0.982143\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.569607 | + | 0.0641793i | −0.569607 | + | 0.0641793i | ||||
\(863\) | 1.24698i | 1.24698i | 0.781831 | + | 0.623490i | \(0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.144356 | − | 0.161534i | 0.144356 | − | 0.161534i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.17852 | − | 0.200238i | 1.17852 | − | 0.200238i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.0648927 | − | 1.15552i | 0.0648927 | − | 1.15552i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.846724 | − | 0.532032i | \(-0.178571\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.985871 | − | 0.167506i | \(-0.946429\pi\) | ||||
0.985871 | + | 0.167506i | \(0.0535714\pi\) | |||||||
\(882\) | −0.660558 | −0.660558 | ||||||||
\(883\) | −1.24698 | −1.24698 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.30040 | + | 0.0730290i | 1.30040 | + | 0.0730290i | ||||
\(887\) | 0 | 0 | −0.276836 | − | 0.960917i | \(-0.589286\pi\) | ||||
0.276836 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.21623 | + | 1.08689i | 1.21623 | + | 1.08689i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.644649 | + | 0.721362i | −0.644649 | + | 0.721362i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.389222 | − | 0.244564i | −0.389222 | − | 0.244564i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.549531 | − | 0.874573i | −0.549531 | − | 0.874573i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.398570 | + | 0.398570i | −0.398570 | + | 0.398570i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.643997 | − | 1.84044i | 0.643997 | − | 1.84044i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.442244 | − | 1.93760i | 0.442244 | − | 1.93760i | 0.111964 | − | 0.993712i | \(-0.464286\pi\) |
0.330279 | − | 0.943883i | \(-0.392857\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −1.11108 | − | 0.614073i | −1.11108 | − | 0.614073i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.15552 | + | 1.62856i | −1.15552 | + | 1.62856i | −0.532032 | + | 0.846724i | \(0.678571\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.03739 | + | 1.65099i | 1.03739 | + | 1.65099i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.0409633 | − | 0.729419i | −0.0409633 | − | 0.729419i | ||||
\(929\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.226011 | − | 0.990220i | −0.226011 | − | 0.990220i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(938\) | −0.0428654 | + | 0.0604131i | −0.0428654 | + | 0.0604131i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.985871 | − | 0.167506i | \(-0.0535714\pi\) | ||||
−0.985871 | + | 0.167506i | \(0.946429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.414139 | − | 0.999819i | 0.414139 | − | 0.999819i | ||||
\(947\) | −0.314692 | + | 1.37876i | −0.314692 | + | 1.37876i | 0.532032 | + | 0.846724i | \(0.321429\pi\) |
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.249799 | + | 0.223234i | −0.249799 | + | 0.223234i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.532032 | + | 0.846724i | \(0.321429\pi\) | |||||||
\(954\) | −0.521183 | + | 0.369799i | −0.521183 | + | 0.369799i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.304967 | − | 0.633270i | 0.304967 | − | 0.633270i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.400969 | − | 0.193096i | −0.400969 | − | 0.193096i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.943883 | − | 0.330279i | −0.943883 | − | 0.330279i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.68280 | − | 1.05737i | 1.68280 | − | 1.05737i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.484586 | − | 0.267821i | −0.484586 | − | 0.267821i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(968\) | 0.0624579 | − | 0.0218550i | 0.0624579 | − | 0.0218550i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.304967 | + | 0.633270i | −0.304967 | + | 0.633270i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.965916 | + | 1.74769i | 0.965916 | + | 1.74769i | 0.532032 | + | 0.846724i | \(0.321429\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.06925 | − | 0.442896i | 1.06925 | − | 0.442896i | ||||
\(982\) | 0.476502 | + | 0.862165i | 0.476502 | + | 0.862165i | ||||
\(983\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.378036 | + | 0.423022i | −0.378036 | + | 0.423022i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.56737 | − | 1.11211i | −1.56737 | − | 1.11211i | −0.943883 | − | 0.330279i | \(-0.892857\pi\) |
−0.623490 | − | 0.781831i | \(-0.714286\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.03534 | − | 0.298277i | 1.03534 | − | 0.298277i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(998\) | −0.357391 | − | 0.448154i | −0.357391 | − | 0.448154i | ||||
\(999\) | 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 | 2359.1.cv.a.1301.1 | ✓ | 24 | |
7.6 | odd | 2 | CM | 2359.1.cv.a.1301.1 | ✓ | 24 | |
337.43 | even | 56 | inner | 2359.1.cv.a.1728.1 | yes | 24 | |
2359.1728 | odd | 56 | inner | 2359.1.cv.a.1728.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2359.1.cv.a.1301.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2359.1.cv.a.1301.1 | ✓ | 24 | 7.6 | odd | 2 | CM | |
2359.1.cv.a.1728.1 | yes | 24 | 337.43 | even | 56 | inner | |
2359.1.cv.a.1728.1 | yes | 24 | 2359.1728 | odd | 56 | inner |