Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2008,1,Mod(3,2008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2008, base_ring=CyclotomicField(250))
chi = DirichletCharacter(H, H._module([125, 125, 16]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2008.3");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2008 = 2^{3} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2008.bd (of order \(250\), degree \(100\), 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: | \(1.00212254537\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Coefficient field: | \(\Q(\zeta_{250})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{100} - x^{75} + x^{50} - x^{25} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{125}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{125} - \cdots)\) |
Embedding invariants
Embedding label | 459.1 | ||
Root | \(0.711536 + 0.702650i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.459 |
Dual form | 2008.1.bd.a.35.1 |
$q$-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 \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{61}{125}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(3\) | 0.811554 | − | 0.559018i | 0.811554 | − | 0.559018i | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(4\) | −0.425779 | − | 0.904827i | −0.425779 | − | 0.904827i | ||||
\(5\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(6\) | −0.0371420 | − | 0.984754i | −0.0371420 | − | 0.984754i | ||||
\(7\) | 0 | 0 | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) | ||||
0.997159 | + | 0.0753268i | \(0.0240000\pi\) | |||||||
\(8\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(9\) | −0.0102928 | + | 0.0269825i | −0.0102928 | + | 0.0269825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.96732 | − | 0.198446i | 1.96732 | − | 0.198446i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(12\) | −0.851357 | − | 0.496298i | −0.851357 | − | 0.496298i | ||||
\(13\) | 0 | 0 | 0.837528 | − | 0.546394i | \(-0.184000\pi\) | ||||
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(17\) | −1.51890 | − | 0.557644i | −1.51890 | − | 0.557644i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(18\) | 0.0172669 | + | 0.0231485i | 0.0172669 | + | 0.0231485i | ||||
\(19\) | 0.256228 | − | 1.84182i | 0.256228 | − | 1.84182i | −0.236499 | − | 0.971632i | \(-0.576000\pi\) |
0.492727 | − | 0.870184i | \(-0.336000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.886590 | − | 1.76740i | 0.886590 | − | 1.76740i | ||||
\(23\) | 0 | 0 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
−0.617860 | + | 0.786288i | \(0.712000\pi\) | |||||||
\(24\) | −0.875218 | + | 0.452895i | −0.875218 | + | 0.452895i | ||||
\(25\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.239790 | + | 0.985151i | 0.239790 | + | 0.985151i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) | ||||
−0.0125660 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.745941 | − | 0.666012i | \(-0.232000\pi\) | ||||
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(32\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(33\) | 1.48565 | − | 1.26082i | 1.48565 | − | 1.26082i | ||||
\(34\) | −1.28470 | + | 0.983652i | −1.28470 | + | 0.983652i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0287970 | − | 0.00217537i | 0.0287970 | − | 0.00217537i | ||||
\(37\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(38\) | −1.41780 | − | 1.20323i | −1.41780 | − | 1.20323i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50758 | − | 0.229077i | 1.50758 | − | 0.229077i | 0.656586 | − | 0.754251i | \(-0.272000\pi\) |
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.125694 | + | 1.10664i | −0.125694 | + | 1.10664i | 0.762443 | + | 0.647056i | \(0.224000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(44\) | −1.01720 | − | 1.69559i | −1.01720 | − | 1.69559i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(48\) | −0.0865734 | + | 0.981645i | −0.0865734 | + | 0.981645i | ||||
\(49\) | 0.988652 | + | 0.150226i | 0.988652 | + | 0.150226i | ||||
\(50\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(51\) | −1.54441 | + | 0.396536i | −1.54441 | + | 0.396536i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.675333 | − | 0.737513i | \(-0.736000\pi\) | ||||
0.675333 | + | 0.737513i | \(0.264000\pi\) | |||||||
\(54\) | 0.960276 | + | 0.325409i | 0.960276 | + | 0.325409i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.821665 | − | 1.63797i | −0.821665 | − | 1.63797i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.40048 | + | 0.514167i | −1.40048 | + | 0.514167i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.492727 | − | 0.870184i | \(-0.336000\pi\) | ||||
−0.492727 | + | 0.870184i | \(0.664000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.968583 | + | 0.248690i | 0.968583 | + | 0.248690i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.268490 | − | 1.92996i | −0.268490 | − | 1.92996i | ||||
\(67\) | −0.987118 | + | 0.974791i | −0.987118 | + | 0.974791i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(68\) | 0.142146 | + | 1.61178i | 0.142146 | + | 1.61178i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.260842 | − | 0.965382i | \(-0.584000\pi\) | ||||
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(72\) | 0.0135935 | − | 0.0254797i | 0.0135935 | − | 0.0254797i | ||||
\(73\) | −0.0357930 | + | 0.120372i | −0.0357930 | + | 0.120372i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.548776 | + | 0.818515i | −0.548776 | + | 0.818515i | ||||
\(76\) | −1.77562 | + | 0.552365i | −1.77562 | + | 0.552365i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.947098 | − | 0.320944i | \(-0.104000\pi\) | ||||
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.723777 | + | 0.646223i | 0.723777 | + | 0.646223i | ||||
\(82\) | 0.614386 | − | 1.39564i | 0.614386 | − | 1.39564i | ||||
\(83\) | −0.612542 | + | 0.260514i | −0.612542 | + | 0.260514i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.867013 | + | 0.699092i | 0.867013 | + | 0.699092i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.97668 | − | 0.0496898i | −1.97668 | − | 0.0496898i | ||||
\(89\) | −1.11128 | + | 0.315299i | −1.11128 | + | 0.315299i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.782442 | + | 0.599088i | 0.782442 | + | 0.599088i | ||||
\(97\) | 0.243329 | − | 0.405608i | 0.243329 | − | 0.405608i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(98\) | 0.656586 | − | 0.754251i | 0.656586 | − | 0.754251i | ||||
\(99\) | −0.0148947 | + | 0.0551259i | −0.0148947 | + | 0.0551259i | ||||
\(100\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(101\) | 0 | 0 | −0.402906 | − | 0.915241i | \(-0.632000\pi\) | ||||
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(102\) | −0.492727 | + | 1.51646i | −0.492727 | + | 1.51646i | ||||
\(103\) | 0 | 0 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
0.379779 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.965603 | + | 1.70531i | 0.965603 | + | 1.70531i | 0.656586 | + | 0.754251i | \(0.272000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(108\) | 0.789294 | − | 0.636425i | 0.789294 | − | 0.636425i | ||||
\(109\) | 0 | 0 | −0.954865 | − | 0.297042i | \(-0.904000\pi\) | ||||
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0609840 | + | 0.0443075i | 0.0609840 | + | 0.0443075i | 0.617860 | − | 0.786288i | \(-0.288000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(114\) | −1.82325 | − | 0.183913i | −1.82325 | − | 0.183913i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.316290 | + | 1.45797i | −0.316290 | + | 1.45797i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.85111 | − | 0.581102i | 2.85111 | − | 0.581102i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.09542 | − | 1.02867i | 1.09542 | − | 1.02867i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(128\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(129\) | 0.516622 | + | 0.968360i | 0.516622 | + | 0.968360i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.08287 | + | 1.37806i | 1.08287 | + | 1.37806i | 0.920232 | + | 0.391374i | \(0.128000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(132\) | −1.77338 | − | 0.807429i | −1.77338 | − | 0.807429i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.294119 | + | 1.35577i | 0.294119 | + | 1.35577i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.43703 | + | 0.743616i | 1.43703 | + | 0.743616i | ||||
\(137\) | −1.34385 | − | 0.135555i | −1.34385 | − | 0.135555i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.14249 | − | 1.18640i | 1.14249 | − | 1.18640i | 0.162637 | − | 0.986686i | \(-0.448000\pi\) |
0.979855 | − | 0.199710i | \(-0.0640000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.0142295 | − | 0.0251301i | −0.0142295 | − | 0.0251301i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.0824547 | + | 0.0947197i | 0.0824547 | + | 0.0947197i | ||||
\(147\) | 0.886323 | − | 0.430758i | 0.886323 | − | 0.430758i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(150\) | 0.397046 | + | 0.901929i | 0.397046 | + | 0.901929i | ||||
\(151\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(152\) | −0.485049 | + | 1.79518i | −0.485049 | + | 1.79518i | ||||
\(153\) | 0.0306805 | − | 0.0352441i | 0.0306805 | − | 0.0352441i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.933443 | − | 0.264842i | 0.933443 | − | 0.264842i | ||||
\(163\) | −0.0251241 | 0.000631572i | −0.0251241 | 0.000631572i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) | ||
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(164\) | −0.849171 | − | 1.26656i | −0.849171 | − | 1.26656i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.108258 | + | 0.656777i | −0.108258 | + | 0.656777i | ||||
\(167\) | 0 | 0 | −0.823533 | − | 0.567269i | \(-0.808000\pi\) | ||||
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.402906 | − | 0.915241i | 0.402906 | − | 0.915241i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0470596 | + | 0.0258712i | 0.0470596 | + | 0.0258712i | ||||
\(172\) | 1.05483 | − | 0.357451i | 1.05483 | − | 0.357451i | ||||
\(173\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.10111 | + | 1.64234i | −1.10111 | + | 1.64234i | ||||
\(177\) | −0.849137 | + | 1.20017i | −0.849137 | + | 1.20017i | ||||
\(178\) | −0.329239 | + | 1.10723i | −0.329239 | + | 1.10723i | ||||
\(179\) | −0.940219 | + | 1.76235i | −0.940219 | + | 1.76235i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.899405 | − | 0.437116i | \(-0.856000\pi\) | ||||
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.09883 | − | 0.795645i | −3.09883 | − | 0.795645i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.332820 | − | 0.942991i | \(-0.392000\pi\) | ||||
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(192\) | 0.925080 | − | 0.339630i | 0.925080 | − | 0.339630i | ||||
\(193\) | −0.674891 | − | 0.440292i | −0.674891 | − | 0.440292i | 0.162637 | − | 0.986686i | \(-0.448000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(194\) | −0.212084 | − | 0.422785i | −0.212084 | − | 0.422785i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.285019 | − | 0.958522i | −0.285019 | − | 0.958522i | ||||
\(197\) | 0 | 0 | −0.947098 | − | 0.320944i | \(-0.896000\pi\) | ||||
0.947098 | + | 0.320944i | \(0.104000\pi\) | |||||||
\(198\) | 0.0385633 | + | 0.0421140i | 0.0385633 | + | 0.0421140i | ||||
\(199\) | 0 | 0 | −0.850994 | − | 0.525175i | \(-0.824000\pi\) | ||||
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(200\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(201\) | −0.256174 | + | 1.34291i | −0.256174 | + | 1.34291i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.01637 | + | 1.22858i | 1.01637 | + | 1.22858i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.138583 | − | 3.67429i | 0.138583 | − | 3.67429i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0750855 | − | 1.19345i | −0.0750855 | − | 1.19345i | −0.837528 | − | 0.546394i | \(-0.816000\pi\) |
0.762443 | − | 0.647056i | \(-0.224000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.95723 | + | 0.0984643i | 1.95723 | + | 0.0984643i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.114427 | − | 1.00744i | −0.114427 | − | 1.00744i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0382422 | + | 0.117697i | 0.0382422 | + | 0.117697i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.356412 | − | 0.934329i | \(-0.616000\pi\) | ||||
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.000362896 | − | 0.0288768i | −0.000362896 | − | 0.0288768i | ||||
\(226\) | 0.0700869 | − | 0.0277494i | 0.0700869 | − | 0.0277494i | ||||
\(227\) | 1.76227 | − | 0.911912i | 1.76227 | − | 0.911912i | 0.823533 | − | 0.567269i | \(-0.192000\pi\) |
0.938734 | − | 0.344643i | \(-0.112000\pi\) | |||||||
\(228\) | −1.13223 | + | 1.44088i | −1.13223 | + | 1.44088i | ||||
\(229\) | 0 | 0 | 0.448383 | − | 0.893841i | \(-0.352000\pi\) | ||||
−0.448383 | + | 0.893841i | \(0.648000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.15040 | + | 1.54226i | 1.15040 | + | 1.54226i | 0.793990 | + | 0.607930i | \(0.208000\pi\) |
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.06153 | + | 1.04827i | 1.06153 | + | 1.04827i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.863923 | − | 0.503623i | \(-0.832000\pi\) | ||||
0.863923 | + | 0.503623i | \(0.168000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.485049 | − | 0.192044i | −0.485049 | − | 0.192044i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(242\) | 1.03706 | − | 2.71864i | 1.03706 | − | 2.71864i | ||||
\(243\) | −0.0572846 | − | 0.00723673i | −0.0572846 | − | 0.00723673i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.281579 | − | 1.47609i | −0.281579 | − | 1.47609i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.351479 | + | 0.553843i | −0.351479 | + | 0.553843i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.997159 | + | 0.0753268i | −0.997159 | + | 0.0753268i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(257\) | −0.0749998 | − | 1.98849i | −0.0749998 | − | 1.98849i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(258\) | 1.09443 | + | 0.0826750i | 1.09443 | + | 0.0826750i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.74376 | − | 0.175895i | 1.74376 | − | 0.175895i | ||||
\(263\) | 0 | 0 | −0.863923 | − | 0.503623i | \(-0.832000\pi\) | ||||
0.863923 | + | 0.503623i | \(0.168000\pi\) | |||||||
\(264\) | −1.63196 | + | 1.06467i | −1.63196 | + | 1.06467i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.725607 | + | 0.877109i | −0.725607 | + | 0.877109i | ||||
\(268\) | 1.30231 | + | 0.478125i | 1.30231 | + | 0.478125i | ||||
\(269\) | 0 | 0 | −0.597905 | − | 0.801567i | \(-0.704000\pi\) | ||||
0.597905 | + | 0.801567i | \(0.296000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(272\) | 1.39786 | − | 0.814879i | 1.39786 | − | 0.814879i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.834522 | + | 1.06201i | −0.834522 | + | 1.06201i | ||||
\(275\) | −1.75612 | + | 0.908729i | −1.75612 | + | 0.908729i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(278\) | −0.389529 | − | 1.60034i | −0.389529 | − | 1.60034i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.65863 | + | 0.381706i | −1.65863 | + | 0.381706i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.161209 | + | 0.496150i | 0.161209 | + | 0.496150i | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.0288426 | − | 0.00145101i | −0.0288426 | − | 0.00145101i | ||||
\(289\) | 1.23366 | + | 1.04696i | 1.23366 | + | 1.04696i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0292678 | − | 0.465198i | −0.0292678 | − | 0.465198i | ||||
\(292\) | 0.124156 | − | 0.0188655i | 0.124156 | − | 0.0188655i | ||||
\(293\) | 0 | 0 | 0.0376902 | − | 0.999289i | \(-0.488000\pi\) | ||||
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(294\) | 0.111215 | − | 0.979159i | 0.111215 | − | 0.979159i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.667242 | + | 1.89052i | 0.667242 | + | 1.89052i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.974271 | + | 0.148041i | 0.974271 | + | 0.148041i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.25582 | + | 1.37144i | 1.25582 | + | 1.37144i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.0133182 | − | 0.0447891i | −0.0133182 | − | 0.0447891i | ||||
\(307\) | −1.64131 | − | 0.334525i | −1.64131 | − | 0.334525i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.332820 | − | 0.942991i | \(-0.392000\pi\) | ||||
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.194483 | − | 1.17989i | −0.194483 | − | 1.17989i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
0.693653 | − | 0.720309i | \(-0.256000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.137790 | − | 0.990461i | \(-0.544000\pi\) | ||||
0.137790 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.73694 | + | 0.844160i | 1.73694 | + | 0.844160i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.41626 | + | 2.65466i | −1.41626 | + | 2.65466i | ||||
\(324\) | 0.276550 | − | 0.930041i | 0.276550 | − | 0.930041i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.0139954 | + | 0.0208746i | −0.0139954 | + | 0.0208746i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.52440 | + | 0.0383205i | −1.52440 | + | 0.0383205i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.706139 | + | 0.388203i | 0.706139 | + | 0.388203i | 0.793990 | − | 0.607930i | \(-0.208000\pi\) |
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(332\) | 0.496528 | + | 0.443324i | 0.496528 | + | 0.443324i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.10781 | + | 0.893250i | 1.10781 | + | 0.893250i | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(338\) | −0.556876 | − | 0.830596i | −0.556876 | − | 0.830596i | ||||
\(339\) | 0.0742605 | + | 0.00186676i | 0.0742605 | + | 0.00186676i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.0470596 | − | 0.0258712i | 0.0470596 | − | 0.0258712i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.263401 | − | 1.08216i | 0.263401 | − | 1.08216i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.37189 | − | 1.05041i | −1.37189 | − | 1.05041i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.379779 | − | 0.925077i | \(-0.624000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.656586 | − | 0.754251i | \(-0.272000\pi\) | ||||
−0.656586 | + | 0.754251i | \(0.728000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.796668 | + | 1.80971i | 0.796668 | + | 1.80971i | ||||
\(353\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(354\) | 0.558345 | + | 1.36003i | 0.558345 | + | 1.36003i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.758452 | + | 0.871270i | 0.758452 | + | 0.871270i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.984210 | + | 1.73817i | 0.984210 | + | 1.73817i | ||||
\(359\) | 0 | 0 | 0.778462 | − | 0.627691i | \(-0.216000\pi\) | ||||
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.36460 | − | 0.670899i | −2.36460 | − | 0.670899i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.98899 | − | 2.06542i | 1.98899 | − | 2.06542i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.910106 | − | 0.414376i | \(-0.136000\pi\) | ||||
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.00933621 | + | 0.0430362i | −0.00933621 | + | 0.0430362i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.470704 | − | 0.882291i | \(-0.656000\pi\) | ||||
0.470704 | + | 0.882291i | \(0.344000\pi\) | |||||||
\(374\) | −2.33222 | + | 2.19010i | −2.33222 | + | 2.19010i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.31128 | − | 1.23137i | 1.31128 | − | 1.23137i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
0.954865 | − | 0.297042i | \(-0.0960000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.910106 | − | 0.414376i | \(-0.864000\pi\) | ||||
0.910106 | + | 0.414376i | \(0.136000\pi\) | |||||||
\(384\) | 0.208923 | − | 0.963053i | 0.208923 | − | 0.963053i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.733375 | + | 0.333909i | −0.733375 | + | 0.333909i | ||||
\(387\) | −0.0285661 | − | 0.0147820i | −0.0285661 | − | 0.0147820i | ||||
\(388\) | −0.470610 | − | 0.0474709i | −0.470610 | − | 0.0474709i | ||||
\(389\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.962028 | − | 0.272952i | −0.962028 | − | 0.272952i | ||||
\(393\) | 1.64917 | + | 0.513027i | 1.64917 | + | 0.513027i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.0562213 | − | 0.00999429i | 0.0562213 | − | 0.00999429i | ||||
\(397\) | 0 | 0 | −0.656586 | − | 0.754251i | \(-0.728000\pi\) | ||||
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(401\) | −0.785286 | − | 1.78385i | −0.785286 | − | 1.78385i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(402\) | 0.996593 | + | 0.935863i | 0.996593 | + | 0.935863i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.58193 | − | 0.199844i | 1.58193 | − | 0.199844i | ||||
\(409\) | 0.134814 | − | 0.553868i | 0.134814 | − | 0.553868i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.16638 | + | 0.641224i | −1.16638 | + | 0.641224i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.263978 | − | 1.60150i | 0.263978 | − | 1.60150i | ||||
\(418\) | −3.02805 | − | 2.08579i | −3.02805 | − | 2.08579i | ||||
\(419\) | −0.524568 | + | 0.223098i | −0.524568 | + | 0.223098i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.745941 | − | 0.666012i | \(-0.768000\pi\) | ||||
0.745941 | + | 0.666012i | \(0.232000\pi\) | |||||||
\(422\) | −1.04790 | − | 0.576086i | −1.04790 | − | 0.576086i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.61752 | − | 0.0406613i | 1.61752 | − | 0.0406613i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.13188 | − | 1.59979i | 1.13188 | − | 1.59979i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.260842 | − | 0.965382i | \(-0.584000\pi\) | ||||
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(432\) | −0.911919 | − | 0.443198i | −0.911919 | − | 0.443198i | ||||
\(433\) | 0.0915446 | − | 1.45506i | 0.0915446 | − | 1.45506i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.119866 | + | 0.0307765i | 0.119866 | + | 0.0307765i | ||||
\(439\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0142295 | + | 0.0251301i | −0.0142295 | + | 0.0251301i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.580169 | − | 0.213001i | 0.580169 | − | 0.213001i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.07242 | − | 1.17116i | −1.07242 | − | 1.17116i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
−0.0878512 | − | 0.996134i | \(-0.528000\pi\) | |||||||
\(450\) | −0.0245759 | − | 0.0151666i | −0.0245759 | − | 0.0151666i | ||||
\(451\) | 2.92043 | − | 0.749840i | 2.92043 | − | 0.749840i | ||||
\(452\) | 0.0141249 | − | 0.0740452i | 0.0141249 | − | 0.0740452i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.174317 | − | 1.97656i | 0.174317 | − | 1.97656i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.609894 | + | 1.72804i | 0.609894 | + | 1.72804i | ||||
\(457\) | −1.05511 | − | 0.187564i | −1.05511 | − | 0.187564i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.185146 | − | 1.63007i | 0.185146 | − | 1.63007i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.988652 | − | 0.150226i | \(-0.0480000\pi\) | ||||
−0.988652 | + | 0.150226i | \(0.952000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.379779 | − | 0.925077i | \(-0.376000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.91859 | − | 0.144933i | 1.91859 | − | 0.144933i | ||||
\(467\) | 0.207708 | + | 1.82871i | 0.207708 | + | 1.82871i | 0.492727 | + | 0.870184i | \(0.336000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.45388 | − | 0.334586i | 1.45388 | − | 0.334586i | ||||
\(473\) | −0.0276732 | + | 2.20205i | −0.0276732 | + | 2.20205i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.439782 | + | 1.80680i | 0.439782 | + | 1.80680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
−0.617860 | + | 0.786288i | \(0.712000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.422050 | + | 0.306638i | −0.422050 | + | 0.306638i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73974 | − | 2.33234i | −1.73974 | − | 2.33234i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.0368048 | + | 0.0444894i | −0.0368048 | + | 0.0444894i | ||||
\(487\) | 0 | 0 | −0.711536 | − | 0.702650i | \(-0.752000\pi\) | ||||
0.711536 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0207427 | + | 0.0135323i | −0.0207427 | + | 0.0135323i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.98425 | + | 0.200153i | −1.98425 | + | 0.200153i | −0.984564 | + | 0.175023i | \(0.944000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(492\) | −1.39718 | − | 0.553183i | −1.39718 | − | 0.553183i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.279293 | + | 0.593528i | 0.279293 | + | 0.593528i | ||||
\(499\) | −1.62164 | + | 1.11703i | −1.62164 | + | 1.11703i | −0.711536 | + | 0.702650i | \(0.752000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.470704 | + | 0.882291i | −0.470704 | + | 0.882291i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.184656 | − | 0.968000i | −0.184656 | − | 0.968000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) | ||||
0.997159 | + | 0.0753268i | \(0.0240000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(513\) | 1.87591 | − | 0.189225i | 1.87591 | − | 0.189225i | ||||
\(514\) | −1.71912 | − | 1.00216i | −1.71912 | − | 1.00216i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.656231 | − | 0.879761i | 0.656231 | − | 0.879761i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.275233 | + | 1.97842i | −0.275233 | + | 1.97842i | −0.0878512 | + | 0.996134i | \(0.528000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.13448 | + | 0.661344i | −1.13448 | + | 0.661344i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(524\) | 0.785842 | − | 1.56656i | 0.785842 | − | 1.56656i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0.0244855 | + | 1.94839i | 0.0244855 | + | 1.94839i | ||||
\(529\) | −0.236499 | − | 0.971632i | −0.236499 | − | 0.971632i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.000541397 | − | 0.0430808i | 0.000541397 | − | 0.0430808i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.351767 | + | 1.08263i | 0.351767 | + | 1.08263i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.10151 | − | 0.843386i | 1.10151 | − | 0.843386i | ||||
\(537\) | 0.222149 | + | 1.95584i | 0.222149 | + | 1.95584i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.97481 | + | 0.0993483i | 1.97481 | + | 0.0993483i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.379779 | − | 0.925077i | \(-0.376000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.0609840 | − | 1.61688i | 0.0609840 | − | 1.61688i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.93873 | + | 0.344643i | 1.93873 | + | 0.344643i | 1.00000 | \(0\) | ||
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(548\) | 0.449528 | + | 1.27366i | 0.449528 | + | 1.27366i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.173708 | + | 1.96966i | −0.173708 | + | 1.96966i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.55993 | − | 0.528615i | −1.55993 | − | 0.528615i | ||||
\(557\) | 0 | 0 | −0.285019 | − | 0.958522i | \(-0.592000\pi\) | ||||
0.285019 | + | 0.958522i | \(0.408000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.95965 | + | 1.08659i | −2.95965 | + | 1.08659i | ||||
\(562\) | −0.566455 | + | 1.60496i | −0.566455 | + | 1.60496i | ||||
\(563\) | −0.977684 | + | 1.72664i | −0.977684 | + | 1.72664i | −0.379779 | + | 0.925077i | \(0.624000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.505293 | + | 0.129737i | 0.505293 | + | 0.129737i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.41589 | + | 1.39820i | −1.41589 | + | 1.39820i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0563084 | − | 0.894997i | 0.0563084 | − | 0.894997i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.920232 | − | 0.391374i | \(-0.128000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0166798 | + | 0.0235751i | −0.0166798 | + | 0.0235751i | ||||
\(577\) | −1.00171 | + | 1.49408i | −1.00171 | + | 1.49408i | −0.137790 | + | 0.990461i | \(0.544000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(578\) | 1.54500 | − | 0.480623i | 1.54500 | − | 0.480623i | ||||
\(579\) | −0.793841 | + | 0.0199556i | −0.793841 | + | 0.0199556i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −0.408462 | − | 0.224554i | −0.408462 | − | 0.224554i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0.0505974 | − | 0.114937i | 0.0505974 | − | 0.114937i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.308067 | + | 1.86898i | −0.308067 | + | 1.86898i | 0.162637 | + | 0.986686i | \(0.448000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(588\) | −0.767139 | − | 0.618561i | −0.767139 | − | 0.618561i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.71731 | − | 0.944098i | 1.71731 | − | 0.944098i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
0.954865 | − | 0.297042i | \(-0.0960000\pi\) | |||||||
\(594\) | 1.95375 | + | 0.449621i | 1.95375 | + | 0.449621i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.514440 | − | 0.857527i | \(-0.328000\pi\) | ||||
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(600\) | 0.647036 | − | 0.743281i | 0.647036 | − | 0.743281i | ||||
\(601\) | 0.505293 | − | 1.87010i | 0.505293 | − | 1.87010i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
0.492727 | − | 0.870184i | \(-0.336000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0161421 | − | 0.0366683i | −0.0161421 | − | 0.0366683i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.656586 | − | 0.754251i | \(-0.728000\pi\) | ||||
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(608\) | 1.83085 | − | 0.325465i | 1.83085 | − | 0.325465i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.0449530 | − | 0.0127543i | −0.0449530 | − | 0.0127543i | ||||
\(613\) | 0 | 0 | 0.850994 | − | 0.525175i | \(-0.176000\pi\) | ||||
−0.850994 | + | 0.525175i | \(0.824000\pi\) | |||||||
\(614\) | −1.16191 | + | 1.20656i | −1.16191 | + | 1.20656i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.376582 | − | 0.194868i | −0.376582 | − | 0.194868i | 0.260842 | − | 0.965382i | \(-0.416000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.407913 | − | 1.88032i | −0.407913 | − | 1.88032i | −0.470704 | − | 0.882291i | \(-0.656000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(626\) | −1.10042 | − | 0.468009i | −1.10042 | − | 0.468009i | ||||
\(627\) | −1.94152 | − | 3.05935i | −1.94152 | − | 3.05935i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.470704 | − | 0.882291i | \(-0.656000\pi\) | ||||
0.470704 | + | 0.882291i | \(0.344000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.728096 | − | 0.926575i | −0.728096 | − | 0.926575i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.259955 | + | 0.269945i | −0.259955 | + | 0.269945i | −0.837528 | − | 0.546394i | \(-0.816000\pi\) |
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(642\) | 1.64345 | − | 1.01422i | 1.64345 | − | 1.01422i | ||||
\(643\) | 0.169031 | + | 0.0479583i | 0.169031 | + | 0.0479583i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.48253 | + | 2.61823i | 1.48253 | + | 2.61823i | ||||
\(647\) | 0 | 0 | 0.984564 | − | 0.175023i | \(-0.0560000\pi\) | ||||
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(648\) | −0.637077 | − | 0.731840i | −0.637077 | − | 0.731840i | ||||
\(649\) | −2.65316 | + | 1.28945i | −2.65316 | + | 1.28945i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.0101259 | + | 0.0230019i | 0.0101259 | + | 0.0230019i | ||||
\(653\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.784461 | + | 1.30763i | −0.784461 | + | 1.30763i | ||||
\(657\) | −0.00287954 | − | 0.00220476i | −0.00287954 | − | 0.00220476i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.73879 | + | 0.219661i | −1.73879 | + | 0.219661i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.974527 | − | 0.224271i | \(-0.928000\pi\) | ||||
0.974527 | + | 0.224271i | \(0.0720000\pi\) | |||||||
\(662\) | 0.706139 | − | 0.388203i | 0.706139 | − | 0.388203i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.640363 | − | 0.181687i | 0.640363 | − | 0.181687i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.67351 | + | 0.920019i | 1.67351 | + | 0.920019i | 0.979855 | + | 0.199710i | \(0.0640000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(674\) | 1.34779 | − | 0.456726i | 1.34779 | − | 0.456726i | ||||
\(675\) | −0.585609 | − | 0.827698i | −0.585609 | − | 0.827698i | ||||
\(676\) | −0.999684 | + | 0.0251301i | −0.999684 | + | 0.0251301i | ||||
\(677\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(678\) | 0.0413669 | − | 0.0616999i | 0.0413669 | − | 0.0616999i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.920399 | − | 1.72520i | 0.920399 | − | 1.72520i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.292553 | + | 0.142183i | 0.292553 | + | 0.142183i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(684\) | 0.00337199 | − | 0.0535962i | 0.00337199 | − | 0.0535962i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.772557 | − | 0.802245i | −0.772557 | − | 0.802245i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.123532 | − | 0.749445i | −0.123532 | − | 0.749445i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.850994 | − | 0.525175i | \(-0.176000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.62199 | + | 0.595490i | −1.62199 | + | 0.595490i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.41761 | − | 0.492748i | −2.41761 | − | 0.492748i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.79576 | + | 0.608531i | 1.79576 | + | 0.608531i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.850994 | − | 0.525175i | \(-0.824000\pi\) | ||||
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.95486 | + | 0.297042i | 1.95486 | + | 0.297042i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.542804 | + | 0.656137i | 0.542804 | + | 0.656137i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.44749 | + | 0.257316i | 1.44749 | + | 0.257316i | ||||
\(709\) | 0 | 0 | −0.514440 | − | 0.857527i | \(-0.672000\pi\) | ||||
0.514440 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.14204 | − | 0.173532i | 1.14204 | − | 0.173532i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.99495 | + | 0.100362i | 1.99495 | + | 0.100362i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.793990 | − | 0.607930i | \(-0.208000\pi\) | ||||
−0.793990 | + | 0.607930i | \(0.792000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.83348 | + | 1.63702i | −1.83348 | + | 1.63702i | ||||
\(723\) | −0.500999 | + | 0.115296i | −0.500999 | + | 0.115296i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.678139 | − | 2.78606i | −0.678139 | − | 2.78606i | ||||
\(727\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.912282 | + | 0.472074i | −0.912282 | + | 0.472074i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.808026 | − | 1.61078i | 0.808026 | − | 1.61078i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.74853 | + | 2.11362i | −1.74853 | + | 2.11362i | ||||
\(738\) | 0.0313341 | + | 0.0309428i | 0.0313341 | + | 0.0309428i | ||||
\(739\) | −0.194483 | + | 0.260729i | −0.194483 | + | 0.260729i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.000724520 | − | 0.0192094i | −0.000724520 | − | 0.0192094i | ||||
\(748\) | 0.599497 | + | 3.14268i | 0.599497 | + | 3.14268i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.767139 | + | 0.618561i | −0.767139 | + | 0.618561i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(758\) | −0.337063 | − | 1.76695i | −0.337063 | − | 1.76695i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.660390 | + | 0.0834267i | 0.660390 | + | 0.0834267i | 0.448383 | − | 0.893841i | \(-0.352000\pi\) |
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.701186 | − | 0.692430i | −0.701186 | − | 0.692430i | ||||
\(769\) | 1.13224 | − | 1.36864i | 1.13224 | − | 1.36864i | 0.212007 | − | 0.977268i | \(-0.432000\pi\) |
0.920232 | − | 0.391374i | \(-0.128000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.17247 | − | 1.57184i | −1.17247 | − | 1.57184i | ||||
\(772\) | −0.111033 | + | 0.798127i | −0.111033 | + | 0.798127i | ||||
\(773\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(774\) | −0.0277873 | + | 0.0161986i | −0.0277873 | + | 0.0161986i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.292246 | + | 0.371913i | −0.292246 | + | 0.371913i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0356323 | − | 2.83538i | −0.0356323 | − | 2.83538i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.745941 | + | 0.666012i | −0.745941 | + | 0.666012i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.31683 | − | 1.11754i | 1.31683 | − | 1.11754i | ||||
\(787\) | 1.49069 | − | 1.14137i | 1.49069 | − | 1.14137i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.954865 | − | 0.297042i | \(-0.0960000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.0216864 | − | 0.0528244i | 0.0216864 | − | 0.0528244i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.514440 | − | 0.857527i | \(-0.672000\pi\) | ||||
0.514440 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(801\) | 0.00293067 | − | 0.0332305i | 0.00293067 | − | 0.0332305i | ||||
\(802\) | −1.92694 | − | 0.292798i | −1.92694 | − | 0.292798i | ||||
\(803\) | −0.0465290 | + | 0.243914i | −0.0465290 | + | 0.243914i | ||||
\(804\) | 1.32418 | − | 0.339991i | 1.32418 | − | 0.339991i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.74049 | − | 0.354739i | −1.74049 | − | 0.354739i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.0210488 | − | 0.0137320i | −0.0210488 | − | 0.0137320i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.678905 | − | 1.44275i | 0.678905 | − | 1.44275i | ||||
\(817\) | 2.00601 | + | 0.515057i | 2.00601 | + | 0.515057i | ||||
\(818\) | −0.395409 | − | 0.410604i | −0.395409 | − | 0.410604i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(822\) | −0.0835754 | + | 1.32839i | −0.0835754 | + | 1.32839i | ||||
\(823\) | 0 | 0 | −0.899405 | − | 0.437116i | \(-0.856000\pi\) | ||||
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.917187 | + | 1.71918i | −0.917187 | + | 1.71918i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.06300 | − | 1.50244i | 1.06300 | − | 1.50244i | 0.212007 | − | 0.977268i | \(-0.432000\pi\) |
0.850994 | − | 0.525175i | \(-0.176000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.41789 | − | 0.779494i | −1.41789 | − | 0.779494i | ||||
\(834\) | −1.21074 | − | 1.08101i | −1.21074 | − | 1.08101i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.38360 | + | 1.43904i | −3.38360 | + | 1.43904i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.0927094 | + | 0.562449i | −0.0927094 | + | 0.562449i | ||||
\(839\) | 0 | 0 | −0.778462 | − | 0.627691i | \(-0.784000\pi\) | ||||
0.778462 | + | 0.627691i | \(0.216000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.999684 | − | 0.0251301i | −0.999684 | − | 0.0251301i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.13269 | + | 1.23698i | −1.13269 | + | 1.23698i | ||||
\(844\) | −1.04790 | + | 0.576086i | −1.04790 | + | 0.576086i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.408186 | + | 0.312534i | 0.408186 | + | 0.312534i | ||||
\(850\) | 0.832381 | − | 1.38751i | 0.832381 | − | 1.38751i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.744257 | − | 1.81288i | −0.744257 | − | 1.81288i | ||||
\(857\) | 0.0226039 | − | 0.0109856i | 0.0226039 | − | 0.0109856i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.86496 | − | 0.331528i | 1.86496 | − | 0.331528i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(864\) | −0.862835 | + | 0.532482i | −0.862835 | + | 0.532482i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | ||||
\(867\) | 1.58645 | + | 0.160027i | 1.58645 | + | 0.160027i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.00843980 | + | 0.0107405i | 0.00843980 | + | 0.0107405i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.0902131 | − | 0.0847157i | 0.0902131 | − | 0.0847157i | ||||
\(877\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.237115 | − | 0.222666i | 0.237115 | − | 0.222666i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(882\) | 0.0135935 | + | 0.0254797i | 0.0135935 | + | 0.0254797i | ||||
\(883\) | 0.123051 | − | 0.0250798i | 0.123051 | − | 0.0250798i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.131028 | − | 0.603985i | 0.131028 | − | 0.603985i | ||||
\(887\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.55214 | + | 1.12770i | 1.55214 | + | 1.12770i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.56347 | + | 0.277933i | −1.56347 | + | 0.277933i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.0259740 | + | 0.0126235i | −0.0259740 | + | 0.0126235i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.931736 | − | 2.86759i | 0.931736 | − | 2.86759i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0549499 | − | 0.0516014i | −0.0549499 | − | 0.0516014i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.0903883 | − | 0.150669i | 0.0903883 | − | 0.150669i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(908\) | −1.57546 | − | 1.20627i | −1.57546 | − | 1.20627i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.236499 | − | 0.971632i | \(-0.424000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(912\) | 1.78583 | + | 0.410977i | 1.78583 | + | 0.410977i | ||||
\(913\) | −1.15337 | + | 0.634070i | −1.15337 | + | 0.634070i | ||||
\(914\) | −0.723723 | + | 0.790359i | −0.723723 | + | 0.790359i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.27710 | − | 1.02976i | −1.27710 | − | 1.02976i | ||||
\(919\) | 0 | 0 | 0.162637 | − | 0.986686i | \(-0.448000\pi\) | ||||
−0.162637 | + | 0.986686i | \(0.552000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.51902 | + | 0.646037i | −1.51902 | + | 0.646037i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.932798 | − | 1.39129i | 0.932798 | − | 1.39129i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
0.920232 | − | 0.391374i | \(-0.128000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.530008 | − | 1.78242i | 0.530008 | − | 1.78242i | ||||
\(932\) | 0.905660 | − | 1.69758i | 0.905660 | − | 1.69758i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.65532 | + | 0.804496i | 1.65532 | + | 0.804496i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.231444 | + | 0.228554i | −0.231444 | + | 0.228554i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.817413 | − | 0.848824i | −0.817413 | − | 0.848824i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.425779 | − | 0.904827i | \(-0.360000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.496528 | − | 1.40683i | 0.496528 | − | 1.40683i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.84442 | + | 1.20328i | 1.84442 | + | 1.20328i | ||||
\(947\) | −0.571620 | − | 1.13951i | −0.571620 | − | 1.13951i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.402906 | − | 0.915241i | \(-0.368000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.76118 | + | 0.596812i | 1.76118 | + | 0.596812i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.86361 | + | 0.478493i | −1.86361 | + | 0.478493i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.112856 | − | 0.993611i | 0.112856 | − | 0.993611i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.0559524 | + | 0.00850196i | −0.0559524 | + | 0.00850196i | ||||
\(964\) | 0.0327567 | + | 0.520654i | 0.0327567 | + | 0.520654i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(968\) | −2.90146 | + | 0.219181i | −2.90146 | + | 0.219181i | ||||
\(969\) | 0.334625 | + | 2.94611i | 0.334625 | + | 2.94611i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.47698 | − | 1.25346i | 1.47698 | − | 1.25346i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
0.899405 | − | 0.437116i | \(-0.144000\pi\) | |||||||
\(972\) | 0.0178426 | + | 0.0549139i | 0.0178426 | + | 0.0549139i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.389529 | − | 1.60034i | −0.389529 | − | 1.60034i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
0.356412 | − | 0.934329i | \(-0.384000\pi\) | |||||||
\(978\) | 0.000311217 | 0.0247646i | 0.000311217 | 0.0247646i | ||||||
\(979\) | −2.12368 | + | 0.840823i | −2.12368 | + | 0.840823i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.894219 | + | 1.78260i | −0.894219 | + | 1.78260i | ||||
\(983\) | 0 | 0 | 0.863923 | − | 0.503623i | \(-0.168000\pi\) | ||||
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(984\) | −1.21571 | + | 0.883268i | −1.21571 | + | 0.883268i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.837528 | − | 0.546394i | \(-0.184000\pi\) | ||||
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.790083 | − | 0.0796964i | 0.790083 | − | 0.0796964i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.650785 | + | 0.0822132i | 0.650785 | + | 0.0822132i | ||||
\(997\) | 0 | 0 | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) | ||||
0.997159 | + | 0.0753268i | \(0.0240000\pi\) | |||||||
\(998\) | 0.0742168 | + | 1.96773i | 0.0742168 | + | 1.96773i | ||||
\(999\) | 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 | 2008.1.bd.a.459.1 | yes | 100 | |
8.3 | odd | 2 | CM | 2008.1.bd.a.459.1 | yes | 100 | |
251.35 | even | 125 | inner | 2008.1.bd.a.35.1 | ✓ | 100 | |
2008.35 | odd | 250 | inner | 2008.1.bd.a.35.1 | ✓ | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.bd.a.35.1 | ✓ | 100 | 251.35 | even | 125 | inner | |
2008.1.bd.a.35.1 | ✓ | 100 | 2008.35 | odd | 250 | inner | |
2008.1.bd.a.459.1 | yes | 100 | 1.1 | even | 1 | trivial | |
2008.1.bd.a.459.1 | yes | 100 | 8.3 | odd | 2 | CM |