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 | 363.1 | ||
Root | \(-0.793990 + 0.607930i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.363 |
Dual form | 2008.1.bd.a.1571.1 |
$q$-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 \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{94}{125}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(3\) | −1.95919 | − | 0.197625i | −1.95919 | − | 0.197625i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(4\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(5\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(6\) | 1.40111 | − | 1.38361i | 1.40111 | − | 1.38361i | ||||
\(7\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(8\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(9\) | 2.81950 | + | 0.574659i | 2.81950 | + | 0.574659i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.02855 | − | 1.71451i | 1.02855 | − | 1.71451i | 0.492727 | − | 0.870184i | \(-0.336000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(12\) | 0.172990 | + | 1.96152i | 0.172990 | + | 1.96152i | ||||
\(13\) | 0 | 0 | 0.910106 | − | 0.414376i | \(-0.136000\pi\) | ||||
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(17\) | −0.725499 | + | 1.44627i | −0.725499 | + | 1.44627i | 0.162637 | + | 0.986686i | \(0.448000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(18\) | −2.24000 | + | 1.80616i | −2.24000 | + | 1.80616i | ||||
\(19\) | −0.0296998 | + | 0.122019i | −0.0296998 | + | 0.122019i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.665429 | + | 1.88539i | 0.665429 | + | 1.88539i | ||||
\(23\) | 0 | 0 | −0.988652 | − | 0.150226i | \(-0.952000\pi\) | ||||
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(24\) | −1.62164 | − | 1.11703i | −1.62164 | − | 1.11703i | ||||
\(25\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.53011 | − | 1.09816i | −3.53011 | − | 1.09816i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.260842 | − | 0.965382i | \(-0.584000\pi\) | ||||
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.920232 | − | 0.391374i | \(-0.128000\pi\) | ||||
−0.920232 | + | 0.391374i | \(0.872000\pi\) | |||||||
\(32\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(33\) | −2.35396 | + | 3.15578i | −2.35396 | + | 3.15578i | ||||
\(34\) | −0.651916 | − | 1.48089i | −0.651916 | − | 1.48089i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0361584 | − | 2.87724i | 0.0361584 | − | 2.87724i | ||||
\(37\) | 0 | 0 | 0.492727 | − | 0.870184i | \(-0.336000\pi\) | ||||
−0.492727 | + | 0.870184i | \(0.664000\pi\) | |||||||
\(38\) | −0.0750855 | − | 0.100662i | −0.0750855 | − | 0.100662i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.19543 | + | 0.0300508i | 1.19543 | + | 0.0300508i | 0.617860 | − | 0.786288i | \(-0.288000\pi\) |
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.225628 | − | 0.234298i | 0.225628 | − | 0.234298i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(44\) | −1.87687 | − | 0.689068i | −1.87687 | − | 0.689068i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(48\) | 1.89436 | − | 0.537477i | 1.89436 | − | 0.537477i | ||||
\(49\) | −0.999684 | + | 0.0251301i | −0.999684 | + | 0.0251301i | ||||
\(50\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(51\) | 1.70721 | − | 2.69013i | 1.70721 | − | 2.69013i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.137790 | − | 0.990461i | \(-0.544000\pi\) | ||||
0.137790 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(54\) | 3.09632 | − | 2.02001i | 3.09632 | − | 2.02001i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0823014 | − | 0.233188i | 0.0823014 | − | 0.233188i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.825233 | + | 1.64508i | 0.825233 | + | 1.64508i | 0.762443 | + | 0.647056i | \(0.224000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.984564 | − | 0.175023i | \(-0.944000\pi\) | ||||
0.984564 | + | 0.175023i | \(0.0560000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.931100 | − | 3.82533i | −0.931100 | − | 3.82533i | ||||
\(67\) | −0.603082 | − | 0.461758i | −0.603082 | − | 0.461758i | 0.260842 | − | 0.965382i | \(-0.416000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(68\) | 1.55659 | + | 0.441646i | 1.55659 | + | 0.441646i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.675333 | − | 0.737513i | \(-0.736000\pi\) | ||||
0.675333 | + | 0.737513i | \(0.264000\pi\) | |||||||
\(72\) | 2.19390 | + | 1.86188i | 2.19390 | + | 1.86188i | ||||
\(73\) | 0.410693 | − | 1.89313i | 0.410693 | − | 1.89313i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.448383 | − | 0.893841i | \(-0.352000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.320254 | + | 1.94291i | −0.320254 | + | 1.94291i | ||||
\(76\) | 0.125422 | + | 0.00630973i | 0.125422 | + | 0.00630973i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.837528 | − | 0.546394i | \(-0.816000\pi\) | ||||
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.05119 | + | 1.72296i | 4.05119 | + | 1.72296i | ||||
\(82\) | −0.785152 | + | 0.901941i | −0.785152 | + | 0.901941i | ||||
\(83\) | 0.830793 | − | 1.23915i | 0.830793 | − | 1.23915i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0367093 | + | 0.323196i | 0.0367093 | + | 0.323196i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.72730 | − | 1.00693i | 1.72730 | − | 1.00693i | ||||
\(89\) | −0.633085 | + | 0.327599i | −0.633085 | + | 0.327599i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.793375 | + | 1.80223i | −0.793375 | + | 1.80223i | ||||
\(97\) | 1.79273 | − | 0.658175i | 1.79273 | − | 0.658175i | 0.793990 | − | 0.607930i | \(-0.208000\pi\) |
0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | |||||||
\(98\) | 0.617860 | − | 0.786288i | 0.617860 | − | 0.786288i | ||||
\(99\) | 3.88527 | − | 4.24300i | 3.88527 | − | 4.24300i | ||||
\(100\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(101\) | 0 | 0 | −0.656586 | − | 0.754251i | \(-0.728000\pi\) | ||||
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(102\) | 0.984564 | + | 3.03018i | 0.984564 | + | 3.03018i | ||||
\(103\) | 0 | 0 | −0.947098 | − | 0.320944i | \(-0.896000\pi\) | ||||
0.947098 | + | 0.320944i | \(0.104000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.926877 | − | 0.164768i | 0.926877 | − | 0.164768i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(108\) | −0.417227 | + | 3.67336i | −0.417227 | + | 3.67336i | ||||
\(109\) | 0 | 0 | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | ||||
−0.998737 | + | 0.0502443i | \(0.984000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.15129 | − | 0.836460i | 1.15129 | − | 0.836460i | 0.162637 | − | 0.986686i | \(-0.448000\pi\) |
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(114\) | 0.127213 | + | 0.212054i | 0.127213 | + | 0.212054i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.79358 | − | 0.412762i | −1.79358 | − | 0.412762i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.41092 | − | 2.64464i | −1.41092 | − | 2.64464i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.33614 | − | 0.295123i | −2.33614 | − | 0.295123i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
0.556876 | + | 0.830596i | \(0.312000\pi\) | |||||||
\(128\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(129\) | −0.488350 | + | 0.414444i | −0.488350 | + | 0.414444i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.841895 | + | 0.127926i | −0.841895 | + | 0.127926i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(132\) | 3.54097 | + | 1.72093i | 3.54097 | + | 1.72093i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.740210 | − | 0.170347i | 0.740210 | − | 0.170347i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.33250 | + | 0.917860i | −1.33250 | + | 0.917860i | ||||
\(137\) | 0.141770 | + | 0.236318i | 0.141770 | + | 0.236318i | 0.920232 | − | 0.391374i | \(-0.128000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.755723 | − | 1.84081i | −0.755723 | − | 1.84081i | −0.470704 | − | 0.882291i | \(-0.656000\pi\) |
−0.285019 | − | 0.958522i | \(-0.592000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.83305 | + | 0.503623i | −2.83305 | + | 0.503623i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.19690 | + | 1.52317i | 1.19690 | + | 1.52317i | ||||
\(147\) | 1.96353 | + | 0.148328i | 1.96353 | + | 0.148328i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(150\) | −1.29290 | − | 1.48522i | −1.29290 | − | 1.48522i | ||||
\(151\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(152\) | −0.0848090 | + | 0.0926177i | −0.0848090 | + | 0.0926177i | ||||
\(153\) | −2.87666 | + | 3.66083i | −2.87666 | + | 3.66083i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.90989 | + | 2.02323i | −3.90989 | + | 2.02323i | ||||
\(163\) | −0.450694 | + | 0.262732i | −0.450694 | + | 0.262732i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(164\) | −0.194483 | − | 1.17989i | −0.194483 | − | 1.17989i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.425215 | + | 1.43000i | 0.425215 | + | 1.43000i | ||||
\(167\) | 0 | 0 | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) | ||||
−0.994951 | + | 0.100362i | \(0.968000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.656586 | − | 0.754251i | 0.656586 | − | 0.754251i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.153858 | + | 0.326964i | −0.153858 | + | 0.326964i | ||||
\(172\) | −0.272426 | − | 0.177728i | −0.272426 | − | 0.177728i | ||||
\(173\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.325172 | + | 1.97275i | −0.325172 | + | 1.97275i | ||||
\(177\) | −1.29168 | − | 3.38611i | −1.29168 | − | 3.38611i | ||||
\(178\) | 0.151124 | − | 0.696620i | 0.151124 | − | 0.696620i | ||||
\(179\) | 0.751353 | + | 0.637644i | 0.751353 | + | 0.637644i | 0.938734 | − | 0.344643i | \(-0.112000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.997159 | − | 0.0753268i | \(-0.0240000\pi\) | ||||
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73342 | + | 2.73144i | 1.73342 | + | 2.73144i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.745941 | − | 0.666012i | \(-0.768000\pi\) | ||||
0.745941 | + | 0.666012i | \(0.232000\pi\) | |||||||
\(192\) | −0.882924 | − | 1.76009i | −0.882924 | − | 1.76009i | ||||
\(193\) | −1.19513 | − | 0.544146i | −1.19513 | − | 0.544146i | −0.285019 | − | 0.958522i | \(-0.592000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(194\) | −0.635595 | + | 1.80086i | −0.635595 | + | 1.80086i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.212007 | + | 0.977268i | 0.212007 | + | 0.977268i | ||||
\(197\) | 0 | 0 | 0.837528 | − | 0.546394i | \(-0.184000\pi\) | ||||
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(198\) | 0.792724 | + | 5.69824i | 0.792724 | + | 5.69824i | ||||
\(199\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(200\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(201\) | 1.09029 | + | 1.02386i | 1.09029 | + | 1.02386i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.96238 | − | 1.17289i | −2.96238 | − | 1.17289i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.178654 | + | 0.176423i | 0.178654 | + | 0.176423i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.50801 | + | 0.387191i | −1.50801 | + | 0.387191i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.463857 | + | 0.819198i | −0.463857 | + | 0.819198i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.56442 | − | 2.66296i | −2.56442 | − | 2.66296i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.17875 | + | 3.62783i | −1.17875 | + | 3.62783i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.979855 | − | 0.199710i | \(-0.0640000\pi\) | ||||
−0.979855 | + | 0.199710i | \(0.936000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.750563 | − | 2.77785i | 0.750563 | − | 2.77785i | ||||
\(226\) | −0.0893554 | + | 1.42026i | −0.0893554 | + | 1.42026i | ||||
\(227\) | 1.44333 | + | 0.994203i | 1.44333 | + | 0.994203i | 0.994951 | + | 0.100362i | \(0.0320000\pi\) |
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(228\) | −0.244479 | − | 0.0371486i | −0.244479 | − | 0.0371486i | ||||
\(229\) | 0 | 0 | −0.332820 | − | 0.942991i | \(-0.608000\pi\) | ||||
0.332820 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.38276 | − | 1.11495i | 1.38276 | − | 1.11495i | 0.402906 | − | 0.915241i | \(-0.368000\pi\) |
0.979855 | − | 0.199710i | \(-0.0640000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.46131 | − | 1.11887i | 1.46131 | − | 1.11887i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.0848090 | − | 1.34800i | −0.0848090 | − | 1.34800i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
0.693653 | − | 0.720309i | \(-0.256000\pi\) | |||||||
\(242\) | 2.93709 | + | 0.598625i | 2.93709 | + | 0.598625i | ||||
\(243\) | −4.35684 | − | 2.39519i | −4.35684 | − | 2.39519i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.71651 | − | 1.61191i | 1.71651 | − | 1.61191i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.87257 | + | 2.26354i | −1.87257 | + | 2.26354i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.0125660 | − | 0.999921i | 0.0125660 | − | 0.999921i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(257\) | 0.732084 | − | 0.722942i | 0.732084 | − | 0.722942i | −0.236499 | − | 0.971632i | \(-0.576000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(258\) | −0.00804864 | − | 0.640456i | −0.00804864 | − | 0.640456i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.438075 | − | 0.730234i | 0.438075 | − | 0.730234i | ||||
\(263\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(264\) | −3.58310 | + | 1.63140i | −3.58310 | + | 1.63140i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.30507 | − | 0.516715i | 1.30507 | − | 0.516715i | ||||
\(268\) | −0.340573 | + | 0.678925i | −0.340573 | + | 0.678925i | ||||
\(269\) | 0 | 0 | 0.778462 | − | 0.627691i | \(-0.216000\pi\) | ||||
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(272\) | 0.142146 | − | 1.61178i | 0.142146 | − | 1.61178i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.272453 | − | 0.0413993i | −0.272453 | − | 0.0413993i | ||||
\(275\) | −1.64655 | − | 1.13418i | −1.64655 | − | 1.13418i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.260842 | − | 0.965382i | \(-0.416000\pi\) | ||||
−0.260842 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(278\) | 1.90009 | + | 0.591084i | 1.90009 | + | 0.591084i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.0435376 | + | 1.15432i | −0.0435376 | + | 1.15432i | 0.793990 | + | 0.607930i | \(0.208000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.417379 | + | 1.28456i | −0.417379 | + | 1.28456i | 0.492727 | + | 0.870184i | \(0.336000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.41781 | − | 2.50393i | 1.41781 | − | 2.50393i | ||||
\(289\) | −0.967431 | − | 1.29696i | −0.967431 | − | 1.29696i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.64236 | + | 0.935199i | −3.64236 | + | 0.935199i | ||||
\(292\) | −1.93655 | − | 0.0486812i | −1.93655 | − | 0.0486812i | ||||
\(293\) | 0 | 0 | −0.711536 | − | 0.702650i | \(-0.752000\pi\) | ||||
0.711536 | + | 0.702650i | \(0.248000\pi\) | |||||||
\(294\) | −1.36589 | + | 1.41838i | −1.36589 | + | 1.41838i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.51371 | + | 4.92290i | −5.51371 | + | 4.92290i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.96851 | − | 0.0494844i | 1.96851 | − | 0.0494844i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.0173038 | − | 0.124383i | −0.0173038 | − | 0.124383i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.987071 | − | 4.55000i | −0.987071 | − | 4.55000i | ||||
\(307\) | 0.856781 | − | 1.60596i | 0.856781 | − | 1.60596i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.793990 | − | 0.607930i | \(-0.208000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.745941 | − | 0.666012i | \(-0.768000\pi\) | ||||
0.745941 | + | 0.666012i | \(0.232000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.443754 | − | 1.49235i | 0.443754 | − | 1.49235i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
0.823533 | − | 0.567269i | \(-0.192000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.236499 | − | 0.971632i | \(-0.576000\pi\) | ||||
0.236499 | + | 0.971632i | \(0.424000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.84849 | + | 0.139637i | −1.84849 | + | 0.139637i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.154924 | − | 0.131478i | −0.154924 | − | 0.131478i | ||||
\(324\) | 0.933330 | − | 4.30228i | 0.933330 | − | 4.30228i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.0848450 | − | 0.514737i | 0.0848450 | − | 0.514737i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.03309 | + | 0.602238i | 1.03309 | + | 0.602238i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.559121 | + | 1.18819i | −0.559121 | + | 1.18819i | 0.402906 | + | 0.915241i | \(0.368000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(332\) | −1.37288 | − | 0.583883i | −1.37288 | − | 0.583883i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.179214 | + | 1.57784i | 0.179214 | + | 1.57784i | 0.693653 | + | 0.720309i | \(0.256000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(338\) | 0.162637 | + | 0.986686i | 0.162637 | + | 0.986686i | ||||
\(339\) | −2.42090 | + | 1.41126i | −2.42090 | + | 1.41126i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.153858 | − | 0.326964i | −0.153858 | − | 0.326964i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.310593 | − | 0.0966200i | 0.310593 | − | 0.0966200i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.0707916 | + | 0.160810i | −0.0707916 | + | 0.160810i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
−0.617860 | + | 0.786288i | \(0.712000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.31276 | − | 1.50803i | −1.31276 | − | 1.50803i | ||||
\(353\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(354\) | 3.43239 | + | 1.16313i | 3.43239 | + | 1.16313i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.440425 | + | 0.560485i | 0.440425 | + | 0.560485i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.970244 | + | 0.172477i | −0.970244 | + | 0.172477i | ||||
\(359\) | 0 | 0 | 0.112856 | − | 0.993611i | \(-0.464000\pi\) | ||||
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.874130 | + | 0.452332i | 0.874130 | + | 0.452332i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.24161 | + | 5.46019i | 2.24161 | + | 5.46019i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.899405 | − | 0.437116i | \(-0.144000\pi\) | ||||
−0.899405 | + | 0.437116i | \(0.856000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.35325 | + | 0.771694i | 3.35325 | + | 0.771694i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.762443 | − | 0.647056i | \(-0.224000\pi\) | ||||
−0.762443 | + | 0.647056i | \(0.776000\pi\) | |||||||
\(374\) | −3.20954 | − | 0.405459i | −3.20954 | − | 0.405459i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.97859 | + | 0.249954i | 1.97859 | + | 0.249954i | 0.998737 | + | 0.0502443i | \(0.0160000\pi\) |
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.899405 | − | 0.437116i | \(-0.856000\pi\) | ||||
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(384\) | 1.91897 | + | 0.441618i | 1.91897 | + | 0.441618i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.18107 | − | 0.574008i | 1.18107 | − | 0.574008i | ||||
\(387\) | 0.770799 | − | 0.530945i | 0.770799 | − | 0.530945i | ||||
\(388\) | −0.982440 | − | 1.63764i | −0.982440 | − | 1.63764i | ||||
\(389\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.888136 | − | 0.459580i | −0.888136 | − | 0.459580i | ||||
\(393\) | 1.67471 | − | 0.0842511i | 1.67471 | − | 0.0842511i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.89587 | − | 3.02139i | −4.89587 | − | 3.02139i | ||||
\(397\) | 0 | 0 | −0.617860 | − | 0.786288i | \(-0.712000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(401\) | −0.0494937 | − | 0.0568557i | −0.0494937 | − | 0.0568557i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(402\) | −1.48387 | + | 0.187457i | −1.48387 | + | 0.187457i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 2.79202 | − | 1.53492i | 2.79202 | − | 1.53492i | ||||
\(409\) | 0.404876 | − | 0.125950i | 0.404876 | − | 0.125950i | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) |
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.231051 | − | 0.491008i | −0.231051 | − | 0.491008i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.11681 | + | 3.75585i | 1.11681 | + | 3.75585i | ||||
\(418\) | −0.249815 | + | 0.0251991i | −0.249815 | + | 0.0251991i | ||||
\(419\) | −0.236123 | + | 0.352184i | −0.236123 | + | 0.352184i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(422\) | 0.662906 | − | 1.40875i | 0.662906 | − | 1.40875i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.39786 | + | 0.814879i | 1.39786 | + | 0.814879i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.335529 | − | 0.879585i | −0.335529 | − | 0.879585i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.675333 | − | 0.737513i | \(-0.736000\pi\) | ||||
0.675333 | + | 0.737513i | \(0.264000\pi\) | |||||||
\(432\) | 3.68647 | − | 0.278481i | 3.68647 | − | 0.278481i | ||||
\(433\) | −1.92189 | − | 0.493458i | −1.92189 | − | 0.493458i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.929776 | − | 0.368125i | \(-0.880000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −2.04393 | − | 3.22071i | −2.04393 | − | 3.22071i | ||||
\(439\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.83305 | − | 0.503623i | −2.83305 | − | 0.503623i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.277116 | + | 0.552424i | 0.277116 | + | 0.552424i | 0.988652 | − | 0.150226i | \(-0.0480000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.111033 | − | 0.798127i | −0.111033 | − | 0.798127i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
0.850994 | − | 0.525175i | \(-0.176000\pi\) | |||||||
\(450\) | 1.66195 | + | 2.34899i | 1.66195 | + | 2.34899i | ||||
\(451\) | 1.28109 | − | 2.01867i | 1.28109 | − | 2.01867i | ||||
\(452\) | −1.03737 | − | 0.974159i | −1.03737 | − | 0.974159i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.68606 | + | 0.478379i | −1.68606 | + | 0.478379i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.184460 | − | 0.164695i | 0.184460 | − | 0.164695i | ||||
\(457\) | −1.08489 | + | 0.669518i | −1.08489 | + | 0.669518i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.14932 | − | 4.30877i | 4.14932 | − | 4.30877i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) | ||||
0.999684 | + | 0.0251301i | \(0.00800000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.947098 | − | 0.320944i | \(-0.104000\pi\) | ||||
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.0223207 | + | 1.77613i | −0.0223207 | + | 1.77613i | ||||
\(467\) | −0.772557 | − | 0.802245i | −0.772557 | − | 0.802245i | 0.212007 | − | 0.977268i | \(-0.432000\pi\) |
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.0693674 | + | 1.83916i | −0.0693674 | + | 1.83916i | ||||
\(473\) | −0.169637 | − | 0.627829i | −0.169637 | − | 0.627829i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.119913 | + | 0.0373028i | 0.119913 | + | 0.0373028i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.988652 | − | 0.150226i | \(-0.952000\pi\) | ||||
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.09271 | + | 0.793901i | 1.09271 | + | 0.793901i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.33342 | + | 1.88149i | −2.33342 | + | 1.88149i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.62268 | − | 1.83025i | 4.62268 | − | 1.83025i | ||||
\(487\) | 0 | 0 | 0.793990 | − | 0.607930i | \(-0.208000\pi\) | ||||
−0.793990 | + | 0.607930i | \(0.792000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.934916 | − | 0.425672i | 0.934916 | − | 0.425672i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0129289 | + | 0.0215514i | −0.0129289 | + | 0.0215514i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(492\) | 0.147853 | + | 2.35006i | 0.147853 | + | 2.35006i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.550472 | − | 2.88567i | −0.550472 | − | 2.88567i | ||||
\(499\) | 1.69340 | + | 0.170815i | 1.69340 | + | 0.170815i | 0.899405 | − | 0.437116i | \(-0.144000\pi\) |
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.762443 | + | 0.647056i | 0.762443 | + | 0.647056i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.43543 | + | 1.34796i | −1.43543 | + | 1.34796i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.0627905 | + | 0.998027i | 0.0627905 | + | 0.998027i | ||||
\(513\) | 0.238839 | − | 0.398124i | 0.238839 | − | 0.398124i | ||||
\(514\) | 0.0903883 | + | 1.02490i | 0.0903883 | + | 1.02490i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.498611 | + | 0.402041i | 0.498611 | + | 0.402041i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.233059 | + | 0.957499i | −0.233059 | + | 0.957499i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.108559 | + | 1.23094i | −0.108559 | + | 1.23094i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(524\) | 0.283415 | + | 0.803012i | 0.283415 | + | 0.803012i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.02694 | − | 3.80072i | 1.02694 | − | 3.80072i | ||||
\(529\) | 0.954865 | + | 0.297042i | 0.954865 | + | 0.297042i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.38138 | + | 5.11254i | 1.38138 | + | 5.11254i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −0.433749 | + | 1.33494i | −0.433749 | + | 1.33494i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.306031 | − | 0.695179i | −0.306031 | − | 0.695179i | ||||
\(537\) | −1.34603 | − | 1.39775i | −1.34603 | − | 1.39775i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.985143 | + | 1.73982i | −0.985143 | + | 1.73982i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.947098 | − | 0.320944i | \(-0.104000\pi\) | ||||
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.15129 | + | 1.13691i | 1.15129 | + | 1.13691i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.44838 | − | 0.893841i | 1.44838 | − | 0.893841i | 0.448383 | − | 0.893841i | \(-0.352000\pi\) |
1.00000 | \(0\) | |||||||||
\(548\) | 0.205567 | − | 0.183540i | 0.205567 | − | 0.183540i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.92345 | − | 0.545731i | 1.92345 | − | 0.545731i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.66660 | + | 1.08727i | −1.66660 | + | 1.08727i | ||||
\(557\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.85630 | − | 5.69397i | −2.85630 | − | 5.69397i | ||||
\(562\) | −0.861670 | − | 0.769341i | −0.861670 | − | 0.769341i | ||||
\(563\) | −1.72556 | − | 0.306748i | −1.72556 | − | 0.306748i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.723723 | − | 1.14040i | −0.723723 | − | 1.14040i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.816920 | − | 0.625487i | −0.816920 | − | 0.625487i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.644727 | − | 0.165538i | −0.644727 | − | 0.165538i | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.02556 | + | 2.68850i | 1.02556 | + | 2.68850i | ||||
\(577\) | −0.324350 | + | 1.96777i | −0.324350 | + | 1.96777i | −0.0878512 | + | 0.996134i | \(0.528000\pi\) |
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(578\) | 1.61599 | + | 0.0812970i | 1.61599 | + | 0.0812970i | ||||
\(579\) | 2.23394 | + | 1.30227i | 2.23394 | + | 1.30227i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.60114 | − | 3.40260i | 1.60114 | − | 3.40260i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.27192 | − | 1.46111i | 1.27192 | − | 1.46111i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.477423 | + | 1.60558i | 0.477423 | + | 1.60558i | 0.762443 | + | 0.647056i | \(0.224000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(588\) | −0.222229 | − | 1.95655i | −0.222229 | − | 1.95655i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.400832 | + | 0.851811i | 0.400832 | + | 0.851811i | 0.998737 | + | 0.0502443i | \(0.0160000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(594\) | −0.278591 | − | 7.38636i | −0.278591 | − | 7.38636i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(600\) | −1.21665 | + | 1.54830i | −1.21665 | + | 1.54830i | ||||
\(601\) | −0.723723 | + | 0.790359i | −0.723723 | + | 0.790359i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.43504 | − | 1.64849i | −1.43504 | − | 1.64849i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.617860 | − | 0.786288i | \(-0.712000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(608\) | 0.106869 | + | 0.0659520i | 0.106869 | + | 0.0659520i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.13502 | + | 2.13973i | 4.13502 | + | 2.13973i | ||||
\(613\) | 0 | 0 | 0.577573 | − | 0.816339i | \(-0.304000\pi\) | ||||
−0.577573 | + | 0.816339i | \(0.696000\pi\) | |||||||
\(614\) | 0.691278 | + | 1.68384i | 0.691278 | + | 1.68384i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.60511 | + | 1.10564i | −1.60511 | + | 1.10564i | −0.675333 | + | 0.737513i | \(0.736000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.73103 | − | 0.398366i | 1.73103 | − | 0.398366i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(626\) | 0.867013 | + | 1.29318i | 0.867013 | + | 1.29318i | ||||
\(627\) | −0.315152 | − | 0.380953i | −0.315152 | − | 0.380953i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.762443 | − | 0.647056i | \(-0.224000\pi\) | ||||
−0.762443 | + | 0.647056i | \(0.776000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.03099 | − | 0.460559i | 3.03099 | − | 0.460559i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.553694 | − | 1.34870i | −0.553694 | − | 1.34870i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
0.356412 | − | 0.934329i | \(-0.384000\pi\) | |||||||
\(642\) | 1.07068 | − | 1.51329i | 1.07068 | − | 1.51329i | ||||
\(643\) | 1.70882 | + | 0.884257i | 1.70882 | + | 0.884257i | 0.979855 | + | 0.199710i | \(0.0640000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.200058 | − | 0.0355637i | 0.200058 | − | 0.0355637i | ||||
\(647\) | 0 | 0 | −0.850994 | − | 0.525175i | \(-0.824000\pi\) | ||||
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(648\) | 2.72004 | + | 3.46152i | 2.72004 | + | 3.46152i | ||||
\(649\) | 3.66931 | + | 0.277185i | 3.66931 | + | 0.277185i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.342530 | + | 0.393480i | 0.342530 | + | 0.393480i | ||||
\(653\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.12255 | + | 0.412127i | −1.12255 | + | 0.412127i | ||||
\(657\) | 2.24585 | − | 5.10168i | 2.24585 | − | 5.10168i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.746226 | + | 0.410241i | −0.746226 | + | 0.410241i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) | ||||
0.0376902 | + | 0.999289i | \(0.488000\pi\) | |||||||
\(662\) | −0.559121 | − | 1.18819i | −0.559121 | − | 1.18819i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.32500 | − | 0.685639i | 1.32500 | − | 0.685639i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.850483 | + | 1.80737i | −0.850483 | + | 1.80737i | −0.379779 | + | 0.925077i | \(0.624000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(674\) | −1.32998 | − | 0.867664i | −1.32998 | − | 0.867664i | ||||
\(675\) | −1.31765 | + | 3.45419i | −1.31765 | + | 3.45419i | ||||
\(676\) | −0.863923 | − | 0.503623i | −0.863923 | − | 0.503623i | ||||
\(677\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(678\) | 0.455744 | − | 2.76490i | 0.455744 | − | 2.76490i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.63128 | − | 2.23307i | −2.63128 | − | 2.23307i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.568419 | − | 0.0429392i | 0.568419 | − | 0.0429392i | 0.212007 | − | 0.977268i | \(-0.432000\pi\) |
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(684\) | 0.350003 | + | 0.0898654i | 0.350003 | + | 0.0898654i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.123532 | + | 0.300904i | −0.123532 | + | 0.300904i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.539883 | − | 1.81563i | 0.539883 | − | 1.81563i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.577573 | − | 0.816339i | \(-0.304000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.0787820 | − | 0.157050i | −0.0787820 | − | 0.157050i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.910747 | + | 1.70711i | −0.910747 | + | 1.70711i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.92943 | + | 1.91113i | −2.92943 | + | 1.91113i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.99874 | − | 0.0502443i | 1.99874 | − | 0.0502443i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.348445 | + | 0.137959i | 0.348445 | + | 0.137959i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.08410 | + | 1.90329i | −3.08410 | + | 1.90329i | ||||
\(709\) | 0 | 0 | −0.938734 | − | 0.344643i | \(-0.888000\pi\) | ||||
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.712599 | − | 0.0179133i | −0.712599 | − | 0.0179133i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.485560 | − | 0.857527i | 0.485560 | − | 0.857527i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.402906 | − | 0.915241i | \(-0.632000\pi\) | ||||
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.905719 | + | 0.385201i | −0.905719 | + | 0.385201i | ||||
\(723\) | −0.100242 | + | 2.65774i | −0.100242 | + | 2.65774i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.63600 | − | 1.75326i | −5.63600 | − | 1.75326i | ||||
\(727\) | 0 | 0 | 0.260842 | − | 0.965382i | \(-0.416000\pi\) | ||||
−0.260842 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.43704 | + | 3.05634i | 4.43704 | + | 3.05634i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.175165 | + | 0.496301i | 0.175165 | + | 0.496301i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.41199 | + | 0.559047i | −1.41199 | + | 0.559047i | ||||
\(738\) | −2.73205 | + | 2.09183i | −2.73205 | + | 2.09183i | ||||
\(739\) | 0.443754 | + | 0.357808i | 0.443754 | + | 0.357808i | 0.823533 | − | 0.567269i | \(-0.192000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.05451 | − | 3.01637i | 3.05451 | − | 3.01637i | ||||
\(748\) | 2.35825 | − | 2.21454i | 2.35825 | − | 2.21454i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.222229 | + | 1.95655i | −0.222229 | + | 1.95655i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(758\) | −1.45380 | + | 1.36520i | −1.45380 | + | 1.36520i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.30735 | − | 0.718720i | −1.30735 | − | 0.718720i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.56347 | + | 1.19709i | −1.56347 | + | 1.19709i | ||||
\(769\) | −1.53140 | + | 0.606325i | −1.53140 | + | 0.606325i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.57716 | + | 1.27170i | −1.57716 | + | 1.27170i | ||||
\(772\) | −0.310564 | + | 1.27592i | −0.310564 | + | 1.27592i | ||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | −0.0822258 | + | 0.932348i | −0.0822258 | + | 0.932348i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.88806 | + | 0.286890i | 1.88806 | + | 0.286890i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0391708 | + | 0.144972i | −0.0391708 | + | 0.144972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.920232 | − | 0.391374i | 0.920232 | − | 0.391374i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.00258 | + | 1.34409i | −1.00258 | + | 1.34409i | ||||
\(787\) | 0.361313 | + | 0.820758i | 0.361313 | + | 0.820758i | 0.998737 | + | 0.0502443i | \(0.0160000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.44877 | − | 1.84643i | 5.44877 | − | 1.84643i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.938734 | − | 0.344643i | \(-0.888000\pi\) | ||||
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(801\) | −1.97324 | + | 0.559859i | −1.97324 | + | 0.559859i | ||||
\(802\) | 0.0753566 | − | 0.00189432i | 0.0753566 | − | 0.00189432i | ||||
\(803\) | −2.82338 | − | 2.65133i | −2.82338 | − | 2.65133i | ||||
\(804\) | 0.801419 | − | 1.26283i | 0.801419 | − | 1.26283i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.775280 | + | 1.45319i | −0.775280 | + | 1.45319i | 0.112856 | + | 0.993611i | \(0.464000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.474787 | − | 0.216173i | −0.474787 | − | 0.216173i | 0.162637 | − | 0.986686i | \(-0.448000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.597019 | + | 3.12968i | −0.597019 | + | 3.12968i | ||||
\(817\) | 0.0218876 | + | 0.0344894i | 0.0218876 | + | 0.0344894i | ||||
\(818\) | −0.161032 | + | 0.392246i | −0.161032 | + | 0.392246i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(822\) | 0.525605 | + | 0.134952i | 0.525605 | + | 0.134952i | ||||
\(823\) | 0 | 0 | 0.997159 | − | 0.0753268i | \(-0.0240000\pi\) | ||||
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.00175 | + | 2.54747i | 3.00175 | + | 2.54747i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.396954 | − | 1.04061i | −0.396954 | − | 1.04061i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.577573 | − | 0.816339i | \(-0.304000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.688925 | − | 1.46404i | 0.688925 | − | 1.46404i | ||||
\(834\) | −3.60581 | − | 1.53355i | −3.60581 | − | 1.53355i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.139822 | − | 0.208548i | 0.139822 | − | 0.208548i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.120852 | − | 0.406427i | −0.120852 | − | 0.406427i | ||||
\(839\) | 0 | 0 | −0.112856 | − | 0.993611i | \(-0.536000\pi\) | ||||
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.863923 | + | 0.503623i | −0.863923 | + | 0.503623i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.313422 | − | 2.25293i | 0.313422 | − | 2.25293i | ||||
\(844\) | 0.662906 | + | 1.40875i | 0.662906 | + | 1.40875i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.07158 | − | 2.43421i | 1.07158 | − | 2.43421i | ||||
\(850\) | −1.51890 | + | 0.557644i | −1.51890 | + | 0.557644i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.891606 | + | 0.302139i | 0.891606 | + | 0.302139i | ||||
\(857\) | −0.520201 | − | 0.0392967i | −0.520201 | − | 0.0392967i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.42546 | − | 0.879697i | −1.42546 | − | 0.879697i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.888136 | − | 0.459580i | \(-0.848000\pi\) | ||||
0.888136 | + | 0.459580i | \(0.152000\pi\) | |||||||
\(864\) | −2.13527 | + | 3.01799i | −2.13527 | + | 3.01799i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | ||||
\(867\) | 1.63906 | + | 2.73218i | 1.63906 | + | 2.73218i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.43282 | − | 0.825517i | 5.43282 | − | 0.825517i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.78445 | + | 0.478087i | 3.78445 | + | 0.478087i | ||||
\(877\) | 0 | 0 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
0.556876 | + | 0.830596i | \(0.312000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.565544 | + | 0.0714448i | 0.565544 | + | 0.0714448i | 0.402906 | − | 0.915241i | \(-0.368000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(882\) | 2.19390 | − | 1.86188i | 2.19390 | − | 1.86188i | ||||
\(883\) | −0.911832 | − | 1.70914i | −0.911832 | − | 1.70914i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
−0.236499 | − | 0.971632i | \(-0.576000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.602291 | − | 0.138607i | −0.602291 | − | 0.138607i | ||||
\(887\) | 0 | 0 | 0.974527 | − | 0.224271i | \(-0.0720000\pi\) | ||||
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.12091 | − | 5.17364i | 7.12091 | − | 5.17364i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.685742 | + | 0.423192i | 0.685742 | + | 0.423192i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.86929 | − | 0.216750i | −2.86929 | − | 0.216750i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.738818 | + | 2.27385i | 0.738818 | + | 2.27385i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.41185 | − | 0.178358i | 1.41185 | − | 0.178358i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.80618 | + | 0.663112i | −1.80618 | + | 0.663112i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(908\) | 0.706139 | − | 1.60406i | 0.706139 | − | 1.60406i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(912\) | 0.00932023 | + | 0.247110i | 0.00932023 | + | 0.247110i | ||||
\(913\) | −1.27002 | − | 2.69894i | −1.27002 | − | 2.69894i | ||||
\(914\) | 0.175662 | − | 1.26269i | 0.175662 | − | 1.26269i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.675088 | + | 5.94362i | 0.675088 | + | 5.94362i | ||||
\(919\) | 0 | 0 | −0.285019 | − | 0.958522i | \(-0.592000\pi\) | ||||
0.285019 | + | 0.958522i | \(0.408000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.99597 | + | 2.97705i | −1.99597 | + | 2.97705i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.296034 | + | 1.79598i | −0.296034 | + | 1.79598i | 0.260842 | + | 0.965382i | \(0.416000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0266241 | − | 0.122726i | 0.0266241 | − | 0.122726i | ||||
\(932\) | −1.35431 | − | 1.14935i | −1.35431 | − | 1.14935i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.11059 | − | 0.0838953i | 1.11059 | − | 0.0838953i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.452605 | − | 0.346544i | −0.452605 | − | 0.346544i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.16432 | + | 2.83609i | −1.16432 | + | 2.83609i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.37288 | − | 1.22577i | −1.37288 | − | 1.22577i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.591881 | + | 0.269486i | 0.591881 | + | 0.269486i | ||||
\(947\) | 0.618896 | − | 1.75354i | 0.618896 | − | 1.75354i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.656586 | − | 0.754251i | \(-0.272000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.105178 | + | 0.0686168i | −0.105178 | + | 0.0686168i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.951775 | + | 1.49976i | −0.951775 | + | 1.49976i | −0.0878512 | + | 0.996134i | \(0.528000\pi\) |
−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 | ||||||||
\(961\) | 0.693653 | − | 0.720309i | 0.693653 | − | 0.720309i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.70802 | + | 0.0680742i | 2.70802 | + | 0.0680742i | ||||
\(964\) | −1.30823 | + | 0.335897i | −1.30823 | + | 0.335897i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.492727 | − | 0.870184i | \(-0.336000\pi\) | ||||
−0.492727 | + | 0.870184i | \(0.664000\pi\) | |||||||
\(968\) | 0.0376664 | − | 2.99724i | 0.0376664 | − | 2.99724i | ||||
\(969\) | 0.277542 | + | 0.288207i | 0.277542 | + | 0.288207i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.640747 | + | 0.859002i | −0.640747 | + | 0.859002i | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) |
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(972\) | −1.53638 | + | 4.72849i | −1.53638 | + | 4.72849i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.90009 | + | 0.591084i | 1.90009 | + | 0.591084i | 0.979855 | + | 0.199710i | \(0.0640000\pi\) |
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(978\) | −0.267952 | + | 0.991699i | −0.267952 | + | 0.991699i | ||||
\(979\) | −0.0894889 | + | 1.42238i | −0.0894889 | + | 1.42238i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.00836445 | − | 0.0236993i | −0.00836445 | − | 0.0236993i | ||||
\(983\) | 0 | 0 | 0.0878512 | − | 0.996134i | \(-0.472000\pi\) | ||||
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(984\) | −1.90500 | − | 1.38406i | −1.90500 | − | 1.38406i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.910106 | − | 0.414376i | \(-0.136000\pi\) | ||||
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.33024 | − | 2.21740i | 1.33024 | − | 2.21740i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.57433 | + | 1.41525i | 2.57433 | + | 1.41525i | ||||
\(997\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(998\) | −1.21103 | + | 1.19590i | −1.21103 | + | 1.19590i | ||||
\(999\) | 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.363.1 | ✓ | 100 | |
8.3 | odd | 2 | CM | 2008.1.bd.a.363.1 | ✓ | 100 | |
251.65 | even | 125 | inner | 2008.1.bd.a.1571.1 | yes | 100 | |
2008.1571 | odd | 250 | inner | 2008.1.bd.a.1571.1 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.bd.a.363.1 | ✓ | 100 | 1.1 | even | 1 | trivial | |
2008.1.bd.a.363.1 | ✓ | 100 | 8.3 | odd | 2 | CM | |
2008.1.bd.a.1571.1 | yes | 100 | 251.65 | even | 125 | inner | |
2008.1.bd.a.1571.1 | yes | 100 | 2008.1571 | odd | 250 | inner |