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 | 403.1 | ||
Root | \(0.962028 - 0.272952i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.403 |
Dual form | 2008.1.bd.a.1435.1 |
$q$-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 \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{59}{125}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(3\) | −0.253214 | + | 1.53620i | −0.253214 | + | 1.53620i | 0.492727 | + | 0.870184i | \(0.336000\pi\) |
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(4\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(5\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(6\) | 0.136778 | + | 1.55090i | 0.136778 | + | 1.55090i | ||||
\(7\) | 0 | 0 | −0.984564 | − | 0.175023i | \(-0.944000\pi\) | ||||
0.984564 | + | 0.175023i | \(0.0560000\pi\) | |||||||
\(8\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(9\) | −1.34868 | − | 0.457028i | −1.34868 | − | 0.457028i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.535114 | + | 1.79959i | −0.535114 | + | 1.79959i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(12\) | 0.518175 | + | 1.46817i | 0.518175 | + | 1.46817i | ||||
\(13\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(17\) | 1.57682 | − | 0.362878i | 1.57682 | − | 0.362878i | 0.656586 | − | 0.754251i | \(-0.272000\pi\) |
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(18\) | −1.41997 | − | 0.107266i | −1.41997 | − | 0.107266i | ||||
\(19\) | −1.24917 | + | 0.254600i | −1.24917 | + | 0.254600i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0707621 | + | 1.87613i | −0.0707621 | + | 1.87613i | ||||
\(23\) | 0 | 0 | −0.514440 | − | 0.857527i | \(-0.672000\pi\) | ||||
0.514440 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(24\) | 0.867013 | + | 1.29318i | 0.867013 | + | 1.29318i | ||||
\(25\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.310739 | − | 0.582452i | 0.310739 | − | 0.582452i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.850994 | − | 0.525175i | \(-0.824000\pi\) | ||||
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.793990 | − | 0.607930i | \(-0.208000\pi\) | ||||
−0.793990 | + | 0.607930i | \(0.792000\pi\) | |||||||
\(32\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(33\) | −2.62903 | − | 1.27772i | −2.62903 | − | 1.27772i | ||||
\(34\) | 1.43703 | − | 0.743616i | 1.43703 | − | 0.743616i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.40203 | + | 0.249235i | −1.40203 | + | 0.249235i | ||||
\(37\) | 0 | 0 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(38\) | −1.14660 | + | 0.557256i | −1.14660 | + | 0.557256i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.68860 | − | 0.619947i | 1.68860 | − | 0.619947i | 0.693653 | − | 0.720309i | \(-0.256000\pi\) |
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.342530 | − | 1.26771i | 0.342530 | − | 1.26771i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
0.899405 | − | 0.437116i | \(-0.144000\pi\) | |||||||
\(44\) | 0.398037 | + | 1.83479i | 0.398037 | + | 1.83479i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(48\) | 1.16137 | + | 1.03693i | 1.16137 | + | 1.03693i | ||||
\(49\) | 0.938734 | + | 0.344643i | 0.938734 | + | 0.344643i | ||||
\(50\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(51\) | 0.158179 | + | 2.51419i | 0.158179 | + | 2.51419i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(54\) | 0.156127 | − | 0.641431i | 0.156127 | − | 0.641431i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0748091 | − | 1.98343i | −0.0748091 | − | 1.98343i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.54753 | − | 0.356138i | −1.54753 | − | 0.356138i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.778462 | − | 0.627691i | \(-0.784000\pi\) | ||||
0.778462 | + | 0.627691i | \(0.216000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.86419 | − | 0.583767i | −2.86419 | − | 0.583767i | ||||
\(67\) | 1.29938 | + | 0.368667i | 1.29938 | + | 0.368667i | 0.850994 | − | 0.525175i | \(-0.176000\pi\) |
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(68\) | 1.20696 | − | 1.07763i | 1.20696 | − | 1.07763i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(72\) | −1.29600 | + | 0.590077i | −1.29600 | + | 0.590077i | ||||
\(73\) | −1.83845 | − | 0.279352i | −1.83845 | − | 0.279352i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.02225 | − | 1.17431i | −1.02225 | − | 1.17431i | ||||
\(76\) | −0.971998 | + | 0.824898i | −0.971998 | + | 0.824898i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.236499 | − | 0.971632i | \(-0.576000\pi\) | ||||
0.236499 | + | 0.971632i | \(0.424000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.314577 | − | 0.240861i | −0.314577 | − | 0.240861i | ||||
\(82\) | 1.48138 | − | 1.02041i | 1.48138 | − | 1.02041i | ||||
\(83\) | −0.573365 | − | 1.30245i | −0.573365 | − | 1.30245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.356412 | − | 0.934329i | \(-0.384000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.0165014 | − | 1.31307i | 0.0165014 | − | 1.31307i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.841825 | + | 1.67816i | 0.841825 | + | 1.67816i | ||||
\(89\) | −0.698970 | − | 0.297271i | −0.698970 | − | 0.297271i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.38276 | + | 0.715531i | 1.38276 | + | 0.715531i | ||||
\(97\) | −0.199585 | + | 0.920008i | −0.199585 | + | 0.920008i | 0.762443 | + | 0.647056i | \(0.224000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(98\) | 0.994951 | + | 0.100362i | 0.994951 | + | 0.100362i | ||||
\(99\) | 1.54416 | − | 2.18252i | 1.54416 | − | 2.18252i | ||||
\(100\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(101\) | 0 | 0 | −0.823533 | − | 0.567269i | \(-0.808000\pi\) | ||||
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(102\) | 0.778462 | + | 2.39586i | 0.778462 | + | 2.39586i | ||||
\(103\) | 0 | 0 | 0.137790 | − | 0.990461i | \(-0.456000\pi\) | ||||
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.30397 | − | 1.05142i | 1.30397 | − | 1.05142i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.994951 | − | 0.100362i | \(-0.0320000\pi\) | |||||||
\(108\) | −0.00829557 | − | 0.660106i | −0.00829557 | − | 0.660106i | ||||
\(109\) | 0 | 0 | −0.762443 | − | 0.647056i | \(-0.776000\pi\) | ||||
0.762443 | + | 0.647056i | \(0.224000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.142146 | − | 0.103275i | 0.142146 | − | 0.103275i | −0.514440 | − | 0.857527i | \(-0.672000\pi\) |
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(114\) | −0.565718 | − | 1.90251i | −0.565718 | − | 1.90251i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.58748 | + | 0.0399061i | −1.58748 | + | 0.0399061i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.11466 | − | 1.37958i | −2.11466 | − | 1.37958i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.524782 | + | 2.75101i | 0.524782 | + | 2.75101i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.402906 | − | 0.915241i | \(-0.368000\pi\) | ||||
−0.402906 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(128\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(129\) | 1.86072 | + | 0.847195i | 1.86072 | + | 0.847195i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.02077 | − | 1.70153i | 1.02077 | − | 1.70153i | 0.402906 | − | 0.915241i | \(-0.368000\pi\) |
0.617860 | − | 0.786288i | \(-0.288000\pi\) | |||||||
\(132\) | −2.91938 | + | 0.146868i | −2.91938 | + | 0.146868i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.35024 | + | 0.0339424i | 1.35024 | + | 0.0339424i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.901044 | − | 1.34393i | 0.901044 | − | 1.34393i | ||||
\(137\) | −0.203169 | − | 0.683257i | −0.203169 | − | 0.683257i | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) |
0.793990 | − | 0.607930i | \(-0.208000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.219668 | + | 0.239894i | −0.219668 | + | 0.239894i | −0.837528 | − | 0.546394i | \(-0.816000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.10854 | + | 0.893841i | −1.10854 | + | 0.893841i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.85016 | + | 0.186628i | −1.85016 | + | 0.186628i | ||||
\(147\) | −0.767139 | + | 1.35481i | −0.767139 | + | 1.35481i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(150\) | −1.28218 | − | 0.883195i | −1.28218 | − | 0.883195i | ||||
\(151\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(152\) | −0.736317 | + | 1.04071i | −0.736317 | + | 1.04071i | ||||
\(153\) | −2.29247 | − | 0.231244i | −2.29247 | − | 0.231244i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.364594 | − | 0.155061i | −0.364594 | − | 0.155061i | ||||
\(163\) | 0.763143 | + | 1.52131i | 0.763143 | + | 1.52131i | 0.850994 | + | 0.525175i | \(0.176000\pi\) |
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(164\) | 1.18107 | − | 1.35676i | 1.18107 | − | 1.35676i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.879258 | − | 1.11894i | −0.879258 | − | 1.11894i | ||||
\(167\) | 0 | 0 | −0.162637 | − | 0.986686i | \(-0.552000\pi\) | ||||
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.823533 | − | 0.567269i | 0.823533 | − | 0.567269i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.80109 | + | 0.227530i | 1.80109 | + | 0.227530i | ||||
\(172\) | −0.310564 | − | 1.27592i | −0.310564 | − | 1.27592i | ||||
\(173\) | 0 | 0 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
0.379779 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.23272 | + | 1.41608i | 1.23272 | + | 1.41608i | ||||
\(177\) | 0.938953 | − | 2.28713i | 0.938953 | − | 2.28713i | ||||
\(178\) | −0.750939 | − | 0.114105i | −0.750939 | − | 0.114105i | ||||
\(179\) | 1.08831 | − | 0.495514i | 1.08831 | − | 0.495514i | 0.212007 | − | 0.977268i | \(-0.432000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.492727 | − | 0.870184i | \(-0.664000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.190745 | + | 3.03181i | −0.190745 | + | 3.03181i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.711536 | − | 0.702650i | \(-0.248000\pi\) | ||||
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(192\) | 1.51726 | + | 0.349173i | 1.51726 | + | 0.349173i | ||||
\(193\) | 1.57272 | + | 0.489247i | 1.57272 | + | 0.489247i | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(194\) | 0.0354818 | + | 0.940739i | 0.0354818 | + | 0.940739i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.988652 | − | 0.150226i | 0.988652 | − | 0.150226i | ||||
\(197\) | 0 | 0 | 0.236499 | − | 0.971632i | \(-0.424000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(198\) | 0.952882 | − | 2.49797i | 0.952882 | − | 2.49797i | ||||
\(199\) | 0 | 0 | 0.693653 | − | 0.720309i | \(-0.256000\pi\) | ||||
−0.693653 | + | 0.720309i | \(0.744000\pi\) | |||||||
\(200\) | 0.0627905 | + | 0.998027i | 0.0627905 | + | 0.998027i | ||||
\(201\) | −0.895365 | + | 1.90275i | −0.895365 | + | 1.90275i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.34983 | + | 2.12699i | 1.34983 | + | 2.12699i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.210271 | − | 2.38423i | 0.210271 | − | 2.38423i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.85427 | + | 0.734157i | 1.85427 | + | 0.734157i | 0.954865 | + | 0.297042i | \(0.0960000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.00152 | − | 1.34267i | 1.00152 | − | 1.34267i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.172197 | − | 0.637305i | −0.172197 | − | 0.637305i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.894661 | − | 2.75348i | 0.894661 | − | 2.75348i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.947098 | − | 0.320944i | \(-0.104000\pi\) | ||||
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.21183 | − | 0.747856i | 1.21183 | − | 0.747856i | ||||
\(226\) | 0.111997 | − | 0.135381i | 0.111997 | − | 0.135381i | ||||
\(227\) | −0.811890 | − | 1.21096i | −0.811890 | − | 1.21096i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.162637 | − | 0.986686i | \(-0.448000\pi\) | |||||||
\(228\) | −1.02108 | − | 1.70206i | −1.02108 | − | 1.70206i | ||||
\(229\) | 0 | 0 | 0.0376902 | − | 0.999289i | \(-0.488000\pi\) | ||||
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.83523 | − | 0.138636i | −1.83523 | − | 0.138636i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.52768 | + | 0.433442i | −1.52768 | + | 0.433442i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.332820 | − | 0.942991i | \(-0.608000\pi\) | ||||
0.332820 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.736317 | − | 0.890055i | −0.736317 | − | 0.890055i | 0.260842 | − | 0.965382i | \(-0.416000\pi\) |
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(242\) | −2.39131 | − | 0.810346i | −2.39131 | − | 0.810346i | ||||
\(243\) | 0.930899 | − | 0.874172i | 0.930899 | − | 0.874172i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.19244 | + | 2.53407i | 1.19244 | + | 2.53407i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.14601 | − | 0.551001i | 2.14601 | − | 0.551001i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.984564 | + | 0.175023i | −0.984564 | + | 0.175023i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.425779 | − | 0.904827i | −0.425779 | − | 0.904827i | ||||
\(257\) | 0.0500786 | + | 0.567835i | 0.0500786 | + | 0.567835i | 0.979855 | + | 0.199710i | \(0.0640000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(258\) | 2.01295 | + | 0.357836i | 2.01295 | + | 0.357836i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.565544 | − | 1.90193i | 0.565544 | − | 1.90193i | ||||
\(263\) | 0 | 0 | −0.332820 | − | 0.942991i | \(-0.608000\pi\) | ||||
0.332820 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(264\) | −2.79114 | + | 0.868275i | −2.79114 | + | 0.868275i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.633655 | − | 0.998481i | 0.633655 | − | 0.998481i | ||||
\(268\) | 1.31626 | − | 0.302915i | 1.31626 | − | 0.302915i | ||||
\(269\) | 0 | 0 | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) | ||||
0.997159 | + | 0.0753268i | \(0.0240000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(272\) | 0.538513 | − | 1.52579i | 0.538513 | − | 1.52579i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.366705 | − | 0.611265i | −0.366705 | − | 0.611265i | ||||
\(275\) | −1.04552 | − | 1.55942i | −1.04552 | − | 1.55942i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.850994 | − | 0.525175i | \(-0.176000\pi\) | ||||
−0.850994 | + | 0.525175i | \(0.824000\pi\) | |||||||
\(278\) | −0.153108 | + | 0.286987i | −0.153108 | + | 0.286987i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.19853 | + | 0.698680i | −1.19853 | + | 0.698680i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.356960 | − | 1.09861i | 0.356960 | − | 1.09861i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
0.954865 | − | 0.297042i | \(-0.0960000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.851425 | + | 1.14144i | −0.851425 | + | 1.14144i | ||||
\(289\) | 1.45527 | − | 0.707268i | 1.45527 | − | 0.707268i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.36277 | − | 0.539561i | −1.36277 | − | 0.539561i | ||||
\(292\) | −1.74563 | + | 0.640882i | −1.74563 | + | 0.640882i | ||||
\(293\) | 0 | 0 | 0.0878512 | − | 0.996134i | \(-0.472000\pi\) | ||||
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(294\) | −0.406111 | + | 1.50303i | −0.406111 | + | 1.50303i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.881896 | + | 0.870882i | 0.881896 | + | 0.870882i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.46154 | − | 0.536583i | −1.46154 | − | 0.536583i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.454371 | + | 1.19113i | −0.454371 | + | 1.19113i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.27796 | + | 0.346135i | −2.27796 | + | 0.346135i | ||||
\(307\) | −1.59945 | + | 1.04347i | −1.59945 | + | 1.04347i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.711536 | − | 0.702650i | \(-0.248000\pi\) | ||||
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.23221 | + | 1.56811i | −1.23221 | + | 1.56811i | −0.556876 | + | 0.830596i | \(0.688000\pi\) |
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.979855 | − | 0.199710i | \(-0.936000\pi\) | ||||
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.28500 | + | 2.26938i | 1.28500 | + | 2.26938i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.87732 | + | 0.854752i | −1.87732 | + | 0.854752i | ||||
\(324\) | −0.391702 | − | 0.0595190i | −0.391702 | − | 0.0595190i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.11750 | + | 1.28373i | 1.11750 | + | 1.28373i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.806556 | − | 1.60785i | 0.806556 | − | 1.60785i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.63408 | − | 0.206432i | −1.63408 | − | 0.206432i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(332\) | −1.12990 | − | 0.865128i | −1.12990 | − | 0.865128i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.0241778 | + | 1.92390i | −0.0241778 | + | 1.92390i | 0.260842 | + | 0.965382i | \(0.416000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(338\) | 0.656586 | − | 0.754251i | 0.656586 | − | 0.754251i | ||||
\(339\) | 0.122658 | + | 0.244515i | 0.122658 | + | 0.244515i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.80109 | − | 0.227530i | 1.80109 | − | 0.227530i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.618115 | − | 1.15860i | −0.618115 | − | 1.15860i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.591178 | + | 0.305914i | 0.591178 | + | 0.305914i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.994951 | − | 0.100362i | \(-0.968000\pi\) | ||||
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.54616 | + | 1.06503i | 1.54616 | + | 1.06503i | ||||
\(353\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(354\) | 0.340668 | − | 2.44878i | 0.340668 | − | 2.44878i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.755723 | + | 0.0762306i | −0.755723 | + | 0.0762306i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.930893 | − | 0.750600i | 0.930893 | − | 0.750600i | ||||
\(359\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.575363 | − | 0.244701i | 0.575363 | − | 0.244701i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.65477 | − | 2.89921i | 2.65477 | − | 2.89921i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.56072 | + | 0.0643715i | −2.56072 | + | 0.0643715i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.910106 | − | 0.414376i | \(-0.864000\pi\) | ||||
0.910106 | + | 0.414376i | \(0.136000\pi\) | |||||||
\(374\) | 0.569228 | + | 2.98400i | 0.569228 | + | 2.98400i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.184656 | − | 0.968000i | −0.184656 | − | 0.968000i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
0.762443 | − | 0.647056i | \(-0.224000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | ||||
−0.998737 | + | 0.0502443i | \(0.984000\pi\) | |||||||
\(384\) | 1.55643 | − | 0.0391257i | 1.55643 | − | 0.0391257i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.64498 | + | 0.0827557i | 1.64498 | + | 0.0827557i | ||||
\(387\) | −1.04134 | + | 1.55319i | −1.04134 | + | 1.55319i | ||||
\(388\) | 0.268319 | + | 0.902360i | 0.268319 | + | 0.902360i | ||||
\(389\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.920232 | − | 0.391374i | 0.920232 | − | 0.391374i | ||||
\(393\) | 2.35541 | + | 1.99895i | 2.35541 | + | 1.99895i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.301726 | − | 2.65646i | 0.301726 | − | 2.65646i | ||||
\(397\) | 0 | 0 | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) | ||||
−0.994951 | + | 0.100362i | \(0.968000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(401\) | −1.42294 | − | 0.980154i | −1.42294 | − | 0.980154i | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(402\) | −0.394041 | + | 2.06564i | −0.394041 | + | 2.06564i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.83639 | + | 1.72448i | 1.83639 | + | 1.72448i | ||||
\(409\) | −0.930725 | − | 1.74456i | −0.930725 | − | 1.74456i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
−0.332820 | − | 0.942991i | \(-0.608000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10106 | − | 0.139096i | 1.10106 | − | 0.139096i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.312901 | − | 0.398198i | −0.312901 | − | 0.398198i | ||||
\(418\) | −0.389270 | − | 2.36162i | −0.389270 | − | 2.36162i | ||||
\(419\) | 0.796668 | + | 1.80971i | 0.796668 | + | 1.80971i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.793990 | − | 0.607930i | \(-0.792000\pi\) | ||||
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(422\) | 1.97859 | + | 0.249954i | 1.97859 | + | 0.249954i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.725499 | + | 1.44627i | −0.725499 | + | 1.44627i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.636151 | − | 1.54956i | 0.636151 | − | 1.54956i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(432\) | −0.325278 | − | 0.574459i | −0.325278 | − | 0.574459i | ||||
\(433\) | 0.348445 | − | 0.137959i | 0.348445 | − | 0.137959i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0.181790 | − | 2.88947i | 0.181790 | − | 2.88947i | ||||
\(439\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.10854 | − | 0.893841i | −1.10854 | − | 0.893841i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.602291 | − | 0.138607i | −0.602291 | − | 0.138607i | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.633085 | + | 1.65962i | −0.633085 | + | 1.65962i | 0.112856 | + | 0.993611i | \(0.464000\pi\) |
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(450\) | 0.987772 | − | 1.02573i | 0.987772 | − | 1.02573i | ||||
\(451\) | 0.212057 | + | 3.37054i | 0.212057 | + | 3.37054i | ||||
\(452\) | 0.0748104 | − | 0.158980i | 0.0748104 | − | 0.158980i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.08754 | − | 0.971004i | −1.08754 | − | 0.971004i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.41229 | − | 1.39465i | −1.41229 | − | 1.39465i | ||||
\(457\) | 0.218622 | + | 1.92479i | 0.218622 | + | 1.92479i | 0.356412 | + | 0.934329i | \(0.384000\pi\) |
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.278620 | − | 1.03118i | 0.278620 | − | 1.03118i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.137790 | − | 0.990461i | \(-0.544000\pi\) | ||||
0.137790 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.81205 | + | 0.322124i | −1.81205 | + | 0.322124i | ||||
\(467\) | 0.210189 | + | 0.777917i | 0.210189 | + | 0.777917i | 0.988652 | + | 0.150226i | \(0.0480000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.37189 | + | 0.799744i | −1.37189 | + | 0.799744i | ||||
\(473\) | 2.09807 | + | 1.29479i | 2.09807 | + | 1.29479i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.600076 | − | 1.12479i | 0.600076 | − | 1.12479i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.514440 | − | 0.857527i | \(-0.672000\pi\) | ||||
0.514440 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.934532 | − | 0.678977i | −0.934532 | − | 0.678977i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.51771 | − | 0.190192i | −2.51771 | − | 0.190192i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.684255 | − | 1.07821i | 0.684255 | − | 1.07821i | ||||
\(487\) | 0 | 0 | 0.962028 | − | 0.272952i | \(-0.0880000\pi\) | ||||
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.53027 | + | 0.787121i | −2.53027 | + | 0.787121i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.561240 | − | 1.88745i | 0.561240 | − | 1.88745i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
0.448383 | − | 0.893841i | \(-0.352000\pi\) | |||||||
\(492\) | 1.78518 | + | 2.15791i | 1.78518 | + | 2.15791i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.94156 | − | 1.06738i | 1.94156 | − | 1.06738i | ||||
\(499\) | 0.0367093 | − | 0.222708i | 0.0367093 | − | 0.222708i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.910106 | + | 0.414376i | −0.910106 | + | 0.414376i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.662906 | + | 1.40875i | 0.662906 | + | 1.40875i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.984564 | − | 0.175023i | \(-0.944000\pi\) | ||||
0.984564 | + | 0.175023i | \(0.0560000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(513\) | −0.239873 | + | 0.806693i | −0.239873 | + | 0.806693i | ||||
\(514\) | 0.189720 | + | 0.537541i | 0.189720 | + | 0.537541i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.03870 | − | 0.154006i | 2.03870 | − | 0.154006i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.17172 | + | 0.238815i | −1.17172 | + | 0.238815i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.662278 | + | 1.87646i | −0.662278 | + | 1.87646i | −0.236499 | + | 0.971632i | \(0.576000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(524\) | 0.0747860 | − | 1.98282i | 0.0747860 | − | 1.98282i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.48752 | + | 1.53513i | −2.48752 | + | 1.53513i | ||||
\(529\) | −0.470704 | + | 0.882291i | −0.470704 | + | 0.882291i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.92436 | + | 1.18758i | 1.92436 | + | 1.18758i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.365436 | − | 1.12470i | 0.365436 | − | 1.12470i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.19958 | − | 0.620739i | 1.19958 | − | 0.620739i | ||||
\(537\) | 0.485631 | + | 1.79733i | 0.485631 | + | 1.79733i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.12255 | + | 1.50492i | −1.12255 | + | 1.50492i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.137790 | − | 0.990461i | \(-0.544000\pi\) | ||||
0.137790 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.142146 | − | 1.61178i | 0.142146 | − | 1.61178i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.0254731 | + | 0.224271i | 0.0254731 | + | 0.224271i | 1.00000 | \(0\) | ||
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(548\) | −0.507200 | − | 0.500866i | −0.507200 | − | 0.500866i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.40048 | − | 1.25042i | −1.40048 | − | 1.25042i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0769271 | + | 0.316047i | −0.0769271 | + | 0.316047i | ||||
\(557\) | 0 | 0 | 0.988652 | − | 0.150226i | \(-0.0480000\pi\) | ||||
−0.988652 | + | 0.150226i | \(0.952000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.60916 | − | 1.06072i | −4.60916 | − | 1.06072i | ||||
\(562\) | −0.987118 | + | 0.974791i | −0.987118 | + | 0.974791i | ||||
\(563\) | −1.13495 | − | 0.915135i | −1.13495 | − | 0.915135i | −0.137790 | − | 0.990461i | \(-0.544000\pi\) |
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.0725322 | − | 1.15287i | 0.0725322 | − | 1.15287i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.548393 | + | 0.155593i | 0.548393 | + | 0.155593i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.0700869 | − | 0.0277494i | 0.0700869 | − | 0.0277494i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.540811 | + | 1.31732i | −0.540811 | + | 1.31732i | ||||
\(577\) | 0.647036 | + | 0.743281i | 0.647036 | + | 0.743281i | 0.979855 | − | 0.199710i | \(-0.0640000\pi\) |
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(578\) | 1.23366 | − | 1.04696i | 1.23366 | − | 1.04696i | ||||
\(579\) | −1.14981 | + | 2.29213i | −1.14981 | + | 2.29213i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.45414 | − | 0.183701i | −1.45414 | − | 0.183701i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.53140 | + | 1.05487i | −1.53140 | + | 1.05487i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.292246 | − | 0.371913i | −0.292246 | − | 0.371913i | 0.617860 | − | 0.786288i | \(-0.288000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(588\) | −0.0195644 | + | 1.55680i | −0.0195644 | + | 1.55680i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.66185 | − | 0.209940i | 1.66185 | − | 0.209940i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(594\) | 1.07077 | + | 0.624204i | 1.07077 | + | 0.624204i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.212007 | − | 0.977268i | \(-0.432000\pi\) | ||||
−0.212007 | + | 0.977268i | \(0.568000\pi\) | |||||||
\(600\) | −1.54906 | − | 0.156256i | −1.54906 | − | 0.156256i | ||||
\(601\) | 0.0725322 | − | 0.102517i | 0.0725322 | − | 0.102517i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.58396 | − | 1.09107i | −1.58396 | − | 1.09107i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) | ||||
−0.994951 | + | 0.100362i | \(0.968000\pi\) | |||||||
\(608\) | −0.143875 | + | 1.26670i | −0.143875 | + | 1.26670i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.12031 | + | 0.901765i | −2.12031 | + | 0.901765i | ||||
\(613\) | 0 | 0 | −0.693653 | − | 0.720309i | \(-0.744000\pi\) | ||||
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(614\) | −1.28970 | + | 1.40845i | −1.28970 | + | 1.40845i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.11340 | − | 1.66067i | 1.11340 | − | 1.66067i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.577573 | − | 0.816339i | \(-0.304000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.83988 | − | 0.0462510i | −1.83988 | − | 0.0462510i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(626\) | −0.803523 | + | 1.82528i | −0.803523 | + | 1.82528i | ||||
\(627\) | 3.60940 | + | 0.926737i | 3.60940 | + | 0.926737i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.910106 | − | 0.414376i | \(-0.864000\pi\) | ||||
0.910106 | + | 0.414376i | \(0.136000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.59734 | + | 2.66262i | −1.59734 | + | 2.66262i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.575085 | − | 0.628036i | 0.575085 | − | 0.628036i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(642\) | 1.80900 | + | 1.87852i | 1.80900 | + | 1.87852i | ||||
\(643\) | −1.37288 | + | 0.583883i | −1.37288 | + | 0.583883i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.60577 | + | 1.29477i | −1.60577 | + | 1.29477i | ||||
\(647\) | 0 | 0 | 0.112856 | − | 0.993611i | \(-0.464000\pi\) | ||||
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(648\) | −0.394197 | + | 0.0397631i | −0.394197 | + | 0.0397631i | ||||
\(649\) | 1.46901 | − | 2.59435i | 1.46901 | − | 2.59435i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.40164 | + | 0.965485i | 1.40164 | + | 0.965485i | ||||
\(653\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.381361 | − | 1.75792i | 0.381361 | − | 1.75792i | ||||
\(657\) | 2.35181 | + | 1.21698i | 2.35181 | + | 1.21698i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.44644 | − | 1.35830i | −1.44644 | − | 1.35830i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.863923 | − | 0.503623i | \(-0.832000\pi\) | ||||
0.863923 | + | 0.503623i | \(0.168000\pi\) | |||||||
\(662\) | −1.63408 | + | 0.206432i | −1.63408 | + | 0.206432i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.30956 | − | 0.556953i | −1.30956 | − | 0.556953i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.51286 | − | 0.191119i | −1.51286 | − | 0.191119i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(674\) | 0.455037 | + | 1.86947i | 0.455037 | + | 1.86947i | ||||
\(675\) | 0.250714 | + | 0.610697i | 0.250714 | + | 0.610697i | ||||
\(676\) | 0.448383 | − | 0.893841i | 0.448383 | − | 0.893841i | ||||
\(677\) | 0 | 0 | 0.762443 | − | 0.647056i | \(-0.224000\pi\) | ||||
−0.762443 | + | 0.647056i | \(0.776000\pi\) | |||||||
\(678\) | 0.179613 | + | 0.206330i | 0.179613 | + | 0.206330i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.06585 | − | 0.940590i | 2.06585 | − | 0.940590i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.608873 | + | 1.07530i | 0.608873 | + | 1.07530i | 0.988652 | + | 0.150226i | \(0.0480000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(684\) | 1.68792 | − | 0.668294i | 1.68792 | − | 0.668294i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.886828 | − | 0.968481i | −0.886828 | − | 0.968481i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.170270 | + | 0.216686i | −0.170270 | + | 0.216686i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.648683 | + | 0.149283i | 0.648683 | + | 0.149283i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.43766 | − | 1.59030i | 2.43766 | − | 1.59030i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.677679 | − | 2.78417i | 0.677679 | − | 2.78417i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.693653 | − | 0.720309i | \(-0.256000\pi\) | ||||
−0.693653 | + | 0.720309i | \(0.744000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.76244 | + | 0.647056i | 1.76244 | + | 0.647056i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.939097 | + | 1.47978i | 0.939097 | + | 1.47978i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.279022 | − | 2.45657i | −0.279022 | − | 2.45657i | ||||
\(709\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.713023 | + | 0.261776i | −0.713023 | + | 0.261776i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.714981 | − | 0.958522i | 0.714981 | − | 0.958522i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.888136 | − | 0.459580i | \(-0.152000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.496432 | − | 0.380101i | 0.496432 | − | 0.380101i | ||||
\(723\) | 1.55374 | − | 0.905753i | 1.55374 | − | 0.905753i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.85036 | − | 3.46834i | 1.85036 | − | 3.46834i | ||||
\(727\) | 0 | 0 | 0.850994 | − | 0.525175i | \(-0.176000\pi\) | ||||
−0.850994 | + | 0.525175i | \(0.824000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.886550 | + | 1.32232i | 0.886550 | + | 1.32232i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.0800824 | − | 2.12325i | 0.0800824 | − | 2.12325i | ||||
\(732\) | 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 | ||||||||
\(737\) | −1.35877 | + | 2.14107i | −1.35877 | + | 2.14107i | ||||
\(738\) | −2.46426 | + | 0.699175i | −2.46426 | + | 0.699175i | ||||
\(739\) | −1.23221 | + | 0.0930828i | −1.23221 | + | 0.0930828i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.178028 | + | 2.01864i | 0.178028 | + | 2.01864i | ||||
\(748\) | 1.29344 | + | 2.74869i | 1.29344 | + | 2.74869i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.0195644 | − | 1.55680i | −0.0195644 | − | 1.55680i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(758\) | −0.419586 | − | 0.891666i | −0.419586 | − | 0.891666i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.03737 | + | 0.974159i | −1.03737 | + | 0.974159i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.49780 | − | 0.424966i | 1.49780 | − | 0.424966i | ||||
\(769\) | −0.596778 | + | 0.940371i | −0.596778 | + | 0.940371i | 0.402906 | + | 0.915241i | \(0.368000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.884986 | − | 0.0668531i | −0.884986 | − | 0.0668531i | ||||
\(772\) | 1.61389 | − | 0.328935i | 1.61389 | − | 0.328935i | ||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | −0.622364 | + | 1.76337i | −0.622364 | + | 1.76337i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.484297 | + | 0.807282i | 0.484297 | + | 0.807282i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.95151 | + | 1.20434i | −1.95151 | + | 1.20434i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.793990 | − | 0.607930i | 0.793990 | − | 0.607930i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.77853 | + | 1.35038i | 2.77853 | + | 1.35038i | ||||
\(787\) | 1.73103 | − | 0.895746i | 1.73103 | − | 0.895746i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.368388 | − | 2.64804i | −0.368388 | − | 2.64804i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(801\) | 0.806826 | + | 0.720373i | 0.806826 | + | 0.720373i | ||||
\(802\) | −1.62199 | − | 0.595490i | −1.62199 | − | 0.595490i | ||||
\(803\) | 1.48650 | − | 3.15898i | 1.48650 | − | 3.15898i | ||||
\(804\) | 0.132041 | + | 2.09873i | 0.132041 | + | 2.09873i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.932798 | − | 0.608547i | 0.932798 | − | 0.608547i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.62517 | + | 0.505561i | 1.62517 | + | 0.505561i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.20755 | + | 1.21361i | 2.20755 | + | 1.21361i | ||||
\(817\) | −0.105117 | + | 1.67079i | −0.105117 | + | 1.67079i | ||||
\(818\) | −1.33534 | − | 1.45829i | −1.33534 | − | 1.45829i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.745941 | − | 0.666012i | \(-0.232000\pi\) | ||||
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(822\) | 1.03188 | − | 0.408549i | 1.03188 | − | 0.408549i | ||||
\(823\) | 0 | 0 | −0.492727 | − | 0.870184i | \(-0.664000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.66031 | − | 1.21125i | 2.66031 | − | 1.21125i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.306031 | + | 0.745439i | −0.306031 | + | 0.745439i | 0.693653 | + | 0.720309i | \(0.256000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.762443 | − | 0.647056i | \(-0.224000\pi\) | ||||
−0.762443 | + | 0.647056i | \(0.776000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.60528 | + | 0.202793i | 1.60528 | + | 0.202793i | ||||
\(834\) | −0.402099 | − | 0.307873i | −0.402099 | − | 0.307873i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.964351 | − | 2.19062i | −0.964351 | − | 2.19062i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.22170 | + | 1.55473i | 1.22170 | + | 1.55473i | ||||
\(839\) | 0 | 0 | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) | ||||
−0.0125660 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.448383 | + | 0.893841i | 0.448383 | + | 0.893841i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.769825 | − | 2.01809i | −0.769825 | − | 2.01809i | ||||
\(844\) | 1.97859 | − | 0.249954i | 1.97859 | − | 0.249954i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.59729 | + | 0.826543i | 1.59729 | + | 0.826543i | ||||
\(850\) | −0.343035 | + | 1.58125i | −0.343035 | + | 1.58125i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.230806 | − | 1.65908i | 0.230806 | − | 1.65908i | ||||
\(857\) | 0.838616 | − | 1.48104i | 0.838616 | − | 1.48104i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0533808 | + | 0.469976i | −0.0533808 | + | 0.469976i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.920232 | − | 0.391374i | \(-0.128000\pi\) | ||||
−0.920232 | + | 0.391374i | \(0.872000\pi\) | |||||||
\(864\) | −0.457921 | − | 0.475518i | −0.457921 | − | 0.475518i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.303189 | − | 0.220280i | 0.303189 | − | 0.220280i | ||||
\(867\) | 0.718008 | + | 2.41467i | 0.718008 | + | 2.41467i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.689646 | − | 1.14958i | 0.689646 | − | 1.14958i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.542503 | − | 2.84390i | −0.542503 | − | 2.84390i | ||||
\(877\) | 0 | 0 | 0.402906 | − | 0.915241i | \(-0.368000\pi\) | ||||
−0.402906 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.231551 | − | 1.21383i | −0.231551 | − | 1.21383i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
0.656586 | − | 0.754251i | \(-0.272000\pi\) | |||||||
\(882\) | −1.29600 | − | 0.590077i | −1.29600 | − | 0.590077i | ||||
\(883\) | 1.55743 | + | 1.01605i | 1.55743 | + | 1.01605i | 0.979855 | + | 0.199710i | \(0.0640000\pi\) |
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.617839 | + | 0.0155313i | −0.617839 | + | 0.0155313i | ||||
\(887\) | 0 | 0 | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) | ||||
0.999684 | + | 0.0251301i | \(0.00800000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.601786 | − | 0.437223i | 0.601786 | − | 0.437223i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.200464 | + | 1.76492i | −0.200464 | + | 1.76492i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.701651 | − | 1.23915i | 0.701651 | − | 1.23915i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 1.04361 | + | 3.21192i | 1.04361 | + | 3.21192i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.0329233 | − | 0.172590i | 0.0329233 | − | 0.172590i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.316290 | + | 1.45797i | −0.316290 | + | 1.45797i | 0.492727 | + | 0.870184i | \(0.336000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(908\) | −1.29485 | − | 0.670039i | −1.29485 | − | 0.670039i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.470704 | − | 0.882291i | \(-0.656000\pi\) | ||||
0.470704 | + | 0.882291i | \(0.344000\pi\) | |||||||
\(912\) | −1.71475 | − | 0.999613i | −1.71475 | − | 0.999613i | ||||
\(913\) | 2.65070 | − | 0.334862i | 2.65070 | − | 0.334862i | ||||
\(914\) | 0.690429 | + | 1.80995i | 0.690429 | + | 1.80995i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0134225 | − | 1.06807i | 0.0134225 | − | 1.06807i | ||||
\(919\) | 0 | 0 | −0.617860 | − | 0.786288i | \(-0.712000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.19796 | − | 2.72129i | −1.19796 | − | 2.72129i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.25390 | + | 1.44042i | 1.25390 | + | 1.44042i | 0.850994 | + | 0.525175i | \(0.176000\pi\) |
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.26038 | − | 0.191515i | −1.26038 | − | 0.191515i | ||||
\(932\) | −1.67502 | + | 0.762643i | −1.67502 | + | 0.762643i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.397046 | + | 0.701205i | 0.397046 | + | 0.701205i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.18880 | − | 0.337292i | −1.18880 | − | 0.337292i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.09691 | − | 2.28998i | −2.09691 | − | 2.28998i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.12990 | + | 1.11579i | −1.12990 | + | 1.11579i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.35416 | + | 0.732337i | 2.35416 | + | 0.732337i | ||||
\(947\) | −0.0403908 | − | 1.07089i | −0.0403908 | − | 1.07089i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.823533 | − | 0.567269i | \(-0.192000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.301500 | − | 1.23868i | 0.301500 | − | 1.23868i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.115564 | + | 1.83683i | 0.115564 | + | 1.83683i | 0.448383 | + | 0.893841i | \(0.352000\pi\) |
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.260842 | − | 0.965382i | 0.260842 | − | 0.965382i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.23917 | + | 0.822078i | −2.23917 | + | 0.822078i | ||||
\(964\) | −1.07403 | − | 0.425237i | −1.07403 | − | 0.425237i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(968\) | −2.48591 | + | 0.441913i | −2.48591 | + | 0.441913i | ||||
\(969\) | −0.837703 | − | 3.10036i | −0.837703 | − | 3.10036i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.112948 | + | 0.0548935i | 0.112948 | + | 0.0548935i | 0.492727 | − | 0.870184i | \(-0.336000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(972\) | 0.394617 | − | 1.21451i | 0.394617 | − | 1.21451i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.153108 | + | 0.286987i | −0.153108 | + | 0.286987i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(978\) | −2.25502 | + | 1.39164i | −2.25502 | + | 1.39164i | ||||
\(979\) | 0.908996 | − | 1.09879i | 0.908996 | − | 1.09879i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.0742168 | − | 1.96773i | 0.0742168 | − | 1.96773i | ||||
\(983\) | 0 | 0 | 0.332820 | − | 0.942991i | \(-0.392000\pi\) | ||||
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(984\) | 2.26574 | + | 1.64616i | 2.26574 | + | 1.64616i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.730891 | − | 2.45799i | 0.730891 | − | 2.45799i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.61511 | − | 1.51669i | 1.61511 | − | 1.51669i | ||||
\(997\) | 0 | 0 | −0.984564 | − | 0.175023i | \(-0.944000\pi\) | ||||
0.984564 | + | 0.175023i | \(0.0560000\pi\) | |||||||
\(998\) | −0.0198291 | − | 0.224840i | −0.0198291 | − | 0.224840i | ||||
\(999\) | 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.403.1 | ✓ | 100 | |
8.3 | odd | 2 | CM | 2008.1.bd.a.403.1 | ✓ | 100 | |
251.180 | even | 125 | inner | 2008.1.bd.a.1435.1 | yes | 100 | |
2008.1435 | odd | 250 | inner | 2008.1.bd.a.1435.1 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.bd.a.403.1 | ✓ | 100 | 1.1 | even | 1 | trivial | |
2008.1.bd.a.403.1 | ✓ | 100 | 8.3 | odd | 2 | CM | |
2008.1.bd.a.1435.1 | yes | 100 | 251.180 | even | 125 | inner | |
2008.1.bd.a.1435.1 | yes | 100 | 2008.1435 | odd | 250 | inner |