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 | 227.1 | ||
Root | \(-0.979855 - 0.199710i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.227 |
Dual form | 2008.1.bd.a.115.1 |
$q$-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 \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{48}{125}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(3\) | −1.27992 | − | 0.622047i | −1.27992 | − | 0.622047i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(4\) | 0.0627905 | + | 0.998027i | 0.0627905 | + | 0.998027i | ||||
\(5\) | 0 | 0 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(6\) | −0.507200 | − | 1.32962i | −0.507200 | − | 1.32962i | ||||
\(7\) | 0 | 0 | −0.745941 | − | 0.666012i | \(-0.768000\pi\) | ||||
0.745941 | + | 0.666012i | \(0.232000\pi\) | |||||||
\(8\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(9\) | 0.633388 | + | 0.806049i | 0.633388 | + | 0.806049i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.225071 | − | 0.0170022i | −0.225071 | − | 0.0170022i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(12\) | 0.540453 | − | 1.31645i | 0.540453 | − | 1.31645i | ||||
\(13\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(17\) | 0.161209 | + | 0.596639i | 0.161209 | + | 0.596639i | 0.998737 | + | 0.0502443i | \(0.0160000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(18\) | −0.0900591 | + | 1.02117i | −0.0900591 | + | 1.02117i | ||||
\(19\) | −0.499529 | + | 1.67992i | −0.499529 | + | 1.67992i | 0.212007 | + | 0.977268i | \(0.432000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.152431 | − | 0.166466i | −0.152431 | − | 0.166466i | ||||
\(23\) | 0 | 0 | −0.778462 | − | 0.627691i | \(-0.784000\pi\) | ||||
0.778462 | + | 0.627691i | \(0.216000\pi\) | |||||||
\(24\) | 1.29515 | − | 0.589686i | 1.29515 | − | 0.589686i | ||||
\(25\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.00758238 | − | 0.0349517i | −0.00758238 | − | 0.0349517i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.920232 | − | 0.391374i | \(-0.128000\pi\) | ||||
−0.920232 | + | 0.391374i | \(0.872000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.236499 | − | 0.971632i | \(-0.576000\pi\) | ||||
0.236499 | + | 0.971632i | \(0.424000\pi\) | |||||||
\(32\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(33\) | 0.277497 | + | 0.161766i | 0.277497 | + | 0.161766i | ||||
\(34\) | −0.290911 | + | 0.545286i | −0.290911 | + | 0.545286i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.764688 | + | 0.682750i | −0.764688 | + | 0.682750i | ||||
\(37\) | 0 | 0 | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) | ||||
0.0376902 | + | 0.999289i | \(0.488000\pi\) | |||||||
\(38\) | −1.51412 | + | 0.882657i | −1.51412 | + | 0.882657i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.194999 | + | 1.71681i | −0.194999 | + | 1.71681i | 0.402906 | + | 0.915241i | \(0.368000\pi\) |
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.77403 | + | 0.917999i | −1.77403 | + | 0.917999i | −0.863923 | + | 0.503623i | \(0.832000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(44\) | 0.00283632 | − | 0.225695i | 0.00283632 | − | 0.225695i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(48\) | 1.34779 | + | 0.456726i | 1.34779 | + | 0.456726i | ||||
\(49\) | 0.112856 | + | 0.993611i | 0.112856 | + | 0.993611i | ||||
\(50\) | 0.968583 | + | 0.248690i | 0.968583 | + | 0.248690i | ||||
\(51\) | 0.164803 | − | 0.863928i | 0.164803 | − | 0.863928i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.162637 | − | 0.986686i | \(-0.448000\pi\) | ||||
−0.162637 | + | 0.986686i | \(0.552000\pi\) | |||||||
\(54\) | 0.0183988 | − | 0.0306692i | 0.0183988 | − | 0.0306692i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.68434 | − | 1.83943i | 1.68434 | − | 1.83943i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.123378 | + | 0.456624i | −0.123378 | + | 0.456624i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.711536 | − | 0.702650i | \(-0.248000\pi\) | ||||
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.0915497 | + | 0.307882i | 0.0915497 | + | 0.307882i | ||||
\(67\) | 1.61389 | − | 0.328935i | 1.61389 | − | 0.328935i | 0.693653 | − | 0.720309i | \(-0.256000\pi\) |
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(68\) | −0.585339 | + | 0.198354i | −0.585339 | + | 0.198354i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.556876 | − | 0.830596i | \(-0.312000\pi\) | ||||
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(72\) | −1.02481 | − | 0.0257617i | −1.02481 | − | 0.0257617i | ||||
\(73\) | 0.838414 | + | 0.149042i | 0.838414 | + | 0.149042i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.42127 | + | 0.0715012i | −1.42127 | + | 0.0715012i | ||||
\(76\) | −1.70797 | − | 0.393060i | −1.70797 | − | 0.393060i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.514440 | − | 0.857527i | \(-0.672000\pi\) | ||||
0.514440 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.230406 | − | 0.946599i | 0.230406 | − | 0.946599i | ||||
\(82\) | −1.31738 | + | 1.11801i | −1.31738 | + | 1.11801i | ||||
\(83\) | −0.263142 | − | 0.0818589i | −0.263142 | − | 0.0818589i | 0.162637 | − | 0.986686i | \(-0.448000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.92163 | − | 0.545214i | −1.92163 | − | 0.545214i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.156566 | − | 0.162583i | 0.156566 | − | 0.162583i | ||||
\(89\) | −1.09982 | + | 0.717509i | −1.09982 | + | 0.717509i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.669845 | + | 1.25556i | 0.669845 | + | 1.25556i | ||||
\(97\) | 0.00532818 | + | 0.423981i | 0.00532818 | + | 0.423981i | 0.979855 | + | 0.199710i | \(0.0640000\pi\) |
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(98\) | −0.597905 | + | 0.801567i | −0.597905 | + | 0.801567i | ||||
\(99\) | −0.128853 | − | 0.192188i | −0.128853 | − | 0.192188i | ||||
\(100\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(101\) | 0 | 0 | −0.762443 | − | 0.647056i | \(-0.776000\pi\) | ||||
0.762443 | + | 0.647056i | \(0.224000\pi\) | |||||||
\(102\) | 0.711536 | − | 0.516961i | 0.711536 | − | 0.516961i | ||||
\(103\) | 0 | 0 | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) | ||||
−0.994951 | + | 0.100362i | \(0.968000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.40692 | − | 1.38935i | −1.40692 | − | 1.38935i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.597905 | − | 0.801567i | \(-0.704000\pi\) | |||||||
\(108\) | 0.0344067 | − | 0.00976206i | 0.0344067 | − | 0.00976206i | ||||
\(109\) | 0 | 0 | 0.974527 | − | 0.224271i | \(-0.0720000\pi\) | ||||
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.220275 | − | 0.677936i | 0.220275 | − | 0.677936i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | |||||||
\(114\) | 2.48701 | − | 0.187872i | 2.48701 | − | 0.187872i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.402519 | + | 0.248407i | −0.402519 | + | 0.248407i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.938284 | − | 0.142572i | −0.938284 | − | 0.142572i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.31752 | − | 2.07608i | 1.31752 | − | 2.07608i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(128\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(129\) | 2.84165 | − | 0.0714335i | 2.84165 | − | 0.0714335i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.44759 | − | 1.16723i | 1.44759 | − | 1.16723i | 0.492727 | − | 0.870184i | \(-0.336000\pi\) |
0.954865 | − | 0.297042i | \(-0.0960000\pi\) | |||||||
\(132\) | −0.144023 | + | 0.287107i | −0.144023 | + | 0.287107i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.40164 | + | 0.864997i | 1.40164 | + | 0.864997i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.562476 | − | 0.256098i | −0.562476 | − | 0.256098i | ||||
\(137\) | −0.324350 | + | 0.0245019i | −0.324350 | + | 0.0245019i | −0.236499 | − | 0.971632i | \(-0.576000\pi\) |
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.48138 | + | 1.02041i | 1.48138 | + | 1.02041i | 0.988652 | + | 0.150226i | \(0.0480000\pi\) |
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.729418 | − | 0.720309i | −0.729418 | − | 0.720309i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.509151 | + | 0.682581i | 0.509151 | + | 0.682581i | ||||
\(147\) | 0.473626 | − | 1.34194i | 0.473626 | − | 1.34194i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(150\) | −1.08501 | − | 0.920807i | −1.08501 | − | 0.920807i | ||||
\(151\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(152\) | −0.975988 | − | 1.45571i | −0.975988 | − | 1.45571i | ||||
\(153\) | −0.378813 | + | 0.507846i | −0.378813 | + | 0.507846i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.815950 | − | 0.532317i | 0.815950 | − | 0.532317i | ||||
\(163\) | 1.27664 | − | 1.32570i | 1.27664 | − | 1.32570i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
0.920232 | − | 0.391374i | \(-0.128000\pi\) | |||||||
\(164\) | −1.72566 | − | 0.0868145i | −1.72566 | − | 0.0868145i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.135786 | − | 0.239806i | −0.135786 | − | 0.239806i | ||||
\(167\) | 0 | 0 | 0.899405 | − | 0.437116i | \(-0.144000\pi\) | ||||
−0.899405 | + | 0.437116i | \(0.856000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.762443 | − | 0.647056i | 0.762443 | − | 0.647056i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.67049 | + | 0.661395i | −1.67049 | + | 0.661395i | ||||
\(172\) | −1.02758 | − | 1.71289i | −1.02758 | − | 1.71289i | ||||
\(173\) | 0 | 0 | −0.656586 | − | 0.754251i | \(-0.728000\pi\) | ||||
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.225428 | − | 0.0113408i | 0.225428 | − | 0.0113408i | ||||
\(177\) | 0.441954 | − | 0.507694i | 0.441954 | − | 0.507694i | ||||
\(178\) | −1.29290 | − | 0.229835i | −1.29290 | − | 0.229835i | ||||
\(179\) | 0.0753566 | + | 0.00189432i | 0.0753566 | + | 0.00189432i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.332820 | − | 0.942991i | \(-0.608000\pi\) | ||||
0.332820 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0261393 | − | 0.137027i | −0.0261393 | − | 0.137027i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.137790 | − | 0.990461i | \(-0.456000\pi\) | ||||
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(192\) | −0.371196 | + | 1.37381i | −0.371196 | + | 1.37381i | ||||
\(193\) | 1.43146 | + | 0.525541i | 1.43146 | + | 0.525541i | 0.938734 | − | 0.344643i | \(-0.112000\pi\) |
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(194\) | −0.286351 | + | 0.312716i | −0.286351 | + | 0.312716i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.984564 | + | 0.175023i | −0.984564 | + | 0.175023i | ||||
\(197\) | 0 | 0 | 0.514440 | − | 0.857527i | \(-0.328000\pi\) | ||||
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(198\) | 0.0376319 | − | 0.228305i | 0.0376319 | − | 0.228305i | ||||
\(199\) | 0 | 0 | −0.402906 | − | 0.915241i | \(-0.632000\pi\) | ||||
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(200\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(201\) | −2.27025 | − | 0.582902i | −2.27025 | − | 0.582902i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.872571 | + | 0.110231i | 0.872571 | + | 0.110231i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.140992 | − | 0.369609i | 0.140992 | − | 0.369609i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0748104 | − | 0.158980i | 0.0748104 | − | 0.158980i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.0745249 | − | 1.97590i | −0.0745249 | − | 1.97590i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.0317640 | + | 0.0164368i | 0.0317640 | + | 0.0164368i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.980390 | − | 0.712295i | −0.980390 | − | 0.712295i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.617860 | − | 0.786288i | \(-0.288000\pi\) | ||||
−0.617860 | + | 0.786288i | \(0.712000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.943359 | + | 0.401210i | 0.943359 | + | 0.401210i | ||||
\(226\) | 0.624652 | − | 0.343405i | 0.624652 | − | 0.343405i | ||||
\(227\) | 1.16025 | − | 0.528266i | 1.16025 | − | 0.528266i | 0.260842 | − | 0.965382i | \(-0.416000\pi\) |
0.899405 | + | 0.437116i | \(0.144000\pi\) | |||||||
\(228\) | 1.94156 | + | 1.56552i | 1.94156 | + | 1.56552i | ||||
\(229\) | 0 | 0 | −0.675333 | − | 0.737513i | \(-0.736000\pi\) | ||||
0.675333 | + | 0.737513i | \(0.264000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.147156 | − | 1.66858i | 0.147156 | − | 1.66858i | −0.470704 | − | 0.882291i | \(-0.656000\pi\) |
0.617860 | − | 0.786288i | \(-0.288000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.463469 | − | 0.0944624i | −0.463469 | − | 0.0944624i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.379779 | − | 0.925077i | \(-0.376000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.975988 | − | 0.536554i | −0.975988 | − | 0.536554i | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(242\) | −0.586382 | − | 0.746230i | −0.586382 | − | 0.746230i | ||||
\(243\) | −0.906527 | + | 1.09580i | −0.906527 | + | 1.09580i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.38160 | − | 0.611491i | 2.38160 | − | 0.611491i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.285880 | + | 0.268459i | 0.285880 | + | 0.268459i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.745941 | + | 0.666012i | −0.745941 | + | 0.666012i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(257\) | −0.710799 | − | 1.86335i | −0.710799 | − | 1.86335i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.285019 | − | 0.958522i | \(-0.592000\pi\) | |||||||
\(258\) | 2.12037 | + | 1.89317i | 2.12037 | + | 1.89317i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.85427 | + | 0.140074i | 1.85427 | + | 0.140074i | ||||
\(263\) | 0 | 0 | 0.379779 | − | 0.925077i | \(-0.376000\pi\) | ||||
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(264\) | −0.301526 | + | 0.110701i | −0.301526 | + | 0.110701i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.85400 | − | 0.234215i | 1.85400 | − | 0.234215i | ||||
\(268\) | 0.429623 | + | 1.59005i | 0.429623 | + | 1.59005i | ||||
\(269\) | 0 | 0 | 0.0878512 | − | 0.996134i | \(-0.472000\pi\) | ||||
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | −0.234716 | − | 0.571729i | −0.234716 | − | 0.571729i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.253214 | − | 0.204172i | −0.253214 | − | 0.204172i | ||||
\(275\) | −0.205423 | + | 0.0935299i | −0.205423 | + | 0.0935299i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(278\) | 0.381361 | + | 1.75792i | 0.381361 | + | 1.75792i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.465416 | + | 0.657817i | 0.465416 | + | 0.657817i | 0.979855 | − | 0.199710i | \(-0.0640000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.901044 | + | 0.654647i | 0.901044 | + | 0.654647i | 0.938734 | − | 0.344643i | \(-0.112000\pi\) |
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.0386374 | − | 1.02440i | −0.0386374 | − | 1.02440i | ||||
\(289\) | 0.533934 | − | 0.311256i | 0.533934 | − | 0.311256i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.256916 | − | 0.545975i | 0.256916 | − | 0.545975i | ||||
\(292\) | −0.0961038 | + | 0.846118i | −0.0961038 | + | 0.846118i | ||||
\(293\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(294\) | 1.26388 | − | 0.654015i | 1.26388 | − | 0.654015i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.00111232 | + | 0.00799556i | 0.00111232 | + | 0.00799556i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.160603 | − | 1.41398i | −0.160603 | − | 1.41398i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.285040 | − | 1.72928i | 0.285040 | − | 1.72928i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.623787 | + | 0.110889i | −0.623787 | + | 0.110889i | ||||
\(307\) | 1.85616 | − | 0.282044i | 1.85616 | − | 0.282044i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.137790 | − | 0.990461i | \(-0.456000\pi\) | ||||
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.0865734 | + | 0.152893i | −0.0865734 | + | 0.152893i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.285019 | − | 0.958522i | \(-0.592000\pi\) | ||||
0.285019 | + | 0.958522i | \(0.408000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.936502 | + | 2.65343i | 0.936502 | + | 2.65343i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.08283 | − | 0.0272203i | −1.08283 | − | 0.0272203i | ||||
\(324\) | 0.959198 | + | 0.170514i | 0.959198 | + | 0.170514i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.83814 | − | 0.0924728i | 1.83814 | − | 0.0924728i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.19853 | − | 1.24458i | −1.19853 | − | 1.24458i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.41780 | + | 0.561348i | −1.41780 | + | 0.561348i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(332\) | 0.0651745 | − | 0.267763i | 0.0651745 | − | 0.267763i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.88530 | − | 0.534907i | −1.88530 | − | 0.534907i | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) |
−0.888136 | − | 0.459580i | \(-0.848000\pi\) | |||||||
\(338\) | 0.998737 | + | 0.0502443i | 0.998737 | + | 0.0502443i | ||||
\(339\) | −0.703641 | + | 0.730681i | −0.703641 | + | 0.730681i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −1.67049 | − | 0.661395i | −1.67049 | − | 0.661395i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.423479 | − | 1.95207i | 0.423479 | − | 1.95207i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.357527 | + | 0.670152i | 0.357527 | + | 0.670152i | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.172093 | + | 0.146049i | 0.172093 | + | 0.146049i | ||||
\(353\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(354\) | 0.669711 | − | 0.0675545i | 0.669711 | − | 0.0675545i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.785152 | − | 1.05259i | −0.785152 | − | 1.05259i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.0536358 | + | 0.0529660i | 0.0536358 | + | 0.0529660i | ||||
\(359\) | 0 | 0 | 0.962028 | − | 0.272952i | \(-0.0880000\pi\) | ||||
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.73507 | − | 1.13194i | −1.73507 | − | 1.13194i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.11224 | + | 0.766137i | 1.11224 | + | 0.766137i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.448383 | − | 0.893841i | \(-0.648000\pi\) | ||||
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.50734 | + | 0.930227i | −1.50734 | + | 0.930227i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.999684 | − | 0.0251301i | \(-0.00800000\pi\) | ||||
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(374\) | 0.0747469 | − | 0.117782i | 0.0747469 | − | 0.117782i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.356667 | + | 0.562018i | −0.356667 | + | 0.562018i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.448383 | − | 0.893841i | \(-0.352000\pi\) | ||||
−0.448383 | + | 0.893841i | \(0.648000\pi\) | |||||||
\(384\) | −1.21103 | + | 0.747361i | −1.21103 | + | 0.747361i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.683733 | + | 1.36301i | 0.683733 | + | 1.36301i | ||||
\(387\) | −1.86360 | − | 0.848506i | −1.86360 | − | 0.848506i | ||||
\(388\) | −0.422810 | + | 0.0319396i | −0.422810 | + | 0.0319396i | ||||
\(389\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.837528 | − | 0.546394i | −0.837528 | − | 0.546394i | ||||
\(393\) | −2.57887 | + | 0.593482i | −2.57887 | + | 0.593482i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.183718 | − | 0.140666i | 0.183718 | − | 0.140666i | ||||
\(397\) | 0 | 0 | −0.597905 | − | 0.801567i | \(-0.704000\pi\) | ||||
0.597905 | + | 0.801567i | \(0.296000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(401\) | 0.880732 | + | 0.747444i | 0.880732 | + | 0.747444i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(402\) | −1.25592 | − | 1.97901i | −1.25592 | − | 1.97901i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.560619 | + | 0.677671i | 0.560619 | + | 0.677671i | ||||
\(409\) | −0.417469 | + | 1.92437i | −0.417469 | + | 1.92437i | −0.0376902 | + | 0.999289i | \(0.512000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.430383 | + | 0.170401i | 0.430383 | + | 0.170401i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.26130 | − | 2.22753i | −1.26130 | − | 2.22753i | ||||
\(418\) | 0.355793 | − | 0.172917i | 0.355793 | − | 0.172917i | ||||
\(419\) | −1.88025 | − | 0.584913i | −1.88025 | − | 0.584913i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.888136 | − | 0.459580i | \(-0.848000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.236499 | − | 0.971632i | \(-0.424000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(422\) | 0.163364 | − | 0.0646804i | 0.163364 | − | 0.0646804i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.428701 | + | 0.445175i | 0.428701 | + | 0.445175i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.29827 | − | 1.49138i | 1.29827 | − | 1.49138i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.556876 | − | 0.830596i | \(-0.312000\pi\) | ||||
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(432\) | 0.0119032 | + | 0.0337258i | 0.0119032 | + | 0.0337258i | ||||
\(433\) | −0.456288 | − | 0.969661i | −0.456288 | − | 0.969661i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.227074 | − | 1.19036i | −0.227074 | − | 1.19036i | ||||
\(439\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.729418 | + | 0.720309i | −0.729418 | + | 0.720309i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.422050 | + | 1.56202i | −0.422050 | + | 1.56202i | 0.356412 | + | 0.934329i | \(0.384000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.153108 | + | 0.928874i | −0.153108 | + | 0.928874i | 0.793990 | + | 0.607930i | \(0.208000\pi\) |
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(450\) | 0.413032 | + | 0.938243i | 0.413032 | + | 0.938243i | ||||
\(451\) | 0.0730782 | − | 0.383089i | 0.0730782 | − | 0.383089i | ||||
\(452\) | 0.690429 | + | 0.177272i | 0.690429 | + | 0.177272i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.20741 | + | 0.409154i | 1.20741 | + | 0.409154i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.343662 | + | 2.47030i | 0.343662 | + | 2.47030i | ||||
\(457\) | 1.15759 | + | 0.886324i | 1.15759 | + | 0.886324i | 0.994951 | − | 0.100362i | \(-0.0320000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.0196312 | − | 0.0101585i | 0.0196312 | − | 0.0101585i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.112856 | − | 0.993611i | \(-0.464000\pi\) | ||||
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.994951 | − | 0.100362i | \(-0.968000\pi\) | ||||
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.24949 | − | 1.11561i | 1.24949 | − | 1.11561i | ||||
\(467\) | −1.69610 | − | 0.877673i | −1.69610 | − | 0.877673i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
−0.711536 | − | 0.702650i | \(-0.752000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.273191 | − | 0.386127i | −0.273191 | − | 0.386127i | ||||
\(473\) | 0.414891 | − | 0.176453i | 0.414891 | − | 0.176453i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.371566 | + | 1.71277i | 0.371566 | + | 1.71277i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.778462 | − | 0.627691i | \(-0.784000\pi\) | ||||
0.778462 | + | 0.627691i | \(0.216000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.344168 | − | 1.05924i | −0.344168 | − | 1.05924i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0833755 | − | 0.945384i | 0.0833755 | − | 0.945384i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.41096 | + | 0.178245i | −1.41096 | + | 0.178245i | ||||
\(487\) | 0 | 0 | −0.979855 | − | 0.199710i | \(-0.936000\pi\) | ||||
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.45865 | + | 0.902658i | −2.45865 | + | 0.902658i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.48764 | + | 0.112379i | 1.48764 | + | 0.112379i | 0.793990 | − | 0.607930i | \(-0.208000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(492\) | 2.15471 | + | 1.18456i | 2.15471 | + | 1.18456i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.0246246 | + | 0.391397i | 0.0246246 | + | 0.391397i | ||||
\(499\) | 1.42824 | + | 0.694131i | 1.42824 | + | 0.694131i | 0.979855 | − | 0.199710i | \(-0.0640000\pi\) |
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.999684 | − | 0.0251301i | −0.999684 | − | 0.0251301i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.37836 | + | 0.353903i | −1.37836 | + | 0.353903i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.745941 | − | 0.666012i | \(-0.768000\pi\) | ||||
0.745941 | + | 0.666012i | \(0.232000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(513\) | 0.0625037 | + | 0.00472162i | 0.0625037 | + | 0.00472162i | ||||
\(514\) | 0.757400 | − | 1.84490i | 0.757400 | − | 1.84490i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.249721 | + | 2.83156i | 0.249721 | + | 2.83156i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.0214849 | − | 0.0722537i | 0.0214849 | − | 0.0722537i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.454144 | + | 1.10622i | 0.454144 | + | 1.10622i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(524\) | 1.25582 | + | 1.37144i | 1.25582 | + | 1.37144i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.295583 | − | 0.125711i | −0.295583 | − | 0.125711i | ||||
\(529\) | 0.212007 | + | 0.977268i | 0.212007 | + | 0.977268i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.446207 | + | 0.189771i | −0.446207 | + | 0.189771i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 1.51184 | + | 1.09842i | 1.51184 | + | 1.09842i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.775280 | + | 1.45319i | −0.775280 | + | 1.45319i | ||||
\(537\) | −0.0952719 | − | 0.0492999i | −0.0952719 | − | 0.0492999i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.00850716 | − | 0.225552i | −0.00850716 | − | 0.225552i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.994951 | − | 0.100362i | \(-0.968000\pi\) | ||||
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.220275 | − | 0.577447i | 0.220275 | − | 0.577447i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.26084 | + | 0.965382i | 1.26084 | + | 0.965382i | 1.00000 | \(0\) | ||
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(548\) | −0.0448196 | − | 0.322172i | −0.0448196 | − | 0.322172i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.213772 | − | 0.0724411i | −0.213772 | − | 0.0724411i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.925379 | + | 1.54253i | −0.925379 | + | 1.54253i | ||||
\(557\) | 0 | 0 | 0.984564 | − | 0.175023i | \(-0.0560000\pi\) | ||||
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0517812 | + | 0.191644i | −0.0517812 | + | 0.191644i | ||||
\(562\) | −0.111033 | + | 0.798127i | −0.111033 | + | 0.798127i | ||||
\(563\) | 0.907100 | − | 0.895772i | 0.907100 | − | 0.895772i | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) |
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.208696 | + | 1.09402i | 0.208696 | + | 1.09402i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.95414 | + | 0.398285i | −1.95414 | + | 0.398285i | −0.962028 | + | 0.272952i | \(0.912000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.575085 | + | 1.22212i | 0.575085 | + | 1.22212i | 0.954865 | + | 0.297042i | \(0.0960000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.673087 | − | 0.773207i | 0.673087 | − | 0.773207i | ||||
\(577\) | −0.664798 | + | 0.0334446i | −0.664798 | + | 0.0334446i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(578\) | 0.602291 | + | 0.138607i | 0.602291 | + | 0.138607i | ||||
\(579\) | −1.50524 | − | 1.56309i | −1.50524 | − | 1.56309i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.561029 | − | 0.222127i | 0.561029 | − | 0.222127i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.649264 | + | 0.551006i | −0.649264 | + | 0.551006i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.506957 | − | 0.895314i | −0.506957 | − | 0.895314i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
0.492727 | − | 0.870184i | \(-0.336000\pi\) | |||||||
\(588\) | 1.36903 | + | 0.388430i | 1.36903 | + | 0.388430i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.83845 | − | 0.727894i | −1.83845 | − | 0.727894i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
−0.863923 | − | 0.503623i | \(-0.832000\pi\) | |||||||
\(594\) | −0.00466249 | + | 0.00658995i | −0.00466249 | + | 0.00658995i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(600\) | 0.850861 | − | 1.14069i | 0.850861 | − | 1.14069i | ||||
\(601\) | 0.208696 | + | 0.311276i | 0.208696 | + | 0.311276i | 0.920232 | − | 0.391374i | \(-0.128000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.28735 | + | 1.09253i | 1.28735 | + | 1.09253i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.597905 | − | 0.801567i | \(-0.704000\pi\) | ||||
0.597905 | + | 0.801567i | \(0.296000\pi\) | |||||||
\(608\) | 1.39156 | − | 1.06547i | 1.39156 | − | 1.06547i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.530630 | − | 0.346177i | −0.530630 | − | 0.346177i | ||||
\(613\) | 0 | 0 | 0.402906 | − | 0.915241i | \(-0.368000\pi\) | ||||
−0.402906 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(614\) | 1.54616 | + | 1.06503i | 1.54616 | + | 1.06503i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.54899 | − | 0.705263i | −1.54899 | − | 0.705263i | −0.556876 | − | 0.830596i | \(-0.688000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.42546 | − | 0.879697i | −1.42546 | − | 0.879697i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(626\) | −0.167772 | + | 0.0521909i | −0.167772 | + | 0.0521909i | ||||
\(627\) | −0.410372 | + | 0.385365i | −0.410372 | + | 0.385365i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.999684 | − | 0.0251301i | \(-0.00800000\pi\) | ||||
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.194644 | + | 0.156946i | −0.194644 | + | 0.156946i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.59532 | + | 1.09889i | 1.59532 | + | 1.09889i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(642\) | −1.13372 | + | 2.57535i | −1.13372 | + | 2.57535i | ||||
\(643\) | 1.58644 | + | 1.03498i | 1.58644 | + | 1.03498i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.770717 | − | 0.761093i | −0.770717 | − | 0.761093i | ||||
\(647\) | 0 | 0 | 0.793990 | − | 0.607930i | \(-0.208000\pi\) | ||||
−0.793990 | + | 0.607930i | \(0.792000\pi\) | |||||||
\(648\) | 0.582501 | + | 0.780916i | 0.582501 | + | 0.780916i | ||||
\(649\) | 0.0355324 | − | 0.100675i | 0.0355324 | − | 0.100675i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.40325 | + | 1.19088i | 1.40325 | + | 1.19088i | ||||
\(653\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.0217122 | − | 1.72771i | −0.0217122 | − | 1.72771i | ||||
\(657\) | 0.410906 | + | 0.770205i | 0.410906 | + | 0.770205i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.18532 | + | 1.43281i | 1.18532 | + | 1.43281i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.577573 | − | 0.816339i | \(-0.304000\pi\) | ||||
−0.577573 | + | 0.816339i | \(0.696000\pi\) | |||||||
\(662\) | −1.41780 | − | 0.561348i | −1.41780 | − | 0.561348i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.230806 | − | 0.150576i | 0.230806 | − | 0.150576i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.81218 | − | 0.717495i | 1.81218 | − | 0.717495i | 0.823533 | − | 0.567269i | \(-0.192000\pi\) |
0.988652 | − | 0.150226i | \(-0.0480000\pi\) | |||||||
\(674\) | −1.00815 | − | 1.68050i | −1.00815 | − | 1.68050i | ||||
\(675\) | −0.0234826 | − | 0.0269756i | −0.0234826 | − | 0.0269756i | ||||
\(676\) | 0.693653 | + | 0.720309i | 0.693653 | + | 0.720309i | ||||
\(677\) | 0 | 0 | −0.974527 | − | 0.224271i | \(-0.928000\pi\) | ||||
0.974527 | + | 0.224271i | \(0.0720000\pi\) | |||||||
\(678\) | −1.01312 | + | 0.0509678i | −1.01312 | + | 0.0509678i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.81363 | − | 0.0455910i | −1.81363 | − | 0.0455910i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.327979 | − | 0.929274i | −0.327979 | − | 0.929274i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
0.656586 | − | 0.754251i | \(-0.272000\pi\) | |||||||
\(684\) | −0.764981 | − | 1.62567i | −0.764981 | − | 1.62567i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.64498 | − | 1.13310i | 1.64498 | − | 1.13310i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.980479 | − | 1.73158i | 0.980479 | − | 1.73158i | 0.402906 | − | 0.915241i | \(-0.368000\pi\) |
0.577573 | − | 0.816339i | \(-0.304000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.198124 | + | 0.733264i | −0.198124 | + | 0.733264i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.05575 | + | 0.160421i | −1.05575 | + | 0.160421i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.22628 | + | 2.04411i | −1.22628 | + | 2.04411i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.402906 | − | 0.915241i | \(-0.632000\pi\) | ||||
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.0254731 | + | 0.224271i | 0.0254731 | + | 0.224271i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.124591 | − | 0.0157395i | −0.124591 | − | 0.0157395i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.534443 | + | 0.409204i | 0.534443 | + | 0.409204i | ||||
\(709\) | 0 | 0 | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) | ||||
−0.0125660 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.148200 | − | 1.30478i | 0.148200 | − | 1.30478i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.00284110 | + | 0.0753268i | 0.00284110 | + | 0.0753268i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.470704 | − | 0.882291i | \(-0.344000\pi\) | ||||
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.489944 | − | 2.01288i | −0.489944 | − | 2.01288i | ||||
\(723\) | 0.915422 | + | 1.29385i | 0.915422 | + | 1.29385i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.286331 | + | 1.31987i | 0.286331 | + | 1.31987i | ||||
\(727\) | 0 | 0 | −0.920232 | − | 0.391374i | \(-0.872000\pi\) | ||||
0.920232 | + | 0.391374i | \(0.128000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.955262 | − | 0.434936i | 0.955262 | − | 0.434936i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.833703 | − | 0.910465i | −0.833703 | − | 0.910465i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.368832 | + | 0.0465943i | −0.368832 | + | 0.0465943i | ||||
\(738\) | −1.73559 | − | 0.353741i | −1.73559 | − | 0.353741i | ||||
\(739\) | −0.0865734 | − | 0.981645i | −0.0865734 | − | 0.981645i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
0.823533 | − | 0.567269i | \(-0.192000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.876307 | − | 0.481754i | \(-0.840000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.100689 | − | 0.263954i | −0.100689 | − | 0.263954i | ||||
\(748\) | 0.135116 | − | 0.0346918i | 0.135116 | − | 0.0346918i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.728969 | − | 0.684547i | \(-0.760000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.36903 | − | 0.388430i | 1.36903 | − | 0.388430i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(758\) | −0.644727 | + | 0.165538i | −0.644727 | + | 0.165538i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.175662 | − | 0.212338i | 0.175662 | − | 0.212338i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.39440 | − | 0.284202i | −1.39440 | − | 0.284202i | ||||
\(769\) | 1.80586 | − | 0.228133i | 1.80586 | − | 0.228133i | 0.850994 | − | 0.525175i | \(-0.176000\pi\) |
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.249327 | + | 2.82708i | −0.249327 | + | 2.82708i | ||||
\(772\) | −0.434622 | + | 1.46164i | −0.434622 | + | 1.46164i | ||||
\(773\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(774\) | −0.777664 | − | 1.89426i | −0.777664 | − | 1.89426i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.330079 | − | 0.266150i | −0.330079 | − | 0.266150i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.78669 | − | 1.18518i | −2.78669 | − | 1.18518i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.236499 | − | 0.971632i | −0.236499 | − | 0.971632i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.28618 | − | 1.33273i | −2.28618 | − | 1.33273i | ||||
\(787\) | −0.245558 | + | 0.460276i | −0.245558 | + | 0.460276i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.230217 | + | 0.0232222i | 0.230217 | + | 0.0232222i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) | ||||
−0.0125660 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(801\) | −1.27496 | − | 0.432046i | −1.27496 | − | 0.432046i | ||||
\(802\) | 0.130366 | + | 1.14777i | 0.130366 | + | 1.14777i | ||||
\(803\) | −0.186169 | − | 0.0478001i | −0.186169 | − | 0.0478001i | ||||
\(804\) | 0.439201 | − | 2.30237i | 0.439201 | − | 2.30237i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.79956 | + | 0.273442i | −1.79956 | + | 0.273442i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.72771 | + | 0.634303i | 1.72771 | + | 0.634303i | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.0552247 | + | 0.877771i | −0.0552247 | + | 0.877771i | ||||
\(817\) | −0.655984 | − | 3.43879i | −0.655984 | − | 3.43879i | ||||
\(818\) | −1.62164 | + | 1.11703i | −1.62164 | + | 1.11703i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.947098 | − | 0.320944i | \(-0.104000\pi\) | ||||
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(822\) | 0.197088 | + | 0.418834i | 0.197088 | + | 0.418834i | ||||
\(823\) | 0 | 0 | −0.332820 | − | 0.942991i | \(-0.608000\pi\) | ||||
0.332820 | + | 0.942991i | \(0.392000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.321104 | + | 0.00807192i | 0.321104 | + | 0.00807192i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.25390 | − | 1.44042i | 1.25390 | − | 1.44042i | 0.402906 | − | 0.915241i | \(-0.368000\pi\) |
0.850994 | − | 0.525175i | \(-0.176000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.974527 | − | 0.224271i | \(-0.928000\pi\) | ||||
0.974527 | + | 0.224271i | \(0.0720000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.574633 | + | 0.227513i | −0.574633 | + | 0.227513i | ||||
\(834\) | 0.605399 | − | 2.48722i | 0.605399 | − | 2.48722i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.377732 | + | 0.117506i | 0.377732 | + | 0.117506i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.970244 | − | 1.71350i | −0.970244 | − | 1.71350i | ||||
\(839\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.693653 | − | 0.720309i | 0.693653 | − | 0.720309i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.186501 | − | 1.13146i | −0.186501 | − | 1.13146i | ||||
\(844\) | 0.163364 | + | 0.0646804i | 0.163364 | + | 0.0646804i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.746041 | − | 1.39839i | −0.746041 | − | 1.39839i | ||||
\(850\) | 0.00776624 | + | 0.617985i | 0.00776624 | + | 0.617985i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.96732 | − | 0.198446i | 1.96732 | − | 0.198446i | ||||
\(857\) | −0.612542 | + | 1.73554i | −0.612542 | + | 1.73554i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.816920 | + | 0.625487i | −0.816920 | + | 0.625487i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.837528 | − | 0.546394i | \(-0.816000\pi\) | ||||
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(864\) | −0.0144098 | + | 0.0327334i | −0.0144098 | + | 0.0327334i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | ||||
\(867\) | −0.877008 | + | 0.0662504i | −0.877008 | + | 0.0662504i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.338375 | + | 0.272839i | −0.338375 | + | 0.272839i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.649330 | − | 1.02318i | 0.649330 | − | 1.02318i | ||||
\(877\) | 0 | 0 | 0.954865 | − | 0.297042i | \(-0.0960000\pi\) | ||||
−0.954865 | + | 0.297042i | \(0.904000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.528033 | − | 0.832047i | 0.528033 | − | 0.832047i | −0.470704 | − | 0.882291i | \(-0.656000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(882\) | −1.02481 | + | 0.0257617i | −1.02481 | + | 0.0257617i | ||||
\(883\) | −0.841895 | − | 0.127926i | −0.841895 | − | 0.127926i | −0.285019 | − | 0.958522i | \(-0.592000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.37694 | + | 0.849750i | −1.37694 | + | 0.849750i | ||||
\(887\) | 0 | 0 | −0.850994 | − | 0.525175i | \(-0.824000\pi\) | ||||
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.0679521 | + | 0.209135i | −0.0679521 | + | 0.209135i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.747469 | + | 0.572310i | −0.747469 | + | 0.572310i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.341184 | + | 0.966690i | −0.341184 | + | 0.966690i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.315514 | − | 0.229235i | 0.315514 | − | 0.229235i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.381950 | + | 0.601857i | 0.381950 | + | 0.601857i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.0238026 | − | 1.89405i | −0.0238026 | − | 1.89405i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(908\) | 0.600076 | + | 1.12479i | 0.600076 | + | 1.12479i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.212007 | − | 0.977268i | \(-0.432000\pi\) | ||||
−0.212007 | + | 0.977268i | \(0.568000\pi\) | |||||||
\(912\) | −1.44052 | + | 2.03603i | −1.44052 | + | 2.03603i | ||||
\(913\) | 0.0578340 | + | 0.0228981i | 0.0578340 | + | 0.0228981i | ||||
\(914\) | 0.237115 | + | 1.43853i | 0.237115 | + | 1.43853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0212645 | + | 0.00603328i | 0.0212645 | + | 0.00603328i | ||||
\(919\) | 0 | 0 | −0.492727 | − | 0.870184i | \(-0.664000\pi\) | ||||
0.492727 | + | 0.870184i | \(0.336000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.55118 | − | 0.793627i | −2.55118 | − | 0.793627i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.87510 | − | 0.0943321i | 1.87510 | − | 0.0943321i | 0.920232 | − | 0.391374i | \(-0.128000\pi\) |
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.72556 | − | 0.306748i | −1.72556 | − | 0.306748i | ||||
\(932\) | 1.67453 | + | 0.0420943i | 1.67453 | + | 0.0420943i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −0.635595 | − | 1.80086i | −0.635595 | − | 1.80086i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.965603 | − | 0.196805i | 0.965603 | − | 0.196805i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.205914 | − | 0.141838i | 0.205914 | − | 0.141838i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.0651745 | − | 0.468486i | 0.0651745 | − | 0.468486i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.423233 | + | 0.155384i | 0.423233 | + | 0.155384i | ||||
\(947\) | 1.34002 | − | 1.46340i | 1.34002 | − | 1.46340i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
0.762443 | − | 0.647056i | \(-0.224000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −0.901614 | + | 1.50291i | −0.901614 | + | 1.50291i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.313874 | − | 1.64539i | 0.313874 | − | 1.64539i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
0.693653 | − | 0.720309i | \(-0.256000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.888136 | + | 0.459580i | −0.888136 | + | 0.459580i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.228760 | − | 2.01405i | 0.228760 | − | 2.01405i | ||||
\(964\) | 0.474212 | − | 1.00775i | 0.474212 | − | 1.00775i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) | ||||
0.0376902 | + | 0.999289i | \(0.488000\pi\) | |||||||
\(968\) | 0.707938 | − | 0.632081i | 0.707938 | − | 0.632081i | ||||
\(969\) | 1.36900 | + | 0.708412i | 1.36900 | + | 0.708412i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.323766 | + | 0.188739i | 0.323766 | + | 0.188739i | 0.656586 | − | 0.754251i | \(-0.272000\pi\) |
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(972\) | −1.15056 | − | 0.835932i | −1.15056 | − | 0.835932i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.381361 | + | 1.75792i | 0.381361 | + | 1.75792i | 0.617860 | + | 0.786288i | \(0.288000\pi\) |
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(978\) | −2.41019 | − | 1.02505i | −2.41019 | − | 1.02505i | ||||
\(979\) | 0.259737 | − | 0.142792i | 0.259737 | − | 0.142792i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.00752 | + | 1.10028i | 1.00752 | + | 1.10028i | ||||
\(983\) | 0 | 0 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
0.379779 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(984\) | 0.759826 | + | 2.33850i | 0.759826 | + | 2.33850i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.16385 | + | 0.163461i | 2.16385 | + | 0.163461i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.249979 | + | 0.302173i | −0.249979 | + | 0.302173i | ||||
\(997\) | 0 | 0 | −0.745941 | − | 0.666012i | \(-0.768000\pi\) | ||||
0.745941 | + | 0.666012i | \(0.232000\pi\) | |||||||
\(998\) | 0.565975 | + | 1.48370i | 0.565975 | + | 1.48370i | ||||
\(999\) | 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.227.1 | yes | 100 | |
8.3 | odd | 2 | CM | 2008.1.bd.a.227.1 | yes | 100 | |
251.115 | even | 125 | inner | 2008.1.bd.a.115.1 | ✓ | 100 | |
2008.115 | odd | 250 | inner | 2008.1.bd.a.115.1 | ✓ | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.bd.a.115.1 | ✓ | 100 | 251.115 | even | 125 | inner | |
2008.1.bd.a.115.1 | ✓ | 100 | 2008.115 | odd | 250 | inner | |
2008.1.bd.a.227.1 | yes | 100 | 1.1 | even | 1 | trivial | |
2008.1.bd.a.227.1 | yes | 100 | 8.3 | odd | 2 | CM |