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 | 683.1 | ||
Root | \(0.999684 - 0.0251301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2008.683 |
Dual form | 2008.1.bd.a.147.1 |
$q$-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 \(\left(\mathbb{Z}/2008\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(503\) | \(1005\) |
\(\chi(n)\) | \(e\left(\frac{119}{125}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(3\) | 0.702235 | + | 0.626989i | 0.702235 | + | 0.626989i | 0.938734 | − | 0.344643i | \(-0.112000\pi\) |
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(4\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(5\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(6\) | −0.930725 | + | 0.141424i | −0.930725 | + | 0.141424i | ||||
\(7\) | 0 | 0 | −0.954865 | − | 0.297042i | \(-0.904000\pi\) | ||||
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(8\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(9\) | −0.0128376 | − | 0.113025i | −0.0128376 | − | 0.113025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.51568 | − | 0.644618i | 1.51568 | − | 0.644618i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(12\) | 0.484297 | − | 0.807282i | 0.484297 | − | 0.807282i | ||||
\(13\) | 0 | 0 | −0.675333 | − | 0.737513i | \(-0.736000\pi\) | ||||
0.675333 | + | 0.737513i | \(0.264000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(17\) | −0.263152 | − | 1.59649i | −0.263152 | − | 1.59649i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
0.448383 | − | 0.893841i | \(-0.352000\pi\) | |||||||
\(18\) | 0.0952698 | + | 0.0621530i | 0.0952698 | + | 0.0621530i | ||||
\(19\) | 0.106869 | + | 0.0659520i | 0.106869 | + | 0.0659520i | 0.577573 | − | 0.816339i | \(-0.304000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.469445 | + | 1.57875i | −0.469445 | + | 1.57875i | ||||
\(23\) | 0 | 0 | 0.888136 | − | 0.459580i | \(-0.152000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(24\) | 0.313319 | + | 0.887739i | 0.313319 | + | 0.887739i | ||||
\(25\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.605582 | − | 0.855927i | 0.605582 | − | 0.855927i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.998737 | − | 0.0502443i | \(-0.984000\pi\) | ||||
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.974527 | − | 0.224271i | \(-0.928000\pi\) | ||||
0.974527 | + | 0.224271i | \(0.0720000\pi\) | |||||||
\(32\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(33\) | 1.46853 | + | 0.497642i | 1.46853 | + | 0.497642i | ||||
\(34\) | 1.39786 | + | 0.814879i | 1.39786 | + | 0.814879i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.108617 | + | 0.0337888i | −0.108617 | + | 0.0337888i | ||||
\(37\) | 0 | 0 | −0.979855 | − | 0.199710i | \(-0.936000\pi\) | ||||
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(38\) | −0.118938 | + | 0.0403044i | −0.118938 | + | 0.0403044i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.55993 | + | 1.07452i | −1.55993 | + | 1.07452i | −0.597905 | + | 0.801567i | \(0.704000\pi\) |
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.27992 | − | 0.622047i | −1.27992 | − | 0.622047i | −0.332820 | − | 0.942991i | \(-0.608000\pi\) |
−0.947098 | + | 0.320944i | \(0.896000\pi\) | |||||||
\(44\) | −0.917210 | − | 1.36805i | −0.917210 | − | 1.36805i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(48\) | −0.883731 | − | 0.324450i | −0.883731 | − | 0.324450i | ||||
\(49\) | 0.823533 | + | 0.567269i | 0.823533 | + | 0.567269i | ||||
\(50\) | 0.728969 | + | 0.684547i | 0.728969 | + | 0.684547i | ||||
\(51\) | 0.816187 | − | 1.28611i | 0.816187 | − | 1.28611i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.984564 | − | 0.175023i | \(-0.944000\pi\) | ||||
0.984564 | + | 0.175023i | \(0.0560000\pi\) | |||||||
\(54\) | 0.273491 | + | 1.01220i | 0.273491 | + | 1.01220i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0336958 | + | 0.113319i | 0.0336958 | + | 0.113319i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.316989 | + | 1.92310i | −0.316989 | + | 1.92310i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.470704 | − | 0.882291i | \(-0.344000\pi\) | ||||
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.31952 | + | 0.814315i | −1.31952 | + | 0.814315i | ||||
\(67\) | 1.99369 | + | 0.0501174i | 1.99369 | + | 0.0501174i | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) |
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(68\) | −1.51890 | + | 0.557644i | −1.51890 | + | 0.557644i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.492727 | − | 0.870184i | \(-0.336000\pi\) | ||||
−0.492727 | + | 0.870184i | \(0.664000\pi\) | |||||||
\(72\) | 0.0432003 | − | 0.105229i | 0.0432003 | − | 0.105229i | ||||
\(73\) | 0.780497 | + | 1.77297i | 0.780497 | + | 1.77297i | 0.617860 | + | 0.786288i | \(0.288000\pi\) |
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.669845 | − | 0.661480i | 0.669845 | − | 0.661480i | ||||
\(76\) | 0.0447586 | − | 0.117334i | 0.0447586 | − | 0.117334i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.260842 | − | 0.965382i | \(-0.416000\pi\) | ||||
−0.260842 | + | 0.965382i | \(0.584000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.851064 | − | 0.195858i | 0.851064 | − | 0.195858i | ||||
\(82\) | 0.166407 | − | 1.88687i | 0.166407 | − | 1.88687i | ||||
\(83\) | −0.0159812 | − | 0.423713i | −0.0159812 | − | 0.423713i | −0.984564 | − | 0.175023i | \(-0.944000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.29515 | − | 0.589686i | 1.29515 | − | 0.589686i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.63875 | + | 0.165302i | 1.63875 | + | 0.165302i | ||||
\(89\) | −0.698099 | + | 1.39164i | −0.698099 | + | 1.39164i | 0.212007 | + | 0.977268i | \(0.432000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.813304 | − | 0.474115i | 0.813304 | − | 0.474115i | ||||
\(97\) | −0.643272 | + | 0.959459i | −0.643272 | + | 0.959459i | 0.356412 | + | 0.934329i | \(0.384000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(98\) | −0.962028 | + | 0.272952i | −0.962028 | + | 0.272952i | ||||
\(99\) | −0.0923153 | − | 0.163034i | −0.0923153 | − | 0.163034i | ||||
\(100\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(101\) | 0 | 0 | −0.0878512 | − | 0.996134i | \(-0.528000\pi\) | ||||
0.0878512 | + | 0.996134i | \(0.472000\pi\) | |||||||
\(102\) | 0.470704 | + | 1.44868i | 0.470704 | + | 1.44868i | ||||
\(103\) | 0 | 0 | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) | ||||
−0.0125660 | + | 0.999921i | \(0.504000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.653011 | − | 1.22401i | −0.653011 | − | 1.22401i | −0.962028 | − | 0.272952i | \(-0.912000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(108\) | −0.954241 | − | 0.434470i | −0.954241 | − | 0.434470i | ||||
\(109\) | 0 | 0 | −0.356412 | − | 0.934329i | \(-0.616000\pi\) | ||||
0.356412 | + | 0.934329i | \(0.384000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.59967 | + | 1.16223i | −1.59967 | + | 1.16223i | −0.711536 | + | 0.702650i | \(0.752000\pi\) |
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(114\) | −0.108793 | − | 0.0462694i | −0.108793 | − | 0.0462694i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.27972 | − | 1.47008i | −1.27972 | − | 1.47008i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.18811 | − | 1.23376i | 1.18811 | − | 1.23376i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.76915 | − | 0.223496i | −1.76915 | − | 0.223496i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.0376902 | − | 0.999289i | \(-0.488000\pi\) | ||||
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(128\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(129\) | −0.508786 | − | 1.23932i | −0.508786 | − | 1.23932i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.756300 | + | 0.391359i | 0.756300 | + | 0.391359i | 0.793990 | − | 0.607930i | \(-0.208000\pi\) |
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(132\) | 0.213652 | − | 1.53577i | 0.213652 | − | 1.53577i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.30944 | + | 1.50422i | −1.30944 | + | 1.50422i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.538513 | − | 1.52579i | 0.538513 | − | 1.52579i | ||||
\(137\) | −1.81205 | − | 0.770665i | −1.81205 | − | 0.770665i | −0.974527 | − | 0.224271i | \(-0.928000\pi\) |
−0.837528 | − | 0.546394i | \(-0.816000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.48764 | − | 0.112379i | 1.48764 | − | 0.112379i | 0.693653 | − | 0.720309i | \(-0.256000\pi\) |
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.0535432 | + | 0.100362i | 0.0535432 | + | 0.100362i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.86361 | − | 0.528753i | −1.86361 | − | 0.528753i | ||||
\(147\) | 0.222642 | + | 0.914702i | 0.222642 | + | 0.914702i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(150\) | 0.0827038 | + | 0.937768i | 0.0827038 | + | 0.937768i | ||||
\(151\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(152\) | 0.0618772 | + | 0.109279i | 0.0618772 | + | 0.109279i | ||||
\(153\) | −0.177064 | + | 0.0502377i | −0.177064 | + | 0.0502377i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.391577 | + | 0.780600i | −0.391577 | + | 0.780600i | ||||
\(163\) | 1.98739 | + | 0.200470i | 1.98739 | + | 0.200470i | 0.998737 | + | 0.0502443i | \(0.0160000\pi\) |
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(164\) | 1.34779 | + | 1.33096i | 1.34779 | + | 1.33096i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.336663 | + | 0.257771i | 0.336663 | + | 0.257771i | ||||
\(167\) | 0 | 0 | 0.745941 | − | 0.666012i | \(-0.232000\pi\) | ||||
−0.745941 | + | 0.666012i | \(0.768000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0878512 | + | 0.996134i | −0.0878512 | + | 0.996134i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.00608226 | − | 0.0129255i | 0.00608226 | − | 0.0129255i | ||||
\(172\) | −0.371196 | + | 1.37381i | −0.371196 | + | 1.37381i | ||||
\(173\) | 0 | 0 | −0.778462 | − | 0.627691i | \(-0.784000\pi\) | ||||
0.778462 | + | 0.627691i | \(0.216000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.17195 | + | 1.15731i | −1.17195 | + | 1.15731i | ||||
\(177\) | −1.42837 | + | 1.15172i | −1.42837 | + | 1.15172i | ||||
\(178\) | −0.627295 | − | 1.42496i | −0.627295 | − | 1.42496i | ||||
\(179\) | −0.744257 | + | 1.81288i | −0.744257 | + | 1.81288i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.236499 | − | 0.971632i | \(-0.424000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.42798 | − | 2.25014i | −1.42798 | − | 2.25014i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(192\) | −0.153108 | + | 0.928874i | −0.153108 | + | 0.928874i | ||||
\(193\) | 0.118658 | − | 0.129583i | 0.118658 | − | 0.129583i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(194\) | −0.329239 | − | 1.10723i | −0.329239 | − | 1.10723i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.402906 | − | 0.915241i | 0.402906 | − | 0.915241i | ||||
\(197\) | 0 | 0 | −0.260842 | − | 0.965382i | \(-0.584000\pi\) | ||||
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(198\) | 0.184464 | + | 0.0327916i | 0.184464 | + | 0.0327916i | ||||
\(199\) | 0 | 0 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(200\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(201\) | 1.36861 | + | 1.28521i | 1.36861 | + | 1.28521i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.41626 | − | 0.560738i | −1.41626 | − | 0.560738i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.204493 | + | 0.0310727i | 0.204493 | + | 0.0310727i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.62243 | + | 0.416570i | −1.62243 | + | 0.416570i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.35936 | + | 0.277059i | 1.35936 | + | 0.277059i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.943021 | − | 0.458313i | 0.943021 | − | 0.458313i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.563543 | + | 1.73441i | −0.563543 | + | 1.73441i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.112856 | − | 0.993611i | \(-0.464000\pi\) | ||||
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.113608 | + | 0.00571535i | −0.113608 | + | 0.00571535i | ||||
\(226\) | 0.124156 | − | 1.97340i | 0.124156 | − | 1.97340i | ||||
\(227\) | −0.583304 | − | 1.65270i | −0.583304 | − | 1.65270i | −0.745941 | − | 0.666012i | \(-0.768000\pi\) |
0.162637 | − | 0.986686i | \(-0.448000\pi\) | |||||||
\(228\) | 0.104998 | − | 0.0543329i | 0.104998 | − | 0.0543329i | ||||
\(229\) | 0 | 0 | 0.285019 | − | 0.958522i | \(-0.408000\pi\) | ||||
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.751067 | − | 0.489988i | −0.751067 | − | 0.489988i | 0.112856 | − | 0.993611i | \(-0.464000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.94844 | − | 0.0489799i | 1.94844 | − | 0.0489799i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.514440 | − | 0.857527i | \(-0.328000\pi\) | ||||
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0618772 | + | 0.983510i | 0.0618772 | + | 0.983510i | 0.899405 | + | 0.437116i | \(0.144000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(242\) | 0.193303 | + | 1.70188i | 0.193303 | + | 1.70188i | ||||
\(243\) | −0.198355 | − | 0.109047i | −0.198355 | − | 0.109047i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.29991 | − | 1.22069i | 1.29991 | − | 1.22069i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.254441 | − | 0.307566i | 0.254441 | − | 0.307566i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.954865 | − | 0.297042i | 0.954865 | − | 0.297042i | ||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(257\) | 1.81958 | − | 0.276485i | 1.81958 | − | 0.276485i | 0.850994 | − | 0.525175i | \(-0.176000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(258\) | 1.27922 | + | 0.397944i | 1.27922 | + | 0.397944i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.783631 | + | 0.333278i | −0.783631 | + | 0.333278i | ||||
\(263\) | 0 | 0 | 0.514440 | − | 0.857527i | \(-0.328000\pi\) | ||||
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(264\) | 1.04714 | + | 1.14356i | 1.04714 | + | 1.14356i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.36277 | + | 0.539561i | −1.36277 | + | 0.539561i | ||||
\(268\) | −0.324350 | − | 1.96777i | −0.324350 | − | 1.96777i | ||||
\(269\) | 0 | 0 | −0.837528 | − | 0.546394i | \(-0.816000\pi\) | ||||
0.837528 | + | 0.546394i | \(0.184000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(272\) | 0.832381 | + | 1.38751i | 0.832381 | + | 1.38751i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.74885 | − | 0.904972i | 1.74885 | − | 0.904972i | ||||
\(275\) | −0.548175 | − | 1.55317i | −0.548175 | − | 1.55317i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | ||||
−0.998737 | + | 0.0502443i | \(0.984000\pi\) | |||||||
\(278\) | −0.861670 | + | 1.21788i | −0.861670 | + | 1.21788i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.738843 | + | 0.940252i | −0.738843 | + | 0.940252i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.304522 | − | 0.937223i | 0.304522 | − | 0.937223i | −0.675333 | − | 0.737513i | \(-0.736000\pi\) |
0.979855 | − | 0.199710i | \(-0.0640000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.111460 | − | 0.0227173i | −0.111460 | − | 0.0227173i | ||||
\(289\) | −1.53244 | + | 0.519298i | −1.53244 | + | 0.519298i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.05330 | + | 0.270441i | −1.05330 | + | 0.270441i | ||||
\(292\) | 1.59532 | − | 1.09889i | 1.59532 | − | 1.09889i | ||||
\(293\) | 0 | 0 | −0.988652 | − | 0.150226i | \(-0.952000\pi\) | ||||
0.988652 | + | 0.150226i | \(0.0480000\pi\) | |||||||
\(294\) | −0.846707 | − | 0.411504i | −0.846707 | − | 0.411504i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.366123 | − | 1.68768i | 0.366123 | − | 1.68768i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.775280 | − | 0.534031i | −0.775280 | − | 0.534031i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.123643 | − | 0.0219796i | −0.123643 | − | 0.0219796i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.0741563 | − | 0.168453i | 0.0741563 | − | 0.168453i | ||||
\(307\) | −0.936894 | − | 0.972897i | −0.936894 | − | 0.972897i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.212007 | − | 0.977268i | \(-0.568000\pi\) | ||||
0.212007 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.32998 | + | 1.01832i | −1.32998 | + | 1.01832i | −0.332820 | + | 0.942991i | \(0.608000\pi\) |
−0.997159 | + | 0.0753268i | \(0.976000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.850994 | − | 0.525175i | \(-0.176000\pi\) | ||||
−0.850994 | + | 0.525175i | \(0.824000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.308873 | − | 1.26897i | 0.308873 | − | 1.26897i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0771690 | − | 0.187970i | 0.0771690 | − | 0.187970i | ||||
\(324\) | −0.351862 | − | 0.799289i | −0.351862 | − | 0.799289i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.42127 | + | 1.40352i | −1.42127 | + | 1.40352i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.88463 | + | 0.190105i | −1.88463 | + | 0.190105i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.0748104 | − | 0.158980i | 0.0748104 | − | 0.158980i | −0.863923 | − | 0.503623i | \(-0.832000\pi\) |
0.938734 | + | 0.344643i | \(0.112000\pi\) | |||||||
\(332\) | −0.413213 | + | 0.0950940i | −0.413213 | + | 0.0950940i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.81964 | − | 0.828489i | 1.81964 | − | 0.828489i | 0.899405 | − | 0.437116i | \(-0.144000\pi\) |
0.920232 | − | 0.391374i | \(-0.128000\pi\) | |||||||
\(338\) | −0.711536 | − | 0.702650i | −0.711536 | − | 0.702650i | ||||
\(339\) | −1.85205 | − | 0.186818i | −1.85205 | − | 0.186818i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.00608226 | + | 0.0129255i | 0.00608226 | + | 0.0129255i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.821927 | − | 1.16171i | −0.821927 | − | 1.16171i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.888873 | − | 0.518167i | 0.888873 | − | 0.518167i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.962028 | − | 0.272952i | \(-0.0880000\pi\) | ||||
−0.962028 | + | 0.272952i | \(0.912000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.144697 | − | 1.64070i | −0.144697 | − | 1.64070i | ||||
\(353\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(354\) | 0.0230569 | − | 1.83471i | 0.0230569 | − | 1.83471i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.49780 | + | 0.424966i | 1.49780 | + | 0.424966i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.922443 | − | 1.72904i | −0.922443 | − | 1.72904i | ||||
\(359\) | 0 | 0 | −0.910106 | − | 0.414376i | \(-0.864000\pi\) | ||||
0.910106 | + | 0.414376i | \(0.136000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.441312 | − | 0.879745i | −0.441312 | − | 0.879745i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.60788 | − | 0.121462i | 1.60788 | − | 0.121462i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.137790 | − | 0.990461i | \(-0.544000\pi\) | ||||
0.137790 | + | 0.990461i | \(0.456000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.141473 | + | 0.162516i | 0.141473 | + | 0.162516i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
0.379779 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(374\) | 2.64399 | + | 0.334014i | 2.64399 | + | 0.334014i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.469268 | + | 0.0592824i | 0.469268 | + | 0.0592824i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.137790 | − | 0.990461i | \(-0.456000\pi\) | ||||
−0.137790 | + | 0.990461i | \(0.544000\pi\) | |||||||
\(384\) | −0.618115 | − | 0.710058i | −0.618115 | − | 0.710058i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0242101 | + | 0.174026i | 0.0242101 | + | 0.174026i | ||||
\(387\) | −0.0538755 | + | 0.152648i | −0.0538755 | + | 0.152648i | ||||
\(388\) | 1.06300 | + | 0.452093i | 1.06300 | + | 0.452093i | ||||
\(389\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.448383 | + | 0.893841i | 0.448383 | + | 0.893841i | ||||
\(393\) | 0.285723 | + | 0.749018i | 0.285723 | + | 0.749018i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.142848 | + | 0.121230i | −0.142848 | + | 0.121230i | ||||
\(397\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(401\) | −0.108559 | − | 1.23094i | −0.108559 | − | 1.23094i | −0.837528 | − | 0.546394i | \(-0.816000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(402\) | −1.86266 | + | 0.235309i | −1.86266 | + | 0.235309i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 1.33482 | − | 0.733822i | 1.33482 | − | 0.733822i | ||||
\(409\) | 0.465416 | + | 0.657817i | 0.465416 | + | 0.657817i | 0.979855 | − | 0.199710i | \(-0.0640000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.789290 | − | 1.67733i | −0.789290 | − | 1.67733i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.11514 | + | 0.853820i | 1.11514 | + | 0.853820i | ||||
\(418\) | −0.154291 | + | 0.137758i | −0.154291 | + | 0.137758i | ||||
\(419\) | −0.0303712 | − | 0.805240i | −0.0303712 | − | 0.805240i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.899405 | − | 0.437116i | \(-0.144000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.974527 | − | 0.224271i | \(-0.0720000\pi\) | ||||
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(422\) | 0.713204 | − | 1.51564i | 0.713204 | − | 1.51564i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.60986 | + | 0.162389i | −1.60986 | + | 0.162389i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.07997 | + | 0.870800i | −1.07997 | + | 0.870800i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.492727 | − | 0.870184i | \(-0.336000\pi\) | ||||
−0.492727 | + | 0.870184i | \(0.664000\pi\) | |||||||
\(432\) | −0.247968 | + | 1.01875i | −0.247968 | + | 1.01875i | ||||
\(433\) | −1.92189 | − | 0.493458i | −1.92189 | − | 0.493458i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.929776 | − | 0.368125i | \(-0.880000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.977168 | − | 1.53977i | −0.977168 | − | 1.53977i | ||||
\(439\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0535432 | − | 0.100362i | 0.0535432 | − | 0.100362i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.100515 | − | 0.609805i | 0.100515 | − | 0.609805i | −0.888136 | − | 0.459580i | \(-0.848000\pi\) |
0.988652 | − | 0.150226i | \(-0.0480000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.70118 | + | 0.302413i | 1.70118 | + | 0.302413i | 0.938734 | − | 0.344643i | \(-0.112000\pi\) |
0.762443 | + | 0.647056i | \(0.224000\pi\) | |||||||
\(450\) | 0.0680124 | − | 0.0911792i | 0.0680124 | − | 0.0911792i | ||||
\(451\) | −1.67171 | + | 2.63419i | −1.67171 | + | 2.63419i | ||||
\(452\) | 1.44139 | + | 1.35356i | 1.44139 | + | 1.35356i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.64524 | + | 0.604026i | 1.64524 | + | 0.604026i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.0250641 | + | 0.115536i | −0.0250641 | + | 0.115536i | ||||
\(457\) | −0.971998 | − | 0.824898i | −0.971998 | − | 0.824898i | 0.0125660 | − | 0.999921i | \(-0.496000\pi\) |
−0.984564 | + | 0.175023i | \(0.944000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.52584 | − | 0.741567i | −1.52584 | − | 0.741567i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.823533 | − | 0.567269i | \(-0.192000\pi\) | ||||
−0.823533 | + | 0.567269i | \(0.808000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.856290 | − | 0.266377i | 0.856290 | − | 0.266377i | ||||
\(467\) | −0.0677975 | + | 0.0329499i | −0.0677975 | + | 0.0329499i | −0.470704 | − | 0.882291i | \(-0.656000\pi\) |
0.402906 | + | 0.915241i | \(0.368000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.20424 | + | 1.53252i | −1.20424 | + | 1.53252i | ||||
\(473\) | −2.34093 | − | 0.117767i | −2.34093 | − | 0.117767i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.0725322 | − | 0.102517i | 0.0725322 | − | 0.102517i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.888136 | − | 0.459580i | \(-0.152000\pi\) | ||||
−0.888136 | + | 0.459580i | \(0.848000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −0.797250 | − | 0.579236i | −0.797250 | − | 0.579236i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.43454 | − | 0.935877i | −1.43454 | − | 0.935877i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.210458 | − | 0.0833264i | 0.210458 | − | 0.0833264i | ||||
\(487\) | 0 | 0 | 0.999684 | − | 0.0251301i | \(-0.00800000\pi\) | ||||
−0.999684 | + | 0.0251301i | \(0.992000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.26992 | + | 1.38685i | 1.26992 | + | 1.38685i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.75739 | − | 0.747418i | 1.75739 | − | 0.747418i | 0.762443 | − | 0.647056i | \(-0.224000\pi\) |
0.994951 | − | 0.100362i | \(-0.0320000\pi\) | |||||||
\(492\) | 0.111969 | + | 1.77969i | 0.111969 | + | 1.77969i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.0747971 | + | 0.392100i | 0.0747971 | + | 0.392100i | ||||
\(499\) | −1.13747 | − | 1.01559i | −1.13747 | − | 1.01559i | −0.999684 | − | 0.0251301i | \(-0.992000\pi\) |
−0.137790 | − | 0.990461i | \(-0.544000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.379779 | + | 0.925077i | −0.379779 | + | 0.925077i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.686257 | + | 0.644438i | −0.686257 | + | 0.644438i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.954865 | − | 0.297042i | \(-0.904000\pi\) | ||||
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.0627905 | + | 0.998027i | 0.0627905 | + | 0.998027i | ||||
\(513\) | 0.121168 | − | 0.0515326i | 0.121168 | − | 0.0515326i | ||||
\(514\) | −0.946807 | + | 1.57825i | −0.946807 | + | 1.57825i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.12203 | + | 0.731999i | −1.12203 | + | 0.731999i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.66770 | + | 1.02919i | 1.66770 | + | 1.02919i | 0.938734 | + | 0.344643i | \(0.112000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.989810 | + | 1.64993i | 0.989810 | + | 1.64993i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
0.260842 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(524\) | 0.242711 | − | 0.816237i | 0.242711 | − | 0.816237i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.54860 | + | 0.0779068i | −1.54860 | + | 0.0779068i | ||||
\(529\) | 0.577573 | − | 0.816339i | 0.577573 | − | 0.816339i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.221427 | + | 0.0111395i | 0.221427 | + | 0.0111395i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.452927 | − | 1.39396i | 0.452927 | − | 1.39396i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.72294 | + | 1.00438i | 1.72294 | + | 1.00438i | ||||
\(537\) | −1.65930 | + | 0.806429i | −1.65930 | + | 0.806429i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.61389 | + | 0.328935i | 1.61389 | + | 0.328935i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.0125660 | − | 0.999921i | \(-0.504000\pi\) | ||||
0.0125660 | + | 0.999921i | \(0.496000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.59967 | − | 0.243070i | −1.59967 | − | 0.243070i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.16264 | + | 0.986686i | 1.16264 | + | 0.986686i | 1.00000 | \(0\) | ||
0.162637 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(548\) | −0.417469 | + | 1.92437i | −0.417469 | + | 1.92437i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.54616 | + | 0.567649i | 1.54616 | + | 0.567649i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.389145 | − | 1.44024i | −0.389145 | − | 1.44024i | ||||
\(557\) | 0 | 0 | 0.402906 | − | 0.915241i | \(-0.368000\pi\) | ||||
−0.402906 | + | 0.915241i | \(0.632000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.408034 | − | 2.47546i | 0.408034 | − | 2.47546i | ||||
\(562\) | −0.253520 | − | 1.16863i | −0.253520 | − | 1.16863i | ||||
\(563\) | −0.824962 | + | 1.54632i | −0.824962 | + | 1.54632i | 0.0125660 | + | 0.999921i | \(0.496000\pi\) |
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.528033 | + | 0.832047i | 0.528033 | + | 0.832047i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.83988 | − | 0.0462510i | −1.83988 | − | 0.0462510i | −0.910106 | − | 0.414376i | \(-0.864000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.552130 | − | 0.141763i | −0.552130 | − | 0.141763i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
−0.514440 | + | 0.857527i | \(0.672000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.0885510 | − | 0.0714007i | 0.0885510 | − | 0.0714007i | ||||
\(577\) | 0.336555 | − | 0.332352i | 0.336555 | − | 0.332352i | −0.514440 | − | 0.857527i | \(-0.672000\pi\) |
0.850994 | + | 0.525175i | \(0.176000\pi\) | |||||||
\(578\) | 0.576687 | − | 1.51178i | 0.576687 | − | 1.51178i | ||||
\(579\) | 0.164572 | − | 0.0166006i | 0.164572 | − | 0.0166006i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.463019 | − | 0.983966i | 0.463019 | − | 0.983966i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.170182 | + | 1.92968i | −0.170182 | + | 1.92968i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.414211 | + | 0.317147i | 0.414211 | + | 0.317147i | 0.793990 | − | 0.607930i | \(-0.208000\pi\) |
−0.379779 | + | 0.925077i | \(0.624000\pi\) | |||||||
\(588\) | 0.856781 | − | 0.390096i | 0.856781 | − | 0.390096i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.590686 | − | 1.25527i | −0.590686 | − | 1.25527i | −0.947098 | − | 0.320944i | \(-0.896000\pi\) |
0.356412 | − | 0.934329i | \(-0.384000\pi\) | |||||||
\(594\) | 1.06701 | + | 1.35787i | 1.06701 | + | 1.35787i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.556876 | − | 0.830596i | \(-0.312000\pi\) | ||||
−0.556876 | + | 0.830596i | \(0.688000\pi\) | |||||||
\(600\) | 0.905660 | − | 0.256959i | 0.905660 | − | 0.256959i | ||||
\(601\) | 0.528033 | + | 0.932536i | 0.528033 | + | 0.932536i | 0.998737 | + | 0.0502443i | \(0.0160000\pi\) |
−0.470704 | + | 0.882291i | \(0.656000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.0199296 | − | 0.225979i | −0.0199296 | − | 0.225979i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.962028 | − | 0.272952i | \(-0.912000\pi\) | ||||
0.962028 | + | 0.272952i | \(0.0880000\pi\) | |||||||
\(608\) | 0.0957483 | − | 0.0812580i | 0.0957483 | − | 0.0812580i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.0825264 | + | 0.164515i | 0.0825264 | + | 0.164515i | ||||
\(613\) | 0 | 0 | −0.597905 | − | 0.801567i | \(-0.704000\pi\) | ||||
0.597905 | + | 0.801567i | \(0.296000\pi\) | |||||||
\(614\) | 1.34683 | − | 0.101741i | 1.34683 | − | 0.101741i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.437049 | + | 1.23831i | −0.437049 | + | 1.23831i | 0.492727 | + | 0.870184i | \(0.336000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.588804 | − | 0.676387i | 0.588804 | − | 0.676387i | −0.379779 | − | 0.925077i | \(-0.624000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(626\) | 0.0631332 | − | 1.67387i | 0.0631332 | − | 1.67387i | ||||
\(627\) | 0.124120 | + | 0.150035i | 0.124120 | + | 0.150035i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.379779 | − | 0.925077i | \(-0.624000\pi\) | ||||
0.379779 | + | 0.925077i | \(0.376000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.40051 | − | 0.724717i | −1.40051 | − | 0.724717i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.45380 | + | 0.109822i | −1.45380 | + | 0.109822i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
−0.675333 | + | 0.737513i | \(0.736000\pi\) | |||||||
\(642\) | 0.780877 | + | 1.04686i | 0.780877 | + | 1.04686i | ||||
\(643\) | 0.841825 | + | 1.67816i | 0.841825 | + | 1.67816i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
0.112856 | + | 0.993611i | \(0.464000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.0956444 | + | 0.179277i | 0.0956444 | + | 0.179277i | ||||
\(647\) | 0 | 0 | 0.762443 | − | 0.647056i | \(-0.224000\pi\) | ||||
−0.762443 | + | 0.647056i | \(0.776000\pi\) | |||||||
\(648\) | 0.840148 | + | 0.238371i | 0.840148 | + | 0.238371i | ||||
\(649\) | 0.759213 | + | 3.11915i | 0.759213 | + | 3.11915i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.175480 | − | 1.98975i | −0.175480 | − | 1.98975i | ||||
\(653\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.05483 | − | 1.57331i | 1.05483 | − | 1.57331i | ||||
\(657\) | 0.190370 | − | 0.110976i | 0.190370 | − | 0.110976i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.746226 | + | 0.410241i | −0.746226 | + | 0.410241i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.617860 | − | 0.786288i | \(-0.712000\pi\) | ||||
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(662\) | 0.0748104 | + | 0.158980i | 0.0748104 | + | 0.158980i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.190121 | − | 0.379001i | 0.190121 | − | 0.379001i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.303506 | + | 0.644982i | −0.303506 | + | 0.644982i | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) |
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(674\) | −0.521518 | + | 1.93015i | −0.521518 | + | 1.93015i | ||||
\(675\) | −0.816213 | − | 0.658131i | −0.816213 | − | 0.658131i | ||||
\(676\) | 0.994951 | − | 0.100362i | 0.994951 | − | 0.100362i | ||||
\(677\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(678\) | 1.32449 | − | 1.30795i | 1.32449 | − | 1.30795i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.626607 | − | 1.52631i | 0.626607 | − | 1.52631i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.375556 | + | 1.54293i | −0.375556 | + | 1.54293i | 0.402906 | + | 0.915241i | \(0.368000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(684\) | −0.0138362 | − | 0.00355253i | −0.0138362 | − | 0.00355253i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.41903 | + | 0.107195i | 1.41903 | + | 0.107195i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0199546 | − | 0.0152786i | 0.0199546 | − | 0.0152786i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
0.617860 | + | 0.786288i | \(0.288000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.167334 | + | 1.01518i | −0.167334 | + | 1.01518i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.12596 | + | 2.20766i | 2.12596 | + | 2.20766i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.220208 | − | 0.814997i | −0.220208 | − | 0.814997i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.597905 | − | 0.801567i | \(-0.296000\pi\) | ||||
−0.597905 | + | 0.801567i | \(0.704000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.35641 | + | 0.934329i | 1.35641 | + | 0.934329i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.348445 | + | 0.137959i | 0.348445 | + | 0.137959i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.39897 | + | 1.18725i | 1.39897 | + | 1.18725i | ||||
\(709\) | 0 | 0 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
0.556876 | + | 0.830596i | \(0.312000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.28218 | + | 0.883195i | −1.28218 | + | 0.883195i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.92023 | + | 0.391374i | 1.92023 | + | 0.391374i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.863923 | − | 0.503623i | \(-0.832000\pi\) | ||||
0.863923 | + | 0.503623i | \(0.168000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.959158 | + | 0.220734i | 0.959158 | + | 0.220734i | ||||
\(723\) | −0.573198 | + | 0.729451i | −0.573198 | + | 0.729451i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.931316 | + | 1.31632i | −0.931316 | + | 1.31632i | ||||
\(727\) | 0 | 0 | 0.998737 | − | 0.0502443i | \(-0.0160000\pi\) | ||||
−0.998737 | + | 0.0502443i | \(0.984000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.361575 | − | 1.02447i | −0.361575 | − | 1.02447i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.656279 | + | 2.20707i | −0.656279 | + | 2.20707i | ||||
\(732\) | 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 | ||||||||
\(737\) | 3.05410 | − | 1.20921i | 3.05410 | − | 1.20921i | ||||
\(738\) | −0.215399 | + | 0.00541471i | −0.215399 | + | 0.00541471i | ||||
\(739\) | −1.32998 | + | 0.867664i | −1.32998 | + | 0.867664i | −0.997159 | − | 0.0753268i | \(-0.976000\pi\) |
−0.332820 | + | 0.942991i | \(0.608000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0476848 | + | 0.00724570i | −0.0476848 | + | 0.00724570i | ||||
\(748\) | −1.94271 | + | 1.82432i | −1.94271 | + | 1.82432i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.856781 | + | 0.390096i | 0.856781 | + | 0.390096i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(758\) | −0.344801 | + | 0.323789i | −0.344801 | + | 0.323789i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.371566 | + | 0.204270i | 0.371566 | + | 0.204270i | 0.656586 | − | 0.754251i | \(-0.272000\pi\) |
−0.285019 | + | 0.958522i | \(0.592000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.941111 | − | 0.0236577i | 0.941111 | − | 0.0236577i | ||||
\(769\) | 0.618896 | − | 0.245038i | 0.618896 | − | 0.245038i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.45112 | + | 0.946698i | 1.45112 | + | 0.946698i | ||||
\(772\) | −0.149522 | − | 0.0922744i | −0.149522 | − | 0.0922744i | ||||
\(773\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(774\) | −0.0832755 | − | 0.138813i | −0.0832755 | − | 0.138813i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.02593 | + | 0.530882i | −1.02593 | + | 0.530882i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.237575 | + | 0.0119519i | −0.237575 | + | 0.0119519i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.974527 | − | 0.224271i | −0.974527 | − | 0.224271i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.759255 | − | 0.257289i | −0.759255 | − | 0.257289i | ||||
\(787\) | −0.281012 | − | 0.163816i | −0.281012 | − | 0.163816i | 0.356412 | − | 0.934329i | \(-0.384000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.00235432 | − | 0.187341i | −0.00235432 | − | 0.187341i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.556876 | − | 0.830596i | \(-0.688000\pi\) | ||||
0.556876 | + | 0.830596i | \(0.312000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(801\) | 0.166252 | + | 0.0610370i | 0.166252 | + | 0.0610370i | ||||
\(802\) | 1.01766 | + | 0.700985i | 1.01766 | + | 0.700985i | ||||
\(803\) | 2.32588 | + | 2.18414i | 2.32588 | + | 2.18414i | ||||
\(804\) | 1.00600 | − | 1.58520i | 1.00600 | − | 1.58520i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.461723 | − | 0.479466i | −0.461723 | − | 0.479466i | 0.448383 | − | 0.893841i | \(-0.352000\pi\) |
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.34896 | + | 1.47316i | −1.34896 | + | 1.47316i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.711536 | + | 0.702650i | \(0.752000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.285425 | + | 1.49625i | −0.285425 | + | 1.49625i | ||||
\(817\) | −0.0957580 | − | 0.150891i | −0.0957580 | − | 0.150891i | ||||
\(818\) | −0.803523 | − | 0.0606993i | −0.803523 | − | 0.0606993i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.938734 | − | 0.344643i | \(-0.112000\pi\) | ||||
−0.938734 | + | 0.344643i | \(0.888000\pi\) | |||||||
\(822\) | 1.79551 | + | 0.461010i | 1.79551 | + | 0.461010i | ||||
\(823\) | 0 | 0 | 0.236499 | − | 0.971632i | \(-0.424000\pi\) | ||||
−0.236499 | + | 0.971632i | \(0.576000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.588870 | − | 1.43439i | 0.588870 | − | 1.43439i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.0586808 | − | 0.0473156i | 0.0586808 | − | 0.0473156i | −0.597905 | − | 0.801567i | \(-0.704000\pi\) |
0.656586 | + | 0.754251i | \(0.272000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.356412 | − | 0.934329i | \(-0.384000\pi\) | ||||
−0.356412 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.688925 | − | 1.46404i | 0.688925 | − | 1.46404i | ||||
\(834\) | −1.36869 | + | 0.314981i | −1.36869 | + | 0.314981i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.00779584 | − | 0.206693i | −0.00779584 | − | 0.206693i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.639808 | + | 0.489878i | 0.639808 | + | 0.489878i | ||||
\(839\) | 0 | 0 | 0.910106 | − | 0.414376i | \(-0.136000\pi\) | ||||
−0.910106 | + | 0.414376i | \(0.864000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.994951 | + | 0.100362i | 0.994951 | + | 0.100362i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.10837 | + | 0.197031i | −1.10837 | + | 0.197031i | ||||
\(844\) | 0.713204 | + | 1.51564i | 0.713204 | + | 1.51564i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.801475 | − | 0.467219i | 0.801475 | − | 0.467219i | ||||
\(850\) | 0.901044 | − | 1.34393i | 0.901044 | − | 1.34393i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.0174330 | − | 1.38720i | 0.0174330 | − | 1.38720i | ||||
\(857\) | −0.472401 | − | 1.94081i | −0.472401 | − | 1.94081i | −0.285019 | − | 0.958522i | \(-0.592000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.397753 | − | 0.337558i | 0.397753 | − | 0.337558i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.823533 | + | 0.567269i | \(0.192000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.448383 | − | 0.893841i | \(-0.648000\pi\) | ||||
0.448383 | + | 0.893841i | \(0.352000\pi\) | |||||||
\(864\) | −0.626900 | − | 0.840438i | −0.626900 | − | 0.840438i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | ||||
\(867\) | −1.40172 | − | 0.596152i | −1.40172 | − | 0.596152i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.116700 | + | 0.0603884i | 0.116700 | + | 0.0603884i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.80928 | + | 0.228566i | 1.80928 | + | 0.228566i | ||||
\(877\) | 0 | 0 | 0.0376902 | − | 0.999289i | \(-0.488000\pi\) | ||||
−0.0376902 | + | 0.999289i | \(0.512000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.57546 | − | 0.199027i | −1.57546 | − | 0.199027i | −0.711536 | − | 0.702650i | \(-0.752000\pi\) |
−0.863923 | + | 0.503623i | \(0.832000\pi\) | |||||||
\(882\) | 0.0432003 | + | 0.105229i | 0.0432003 | + | 0.105229i | ||||
\(883\) | 1.34372 | − | 1.39536i | 1.34372 | − | 1.39536i | 0.492727 | − | 0.870184i | \(-0.336000\pi\) |
0.850994 | − | 0.525175i | \(-0.176000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.405792 | + | 0.466153i | 0.405792 | + | 0.466153i | ||||
\(887\) | 0 | 0 | 0.656586 | − | 0.754251i | \(-0.272000\pi\) | ||||
−0.656586 | + | 0.754251i | \(0.728000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.16369 | − | 0.845469i | 1.16369 | − | 0.845469i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.31738 | + | 1.11801i | −1.31738 | + | 1.11801i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.0269021 | + | 0.110524i | 0.0269021 | + | 0.110524i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.964091 | − | 2.96717i | −0.964091 | − | 2.96717i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.96171 | + | 0.247822i | −1.96171 | + | 0.247822i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.04552 | + | 1.55942i | −1.04552 | + | 1.55942i | −0.236499 | + | 0.971632i | \(0.576000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(908\) | −1.51412 | + | 0.882657i | −1.51412 | + | 0.882657i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.577573 | − | 0.816339i | \(-0.696000\pi\) | ||||
0.577573 | + | 0.816339i | \(0.304000\pi\) | |||||||
\(912\) | −0.0730452 | − | 0.0929574i | −0.0730452 | − | 0.0929574i | ||||
\(913\) | −0.297355 | − | 0.631912i | −0.297355 | − | 0.631912i | ||||
\(914\) | 1.25517 | − | 0.223128i | 1.25517 | − | 0.223128i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.54399 | − | 0.702988i | 1.54399 | − | 0.702988i | ||||
\(919\) | 0 | 0 | −0.793990 | − | 0.607930i | \(-0.792000\pi\) | ||||
0.793990 | + | 0.607930i | \(0.208000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0479241 | − | 1.27062i | −0.0479241 | − | 1.27062i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.961047 | − | 0.949045i | 0.961047 | − | 0.949045i | −0.0376902 | − | 0.999289i | \(-0.512000\pi\) |
0.998737 | + | 0.0502443i | \(0.0160000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0505974 | + | 0.114937i | 0.0505974 | + | 0.114937i | ||||
\(932\) | −0.340573 | + | 0.829578i | −0.340573 | + | 0.829578i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.0178274 | − | 0.0732420i | 0.0178274 | − | 0.0732420i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.58748 | − | 0.0399061i | −1.58748 | − | 0.0399061i | −0.778462 | − | 0.627691i | \(-0.784000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.57243 | − | 0.118784i | −1.57243 | − | 0.118784i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −0.413213 | − | 1.90475i | −0.413213 | − | 1.90475i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.58291 | − | 1.72865i | 1.58291 | − | 1.72865i | ||||
\(947\) | 0.530008 | + | 1.78242i | 0.530008 | + | 1.78242i | 0.617860 | + | 0.786288i | \(0.288000\pi\) |
−0.0878512 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.0327567 | + | 0.121234i | 0.0327567 | + | 0.121234i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.480511 | − | 0.757165i | 0.480511 | − | 0.757165i | −0.514440 | − | 0.857527i | \(-0.672000\pi\) |
0.994951 | + | 0.100362i | \(0.0320000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.899405 | + | 0.437116i | 0.899405 | + | 0.437116i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.129960 | + | 0.0895195i | −0.129960 | + | 0.0895195i | ||||
\(964\) | 0.954495 | − | 0.245073i | 0.954495 | − | 0.245073i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.979855 | − | 0.199710i | \(-0.936000\pi\) | ||||
0.979855 | + | 0.199710i | \(0.0640000\pi\) | |||||||
\(968\) | 1.63551 | − | 0.508780i | 1.63551 | − | 0.508780i | ||||
\(969\) | 0.172046 | − | 0.0836153i | 0.172046 | − | 0.0836153i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.01496 | − | 0.343940i | −1.01496 | − | 0.343940i | −0.236499 | − | 0.971632i | \(-0.576000\pi\) |
−0.778462 | + | 0.627691i | \(0.784000\pi\) | |||||||
\(972\) | −0.0699472 | + | 0.215275i | −0.0699472 | + | 0.215275i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.861670 | + | 1.21788i | −0.861670 | + | 1.21788i | 0.112856 | + | 0.993611i | \(0.464000\pi\) |
−0.974527 | + | 0.224271i | \(0.928000\pi\) | |||||||
\(978\) | −1.87806 | + | 0.0944813i | −1.87806 | + | 0.0944813i | ||||
\(979\) | −0.161017 | + | 2.55930i | −0.161017 | + | 2.55930i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.544310 | + | 1.83052i | −0.544310 | + | 1.83052i | ||||
\(983\) | 0 | 0 | −0.514440 | − | 0.857527i | \(-0.672000\pi\) | ||||
0.514440 | + | 0.857527i | \(0.328000\pi\) | |||||||
\(984\) | −1.44265 | − | 1.04815i | −1.44265 | − | 1.04815i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.675333 | − | 0.737513i | \(-0.736000\pi\) | ||||
0.675333 | + | 0.737513i | \(0.264000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.152213 | − | 0.0647362i | 0.152213 | − | 0.0647362i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.349796 | − | 0.192302i | −0.349796 | − | 0.192302i | ||||
\(997\) | 0 | 0 | −0.954865 | − | 0.297042i | \(-0.904000\pi\) | ||||
0.954865 | + | 0.297042i | \(0.0960000\pi\) | |||||||
\(998\) | 1.50758 | − | 0.229077i | 1.50758 | − | 0.229077i | ||||
\(999\) | 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.683.1 | yes | 100 | |
8.3 | odd | 2 | CM | 2008.1.bd.a.683.1 | yes | 100 | |
251.147 | even | 125 | inner | 2008.1.bd.a.147.1 | ✓ | 100 | |
2008.147 | odd | 250 | inner | 2008.1.bd.a.147.1 | ✓ | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.1.bd.a.147.1 | ✓ | 100 | 251.147 | even | 125 | inner | |
2008.1.bd.a.147.1 | ✓ | 100 | 2008.147 | odd | 250 | inner | |
2008.1.bd.a.683.1 | yes | 100 | 1.1 | even | 1 | trivial | |
2008.1.bd.a.683.1 | yes | 100 | 8.3 | odd | 2 | CM |