Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1397,1,Mod(126,1397)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1397, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([4, 5]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1397.126");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1397 = 11 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1397.l (of order \(10\), degree \(4\), 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: | \(0.697193822648\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{50})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{15} + x^{10} - x^{5} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{25}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{25} - \cdots)\) |
Embedding invariants
Embedding label | 1269.3 | ||
Root | \(0.992115 + 0.125333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1397.1269 |
Dual form | 1397.1.l.a.1015.3 |
$q$-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 \(\left(\mathbb{Z}/1397\mathbb{Z}\right)^\times\).
\(n\) | \(255\) | \(892\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(3\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(4\) | −0.265616 | − | 0.817483i | −0.265616 | − | 0.817483i | ||||
\(5\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(8\) | 0.215351 | − | 0.662783i | 0.215351 | − | 0.662783i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.484103 | + | 0.351721i | −0.484103 | + | 0.351721i | ||||
\(17\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(18\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | ||||
\(19\) | 0.450527 | − | 1.38658i | 0.450527 | − | 1.38658i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.238883 | − | 0.288760i | 0.238883 | − | 0.288760i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(26\) | −0.0145433 | − | 0.0447596i | −0.0145433 | − | 0.0447596i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(32\) | −0.921143 | −0.921143 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.656814 | −0.656814 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.265616 | + | 0.817483i | −0.265616 | + | 0.817483i | ||||
\(37\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(38\) | 0.442031 | − | 0.321154i | 0.442031 | − | 0.321154i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −0.832549 | + | 0.213762i | −0.832549 | + | 0.213762i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(50\) | 0.303189 | − | 0.220280i | 0.303189 | − | 0.220280i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.0333564 | + | 0.102660i | −0.0333564 | + | 0.102660i | ||||
\(53\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(62\) | 0.0434005 | + | 0.133573i | 0.0434005 | + | 0.133573i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.204822 | + | 0.148812i | 0.204822 | + | 0.148812i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 1.21875 | + | 0.885477i | 1.21875 | + | 0.885477i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(72\) | −0.563797 | + | 0.409622i | −0.563797 | + | 0.409622i | ||||
\(73\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(74\) | −0.202967 | + | 0.624667i | −0.202967 | + | 0.624667i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.25317 | −1.25317 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(82\) | 0.587328 | − | 0.426719i | 0.587328 | − | 0.426719i | ||||
\(83\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.647953 | − | 0.256543i | −0.647953 | − | 0.256543i | ||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.0380748 | − | 0.0276630i | 0.0380748 | − | 0.0276630i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(98\) | −0.374763 | −0.374763 | ||||||||
\(99\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(100\) | −0.859553 | −0.859553 | ||||||||
\(101\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(104\) | −0.0708022 | + | 0.0514408i | −0.0708022 | + | 0.0514408i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(122\) | 0.743615 | 0.743615 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0995431 | − | 0.306362i | 0.0995431 | − | 0.306362i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(128\) | 0.313968 | + | 0.966296i | 0.313968 | + | 0.966296i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.377427 | + | 1.16160i | 0.377427 | + | 1.16160i | ||||
\(137\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.319132 | 0.319132 | ||||||||
\(143\) | −0.0800484 | + | 0.0967619i | −0.0800484 | + | 0.0967619i | ||||
\(144\) | 0.598384 | 0.598384 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.147638 | − | 0.454382i | 0.147638 | − | 0.454382i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.21875 | − | 0.885477i | 1.21875 | − | 0.885477i | ||||
\(149\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(152\) | −0.821980 | − | 0.597204i | −0.821980 | − | 0.597204i | ||||
\(153\) | 1.75261 | 1.75261 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(158\) | 0.215351 | + | 0.662783i | 0.215351 | + | 0.662783i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.115808 | + | 0.356420i | −0.115808 | + | 0.356420i | ||||
\(163\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(164\) | −1.66510 | −1.66510 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.304144 | − | 0.936058i | −0.304144 | − | 0.936058i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.320630 | + | 0.505233i | 0.320630 | + | 0.505233i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.939097 | + | 1.47978i | 0.939097 | + | 1.47978i | ||||
\(188\) | −0.107944 | −0.107944 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.695393 | + | 0.505233i | 0.695393 | + | 0.505233i | ||||
\(197\) | −1.85955 | −1.85955 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(198\) | −0.362989 | + | 0.0931997i | −0.362989 | + | 0.0931997i | ||||
\(199\) | 1.93717 | 1.93717 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(200\) | −0.563797 | − | 0.409622i | −0.563797 | − | 0.409622i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.124106 | + | 0.381959i | −0.124106 | + | 0.381959i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0751457 | 0.0751457 | ||||||||
\(209\) | −1.35556 | − | 0.536702i | −1.35556 | − | 0.536702i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.258183 | + | 0.187581i | −0.258183 | + | 0.187581i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.220095 | 0.220095 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(226\) | −0.386520 | + | 0.280823i | −0.386520 | + | 0.280823i | ||||
\(227\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(234\) | −0.0145433 | + | 0.0447596i | −0.0145433 | + | 0.0447596i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −0.273190 | − | 0.256543i | −0.273190 | − | 0.256543i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.37982 | − | 1.00250i | −1.37982 | − | 1.00250i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.148122 | + | 0.107617i | −0.148122 | + | 0.107617i | ||||
\(248\) | 0.211290 | − | 0.153511i | 0.211290 | − | 0.153511i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.374763 | −0.374763 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.0394285 | + | 0.121348i | −0.0394285 | + | 0.121348i | ||||
\(257\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.187381 | + | 0.136140i | 0.187381 | + | 0.136140i | ||||
\(263\) | −1.98423 | −1.98423 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(272\) | 0.324077 | − | 0.997407i | 0.324077 | − | 0.997407i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(284\) | −0.592168 | − | 0.430235i | −0.592168 | − | 0.430235i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0455845 | + | 0.0117041i | −0.0455845 | + | 0.0117041i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.745220 | + | 0.541434i | 0.745220 | + | 0.541434i | ||||
\(289\) | 0.640176 | − | 1.97026i | 0.640176 | − | 1.97026i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.886520 | + | 0.644095i | −0.886520 | + | 0.644095i | ||||
\(293\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.22138 | 1.22138 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.319132 | 0.319132 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.269589 | + | 0.829708i | 0.269589 | + | 0.829708i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.531374 | + | 0.386066i | 0.531374 | + | 0.386066i | ||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(314\) | 0.587328 | − | 0.426719i | 0.587328 | − | 0.426719i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.493928 | − | 1.52015i | 0.493928 | − | 1.52015i | ||||
\(317\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.789600 | + | 2.43014i | 0.789600 | + | 2.43014i | ||||
\(324\) | 0.695393 | − | 0.505233i | 0.695393 | − | 0.505233i | ||||
\(325\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | ||||
\(326\) | 0.187381 | + | 0.576700i | 0.187381 | + | 0.576700i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.09217 | − | 0.793506i | −1.09217 | − | 0.793506i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(338\) | 0.113982 | − | 0.350799i | 0.113982 | − | 0.350799i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.238883 | − | 0.288760i | 0.238883 | − | 0.288760i | ||||
\(342\) | −0.546380 | −0.546380 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.0578390 | + | 0.919325i | −0.0578390 | + | 0.919325i | ||||
\(353\) | 1.45794 | 1.45794 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.601597 | + | 0.437086i | −0.601597 | + | 0.437086i | ||||
\(359\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.910614 | − | 0.661600i | −0.910614 | − | 0.661600i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | −0.0412417 | + | 0.655518i | −0.0412417 | + | 0.655518i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.0708022 | − | 0.0514408i | −0.0708022 | − | 0.0514408i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.0715733 | + | 0.220280i | −0.0715733 | + | 0.220280i | ||||
\(383\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.215351 | + | 0.662783i | 0.215351 | + | 0.662783i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.563797 | − | 0.409622i | −0.563797 | − | 0.409622i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.799192 | + | 0.316423i | 0.799192 | + | 0.316423i | ||||
\(397\) | −1.98423 | −1.98423 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(398\) | 0.587328 | + | 0.426719i | 0.587328 | + | 0.426719i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.184911 | + | 0.569097i | 0.184911 | + | 0.569097i | ||||
\(401\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0145433 | − | 0.0447596i | −0.0145433 | − | 0.0447596i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.69755 | − | 0.435857i | 1.69755 | − | 0.435857i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.745220 | − | 0.541434i | 0.745220 | − | 0.541434i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.0935855 | + | 0.0679939i | 0.0935855 | + | 0.0679939i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.292765 | − | 0.461324i | −0.292765 | − | 0.461324i | ||||
\(419\) | 1.45794 | 1.45794 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(422\) | 0.147638 | + | 0.454382i | 0.147638 | + | 0.454382i | ||||
\(423\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.731960 | 0.731960 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.263146 | − | 0.809880i | −0.263146 | − | 0.809880i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 1.00000 | ||||||||
\(442\) | 0.0667305 | + | 0.0484825i | 0.0667305 | + | 0.0484825i | ||||
\(443\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(450\) | −0.374763 | −0.374763 | ||||||||
\(451\) | −1.80113 | − | 0.713118i | −1.80113 | − | 0.713118i | ||||
\(452\) | 1.09580 | 1.09580 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.187381 | − | 0.576700i | 0.187381 | − | 0.576700i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.75261 | 1.75261 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(468\) | 0.0873282 | − | 0.0634476i | 0.0873282 | − | 0.0634476i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0680131 | − | 0.209323i | 0.0680131 | − | 0.209323i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.161064 | + | 0.844328i | 0.161064 | + | 0.844328i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(488\) | −0.427306 | − | 1.31511i | −0.427306 | − | 1.31511i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −0.0686150 | −0.0686150 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.224252 | −0.224252 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.147638 | + | 0.454382i | 0.147638 | + | 0.454382i | ||||
\(503\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.695393 | + | 0.505233i | 0.695393 | + | 0.505233i | ||||
\(509\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.783295 | − | 0.569097i | 0.783295 | − | 0.569097i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.116762 | − | 0.0462295i | −0.116762 | − | 0.0462295i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(524\) | −0.164160 | − | 0.505233i | −0.164160 | − | 0.505233i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.601597 | − | 0.437086i | −0.601597 | − | 0.437086i | ||||
\(527\) | −0.656814 | −0.656814 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.196811 | + | 0.142991i | −0.196811 | + | 0.142991i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.546380 | −0.546380 | ||||||||
\(539\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(542\) | 0.187381 | − | 0.576700i | 0.187381 | − | 0.576700i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.30608 | − | 0.948925i | 1.30608 | − | 0.948925i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.98423 | −1.98423 | ||||||||
\(550\) | −0.200808 | − | 0.316423i | −0.200808 | − | 0.316423i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(558\) | 0.0434005 | − | 0.133573i | 0.0434005 | − | 0.133573i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.183384 | − | 0.564398i | −0.183384 | − | 0.564398i | ||||
\(569\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0.100363 | + | 0.0397367i | 0.100363 | + | 0.0397367i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0782352 | − | 0.240783i | −0.0782352 | − | 0.240783i | ||||
\(577\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(578\) | 0.628103 | − | 0.456344i | 0.628103 | − | 0.456344i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.888430 | −0.888430 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.442031 | − | 0.321154i | 0.442031 | − | 0.321154i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.848445 | − | 0.616432i | −0.848445 | − | 0.616432i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.592168 | − | 0.430235i | −0.592168 | − | 0.430235i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(608\) | −0.415000 | + | 1.27724i | −0.415000 | + | 1.27724i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.0127587 | + | 0.00926972i | −0.0127587 | + | 0.00926972i | ||||
\(612\) | −0.465523 | − | 1.43273i | −0.465523 | − | 1.43273i | ||||
\(613\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.66510 | −1.66510 | ||||||||
\(629\) | −2.48502 | − | 1.80547i | −2.48502 | − | 1.80547i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(632\) | 1.04841 | − | 0.761714i | 1.04841 | − | 0.761714i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.125581 | 0.125581 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.851559 | −0.851559 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.295913 | + | 0.910726i | −0.295913 | + | 0.910726i | ||||
\(647\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(648\) | 0.696891 | 0.696891 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.0470631 | −0.0470631 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.429776 | − | 1.32272i | 0.429776 | − | 1.32272i | ||||
\(653\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.358203 | + | 1.10244i | 0.358203 | + | 1.10244i | ||||
\(657\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.27485 | −1.27485 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.531374 | − | 0.386066i | 0.531374 | − | 0.386066i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.06320 | − | 1.67534i | −1.06320 | − | 1.67534i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.684426 | + | 0.497265i | −0.684426 | + | 0.497265i | ||||
\(677\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.136035 | − | 0.0349278i | 0.136035 | − | 0.0349278i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 1.01384 | + | 0.736597i | 1.01384 | + | 0.736597i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.04914 | + | 3.22894i | 1.04914 | + | 3.22894i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.55520 | 2.55520 | ||||||||
\(704\) | 0.161379 | − | 0.195074i | 0.161379 | − | 0.195074i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.442031 | + | 0.321154i | 0.442031 | + | 0.321154i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.70555 | 1.70555 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.130351 | − | 0.401180i | −0.130351 | − | 0.401180i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(734\) | 0.229790 | − | 0.707220i | 0.229790 | − | 0.707220i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −0.725978 | −0.725978 | ||||||||
\(739\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.960256 | − | 1.16075i | 0.960256 | − | 1.16075i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(752\) | 0.0232213 | + | 0.0714678i | 0.0232213 | + | 0.0714678i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0.429776 | − | 0.312251i | 0.429776 | − | 0.312251i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.187381 | + | 0.576700i | 0.187381 | + | 0.576700i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.303189 | − | 0.220280i | 0.303189 | − | 0.220280i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0145433 | + | 0.0447596i | −0.0145433 | + | 0.0447596i | ||||
\(779\) | −2.28488 | − | 1.66006i | −2.28488 | − | 1.66006i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.456288 | − | 0.718995i | −0.456288 | − | 0.718995i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.184911 | − | 0.569097i | 0.184911 | − | 0.569097i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(788\) | 0.493928 | + | 1.52015i | 0.493928 | + | 1.52015i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.373413 | + | 0.588404i | 0.373413 | + | 0.588404i | ||||
\(793\) | −0.249182 | −0.249182 | ||||||||
\(794\) | −0.601597 | − | 0.437086i | −0.601597 | − | 0.437086i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.514543 | − | 1.58360i | −0.514543 | − | 1.58360i | ||||
\(797\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0680131 | + | 0.209323i | 0.0680131 | + | 0.209323i | ||||
\(800\) | −0.284649 | + | 0.876059i | −0.284649 | + | 0.876059i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.23480 | + | 0.317042i | −1.23480 | + | 0.317042i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.00545028 | − | 0.0167742i | 0.00545028 | − | 0.0167742i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.610690 | + | 0.241789i | 0.610690 | + | 0.241789i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.60528 | + | 1.16630i | 1.60528 | + | 1.16630i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(824\) | 0.746826 | 0.746826 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.00982485 | − | 0.0302378i | −0.00982485 | − | 0.0302378i | ||||
\(833\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.0786875 | + | 1.25070i | −0.0786875 | + | 1.25070i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.442031 | + | 0.321154i | 0.442031 | + | 0.321154i | ||||
\(839\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.338621 | − | 1.04217i | 0.338621 | − | 1.04217i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.0470631 | −0.0470631 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.202967 | + | 0.624667i | −0.202967 | + | 0.624667i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.480106 | + | 0.348817i | 0.480106 | + | 0.348817i | ||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.224339 | − | 0.690446i | −0.224339 | − | 0.690446i | ||||
\(863\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.0986173 | − | 0.303513i | 0.0986173 | − | 0.303513i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.18532 | − | 1.43281i | 1.18532 | − | 1.43281i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.450527 | − | 1.38658i | 0.450527 | − | 1.38658i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | ||||
\(883\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(884\) | −0.0584609 | − | 0.179924i | −0.0584609 | − | 0.179924i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.531374 | − | 0.386066i | 0.531374 | − | 0.386066i | ||||
\(887\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.148122 | − | 0.107617i | −0.148122 | − | 0.107617i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.224339 | − | 0.690446i | −0.224339 | − | 0.690446i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.695393 | + | 0.505233i | 0.695393 | + | 0.505233i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.388998 | − | 0.612963i | −0.388998 | − | 0.612963i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.718755 | + | 0.522206i | 0.718755 | + | 0.522206i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(908\) | −1.12517 | + | 0.817483i | −1.12517 | + | 0.817483i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.696891 | 0.696891 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.106940 | −0.106940 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.75261 | 1.75261 | ||||||||
\(926\) | 0.531374 | + | 0.386066i | 0.531374 | + | 0.386066i | ||||
\(927\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.0875163 | 0.0875163 | ||||||||
\(937\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0494726 | + | 0.152261i | −0.0494726 | + | 0.152261i | ||||
\(950\) | −0.168841 | − | 0.519639i | −0.168841 | − | 0.519639i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.477765 | 0.477765 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.265616 | − | 0.817483i | −0.265616 | − | 0.817483i | ||||
\(962\) | 0.0667305 | − | 0.0484825i | 0.0667305 | − | 0.0484825i | ||||
\(963\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | −0.296722 | + | 0.630566i | −0.296722 | + | 0.630566i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.366906 | + | 1.12922i | −0.366906 | + | 1.12922i | ||||
\(977\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.127319 | + | 0.0925027i | 0.127319 | + | 0.0925027i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −0.279281 | − | 0.202909i | −0.279281 | − | 0.202909i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1397.1.l.a.1269.3 | yes | 20 | |
11.3 | even | 5 | inner | 1397.1.l.a.1015.3 | ✓ | 20 | |
127.126 | odd | 2 | CM | 1397.1.l.a.1269.3 | yes | 20 | |
1397.1015 | odd | 10 | inner | 1397.1.l.a.1015.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1397.1.l.a.1015.3 | ✓ | 20 | 11.3 | even | 5 | inner | |
1397.1.l.a.1015.3 | ✓ | 20 | 1397.1015 | odd | 10 | inner | |
1397.1.l.a.1269.3 | yes | 20 | 1.1 | even | 1 | trivial | |
1397.1.l.a.1269.3 | yes | 20 | 127.126 | odd | 2 | CM |