Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,1,Mod(130,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([6, 5]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.130");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.u (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: | \(0.719152683204\) |
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 | 916.4 | ||
Root | \(0.992115 - 0.125333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1441.916 |
Dual form | 1441.1.u.a.785.4 |
$q$-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 \(\left(\mathbb{Z}/1441\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(1311\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{5}\right)\) |
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 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(3\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(4\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(5\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.910614 | + | 0.661600i | −0.910614 | + | 0.661600i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(12\) | 1.45794 | 1.45794 | ||||||||
\(13\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.482809 | − | 1.48593i | 0.482809 | − | 1.48593i | ||||
\(16\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(17\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(20\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | ||||
\(21\) | 0.183089 | 0.183089 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0458709 | + | 0.141176i | 0.0458709 | + | 0.141176i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.148122 | − | 0.107617i | −0.148122 | − | 0.107617i | ||||
\(28\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | ||||
\(29\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.06279 | + | 0.998027i | 1.06279 | + | 0.998027i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.108877 | + | 0.0791038i | −0.108877 | + | 0.0791038i | ||||
\(36\) | 0.347824 | + | 1.07049i | 0.347824 | + | 1.07049i | ||||
\(37\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00441 | + | 0.729747i | 1.00441 | + | 0.729747i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.93717 | 1.93717 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(44\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(45\) | 1.20623 | 1.20623 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(48\) | 0.450527 | − | 1.38658i | 0.450527 | − | 1.38658i | ||||
\(49\) | 0.796258 | + | 0.578516i | 0.796258 | + | 0.578516i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.263146 | − | 0.809880i | −0.263146 | − | 0.809880i | ||||
\(53\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.06320 | − | 0.134314i | −1.06320 | − | 0.134314i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(60\) | −1.26401 | − | 0.918358i | −1.26401 | − | 0.918358i | ||||
\(61\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0436801 | + | 0.134433i | 0.0436801 | + | 0.134433i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(65\) | −0.912576 | −0.912576 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.175086 | + | 0.127207i | −0.175086 | + | 0.127207i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0235315 | − | 0.123357i | −0.0235315 | − | 0.123357i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(80\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | ||||
\(81\) | −0.265337 | + | 0.816623i | −0.265337 | + | 0.816623i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(84\) | 0.0565777 | − | 0.174128i | 0.0565777 | − | 0.174128i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0330462 | − | 0.101706i | −0.0330462 | − | 0.101706i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.479249 | + | 1.01846i | −0.479249 | + | 1.01846i | ||||
\(100\) | 0.148441 | 0.148441 | ||||||||
\(101\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.158736 | − | 0.115328i | −0.158736 | − | 0.115328i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(108\) | −0.148122 | + | 0.107617i | −0.148122 | + | 0.107617i | ||||
\(109\) | −0.374763 | −0.374763 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | ||||
\(113\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.296192 | + | 0.911586i | −0.296192 | + | 0.911586i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.442031 | − | 0.321154i | 0.442031 | − | 0.321154i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.282001 | + | 0.867911i | −0.282001 | + | 0.867911i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.872746 | + | 2.68604i | 0.872746 | + | 2.68604i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | 1.00000 | ||||||||
\(132\) | 1.27760 | − | 0.702367i | 1.27760 | − | 0.702367i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.0606317 | + | 0.186605i | 0.0606317 | + | 0.186605i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(140\) | 0.0415873 | + | 0.127993i | 0.0415873 | + | 0.127993i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.362576 | − | 0.770513i | 0.362576 | − | 0.770513i | ||||
\(144\) | 1.12558 | 1.12558 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.443422 | + | 1.36471i | −0.443422 | + | 1.36471i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.00441 | − | 0.729747i | 1.00441 | − | 0.729747i | ||||
\(157\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.728969 | − | 0.529627i | −0.728969 | − | 0.529627i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(164\) | −0.374763 | −0.374763 | ||||||||
\(165\) | −0.292765 | − | 1.53473i | −0.292765 | − | 1.53473i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.0849327 | + | 0.261396i | −0.0849327 | + | 0.261396i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | ||||
\(173\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0186414 | 0.0186414 | ||||||||
\(176\) | −0.992115 | − | 0.125333i | −0.992115 | − | 0.125333i | ||||
\(177\) | −2.71111 | −2.71111 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(180\) | 0.372746 | − | 1.14720i | 0.372746 | − | 1.14720i | ||||
\(181\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.482809 | − | 1.48593i | 0.482809 | − | 1.48593i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.0186014 | + | 0.0135147i | −0.0186014 | + | 0.0135147i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(192\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | ||||
\(193\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.411140 | − | 1.26536i | −0.411140 | − | 1.26536i | ||||
\(196\) | 0.796258 | − | 0.578516i | 0.796258 | − | 0.578516i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.124106 | + | 0.381959i | −0.124106 | + | 0.381959i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.851559 | −0.851559 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(212\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.67950 | − | 1.22023i | −1.67950 | − | 1.22023i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.456288 | + | 0.969661i | −0.456288 | + | 0.969661i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.135173 | − | 0.0982088i | −0.135173 | − | 0.0982088i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.160442 | − | 0.0882039i | 0.160442 | − | 0.0882039i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(240\) | −1.26401 | + | 0.918358i | −1.26401 | + | 0.918358i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43494 | −1.43494 | ||||||||
\(244\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | ||||
\(245\) | −0.325937 | − | 1.00313i | −0.325937 | − | 1.00313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(252\) | 0.141352 | 0.141352 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(257\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.282001 | + | 0.867911i | −0.282001 | + | 0.867911i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.45794 | 1.45794 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.662318 | 0.662318 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.728969 | − | 2.24353i | −0.728969 | − | 2.24353i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.126135 | − | 0.0916423i | 0.126135 | − | 0.0916423i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.108209 | + | 0.101615i | 0.108209 | + | 0.101615i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0470631 | −0.0470631 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.61221 | − | 1.17134i | 1.61221 | − | 1.17134i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.181646 | − | 0.0229472i | −0.181646 | − | 0.0229472i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.0668769 | + | 0.205826i | 0.0668769 | + | 0.205826i | ||||
\(301\) | 0.0751750 | − | 0.231365i | 0.0751750 | − | 0.231365i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.28488 | − | 1.66006i | −2.28488 | − | 1.66006i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.354888 | + | 1.09223i | 0.354888 | + | 1.09223i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(308\) | −0.124591 | − | 0.0157395i | −0.124591 | − | 0.0157395i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.598617 | + | 1.84235i | 0.598617 | + | 1.84235i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0468099 | − | 0.144066i | 0.0468099 | − | 0.144066i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.07165 | 1.07165 | ||||||||
\(321\) | 2.19334 | − | 1.59355i | 2.19334 | − | 1.59355i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.694661 | + | 0.504701i | 0.694661 | + | 0.504701i | ||||
\(325\) | 0.102265 | + | 0.0742999i | 0.102265 | + | 0.0742999i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.168841 | − | 0.519639i | −0.168841 | − | 0.519639i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.148122 | − | 0.107617i | −0.148122 | − | 0.107617i | ||||
\(337\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.06720 | + | 1.50191i | −2.06720 | + | 1.50191i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.201592 | − | 0.146465i | 0.201592 | − | 0.146465i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.155911 | −0.155911 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.374763 | −0.374763 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41213 | + | 0.362574i | 1.41213 | + | 0.362574i | ||||
\(364\) | −0.106940 | −0.106940 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
1.00000 | \(0\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.341264 | + | 0.247943i | 0.341264 | + | 0.247943i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.0239838 | + | 0.0738147i | 0.0239838 | + | 0.0738147i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.33048 | −1.33048 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0573011 | + | 0.121771i | −0.0573011 | + | 0.121771i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.76401 | + | 1.28163i | −1.76401 | + | 1.28163i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.820513 | + | 0.770513i | 0.820513 | + | 0.770513i | ||||
\(397\) | −1.85955 | −1.85955 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.0458709 | − | 0.141176i | 0.0458709 | − | 0.141176i | ||||
\(401\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.598617 | + | 1.84235i | 0.598617 | + | 1.84235i | ||||
\(405\) | 0.744436 | − | 0.540864i | 0.744436 | − | 0.540864i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.188925 | + | 0.137262i | 0.188925 | + | 0.137262i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | −0.158736 | + | 0.115328i | −0.158736 | + | 0.115328i | ||||
\(421\) | 0.598617 | + | 1.84235i | 0.598617 | + | 1.84235i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.108877 | + | 0.0791038i | −0.108877 | + | 0.0791038i | ||||
\(428\) | −1.85955 | −1.85955 | ||||||||
\(429\) | 1.23173 | + | 0.155604i | 1.23173 | + | 0.155604i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(432\) | 0.0565777 | + | 0.174128i | 0.0565777 | + | 0.174128i | ||||
\(433\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.115808 | + | 0.356420i | −0.115808 | + | 0.356420i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.27485 | −1.27485 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.10783 | −1.10783 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.40281 | + | 1.01920i | 1.40281 | + | 1.01920i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | ||||
\(449\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.273190 | − | 0.256543i | −0.273190 | − | 0.256543i | ||||
\(452\) | 1.75261 | 1.75261 | ||||||||
\(453\) | 2.34039 | − | 1.70039i | 2.34039 | − | 1.70039i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0354140 | + | 0.108993i | −0.0354140 | + | 0.108993i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.41789 | − | 1.03016i | −1.41789 | − | 1.03016i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(468\) | 0.775441 | + | 0.563391i | 0.775441 | + | 0.563391i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.69755 | − | 0.933237i | 1.69755 | − | 0.933237i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.214967 | − | 0.661600i | 0.214967 | − | 0.661600i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(492\) | −0.168841 | − | 0.519639i | −0.168841 | − | 0.519639i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.05703 | − | 0.581107i | 1.05703 | − | 0.581107i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(500\) | 0.738289 | + | 0.536399i | 0.738289 | + | 0.536399i | ||||
\(501\) | −0.728969 | − | 0.529627i | −0.728969 | − | 0.529627i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.07597 | 2.07597 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.400711 | −0.400711 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.82427 | 2.82427 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(524\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(525\) | 0.00839847 | + | 0.0258478i | 0.00839847 | + | 0.0258478i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.273190 | − | 1.43211i | −0.273190 | − | 1.43211i | ||||
\(529\) | 1.00000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.646797 | − | 1.99064i | −0.646797 | − | 1.99064i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.258183 | − | 0.187581i | −0.258183 | − | 0.187581i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.615808 | + | 1.89526i | −0.615808 | + | 1.89526i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.50368 | − | 1.09249i | 1.50368 | − | 1.09249i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.976468 | + | 0.123357i | 0.976468 | + | 0.123357i | ||||
\(540\) | 0.196208 | 0.196208 | ||||||||
\(541\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.324914 | + | 0.236064i | 0.324914 | + | 0.236064i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.20623 | 1.20623 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.33456 | − | 0.969617i | 1.33456 | − | 0.969617i | ||||
\(560\) | 0.134579 | 0.134579 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.580394 | − | 1.78627i | 0.580394 | − | 1.78627i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.0872363 | + | 0.0633809i | 0.0872363 | + | 0.0633809i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | −0.620759 | − | 0.582932i | −0.620759 | − | 0.582932i | ||||
\(573\) | −1.24152 | −1.24152 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.347824 | − | 1.07049i | 0.347824 | − | 1.07049i | ||||
\(577\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.574354 | + | 1.76768i | −0.574354 | + | 1.76768i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.263146 | + | 0.559214i | −0.263146 | + | 0.559214i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.831004 | − | 0.603760i | 0.831004 | − | 0.603760i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(588\) | 1.16089 | + | 0.843439i | 1.16089 | + | 0.843439i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.98423 | −1.98423 | ||||||||
\(605\) | −0.996398 | + | 0.394502i | −0.996398 | + | 0.394502i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.585531 | −0.585531 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.0627905 | + | 0.193249i | −0.0627905 | + | 0.193249i | ||||
\(624\) | −0.383650 | − | 1.18075i | −0.383650 | − | 1.18075i | ||||
\(625\) | 0.911282 | − | 0.662085i | 0.911282 | − | 0.662085i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.06720 | − | 1.50191i | −2.06720 | − | 1.50191i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.728969 | + | 0.529627i | −0.728969 | + | 0.529627i | ||||
\(637\) | 0.838129 | 0.838129 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.935282 | − | 2.87850i | 0.935282 | − | 2.87850i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.348445 | + | 1.82662i | 0.348445 | + | 1.82662i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | ||||
\(656\) | −0.115808 | + | 0.356420i | −0.115808 | + | 0.356420i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.125581 | 0.125581 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(660\) | −1.55008 | − | 0.195821i | −1.55008 | − | 0.195821i | ||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.06320 | − | 0.134314i | −1.06320 | − | 0.134314i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.00839847 | − | 0.0258478i | 0.00839847 | − | 0.0258478i | ||||
\(676\) | 0.222357 | + | 0.161552i | 0.222357 | + | 0.161552i | ||||
\(677\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | ||||
\(689\) | −0.162633 | + | 0.500534i | −0.162633 | + | 0.500534i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.103041 | + | 0.0967619i | 0.103041 | + | 0.0967619i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.50368 | + | 1.09249i | 1.50368 | + | 1.09249i | ||||
\(700\) | 0.00576052 | − | 0.0177291i | 0.00576052 | − | 0.0177291i | ||||
\(701\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.425779 | + | 0.904827i | −0.425779 | + | 0.904827i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0751750 | + | 0.231365i | 0.0751750 | + | 0.231365i | ||||
\(708\) | −0.837780 | + | 2.57842i | −0.837780 | + | 2.57842i | ||||
\(709\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.799696 | + | 0.439637i | −0.799696 | + | 0.439637i | ||||
\(716\) | −1.27485 | −1.27485 | ||||||||
\(717\) | 1.50368 | − | 1.09249i | 1.50368 | − | 1.09249i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(720\) | −0.975863 | − | 0.709006i | −0.975863 | − | 0.709006i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.381145 | − | 1.17304i | −0.381145 | − | 1.17304i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.26401 | − | 0.918358i | −1.26401 | − | 0.918358i | ||||
\(733\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.24408 | − | 0.903875i | 1.24408 | − | 0.903875i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.233525 | −0.233525 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.657096 | + | 2.02233i | −0.657096 | + | 2.02233i | ||||
\(756\) | 0.00710509 | + | 0.0218672i | 0.00710509 | + | 0.0218672i | ||||
\(757\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.0145433 | + | 0.0447596i | −0.0145433 | + | 0.0447596i | ||||
\(764\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.489334 | + | 1.50602i | 0.489334 | + | 1.50602i | ||||
\(768\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | ||||
\(769\) | 1.75261 | 1.75261 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | ||||
\(773\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −1.33048 | −1.33048 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.304144 | − | 0.936058i | −0.304144 | − | 0.936058i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.656841 | + | 2.02155i | 0.656841 | + | 2.02155i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.220095 | 0.220095 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.912576 | −0.912576 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.298393 | + | 0.918358i | 0.298393 | + | 0.918358i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.47340 | − | 1.07049i | 1.47340 | − | 1.07049i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.168841 | + | 0.519639i | −0.168841 | + | 0.519639i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.89288 | −2.89288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0973807 | + | 0.0707512i | 0.0973807 | + | 0.0707512i | ||||
\(820\) | 0.324914 | + | 0.236064i | 0.324914 | + | 0.236064i | ||||
\(821\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
1.00000 | \(0\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.0921464 | + | 0.195821i | −0.0921464 | + | 0.195821i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.34039 | + | 1.70039i | 2.34039 | + | 1.70039i | ||||
\(832\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.662318 | 0.662318 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | ||||
\(845\) | 0.238289 | − | 0.173127i | 0.238289 | − | 0.173127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0800484 | − | 0.0967619i | −0.0800484 | − | 0.0967619i | ||||
\(848\) | 0.618034 | 0.618034 | ||||||||
\(849\) | −1.71963 | + | 1.24939i | −1.71963 | + | 1.24939i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | −1.67950 | + | 1.22023i | −1.67950 | + | 1.22023i | ||||
\(861\) | −0.0212032 | − | 0.0652568i | −0.0212032 | − | 0.0652568i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.0927151 | + | 0.0673615i | 0.0927151 | + | 0.0673615i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.781202 | + | 0.733597i | 0.781202 | + | 0.733597i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.35050 | + | 1.70774i | 2.35050 | + | 1.70774i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.115808 | + | 0.356420i | −0.115808 | + | 0.356420i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.160895 | + | 0.843439i | 0.160895 | + | 0.843439i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.422178 | + | 1.29933i | −0.422178 | + | 1.29933i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.135173 | + | 0.0982088i | −0.135173 | + | 0.0982088i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.354674 | 0.354674 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.41789 | − | 1.03016i | −1.41789 | − | 1.03016i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.673792 | − | 2.07372i | 0.673792 | − | 2.07372i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.303189 | − | 0.220280i | 0.303189 | − | 0.220280i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.35458 | + | 0.984161i | −1.35458 | + | 0.984161i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.278441 | + | 0.856954i | 0.278441 | + | 0.856954i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.0343075 | − | 0.179846i | −0.0343075 | − | 0.179846i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(933\) | −2.28488 | + | 1.66006i | −2.28488 | + | 1.66006i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | ||||
\(945\) | 0.0246400 | 0.0246400 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.06720 | − | 1.50191i | −2.06720 | − | 1.50191i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.738289 | − | 0.536399i | 0.738289 | − | 0.536399i | ||||
\(956\) | −1.27485 | −1.27485 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.482809 | + | 1.48593i | 0.482809 | + | 1.48593i | ||||
\(961\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.69334 | + | 1.23028i | 1.69334 | + | 1.23028i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.422178 | − | 1.29933i | −0.422178 | − | 1.29933i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(972\) | −0.443422 | + | 1.36471i | −0.443422 | + | 1.36471i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.0569496 | + | 0.175273i | −0.0569496 | + | 0.175273i | ||||
\(976\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | ||||
\(977\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.41789 | + | 0.779494i | −1.41789 | + | 0.779494i | ||||
\(980\) | −1.05475 | −1.05475 | ||||||||
\(981\) | 0.341264 | − | 0.247943i | 0.341264 | − | 0.247943i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.07165 | 1.07165 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(998\) | 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 | 1441.1.u.a.916.4 | yes | 20 | |
11.4 | even | 5 | inner | 1441.1.u.a.785.4 | ✓ | 20 | |
131.130 | odd | 2 | CM | 1441.1.u.a.916.4 | yes | 20 | |
1441.785 | odd | 10 | inner | 1441.1.u.a.785.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.1.u.a.785.4 | ✓ | 20 | 11.4 | even | 5 | inner | |
1441.1.u.a.785.4 | ✓ | 20 | 1441.785 | odd | 10 | inner | |
1441.1.u.a.916.4 | yes | 20 | 1.1 | even | 1 | trivial | |
1441.1.u.a.916.4 | yes | 20 | 131.130 | odd | 2 | CM |