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 | 785.2 | ||
Root | \(0.187381 + 0.982287i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1441.785 |
Dual form | 1441.1.u.a.916.2 |
$q$-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 \(\left(\mathbb{Z}/1441\mathbb{Z}\right)^\times\).
\(n\) | \(133\) | \(1311\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{5}\right)\) |
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 | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(3\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(4\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(5\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.222357 | + | 0.161552i | 0.222357 | + | 0.161552i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(12\) | −0.851559 | −0.851559 | ||||||||
\(13\) | 1.60528 | + | 1.16630i | 1.60528 | + | 1.16630i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0330462 | − | 0.101706i | −0.0330462 | − | 0.101706i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(17\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(20\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | ||||
\(21\) | 1.08561 | 1.08561 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.304144 | + | 0.936058i | −0.304144 | + | 0.936058i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.878275 | + | 0.638104i | −0.878275 | + | 0.638104i | ||||
\(28\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | ||||
\(29\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.362576 | + | 0.770513i | 0.362576 | + | 0.770513i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.129521 | + | 0.0941025i | 0.129521 | + | 0.0941025i | ||||
\(36\) | −0.0849327 | + | 0.261396i | −0.0849327 | + | 0.261396i | ||||
\(37\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.36699 | + | 0.993173i | −1.36699 | + | 0.993173i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.85955 | −1.85955 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(44\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(45\) | −0.0345157 | −0.0345157 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(48\) | −0.263146 | − | 0.809880i | −0.263146 | − | 0.809880i | ||||
\(49\) | −0.505828 | + | 0.367505i | −0.505828 | + | 0.367505i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | ||||
\(53\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0235315 | + | 0.123357i | −0.0235315 | + | 0.123357i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(60\) | 0.0865160 | − | 0.0628575i | 0.0865160 | − | 0.0628575i | ||||
\(61\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.108276 | − | 0.333240i | 0.108276 | − | 0.333240i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(65\) | −0.249182 | −0.249182 | ||||||||
\(66\) | 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 | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.678061 | − | 0.492640i | −0.678061 | − | 0.492640i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.11716 | − | 0.614163i | −1.11716 | − | 0.614163i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(80\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | ||||
\(81\) | −0.200741 | − | 0.617816i | −0.200741 | − | 0.617816i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(84\) | 0.335471 | + | 1.03247i | 0.335471 | + | 1.03247i | ||||
\(85\) | 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 | ||||||||
\(91\) | 0.781687 | − | 2.40578i | 0.781687 | − | 2.40578i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.272681 | − | 0.0344476i | 0.272681 | − | 0.0344476i | ||||
\(100\) | −0.984229 | −0.984229 | ||||||||
\(101\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.110295 | + | 0.0801338i | −0.110295 | + | 0.0801338i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(108\) | −0.878275 | − | 0.638104i | −0.878275 | − | 0.638104i | ||||
\(109\) | 1.75261 | 1.75261 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | ||||
\(113\) | 0.450527 | − | 1.38658i | 0.450527 | − | 1.38658i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.168526 | + | 0.518670i | 0.168526 | + | 0.518670i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.20742 | + | 0.877242i | 1.20742 | + | 0.877242i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.0770013 | − | 0.236986i | −0.0770013 | − | 0.236986i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.489334 | − | 1.50602i | 0.489334 | − | 1.50602i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | 1.00000 | ||||||||
\(132\) | −0.620759 | + | 0.582932i | −0.620759 | + | 0.582932i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.0421288 | − | 0.129659i | 0.0421288 | − | 0.129659i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 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 | \(0.400000\pi\) | |||||||
\(140\) | −0.0494726 | + | 0.152261i | −0.0494726 | + | 0.152261i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.96858 | − | 0.248690i | 1.96858 | − | 0.248690i | ||||
\(144\) | −0.274848 | −0.274848 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.164529 | − | 0.506367i | −0.164529 | − | 0.506367i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.115808 | + | 0.356420i | −0.115808 | + | 0.356420i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.36699 | − | 0.993173i | −1.36699 | − | 0.993173i | ||||
\(157\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.425779 | − | 0.309347i | 0.425779 | − | 0.309347i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(164\) | 1.75261 | 1.75261 | ||||||||
\(165\) | −0.0937119 | − | 0.0515186i | −0.0937119 | − | 0.0515186i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.907634 | + | 2.79341i | 0.907634 | + | 2.79341i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | ||||
\(173\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.25474 | 1.25474 | ||||||||
\(176\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(177\) | −0.912576 | −0.912576 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(180\) | −0.0106659 | − | 0.0328264i | −0.0106659 | − | 0.0328264i | ||||
\(181\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.0330462 | − | 0.101706i | −0.0330462 | − | 0.101706i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.11967 | + | 0.813486i | 1.11967 | + | 0.813486i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(192\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | ||||
\(193\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0655712 | − | 0.201807i | 0.0655712 | − | 0.201807i | ||||
\(196\) | −0.505828 | − | 0.367505i | −0.505828 | − | 0.367505i | ||||
\(197\) | 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 | ||||||||
\(205\) | 0.0680131 | + | 0.209323i | 0.0680131 | + | 0.209323i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.98423 | −1.98423 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(212\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.188925 | − | 0.137262i | 0.188925 | − | 0.137262i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.124591 | + | 0.0157395i | −0.124591 | + | 0.0157395i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.218850 | + | 0.159004i | −0.218850 | + | 0.159004i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
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 | ||||||||
\(231\) | 0.791374 | − | 0.743150i | 0.791374 | − | 0.743150i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(240\) | 0.0865160 | + | 0.0628575i | 0.0865160 | + | 0.0628575i | ||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.532426 | −0.532426 | ||||||||
\(244\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | ||||
\(245\) | 0.0242634 | − | 0.0746750i | 0.0242634 | − | 0.0746750i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(252\) | 0.350389 | 0.350389 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(257\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.0770013 | − | 0.236986i | −0.0770013 | − | 0.236986i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.851559 | −0.851559 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0776134 | 0.0776134 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.425779 | − | 1.31041i | 0.425779 | − | 1.31041i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.74270 | + | 1.26615i | 1.74270 | + | 1.26615i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.419064 | + | 0.890557i | 0.419064 | + | 0.890557i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.23432 | −2.23432 | ||||||||
\(288\) | 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 | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.108877 | − | 0.0791038i | −0.108877 | − | 0.0791038i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.203423 | + | 1.06638i | −0.203423 | + | 1.06638i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.258996 | − | 0.797108i | 0.258996 | − | 0.797108i | ||||
\(301\) | 0.732570 | + | 2.25462i | 0.732570 | + | 2.25462i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.28109 | + | 0.930769i | −1.28109 | + | 0.930769i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.00487338 | − | 0.0149987i | 0.00487338 | − | 0.0149987i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(308\) | 0.238883 | − | 1.25227i | 0.238883 | − | 1.25227i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0135974 | + | 0.0418486i | 0.0135974 | + | 0.0418486i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.125581 | 0.125581 | ||||||||
\(321\) | 0.738289 | + | 0.536399i | 0.738289 | + | 0.536399i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.525546 | − | 0.381832i | 0.525546 | − | 0.381832i | ||||
\(325\) | −1.57996 | + | 1.14791i | −1.57996 | + | 1.14791i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.461193 | + | 1.41941i | −0.461193 | + | 1.41941i | ||||
\(328\) | 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 | ||||||||
\(336\) | −0.878275 | + | 0.638104i | −0.878275 | + | 0.638104i | ||||
\(337\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.00441 | + | 0.729747i | 1.00441 | + | 0.729747i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.386520 | − | 0.280823i | −0.386520 | − | 0.280823i | ||||
\(344\) | 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 | ||||||||
\(351\) | −2.15409 | −2.15409 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.75261 | 1.75261 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(354\) | 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 | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.791759 | + | 0.313480i | 0.791759 | + | 0.313480i | ||||
\(364\) | 2.52959 | 2.52959 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.389705 | − | 0.283137i | 0.389705 | − | 0.283137i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.243474 | + | 0.749337i | −0.243474 | + | 0.749337i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.212193 | 0.212193 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.158834 | − | 0.0200654i | 0.158834 | − | 0.0200654i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.413484 | − | 0.300414i | −0.413484 | − | 0.300414i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.117025 | + | 0.248690i | 0.117025 | + | 0.248690i | ||||
\(397\) | 1.07165 | 1.07165 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.304144 | − | 0.936058i | −0.304144 | − | 0.936058i | ||||
\(401\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | ||||
\(405\) | 0.0659986 | + | 0.0479508i | 0.0659986 | + | 0.0479508i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.10528 | − | 0.803030i | 1.10528 | − | 0.803030i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | −0.110295 | − | 0.0801338i | −0.110295 | − | 0.0801338i | ||||
\(421\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.129521 | + | 0.0941025i | 0.129521 | + | 0.0941025i | ||||
\(428\) | 1.07165 | 1.07165 | ||||||||
\(429\) | −0.316616 | + | 1.65976i | −0.316616 | + | 1.65976i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.60528 | + | 1.16630i | 1.60528 | + | 1.16630i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(432\) | 0.335471 | − | 1.03247i | 0.335471 | − | 1.03247i | ||||
\(433\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.93717 | 1.93717 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.171845 | −0.171845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.164388 | − | 0.119435i | 0.164388 | − | 0.119435i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | ||||
\(449\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.746226 | − | 1.58581i | −0.746226 | − | 1.58581i | ||||
\(452\) | 1.45794 | 1.45794 | ||||||||
\(453\) | −0.258183 | − | 0.187581i | −0.258183 | − | 0.187581i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0981650 | + | 0.302121i | 0.0981650 | + | 0.302121i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(458\) | 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 | ||||||||
\(467\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(468\) | −0.441207 | + | 0.320555i | −0.441207 | + | 0.320555i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.35556 | + | 1.27295i | −1.35556 | + | 1.27295i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0524913 | − | 0.161552i | −0.0524913 | − | 0.161552i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(492\) | −0.461193 | + | 1.41941i | −0.461193 | + | 1.41941i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.0251609 | + | 0.0236276i | −0.0251609 | + | 0.0236276i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(500\) | 0.201592 | − | 0.146465i | 0.201592 | − | 0.146465i | ||||
\(501\) | 0.425779 | − | 0.309347i | 0.425779 | − | 0.309347i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.233525 | −0.233525 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.50117 | −2.50117 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.58352 | 1.58352 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(524\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(525\) | −0.330181 | + | 1.01619i | −0.330181 | + | 1.01619i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.746226 | − | 0.410241i | −0.746226 | − | 0.410241i | ||||
\(529\) | 1.00000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.0910184 | + | 0.280126i | −0.0910184 | + | 0.280126i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.81343 | − | 2.04407i | 2.81343 | − | 2.04407i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.0415873 | + | 0.127993i | 0.0415873 | + | 0.127993i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.33456 | + | 0.969617i | 1.33456 | + | 0.969617i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.117158 | + | 0.614163i | −0.117158 | + | 0.614163i | ||||
\(540\) | 0.136332 | 0.136332 | ||||||||
\(541\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.178061 | + | 0.129369i | −0.178061 | + | 0.129369i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0345157 | −0.0345157 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.98509 | − | 2.16880i | −2.98509 | − | 2.16880i | ||||
\(560\) | −0.160097 | −0.160097 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.0565777 | + | 0.174128i | 0.0565777 | + | 0.174128i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.669991 | + | 0.486777i | −0.669991 | + | 0.486777i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0.844844 | + | 1.79538i | 0.844844 | + | 1.79538i | ||||
\(573\) | 1.68969 | 1.68969 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.0849327 | − | 0.261396i | −0.0849327 | − | 0.261396i | ||||
\(577\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.509758 | − | 1.56887i | −0.509758 | − | 1.56887i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.613161 | + | 0.0774602i | −0.613161 | + | 0.0774602i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0554072 | − | 0.0402557i | −0.0554072 | − | 0.0402557i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(588\) | 0.430742 | − | 0.312952i | 0.430742 | − | 0.312952i | ||||
\(589\) | 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 | ||||||||
\(599\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.374763 | −0.374763 | ||||||||
\(605\) | 0.0672897 | + | 0.106032i | 0.0672897 | + | 0.106032i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.187424 | −0.187424 | ||||||||
\(616\) | 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 | ||||||||
\(623\) | 0.637424 | + | 1.96179i | 0.637424 | + | 1.96179i | ||||
\(624\) | 0.522142 | − | 1.60699i | 0.522142 | − | 1.60699i | ||||
\(625\) | −0.770942 | − | 0.560122i | −0.770942 | − | 0.560122i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.00441 | − | 0.729747i | 1.00441 | − | 0.729747i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.425779 | + | 0.309347i | 0.425779 | + | 0.309347i | ||||
\(637\) | −1.24061 | −1.24061 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0614511 | + | 0.189127i | 0.0614511 | + | 0.189127i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.60528 | + | 1.16630i | 1.60528 | + | 1.16630i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.939097 | + | 0.516273i | 0.939097 | + | 0.516273i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.331159 | + | 1.01920i | 0.331159 | + | 1.01920i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | ||||
\(656\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.27485 | −1.27485 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(660\) | 0.0200385 | − | 0.105045i | 0.0200385 | − | 0.105045i | ||||
\(661\) | 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 | ||||||||
\(671\) | −0.0235315 | + | 0.123357i | −0.0235315 | + | 0.123357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.330181 | − | 1.01619i | −0.330181 | − | 1.01619i | ||||
\(676\) | −2.37622 | + | 1.72642i | −2.37622 | + | 1.72642i | ||||
\(677\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 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 | ||||||||
\(688\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | ||||
\(689\) | −0.378954 | − | 1.16630i | −0.378954 | − | 1.16630i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.149189 | − | 0.317042i | −0.149189 | − | 0.317042i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.33456 | − | 0.969617i | 1.33456 | − | 0.969617i | ||||
\(700\) | 0.387737 | + | 1.19333i | 0.387737 | + | 1.19333i | ||||
\(701\) | −0.115808 | + | 0.356420i | −0.115808 | + | 0.356420i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.732570 | − | 2.25462i | 0.732570 | − | 2.25462i | ||||
\(708\) | −0.282001 | − | 0.867911i | −0.282001 | − | 0.867911i | ||||
\(709\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.181646 | + | 0.170577i | −0.181646 | + | 0.170577i | ||||
\(716\) | 1.93717 | 1.93717 | ||||||||
\(717\) | 1.33456 | + | 0.969617i | 1.33456 | + | 0.969617i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(720\) | 0.0279238 | − | 0.0202878i | 0.0279238 | − | 0.0202878i | ||||
\(721\) | 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 | ||||||||
\(729\) | 0.340847 | − | 1.04902i | 0.340847 | − | 1.04902i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.0865160 | − | 0.0628575i | 0.0865160 | − | 0.0628575i | ||||
\(733\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0540930 | + | 0.0393009i | 0.0540930 | + | 0.0393009i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.36620 | −1.36620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.0145433 | − | 0.0447596i | −0.0145433 | − | 0.0447596i | ||||
\(756\) | −0.427675 | + | 1.31625i | −0.427675 | + | 1.31625i | ||||
\(757\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −0.690441 | − | 2.12496i | −0.690441 | − | 2.12496i | ||||
\(764\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.657096 | + | 2.02233i | −0.657096 | + | 2.02233i | ||||
\(768\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | ||||
\(769\) | 1.45794 | 1.45794 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | ||||
\(773\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0.212193 | 0.212193 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.193209 | − | 0.594636i | 0.193209 | − | 0.594636i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.224084 | − | 0.689661i | 0.224084 | − | 0.689661i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.85865 | −1.85865 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.249182 | −0.249182 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0204236 | + | 0.0628575i | −0.0204236 | + | 0.0628575i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.359781 | − | 0.261396i | −0.359781 | − | 0.261396i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.461193 | − | 1.41941i | −0.461193 | − | 1.41941i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.319132 | 0.319132 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.562471 | − | 0.408659i | 0.562471 | − | 0.408659i | ||||
\(820\) | −0.178061 | + | 0.129369i | −0.178061 | + | 0.129369i | ||||
\(821\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.831520 | + | 0.105045i | −0.831520 | + | 0.105045i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.258183 | + | 0.187581i | −0.258183 | + | 0.187581i | ||||
\(832\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.0776134 | 0.0776134 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.500000 | + | 1.53884i | −0.500000 | + | 1.53884i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.450527 | − | 1.38658i | 0.450527 | − | 1.38658i | ||||
\(845\) | −0.298408 | − | 0.216806i | −0.298408 | − | 0.216806i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.23480 | + | 0.317042i | −1.23480 | + | 0.317042i | ||||
\(848\) | 0.618034 | 0.618034 | ||||||||
\(849\) | −0.586660 | − | 0.426234i | −0.586660 | − | 0.426234i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 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 | 0 | ||||||||
\(857\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0.188925 | + | 0.137262i | 0.188925 | + | 0.137262i | ||||
\(861\) | 0.587951 | − | 1.80953i | 0.587951 | − | 1.80953i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.256999 | + | 0.186721i | −0.256999 | + | 0.186721i | ||||
\(876\) | 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 | ||||||||
\(880\) | −0.0534698 | − | 0.113629i | −0.0534698 | − | 0.113629i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.0927151 | − | 0.0673615i | 0.0927151 | − | 0.0673615i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.569258 | − | 0.312952i | −0.569258 | − | 0.312952i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.0751750 | + | 0.231365i | 0.0751750 | + | 0.231365i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.218850 | − | 0.159004i | −0.218850 | − | 0.159004i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.01875 | −2.01875 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.157937 | + | 0.486080i | 0.157937 | + | 0.486080i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.41789 | − | 1.03016i | −1.41789 | − | 1.03016i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.0108648 | + | 0.00789371i | 0.0108648 | + | 0.00789371i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.162633 | + | 0.500534i | −0.162633 | + | 0.500534i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.951325 | + | 0.522996i | 0.951325 | + | 0.522996i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | ||||
\(933\) | −1.28109 | − | 0.930769i | −1.28109 | − | 0.930769i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | ||||
\(945\) | −0.173802 | −0.173802 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.00441 | − | 0.729747i | 1.00441 | − | 0.729747i | ||||
\(952\) | 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 | ||||||||
\(955\) | 0.201592 | + | 0.146465i | 0.201592 | + | 0.146465i | ||||
\(956\) | 1.93717 | 1.93717 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.0330462 | + | 0.101706i | −0.0330462 | + | 0.101706i | ||||
\(961\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.238289 | − | 0.173127i | 0.238289 | − | 0.173127i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0751750 | − | 0.231365i | 0.0751750 | − | 0.231365i | ||||
\(966\) | 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 | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(972\) | −0.164529 | − | 0.506367i | −0.164529 | − | 0.506367i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.513908 | − | 1.58165i | −0.513908 | − | 1.58165i | ||||
\(976\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | ||||
\(977\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.17950 | + | 1.10762i | −1.17950 | + | 1.10762i | ||||
\(980\) | 0.0785180 | 0.0785180 | ||||||||
\(981\) | 0.389705 | + | 0.283137i | 0.389705 | + | 0.283137i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.125581 | 0.125581 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
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 | 1441.1.u.a.785.2 | ✓ | 20 | |
11.3 | even | 5 | inner | 1441.1.u.a.916.2 | yes | 20 | |
131.130 | odd | 2 | CM | 1441.1.u.a.785.2 | ✓ | 20 | |
1441.916 | odd | 10 | inner | 1441.1.u.a.916.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.1.u.a.785.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
1441.1.u.a.785.2 | ✓ | 20 | 131.130 | odd | 2 | CM | |
1441.1.u.a.916.2 | yes | 20 | 11.3 | even | 5 | inner | |
1441.1.u.a.916.2 | yes | 20 | 1441.916 | odd | 10 | inner |