Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [869,1,Mod(157,869)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(869, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 5]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("869.157");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 869 = 11 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 869.j (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: | \(0.433687495978\) |
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 | 157.4 | ||
Root | \(0.929776 + 0.368125i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 869.157 |
Dual form | 869.1.j.a.631.4 |
$q$-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 \(\left(\mathbb{Z}/869\mathbb{Z}\right)^\times\).
\(n\) | \(475\) | \(793\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(3\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(4\) | 0.193209 | − | 0.594636i | 0.193209 | − | 0.594636i | ||||
\(5\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(8\) | 0.147638 | + | 0.454382i | 0.147638 | + | 0.454382i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(10\) | 1.08561 | 1.08561 | ||||||||
\(11\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50441 | − | 1.09302i | 1.50441 | − | 1.09302i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.998582 | + | 0.725513i | 0.998582 | + | 0.725513i | ||||
\(17\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(18\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | ||||
\(19\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(20\) | 0.430742 | − | 0.312952i | 0.430742 | − | 0.312952i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0800484 | + | 1.27233i | −0.0800484 | + | 1.27233i | ||||
\(23\) | −1.98423 | −1.98423 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0849327 | − | 0.261396i | −0.0849327 | − | 0.261396i | ||||
\(26\) | 0.732570 | − | 2.25462i | 0.732570 | − | 2.25462i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(32\) | 1.09580 | 1.09580 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.193209 | + | 0.594636i | 0.193209 | + | 0.594636i | ||||
\(37\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(38\) | −2.04648 | − | 1.48686i | −2.04648 | − | 1.48686i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.125722 | + | 0.386933i | −0.125722 | + | 0.386933i | ||||
\(41\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0.335019 | + | 0.527905i | 0.335019 | + | 0.527905i | ||||
\(45\) | −0.851559 | −0.851559 | ||||||||
\(46\) | −2.04648 | + | 1.48686i | −2.04648 | + | 1.48686i | ||||
\(47\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(50\) | −0.283471 | − | 0.205954i | −0.283471 | − | 0.205954i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.359282 | − | 1.10576i | −0.359282 | − | 1.10576i | ||||
\(53\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.824805 | + | 0.211774i | −0.824805 | + | 0.211774i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(62\) | −0.0494726 | + | 0.152261i | −0.0494726 | + | 0.152261i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.131596 | − | 0.0956103i | 0.131596 | − | 0.0956103i | ||||
\(65\) | 1.58352 | 1.58352 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.45794 | 1.45794 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(72\) | −0.386520 | − | 0.280823i | −0.386520 | − | 0.280823i | ||||
\(73\) | −0.115808 | + | 0.356420i | −0.115808 | + | 0.356420i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.24061 | −1.24061 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(80\) | 0.324805 | + | 0.999648i | 0.324805 | + | 0.999648i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.444215 | − | 0.175877i | −0.444215 | − | 0.175877i | ||||
\(89\) | 1.07165 | 1.07165 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(90\) | −0.878275 | + | 0.638104i | −0.878275 | + | 0.638104i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.383371 | + | 1.17989i | −0.383371 | + | 1.17989i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.522142 | − | 1.60699i | 0.522142 | − | 1.60699i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.41789 | + | 1.03016i | −1.41789 | + | 1.03016i | −0.425779 | + | 0.904827i | \(0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(98\) | −1.27485 | −1.27485 | ||||||||
\(99\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(100\) | −0.171845 | −0.171845 | ||||||||
\(101\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(104\) | 0.718755 | + | 0.522206i | 0.718755 | + | 0.522206i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | −0.691992 | + | 0.836475i | −0.691992 | + | 0.836475i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.36699 | − | 0.993173i | −1.36699 | − | 0.993173i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.187381 | − | 0.982287i | −0.187381 | − | 0.982287i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0242634 | + | 0.0746750i | 0.0242634 | + | 0.0746750i | ||||
\(125\) | 0.335471 | − | 1.03247i | 0.335471 | − | 1.03247i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(128\) | −0.274540 | + | 0.844947i | −0.274540 | + | 0.844947i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.63320 | − | 1.18659i | 1.63320 | − | 1.18659i | ||||
\(131\) | −0.374763 | −0.374763 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.50368 | − | 1.09249i | 1.50368 | − | 1.09249i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 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 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.116762 | + | 1.85588i | −0.116762 | + | 1.85588i | ||||
\(144\) | −1.23432 | −1.23432 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.147638 | + | 0.454382i | 0.147638 | + | 0.454382i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.450527 | + | 1.38658i | 0.450527 | + | 1.38658i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(152\) | 0.766945 | − | 0.557218i | 0.766945 | − | 0.557218i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.106940 | −0.106940 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(158\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.754924 | + | 0.548484i | 0.754924 | + | 0.548484i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | ||||
\(163\) | −1.56720 | + | 1.13864i | −1.56720 | + | 1.13864i | −0.637424 | + | 0.770513i | \(0.720000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.06275 | 2.06275 | ||||||||
\(167\) | −0.101597 | + | 0.0738147i | −0.101597 | + | 0.0738147i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.759544 | − | 2.33764i | 0.759544 | − | 2.33764i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.60528 | + | 1.16630i | 1.60528 | + | 1.16630i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.19554 | + | 0.306962i | −1.19554 | + | 0.306962i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.10528 | − | 0.803030i | 1.10528 | − | 0.803030i | ||||
\(179\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(180\) | −0.164529 | + | 0.506367i | −0.164529 | + | 0.506367i | ||||
\(181\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.292947 | − | 0.901598i | −0.292947 | − | 0.901598i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.665652 | − | 2.04867i | −0.665652 | − | 2.04867i | ||||
\(191\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(194\) | −0.690441 | + | 2.12496i | −0.690441 | + | 2.12496i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.505828 | + | 0.367505i | −0.505828 | + | 0.367505i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | −0.683098 | − | 1.07639i | −0.683098 | − | 1.07639i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0.106234 | − | 0.0771838i | 0.106234 | − | 0.0771838i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.422178 | + | 1.29933i | −0.422178 | + | 1.29933i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | ||||
\(208\) | 2.29528 | 2.29528 | ||||||||
\(209\) | 1.84489 | + | 0.730444i | 1.84489 | + | 0.730444i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0334313 | + | 0.531376i | −0.0334313 | + | 0.531376i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.500000 | − | 1.53884i | −0.500000 | − | 1.53884i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.222357 | + | 0.161552i | 0.222357 | + | 0.161552i | ||||
\(226\) | 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 | \(0.800000\pi\) | |||||||
\(230\) | −2.15409 | −2.15409 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(234\) | 0.732570 | + | 2.25462i | 0.732570 | + | 2.25462i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.263146 | − | 0.809880i | −0.263146 | − | 0.809880i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.93717 | 1.93717 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(242\) | −0.929324 | − | 0.872693i | −0.929324 | − | 0.872693i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.263146 | − | 0.809880i | −0.263146 | − | 0.809880i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.98509 | − | 2.16880i | −2.98509 | − | 2.16880i | ||||
\(248\) | −0.0485396 | − | 0.0352661i | −0.0485396 | − | 0.0352661i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.427675 | − | 1.31625i | −0.427675 | − | 1.31625i | ||||
\(251\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.26480 | − | 1.52888i | 1.26480 | − | 1.52888i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.400262 | + | 1.23188i | 0.400262 | + | 1.23188i | ||||
\(257\) | −0.574633 | + | 1.76854i | −0.574633 | + | 1.76854i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.305950 | − | 0.941617i | 0.305950 | − | 0.941617i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.386520 | + | 0.280823i | −0.386520 | + | 0.280823i | ||||
\(263\) | 1.93717 | 1.93717 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.281687 | − | 0.866942i | 0.281687 | − | 0.866942i | ||||
\(269\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.255547 | + | 0.101178i | 0.255547 | + | 0.101178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.688925 | + | 0.500534i | 0.688925 | + | 0.500534i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.27026 | + | 2.00160i | 1.27026 | + | 2.00160i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.886520 | + | 0.644095i | −0.886520 | + | 0.644095i | ||||
\(289\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.189565 | + | 0.137727i | 0.189565 | + | 0.137727i | ||||
\(293\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.98509 | + | 2.16880i | −2.98509 | + | 2.16880i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.50368 | + | 1.09249i | 1.50368 | + | 1.09249i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.756834 | − | 2.32929i | 0.756834 | − | 2.32929i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.110295 | + | 0.0801338i | −0.110295 | + | 0.0801338i | ||||
\(311\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.193209 | + | 0.594636i | 0.193209 | + | 0.594636i | ||||
\(317\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.138516 | 0.138516 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.505828 | − | 0.367505i | −0.505828 | − | 0.367505i | ||||
\(325\) | −0.413484 | − | 0.300414i | −0.413484 | − | 0.300414i | ||||
\(326\) | −0.763146 | + | 2.34872i | −0.763146 | + | 2.34872i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0.818446 | − | 0.594636i | 0.818446 | − | 0.594636i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.0494726 | + | 0.152261i | −0.0494726 | + | 0.152261i | ||||
\(335\) | 1.00441 | + | 0.729747i | 1.00441 | + | 0.729747i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(338\) | −0.968304 | − | 2.98013i | −0.968304 | − | 2.98013i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.00788530 | − | 0.125333i | 0.00788530 | − | 0.125333i | ||||
\(342\) | 2.52959 | 2.52959 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.17950 | − | 0.856954i | −1.17950 | − | 0.856954i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.698489 | + | 0.844328i | −0.698489 | + | 0.844328i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.207053 | − | 0.637244i | 0.207053 | − | 0.637244i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.66880 | − | 1.21245i | −1.66880 | − | 1.21245i | ||||
\(359\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(360\) | −0.125722 | − | 0.386933i | −0.125722 | − | 0.386933i | ||||
\(361\) | −2.37622 | + | 1.72642i | −2.37622 | + | 1.72642i | ||||
\(362\) | 2.37065 | 2.37065 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.258183 | + | 0.187581i | −0.258183 | + | 0.187581i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(368\) | −1.98142 | − | 1.43958i | −1.98142 | − | 1.43958i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(380\) | −0.854691 | − | 0.620969i | −0.854691 | − | 0.620969i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.338621 | + | 1.04217i | 0.338621 | + | 1.04217i | ||||
\(389\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.147638 | − | 0.454382i | 0.147638 | − | 0.454382i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.851559 | −0.851559 | ||||||||
\(396\) | −0.581331 | − | 0.230165i | −0.581331 | − | 0.230165i | ||||
\(397\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.104834 | − | 0.322645i | 0.104834 | − | 0.322645i | ||||
\(401\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0721631 | + | 0.222095i | −0.0721631 | + | 0.222095i | ||||
\(404\) | 0.207053 | + | 0.637244i | 0.207053 | + | 0.637244i | ||||
\(405\) | 0.688925 | − | 0.500534i | 0.688925 | − | 0.500534i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.781687 | − | 2.40578i | 0.781687 | − | 2.40578i | ||||
\(415\) | 0.425779 | + | 1.31041i | 0.425779 | + | 1.31041i | ||||
\(416\) | 1.64853 | − | 1.19773i | 1.64853 | − | 1.19773i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.45012 | − | 0.629084i | 2.45012 | − | 0.629084i | ||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.303189 | − | 0.220280i | 0.303189 | − | 0.220280i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.21665 | + | 3.74447i | 1.21665 | + | 3.74447i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.75261 | 1.75261 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(440\) | −0.217999 | − | 0.343511i | −0.217999 | − | 0.343511i | ||||
\(441\) | 1.00000 | 1.00000 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.738289 | + | 0.536399i | 0.738289 | + | 0.536399i | ||||
\(446\) | −1.66880 | − | 1.21245i | −1.66880 | − | 1.21245i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(450\) | 0.350389 | 0.350389 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.854691 | + | 0.620969i | −0.854691 | + | 0.620969i | ||||
\(461\) | 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 | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(468\) | 0.940613 | + | 0.683396i | 0.940613 | + | 0.683396i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.441207 | + | 0.320555i | −0.441207 | + | 0.320555i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.878275 | − | 0.638104i | −0.878275 | − | 0.638104i | ||||
\(479\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.99794 | − | 1.45159i | 1.99794 | − | 1.45159i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.620307 | − | 0.0783630i | −0.620307 | − | 0.0783630i | ||||
\(485\) | −1.49245 | −1.49245 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.574633 | − | 1.76854i | −0.574633 | − | 1.76854i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.0627905 | − | 0.998027i | \(-0.480000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.878275 | − | 0.638104i | −0.878275 | − | 0.638104i | ||||
\(491\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −4.70391 | −4.70391 | ||||||||
\(495\) | 0.542804 | − | 0.656137i | 0.542804 | − | 0.656137i | ||||
\(496\) | −0.155007 | −0.155007 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.393950 | + | 1.21245i | −0.393950 | + | 1.21245i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(500\) | −0.549130 | − | 0.398967i | −0.549130 | − | 0.398967i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.912576 | −0.912576 | ||||||||
\(506\) | 0.158834 | − | 2.52460i | 0.158834 | − | 2.52460i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 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 | ||||||||
\(512\) | 0.617158 | + | 0.448391i | 0.617158 | + | 0.448391i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.732570 | + | 2.25462i | 0.732570 | + | 2.25462i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.233787 | + | 0.719522i | 0.233787 | + | 0.719522i | ||||
\(521\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.866986 | − | 0.629902i | −0.866986 | − | 0.629902i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(524\) | −0.0724075 | + | 0.222847i | −0.0724075 | + | 0.222847i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.99794 | − | 1.45159i | 1.99794 | − | 1.45159i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.93717 | 2.93717 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.215246 | + | 0.662460i | 0.215246 | + | 0.662460i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.85865 | −1.85865 | ||||||||
\(539\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.598617 | + | 1.84235i | 0.598617 | + | 1.84235i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.339381 | − | 0.0871383i | 0.339381 | − | 0.0871383i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.335471 | − | 1.03247i | 0.335471 | − | 1.03247i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | −0.187381 | + | 0.982287i | \(0.560000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(558\) | −0.0494726 | − | 0.152261i | −0.0494726 | − | 0.152261i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.08561 | 1.08561 | ||||||||
\(563\) | −1.61803 | + | 1.17557i | −1.61803 | + | 1.17557i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.129521 | + | 0.0941025i | 0.129521 | + | 0.0941025i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.125581 | 0.125581 | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(572\) | 1.08102 | + | 0.428004i | 1.08102 | + | 0.428004i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.168526 | + | 0.518670i | 0.168526 | + | 0.518670i | ||||
\(576\) | −0.0502653 | + | 0.154701i | −0.0502653 | + | 0.154701i | ||||
\(577\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(578\) | 1.03137 | + | 0.749337i | 1.03137 | + | 0.749337i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.179049 | −0.179049 | ||||||||
\(585\) | −1.28109 | + | 0.930769i | −1.28109 | + | 0.930769i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.201592 | + | 0.146465i | 0.201592 | + | 0.146465i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.851559 | −0.851559 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.45359 | + | 4.47368i | −1.45359 | + | 4.47368i | ||||
\(599\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | ||||
\(604\) | 0.911557 | 0.911557 | ||||||||
\(605\) | 0.362576 | − | 0.770513i | 0.362576 | − | 0.770513i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(608\) | −0.671901 | − | 2.06790i | −0.671901 | − | 2.06790i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.85955 | −1.85955 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(620\) | −0.0206617 | + | 0.0635902i | −0.0206617 | + | 0.0635902i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.525546 | − | 0.381832i | 0.525546 | − | 0.381832i | ||||
\(626\) | −0.160097 | −0.160097 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(632\) | −0.386520 | − | 0.280823i | −0.386520 | − | 0.280823i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.243474 | + | 0.749337i | −0.243474 | + | 0.749337i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.85955 | −1.85955 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.612062 | + | 0.444689i | −0.612062 | + | 0.444689i | ||||
\(641\) | −0.613161 | − | 1.88711i | −0.613161 | − | 1.88711i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.303189 | + | 0.220280i | 0.303189 | + | 0.220280i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(648\) | 0.477765 | 0.477765 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −0.651568 | −0.651568 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.374278 | + | 1.15191i | 0.374278 | + | 1.15191i | ||||
\(653\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
0.968583 | − | 0.248690i | \(-0.0800000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.258183 | − | 0.187581i | −0.258183 | − | 0.187581i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.238883 | + | 0.735205i | −0.238883 | + | 0.735205i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.0242634 | + | 0.0746750i | 0.0242634 | + | 0.0746750i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.58275 | 1.58275 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(674\) | −0.690441 | − | 2.12496i | −0.690441 | − | 2.12496i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.24329 | − | 0.903305i | −1.24329 | − | 0.903305i | ||||
\(677\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0857841 | − | 0.135174i | −0.0857841 | − | 0.135174i | ||||
\(683\) | −0.374763 | −0.374763 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(684\) | 1.00368 | − | 0.729215i | 1.00368 | − | 0.729215i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.85865 | −1.85865 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.0102136 | + | 0.162341i | −0.0102136 | + | 0.162341i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(712\) | 0.158216 | + | 0.486940i | 0.158216 | + | 0.486940i | ||||
\(713\) | 0.201592 | − | 0.146465i | 0.201592 | − | 0.146465i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.00937 | + | 1.22012i | −1.00937 | + | 1.22012i | ||||
\(716\) | −1.01166 | −1.01166 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(720\) | −0.850351 | − | 0.617816i | −0.850351 | − | 0.617816i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.15710 | + | 3.56117i | −1.15710 | + | 3.56117i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.940613 | − | 0.683396i | 0.940613 | − | 0.683396i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(730\) | −0.125722 | + | 0.386933i | −0.125722 | + | 0.386933i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.450527 | − | 1.38658i | 0.450527 | − | 1.38658i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(734\) | −0.422178 | − | 1.29933i | −0.422178 | − | 1.29933i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.17432 | −2.17432 | ||||||||
\(737\) | −0.929324 | + | 1.12336i | −0.929324 | + | 1.12336i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.50441 | + | 1.09302i | 1.50441 | + | 1.09302i | 0.968583 | + | 0.248690i | \(0.0800000\pi\) |
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.61803 | −1.61803 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.393950 | − | 1.21245i | −0.393950 | − | 1.21245i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.383650 | + | 1.18075i | −0.383650 | + | 1.18075i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.807274 | 0.807274 | ||||||||
\(761\) | 1.60528 | − | 1.16630i | 1.60528 | − | 1.16630i | 0.728969 | − | 0.684547i | \(-0.240000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.502226 | − | 1.54569i | 0.502226 | − | 1.54569i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.115808 | − | 0.356420i | −0.115808 | − | 0.356420i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0279238 | + | 0.0202878i | 0.0279238 | + | 0.0202878i | ||||
\(776\) | −0.677421 | − | 0.492175i | −0.677421 | − | 0.492175i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0494726 | − | 0.152261i | −0.0494726 | − | 0.152261i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.381424 | − | 1.17390i | −0.381424 | − | 1.17390i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.41789 | − | 1.03016i | −1.41789 | − | 1.03016i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.878275 | + | 0.638104i | −0.878275 | + | 0.638104i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.462756 | − | 0.118815i | 0.462756 | − | 0.118815i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.66880 | + | 1.21245i | −1.66880 | + | 1.21245i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.0930692 | − | 0.286438i | −0.0930692 | − | 0.286438i | ||||
\(801\) | −0.866986 | + | 0.629902i | −0.866986 | + | 0.629902i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.200808 | − | 0.316423i | −0.200808 | − | 0.316423i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.0919969 | + | 0.283137i | 0.0919969 | + | 0.283137i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.414216 | − | 0.300945i | −0.414216 | − | 0.300945i | ||||
\(809\) | −1.56720 | − | 1.13864i | −1.56720 | − | 1.13864i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
−0.637424 | − | 0.770513i | \(-0.720000\pi\) | |||||||
\(810\) | 0.335471 | − | 1.03247i | 0.335471 | − | 1.03247i | ||||
\(811\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | 1.00000 | \(0\) | ||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.64961 | −1.64961 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.0388067 | − | 0.119435i | 0.0388067 | − | 0.119435i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(828\) | −0.383371 | − | 1.17989i | −0.383371 | − | 1.17989i | ||||
\(829\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(830\) | 1.42108 | + | 1.03247i | 1.42108 | + | 1.03247i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.0934710 | − | 0.287674i | 0.0934710 | − | 0.287674i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.106940 | −0.106940 | ||||||||
\(836\) | 0.790797 | − | 0.955910i | 0.790797 | − | 0.955910i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.541587 | + | 1.66683i | 0.541587 | + | 1.66683i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(842\) | 1.80760 | + | 1.31330i | 1.80760 | + | 1.31330i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.69334 | − | 1.23028i | 1.69334 | − | 1.23028i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0.522142 | + | 1.60699i | 0.522142 | + | 1.60699i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.98423 | −1.98423 | −0.992115 | − | 0.125333i | \(-0.960000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.147638 | − | 0.454382i | 0.147638 | − | 0.454382i | ||||
\(863\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.781687 | + | 2.40578i | 0.781687 | + | 2.40578i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.19334 | − | 1.59355i | 2.19334 | − | 1.59355i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.541587 | − | 1.66683i | 0.541587 | − | 1.66683i | ||||
\(874\) | 4.06069 | + | 2.95026i | 4.06069 | + | 2.95026i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.0388067 | + | 0.119435i | 0.0388067 | + | 0.119435i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(878\) | 1.80760 | − | 1.31330i | 1.80760 | − | 1.31330i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.977281 | − | 0.386933i | −0.977281 | − | 0.386933i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 1.03137 | − | 0.749337i | 1.03137 | − | 0.749337i | ||||
\(883\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.263146 | + | 0.809880i | −0.263146 | + | 0.809880i | 0.728969 | + | 0.684547i | \(0.240000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.16340 | 1.16340 | ||||||||
\(891\) | 0.535827 | + | 0.844328i | 0.535827 | + | 0.844328i | ||||
\(892\) | −1.01166 | −1.01166 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.425779 | − | 1.31041i | 0.425779 | − | 1.31041i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.139026 | − | 0.101008i | 0.139026 | − | 0.101008i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.489334 | + | 1.50602i | 0.489334 | + | 1.50602i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.331159 | − | 1.01920i | 0.331159 | − | 1.01920i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.17950 | + | 0.856954i | −1.17950 | + | 0.856954i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.56720 | + | 0.402389i | −1.56720 | + | 0.402389i | ||||
\(914\) | −1.36620 | −1.36620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.101597 | − | 0.0738147i | −0.101597 | − | 0.0738147i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(920\) | 0.249461 | − | 0.767763i | 0.249461 | − | 0.767763i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.613161 | + | 1.88711i | −0.613161 | + | 1.88711i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.62524 | 1.62524 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.888430 | −0.888430 | ||||||||
\(937\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.215351 | + | 0.662783i | 0.215351 | + | 0.662783i | ||||
\(950\) | −0.214845 | + | 0.661225i | −0.214845 | + | 0.661225i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.598617 | − | 1.84235i | 0.598617 | − | 1.84235i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.532426 | −0.532426 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.06275 | 2.06275 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.304144 | + | 0.936058i | −0.304144 | + | 0.936058i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.374278 | − | 1.15191i | 0.374278 | − | 1.15191i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(968\) | 0.418669 | − | 0.230165i | 0.418669 | − | 0.230165i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.53928 | + | 1.11835i | −1.53928 | + | 1.11835i | ||||
\(971\) | 0.598617 | + | 1.84235i | 0.598617 | + | 1.84235i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.91789 | − | 1.39343i | −1.91789 | − | 1.39343i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.683098 | + | 0.825723i | −0.683098 | + | 0.825723i | ||||
\(980\) | −0.532426 | −0.532426 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(988\) | −1.86639 | + | 1.35601i | −1.86639 | + | 1.35601i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.0681659 | − | 1.08347i | 0.0681659 | − | 1.08347i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | −0.111330 | + | 0.0808861i | −0.111330 | + | 0.0808861i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.450527 | − | 1.38658i | 0.450527 | − | 1.38658i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
0.876307 | − | 0.481754i | \(-0.160000\pi\) | |||||||
\(998\) | 0.502226 | + | 1.54569i | 0.502226 | + | 1.54569i | ||||
\(999\) | 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 | 869.1.j.a.157.4 | ✓ | 20 | |
11.4 | even | 5 | inner | 869.1.j.a.631.4 | yes | 20 | |
79.78 | odd | 2 | CM | 869.1.j.a.157.4 | ✓ | 20 | |
869.631 | odd | 10 | inner | 869.1.j.a.631.4 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
869.1.j.a.157.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
869.1.j.a.157.4 | ✓ | 20 | 79.78 | odd | 2 | CM | |
869.1.j.a.631.4 | yes | 20 | 11.4 | even | 5 | inner | |
869.1.j.a.631.4 | yes | 20 | 869.631 | odd | 10 | inner |