Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,1,Mod(194,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 9, 5]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.194");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.bi (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: | \(0.486588387317\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{20}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
Embedding invariants
Embedding label | 584.2 | ||
Root | \(0.453990 + 0.891007i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.584 |
Dual form | 975.1.bi.a.389.2 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.183900 | + | 0.253116i | −0.183900 | + | 0.253116i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(4\) | 0.278768 | + | 0.857960i | 0.278768 | + | 0.857960i | ||||
\(5\) | −0.453990 | − | 0.891007i | −0.453990 | − | 0.891007i | ||||
\(6\) | −0.0966818 | + | 0.297556i | −0.0966818 | + | 0.297556i | ||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | −0.565985 | − | 0.183900i | −0.565985 | − | 0.183900i | ||||
\(9\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(10\) | 0.309017 | + | 0.0489435i | 0.309017 | + | 0.0489435i | ||||
\(11\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(12\) | 0.530249 | + | 0.729825i | 0.530249 | + | 0.729825i | ||||
\(13\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.707107 | − | 0.707107i | −0.707107 | − | 0.707107i | ||||
\(16\) | −0.579192 | + | 0.420808i | −0.579192 | + | 0.420808i | ||||
\(17\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(18\) | 0.312869i | 0.312869i | ||||||||
\(19\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(20\) | 0.637890 | − | 0.637890i | 0.637890 | − | 0.637890i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.530249 | + | 0.172288i | −0.530249 | + | 0.172288i | ||||
\(23\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(24\) | −0.595112 | −0.595112 | ||||||||
\(25\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(26\) | 0.312869 | 0.312869 | ||||||||
\(27\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(30\) | 0.309017 | − | 0.0489435i | 0.309017 | − | 0.0489435i | ||||
\(31\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(32\) | − | 0.819101i | − | 0.819101i | ||||||
\(33\) | 1.69480 | + | 0.550672i | 1.69480 | + | 0.550672i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.729825 | + | 0.530249i | 0.729825 | + | 0.530249i | ||||
\(37\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(40\) | 0.0930960 | + | 0.587785i | 0.0930960 | + | 0.587785i | ||||
\(41\) | 1.59811 | − | 1.16110i | 1.59811 | − | 1.16110i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.17557i | 1.17557i | 0.809017 | + | 0.587785i | \(0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(44\) | −0.496769 | + | 1.52890i | −0.496769 | + | 1.52890i | ||||
\(45\) | −0.891007 | − | 0.453990i | −0.891007 | − | 0.453990i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.87869 | + | 0.610425i | −1.87869 | + | 0.610425i | −0.891007 | + | 0.453990i | \(0.850000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(48\) | −0.420808 | + | 0.579192i | −0.420808 | + | 0.579192i | ||||
\(49\) | −1.00000 | −1.00000 | ||||||||
\(50\) | −0.0966818 | − | 0.297556i | −0.0966818 | − | 0.297556i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.530249 | − | 0.729825i | 0.530249 | − | 0.729825i | ||||
\(53\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(54\) | 0.0966818 | + | 0.297556i | 0.0966818 | + | 0.297556i | ||||
\(55\) | 0.278768 | − | 1.76007i | 0.278768 | − | 1.76007i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.734572 | + | 0.533698i | −0.734572 | + | 0.533698i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(60\) | 0.409551 | − | 0.803789i | 0.409551 | − | 0.803789i | ||||
\(61\) | −1.53884 | − | 1.11803i | −1.53884 | − | 1.11803i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.587785 | − | 0.809017i | \(-0.700000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.371864 | − | 0.270175i | −0.371864 | − | 0.270175i | ||||
\(65\) | −0.453990 | + | 0.891007i | −0.453990 | + | 0.891007i | ||||
\(66\) | −0.451057 | + | 0.327712i | −0.451057 | + | 0.327712i | ||||
\(67\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.550672 | + | 1.69480i | 0.550672 | + | 1.69480i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(72\) | −0.565985 | + | 0.183900i | −0.565985 | + | 0.183900i | ||||
\(73\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.297556 | − | 0.0966818i | 0.297556 | − | 0.0966818i | ||||
\(79\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(80\) | 0.637890 | + | 0.325021i | 0.637890 | + | 0.325021i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(82\) | 0.618034i | 0.618034i | ||||||||
\(83\) | −0.297556 | − | 0.0966818i | −0.297556 | − | 0.0966818i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.297556 | − | 0.216187i | −0.297556 | − | 0.216187i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.623345 | − | 0.857960i | −0.623345 | − | 0.857960i | ||||
\(89\) | −1.14412 | − | 0.831254i | −1.14412 | − | 0.831254i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(90\) | 0.278768 | − | 0.142040i | 0.278768 | − | 0.142040i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.253116 | − | 0.779012i | −0.253116 | − | 0.779012i | ||||
\(97\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(98\) | 0.183900 | − | 0.253116i | 0.183900 | − | 0.253116i | ||||
\(99\) | 1.78201 | 1.78201 | ||||||||
\(100\) | −0.857960 | − | 0.278768i | −0.857960 | − | 0.278768i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(104\) | 0.183900 | + | 0.565985i | 0.183900 | + | 0.565985i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 0.857960 | + | 0.278768i | 0.857960 | + | 0.278768i | ||||
\(109\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(110\) | 0.394238 | + | 0.394238i | 0.394238 | + | 0.394238i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(118\) | − | 0.284079i | − | 0.284079i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.270175 | + | 0.530249i | 0.270175 | + | 0.530249i | ||||
\(121\) | 0.672288 | + | 2.06909i | 0.672288 | + | 2.06909i | ||||
\(122\) | 0.565985 | − | 0.183900i | 0.565985 | − | 0.183900i | ||||
\(123\) | 1.16110 | − | 1.59811i | 1.16110 | − | 1.59811i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.987688 | + | 0.156434i | 0.987688 | + | 0.156434i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.951057 | − | 1.30902i | 0.951057 | − | 1.30902i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(128\) | 0.915783 | − | 0.297556i | 0.915783 | − | 0.297556i | ||||
\(129\) | 0.363271 | + | 1.11803i | 0.363271 | + | 1.11803i | ||||
\(130\) | −0.142040 | − | 0.278768i | −0.142040 | − | 0.278768i | ||||
\(131\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(132\) | 1.60758i | 1.60758i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.987688 | − | 0.156434i | −0.987688 | − | 0.156434i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.831254 | − | 1.14412i | −0.831254 | − | 1.14412i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.156434 | − | 0.987688i | \(-0.450000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | ||||
\(142\) | −0.530249 | − | 0.172288i | −0.530249 | − | 0.172288i | ||||
\(143\) | − | 1.78201i | − | 1.78201i | ||||||
\(144\) | −0.221232 | + | 0.680881i | −0.221232 | + | 0.680881i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.41421 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(150\) | −0.183900 | − | 0.253116i | −0.183900 | − | 0.253116i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.278768 | − | 0.857960i | 0.278768 | − | 0.857960i | ||||
\(157\) | 1.90211i | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.729825 | + | 0.371864i | −0.729825 | + | 0.371864i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.183900 | + | 0.253116i | 0.183900 | + | 0.253116i | ||||
\(163\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(164\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | ||||
\(165\) | −0.278768 | − | 1.76007i | −0.278768 | − | 1.76007i | ||||
\(166\) | 0.0791922 | − | 0.0575365i | 0.0791922 | − | 0.0575365i | ||||
\(167\) | −0.863541 | − | 0.280582i | −0.863541 | − | 0.280582i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00859 | + | 0.327712i | −1.00859 | + | 0.327712i | ||||
\(173\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.27578 | −1.27578 | ||||||||
\(177\) | −0.533698 | + | 0.734572i | −0.533698 | + | 0.734572i | ||||
\(178\) | 0.420808 | − | 0.136729i | 0.420808 | − | 0.136729i | ||||
\(179\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(180\) | 0.141122 | − | 0.891007i | 0.141122 | − | 0.891007i | ||||
\(181\) | −0.190983 | + | 0.587785i | −0.190983 | + | 0.587785i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.80902 | − | 0.587785i | −1.80902 | − | 0.587785i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.04744 | − | 1.44168i | −1.04744 | − | 1.44168i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(192\) | −0.437153 | − | 0.142040i | −0.437153 | − | 0.142040i | ||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.156434 | + | 0.987688i | −0.156434 | + | 0.987688i | ||||
\(196\) | −0.278768 | − | 0.857960i | −0.278768 | − | 0.857960i | ||||
\(197\) | 1.34500 | − | 0.437016i | 1.34500 | − | 0.437016i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(198\) | −0.327712 | + | 0.451057i | −0.327712 | + | 0.451057i | ||||
\(199\) | 1.17557 | 1.17557 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(200\) | 0.481456 | − | 0.349798i | 0.481456 | − | 0.349798i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.76007 | − | 0.896802i | −1.76007 | − | 0.896802i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.680881 | + | 0.221232i | 0.680881 | + | 0.221232i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.951057 | − | 0.690983i | −0.951057 | − | 0.690983i | − | 1.00000i | \(-0.5\pi\) | |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.04744 | + | 1.44168i | 1.04744 | + | 1.44168i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.04744 | − | 0.533698i | 1.04744 | − | 0.533698i | ||||
\(216\) | −0.481456 | + | 0.349798i | −0.481456 | + | 0.349798i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.58779 | − | 0.251480i | 1.58779 | − | 0.251480i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000i | 1.00000i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.831254 | − | 1.14412i | 0.831254 | − | 1.14412i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(234\) | 0.253116 | − | 0.183900i | 0.253116 | − | 0.183900i | ||||
\(235\) | 1.39680 | + | 1.39680i | 1.39680 | + | 1.39680i | ||||
\(236\) | −0.662667 | − | 0.481456i | −0.662667 | − | 0.481456i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.14412 | + | 0.831254i | 1.14412 | + | 0.831254i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(240\) | 0.707107 | + | 0.111995i | 0.707107 | + | 0.111995i | ||||
\(241\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(242\) | −0.647354 | − | 0.210338i | −0.647354 | − | 0.210338i | ||||
\(243\) | − | 1.00000i | − | 1.00000i | ||||||
\(244\) | 0.530249 | − | 1.63194i | 0.530249 | − | 1.63194i | ||||
\(245\) | 0.453990 | + | 0.891007i | 0.453990 | + | 0.891007i | ||||
\(246\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.312869 | −0.312869 | ||||||||
\(250\) | −0.221232 | + | 0.221232i | −0.221232 | + | 0.221232i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.156434 | + | 0.481456i | 0.156434 | + | 0.481456i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0489435 | − | 0.150633i | 0.0489435 | − | 0.150633i | ||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | −0.349798 | − | 0.113656i | −0.349798 | − | 0.113656i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.891007 | − | 0.141122i | −0.891007 | − | 0.141122i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(264\) | −0.857960 | − | 0.623345i | −0.857960 | − | 0.623345i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.34500 | − | 0.437016i | −1.34500 | − | 0.437016i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(270\) | 0.221232 | − | 0.221232i | 0.221232 | − | 0.221232i | ||||
\(271\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.442463 | 0.442463 | ||||||||
\(275\) | −1.69480 | + | 0.550672i | −1.69480 | + | 0.550672i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.690983 | − | 0.951057i | 0.690983 | − | 0.951057i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
1.00000 | \(0\) | |||||||||
\(278\) | 0.183900 | − | 0.0597526i | 0.183900 | − | 0.0597526i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.280582 | − | 0.863541i | 0.280582 | − | 0.863541i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(282\) | − | 0.618034i | − | 0.618034i | ||||||
\(283\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −1.30056 | + | 0.944910i | −1.30056 | + | 0.944910i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.451057 | + | 0.327712i | 0.451057 | + | 0.327712i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.481456 | − | 0.662667i | −0.481456 | − | 0.662667i | ||||
\(289\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.97538i | 1.97538i | 0.156434 | + | 0.987688i | \(0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(294\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | ||||
\(295\) | 0.809017 | + | 0.412215i | 0.809017 | + | 0.412215i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.69480 | − | 0.550672i | 1.69480 | − | 0.550672i | ||||
\(298\) | 0.260074 | − | 0.357960i | 0.260074 | − | 0.357960i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.902113 | −0.902113 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.297556 | + | 1.87869i | −0.297556 | + | 1.87869i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(312\) | 0.349798 | + | 0.481456i | 0.349798 | + | 0.481456i | ||||
\(313\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(314\) | −0.481456 | − | 0.349798i | −0.481456 | − | 0.349798i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.297556 | + | 0.0966818i | 0.297556 | + | 0.0966818i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.0719050 | + | 0.453990i | −0.0719050 | + | 0.453990i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.902113 | 0.902113 | ||||||||
\(325\) | 1.00000 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.11803 | + | 0.363271i | −1.11803 | + | 0.363271i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.496769 | + | 0.253116i | 0.496769 | + | 0.253116i | ||||
\(331\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(332\) | − | 0.282243i | − | 0.282243i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.229825 | − | 0.166977i | 0.229825 | − | 0.166977i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.951057 | + | 1.30902i | 0.951057 | + | 1.30902i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −0.183900 | − | 0.253116i | −0.183900 | − | 0.253116i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.216187 | − | 0.665356i | 0.216187 | − | 0.665356i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −1.00000 | ||||||||
\(352\) | 0.857960 | − | 1.18088i | 0.857960 | − | 1.18088i | ||||
\(353\) | −1.87869 | + | 0.610425i | −1.87869 | + | 0.610425i | −0.891007 | + | 0.453990i | \(0.850000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(354\) | −0.0877853 | − | 0.270175i | −0.0877853 | − | 0.270175i | ||||
\(355\) | 1.26007 | − | 1.26007i | 1.26007 | − | 1.26007i | ||||
\(356\) | 0.394238 | − | 1.21334i | 0.394238 | − | 1.21334i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.59811 | − | 1.16110i | 1.59811 | − | 1.16110i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(360\) | 0.420808 | + | 0.420808i | 0.420808 | + | 0.420808i | ||||
\(361\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(362\) | −0.113656 | − | 0.156434i | −0.113656 | − | 0.156434i | ||||
\(363\) | 1.27877 | + | 1.76007i | 1.27877 | + | 1.76007i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.481456 | − | 0.349798i | 0.481456 | − | 0.349798i | ||||
\(367\) | 1.11803 | + | 0.363271i | 1.11803 | + | 0.363271i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.610425 | − | 1.87869i | 0.610425 | − | 1.87869i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.987688 | − | 0.156434i | 0.987688 | − | 0.156434i | ||||
\(376\) | 1.17557 | 1.17557 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.500000 | − | 1.53884i | 0.500000 | − | 1.53884i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.34500 | + | 0.437016i | 1.34500 | + | 0.437016i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(384\) | 0.779012 | − | 0.565985i | 0.779012 | − | 0.565985i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.690983 | + | 0.951057i | 0.690983 | + | 0.951057i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(390\) | −0.221232 | − | 0.221232i | −0.221232 | − | 0.221232i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.565985 | + | 0.183900i | 0.565985 | + | 0.183900i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.136729 | + | 0.420808i | −0.136729 | + | 0.420808i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.496769 | + | 1.52890i | 0.496769 | + | 1.52890i | ||||
\(397\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(398\) | −0.216187 | + | 0.297556i | −0.216187 | + | 0.297556i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 0.715921i | − | 0.715921i | ||||||
\(401\) | 1.78201 | 1.78201 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.987688 | + | 0.156434i | −0.987688 | + | 0.156434i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(410\) | 0.550672 | − | 0.280582i | 0.550672 | − | 0.280582i | ||||
\(411\) | −1.14412 | − | 0.831254i | −1.14412 | − | 0.831254i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0489435 | + | 0.309017i | 0.0489435 | + | 0.309017i | ||||
\(416\) | −0.662667 | + | 0.481456i | −0.662667 | + | 0.481456i | ||||
\(417\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(422\) | 0.349798 | − | 0.113656i | 0.349798 | − | 0.113656i | ||||
\(423\) | −1.16110 | + | 1.59811i | −1.16110 | + | 1.59811i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.557537 | −0.557537 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.550672 | − | 1.69480i | −0.550672 | − | 1.69480i | ||||
\(430\) | −0.0575365 | + | 0.363271i | −0.0575365 | + | 0.363271i | ||||
\(431\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(432\) | 0.715921i | 0.715921i | ||||||||
\(433\) | −0.587785 | − | 0.190983i | −0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(440\) | −0.481456 | + | 0.944910i | −0.481456 | + | 0.944910i | ||||
\(441\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.221232 | + | 1.39680i | −0.221232 | + | 1.39680i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.34500 | + | 0.437016i | −1.34500 | + | 0.437016i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.907981 | 0.907981 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(450\) | −0.253116 | − | 0.183900i | −0.253116 | − | 0.183900i | ||||
\(451\) | 3.52015 | 3.52015 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.136729 | + | 0.420808i | 0.136729 | + | 0.420808i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.734572 | − | 0.533698i | −0.734572 | − | 0.533698i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(468\) | − | 0.902113i | − | 0.902113i | ||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.610425 | + | 0.0966818i | −0.610425 | + | 0.0966818i | ||||
\(471\) | 0.587785 | + | 1.80902i | 0.587785 | + | 1.80902i | ||||
\(472\) | 0.513904 | − | 0.166977i | 0.513904 | − | 0.166977i | ||||
\(473\) | −1.23134 | + | 1.69480i | −1.23134 | + | 1.69480i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.420808 | + | 0.136729i | −0.420808 | + | 0.136729i | ||||
\(479\) | −0.280582 | − | 0.863541i | −0.280582 | − | 0.863541i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(480\) | −0.579192 | + | 0.579192i | −0.579192 | + | 0.579192i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.58779 | + | 1.15359i | −1.58779 | + | 1.15359i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.253116 | + | 0.183900i | 0.253116 | + | 0.183900i | ||||
\(487\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(488\) | 0.665356 | + | 0.915783i | 0.665356 | + | 0.915783i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.309017 | − | 0.0489435i | −0.309017 | − | 0.0489435i | ||||
\(491\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(492\) | 1.69480 | + | 0.550672i | 1.69480 | + | 0.550672i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.809017 | − | 1.58779i | −0.809017 | − | 1.58779i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.0575365 | − | 0.0791922i | 0.0575365 | − | 0.0791922i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0.141122 | + | 0.891007i | 0.141122 | + | 0.891007i | ||||
\(501\) | −0.907981 | −0.907981 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000i | 1.00000i | ||||||||
\(508\) | 1.38821 | + | 0.451057i | 1.38821 | + | 0.451057i | ||||
\(509\) | 0.253116 | − | 0.183900i | 0.253116 | − | 0.183900i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.595112 | + | 0.819101i | 0.595112 | + | 0.819101i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.857960 | + | 0.623345i | −0.857960 | + | 0.623345i | ||||
\(517\) | −3.34786 | − | 1.08779i | −3.34786 | − | 1.08779i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.420808 | − | 0.420808i | 0.420808 | − | 0.420808i | ||||
\(521\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.11803 | − | 1.53884i | 1.11803 | − | 1.53884i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −1.21334 | + | 0.394238i | −1.21334 | + | 0.394238i | ||||
\(529\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.280582 | + | 0.863541i | −0.280582 | + | 0.863541i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.87869 | − | 0.610425i | −1.87869 | − | 0.610425i | ||||
\(534\) | 0.357960 | − | 0.260074i | 0.357960 | − | 0.260074i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.44168 | − | 1.04744i | −1.44168 | − | 1.04744i | ||||
\(540\) | −0.141122 | − | 0.891007i | −0.141122 | − | 0.891007i | ||||
\(541\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.618034i | 0.618034i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.80902 | + | 0.587785i | −1.80902 | + | 0.587785i | −0.809017 | + | 0.587785i | \(0.800000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0.749885 | − | 1.03213i | 0.749885 | − | 1.03213i | ||||
\(549\) | −1.90211 | −1.90211 | ||||||||
\(550\) | 0.172288 | − | 0.530249i | 0.172288 | − | 0.530249i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.113656 | + | 0.349798i | 0.113656 | + | 0.349798i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.172288 | − | 0.530249i | 0.172288 | − | 0.530249i | ||||
\(557\) | − | 0.907981i | − | 0.907981i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||
0.891007 | − | 0.453990i | \(-0.150000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.951057 | − | 0.690983i | 0.951057 | − | 0.690983i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.166977 | + | 0.229825i | 0.166977 | + | 0.229825i | ||||
\(563\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(564\) | −1.44168 | − | 1.04744i | −1.44168 | − | 1.04744i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.156434 | + | 0.113656i | −0.156434 | + | 0.113656i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.06050i | − | 1.06050i | ||||||
\(569\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.363271 | − | 1.11803i | −0.363271 | − | 1.11803i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(572\) | 1.52890 | − | 0.496769i | 1.52890 | − | 0.496769i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.459650 | −0.459650 | ||||||||
\(577\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(578\) | −0.297556 | + | 0.0966818i | −0.297556 | + | 0.0966818i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.156434 | + | 0.987688i | 0.156434 | + | 0.987688i | ||||
\(586\) | −0.500000 | − | 0.363271i | −0.500000 | − | 0.363271i | ||||
\(587\) | 0.533698 | + | 0.734572i | 0.533698 | + | 0.734572i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(588\) | −0.530249 | − | 0.729825i | −0.530249 | − | 0.729825i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −0.253116 | + | 0.128969i | −0.253116 | + | 0.128969i | ||||
\(591\) | 1.14412 | − | 0.831254i | 1.14412 | − | 0.831254i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.41421i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | −0.172288 | + | 0.530249i | −0.172288 | + | 0.530249i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.394238 | − | 1.21334i | −0.394238 | − | 1.21334i | ||||
\(597\) | 1.11803 | − | 0.363271i | 1.11803 | − | 0.363271i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | 0.349798 | − | 0.481456i | 0.349798 | − | 0.481456i | ||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.53836 | − | 1.53836i | 1.53836 | − | 1.53836i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.90211i | − | 1.90211i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.420808 | − | 0.420808i | −0.420808 | − | 0.420808i | ||||
\(611\) | 1.59811 | + | 1.16110i | 1.59811 | + | 1.16110i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.95106 | − | 0.309017i | −1.95106 | − | 0.309017i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.87869 | + | 0.610425i | 1.87869 | + | 0.610425i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.715921 | 0.715921 | ||||||||
\(625\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(626\) | −0.506233 | −0.506233 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.63194 | + | 0.530249i | −1.63194 | + | 0.530249i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.11803 | − | 0.363271i | −1.11803 | − | 0.363271i | ||||
\(634\) | −0.0791922 | + | 0.0575365i | −0.0791922 | + | 0.0575365i | ||||
\(635\) | −1.59811 | − | 0.253116i | −1.59811 | − | 0.253116i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.44168 | + | 1.04744i | 1.44168 | + | 1.04744i | ||||
\(640\) | −0.680881 | − | 0.680881i | −0.680881 | − | 0.680881i | ||||
\(641\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.831254 | − | 0.831254i | 0.831254 | − | 0.831254i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(648\) | −0.349798 | + | 0.481456i | −0.349798 | + | 0.481456i | ||||
\(649\) | −1.61803 | −1.61803 | ||||||||
\(650\) | −0.183900 | + | 0.253116i | −0.183900 | + | 0.253116i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.437016 | + | 1.34500i | −0.437016 | + | 1.34500i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(660\) | 1.43236 | − | 0.729825i | 1.43236 | − | 0.729825i | ||||
\(661\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.150633 | + | 0.109441i | 0.150633 | + | 0.109441i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 0.819101i | − | 0.819101i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.04744 | − | 3.22369i | −1.04744 | − | 3.22369i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(674\) | −0.506233 | −0.506233 | ||||||||
\(675\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(676\) | −0.902113 | −0.902113 | ||||||||
\(677\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.437016 | − | 1.34500i | 0.437016 | − | 1.34500i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.69480 | − | 0.550672i | −1.69480 | − | 0.550672i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.642040 | + | 1.26007i | −0.642040 | + | 1.26007i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.494689 | − | 0.680881i | −0.494689 | − | 0.680881i | ||||
\(689\) | 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 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0966818 | + | 0.610425i | −0.0966818 | + | 0.610425i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0.183900 | − | 0.253116i | 0.183900 | − | 0.253116i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.253116 | − | 0.779012i | −0.253116 | − | 0.779012i | ||||
\(705\) | 1.76007 | + | 0.896802i | 1.76007 | + | 0.896802i | ||||
\(706\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.779012 | − | 0.253116i | −0.779012 | − | 0.253116i | ||||
\(709\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(710\) | 0.0872179 | + | 0.550672i | 0.0872179 | + | 0.550672i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.494689 | + | 0.680881i | 0.494689 | + | 0.680881i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.58779 | + | 0.809017i | −1.58779 | + | 0.809017i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.34500 | + | 0.437016i | 1.34500 | + | 0.437016i | ||||
\(718\) | 0.618034i | 0.618034i | ||||||||
\(719\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(720\) | 0.707107 | − | 0.111995i | 0.707107 | − | 0.111995i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.297556 | − | 0.0966818i | 0.297556 | − | 0.0966818i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.557537 | −0.557537 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.680668 | −0.680668 | ||||||||
\(727\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − | 1.71592i | − | 1.71592i | ||||||
\(733\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(734\) | −0.297556 | + | 0.216187i | −0.297556 | + | 0.216187i | ||||
\(735\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | ||||
\(739\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.78201i | 1.78201i | 0.453990 | + | 0.891007i | \(0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.642040 | + | 1.26007i | 0.642040 | + | 1.26007i | ||||
\(746\) | −0.0597526 | − | 0.183900i | −0.0597526 | − | 0.183900i | ||||
\(747\) | −0.297556 | + | 0.0966818i | −0.297556 | + | 0.0966818i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.142040 | + | 0.278768i | −0.142040 | + | 0.278768i | ||||
\(751\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(752\) | 0.831254 | − | 1.14412i | 0.831254 | − | 1.14412i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.59811 | − | 1.16110i | −1.59811 | − | 1.16110i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(762\) | 0.297556 | + | 0.409551i | 0.297556 | + | 0.409551i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.357960 | + | 0.260074i | −0.357960 | + | 0.260074i | ||||
\(767\) | 0.863541 | + | 0.280582i | 0.863541 | + | 0.280582i | ||||
\(768\) | − | 0.158384i | − | 0.158384i | ||||||
\(769\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.533698 | + | 0.734572i | −0.533698 | + | 0.734572i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(774\) | −0.367799 | −0.367799 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.891007 | + | 0.141122i | −0.891007 | + | 0.141122i | ||||
\(781\) | −0.981305 | + | 3.02015i | −0.981305 | + | 3.02015i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.579192 | − | 0.420808i | 0.579192 | − | 0.420808i | ||||
\(785\) | 1.69480 | − | 0.863541i | 1.69480 | − | 0.863541i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(788\) | 0.749885 | + | 1.03213i | 0.749885 | + | 1.03213i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.00859 | − | 0.327712i | −1.00859 | − | 0.327712i | ||||
\(793\) | 1.90211i | 1.90211i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.327712 | + | 1.00859i | 0.327712 | + | 1.00859i | ||||
\(797\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.662667 | + | 0.481456i | 0.662667 | + | 0.481456i | ||||
\(801\) | −1.41421 | −1.41421 | ||||||||
\(802\) | −0.327712 | + | 0.451057i | −0.327712 | + | 0.451057i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(810\) | 0.142040 | − | 0.278768i | 0.142040 | − | 0.278768i | ||||
\(811\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.278768 | − | 1.76007i | 0.278768 | − | 1.76007i | ||||
\(821\) | 0.0966818 | + | 0.297556i | 0.0966818 | + | 0.297556i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(822\) | 0.420808 | − | 0.136729i | 0.420808 | − | 0.136729i | ||||
\(823\) | 1.11803 | − | 1.53884i | 1.11803 | − | 1.53884i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.44168 | + | 1.04744i | −1.44168 | + | 1.04744i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.04744 | + | 1.44168i | −1.04744 | + | 1.44168i | −0.156434 | + | 0.987688i | \(0.550000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.363271 | − | 1.11803i | −0.363271 | − | 1.11803i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(830\) | −0.0872179 | − | 0.0444398i | −0.0872179 | − | 0.0444398i | ||||
\(831\) | 0.363271 | − | 1.11803i | 0.363271 | − | 1.11803i | ||||
\(832\) | 0.459650i | 0.459650i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.156434 | − | 0.113656i | 0.156434 | − | 0.113656i | ||||
\(835\) | 0.142040 | + | 0.896802i | 0.142040 | + | 0.896802i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.734572 | + | 0.533698i | 0.734572 | + | 0.533698i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 0.907981i | − | 0.907981i | ||||||
\(844\) | 0.327712 | − | 1.00859i | 0.327712 | − | 1.00859i | ||||
\(845\) | 0.987688 | − | 0.156434i | 0.987688 | − | 0.156434i | ||||
\(846\) | −0.190983 | − | 0.587785i | −0.190983 | − | 0.587785i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.618034 | 0.618034 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −0.944910 | + | 1.30056i | −0.944910 | + | 1.30056i | ||||
\(853\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0.530249 | + | 0.172288i | 0.530249 | + | 0.172288i | ||||
\(859\) | −0.951057 | + | 0.690983i | −0.951057 | + | 0.690983i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | 0.749885 | + | 0.749885i | 0.749885 | + | 0.749885i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0575365 | + | 0.0791922i | 0.0575365 | + | 0.0791922i | ||||
\(863\) | −1.16110 | − | 1.59811i | −1.16110 | − | 1.59811i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.453990 | − | 0.891007i | \(-0.650000\pi\) | |||||||
\(864\) | −0.662667 | − | 0.481456i | −0.662667 | − | 0.481456i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.156434 | − | 0.113656i | 0.156434 | − | 0.113656i | ||||
\(867\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(878\) | −0.481456 | + | 0.156434i | −0.481456 | + | 0.156434i | ||||
\(879\) | 0.610425 | + | 1.87869i | 0.610425 | + | 1.87869i | ||||
\(880\) | 0.579192 | + | 1.13673i | 0.579192 | + | 1.13673i | ||||
\(881\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(882\) | − | 0.312869i | − | 0.312869i | ||||||
\(883\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.896802 | + | 0.142040i | 0.896802 | + | 0.142040i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.312869 | − | 0.312869i | −0.312869 | − | 0.312869i | ||||
\(891\) | 1.44168 | − | 1.04744i | 1.44168 | − | 1.04744i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.136729 | − | 0.420808i | 0.136729 | − | 0.420808i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.166977 | + | 0.229825i | −0.166977 | + | 0.229825i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.857960 | + | 0.278768i | −0.857960 | + | 0.278768i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −0.647354 | + | 0.891007i | −0.647354 | + | 0.891007i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.610425 | − | 0.0966818i | 0.610425 | − | 0.0966818i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(908\) | 1.21334 | + | 0.394238i | 1.21334 | + | 0.394238i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.327712 | − | 0.451057i | −0.327712 | − | 0.451057i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.297556 | + | 1.87869i | 0.297556 | + | 1.87869i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | 1.00000i | \(0.5\pi\) | ||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.270175 | − | 0.0877853i | 0.270175 | − | 0.0877853i | ||||
\(923\) | 1.04744 | − | 1.44168i | 1.04744 | − | 1.44168i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −0.610425 | − | 1.87869i | −0.610425 | − | 1.87869i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.481456 | + | 0.349798i | 0.481456 | + | 0.349798i | ||||
\(937\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | ||||
\(940\) | −0.809017 | + | 1.58779i | −0.809017 | + | 1.58779i | ||||
\(941\) | −1.44168 | + | 1.04744i | −1.44168 | + | 1.04744i | −0.453990 | + | 0.891007i | \(0.650000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(942\) | −0.565985 | − | 0.183900i | −0.565985 | − | 0.183900i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0.200874 | − | 0.618227i | 0.200874 | − | 0.618227i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.202537 | − | 0.623345i | −0.202537 | − | 0.623345i | ||||
\(947\) | −0.863541 | + | 0.280582i | −0.863541 | + | 0.280582i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.312869 | 0.312869 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.394238 | + | 1.21334i | −0.394238 | + | 1.21334i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.270175 | + | 0.0877853i | 0.270175 | + | 0.0877853i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.0719050 | + | 0.453990i | 0.0719050 | + | 0.453990i | ||||
\(961\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(968\) | − | 1.29471i | − | 1.29471i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(972\) | 0.857960 | − | 0.278768i | 0.857960 | − | 0.278768i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(976\) | 1.36176 | 1.36176 | ||||||||
\(977\) | 0.533698 | − | 0.734572i | 0.533698 | − | 0.734572i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.778768 | − | 2.39680i | −0.778768 | − | 2.39680i | ||||
\(980\) | −0.637890 | + | 0.637890i | −0.637890 | + | 0.637890i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.87869 | + | 0.610425i | 1.87869 | + | 0.610425i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(984\) | −0.951057 | + | 0.690983i | −0.951057 | + | 0.690983i | ||||
\(985\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.550672 | + | 0.0872179i | 0.550672 | + | 0.0872179i | ||||
\(991\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.533698 | − | 1.04744i | −0.533698 | − | 1.04744i | ||||
\(996\) | −0.0872179 | − | 0.268429i | −0.0872179 | − | 0.268429i | ||||
\(997\) | 1.11803 | − | 0.363271i | 1.11803 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(998\) | 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 | 975.1.bi.a.584.2 | yes | 16 | |
3.2 | odd | 2 | inner | 975.1.bi.a.584.3 | yes | 16 | |
13.12 | even | 2 | inner | 975.1.bi.a.584.3 | yes | 16 | |
25.14 | even | 10 | inner | 975.1.bi.a.389.2 | ✓ | 16 | |
39.38 | odd | 2 | CM | 975.1.bi.a.584.2 | yes | 16 | |
75.14 | odd | 10 | inner | 975.1.bi.a.389.3 | yes | 16 | |
325.64 | even | 10 | inner | 975.1.bi.a.389.3 | yes | 16 | |
975.389 | odd | 10 | inner | 975.1.bi.a.389.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.1.bi.a.389.2 | ✓ | 16 | 25.14 | even | 10 | inner | |
975.1.bi.a.389.2 | ✓ | 16 | 975.389 | odd | 10 | inner | |
975.1.bi.a.389.3 | yes | 16 | 75.14 | odd | 10 | inner | |
975.1.bi.a.389.3 | yes | 16 | 325.64 | even | 10 | inner | |
975.1.bi.a.584.2 | yes | 16 | 1.1 | even | 1 | trivial | |
975.1.bi.a.584.2 | yes | 16 | 39.38 | odd | 2 | CM | |
975.1.bi.a.584.3 | yes | 16 | 3.2 | odd | 2 | inner | |
975.1.bi.a.584.3 | yes | 16 | 13.12 | even | 2 | inner |