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 | 389.1 | ||
Root | \(0.891007 + 0.453990i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.389 |
Dual form | 975.1.bi.a.584.1 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.16110 | − | 1.59811i | −1.16110 | − | 1.59811i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.453990 | − | 0.891007i | \(-0.650000\pi\) | |||||||
\(3\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(4\) | −0.896802 | + | 2.76007i | −0.896802 | + | 2.76007i | ||||
\(5\) | −0.891007 | − | 0.453990i | −0.891007 | − | 0.453990i | ||||
\(6\) | 0.610425 | + | 1.87869i | 0.610425 | + | 1.87869i | ||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 3.57349 | − | 1.16110i | 3.57349 | − | 1.16110i | ||||
\(9\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(10\) | 0.309017 | + | 1.95106i | 0.309017 | + | 1.95106i | ||||
\(11\) | 0.734572 | − | 0.533698i | 0.734572 | − | 0.533698i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(12\) | 1.70582 | − | 2.34786i | 1.70582 | − | 2.34786i | ||||
\(13\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.707107 | + | 0.707107i | 0.707107 | + | 0.707107i | ||||
\(16\) | −3.65688 | − | 2.65688i | −3.65688 | − | 2.65688i | ||||
\(17\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(18\) | − | 1.97538i | − | 1.97538i | ||||||
\(19\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(20\) | 2.05210 | − | 2.05210i | 2.05210 | − | 2.05210i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.70582 | − | 0.554254i | −1.70582 | − | 0.554254i | ||||
\(23\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(24\) | −3.75739 | −3.75739 | ||||||||
\(25\) | 0.587785 | + | 0.809017i | 0.587785 | + | 0.809017i | ||||
\(26\) | −1.97538 | −1.97538 | ||||||||
\(27\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(30\) | 0.309017 | − | 1.95106i | 0.309017 | − | 1.95106i | ||||
\(31\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(32\) | 5.17160i | 5.17160i | ||||||||
\(33\) | −0.863541 | + | 0.280582i | −0.863541 | + | 0.280582i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.34786 | + | 1.70582i | −2.34786 | + | 1.70582i | ||||
\(37\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(40\) | −3.71113 | − | 0.587785i | −3.71113 | − | 0.587785i | ||||
\(41\) | −0.253116 | − | 0.183900i | −0.253116 | − | 0.183900i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.17557i | − | 1.17557i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(44\) | 0.814279 | + | 2.50609i | 0.814279 | + | 2.50609i | ||||
\(45\) | −0.453990 | − | 0.891007i | −0.453990 | − | 0.891007i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.297556 | − | 0.0966818i | −0.297556 | − | 0.0966818i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(48\) | 2.65688 | + | 3.65688i | 2.65688 | + | 3.65688i | ||||
\(49\) | −1.00000 | −1.00000 | ||||||||
\(50\) | 0.610425 | − | 1.87869i | 0.610425 | − | 1.87869i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.70582 | + | 2.34786i | 1.70582 | + | 2.34786i | ||||
\(53\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(54\) | −0.610425 | + | 1.87869i | −0.610425 | + | 1.87869i | ||||
\(55\) | −0.896802 | + | 0.142040i | −0.896802 | + | 0.142040i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.44168 | − | 1.04744i | −1.44168 | − | 1.04744i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.453990 | − | 0.891007i | \(-0.650000\pi\) | |||||||
\(60\) | −2.58580 | + | 1.31753i | −2.58580 | + | 1.31753i | ||||
\(61\) | 1.53884 | − | 1.11803i | 1.53884 | − | 1.11803i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.60793 | − | 3.34786i | 4.60793 | − | 3.34786i | ||||
\(65\) | −0.891007 | + | 0.453990i | −0.891007 | + | 0.453990i | ||||
\(66\) | 1.45106 | + | 1.05425i | 1.45106 | + | 1.05425i | ||||
\(67\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.280582 | − | 0.863541i | 0.280582 | − | 0.863541i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(72\) | 3.57349 | + | 1.16110i | 3.57349 | + | 1.16110i | ||||
\(73\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.87869 | + | 0.610425i | 1.87869 | + | 0.610425i | ||||
\(79\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(80\) | 2.05210 | + | 4.02748i | 2.05210 | + | 4.02748i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(82\) | 0.618034i | 0.618034i | ||||||||
\(83\) | −1.87869 | + | 0.610425i | −1.87869 | + | 0.610425i | −0.891007 | + | 0.453990i | \(0.850000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.87869 | + | 1.36495i | −1.87869 | + | 1.36495i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00531 | − | 2.76007i | 2.00531 | − | 2.76007i | ||||
\(89\) | 1.14412 | − | 0.831254i | 1.14412 | − | 0.831254i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(90\) | −0.896802 | + | 1.76007i | −0.896802 | + | 1.76007i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.59811 | − | 4.91849i | 1.59811 | − | 4.91849i | ||||
\(97\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(98\) | 1.16110 | + | 1.59811i | 1.16110 | + | 1.59811i | ||||
\(99\) | 0.907981 | 0.907981 | ||||||||
\(100\) | −2.76007 | + | 0.896802i | −2.76007 | + | 0.896802i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(104\) | 1.16110 | − | 3.57349i | 1.16110 | − | 3.57349i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | 2.76007 | − | 0.896802i | 2.76007 | − | 0.896802i | ||||
\(109\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(110\) | 1.26827 | + | 1.26827i | 1.26827 | + | 1.26827i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(118\) | 3.52015i | 3.52015i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 3.34786 | + | 1.70582i | 3.34786 | + | 1.70582i | ||||
\(121\) | −0.0542543 | + | 0.166977i | −0.0542543 | + | 0.166977i | ||||
\(122\) | −3.57349 | − | 1.16110i | −3.57349 | − | 1.16110i | ||||
\(123\) | 0.183900 | + | 0.253116i | 0.183900 | + | 0.253116i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.156434 | − | 0.987688i | −0.156434 | − | 0.987688i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.951057 | − | 1.30902i | −0.951057 | − | 1.30902i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(128\) | −5.78203 | − | 1.87869i | −5.78203 | − | 1.87869i | ||||
\(129\) | −0.363271 | + | 1.11803i | −0.363271 | + | 1.11803i | ||||
\(130\) | 1.76007 | + | 0.896802i | 1.76007 | + | 0.896802i | ||||
\(131\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(132\) | − | 2.63506i | − | 2.63506i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.156434 | + | 0.987688i | 0.156434 | + | 0.987688i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.831254 | + | 1.14412i | −0.831254 | + | 1.14412i | 0.156434 | + | 0.987688i | \(0.450000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.253116 | + | 0.183900i | 0.253116 | + | 0.183900i | ||||
\(142\) | −1.70582 | + | 0.554254i | −1.70582 | + | 0.554254i | ||||
\(143\) | − | 0.907981i | − | 0.907981i | ||||||
\(144\) | −1.39680 | − | 4.29892i | −1.39680 | − | 4.29892i | ||||
\(145\) | 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 | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(150\) | −1.16110 | + | 1.59811i | −1.16110 | + | 1.59811i | ||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.896802 | − | 2.76007i | −0.896802 | − | 2.76007i | ||||
\(157\) | − | 1.90211i | − | 1.90211i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.34786 | − | 4.60793i | 2.34786 | − | 4.60793i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.16110 | − | 1.59811i | 1.16110 | − | 1.59811i | ||||
\(163\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(164\) | 0.734572 | − | 0.533698i | 0.734572 | − | 0.533698i | ||||
\(165\) | 0.896802 | + | 0.142040i | 0.896802 | + | 0.142040i | ||||
\(166\) | 3.15688 | + | 2.29360i | 3.15688 | + | 2.29360i | ||||
\(167\) | 1.69480 | − | 0.550672i | 1.69480 | − | 0.550672i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.309017 | − | 0.951057i | −0.309017 | − | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.24466 | + | 1.05425i | 3.24466 | + | 1.05425i | ||||
\(173\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.10421 | −4.10421 | ||||||||
\(177\) | 1.04744 | + | 1.44168i | 1.04744 | + | 1.44168i | ||||
\(178\) | −2.65688 | − | 0.863271i | −2.65688 | − | 0.863271i | ||||
\(179\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(180\) | 2.86638 | − | 0.453990i | 2.86638 | − | 0.453990i | ||||
\(181\) | −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 | ||||||||
\(188\) | 0.533698 | − | 0.734572i | 0.533698 | − | 0.734572i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(192\) | −5.41695 | + | 1.76007i | −5.41695 | + | 1.76007i | ||||
\(193\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.987688 | − | 0.156434i | 0.987688 | − | 0.156434i | ||||
\(196\) | 0.896802 | − | 2.76007i | 0.896802 | − | 2.76007i | ||||
\(197\) | 1.34500 | + | 0.437016i | 1.34500 | + | 0.437016i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(198\) | −1.05425 | − | 1.45106i | −1.05425 | − | 1.45106i | ||||
\(199\) | −1.17557 | −1.17557 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(200\) | 3.03979 | + | 2.20854i | 3.03979 | + | 2.20854i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.142040 | + | 0.278768i | 0.142040 | + | 0.278768i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.29892 | + | 1.39680i | −4.29892 | + | 1.39680i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.951057 | − | 0.690983i | 0.951057 | − | 0.690983i | − | 1.00000i | \(-0.5\pi\) | |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.533698 | + | 0.734572i | −0.533698 | + | 0.734572i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.533698 | + | 1.04744i | −0.533698 | + | 1.04744i | ||||
\(216\) | −3.03979 | − | 2.20854i | −3.03979 | − | 2.20854i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.412215 | − | 2.60262i | 0.412215 | − | 2.60262i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000i | 1.00000i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.831254 | + | 1.14412i | 0.831254 | + | 1.14412i | 0.987688 | + | 0.156434i | \(0.0500000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(234\) | −1.59811 | − | 1.16110i | −1.59811 | − | 1.16110i | ||||
\(235\) | 0.221232 | + | 0.221232i | 0.221232 | + | 0.221232i | ||||
\(236\) | 4.18391 | − | 3.03979i | 4.18391 | − | 3.03979i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.14412 | + | 0.831254i | −1.14412 | + | 0.831254i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(240\) | −0.707107 | − | 4.46450i | −0.707107 | − | 4.46450i | ||||
\(241\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(242\) | 0.329843 | − | 0.107173i | 0.329843 | − | 0.107173i | ||||
\(243\) | − | 1.00000i | − | 1.00000i | ||||||
\(244\) | 1.70582 | + | 5.24997i | 1.70582 | + | 5.24997i | ||||
\(245\) | 0.891007 | + | 0.453990i | 0.891007 | + | 0.453990i | ||||
\(246\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.97538 | 1.97538 | ||||||||
\(250\) | −1.39680 | + | 1.39680i | −1.39680 | + | 1.39680i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.987688 | + | 3.03979i | −0.987688 | + | 3.03979i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.95106 | + | 6.00473i | 1.95106 | + | 6.00473i | ||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 2.20854 | − | 0.717598i | 2.20854 | − | 0.717598i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.453990 | − | 2.86638i | −0.453990 | − | 2.86638i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(264\) | −2.76007 | + | 2.00531i | −2.76007 | + | 2.00531i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.34500 | + | 0.437016i | −1.34500 | + | 0.437016i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(270\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | ||||
\(271\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.79360 | 2.79360 | ||||||||
\(275\) | 0.863541 | + | 0.280582i | 0.863541 | + | 0.280582i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.690983 | + | 0.951057i | 0.690983 | + | 0.951057i | 1.00000 | \(0\) | ||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(278\) | 1.16110 | + | 0.377263i | 1.16110 | + | 0.377263i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.550672 | + | 1.69480i | 0.550672 | + | 1.69480i | 0.707107 | + | 0.707107i | \(0.250000\pi\) |
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(282\) | − | 0.618034i | − | 0.618034i | ||||||
\(283\) | −0.587785 | + | 0.190983i | −0.587785 | + | 0.190983i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | 2.13181 | + | 1.54885i | 2.13181 | + | 1.54885i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.45106 | + | 1.05425i | −1.45106 | + | 1.05425i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.03979 | + | 4.18391i | −3.03979 | + | 4.18391i | ||||
\(289\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 0.312869i | − | 0.312869i | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(294\) | −0.610425 | − | 1.87869i | −0.610425 | − | 1.87869i | ||||
\(295\) | 0.809017 | + | 1.58779i | 0.809017 | + | 1.58779i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.863541 | − | 0.280582i | −0.863541 | − | 0.280582i | ||||
\(298\) | −1.64204 | − | 2.26007i | −1.64204 | − | 2.26007i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 2.90211 | 2.90211 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.87869 | + | 0.297556i | −1.87869 | + | 0.297556i | ||||
\(306\) | 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 | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(312\) | −2.20854 | + | 3.03979i | −2.20854 | + | 3.03979i | ||||
\(313\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | 1.00000i | \(0.5\pi\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(314\) | −3.03979 | + | 2.20854i | −3.03979 | + | 2.20854i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.87869 | − | 0.610425i | 1.87869 | − | 0.610425i | 0.891007 | − | 0.453990i | \(-0.150000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −5.62559 | + | 0.891007i | −5.62559 | + | 0.891007i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.90211 | −2.90211 | ||||||||
\(325\) | 1.00000 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.11803 | − | 0.363271i | −1.11803 | − | 0.363271i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.814279 | − | 1.59811i | −0.814279 | − | 1.59811i | ||||
\(331\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(332\) | − | 5.73277i | − | 5.73277i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.84786 | − | 2.06909i | −2.84786 | − | 2.06909i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.951057 | + | 1.30902i | −0.951057 | + | 1.30902i | 1.00000i | \(0.5\pi\) | ||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(338\) | −1.16110 | + | 1.59811i | −1.16110 | + | 1.59811i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.36495 | − | 4.20089i | −1.36495 | − | 4.20089i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −1.00000 | ||||||||
\(352\) | 2.76007 | + | 3.79892i | 2.76007 | + | 3.79892i | ||||
\(353\) | −0.297556 | − | 0.0966818i | −0.297556 | − | 0.0966818i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(354\) | 1.08779 | − | 3.34786i | 1.08779 | − | 3.34786i | ||||
\(355\) | −0.642040 | + | 0.642040i | −0.642040 | + | 0.642040i | ||||
\(356\) | 1.26827 | + | 3.90333i | 1.26827 | + | 3.90333i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.253116 | − | 0.183900i | −0.253116 | − | 0.183900i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(360\) | −2.65688 | − | 2.65688i | −2.65688 | − | 2.65688i | ||||
\(361\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(362\) | −0.717598 | + | 0.987688i | −0.717598 | + | 0.987688i | ||||
\(363\) | 0.103198 | − | 0.142040i | 0.103198 | − | 0.142040i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.03979 | + | 2.20854i | 3.03979 | + | 2.20854i | ||||
\(367\) | 1.11803 | − | 0.363271i | 1.11803 | − | 0.363271i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0966818 | − | 0.297556i | −0.0966818 | − | 0.297556i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.156434 | + | 0.987688i | −0.156434 | + | 0.987688i | ||||
\(376\) | −1.17557 | −1.17557 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.500000 | + | 1.53884i | 0.500000 | + | 1.53884i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.34500 | − | 0.437016i | 1.34500 | − | 0.437016i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(384\) | 4.91849 | + | 3.57349i | 4.91849 | + | 3.57349i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.690983 | − | 0.951057i | 0.690983 | − | 0.951057i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(390\) | −1.39680 | − | 1.39680i | −1.39680 | − | 1.39680i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.57349 | + | 1.16110i | −3.57349 | + | 1.16110i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.863271 | − | 2.65688i | −0.863271 | − | 2.65688i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.814279 | + | 2.50609i | −0.814279 | + | 2.50609i | ||||
\(397\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(398\) | 1.36495 | + | 1.87869i | 1.36495 | + | 1.87869i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 4.52015i | − | 4.52015i | ||||||
\(401\) | 0.907981 | 0.907981 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.156434 | − | 0.987688i | 0.156434 | − | 0.987688i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(410\) | 0.280582 | − | 0.550672i | 0.280582 | − | 0.550672i | ||||
\(411\) | 1.14412 | − | 0.831254i | 1.14412 | − | 0.831254i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.95106 | + | 0.309017i | 1.95106 | + | 0.309017i | ||||
\(416\) | 4.18391 | + | 3.03979i | 4.18391 | + | 3.03979i | ||||
\(417\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(422\) | −2.20854 | − | 0.717598i | −2.20854 | − | 0.717598i | ||||
\(423\) | −0.183900 | − | 0.253116i | −0.183900 | − | 0.253116i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.79360 | 1.79360 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.280582 | + | 0.863541i | −0.280582 | + | 0.863541i | ||||
\(430\) | 2.29360 | − | 0.363271i | 2.29360 | − | 0.363271i | ||||
\(431\) | −0.610425 | − | 1.87869i | −0.610425 | − | 1.87869i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(432\) | 4.52015i | 4.52015i | ||||||||
\(433\) | 0.587785 | − | 0.190983i | 0.587785 | − | 0.190983i | − | 1.00000i | \(-0.5\pi\) | |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(440\) | −3.03979 | + | 1.54885i | −3.03979 | + | 1.54885i | ||||
\(441\) | −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 | ||||||||
\(445\) | −1.39680 | + | 0.221232i | −1.39680 | + | 0.221232i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.34500 | − | 0.437016i | −1.34500 | − | 0.437016i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.78201 | 1.78201 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(450\) | 1.59811 | − | 1.16110i | 1.59811 | − | 1.16110i | ||||
\(451\) | −0.284079 | −0.284079 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.863271 | − | 2.65688i | 0.863271 | − | 2.65688i | ||||
\(455\) | 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 | ||||||||
\(461\) | −1.44168 | + | 1.04744i | −1.44168 | + | 1.04744i | −0.453990 | + | 0.891007i | \(0.650000\pi\) |
−0.987688 | + | 0.156434i | \(0.950000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(468\) | 2.90211i | 2.90211i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.0966818 | − | 0.610425i | 0.0966818 | − | 0.610425i | ||||
\(471\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | ||||
\(472\) | −6.36801 | − | 2.06909i | −6.36801 | − | 2.06909i | ||||
\(473\) | −0.627399 | − | 0.863541i | −0.627399 | − | 0.863541i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.65688 | + | 0.863271i | 2.65688 | + | 0.863271i | ||||
\(479\) | −0.550672 | + | 1.69480i | −0.550672 | + | 1.69480i | 0.156434 | + | 0.987688i | \(0.450000\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(480\) | −3.65688 | + | 3.65688i | −3.65688 | + | 3.65688i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.412215 | − | 0.299492i | −0.412215 | − | 0.299492i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.59811 | + | 1.16110i | −1.59811 | + | 1.16110i | ||||
\(487\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(488\) | 4.20089 | − | 5.78203i | 4.20089 | − | 5.78203i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.309017 | − | 1.95106i | −0.309017 | − | 1.95106i | ||||
\(491\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(492\) | −0.863541 | + | 0.280582i | −0.863541 | + | 0.280582i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.809017 | − | 0.412215i | −0.809017 | − | 0.412215i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.29360 | − | 3.15688i | −2.29360 | − | 3.15688i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 2.86638 | + | 0.453990i | 2.86638 | + | 0.453990i | ||||
\(501\) | −1.78201 | −1.78201 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000i | 1.00000i | ||||||||
\(508\) | 4.46589 | − | 1.45106i | 4.46589 | − | 1.45106i | ||||
\(509\) | −1.59811 | − | 1.16110i | −1.59811 | − | 1.16110i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.707107 | − | 0.707107i | \(-0.750000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.75739 | − | 5.17160i | 3.75739 | − | 5.17160i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.76007 | − | 2.00531i | −2.76007 | − | 2.00531i | ||||
\(517\) | −0.270175 | + | 0.0877853i | −0.270175 | + | 0.0877853i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.65688 | + | 2.65688i | −2.65688 | + | 2.65688i | ||||
\(521\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.11803 | + | 1.53884i | 1.11803 | + | 1.53884i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.90333 | + | 1.26827i | 3.90333 | + | 1.26827i | ||||
\(529\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.550672 | − | 1.69480i | −0.550672 | − | 1.69480i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.297556 | + | 0.0966818i | −0.297556 | + | 0.0966818i | ||||
\(534\) | 2.26007 | + | 1.64204i | 2.26007 | + | 1.64204i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.734572 | + | 0.533698i | −0.734572 | + | 0.533698i | ||||
\(540\) | −2.86638 | − | 0.453990i | −2.86638 | − | 0.453990i | ||||
\(541\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(542\) | 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 | \(\pi\) | |||||||||
\(548\) | −2.41239 | − | 3.32037i | −2.41239 | − | 3.32037i | ||||
\(549\) | 1.90211 | 1.90211 | ||||||||
\(550\) | −0.554254 | − | 1.70582i | −0.554254 | − | 1.70582i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.717598 | − | 2.20854i | 0.717598 | − | 2.20854i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.554254 | − | 1.70582i | −0.554254 | − | 1.70582i | ||||
\(557\) | − | 1.78201i | − | 1.78201i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||
0.453990 | − | 0.891007i | \(-0.350000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.951057 | − | 0.690983i | −0.951057 | − | 0.690983i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.06909 | − | 2.84786i | 2.06909 | − | 2.84786i | ||||
\(563\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(564\) | −0.734572 | + | 0.533698i | −0.734572 | + | 0.533698i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.987688 | + | 0.717598i | 0.987688 | + | 0.717598i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 3.41164i | − | 3.41164i | ||||||
\(569\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.363271 | − | 1.11803i | 0.363271 | − | 1.11803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(572\) | 2.50609 | + | 0.814279i | 2.50609 | + | 0.814279i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5.69572 | 5.69572 | ||||||||
\(577\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(578\) | −1.87869 | − | 0.610425i | −1.87869 | − | 0.610425i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.987688 | − | 0.156434i | −0.987688 | − | 0.156434i | ||||
\(586\) | −0.500000 | + | 0.363271i | −0.500000 | + | 0.363271i | ||||
\(587\) | −1.04744 | + | 1.44168i | −1.04744 | + | 1.44168i | −0.156434 | + | 0.987688i | \(0.550000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(588\) | −1.70582 | + | 2.34786i | −1.70582 | + | 2.34786i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.59811 | − | 3.13647i | 1.59811 | − | 3.13647i | ||||
\(591\) | −1.14412 | − | 0.831254i | −1.14412 | − | 0.831254i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.41421i | − | 1.41421i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707107i | \(-0.250000\pi\) | |||||||
\(594\) | 0.554254 | + | 1.70582i | 0.554254 | + | 1.70582i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.26827 | + | 3.90333i | −1.26827 | + | 3.90333i | ||||
\(597\) | 1.11803 | + | 0.363271i | 1.11803 | + | 0.363271i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(600\) | −2.20854 | − | 3.03979i | −2.20854 | − | 3.03979i | ||||
\(601\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.124147 | − | 0.124147i | 0.124147 | − | 0.124147i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.90211i | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.65688 | + | 2.65688i | 2.65688 | + | 2.65688i | ||||
\(611\) | −0.253116 | + | 0.183900i | −0.253116 | + | 0.183900i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0489435 | − | 0.309017i | −0.0489435 | − | 0.309017i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.297556 | − | 0.0966818i | 0.297556 | − | 0.0966818i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.52015 | 4.52015 | ||||||||
\(625\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(626\) | 3.19623 | 3.19623 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.24997 | + | 1.70582i | 5.24997 | + | 1.70582i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.11803 | + | 0.363271i | −1.11803 | + | 0.363271i | ||||
\(634\) | −3.15688 | − | 2.29360i | −3.15688 | − | 2.29360i | ||||
\(635\) | 0.253116 | + | 1.59811i | 0.253116 | + | 1.59811i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.734572 | − | 0.533698i | 0.734572 | − | 0.533698i | ||||
\(640\) | 4.29892 | + | 4.29892i | 4.29892 | + | 4.29892i | ||||
\(641\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(642\) | 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 | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(648\) | 2.20854 | + | 3.03979i | 2.20854 | + | 3.03979i | ||||
\(649\) | −1.61803 | −1.61803 | ||||||||
\(650\) | −1.16110 | − | 1.59811i | −1.16110 | − | 1.59811i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(654\) | 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 | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(660\) | −1.19629 | + | 2.34786i | −1.19629 | + | 2.34786i | ||||
\(661\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00473 | + | 4.36269i | −6.00473 | + | 4.36269i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 5.17160i | 5.17160i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.533698 | − | 1.64255i | 0.533698 | − | 1.64255i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(674\) | 3.19623 | 3.19623 | ||||||||
\(675\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(676\) | 2.90211 | 2.90211 | ||||||||
\(677\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.437016 | − | 1.34500i | −0.437016 | − | 1.34500i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.863541 | − | 0.280582i | 0.863541 | − | 0.280582i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.26007 | − | 0.642040i | 1.26007 | − | 0.642040i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.12334 | + | 4.29892i | −3.12334 | + | 4.29892i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.610425 | − | 0.0966818i | 0.610425 | − | 0.0966818i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 1.16110 | + | 1.59811i | 1.16110 | + | 1.59811i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.59811 | − | 4.91849i | 1.59811 | − | 4.91849i | ||||
\(705\) | −0.142040 | − | 0.278768i | −0.142040 | − | 0.278768i | ||||
\(706\) | 0.190983 | + | 0.587785i | 0.190983 | + | 0.587785i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.91849 | + | 1.59811i | −4.91849 | + | 1.59811i | ||||
\(709\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(710\) | 1.77152 | + | 0.280582i | 1.77152 | + | 0.280582i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.12334 | − | 4.29892i | 3.12334 | − | 4.29892i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.412215 | + | 0.809017i | −0.412215 | + | 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 | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(720\) | −0.707107 | + | 4.46450i | −0.707107 | + | 4.46450i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.87869 | + | 0.610425i | 1.87869 | + | 0.610425i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.79360 | 1.79360 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.346818 | −0.346818 | ||||||||
\(727\) | 0.363271 | + | 0.500000i | 0.363271 | + | 0.500000i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − | 5.52015i | − | 5.52015i | ||||||
\(733\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(734\) | −1.87869 | − | 1.36495i | −1.87869 | − | 1.36495i | ||||
\(735\) | −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 | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.907981i | 0.907981i | 0.891007 | + | 0.453990i | \(0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.26007 | − | 0.642040i | −1.26007 | − | 0.642040i | ||||
\(746\) | 0.377263 | − | 1.16110i | 0.377263 | − | 1.16110i | ||||
\(747\) | −1.87869 | − | 0.610425i | −1.87869 | − | 0.610425i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1.76007 | − | 0.896802i | 1.76007 | − | 0.896802i | ||||
\(751\) | −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 | ||||||||
\(761\) | 0.253116 | − | 0.183900i | 0.253116 | − | 0.183900i | −0.453990 | − | 0.891007i | \(-0.650000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 1.87869 | − | 2.58580i | 1.87869 | − | 2.58580i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.26007 | − | 1.64204i | −2.26007 | − | 1.64204i | ||||
\(767\) | −1.69480 | + | 0.550672i | −1.69480 | + | 0.550672i | ||||
\(768\) | − | 6.31375i | − | 6.31375i | ||||||
\(769\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.04744 | + | 1.44168i | 1.04744 | + | 1.44168i | 0.891007 | + | 0.453990i | \(0.150000\pi\) |
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(774\) | −2.32219 | −2.32219 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −0.453990 | + | 2.86638i | −0.453990 | + | 2.86638i | ||||
\(781\) | −0.254763 | − | 0.784079i | −0.254763 | − | 0.784079i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.65688 | + | 2.65688i | 3.65688 | + | 2.65688i | ||||
\(785\) | −0.863541 | + | 1.69480i | −0.863541 | + | 1.69480i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(788\) | −2.41239 | + | 3.32037i | −2.41239 | + | 3.32037i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.24466 | − | 1.05425i | 3.24466 | − | 1.05425i | ||||
\(793\) | − | 1.90211i | − | 1.90211i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.05425 | − | 3.24466i | 1.05425 | − | 3.24466i | ||||
\(797\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −4.18391 | + | 3.03979i | −4.18391 | + | 3.03979i | ||||
\(801\) | 1.41421 | 1.41421 | ||||||||
\(802\) | −1.05425 | − | 1.45106i | −1.05425 | − | 1.45106i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(810\) | −1.76007 | + | 0.896802i | −1.76007 | + | 0.896802i | ||||
\(811\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.896802 | + | 0.142040i | −0.896802 | + | 0.142040i | ||||
\(821\) | −0.610425 | + | 1.87869i | −0.610425 | + | 1.87869i | −0.156434 | + | 0.987688i | \(0.550000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(822\) | −2.65688 | − | 0.863271i | −2.65688 | − | 0.863271i | ||||
\(823\) | 1.11803 | + | 1.53884i | 1.11803 | + | 1.53884i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.734572 | − | 0.533698i | −0.734572 | − | 0.533698i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.533698 | + | 0.734572i | 0.533698 | + | 0.734572i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.363271 | − | 1.11803i | 0.363271 | − | 1.11803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(830\) | −1.77152 | − | 3.47681i | −1.77152 | − | 3.47681i | ||||
\(831\) | −0.363271 | − | 1.11803i | −0.363271 | − | 1.11803i | ||||
\(832\) | − | 5.69572i | − | 5.69572i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −0.987688 | − | 0.717598i | −0.987688 | − | 0.717598i | ||||
\(835\) | −1.76007 | − | 0.278768i | −1.76007 | − | 0.278768i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.44168 | − | 1.04744i | 1.44168 | − | 1.04744i | 0.453990 | − | 0.891007i | \(-0.350000\pi\) |
0.987688 | − | 0.156434i | \(-0.0500000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.78201i | − | 1.78201i | ||||||
\(844\) | 1.05425 | + | 3.24466i | 1.05425 | + | 3.24466i | ||||
\(845\) | −0.156434 | + | 0.987688i | −0.156434 | + | 0.987688i | ||||
\(846\) | −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 | ||||||||
\(852\) | −1.54885 | − | 2.13181i | −1.54885 | − | 2.13181i | ||||
\(853\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 1.70582 | − | 0.554254i | 1.70582 | − | 0.554254i | ||||
\(859\) | 0.951057 | + | 0.690983i | 0.951057 | + | 0.690983i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(860\) | −2.41239 | − | 2.41239i | −2.41239 | − | 2.41239i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.29360 | + | 3.15688i | −2.29360 | + | 3.15688i | ||||
\(863\) | −0.183900 | + | 0.253116i | −0.183900 | + | 0.253116i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(864\) | 4.18391 | − | 3.03979i | 4.18391 | − | 3.03979i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.987688 | − | 0.717598i | −0.987688 | − | 0.717598i | ||||
\(867\) | −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 | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(878\) | −3.03979 | − | 0.987688i | −3.03979 | − | 0.987688i | ||||
\(879\) | −0.0966818 | + | 0.297556i | −0.0966818 | + | 0.297556i | ||||
\(880\) | 3.65688 | + | 1.86327i | 3.65688 | + | 1.86327i | ||||
\(881\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(882\) | 1.97538i | 1.97538i | ||||||||
\(883\) | 1.53884 | − | 0.500000i | 1.53884 | − | 0.500000i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.278768 | − | 1.76007i | −0.278768 | − | 1.76007i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.97538 | + | 1.97538i | 1.97538 | + | 1.97538i | ||||
\(891\) | 0.734572 | + | 0.533698i | 0.734572 | + | 0.533698i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0.863271 | + | 2.65688i | 0.863271 | + | 2.65688i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.06909 | − | 2.84786i | −2.06909 | − | 2.84786i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −2.76007 | − | 0.896802i | −2.76007 | − | 0.896802i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0.329843 | + | 0.453990i | 0.329843 | + | 0.453990i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0966818 | + | 0.610425i | −0.0966818 | + | 0.610425i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(908\) | −3.90333 | + | 1.26827i | −3.90333 | + | 1.26827i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.05425 | + | 1.45106i | −1.05425 | + | 1.45106i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.87869 | + | 0.297556i | 1.87869 | + | 0.297556i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.587785 | + | 1.80902i | 0.587785 | + | 1.80902i | 0.587785 | + | 0.809017i | \(0.300000\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.34786 | + | 1.08779i | 3.34786 | + | 1.08779i | ||||
\(923\) | −0.533698 | − | 0.734572i | −0.533698 | − | 0.734572i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.0966818 | − | 0.297556i | 0.0966818 | − | 0.297556i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.03979 | − | 2.20854i | 3.03979 | − | 2.20854i | ||||
\(937\) | −0.363271 | + | 0.500000i | −0.363271 | + | 0.500000i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.30902 | − | 0.951057i | 1.30902 | − | 0.951057i | ||||
\(940\) | −0.809017 | + | 0.412215i | −0.809017 | + | 0.412215i | ||||
\(941\) | −0.734572 | − | 0.533698i | −0.734572 | − | 0.533698i | 0.156434 | − | 0.987688i | \(-0.450000\pi\) |
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(942\) | 3.57349 | − | 1.16110i | 3.57349 | − | 1.16110i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 2.48912 | + | 7.66072i | 2.48912 | + | 7.66072i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.651565 | + | 2.00531i | −0.651565 | + | 2.00531i | ||||
\(947\) | 1.69480 | + | 0.550672i | 1.69480 | + | 0.550672i | 0.987688 | − | 0.156434i | \(-0.0500000\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.97538 | −1.97538 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.26827 | − | 3.90333i | −1.26827 | − | 3.90333i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.34786 | − | 1.08779i | 3.34786 | − | 1.08779i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.62559 | + | 0.891007i | 5.62559 | + | 0.891007i | ||||
\(961\) | −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 | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(968\) | 0.659687i | 0.659687i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(972\) | 2.76007 | + | 0.896802i | 2.76007 | + | 0.896802i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(976\) | −8.59783 | −8.59783 | ||||||||
\(977\) | −1.04744 | − | 1.44168i | −1.04744 | − | 1.44168i | −0.891007 | − | 0.453990i | \(-0.850000\pi\) |
−0.156434 | − | 0.987688i | \(-0.550000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.396802 | − | 1.22123i | 0.396802 | − | 1.22123i | ||||
\(980\) | −2.05210 | + | 2.05210i | −2.05210 | + | 2.05210i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.297556 | − | 0.0966818i | 0.297556 | − | 0.0966818i | −0.156434 | − | 0.987688i | \(-0.550000\pi\) |
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(984\) | 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 | ||||||||
\(990\) | 0.280582 | + | 1.77152i | 0.280582 | + | 1.77152i | ||||
\(991\) | 1.30902 | + | 0.951057i | 1.30902 | + | 0.951057i | 1.00000 | \(0\) | ||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.04744 | + | 0.533698i | 1.04744 | + | 0.533698i | ||||
\(996\) | −1.77152 | + | 5.45218i | −1.77152 | + | 5.45218i | ||||
\(997\) | 1.11803 | + | 0.363271i | 1.11803 | + | 0.363271i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 975.1.bi.a.389.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 975.1.bi.a.389.4 | yes | 16 | |
13.12 | even | 2 | inner | 975.1.bi.a.389.4 | yes | 16 | |
25.9 | even | 10 | inner | 975.1.bi.a.584.1 | yes | 16 | |
39.38 | odd | 2 | CM | 975.1.bi.a.389.1 | ✓ | 16 | |
75.59 | odd | 10 | inner | 975.1.bi.a.584.4 | yes | 16 | |
325.259 | even | 10 | inner | 975.1.bi.a.584.4 | yes | 16 | |
975.584 | odd | 10 | inner | 975.1.bi.a.584.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.1.bi.a.389.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
975.1.bi.a.389.1 | ✓ | 16 | 39.38 | odd | 2 | CM | |
975.1.bi.a.389.4 | yes | 16 | 3.2 | odd | 2 | inner | |
975.1.bi.a.389.4 | yes | 16 | 13.12 | even | 2 | inner | |
975.1.bi.a.584.1 | yes | 16 | 25.9 | even | 10 | inner | |
975.1.bi.a.584.1 | yes | 16 | 975.584 | odd | 10 | inner | |
975.1.bi.a.584.4 | yes | 16 | 75.59 | odd | 10 | inner | |
975.1.bi.a.584.4 | yes | 16 | 325.259 | even | 10 | inner |