Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2005,1,Mod(1202,2005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2005, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2005.1202");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2005 = 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2005.g (of order \(4\), degree \(2\), 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: | \(1.00062535033\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{20}\) |
Projective field: | Galois closure of 20.0.8181810539473601738391143798828125.1 |
Embedding invariants
Embedding label | 1202.4 | ||
Root | \(-0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2005.1202 |
Dual form | 2005.1.g.b.1603.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2005\mathbb{Z}\right)^\times\).
\(n\) | \(402\) | \(1206\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26007 | + | 1.26007i | 1.26007 | + | 1.26007i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(3\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | 2.17557i | 2.17557i | ||||||||
\(5\) | 0.309017 | − | 0.951057i | 0.309017 | − | 0.951057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.39680 | + | 1.39680i | 1.39680 | + | 1.39680i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(8\) | −1.48131 | + | 1.48131i | −1.48131 | + | 1.48131i | ||||
\(9\) | − | 1.00000i | − | 1.00000i | ||||||
\(10\) | 1.58779 | − | 0.809017i | 1.58779 | − | 0.809017i | ||||
\(11\) | −1.17557 | −1.17557 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 3.52015i | 3.52015i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.55754 | −1.55754 | ||||||||
\(17\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(18\) | 1.26007 | − | 1.26007i | 1.26007 | − | 1.26007i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 2.06909 | + | 0.672288i | 2.06909 | + | 0.672288i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.48131 | − | 1.48131i | −1.48131 | − | 1.48131i | ||||
\(23\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.03884 | + | 3.03884i | −3.03884 | + | 3.03884i | ||||
\(29\) | 0.618034i | 0.618034i | 0.951057 | + | 0.309017i | \(0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −0.481305 | − | 0.481305i | −0.481305 | − | 0.481305i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.76007 | − | 0.896802i | 1.76007 | − | 0.896802i | ||||
\(36\) | 2.17557 | 2.17557 | ||||||||
\(37\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.951057 | + | 1.86655i | 0.951057 | + | 1.86655i | ||||
\(41\) | −1.90211 | −1.90211 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(44\) | − | 2.55754i | − | 2.55754i | ||||||
\(45\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.90211i | 2.90211i | ||||||||
\(50\) | −0.278768 | − | 1.76007i | −0.278768 | − | 1.76007i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.363271 | + | 1.11803i | −0.363271 | + | 1.11803i | ||||
\(56\) | −4.13818 | −4.13818 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.778768 | + | 0.778768i | −0.778768 | + | 0.778768i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | ||||
\(64\) | 0.344577i | 0.344577i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.34786 | + | 1.08779i | 3.34786 | + | 1.08779i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 1.48131 | + | 1.48131i | 1.48131 | + | 1.48131i | ||||
\(73\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.64204 | − | 1.64204i | −1.64204 | − | 1.64204i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −0.481305 | + | 1.48131i | −0.481305 | + | 1.48131i | ||||
\(81\) | −1.00000 | −1.00000 | ||||||||
\(82\) | −2.39680 | − | 2.39680i | −2.39680 | − | 2.39680i | ||||
\(83\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.52015 | 3.52015 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.74138 | − | 1.74138i | 1.74138 | − | 1.74138i | ||||
\(89\) | − | 1.17557i | − | 1.17557i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(90\) | −0.809017 | − | 1.58779i | −0.809017 | − | 1.58779i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 3.17557i | − | 3.17557i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(98\) | −3.65688 | + | 3.65688i | −3.65688 | + | 3.65688i | ||||
\(99\) | 1.17557i | 1.17557i | ||||||||
\(100\) | 1.27877 | − | 1.76007i | 1.27877 | − | 1.76007i | ||||
\(101\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.642040 | − | 0.642040i | 0.642040 | − | 0.642040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(110\) | −1.86655 | + | 0.951057i | −1.86655 | + | 0.951057i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.17557 | − | 2.17557i | −2.17557 | − | 2.17557i | ||||
\(113\) | −1.39680 | + | 1.39680i | −1.39680 | + | 1.39680i | −0.587785 | + | 0.809017i | \(0.700000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.34458 | −1.34458 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.381966 | 0.381966 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(126\) | 3.52015 | 3.52015 | ||||||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | −0.915497 | + | 0.915497i | −0.915497 | + | 0.915497i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 1.95106 | + | 3.82916i | 1.95106 | + | 3.82916i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.55754i | 1.55754i | ||||||||
\(145\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(146\) | −3.17557 | −3.17557 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.17557i | 1.17557i | 0.809017 | + | 0.587785i | \(0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.90211 | 1.90211 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 4.13818i | − | 4.13818i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.606480 | + | 0.309017i | −0.606480 | + | 0.309017i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | − | 4.13818i | − | 4.13818i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.52015 | 2.52015 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.00000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.03884 | + | 3.03884i | 3.03884 | + | 3.03884i | ||||
\(173\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.309017 | − | 1.95106i | −0.309017 | − | 1.95106i | ||||
\(176\) | 1.83099 | 1.83099 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.48131 | − | 1.48131i | 1.48131 | − | 1.48131i | ||||
\(179\) | 0.618034i | 0.618034i | 0.951057 | + | 0.309017i | \(0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(180\) | 0.672288 | − | 2.06909i | 0.672288 | − | 2.06909i | ||||
\(181\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.74138 | − | 2.74138i | 2.74138 | − | 2.74138i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.31375 | −6.31375 | ||||||||
\(197\) | 1.39680 | + | 1.39680i | 1.39680 | + | 1.39680i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(198\) | −1.48131 | + | 1.48131i | −1.48131 | + | 1.48131i | ||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 2.06909 | − | 0.327712i | 2.06909 | − | 0.327712i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.863271 | + | 0.863271i | −0.863271 | + | 0.863271i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.587785 | + | 1.80902i | −0.587785 | + | 1.80902i | ||||
\(206\) | 1.61803 | 1.61803 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.896802 | − | 1.76007i | −0.896802 | − | 1.76007i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.03884 | − | 2.03884i | 2.03884 | − | 2.03884i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.43236 | − | 0.790322i | −2.43236 | − | 0.790322i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.221232 | + | 0.221232i | −0.221232 | + | 0.221232i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(224\) | − | 1.34458i | − | 1.34458i | ||||||
\(225\) | −0.587785 | + | 0.809017i | −0.587785 | + | 0.809017i | ||||
\(226\) | −3.52015 | −3.52015 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.17557i | − | 1.17557i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.915497 | − | 0.915497i | −0.915497 | − | 0.915497i | ||||
\(233\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.58779 | + | 0.809017i | −1.58779 | + | 0.809017i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(242\) | 0.481305 | + | 0.481305i | 0.481305 | + | 0.481305i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.76007 | + | 0.896802i | 2.76007 | + | 0.896802i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.76007 | − | 0.278768i | −1.76007 | − | 0.278768i | ||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 3.03884 | + | 3.03884i | 3.03884 | + | 3.03884i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.96261 | −1.96261 | ||||||||
\(257\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.618034 | 0.618034 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.642040 | − | 0.642040i | 0.642040 | − | 0.642040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.951057 | + | 0.690983i | 0.951057 | + | 0.690983i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.27877 | + | 3.93564i | −1.27877 | + | 3.93564i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.65688 | − | 2.65688i | −2.65688 | − | 2.65688i | ||||
\(288\) | −0.481305 | + | 0.481305i | −0.481305 | + | 0.481305i | ||||
\(289\) | 1.00000i | 1.00000i | ||||||||
\(290\) | 0.500000 | + | 0.981305i | 0.500000 | + | 0.981305i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.74138 | − | 2.74138i | −2.74138 | − | 2.74138i | ||||
\(293\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.48131 | + | 1.48131i | −1.48131 | + | 1.48131i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.90211 | 3.90211 | ||||||||
\(302\) | 2.39680 | + | 2.39680i | 2.39680 | + | 2.39680i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.642040 | + | 0.642040i | 0.642040 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(308\) | 3.57237 | − | 3.57237i | 3.57237 | − | 3.57237i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.39680 | + | 1.39680i | −1.39680 | + | 1.39680i | −0.587785 | + | 0.809017i | \(0.700000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.896802 | − | 1.76007i | −0.896802 | − | 1.76007i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.726543i | − | 0.726543i | ||||||
\(320\) | 0.327712 | + | 0.106480i | 0.327712 | + | 0.106480i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | − | 2.17557i | − | 2.17557i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.81761 | − | 2.81761i | 2.81761 | − | 2.81761i | ||||
\(329\) | − | 3.52015i | − | 3.52015i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.90211 | 1.90211 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(332\) | 2.17557 | + | 2.17557i | 2.17557 | + | 2.17557i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(338\) | 1.26007 | − | 1.26007i | 1.26007 | − | 1.26007i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.65688 | + | 2.65688i | −2.65688 | + | 2.65688i | ||||
\(344\) | 4.13818i | 4.13818i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.52015 | 3.52015 | ||||||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(350\) | 2.06909 | − | 2.84786i | 2.06909 | − | 2.84786i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.565808 | + | 0.565808i | 0.565808 | + | 0.565808i | ||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.55754 | 2.55754 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.778768 | + | 0.778768i | −0.778768 | + | 0.778768i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 1.86655 | − | 0.951057i | 1.86655 | − | 0.951057i | ||||
\(361\) | −1.00000 | −1.00000 | ||||||||
\(362\) | 0.778768 | + | 0.778768i | 0.778768 | + | 0.778768i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.809017 | + | 1.58779i | 0.809017 | + | 1.58779i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.90211i | 1.90211i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | −0.309017 | + | 0.951057i | \(0.600000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.73311 | 3.73311 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.00000i | 2.00000i | 1.00000i | \(0.5\pi\) | ||||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.00000 | + | 1.00000i | −1.00000 | + | 1.00000i | 1.00000i | \(0.5\pi\) | ||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.06909 | + | 1.05425i | −2.06909 | + | 1.05425i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.39680 | − | 1.39680i | −1.39680 | − | 1.39680i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −4.29892 | − | 4.29892i | −4.29892 | − | 4.29892i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.52015i | 3.52015i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.55754 | −2.55754 | ||||||||
\(397\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.26007 | + | 0.915497i | 1.26007 | + | 0.915497i | ||||
\(401\) | 1.00000 | 1.00000 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(406\) | −2.17557 | −2.17557 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(410\) | −3.02015 | + | 1.53884i | −3.02015 | + | 1.53884i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.39680 | + | 1.39680i | 1.39680 | + | 1.39680i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.642040 | − | 1.26007i | −0.642040 | − | 1.26007i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.08779 | − | 3.34786i | 1.08779 | − | 3.34786i | ||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.642040 | + | 0.642040i | −0.642040 | + | 0.642040i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.52015 | 3.52015 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | −1.11803 | − | 2.19427i | −1.11803 | − | 2.19427i | ||||
\(441\) | 2.90211 | 2.90211 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.11803 | − | 0.363271i | −1.11803 | − | 0.363271i | ||||
\(446\) | −0.557537 | −0.557537 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.481305 | + | 0.481305i | −0.481305 | + | 0.481305i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | −1.76007 | + | 0.278768i | −1.76007 | + | 0.278768i | ||||
\(451\) | 2.23607 | 2.23607 | ||||||||
\(452\) | −3.03884 | − | 3.03884i | −3.03884 | − | 3.03884i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.221232 | − | 0.221232i | −0.221232 | − | 0.221232i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(458\) | 1.48131 | − | 1.48131i | 1.48131 | − | 1.48131i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | − | 0.962611i | − | 0.962611i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −3.02015 | − | 0.981305i | −3.02015 | − | 0.981305i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.64204 | + | 1.64204i | −1.64204 | + | 1.64204i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.03884 | + | 2.03884i | −2.03884 | + | 2.03884i | ||||
\(479\) | 1.17557i | 1.17557i | 0.809017 | + | 0.587785i | \(0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.778768 | + | 0.778768i | 0.778768 | + | 0.778768i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.830994i | 0.830994i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.34786 | + | 4.60793i | 2.34786 | + | 4.60793i | ||||
\(491\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.11803 | + | 0.363271i | 1.11803 | + | 0.363271i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | −1.27877 | − | 1.76007i | −1.27877 | − | 1.76007i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.26007 | − | 1.26007i | 1.26007 | − | 1.26007i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(504\) | 4.13818i | 4.13818i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.52015 | −3.52015 | ||||||||
\(512\) | −1.55754 | − | 1.55754i | −1.55754 | − | 1.55754i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 2.52015i | − | 2.52015i | ||||||
\(515\) | −0.412215 | − | 0.809017i | −0.412215 | − | 0.809017i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.48131 | + | 1.48131i | 1.48131 | + | 1.48131i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 0.778768 | + | 0.778768i | 0.778768 | + | 0.778768i | ||||
\(523\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.61803 | 1.61803 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1.00000i | − | 1.00000i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 3.41164i | − | 3.41164i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.53884 | − | 0.500000i | −1.53884 | − | 0.500000i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.642040 | − | 0.642040i | −0.642040 | − | 0.642040i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.327712 | + | 2.06909i | 0.327712 | + | 2.06909i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.39680 | − | 1.39680i | −1.39680 | − | 1.39680i | −0.809017 | − | 0.587785i | \(-0.800000\pi\) |
−0.587785 | − | 0.809017i | \(-0.700000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.74138 | + | 1.39680i | −2.74138 | + | 1.39680i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.221232 | − | 0.221232i | 0.221232 | − | 0.221232i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.896802 | + | 1.76007i | 0.896802 | + | 1.76007i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.39680 | − | 1.39680i | −1.39680 | − | 1.39680i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 6.69572i | − | 6.69572i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.344577 | 0.344577 | ||||||||
\(577\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.309017 | − | 0.951057i | \(-0.600000\pi\) | |||||||
\(578\) | −1.26007 | + | 1.26007i | −1.26007 | + | 1.26007i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.415497 | + | 1.27877i | −0.415497 | + | 1.27877i | ||||
\(581\) | 2.79360 | 2.79360 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 3.73311i | − | 3.73311i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.642040 | + | 0.642040i | 0.642040 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.55754 | −2.55754 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(602\) | 4.91695 | + | 4.91695i | 4.91695 | + | 4.91695i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.13818i | 4.13818i | ||||||||
\(605\) | 0.118034 | − | 0.363271i | 0.118034 | − | 0.363271i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.221232 | − | 0.221232i | −0.221232 | − | 0.221232i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(614\) | 1.61803i | 1.61803i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.86472 | 4.86472 | ||||||||
\(617\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.778768 | − | 0.778768i | −0.778768 | − | 0.778768i | ||||
\(623\) | 1.64204 | − | 1.64204i | 1.64204 | − | 1.64204i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(626\) | −3.52015 | −3.52015 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 1.08779 | − | 3.34786i | 1.08779 | − | 3.34786i | ||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.915497 | − | 0.915497i | 0.915497 | − | 0.915497i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.587785 | + | 1.15359i | 0.587785 | + | 1.15359i | ||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00000 | − | 1.00000i | 1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
1.00000 | \(0\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 1.48131 | − | 1.48131i | 1.48131 | − | 1.48131i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.642040 | − | 0.642040i | 0.642040 | − | 0.642040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.96261 | 2.96261 | ||||||||
\(657\) | 1.26007 | + | 1.26007i | 1.26007 | + | 1.26007i | ||||
\(658\) | 4.43564 | − | 4.43564i | 4.43564 | − | 4.43564i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 2.39680 | + | 2.39680i | 2.39680 | + | 2.39680i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.96261i | 2.96261i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(674\) | − | 2.52015i | − | 2.52015i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.17557 | 2.17557 | ||||||||
\(677\) | 0.642040 | + | 0.642040i | 0.642040 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.69572 | −6.69572 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.17557 | + | 2.17557i | −2.17557 | + | 2.17557i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(692\) | 3.03884 | + | 3.03884i | 3.03884 | + | 3.03884i | ||||
\(693\) | −1.64204 | + | 1.64204i | −1.64204 | + | 1.64204i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.24466 | − | 0.672288i | 4.24466 | − | 0.672288i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 0.405074i | − | 0.405074i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.90211i | 1.90211i | 0.309017 | + | 0.951057i | \(0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.74138 | + | 1.74138i | 1.74138 | + | 1.74138i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.34458 | −1.34458 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.61803i | − | 1.61803i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(720\) | 1.48131 | + | 0.481305i | 1.48131 | + | 0.481305i | ||||
\(721\) | 1.79360 | 1.79360 | ||||||||
\(722\) | −1.26007 | − | 1.26007i | −1.26007 | − | 1.26007i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.34458i | 1.34458i | ||||||||
\(725\) | 0.363271 | − | 0.500000i | 0.363271 | − | 0.500000i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 1.00000i | ||||||||
\(730\) | −0.981305 | + | 3.02015i | −0.981305 | + | 3.02015i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.221232 | − | 0.221232i | 0.221232 | − | 0.221232i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −2.39680 | + | 2.39680i | −2.39680 | + | 2.39680i | ||||
\(739\) | − | 0.618034i | − | 0.618034i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.11803 | + | 0.363271i | 1.11803 | + | 0.363271i | ||||
\(746\) | −3.17557 | −3.17557 | ||||||||
\(747\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.61803 | −1.61803 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(752\) | 1.96261 | + | 1.96261i | 1.96261 | + | 1.96261i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.587785 | − | 1.80902i | 0.587785 | − | 1.80902i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.642040 | − | 0.642040i | −0.642040 | − | 0.642040i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(758\) | −2.52015 | + | 2.52015i | −2.52015 | + | 2.52015i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.17557 | 1.17557 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.26007 | − | 2.26007i | 2.26007 | − | 2.26007i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.52015 | −2.52015 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | −3.93564 | − | 1.27877i | −3.93564 | − | 1.27877i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.39680 | − | 1.39680i | 1.39680 | − | 1.39680i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(774\) | − | 3.52015i | − | 3.52015i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 4.52015i | − | 4.52015i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(788\) | −3.03884 | + | 3.03884i | −3.03884 | + | 3.03884i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.90211 | −3.90211 | ||||||||
\(792\) | −1.74138 | − | 1.74138i | −1.74138 | − | 1.74138i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | − | 2.52015i | − | 2.52015i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.00000 | + | 1.00000i | 1.00000 | + | 1.00000i | 1.00000 | \(0\) | ||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.106480 | + | 0.672288i | 0.106480 | + | 0.672288i | ||||
\(801\) | −1.17557 | −1.17557 | ||||||||
\(802\) | 1.26007 | + | 1.26007i | 1.26007 | + | 1.26007i | ||||
\(803\) | 1.48131 | − | 1.48131i | 1.48131 | − | 1.48131i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(810\) | −1.58779 | + | 0.809017i | −1.58779 | + | 0.809017i | ||||
\(811\) | 0.618034 | 0.618034 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(812\) | −1.87811 | − | 1.87811i | −1.87811 | − | 1.87811i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −2.03884 | + | 2.03884i | −2.03884 | + | 2.03884i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.93564 | − | 1.27877i | −3.93564 | − | 1.27877i | ||||
\(821\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | 1.90211i | 1.90211i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.26007 | + | 1.26007i | 1.26007 | + | 1.26007i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(830\) | 0.778768 | − | 2.39680i | 0.778768 | − | 2.39680i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.03884 | + | 2.03884i | −2.03884 | + | 2.03884i | ||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.618034 | 0.618034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(846\) | −3.17557 | −3.17557 | ||||||||
\(847\) | 0.533531 | + | 0.533531i | 0.533531 | + | 0.533531i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.642040 | + | 0.642040i | −0.642040 | + | 0.642040i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.221232 | + | 0.221232i | 0.221232 | + | 0.221232i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.61803i | 1.61803i | 0.587785 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(860\) | 3.82916 | − | 1.95106i | 3.82916 | − | 1.95106i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.896802 | − | 1.76007i | −0.896802 | − | 1.76007i | ||||
\(866\) | −1.61803 | −1.61803 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 2.39680 | + | 2.39680i | 2.39680 | + | 2.39680i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.95106 | − | 0.309017i | −1.95106 | − | 0.309017i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.565808 | − | 1.74138i | 0.565808 | − | 1.74138i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 3.65688 | + | 3.65688i | 3.65688 | + | 3.65688i | ||||
\(883\) | 0.221232 | − | 0.221232i | 0.221232 | − | 0.221232i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.951057 | − | 1.86655i | −0.951057 | − | 1.86655i | ||||
\(891\) | 1.17557 | 1.17557 | ||||||||
\(892\) | −0.481305 | − | 0.481305i | −0.481305 | − | 0.481305i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.587785 | + | 0.190983i | 0.587785 | + | 0.190983i | ||||
\(896\) | −2.55754 | −2.55754 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.76007 | − | 1.27877i | −1.76007 | − | 1.27877i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.81761 | + | 2.81761i | 2.81761 | + | 2.81761i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 4.13818i | − | 4.13818i | ||||||
\(905\) | 0.190983 | − | 0.587785i | 0.190983 | − | 0.587785i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.61803 | 1.61803 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.17557 | + | 1.17557i | −1.17557 | + | 1.17557i | ||||
\(914\) | − | 0.557537i | − | 0.557537i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.55754 | 2.55754 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.642040 | − | 0.642040i | −0.642040 | − | 0.642040i | ||||
\(928\) | 0.297463 | − | 0.297463i | 0.297463 | − | 0.297463i | ||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.76007 | − | 3.45434i | −1.76007 | − | 3.45434i | ||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.13818 | −4.13818 | ||||||||
\(947\) | 0.642040 | + | 0.642040i | 0.642040 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.642040 | − | 0.642040i | 0.642040 | − | 0.642040i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.52015 | −3.52015 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.48131 | + | 1.48131i | −1.48131 | + | 1.48131i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.34458i | 1.34458i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(968\) | −0.565808 | + | 0.565808i | −0.565808 | + | 0.565808i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.618034 | −0.618034 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.52015i | 2.52015i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.642040 | + | 0.642040i | 0.642040 | + | 0.642040i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.38197i | 1.38197i | ||||||||
\(980\) | −1.95106 | + | 6.00473i | −1.95106 | + | 6.00473i | ||||
\(981\) | −1.61803 | −1.61803 | ||||||||
\(982\) | −2.03884 | − | 2.03884i | −2.03884 | − | 2.03884i | ||||
\(983\) | −1.39680 | + | 1.39680i | −1.39680 | + | 1.39680i | −0.587785 | + | 0.809017i | \(0.700000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.76007 | − | 0.896802i | 1.76007 | − | 0.896802i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0.951057 | + | 1.86655i | 0.951057 | + | 1.86655i | ||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00000 | − | 1.00000i | −1.00000 | − | 1.00000i | − | 1.00000i | \(-0.5\pi\) | |
−1.00000 | \(\pi\) | |||||||||
\(998\) | 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 | 2005.1.g.b.1202.4 | ✓ | 8 | |
5.3 | odd | 4 | inner | 2005.1.g.b.1603.4 | yes | 8 | |
401.400 | even | 2 | RM | 2005.1.g.b.1202.4 | ✓ | 8 | |
2005.1603 | odd | 4 | inner | 2005.1.g.b.1603.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2005.1.g.b.1202.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
2005.1.g.b.1202.4 | ✓ | 8 | 401.400 | even | 2 | RM | |
2005.1.g.b.1603.4 | yes | 8 | 5.3 | odd | 4 | inner | |
2005.1.g.b.1603.4 | yes | 8 | 2005.1603 | odd | 4 | inner |