Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2020,1,Mod(7,2020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2020, base_ring=CyclotomicField(100))
chi = DirichletCharacter(H, H._module([50, 25, 9]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2020.7");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2020 = 2^{2} \cdot 5 \cdot 101 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2020.cd (of order \(100\), degree \(40\), 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: | \(1.00811132552\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Coefficient field: | \(\Q(\zeta_{100})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{40} - x^{30} + x^{20} - x^{10} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{100}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{100} - \cdots)\) |
Embedding invariants
Embedding label | 1003.1 | ||
Root | \(0.684547 - 0.728969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2020.1003 |
Dual form | 2020.1.cd.a.1587.1 |
$q$-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 \(\left(\mathbb{Z}/2020\mathbb{Z}\right)^\times\).
\(n\) | \(1011\) | \(1617\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{59}{100}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.481754 | + | 0.876307i | 0.481754 | + | 0.876307i | ||||
\(3\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(4\) | −0.535827 | + | 0.844328i | −0.535827 | + | 0.844328i | ||||
\(5\) | 0.125333 | − | 0.992115i | 0.125333 | − | 0.992115i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.982287 | − | 0.187381i | \(-0.940000\pi\) | ||||
0.982287 | + | 0.187381i | \(0.0600000\pi\) | |||||||
\(8\) | −0.998027 | − | 0.0627905i | −0.998027 | − | 0.0627905i | ||||
\(9\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(10\) | 0.929776 | − | 0.368125i | 0.929776 | − | 0.368125i | ||||
\(11\) | 0 | 0 | 0.509041 | − | 0.860742i | \(-0.330000\pi\) | ||||
−0.509041 | + | 0.860742i | \(0.670000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.01385 | + | 0.689010i | 1.01385 | + | 0.689010i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.425779 | − | 0.904827i | −0.425779 | − | 0.904827i | ||||
\(17\) | −0.278768 | − | 1.76007i | −0.278768 | − | 1.76007i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(18\) | 0.684547 | + | 0.728969i | 0.684547 | + | 0.728969i | ||||
\(19\) | 0 | 0 | −0.904827 | − | 0.425779i | \(-0.860000\pi\) | ||||
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(20\) | 0.770513 | + | 0.637424i | 0.770513 | + | 0.637424i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.999507 | − | 0.0314108i | \(-0.0100000\pi\) | ||||
−0.999507 | + | 0.0314108i | \(0.990000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.968583 | − | 0.248690i | −0.968583 | − | 0.248690i | ||||
\(26\) | −0.115359 | + | 1.22037i | −0.115359 | + | 1.22037i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.258768 | + | 0.175858i | 0.258768 | + | 0.175858i | 0.684547 | − | 0.728969i | \(-0.260000\pi\) |
−0.425779 | + | 0.904827i | \(0.640000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.187381 | − | 0.982287i | \(-0.440000\pi\) | ||||
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(32\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.40807 | − | 1.09221i | 1.40807 | − | 1.09221i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.309017 | + | 0.951057i | −0.309017 | + | 0.951057i | ||||
\(37\) | 1.54225 | − | 1.19629i | 1.54225 | − | 1.19629i | 0.637424 | − | 0.770513i | \(-0.280000\pi\) |
0.904827 | − | 0.425779i | \(-0.140000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.187381 | + | 0.982287i | −0.187381 | + | 0.982287i | ||||
\(41\) | −0.294372 | + | 1.85859i | −0.294372 | + | 1.85859i | 0.187381 | + | 0.982287i | \(0.440000\pi\) |
−0.481754 | + | 0.876307i | \(0.660000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.995562 | − | 0.0941083i | \(-0.970000\pi\) | ||||
0.995562 | + | 0.0941083i | \(0.0300000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.125333 | − | 0.992115i | −0.125333 | − | 0.992115i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.995562 | − | 0.0941083i | \(-0.0300000\pi\) | ||||
−0.995562 | + | 0.0941083i | \(0.970000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.929776 | + | 0.368125i | 0.929776 | + | 0.368125i | ||||
\(50\) | −0.248690 | − | 0.968583i | −0.248690 | − | 0.968583i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.12500 | + | 0.486829i | −1.12500 | + | 0.486829i | ||||
\(53\) | −1.65875 | + | 1.05267i | −1.65875 | + | 1.05267i | −0.728969 | + | 0.684547i | \(0.760000\pi\) |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0294436 | + | 0.311480i | −0.0294436 | + | 0.311480i | ||||
\(59\) | 0 | 0 | 0.338738 | − | 0.940881i | \(-0.390000\pi\) | ||||
−0.338738 | + | 0.940881i | \(0.610000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.288521 | + | 1.29077i | 0.288521 | + | 1.29077i | 0.876307 | + | 0.481754i | \(0.160000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.992115 | + | 0.125333i | 0.992115 | + | 0.125333i | ||||
\(65\) | 0.810645 | − | 0.919497i | 0.810645 | − | 0.919497i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(68\) | 1.63545 | + | 0.707723i | 1.63545 | + | 0.707723i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) | ||||
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(72\) | −0.982287 | + | 0.187381i | −0.982287 | + | 0.187381i | ||||
\(73\) | 0.929324 | + | 0.872693i | 0.929324 | + | 0.872693i | 0.992115 | − | 0.125333i | \(-0.0400000\pi\) |
−0.0627905 | + | 0.998027i | \(0.520000\pi\) | |||||||
\(74\) | 1.79130 | + | 0.775167i | 1.79130 | + | 0.775167i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.684547 | − | 0.728969i | \(-0.740000\pi\) | ||||
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(80\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(81\) | 0.876307 | − | 0.481754i | 0.876307 | − | 0.481754i | ||||
\(82\) | −1.77051 | + | 0.637424i | −1.77051 | + | 0.637424i | ||||
\(83\) | 0 | 0 | 0.728969 | − | 0.684547i | \(-0.240000\pi\) | ||||
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.78113 | + | 0.0559744i | −1.78113 | + | 0.0559744i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.61971 | + | 0.583132i | −1.61971 | + | 0.583132i | −0.982287 | − | 0.187381i | \(-0.940000\pi\) |
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(90\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.360844 | − | 1.61432i | −0.360844 | − | 1.61432i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
0.368125 | − | 0.929776i | \(-0.380000\pi\) | |||||||
\(98\) | 0.125333 | + | 0.992115i | 0.125333 | + | 0.992115i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(101\) | −0.844328 | − | 0.535827i | −0.844328 | − | 0.535827i | ||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(104\) | −0.968583 | − | 0.751310i | −0.968583 | − | 0.751310i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.72157 | − | 0.946441i | −1.72157 | − | 0.946441i | ||||
\(107\) | 0 | 0 | −0.987688 | − | 0.156434i | \(-0.950000\pi\) | ||||
0.987688 | + | 0.156434i | \(0.0500000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.369000 | − | 0.418549i | −0.369000 | − | 0.418549i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.871808 | − | 0.410241i | −0.871808 | − | 0.410241i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.287137 | + | 0.124255i | −0.287137 | + | 0.124255i | ||||
\(117\) | 1.15334 | + | 0.415230i | 1.15334 | + | 0.415230i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.481754 | − | 0.876307i | −0.481754 | − | 0.876307i | ||||
\(122\) | −0.992115 | + | 0.874667i | −0.992115 | + | 0.874667i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.368125 | + | 0.929776i | −0.368125 | + | 0.929776i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(128\) | 0.368125 | + | 0.929776i | 0.368125 | + | 0.929776i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.19629 | + | 0.267403i | 1.19629 | + | 0.267403i | ||||
\(131\) | 0 | 0 | −0.125333 | − | 0.992115i | \(-0.540000\pi\) | ||||
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.167702 | + | 1.77410i | 0.167702 | + | 1.77410i | ||||
\(137\) | −0.903951 | − | 1.77410i | −0.903951 | − | 1.77410i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
−0.368125 | − | 0.929776i | \(-0.620000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.661312 | − | 0.750111i | \(-0.270000\pi\) | ||||
−0.661312 | + | 0.750111i | \(0.730000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.637424 | − | 0.770513i | −0.637424 | − | 0.770513i | ||||
\(145\) | 0.206904 | − | 0.234686i | 0.206904 | − | 0.234686i | ||||
\(146\) | −0.317042 | + | 1.23480i | −0.317042 | + | 1.23480i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.183684 | + | 1.94317i | 0.183684 | + | 1.94317i | ||||
\(149\) | −0.0410582 | + | 0.183684i | −0.0410582 | + | 0.183684i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.960294 | − | 0.278991i | \(-0.0900000\pi\) | ||||
−0.960294 | + | 0.278991i | \(0.910000\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.707723 | − | 1.63545i | −0.707723 | − | 1.63545i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.65313 | + | 0.977659i | −1.65313 | + | 0.977659i | −0.684547 | + | 0.728969i | \(0.740000\pi\) |
−0.968583 | + | 0.248690i | \(0.920000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.728969 | − | 0.684547i | −0.728969 | − | 0.684547i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.844328 | + | 0.535827i | 0.844328 | + | 0.535827i | ||||
\(163\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(164\) | −1.41153 | − | 1.24443i | −1.41153 | − | 1.24443i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
−0.637424 | + | 0.770513i | \(0.720000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.185027 | + | 0.467324i | 0.185027 | + | 0.467324i | ||||
\(170\) | −0.907118 | − | 1.53385i | −0.907118 | − | 1.53385i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.200808 | − | 1.05267i | −0.200808 | − | 1.05267i | −0.929776 | − | 0.368125i | \(-0.880000\pi\) |
0.728969 | − | 0.684547i | \(-0.240000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.29130 | − | 1.13844i | −1.29130 | − | 1.13844i | ||||
\(179\) | 0 | 0 | 0.684547 | − | 0.728969i | \(-0.260000\pi\) | ||||
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(180\) | 0.904827 | + | 0.425779i | 0.904827 | + | 0.425779i | ||||
\(181\) | −0.125333 | + | 1.99211i | −0.125333 | + | 1.99211i | 1.00000i | \(0.5\pi\) | ||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.993564 | − | 1.68003i | −0.993564 | − | 1.68003i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.860742 | − | 0.509041i | \(-0.830000\pi\) | ||||
0.860742 | + | 0.509041i | \(0.170000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.583132 | − | 0.344863i | −0.583132 | − | 0.344863i | 0.187381 | − | 0.982287i | \(-0.440000\pi\) |
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(194\) | 1.24080 | − | 1.09392i | 1.24080 | − | 1.09392i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.809017 | + | 0.587785i | −0.809017 | + | 0.587785i | ||||
\(197\) | 0.551113 | + | 1.89694i | 0.551113 | + | 1.89694i | 0.425779 | + | 0.904827i | \(0.360000\pi\) |
0.125333 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.612907 | − | 0.790155i | \(-0.290000\pi\) | ||||
−0.612907 | + | 0.790155i | \(0.710000\pi\) | |||||||
\(200\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.0627905 | − | 0.998027i | 0.0627905 | − | 0.998027i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.80704 | + | 0.524995i | 1.80704 | + | 0.524995i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.191760 | − | 1.21072i | 0.191760 | − | 1.21072i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.248690 | − | 0.968583i | \(-0.580000\pi\) | ||||
0.248690 | + | 0.968583i | \(0.420000\pi\) | |||||||
\(212\) | − | 1.96457i | − | 1.96457i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.189010 | − | 0.524995i | 0.189010 | − | 0.524995i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.930079 | − | 1.97652i | 0.930079 | − | 1.97652i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.661312 | − | 0.750111i | \(-0.730000\pi\) | ||||
0.661312 | + | 0.750111i | \(0.270000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.00000 | −1.00000 | ||||||||
\(226\) | −0.0604991 | − | 0.961606i | −0.0604991 | − | 0.961606i | ||||
\(227\) | 0 | 0 | −0.975917 | − | 0.218143i | \(-0.930000\pi\) | ||||
0.975917 | + | 0.218143i | \(0.0700000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.446460 | + | 1.03171i | −0.446460 | + | 1.03171i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.247215 | − | 0.191760i | −0.247215 | − | 0.191760i | ||||
\(233\) | 1.24080 | − | 0.843250i | 1.24080 | − | 0.843250i | 0.248690 | − | 0.968583i | \(-0.420000\pi\) |
0.992115 | + | 0.125333i | \(0.0400000\pi\) | |||||||
\(234\) | 0.191760 | + | 1.21072i | 0.191760 | + | 1.21072i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.125333 | − | 0.992115i | \(-0.460000\pi\) | ||||
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.0285204 | − | 0.0559744i | 0.0285204 | − | 0.0559744i | −0.876307 | − | 0.481754i | \(-0.840000\pi\) |
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(242\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.24443 | − | 0.448023i | −1.24443 | − | 0.448023i | ||||
\(245\) | 0.481754 | − | 0.876307i | 0.481754 | − | 0.876307i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.992115 | + | 0.125333i | −0.992115 | + | 0.125333i | ||||
\(251\) | 0 | 0 | 0.368125 | − | 0.929776i | \(-0.380000\pi\) | ||||
−0.368125 | + | 0.929776i | \(0.620000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(257\) | 0.0312307 | − | 0.121636i | 0.0312307 | − | 0.121636i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.982287 | + | 0.187381i | \(0.0600000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.341991 | + | 1.17714i | 0.341991 | + | 1.17714i | ||||
\(261\) | 0.294372 | + | 0.105981i | 0.294372 | + | 0.105981i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.535827 | − | 0.844328i | \(-0.320000\pi\) | ||||
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.836475 | + | 1.77760i | 0.836475 | + | 1.77760i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.22521 | + | 1.57953i | 1.22521 | + | 1.57953i | 0.637424 | + | 0.770513i | \(0.280000\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(272\) | −1.47387 | + | 1.00164i | −1.47387 | + | 1.00164i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.11918 | − | 1.64682i | 1.11918 | − | 1.64682i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.656137 | − | 0.542804i | 0.656137 | − | 0.542804i | −0.248690 | − | 0.968583i | \(-0.580000\pi\) |
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.23098 | − | 1.15596i | 1.23098 | − | 1.15596i | 0.248690 | − | 0.968583i | \(-0.420000\pi\) |
0.982287 | − | 0.187381i | \(-0.0600000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.960294 | − | 0.278991i | \(-0.910000\pi\) | ||||
0.960294 | + | 0.278991i | \(0.0900000\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.368125 | − | 0.929776i | 0.368125 | − | 0.929776i | ||||
\(289\) | −2.06909 | + | 0.672288i | −2.06909 | + | 0.672288i | ||||
\(290\) | 0.305334 | + | 0.0682502i | 0.305334 | + | 0.0682502i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.23480 | + | 0.317042i | −1.23480 | + | 0.317042i | ||||
\(293\) | 1.93717i | 1.93717i | 0.248690 | + | 0.968583i | \(0.420000\pi\) | ||||
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.61432 | + | 1.09709i | −1.61432 | + | 1.09709i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.180743 | + | 0.0525108i | −0.180743 | + | 0.0525108i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.31675 | − | 0.124470i | 1.31675 | − | 0.124470i | ||||
\(306\) | 1.09221 | − | 1.40807i | 1.09221 | − | 1.40807i | ||||
\(307\) | 0 | 0 | 0.975917 | − | 0.218143i | \(-0.0700000\pi\) | ||||
−0.975917 | + | 0.218143i | \(0.930000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.750111 | − | 0.661312i | \(-0.230000\pi\) | ||||
−0.750111 | + | 0.661312i | \(0.770000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.90211 | −1.90211 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(314\) | −1.65313 | − | 0.977659i | −1.65313 | − | 0.977659i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.462200 | + | 0.907118i | −0.462200 | + | 0.907118i | 0.535827 | + | 0.844328i | \(0.320000\pi\) |
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.248690 | − | 0.968583i | 0.248690 | − | 0.968583i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.0627905 | + | 0.998027i | −0.0627905 | + | 0.998027i | ||||
\(325\) | −0.810645 | − | 0.919497i | −0.810645 | − | 0.919497i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.410494 | − | 1.83644i | 0.410494 | − | 1.83644i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.0314108 | − | 0.999507i | \(-0.510000\pi\) | ||||
0.0314108 | + | 0.999507i | \(0.490000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.19629 | − | 1.54225i | 1.19629 | − | 1.54225i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.52888 | − | 0.193142i | −1.52888 | − | 0.193142i | −0.684547 | − | 0.728969i | \(-0.740000\pi\) |
−0.844328 | + | 0.535827i | \(0.820000\pi\) | |||||||
\(338\) | −0.320382 | + | 0.387276i | −0.320382 | + | 0.387276i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.907118 | − | 1.53385i | 0.907118 | − | 1.53385i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.825723 | − | 0.683098i | 0.825723 | − | 0.683098i | ||||
\(347\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.375530 | − | 0.222088i | 0.375530 | − | 0.222088i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.41789 | − | 0.779494i | −1.41789 | − | 0.779494i | −0.425779 | − | 0.904827i | \(-0.640000\pi\) |
−0.992115 | + | 0.125333i | \(0.960000\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.375530 | − | 1.68003i | 0.375530 | − | 1.68003i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.248690 | − | 0.968583i | \(-0.420000\pi\) | ||||
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(360\) | 0.0627905 | + | 0.998027i | 0.0627905 | + | 0.998027i | ||||
\(361\) | 0.637424 | + | 0.770513i | 0.637424 | + | 0.770513i | ||||
\(362\) | −1.80608 | + | 0.849878i | −1.80608 | + | 0.849878i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.982287 | − | 0.812619i | 0.982287 | − | 0.812619i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.612907 | − | 0.790155i | \(-0.710000\pi\) | ||||
0.612907 | + | 0.790155i | \(0.290000\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.177089 | + | 1.87341i | 0.177089 | + | 1.87341i | ||||
\(370\) | 0.993564 | − | 1.68003i | 0.993564 | − | 1.68003i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.245229 | + | 0.360844i | 0.245229 | + | 0.360844i | 0.929776 | − | 0.368125i | \(-0.120000\pi\) |
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.141183 | + | 0.356587i | 0.141183 | + | 0.356587i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.750111 | − | 0.661312i | \(-0.230000\pi\) | ||||
−0.750111 | + | 0.661312i | \(0.770000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0212800 | − | 0.677142i | 0.0212800 | − | 0.677142i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.55637 | + | 0.560327i | 1.55637 | + | 0.560327i | ||||
\(389\) | 0.833304 | − | 0.360603i | 0.833304 | − | 0.360603i | 0.0627905 | − | 0.998027i | \(-0.480000\pi\) |
0.770513 | + | 0.637424i | \(0.220000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.904827 | − | 0.425779i | −0.904827 | − | 0.425779i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.39680 | + | 1.39680i | −1.39680 | + | 1.39680i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0469702 | + | 0.246226i | −0.0469702 | + | 0.246226i | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.187381 | + | 0.982287i | 0.187381 | + | 0.982287i | ||||
\(401\) | −1.24869 | − | 0.968583i | −1.24869 | − | 0.968583i | −0.248690 | − | 0.968583i | \(-0.580000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.904827 | − | 0.425779i | 0.904827 | − | 0.425779i | ||||
\(405\) | −0.368125 | − | 0.929776i | −0.368125 | − | 0.929776i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.844328 | + | 1.53583i | −0.844328 | + | 1.53583i | 1.00000i | \(0.5\pi\) | ||
−0.844328 | + | 0.535827i | \(0.820000\pi\) | |||||||
\(410\) | 0.410494 | + | 1.83644i | 0.410494 | + | 1.83644i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.15334 | − | 0.415230i | 1.15334 | − | 0.415230i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.397148 | − | 0.917755i | \(-0.630000\pi\) | ||||
0.397148 | + | 0.917755i | \(0.370000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.856954 | + | 1.17950i | −0.856954 | + | 1.17950i | 0.125333 | + | 0.992115i | \(0.460000\pi\) |
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.72157 | − | 0.946441i | 1.72157 | − | 0.946441i | ||||
\(425\) | −0.167702 | + | 1.77410i | −0.167702 | + | 1.77410i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.917755 | − | 0.397148i | \(-0.870000\pi\) | ||||
0.917755 | + | 0.397148i | \(0.130000\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.43211 | − | 0.273190i | 1.43211 | − | 0.273190i | 0.587785 | − | 0.809017i | \(-0.300000\pi\) |
0.844328 | + | 0.535827i | \(0.180000\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.551113 | − | 0.0872876i | 0.551113 | − | 0.0872876i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.995562 | − | 0.0941083i | \(-0.0300000\pi\) | ||||
−0.995562 | + | 0.0941083i | \(0.970000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.992115 | + | 0.125333i | 0.992115 | + | 0.125333i | ||||
\(442\) | 2.18011 | − | 0.137161i | 2.18011 | − | 0.137161i | ||||
\(443\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.375530 | + | 1.68003i | 0.375530 | + | 1.68003i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.32608 | + | 0.340480i | 1.32608 | + | 0.340480i | 0.844328 | − | 0.535827i | \(-0.180000\pi\) |
0.481754 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(450\) | −0.481754 | − | 0.876307i | −0.481754 | − | 0.876307i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.813516 | − | 0.516273i | 0.813516 | − | 0.516273i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.06320 | − | 1.67534i | −1.06320 | − | 1.67534i | −0.637424 | − | 0.770513i | \(-0.720000\pi\) |
−0.425779 | − | 0.904827i | \(-0.640000\pi\) | |||||||
\(458\) | −1.11918 | + | 0.105793i | −1.11918 | + | 0.105793i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.462200 | − | 0.907118i | −0.462200 | − | 0.907118i | −0.998027 | − | 0.0627905i | \(-0.980000\pi\) |
0.535827 | − | 0.844328i | \(-0.320000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(464\) | 0.0489435 | − | 0.309017i | 0.0489435 | − | 0.309017i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.33671 | + | 0.681087i | 1.33671 | + | 0.681087i | ||||
\(467\) | 0 | 0 | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) | ||||
0.0627905 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(468\) | −0.968583 | + | 0.751310i | −0.968583 | + | 0.751310i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.34484 | + | 1.43211i | −1.34484 | + | 1.43211i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.0941083 | − | 0.995562i | \(-0.470000\pi\) | ||||
−0.0941083 | + | 0.995562i | \(0.530000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.38786 | − | 0.150232i | 2.38786 | − | 0.150232i | ||||
\(482\) | 0.0627905 | − | 0.00197327i | 0.0627905 | − | 0.00197327i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.998027 | + | 0.0627905i | 0.998027 | + | 0.0627905i | ||||
\(485\) | −1.64682 | + | 0.155670i | −1.64682 | + | 0.155670i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | −0.684547 | − | 0.728969i | \(-0.740000\pi\) | ||||
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(488\) | −0.206904 | − | 1.30634i | −0.206904 | − | 1.30634i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | 1.00000 | ||||||||
\(491\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.237388 | − | 0.504474i | 0.237388 | − | 0.504474i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(500\) | −0.587785 | − | 0.809017i | −0.587785 | − | 0.809017i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.481754 | − | 0.876307i | \(-0.660000\pi\) | ||||
0.481754 | + | 0.876307i | \(0.340000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.637424 | + | 0.770513i | −0.637424 | + | 0.770513i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.866986 | − | 1.36615i | 0.866986 | − | 1.36615i | −0.0627905 | − | 0.998027i | \(-0.520000\pi\) |
0.929776 | − | 0.368125i | \(-0.120000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.982287 | − | 0.187381i | −0.982287 | − | 0.187381i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.121636 | − | 0.0312307i | 0.121636 | − | 0.0312307i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.866781 | + | 0.866781i | −0.866781 | + | 0.866781i | ||||
\(521\) | 0.0534698 | + | 0.113629i | 0.0534698 | + | 0.113629i | 0.929776 | − | 0.368125i | \(-0.120000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(522\) | 0.0489435 | + | 0.309017i | 0.0489435 | + | 0.309017i | ||||
\(523\) | 0 | 0 | −0.684547 | − | 0.728969i | \(-0.740000\pi\) | ||||
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.998027 | − | 0.0627905i | 0.998027 | − | 0.0627905i | ||||
\(530\) | −1.15475 | + | 1.58937i | −1.15475 | + | 1.58937i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.57904 | + | 1.68150i | −1.57904 | + | 1.68150i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.793904 | + | 1.83460i | −0.793904 | + | 1.83460i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.598617 | + | 1.84235i | −0.598617 | + | 1.84235i | −0.0627905 | + | 0.998027i | \(0.520000\pi\) |
−0.535827 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.58779 | − | 0.809017i | −1.58779 | − | 0.809017i | ||||
\(545\) | −0.461496 | + | 0.313633i | −0.461496 | + | 0.313633i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.425779 | − | 0.904827i | \(-0.640000\pi\) | ||||
0.425779 | + | 0.904827i | \(0.360000\pi\) | |||||||
\(548\) | 1.98229 | + | 0.187381i | 1.98229 | + | 0.187381i | ||||
\(549\) | 0.600459 | + | 1.17847i | 0.600459 | + | 1.17847i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.791759 | + | 0.313480i | 0.791759 | + | 0.313480i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.03171 | + | 0.446460i | −1.03171 | + | 0.446460i | −0.844328 | − | 0.535827i | \(-0.820000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.60601 | + | 0.521823i | 1.60601 | + | 0.521823i | ||||
\(563\) | 0 | 0 | 0.0941083 | − | 0.995562i | \(-0.470000\pi\) | ||||
−0.0941083 | + | 0.995562i | \(0.530000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.516273 | + | 0.813516i | −0.516273 | + | 0.813516i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.60528 | + | 0.202793i | 1.60528 | + | 0.202793i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.995562 | − | 0.0941083i | \(-0.0300000\pi\) | ||||
−0.995562 | + | 0.0941083i | \(0.970000\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.992115 | − | 0.125333i | 0.992115 | − | 0.125333i | ||||
\(577\) | 1.77760 | − | 0.339095i | 1.77760 | − | 0.339095i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(578\) | −1.58592 | − | 1.48928i | −1.58592 | − | 1.48928i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.0872876 | + | 0.300446i | 0.0872876 | + | 0.300446i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −0.872693 | − | 0.929324i | −0.872693 | − | 0.929324i | ||||
\(585\) | 0.556508 | − | 1.09221i | 0.556508 | − | 1.09221i | ||||
\(586\) | −1.69755 | + | 0.933237i | −1.69755 | + | 0.933237i | ||||
\(587\) | 0 | 0 | 0.940881 | − | 0.338738i | \(-0.110000\pi\) | ||||
−0.940881 | + | 0.338738i | \(0.890000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.73910 | − | 0.886114i | −1.73910 | − | 0.886114i | ||||
\(593\) | −1.12361 | + | 1.65334i | −1.12361 | + | 1.65334i | −0.535827 | + | 0.844328i | \(0.680000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.133089 | − | 0.133089i | −0.133089 | − | 0.133089i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.562083 | − | 0.827081i | \(-0.690000\pi\) | ||||
0.562083 | + | 0.827081i | \(0.310000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.297740 | + | 0.541587i | −0.297740 | + | 0.541587i | −0.982287 | − | 0.187381i | \(-0.940000\pi\) |
0.684547 | + | 0.728969i | \(0.260000\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.929776 | + | 0.368125i | −0.929776 | + | 0.368125i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.743425 | + | 1.09392i | 0.743425 | + | 1.09392i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.76007 | + | 0.278768i | 1.76007 | + | 0.278768i | ||||
\(613\) | 0.273190 | − | 1.43211i | 0.273190 | − | 1.43211i | −0.535827 | − | 0.844328i | \(-0.680000\pi\) |
0.809017 | − | 0.587785i | \(-0.200000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0931997 | + | 0.362989i | 0.0931997 | + | 0.362989i | 0.998027 | − | 0.0627905i | \(-0.0200000\pi\) |
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.187381 | − | 0.982287i | \(-0.560000\pi\) | ||||
0.187381 | + | 0.982287i | \(0.440000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.876307 | + | 0.481754i | 0.876307 | + | 0.481754i | ||||
\(626\) | −0.916350 | − | 1.66683i | −0.916350 | − | 1.66683i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.0603271 | − | 1.91964i | 0.0603271 | − | 1.91964i | ||||
\(629\) | −2.53549 | − | 2.38099i | −2.53549 | − | 2.38099i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.535827 | − | 0.844328i | \(-0.680000\pi\) | ||||
0.535827 | + | 0.844328i | \(0.320000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.01758 | + | 0.0319788i | −1.01758 | + | 0.0319788i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.689010 | + | 1.01385i | 0.689010 | + | 1.01385i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.968583 | − | 0.248690i | 0.968583 | − | 0.248690i | ||||
\(641\) | −0.141183 | − | 1.49356i | −0.141183 | − | 1.49356i | −0.728969 | − | 0.684547i | \(-0.760000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.612907 | − | 0.790155i | \(-0.710000\pi\) | ||||
0.612907 | + | 0.790155i | \(0.290000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(648\) | −0.904827 | + | 0.425779i | −0.904827 | + | 0.425779i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.415230 | − | 1.15334i | 0.415230 | − | 1.15334i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.0854486 | + | 0.903951i | 0.0854486 | + | 0.903951i | 0.929776 | + | 0.368125i | \(0.120000\pi\) |
−0.844328 | + | 0.535827i | \(0.820000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.80704 | − | 0.524995i | 1.80704 | − | 0.524995i | ||||
\(657\) | 1.11716 | + | 0.614163i | 1.11716 | + | 0.614163i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.975917 | − | 0.218143i | \(-0.930000\pi\) | ||||
0.975917 | + | 0.218143i | \(0.0700000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.583132 | − | 0.344863i | 0.583132 | − | 0.344863i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
0.770513 | + | 0.637424i | \(0.220000\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.92780 | + | 0.305334i | 1.92780 | + | 0.305334i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.67534 | + | 0.211645i | 1.67534 | + | 0.211645i | 0.904827 | − | 0.425779i | \(-0.140000\pi\) |
0.770513 | + | 0.637424i | \(0.220000\pi\) | |||||||
\(674\) | −0.567290 | − | 1.43281i | −0.567290 | − | 1.43281i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.493717 | − | 0.0941816i | −0.493717 | − | 0.0941816i | ||||
\(677\) | 0.0385038 | − | 0.0496387i | 0.0385038 | − | 0.0496387i | −0.770513 | − | 0.637424i | \(-0.780000\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.78113 | + | 0.0559744i | 1.78113 | + | 0.0559744i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.750111 | − | 0.661312i | \(-0.770000\pi\) | ||||
0.750111 | + | 0.661312i | \(0.230000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.87341 | + | 0.674469i | −1.87341 | + | 0.674469i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.40701 | − | 0.0756435i | −2.40701 | − | 0.0756435i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.904827 | − | 0.425779i | \(-0.140000\pi\) | ||||
−0.904827 | + | 0.425779i | \(0.860000\pi\) | |||||||
\(692\) | 0.996398 | + | 0.394502i | 0.996398 | + | 0.394502i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.35332 | 3.35332 | ||||||||
\(698\) | 0.375530 | + | 0.222088i | 0.375530 | + | 0.222088i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.41789 | − | 1.03016i | 1.41789 | − | 1.03016i | 0.425779 | − | 0.904827i | \(-0.360000\pi\) |
0.992115 | − | 0.125333i | \(-0.0400000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.61803i | − | 1.61803i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.977659 | − | 0.284036i | −0.977659 | − | 0.284036i | −0.248690 | − | 0.968583i | \(-0.580000\pi\) |
−0.728969 | + | 0.684547i | \(0.760000\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.65313 | − | 0.480279i | 1.65313 | − | 0.480279i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.338738 | − | 0.940881i | \(-0.610000\pi\) | ||||
0.338738 | + | 0.940881i | \(0.390000\pi\) | |||||||
\(720\) | −0.844328 | + | 0.535827i | −0.844328 | + | 0.535827i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.368125 | + | 0.929776i | −0.368125 | + | 0.929776i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.61484 | − | 1.17325i | −1.61484 | − | 1.17325i | ||||
\(725\) | −0.206904 | − | 0.234686i | −0.206904 | − | 0.234686i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.960294 | − | 0.278991i | \(-0.910000\pi\) | ||||
0.960294 | + | 0.278991i | \(0.0900000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.728969 | − | 0.684547i | 0.728969 | − | 0.684547i | ||||
\(730\) | 1.18532 | + | 0.469303i | 1.18532 | + | 0.469303i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.35041 | + | 1.11716i | −1.35041 | + | 1.11716i | −0.368125 | + | 0.929776i | \(0.620000\pi\) |
−0.982287 | + | 0.187381i | \(0.940000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.55637 | + | 1.05771i | −1.55637 | + | 1.05771i | ||||
\(739\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(740\) | 1.95087 | + | 0.0613086i | 1.95087 | + | 0.0613086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.177089 | + | 0.0637561i | 0.177089 | + | 0.0637561i | ||||
\(746\) | −0.198070 | + | 0.388734i | −0.198070 | + | 0.388734i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.244464 | + | 0.295507i | −0.244464 | + | 0.295507i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.239615 | + | 0.435857i | −0.239615 | + | 0.435857i | −0.968583 | − | 0.248690i | \(-0.920000\pi\) |
0.728969 | + | 0.684547i | \(0.240000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.683098 | + | 0.825723i | −0.683098 | + | 0.825723i | −0.992115 | − | 0.125333i | \(-0.960000\pi\) |
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.71126 | + | 0.497166i | −1.71126 | + | 0.497166i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.896802 | − | 1.76007i | 0.896802 | − | 1.76007i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
0.587785 | − | 0.809017i | \(-0.300000\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.603635 | − | 0.307568i | 0.603635 | − | 0.307568i | ||||
\(773\) | −1.18738 | − | 0.982287i | −1.18738 | − | 0.982287i | −0.187381 | − | 0.982287i | \(-0.560000\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.258768 | + | 1.63380i | 0.258768 | + | 1.63380i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.717446 | + | 0.556508i | 0.717446 | + | 0.556508i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.0627905 | − | 0.998027i | −0.0627905 | − | 0.998027i | ||||
\(785\) | 0.762757 | + | 1.76263i | 0.762757 | + | 1.76263i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.661312 | − | 0.750111i | \(-0.730000\pi\) | ||||
0.661312 | + | 0.750111i | \(0.270000\pi\) | |||||||
\(788\) | −1.89694 | − | 0.551113i | −1.89694 | − | 0.551113i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.596837 | + | 1.50744i | −0.596837 | + | 1.50744i | ||||
\(794\) | −0.238398 | + | 0.0774602i | −0.238398 | + | 0.0774602i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.93334 | − | 0.496398i | 1.93334 | − | 0.496398i | 0.951057 | − | 0.309017i | \(-0.100000\pi\) |
0.982287 | − | 0.187381i | \(-0.0600000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.770513 | + | 0.637424i | −0.770513 | + | 0.637424i | ||||
\(801\) | −1.42381 | + | 0.967618i | −1.42381 | + | 0.967618i | ||||
\(802\) | 0.247215 | − | 1.56085i | 0.247215 | − | 1.56085i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.809017 | + | 0.587785i | 0.809017 | + | 0.587785i | ||||
\(809\) | 0.125581i | 0.125581i | 0.998027 | + | 0.0627905i | \(0.0200000\pi\) | ||||
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(810\) | 0.637424 | − | 0.770513i | 0.637424 | − | 0.770513i | ||||
\(811\) | 0 | 0 | 0.612907 | − | 0.790155i | \(-0.290000\pi\) | ||||
−0.612907 | + | 0.790155i | \(0.710000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.75261 | −1.75261 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.41153 | + | 1.24443i | −1.41153 | + | 1.24443i | ||||
\(821\) | −0.836475 | + | 0.159566i | −0.836475 | + | 0.159566i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
−0.248690 | + | 0.968583i | \(0.580000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | −0.929776 | − | 0.368125i | \(-0.880000\pi\) | ||||
0.929776 | + | 0.368125i | \(0.120000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.338738 | − | 0.940881i | \(-0.610000\pi\) | ||||
0.338738 | + | 0.940881i | \(0.390000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.124591 | + | 1.98031i | −0.124591 | + | 1.98031i | 0.0627905 | + | 0.998027i | \(0.480000\pi\) |
−0.187381 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.919497 | + | 0.810645i | 0.919497 | + | 0.810645i | ||||
\(833\) | 0.388734 | − | 1.73910i | 0.388734 | − | 1.73910i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.982287 | − | 0.187381i | \(-0.940000\pi\) | ||||
0.982287 | + | 0.187381i | \(0.0600000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.332090 | − | 0.838763i | −0.332090 | − | 0.838763i | ||||
\(842\) | −1.44644 | − | 0.182728i | −1.44644 | − | 0.182728i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.486829 | − | 0.124997i | 0.486829 | − | 0.124997i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.65875 | + | 1.05267i | 1.65875 | + | 1.05267i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.63545 | + | 0.707723i | −1.63545 | + | 0.707723i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.876307 | − | 0.518246i | 0.876307 | − | 0.518246i | − | 1.00000i | \(-0.5\pi\) | |
0.876307 | + | 0.481754i | \(0.160000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −0.0747498 | − | 0.172737i | −0.0747498 | − | 0.172737i | 0.876307 | − | 0.481754i | \(-0.160000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.960294 | − | 0.278991i | \(-0.0900000\pi\) | ||||
−0.960294 | + | 0.278991i | \(0.910000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.968583 | − | 0.248690i | \(-0.920000\pi\) | ||||
0.968583 | + | 0.248690i | \(0.0800000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.06954 | + | 0.0672897i | −1.06954 | + | 0.0672897i | ||||
\(866\) | 0.929324 | + | 1.12336i | 0.929324 | + | 1.12336i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.341991 | + | 0.440892i | 0.341991 | + | 0.440892i | ||||
\(873\) | −0.750973 | − | 1.47387i | −0.750973 | − | 1.47387i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.56720 | + | 1.13864i | 1.56720 | + | 1.13864i | 0.929776 | + | 0.368125i | \(0.120000\pi\) |
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.91964 | + | 0.0603271i | −1.91964 | + | 0.0603271i | −0.968583 | − | 0.248690i | \(-0.920000\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(882\) | 0.368125 | + | 0.929776i | 0.368125 | + | 0.929776i | ||||
\(883\) | 0 | 0 | −0.637424 | − | 0.770513i | \(-0.720000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(884\) | 1.17047 | + | 1.84436i | 1.17047 | + | 1.84436i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 0.0314108 | − | 0.999507i | \(-0.490000\pi\) | ||||
−0.0314108 | + | 0.999507i | \(0.510000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.29130 | + | 1.13844i | −1.29130 | + | 1.13844i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.340480 | + | 1.32608i | 0.340480 | + | 1.32608i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.535827 | − | 0.844328i | 0.535827 | − | 0.844328i | ||||
\(901\) | 2.31518 | + | 2.62606i | 2.31518 | + | 2.62606i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.844328 | + | 0.464173i | 0.844328 | + | 0.464173i | ||||
\(905\) | 1.96070 | + | 0.374023i | 1.96070 | + | 0.374023i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.876307 | − | 0.481754i | \(-0.160000\pi\) | ||||
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.278991 | − | 0.960294i | \(-0.410000\pi\) | ||||
−0.278991 | + | 0.960294i | \(0.590000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0.955910 | − | 1.73879i | 0.955910 | − | 1.73879i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.631875 | − | 0.929776i | −0.631875 | − | 0.929776i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.572247 | − | 0.842037i | 0.572247 | − | 0.842037i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.79130 | + | 0.775167i | −1.79130 | + | 0.775167i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.294372 | − | 0.105981i | 0.294372 | − | 0.105981i | ||||
\(929\) | −1.03016 | + | 0.566335i | −1.03016 | + | 0.566335i | −0.904827 | − | 0.425779i | \(-0.860000\pi\) |
−0.125333 | + | 0.992115i | \(0.540000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.0471231 | + | 1.49948i | 0.0471231 | + | 1.49948i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.12500 | − | 0.486829i | −1.12500 | − | 0.486829i | ||||
\(937\) | 0.182728 | + | 0.171593i | 0.182728 | + | 0.171593i | 0.770513 | − | 0.637424i | \(-0.220000\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.96661 | − | 0.311480i | 1.96661 | − | 0.311480i | 0.968583 | − | 0.248690i | \(-0.0800000\pi\) |
0.998027 | − | 0.0627905i | \(-0.0200000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.998027 | − | 0.0627905i | \(-0.0200000\pi\) | ||||
−0.998027 | + | 0.0627905i | \(0.980000\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.340898 | + | 1.52509i | 0.340898 | + | 1.52509i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.80902 | + | 0.587785i | 1.80902 | + | 0.587785i | 1.00000 | \(0\) | ||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(954\) | −1.90285 | − | 0.488570i | −1.90285 | − | 0.488570i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.929776 | − | 0.368125i | −0.929776 | − | 0.368125i | ||||
\(962\) | 1.28201 | + | 2.02013i | 1.28201 | + | 2.02013i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.0319788 | + | 0.0540731i | 0.0319788 | + | 0.0540731i | ||||
\(965\) | −0.415230 | + | 0.535311i | −0.415230 | + | 0.535311i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.995562 | − | 0.0941083i | \(-0.970000\pi\) | ||||
0.995562 | + | 0.0941083i | \(0.0300000\pi\) | |||||||
\(968\) | 0.425779 | + | 0.904827i | 0.425779 | + | 0.904827i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.929776 | − | 1.36812i | −0.929776 | − | 1.36812i | ||||
\(971\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.04508 | − | 0.810645i | 1.04508 | − | 0.810645i | ||||
\(977\) | −0.627617 | + | 1.45034i | −0.627617 | + | 1.45034i | 0.248690 | + | 0.968583i | \(0.420000\pi\) |
−0.876307 | + | 0.481754i | \(0.840000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.481754 | + | 0.876307i | 0.481754 | + | 0.876307i | ||||
\(981\) | −0.461496 | − | 0.313633i | −0.461496 | − | 0.313633i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.929776 | − | 0.368125i | \(-0.120000\pi\) | ||||
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.95106 | − | 0.309017i | 1.95106 | − | 0.309017i | ||||
\(986\) | 0.556436 | − | 0.0350080i | 0.556436 | − | 0.0350080i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.904827 | − | 0.425779i | \(-0.860000\pi\) | ||||
0.904827 | + | 0.425779i | \(0.140000\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.929776 | − | 0.631875i | −0.929776 | − | 0.631875i | − | 1.00000i | \(-0.5\pi\) | |
−0.929776 | + | 0.368125i | \(0.880000\pi\) | |||||||
\(998\) | 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 | 2020.1.cd.a.1003.1 | yes | 40 | |
4.3 | odd | 2 | CM | 2020.1.cd.a.1003.1 | yes | 40 | |
5.2 | odd | 4 | 2020.1.ca.a.1407.1 | yes | 40 | ||
20.7 | even | 4 | 2020.1.ca.a.1407.1 | yes | 40 | ||
101.72 | odd | 100 | 2020.1.ca.a.1183.1 | ✓ | 40 | ||
404.375 | even | 100 | 2020.1.ca.a.1183.1 | ✓ | 40 | ||
505.72 | even | 100 | inner | 2020.1.cd.a.1587.1 | yes | 40 | |
2020.1587 | odd | 100 | inner | 2020.1.cd.a.1587.1 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2020.1.ca.a.1183.1 | ✓ | 40 | 101.72 | odd | 100 | ||
2020.1.ca.a.1183.1 | ✓ | 40 | 404.375 | even | 100 | ||
2020.1.ca.a.1407.1 | yes | 40 | 5.2 | odd | 4 | ||
2020.1.ca.a.1407.1 | yes | 40 | 20.7 | even | 4 | ||
2020.1.cd.a.1003.1 | yes | 40 | 1.1 | even | 1 | trivial | |
2020.1.cd.a.1003.1 | yes | 40 | 4.3 | odd | 2 | CM | |
2020.1.cd.a.1587.1 | yes | 40 | 505.72 | even | 100 | inner | |
2020.1.cd.a.1587.1 | yes | 40 | 2020.1587 | odd | 100 | inner |