Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2004,1,Mod(2003,2004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2004.2003");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.g (of order \(2\), degree \(1\), 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: | \(1.00012628532\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\Q(\zeta_{22})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{22}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{22} + \cdots)\) |
Embedding invariants
Embedding label | 2003.4 | ||
Root | \(0.654861 + 0.755750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2004.2003 |
Dual form | 2004.1.g.f.2003.3 |
$q$-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 \(\left(\mathbb{Z}/2004\mathbb{Z}\right)^\times\).
\(n\) | \(673\) | \(1003\) | \(1337\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(3\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(4\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(7\) | 1.08128i | 1.08128i | 0.841254 | + | 0.540641i | \(0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(8\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(9\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(12\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −0.983568 | − | 0.449181i | −0.983568 | − | 0.449181i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(19\) | 0.563465i | 0.563465i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.07028 | + | 0.153882i | −1.07028 | + | 0.153882i | ||||
\(22\) | 0.544078 | − | 1.19136i | 0.544078 | − | 1.19136i | ||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(25\) | −1.00000 | −1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(28\) | 0.817178 | − | 0.708089i | 0.817178 | − | 0.708089i | ||||
\(29\) | − | 1.08128i | − | 1.08128i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(32\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(33\) | −0.186393 | − | 1.29639i | −0.186393 | − | 1.29639i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | −0.512546 | − | 0.234072i | −0.512546 | − | 0.234072i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0.304632 | − | 1.03748i | 0.304632 | − | 1.03748i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(48\) | −1.00000 | −1.00000 | ||||||||
\(49\) | −0.169170 | −0.169170 | ||||||||
\(50\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 1.00000 | 1.00000 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.304632 | + | 1.03748i | 0.304632 | + | 1.03748i | ||||
\(57\) | −0.557730 | + | 0.0801894i | −0.557730 | + | 0.0801894i | ||||
\(58\) | 0.983568 | + | 0.449181i | 0.983568 | + | 0.449181i | ||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.284630 | 0.284630 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(62\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | ||||
\(63\) | −0.304632 | − | 1.03748i | −0.304632 | − | 1.03748i | ||||
\(64\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | −0.841254 | + | 0.540641i | −0.841254 | + | 0.540641i | ||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(76\) | 0.425839 | − | 0.368991i | 0.425839 | − | 0.368991i | ||||
\(77\) | − | 1.41618i | − | 1.41618i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.841254 | − | 0.540641i | 0.841254 | − | 0.540641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0.817178 | + | 0.708089i | 0.817178 | + | 0.708089i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.07028 | − | 0.153882i | 1.07028 | − | 0.153882i | ||||
\(88\) | −1.25667 | + | 0.368991i | −1.25667 | + | 0.368991i | ||||
\(89\) | 1.97964i | 1.97964i | 0.142315 | + | 0.989821i | \(0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.80075 | + | 0.258908i | −1.80075 | + | 0.258908i | ||||
\(94\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(97\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(98\) | 0.0702757 | − | 0.153882i | 0.0702757 | − | 0.153882i | ||||
\(99\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(100\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(108\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.07028 | − | 0.153882i | −1.07028 | − | 0.153882i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0.158746 | − | 0.540641i | 0.158746 | − | 0.540641i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.817178 | + | 0.708089i | −0.817178 | + | 0.708089i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.715370 | 0.715370 | ||||||||
\(122\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.37491 | − | 1.19136i | 1.37491 | − | 1.19136i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.07028 | + | 0.153882i | 1.07028 | + | 0.153882i | ||||
\(127\) | − | 1.51150i | − | 1.51150i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(128\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | −0.857685 | + | 0.989821i | −0.857685 | + | 0.989821i | ||||
\(133\) | −0.609264 | −0.609264 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.51150i | 1.51150i | 0.654861 | + | 0.755750i | \(0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.273100 | − | 1.89945i | −0.273100 | − | 1.89945i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0240754 | − | 0.167448i | −0.0240754 | − | 0.167448i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 0.158746 | + | 0.540641i | 0.158746 | + | 0.540641i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.28820 | + | 0.588302i | 1.28820 | + | 0.588302i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −1.00000 | ||||||||
\(168\) | −0.983568 | + | 0.449181i | −0.983568 | + | 0.449181i | ||||
\(169\) | 1.00000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.158746 | − | 0.540641i | −0.158746 | − | 0.540641i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.51150i | 1.51150i | 0.654861 | + | 0.755750i | \(0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(174\) | −0.304632 | + | 1.03748i | −0.304632 | + | 1.03748i | ||||
\(175\) | − | 1.08128i | − | 1.08128i | ||||||
\(176\) | 0.186393 | − | 1.29639i | 0.186393 | − | 1.29639i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.80075 | − | 0.822373i | −1.80075 | − | 0.822373i | ||||
\(179\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.512546 | − | 1.74557i | 0.512546 | − | 1.74557i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 1.25667 | + | 1.45027i | 1.25667 | + | 1.45027i | ||||
\(189\) | 0.983568 | − | 0.449181i | 0.983568 | − | 0.449181i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(192\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 0.544078 | − | 1.19136i | 0.544078 | − | 1.19136i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.110783 | + | 0.127850i | 0.110783 | + | 0.127850i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | −0.186393 | + | 1.29639i | −0.186393 | + | 1.29639i | ||||
\(199\) | 1.51150i | 1.51150i | 0.654861 | + | 0.755750i | \(0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(200\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.16917 | 1.16917 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.737982i | − | 0.737982i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(217\) | −1.96714 | −1.96714 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.97964i | − | 1.97964i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(224\) | 0.584585 | − | 0.909632i | 0.584585 | − | 0.909632i | ||||
\(225\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0.425839 | + | 0.368991i | 0.425839 | + | 0.368991i | ||||
\(229\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.40176 | − | 0.201543i | 1.40176 | − | 0.201543i | ||||
\(232\) | −0.304632 | − | 1.03748i | −0.304632 | − | 1.03748i | ||||
\(233\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | −0.297176 | + | 0.650724i | −0.297176 | + | 0.650724i | ||||
\(243\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(244\) | −0.186393 | − | 0.215109i | −0.186393 | − | 0.215109i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.512546 | + | 1.74557i | 0.512546 | + | 1.74557i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(252\) | −0.584585 | + | 0.909632i | −0.584585 | + | 0.909632i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.37491 | + | 0.627899i | 1.37491 | + | 0.627899i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.304632 | + | 1.03748i | 0.304632 | + | 1.03748i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.284630 | 0.284630 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(264\) | −0.544078 | − | 1.19136i | −0.544078 | − | 1.19136i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.253098 | − | 0.554206i | 0.253098 | − | 0.554206i | ||||
\(267\) | −1.95949 | + | 0.281733i | −1.95949 | + | 0.281733i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.37491 | − | 0.627899i | −1.37491 | − | 0.627899i | ||||
\(275\) | 1.30972 | 1.30972 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.512546 | − | 1.74557i | −0.512546 | − | 1.74557i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.97964i | 1.97964i | 0.142315 | + | 0.989821i | \(0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(282\) | 1.84125 | + | 0.540641i | 1.84125 | + | 0.540641i | ||||
\(283\) | 1.51150i | 1.51150i | 0.654861 | + | 0.755750i | \(0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.959493 | + | 0.281733i | 0.959493 | + | 0.281733i | ||||
\(289\) | −1.00000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.186393 | − | 1.29639i | −0.186393 | − | 1.29639i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(294\) | 0.162317 | + | 0.0476607i | 0.162317 | + | 0.0476607i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.544078 | + | 1.19136i | 0.544078 | + | 1.19136i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.557730 | − | 0.0801894i | −0.557730 | − | 0.0801894i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | −1.07028 | + | 0.927399i | −1.07028 | + | 0.927399i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | −0.345139 | + | 0.755750i | −0.345139 | + | 0.755750i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.97964i | − | 1.97964i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.41618i | 1.41618i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.239446 | + | 1.66538i | 0.239446 | + | 1.66538i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.959493 | − | 0.281733i | −0.959493 | − | 0.281733i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.07496i | − | 2.07496i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 1.08128i | − | 1.08128i | ||||||
\(337\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(338\) | −0.415415 | + | 0.909632i | −0.415415 | + | 0.909632i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.38273i | − | 2.38273i | ||||||
\(342\) | 0.557730 | + | 0.0801894i | 0.557730 | + | 0.0801894i | ||||
\(343\) | 0.898361i | 0.898361i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.37491 | − | 0.627899i | −1.37491 | − | 0.627899i | ||||
\(347\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(348\) | −0.817178 | − | 0.708089i | −0.817178 | − | 0.708089i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0.983568 | + | 0.449181i | 0.983568 | + | 0.449181i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.10181 | + | 0.708089i | 1.10181 | + | 0.708089i | ||||
\(353\) | 1.08128i | 1.08128i | 0.841254 | + | 0.540641i | \(0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.49611 | − | 1.29639i | 1.49611 | − | 1.29639i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(359\) | −0.830830 | −0.830830 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.682507 | 0.682507 | ||||||||
\(362\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(363\) | 0.101808 | + | 0.708089i | 0.101808 | + | 0.708089i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.273100 | − | 0.0801894i | −0.273100 | − | 0.0801894i | ||||
\(367\) | − | 0.563465i | − | 0.563465i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.37491 | + | 1.19136i | 1.37491 | + | 1.19136i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.84125 | + | 0.540641i | −1.84125 | + | 0.540641i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.08128i | 1.08128i | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.49611 | − | 0.215109i | 1.49611 | − | 0.215109i | ||||
\(382\) | −0.345139 | + | 0.755750i | −0.345139 | + | 0.755750i | ||||
\(383\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(384\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.857685 | + | 0.989821i | 0.857685 | + | 0.989821i | ||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.162317 | + | 0.0476607i | −0.162317 | + | 0.0476607i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.10181 | − | 0.708089i | −1.10181 | − | 0.708089i | ||||
\(397\) | 0.284630 | 0.284630 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(398\) | −1.37491 | − | 0.627899i | −1.37491 | − | 0.627899i | ||||
\(399\) | −0.0867074 | − | 0.603063i | −0.0867074 | − | 0.603063i | ||||
\(400\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.485691 | + | 1.06351i | −0.485691 | + | 1.06351i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.30972 | 1.30972 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.49611 | + | 0.215109i | −1.49611 | + | 0.215109i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.671292 | + | 0.306569i | 0.671292 | + | 0.306569i | ||||
\(419\) | 0.830830 | 0.830830 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(422\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | ||||
\(423\) | 1.84125 | − | 0.540641i | 1.84125 | − | 0.540641i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.307765i | 0.307765i | ||||||||
\(428\) | −1.10181 | − | 1.27155i | −1.10181 | − | 1.27155i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.284630 | 0.284630 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(432\) | 0.959493 | − | 0.281733i | 0.959493 | − | 0.281733i | ||||
\(433\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(434\) | 0.817178 | − | 1.78937i | 0.817178 | − | 1.78937i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.162317 | − | 0.0476607i | 0.162317 | − | 0.0476607i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.80075 | + | 0.822373i | 1.80075 | + | 0.822373i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.584585 | + | 0.909632i | 0.584585 | + | 0.909632i | ||||
\(449\) | 0.563465i | 0.563465i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(450\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.512546 | + | 0.234072i | −0.512546 | + | 0.234072i | ||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 0.563465i | − | 0.563465i | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||
0.959493 | − | 0.281733i | \(-0.0909091\pi\) | |||||||
\(462\) | −0.398983 | + | 1.35881i | −0.398983 | + | 1.35881i | ||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 1.07028 | + | 0.153882i | 1.07028 | + | 0.153882i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | ||||
\(467\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.118239 | + | 0.822373i | 0.118239 | + | 0.822373i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 0.563465i | − | 0.563465i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.118239 | − | 0.258908i | 0.118239 | − | 0.258908i | ||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.468468 | − | 0.540641i | −0.468468 | − | 0.540641i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.959493 | + | 0.281733i | −0.959493 | + | 0.281733i | ||||
\(487\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(488\) | 0.273100 | − | 0.0801894i | 0.273100 | − | 0.0801894i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.00000 | 2.00000 | 1.00000 | \(0\) | ||||||
1.00000 | \(0\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.80075 | − | 0.258908i | −1.80075 | − | 0.258908i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(502\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(503\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(504\) | −0.584585 | − | 0.909632i | −0.584585 | − | 0.909632i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.142315 | + | 0.989821i | 0.142315 | + | 0.989821i | ||||
\(508\) | −1.14231 | + | 0.989821i | −1.14231 | + | 0.989821i | ||||
\(509\) | − | 1.51150i | − | 1.51150i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(513\) | 0.512546 | − | 0.234072i | 0.512546 | − | 0.234072i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.51334 | 2.51334 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.49611 | + | 0.215109i | −1.49611 | + | 0.215109i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | −1.07028 | − | 0.153882i | −1.07028 | − | 0.153882i | ||||
\(523\) | − | 1.81926i | − | 1.81926i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.07028 | − | 0.153882i | 1.07028 | − | 0.153882i | ||||
\(526\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.30972 | 1.30972 | ||||||||
\(529\) | 1.00000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.398983 | + | 0.460451i | 0.398983 | + | 0.460451i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.557730 | − | 1.89945i | 0.557730 | − | 1.89945i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.221566 | 0.221566 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.273100 | + | 1.89945i | 0.273100 | + | 1.89945i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(548\) | 1.14231 | − | 0.989821i | 1.14231 | − | 0.989821i | ||||
\(549\) | −0.273100 | + | 0.0801894i | −0.273100 | + | 0.0801894i | ||||
\(550\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(551\) | 0.609264 | 0.609264 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 1.51150i | − | 1.51150i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(558\) | 1.80075 | + | 0.258908i | 1.80075 | + | 0.258908i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.80075 | − | 0.822373i | −1.80075 | − | 0.822373i | ||||
\(563\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(564\) | −1.25667 | + | 1.45027i | −1.25667 | + | 1.45027i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.37491 | − | 0.627899i | −1.37491 | − | 0.627899i | ||||
\(567\) | 0.584585 | + | 0.909632i | 0.584585 | + | 0.909632i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.118239 | + | 0.822373i | 0.118239 | + | 0.822373i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(577\) | −0.830830 | −0.830830 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(578\) | 0.415415 | − | 0.909632i | 0.415415 | − | 0.909632i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.25667 | + | 0.368991i | 1.25667 | + | 0.368991i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.65486 | − | 0.755750i | −1.65486 | − | 0.755750i | ||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | −0.110783 | + | 0.127850i | −0.110783 | + | 0.127850i | ||||
\(589\) | −1.02509 | −1.02509 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | −1.30972 | −1.30972 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.49611 | + | 0.215109i | −1.49611 | + | 0.215109i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(600\) | −0.415415 | − | 0.909632i | −0.415415 | − | 0.909632i | ||||
\(601\) | 1.68251 | 1.68251 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0.304632 | − | 0.474017i | 0.304632 | − | 0.474017i | ||||
\(609\) | 0.166390 | + | 1.15727i | 0.166390 | + | 1.15727i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.830830 | −0.830830 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.398983 | − | 1.35881i | −0.398983 | − | 1.35881i | ||||
\(617\) | − | 1.08128i | − | 1.08128i | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||
0.841254 | − | 0.540641i | \(-0.181818\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.830830 | − | 1.81926i | 0.830830 | − | 1.81926i | ||||
\(623\) | −2.14055 | −2.14055 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.730471 | − | 0.105026i | 0.730471 | − | 0.105026i | ||||
\(628\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.97964i | − | 1.97964i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.80075 | + | 0.258908i | −1.80075 | + | 0.258908i | ||||
\(634\) | 1.80075 | + | 0.822373i | 1.80075 | + | 0.822373i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.28820 | − | 0.588302i | −1.28820 | − | 0.588302i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | −1.61435 | − | 0.474017i | −1.61435 | − | 0.474017i | ||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | 0.654861 | − | 0.755750i | 0.654861 | − | 0.755750i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.279953 | − | 1.94711i | −0.279953 | − | 1.94711i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.81926i | − | 1.81926i | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||
0.415415 | − | 0.909632i | \(-0.363636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.88745 | + | 0.861971i | 1.88745 | + | 0.861971i | ||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0.654861 | + | 0.755750i | 0.654861 | + | 0.755750i | ||||
\(669\) | 1.95949 | − | 0.281733i | 1.95949 | − | 0.281733i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.372786 | −0.372786 | ||||||||
\(672\) | 0.983568 | + | 0.449181i | 0.983568 | + | 0.449181i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0.797176 | − | 1.74557i | 0.797176 | − | 1.74557i | ||||
\(675\) | 0.415415 | + | 0.909632i | 0.415415 | + | 0.909632i | ||||
\(676\) | −0.654861 | − | 0.755750i | −0.654861 | − | 0.755750i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.41618i | − | 1.41618i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.16741 | + | 0.989821i | 2.16741 | + | 0.989821i | ||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | −0.304632 | + | 0.474017i | −0.304632 | + | 0.474017i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.817178 | − | 0.373193i | −0.817178 | − | 0.373193i | ||||
\(687\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | 1.14231 | − | 0.989821i | 1.14231 | − | 0.989821i | ||||
\(693\) | 0.398983 | + | 1.35881i | 0.398983 | + | 1.35881i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.983568 | − | 0.449181i | 0.983568 | − | 0.449181i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.80075 | + | 0.258908i | −1.80075 | + | 0.258908i | ||||
\(700\) | −0.817178 | + | 0.708089i | −0.817178 | + | 0.708089i | ||||
\(701\) | − | 1.97964i | − | 1.97964i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.983568 | − | 0.449181i | −0.983568 | − | 0.449181i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.557730 | + | 1.89945i | 0.557730 | + | 1.89945i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(717\) | −0.0405070 | − | 0.281733i | −0.0405070 | − | 0.281733i | ||||
\(718\) | 0.345139 | − | 0.755750i | 0.345139 | − | 0.755750i | ||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.283524 | + | 0.620830i | −0.283524 | + | 0.620830i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.25667 | − | 1.45027i | −1.25667 | − | 1.45027i | ||||
\(725\) | 1.08128i | 1.08128i | ||||||||
\(726\) | −0.686393 | − | 0.201543i | −0.686393 | − | 0.201543i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.654861 | + | 0.755750i | −0.654861 | + | 0.755750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.186393 | − | 0.215109i | 0.186393 | − | 0.215109i | ||||
\(733\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(734\) | 0.512546 | + | 0.234072i | 0.512546 | + | 0.234072i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.00000 | −2.00000 | −1.00000 | \(\pi\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | −1.65486 | + | 0.755750i | −1.65486 | + | 0.755750i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.81926i | 1.81926i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0.273100 | − | 1.89945i | 0.273100 | − | 1.89945i | ||||
\(753\) | −0.239446 | − | 1.66538i | −0.239446 | − | 1.66538i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.983568 | − | 0.449181i | −0.983568 | − | 0.449181i | ||||
\(757\) | −1.30972 | −1.30972 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.97964i | 1.97964i | 0.142315 | + | 0.989821i | \(0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(762\) | −0.425839 | + | 1.45027i | −0.425839 | + | 1.45027i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −0.544078 | − | 0.627899i | −0.544078 | − | 0.627899i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.81926i | − | 1.81926i | ||||||
\(776\) | −1.25667 | + | 0.368991i | −1.25667 | + | 0.368991i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.983568 | + | 0.449181i | −0.983568 | + | 0.449181i | ||||
\(784\) | 0.0240754 | − | 0.167448i | 0.0240754 | − | 0.167448i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.0405070 | + | 0.281733i | 0.0405070 | + | 0.281733i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.10181 | − | 0.708089i | 1.10181 | − | 0.708089i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.14231 | − | 0.989821i | 1.14231 | − | 0.989821i | ||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0.584585 | + | 0.171650i | 0.584585 | + | 0.171650i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.841254 | + | 0.540641i | 0.841254 | + | 0.540641i | ||||
\(801\) | −0.557730 | − | 1.89945i | −0.557730 | − | 1.89945i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1.51150i | − | 1.51150i | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||
0.654861 | − | 0.755750i | \(-0.272727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(812\) | −0.765644 | − | 0.883600i | −0.765644 | − | 0.883600i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.544078 | + | 1.19136i | −0.544078 | + | 1.19136i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 0.425839 | − | 1.45027i | 0.425839 | − | 1.45027i | ||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.186393 | + | 1.29639i | 0.186393 | + | 1.29639i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.557730 | + | 0.483276i | −0.557730 | + | 0.483276i | ||||
\(837\) | 1.65486 | − | 0.755750i | 1.65486 | − | 0.755750i | ||||
\(838\) | −0.345139 | + | 0.755750i | −0.345139 | + | 0.755750i | ||||
\(839\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.169170 | −0.169170 | ||||||||
\(842\) | −0.698939 | + | 1.53046i | −0.698939 | + | 1.53046i | ||||
\(843\) | −1.95949 | + | 0.281733i | −1.95949 | + | 0.281733i | ||||
\(844\) | 1.37491 | − | 1.19136i | 1.37491 | − | 1.19136i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.273100 | + | 1.89945i | −0.273100 | + | 1.89945i | ||||
\(847\) | 0.773517i | 0.773517i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.49611 | + | 0.215109i | −1.49611 | + | 0.215109i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.30972 | 1.30972 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(854\) | −0.279953 | − | 0.127850i | −0.279953 | − | 0.127850i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.61435 | − | 0.474017i | 1.61435 | − | 0.474017i | ||||
\(857\) | 0.563465i | 0.563465i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.08128i | 1.08128i | 0.841254 | + | 0.540641i | \(0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.118239 | + | 0.258908i | −0.118239 | + | 0.258908i | ||||
\(863\) | 1.30972 | 1.30972 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(864\) | −0.142315 | + | 0.989821i | −0.142315 | + | 0.989821i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.797176 | + | 1.74557i | −0.797176 | + | 1.74557i | ||||
\(867\) | −0.142315 | − | 0.989821i | −0.142315 | − | 0.989821i | ||||
\(868\) | 1.28820 | + | 1.48666i | 1.28820 | + | 1.48666i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.25667 | − | 0.368991i | 1.25667 | − | 0.368991i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.91899 | −1.91899 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.80075 | + | 0.258908i | −1.80075 | + | 0.258908i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −0.0240754 | + | 0.167448i | −0.0240754 | + | 0.167448i | ||||
\(883\) | 1.08128i | 1.08128i | 0.841254 | + | 0.540641i | \(0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.63436 | 1.63436 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.10181 | + | 0.708089i | −1.10181 | + | 0.708089i | ||||
\(892\) | −1.49611 | + | 1.29639i | −1.49611 | + | 1.29639i | ||||
\(893\) | − | 1.08128i | − | 1.08128i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.07028 | + | 0.153882i | −1.07028 | + | 0.153882i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.512546 | − | 0.234072i | −0.512546 | − | 0.234072i | ||||
\(899\) | 1.96714 | 1.96714 | ||||||||
\(900\) | −0.841254 | − | 0.540641i | −0.841254 | − | 0.540641i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.97964i | − | 1.97964i | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||
0.142315 | − | 0.989821i | \(-0.454545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.91899 | 1.91899 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(912\) | − | 0.563465i | − | 0.563465i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.10181 | + | 1.27155i | 1.10181 | + | 1.27155i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.563465i | 0.563465i | 0.959493 | + | 0.281733i | \(0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.512546 | + | 0.234072i | 0.512546 | + | 0.234072i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.07028 | − | 0.927399i | −1.07028 | − | 0.927399i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.584585 | + | 0.909632i | −0.584585 | + | 0.909632i | ||||
\(929\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.0953214i | − | 0.0953214i | ||||||
\(932\) | 1.37491 | − | 1.19136i | 1.37491 | − | 1.19136i | ||||
\(933\) | −0.284630 | − | 1.97964i | −0.284630 | − | 1.97964i | ||||
\(934\) | 0.698939 | − | 1.53046i | 0.698939 | − | 1.53046i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | −0.797176 | − | 0.234072i | −0.797176 | − | 0.234072i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.284630 | −0.284630 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.512546 | + | 0.234072i | 0.512546 | + | 0.234072i | ||||
\(951\) | 1.95949 | − | 0.281733i | 1.95949 | − | 0.281733i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.186393 | + | 0.215109i | 0.186393 | + | 0.215109i | ||||
\(957\) | −1.40176 | + | 0.201543i | −1.40176 | + | 0.201543i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.63436 | −1.63436 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.30972 | −2.30972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.61435 | + | 0.474017i | −1.61435 | + | 0.474017i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.81926i | 1.81926i | 0.415415 | + | 0.909632i | \(0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(968\) | 0.686393 | − | 0.201543i | 0.686393 | − | 0.201543i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(972\) | 0.142315 | − | 0.989821i | 0.142315 | − | 0.989821i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.0405070 | + | 0.281733i | −0.0405070 | + | 0.281733i | ||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 2.59278i | − | 2.59278i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.830830 | + | 1.81926i | −0.830830 | + | 1.81926i | ||||
\(983\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.05384 | − | 0.295298i | 2.05384 | − | 0.295298i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(992\) | 0.983568 | − | 1.53046i | 0.983568 | − | 1.53046i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.68251 | −1.68251 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(998\) | 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 | 2004.1.g.f.2003.4 | yes | 10 | |
3.2 | odd | 2 | 2004.1.g.e.2003.7 | ✓ | 10 | ||
4.3 | odd | 2 | 2004.1.g.e.2003.8 | yes | 10 | ||
12.11 | even | 2 | inner | 2004.1.g.f.2003.3 | yes | 10 | |
167.166 | odd | 2 | CM | 2004.1.g.f.2003.4 | yes | 10 | |
501.500 | even | 2 | 2004.1.g.e.2003.7 | ✓ | 10 | ||
668.667 | even | 2 | 2004.1.g.e.2003.8 | yes | 10 | ||
2004.2003 | odd | 2 | inner | 2004.1.g.f.2003.3 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2004.1.g.e.2003.7 | ✓ | 10 | 3.2 | odd | 2 | ||
2004.1.g.e.2003.7 | ✓ | 10 | 501.500 | even | 2 | ||
2004.1.g.e.2003.8 | yes | 10 | 4.3 | odd | 2 | ||
2004.1.g.e.2003.8 | yes | 10 | 668.667 | even | 2 | ||
2004.1.g.f.2003.3 | yes | 10 | 12.11 | even | 2 | inner | |
2004.1.g.f.2003.3 | yes | 10 | 2004.2003 | odd | 2 | inner | |
2004.1.g.f.2003.4 | yes | 10 | 1.1 | even | 1 | trivial | |
2004.1.g.f.2003.4 | yes | 10 | 167.166 | odd | 2 | CM |