Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(961,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.961");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.bg (of order \(3\), degree \(2\), not 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: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1201.2 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1201 |
Dual form | 1680.2.bg.q.961.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.32288 | + | 2.29129i | 0.500000 | + | 0.866025i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.822876 | + | 1.42526i | −0.248106 | + | 0.429733i | −0.963000 | − | 0.269500i | \(-0.913142\pi\) |
0.714894 | + | 0.699233i | \(0.246475\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.64575 | −0.733799 | −0.366900 | − | 0.930261i | \(-0.619581\pi\) | ||||
−0.366900 | + | 0.930261i | \(0.619581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.822876 | − | 1.42526i | 0.199577 | − | 0.345677i | −0.748815 | − | 0.662780i | \(-0.769377\pi\) |
0.948391 | + | 0.317103i | \(0.102710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.14575 | + | 7.18065i | 0.951101 | + | 1.64735i | 0.743049 | + | 0.669237i | \(0.233379\pi\) |
0.208051 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.64575 | 0.577350 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.822876 | + | 1.42526i | 0.171581 | + | 0.297188i | 0.938973 | − | 0.343991i | \(-0.111779\pi\) |
−0.767391 | + | 0.641179i | \(0.778446\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.64575 | 1.41978 | 0.709890 | − | 0.704312i | \(-0.248745\pi\) | ||||
0.709890 | + | 0.704312i | \(0.248745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.14575 | + | 3.71655i | −0.385388 | + | 0.667512i | −0.991823 | − | 0.127621i | \(-0.959266\pi\) |
0.606435 | + | 0.795133i | \(0.292599\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.822876 | + | 1.42526i | 0.143244 | + | 0.248106i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.32288 | − | 2.29129i | 0.223607 | − | 0.387298i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.322876 | − | 0.559237i | −0.0530804 | − | 0.0919380i | 0.838264 | − | 0.545264i | \(-0.183571\pi\) |
−0.891345 | + | 0.453326i | \(0.850237\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.32288 | + | 2.29129i | −0.211830 | + | 0.366900i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.93725 | 0.771070 | 0.385535 | − | 0.922693i | \(-0.374017\pi\) | ||||
0.385535 | + | 0.922693i | \(0.374017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.93725 | 0.905423 | 0.452711 | − | 0.891657i | \(-0.350457\pi\) | ||||
0.452711 | + | 0.891657i | \(0.350457\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.50000 | + | 6.06218i | −0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.822876 | − | 1.42526i | −0.115226 | − | 0.199577i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.64575 | + | 2.85052i | −0.226061 | + | 0.391550i | −0.956637 | − | 0.291282i | \(-0.905918\pi\) |
0.730576 | + | 0.682831i | \(0.239252\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.64575 | 0.221913 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.29150 | 1.09824 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.46863 | − | 9.47194i | 0.711955 | − | 1.23314i | −0.252168 | − | 0.967684i | \(-0.581144\pi\) |
0.964122 | − | 0.265458i | \(-0.0855232\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.32288 | − | 2.29129i | 0.166667 | − | 0.288675i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.32288 | + | 2.29129i | 0.164083 | + | 0.284199i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.322876 | − | 0.559237i | 0.0394455 | − | 0.0683217i | −0.845629 | − | 0.533772i | \(-0.820774\pi\) |
0.885074 | + | 0.465450i | \(0.154108\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.64575 | 0.198125 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.6458 | −1.61945 | −0.809726 | − | 0.586808i | \(-0.800384\pi\) | ||||
−0.809726 | + | 0.586808i | \(0.800384\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.61438 | + | 11.4564i | −0.774154 | + | 1.34087i | 0.161114 | + | 0.986936i | \(0.448491\pi\) |
−0.935269 | + | 0.353939i | \(0.884842\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.35425 | −0.496213 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.14575 | + | 1.98450i | 0.128907 | + | 0.223274i | 0.923253 | − | 0.384192i | \(-0.125520\pi\) |
−0.794346 | + | 0.607465i | \(0.792186\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.9373 | 1.20052 | 0.600260 | − | 0.799805i | \(-0.295064\pi\) | ||||
0.600260 | + | 0.799805i | \(0.295064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.64575 | −0.178507 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.82288 | − | 6.62141i | 0.409855 | − | 0.709890i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.11438 | + | 12.3225i | 0.754123 | + | 1.30618i | 0.945809 | + | 0.324722i | \(0.105271\pi\) |
−0.191687 | + | 0.981456i | \(0.561396\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50000 | − | 6.06218i | −0.366900 | − | 0.635489i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.14575 | + | 3.71655i | 0.222504 | + | 0.385388i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.14575 | − | 7.18065i | 0.425345 | − | 0.736719i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.64575 | 0.165404 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.46863 | − | 4.27579i | 0.245638 | − | 0.425457i | −0.716673 | − | 0.697409i | \(-0.754336\pi\) |
0.962311 | + | 0.271953i | \(0.0876694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.67712 | + | 8.10102i | 0.460851 | + | 0.798217i | 0.999004 | − | 0.0446304i | \(-0.0142110\pi\) |
−0.538153 | + | 0.842847i | \(0.680878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.32288 | − | 2.29129i | −0.129099 | − | 0.223607i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.46863 | − | 14.6681i | −0.818693 | − | 1.41802i | −0.906645 | − | 0.421893i | \(-0.861366\pi\) |
0.0879524 | − | 0.996125i | \(-0.471968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.50000 | − | 11.2583i | 0.622587 | − | 1.07835i | −0.366415 | − | 0.930451i | \(-0.619415\pi\) |
0.989002 | − | 0.147901i | \(-0.0472517\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.645751 | −0.0612920 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.822876 | − | 1.42526i | 0.0767336 | − | 0.132906i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.32288 | + | 2.29129i | 0.122300 | + | 0.211830i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.35425 | 0.399153 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.14575 | + | 7.18065i | 0.376886 | + | 0.652787i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.46863 | − | 4.27579i | 0.222589 | − | 0.385535i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.06275 | 0.183039 | 0.0915196 | − | 0.995803i | \(-0.470828\pi\) | ||||
0.0915196 | + | 0.995803i | \(0.470828\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.96863 | − | 5.14181i | 0.261373 | − | 0.452711i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.6458 | + | 18.4390i | 0.930124 | + | 1.61102i | 0.783107 | + | 0.621887i | \(0.213634\pi\) |
0.147017 | + | 0.989134i | \(0.453033\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.9686 | + | 18.9982i | −0.951101 | + | 1.64735i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.1144 | − | 17.5186i | 0.864130 | − | 1.49672i | −0.00377913 | − | 0.999993i | \(-0.501203\pi\) |
0.867909 | − | 0.496724i | \(-0.165464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.00000 | −0.424094 | −0.212047 | − | 0.977259i | \(-0.568013\pi\) | ||||
−0.212047 | + | 0.977259i | \(0.568013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.17712 | − | 3.77089i | 0.182060 | − | 0.315338i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.82288 | − | 6.62141i | −0.317473 | − | 0.549879i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.50000 | + | 6.06218i | 0.288675 | + | 0.500000i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.29150 | + | 5.70105i | 0.269650 | + | 0.467048i | 0.968772 | − | 0.247955i | \(-0.0797585\pi\) |
−0.699121 | + | 0.715003i | \(0.746425\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.29150 | + | 3.96900i | −0.186480 | + | 0.322993i | −0.944074 | − | 0.329733i | \(-0.893041\pi\) |
0.757594 | + | 0.652726i | \(0.226375\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.64575 | −0.133051 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.29150 | 0.344702 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.645751 | − | 1.11847i | 0.0515366 | − | 0.0892639i | −0.839106 | − | 0.543968i | \(-0.816921\pi\) |
0.890643 | + | 0.454704i | \(0.150255\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.64575 | + | 2.85052i | 0.130517 | + | 0.226061i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.17712 | + | 3.77089i | −0.171581 | + | 0.297188i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.00000 | − | 13.8564i | −0.626608 | − | 1.08532i | −0.988227 | − | 0.152992i | \(-0.951109\pi\) |
0.361619 | − | 0.932326i | \(-0.382224\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.822876 | − | 1.42526i | 0.0640608 | − | 0.110957i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.6458 | −1.52023 | −0.760117 | − | 0.649786i | \(-0.774858\pi\) | ||||
−0.760117 | + | 0.649786i | \(0.774858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | −0.461538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.14575 | − | 7.18065i | 0.317034 | − | 0.549118i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.93725 | − | 8.55157i | −0.375372 | − | 0.650164i | 0.615010 | − | 0.788519i | \(-0.289152\pi\) |
−0.990383 | + | 0.138355i | \(0.955819\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.64575 | −0.200000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.46863 | − | 9.47194i | −0.411047 | − | 0.711955i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.291503 | − | 0.504897i | 0.0217879 | − | 0.0377378i | −0.854926 | − | 0.518750i | \(-0.826397\pi\) |
0.876714 | + | 0.481012i | \(0.159731\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29150 | −0.318985 | −0.159492 | − | 0.987199i | \(-0.550986\pi\) | ||||
−0.159492 | + | 0.987199i | \(0.550986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.322876 | + | 0.559237i | −0.0237383 | + | 0.0411159i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.35425 | + | 2.34563i | 0.0990325 | + | 0.171529i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.32288 | − | 2.29129i | −0.0962250 | − | 0.166667i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.58301 | + | 16.5983i | 0.693402 | + | 1.20101i | 0.970716 | + | 0.240228i | \(0.0772223\pi\) |
−0.277315 | + | 0.960779i | \(0.589444\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.03137 | − | 6.98254i | 0.290185 | − | 0.502614i | −0.683669 | − | 0.729793i | \(-0.739617\pi\) |
0.973853 | + | 0.227178i | \(0.0729500\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.64575 | 0.189466 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.93725 | −0.351765 | −0.175882 | − | 0.984411i | \(-0.556278\pi\) | ||||
−0.175882 | + | 0.984411i | \(0.556278\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5830 | + | 20.0624i | −0.821097 | + | 1.42218i | 0.0837682 | + | 0.996485i | \(0.473304\pi\) |
−0.904866 | + | 0.425697i | \(0.860029\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.322876 | − | 0.559237i | −0.0227739 | − | 0.0394455i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.1144 | + | 17.5186i | 0.709890 | + | 1.22957i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.46863 | − | 4.27579i | −0.172416 | − | 0.298634i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.822876 | − | 1.42526i | 0.0571938 | − | 0.0990626i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.6458 | −0.943896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.58301 | −0.590878 | −0.295439 | − | 0.955362i | \(-0.595466\pi\) | ||||
−0.295439 | + | 0.955362i | \(0.595466\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.82288 | + | 11.8176i | −0.467496 | + | 0.809726i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.96863 | − | 5.14181i | −0.202459 | − | 0.350669i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3542 | −0.770777 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.61438 | + | 11.4564i | 0.446958 | + | 0.774154i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.17712 | + | 3.77089i | −0.146449 | + | 0.253658i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8745 | −1.19697 | −0.598483 | − | 0.801136i | \(-0.704230\pi\) | ||||
−0.598483 | + | 0.801136i | \(0.704230\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.82288 | − | 17.0137i | 0.651967 | − | 1.12924i | −0.330678 | − | 0.943744i | \(-0.607277\pi\) |
0.982645 | − | 0.185497i | \(-0.0593893\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50000 | + | 6.06218i | 0.231287 | + | 0.400600i | 0.958187 | − | 0.286143i | \(-0.0923732\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.17712 | + | 3.77089i | −0.143244 | + | 0.248106i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.6458 | − | 18.4390i | −0.697426 | − | 1.20798i | −0.969356 | − | 0.245661i | \(-0.920995\pi\) |
0.271930 | − | 0.962317i | \(-0.412338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.00000 | − | 5.19615i | 0.195698 | − | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.29150 | 0.148849 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.35425 | − | 11.0059i | 0.409313 | − | 0.708951i | −0.585500 | − | 0.810673i | \(-0.699102\pi\) |
0.994813 | + | 0.101721i | \(0.0324350\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.00000 | 0.447214 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.9686 | − | 18.9982i | −0.697917 | − | 1.20883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.46863 | − | 9.47194i | 0.346560 | − | 0.600260i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9373 | 0.690353 | 0.345177 | − | 0.938538i | \(-0.387819\pi\) | ||||
0.345177 | + | 0.938538i | \(0.387819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.70850 | −0.170282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.822876 | + | 1.42526i | −0.0515305 | + | 0.0892534i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.76013 | − | 4.78068i | −0.172172 | − | 0.298211i | 0.767007 | − | 0.641639i | \(-0.221745\pi\) |
−0.939179 | + | 0.343428i | \(0.888412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.854249 | − | 1.47960i | 0.0530804 | − | 0.0919380i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.82288 | − | 6.62141i | −0.236630 | − | 0.409855i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.2288 | + | 24.6449i | −0.877383 | + | 1.51967i | −0.0231800 | + | 0.999731i | \(0.507379\pi\) |
−0.854203 | + | 0.519940i | \(0.825954\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.29150 | 0.202195 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.2288 | 0.870786 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.9373 | + | 24.1400i | −0.849769 | + | 1.47184i | 0.0316446 | + | 0.999499i | \(0.489926\pi\) |
−0.881414 | + | 0.472345i | \(0.843408\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.70850 | + | 6.42331i | 0.225275 | + | 0.390188i | 0.956402 | − | 0.292054i | \(-0.0943386\pi\) |
−0.731127 | + | 0.682242i | \(0.761005\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.00000 | −0.423659 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.822876 | − | 1.42526i | −0.0496213 | − | 0.0859466i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3229 | − | 17.8797i | 0.620241 | − | 1.07429i | −0.369199 | − | 0.929350i | \(-0.620368\pi\) |
0.989441 | − | 0.144939i | \(-0.0462987\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.29150 | 0.256926 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0000 | 1.43172 | 0.715860 | − | 0.698244i | \(-0.246035\pi\) | ||||
0.715860 | + | 0.698244i | \(0.246035\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.32288 | + | 12.6836i | −0.435300 | + | 0.753961i | −0.997320 | − | 0.0731621i | \(-0.976691\pi\) |
0.562020 | + | 0.827123i | \(0.310024\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.14575 | − | 7.18065i | −0.245573 | − | 0.425345i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.53137 | + | 11.3127i | 0.385535 | + | 0.667766i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.14575 | + | 12.3768i | 0.420338 | + | 0.728047i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.00000 | − | 6.92820i | 0.234484 | − | 0.406138i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9373 | −0.636792 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.822876 | − | 1.42526i | 0.0477481 | − | 0.0827021i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.17712 | − | 3.77089i | −0.125906 | − | 0.218076i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.85425 | + | 13.6040i | 0.452711 | + | 0.784119i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.46863 | − | 4.27579i | −0.141819 | − | 0.245638i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | + | 6.92820i | −0.229039 | + | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.9373 | −1.59446 | −0.797232 | − | 0.603674i | \(-0.793703\pi\) | ||||
−0.797232 | + | 0.603674i | \(0.793703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.35425 | 0.532145 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.82288 | − | 11.8176i | 0.386890 | − | 0.670113i | −0.605140 | − | 0.796119i | \(-0.706883\pi\) |
0.992029 | + | 0.126007i | \(0.0402161\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6144 | + | 18.3846i | 0.599960 | + | 1.03916i | 0.992826 | + | 0.119566i | \(0.0381502\pi\) |
−0.392866 | + | 0.919596i | \(0.628516\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.64575 | −0.149071 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.7601 | − | 20.3691i | −0.660515 | − | 1.14404i | −0.980481 | − | 0.196616i | \(-0.937005\pi\) |
0.319966 | − | 0.947429i | \(-0.396329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.29150 | + | 10.8972i | −0.352257 | + | 0.610126i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.9373 | −0.945345 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6458 | 0.759270 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.32288 | − | 2.29129i | 0.0733799 | − | 0.127098i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.50000 | − | 11.2583i | −0.359451 | − | 0.622587i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.93725 | + | 13.7477i | −0.437595 | + | 0.757937i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0830 | − | 17.4643i | −0.554212 | − | 0.959923i | −0.997964 | − | 0.0637740i | \(-0.979686\pi\) |
0.443752 | − | 0.896149i | \(-0.353647\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.322876 | + | 0.559237i | −0.0176935 | + | 0.0306460i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.645751 | −0.0352812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.2288 | −1.81009 | −0.905043 | − | 0.425320i | \(-0.860161\pi\) | ||||
−0.905043 | + | 0.425320i | \(0.860161\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | − | 5.19615i | 0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.53137 | − | 6.11652i | −0.191235 | − | 0.331228i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.822876 | − | 1.42526i | −0.0443021 | − | 0.0767336i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.58301 | − | 11.4021i | 0.353394 | − | 0.612097i | −0.633448 | − | 0.773786i | \(-0.718361\pi\) |
0.986842 | + | 0.161689i | \(0.0516941\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0000 | −0.535288 | −0.267644 | − | 0.963518i | \(-0.586245\pi\) | ||||
−0.267644 | + | 0.963518i | \(0.586245\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.64575 | 0.141220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0516 | − | 31.2663i | 0.960791 | − | 1.66414i | 0.240271 | − | 0.970706i | \(-0.422764\pi\) |
0.720520 | − | 0.693434i | \(-0.243903\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.82288 | + | 11.8176i | 0.362121 | + | 0.627211i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.17712 | − | 3.77089i | 0.115226 | − | 0.199577i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4059 | − | 18.0235i | −0.549201 | − | 0.951245i | −0.998329 | − | 0.0577773i | \(-0.981599\pi\) |
0.449128 | − | 0.893467i | \(-0.351735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24.8745 | + | 43.0839i | −1.30918 | + | 2.26757i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.29150 | 0.435191 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.2288 | 0.692425 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.61438 | − | 6.26029i | 0.188669 | − | 0.326784i | −0.756138 | − | 0.654413i | \(-0.772916\pi\) |
0.944807 | + | 0.327628i | \(0.106249\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.46863 | − | 4.27579i | −0.128512 | − | 0.222589i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.70850 | −0.452123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.0313730 | − | 0.0543397i | −0.00162443 | − | 0.00281360i | 0.865212 | − | 0.501406i | \(-0.167184\pi\) |
−0.866836 | + | 0.498593i | \(0.833850\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.2288 | −1.04183 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7085 | 0.806891 | 0.403446 | − | 0.915004i | \(-0.367812\pi\) | ||||
0.403446 | + | 0.915004i | \(0.367812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.03137 | − | 1.78639i | 0.0528388 | − | 0.0915196i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.6458 | − | 23.6351i | −0.697265 | − | 1.20770i | −0.969411 | − | 0.245443i | \(-0.921067\pi\) |
0.272146 | − | 0.962256i | \(-0.412267\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.17712 | + | 3.77089i | 0.110957 | + | 0.192182i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.96863 | − | 5.14181i | −0.150904 | − | 0.261373i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.239870 | − | 0.415468i | 0.0121619 | − | 0.0210651i | −0.859880 | − | 0.510496i | \(-0.829462\pi\) |
0.872042 | + | 0.489430i | \(0.162795\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.70850 | 0.136975 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.2915 | 1.07401 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.14575 | − | 1.98450i | 0.0576490 | − | 0.0998510i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.67712 | + | 9.83307i | 0.284927 | + | 0.493508i | 0.972591 | − | 0.232521i | \(-0.0746974\pi\) |
−0.687665 | + | 0.726028i | \(0.741364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.9686 | + | 18.9982i | 0.549118 | + | 0.951101i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.35425 | − | 7.54178i | −0.217441 | − | 0.376619i | 0.736584 | − | 0.676346i | \(-0.236438\pi\) |
−0.954025 | + | 0.299727i | \(0.903104\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.67712 | − | 9.83307i | 0.282798 | − | 0.489820i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.06275 | 0.0526784 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.08301 | + | 5.33992i | −0.152445 | + | 0.264042i | −0.932126 | − | 0.362135i | \(-0.882048\pi\) |
0.779681 | + | 0.626177i | \(0.215381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1144 | − | 17.5186i | −0.498905 | − | 0.864130i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.9373 | 1.42391 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.46863 | − | 9.47194i | −0.268444 | − | 0.464959i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.50000 | + | 4.33013i | −0.122426 | + | 0.212047i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.2915 | −1.04016 | −0.520079 | − | 0.854118i | \(-0.674097\pi\) | ||||
−0.520079 | + | 0.854118i | \(0.674097\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5830 | −0.954417 | −0.477209 | − | 0.878790i | \(-0.658351\pi\) | ||||
−0.477209 | + | 0.878790i | \(0.658351\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.822876 | + | 1.42526i | 0.0399153 | + | 0.0691354i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.5830 | − | 18.3303i | 0.512148 | − | 0.887066i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.17712 | − | 3.77089i | −0.105113 | − | 0.182060i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.9373 | − | 34.5323i | 0.960344 | − | 1.66336i | 0.238708 | − | 0.971091i | \(-0.423276\pi\) |
0.721636 | − | 0.692273i | \(-0.243390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.35425 | 0.161195 | 0.0805975 | − | 0.996747i | \(-0.474317\pi\) | ||||
0.0805975 | + | 0.996747i | \(0.474317\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.64575 | −0.366586 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.82288 | + | 11.8176i | −0.326382 | + | 0.565311i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.64575 | + | 4.58258i | 0.126275 | + | 0.218714i | 0.922231 | − | 0.386640i | \(-0.126365\pi\) |
−0.795956 | + | 0.605355i | \(0.793031\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.93725 | + | 8.55157i | 0.234576 | + | 0.406298i | 0.959149 | − | 0.282900i | \(-0.0912965\pi\) |
−0.724573 | + | 0.689198i | \(0.757963\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.11438 | − | 12.3225i | 0.337254 | − | 0.584141i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.58301 | 0.311365 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.5830 | −0.593829 | −0.296914 | − | 0.954904i | \(-0.595958\pi\) | ||||
−0.296914 | + | 0.954904i | \(0.595958\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.06275 | + | 7.03688i | −0.191307 | + | 0.331354i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.29150 | + | 3.96900i | 0.107664 | + | 0.186480i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.50000 | + | 6.06218i | −0.164083 | + | 0.284199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.32288 | + | 12.6836i | 0.342550 | + | 0.593313i | 0.984905 | − | 0.173093i | \(-0.0553762\pi\) |
−0.642356 | + | 0.766407i | \(0.722043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.822876 | + | 1.42526i | −0.0384085 | + | 0.0665256i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.6458 | −0.914994 | −0.457497 | − | 0.889211i | \(-0.651254\pi\) | ||||
−0.457497 | + | 0.889211i | \(0.651254\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.5203 | −0.488918 | −0.244459 | − | 0.969660i | \(-0.578610\pi\) | ||||
−0.244459 | + | 0.969660i | \(0.578610\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.14575 | − | 3.71655i | 0.0995068 | − | 0.172351i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.8745 | − | 32.6916i | −0.873408 | − | 1.51279i | −0.858449 | − | 0.512899i | \(-0.828572\pi\) |
−0.0149591 | − | 0.999888i | \(-0.504762\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.70850 | 0.0788911 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.645751 | − | 1.11847i | −0.0297546 | − | 0.0515366i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.88562 | + | 8.46215i | −0.224641 | + | 0.389090i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.29150 | −0.380440 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.29150 | 0.150708 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.29150 | + | 5.70105i | −0.150393 | + | 0.260488i | −0.931372 | − | 0.364069i | \(-0.881387\pi\) |
0.780979 | + | 0.624557i | \(0.214720\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.854249 | + | 1.47960i | 0.0389504 | + | 0.0674641i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.17712 | + | 3.77089i | 0.0990626 | + | 0.171581i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.00000 | − | 6.92820i | −0.181631 | − | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.32288 | + | 2.29129i | −0.0599452 | + | 0.103828i | −0.894441 | − | 0.447187i | \(-0.852426\pi\) |
0.834495 | + | 0.551015i | \(0.185759\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.12549 | −0.0959221 | −0.0479611 | − | 0.998849i | \(-0.515272\pi\) | ||||
−0.0479611 | + | 0.998849i | \(0.515272\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.29150 | − | 10.8972i | 0.283355 | − | 0.490785i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.822876 | − | 1.42526i | −0.0369855 | − | 0.0640608i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.0516 | − | 31.2663i | −0.809726 | − | 1.40249i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7288 | + | 23.7789i | 0.614584 | + | 1.06449i | 0.990457 | + | 0.137819i | \(0.0440093\pi\) |
−0.375874 | + | 0.926671i | \(0.622657\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.82288 | + | 17.0137i | −0.438854 | + | 0.760117i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.4575 | −1.00133 | −0.500666 | − | 0.865641i | \(-0.666911\pi\) | ||||
−0.500666 | + | 0.865641i | \(0.666911\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.93725 | −0.219705 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.00000 | + | 5.19615i | −0.133235 | + | 0.230769i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.9373 | + | 24.1400i | 0.617758 | + | 1.06999i | 0.989894 | + | 0.141810i | \(0.0452922\pi\) |
−0.372136 | + | 0.928178i | \(0.621374\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.0000 | −1.54831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.14575 | − | 7.18065i | −0.183039 | − | 0.317034i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.67712 | − | 8.10102i | 0.206099 | − | 0.356973i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.87451 | −0.434280 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.87451 | −0.433443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.06275 | − | 1.84073i | 0.0465598 | − | 0.0806439i | −0.841806 | − | 0.539780i | \(-0.818508\pi\) |
0.888366 | + | 0.459136i | \(0.151841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6144 | + | 27.0449i | 0.682769 | + | 1.18259i | 0.974132 | + | 0.225978i | \(0.0725578\pi\) |
−0.291363 | + | 0.956612i | \(0.594109\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.32288 | + | 2.29129i | −0.0577350 | + | 0.100000i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.53137 | + | 6.11652i | 0.153829 | + | 0.266440i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.1458 | − | 17.5730i | 0.441120 | − | 0.764042i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9373 | −0.474636 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −13.0627 | −0.565810 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.46863 | + | 14.6681i | −0.366131 | + | 0.634157i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.291503 | − | 0.504897i | −0.0125793 | − | 0.0217879i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.76013 | − | 9.97684i | −0.248106 | − | 0.429733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.3745 | − | 31.8256i | −0.789982 | − | 1.36829i | −0.925977 | − | 0.377579i | \(-0.876757\pi\) |
0.135996 | − | 0.990709i | \(-0.456577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.14575 | + | 3.71655i | −0.0920830 | + | 0.159492i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.0000 | −0.556859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.2915 | 1.85101 | 0.925505 | − | 0.378734i | \(-0.123641\pi\) | ||||
0.925505 | + | 0.378734i | \(0.123641\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.00000 | + | 6.92820i | −0.170716 | + | 0.295689i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 31.6974 | + | 54.9015i | 1.35035 | + | 2.33888i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.03137 | + | 5.25049i | −0.128907 | + | 0.223274i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.322876 | + | 0.559237i | 0.0137053 | + | 0.0237383i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.00000 | − | 15.5885i | 0.381342 | − | 0.660504i | −0.609912 | − | 0.792469i | \(-0.708795\pi\) |
0.991254 | + | 0.131965i | \(0.0421286\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7085 | −0.664399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.70850 | 0.114353 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2915 | + | 31.6818i | −0.770895 | + | 1.33523i | 0.166178 | + | 0.986096i | \(0.446857\pi\) |
−0.937073 | + | 0.349133i | \(0.886476\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.00000 | − | 5.19615i | −0.126211 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.64575 | −0.111111 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.88562 | + | 3.26599i | 0.0790494 | + | 0.136918i | 0.902840 | − | 0.429977i | \(-0.141478\pi\) |
−0.823791 | + | 0.566894i | \(0.808145\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.1458 | − | 38.3576i | 0.926771 | − | 1.60521i | 0.138083 | − | 0.990421i | \(-0.455906\pi\) |
0.788688 | − | 0.614793i | \(-0.210761\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.1660 | 0.800672 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.64575 | −0.0686326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.2601 | − | 36.8236i | 0.885071 | − | 1.53299i | 0.0394383 | − | 0.999222i | \(-0.487443\pi\) |
0.845633 | − | 0.533766i | \(-0.179224\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.03137 | − | 6.98254i | −0.167538 | − | 0.290185i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.4686 | + | 25.0604i | 0.600260 | + | 1.03968i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.70850 | − | 4.69126i | −0.112174 | − | 0.194292i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.32288 | − | 2.29129i | 0.0546942 | − | 0.0947331i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −16.9373 | −0.699075 | −0.349538 | − | 0.936922i | \(-0.613661\pi\) | ||||
−0.349538 | + | 0.936922i | \(0.613661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.5830 | −1.46617 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.46863 | + | 4.27579i | −0.101546 | + | 0.175882i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.5314 | + | 21.7050i | 0.514602 | + | 0.891316i | 0.999856 | + | 0.0169436i | \(0.00539357\pi\) |
−0.485255 | + | 0.874373i | \(0.661273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.17712 | − | 3.77089i | −0.0892534 | − | 0.154591i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.5830 | + | 20.0624i | 0.474061 | + | 0.821097i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.06275 | − | 1.84073i | 0.0434226 | − | 0.0752102i | −0.843497 | − | 0.537133i | \(-0.819507\pi\) |
0.886920 | + | 0.461923i | \(0.152840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.5830 | −1.53304 | −0.766521 | − | 0.642219i | \(-0.778014\pi\) | ||||
−0.766521 | + | 0.642219i | \(0.778014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.645751 | −0.0262970 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.14575 | − | 7.18065i | 0.168549 | − | 0.291935i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.38562 | − | 14.5243i | −0.340362 | − | 0.589524i | 0.644138 | − | 0.764909i | \(-0.277216\pi\) |
−0.984500 | + | 0.175385i | \(0.943883\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 20.2288 | 0.819711 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.93725 | − | 13.7477i | −0.321107 | − | 0.556174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.5830 | − | 35.6508i | 0.831340 | − | 1.43992i | −0.0656363 | − | 0.997844i | \(-0.520908\pi\) |
0.896976 | − | 0.442079i | \(-0.145759\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.93725 | −0.199089 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.29150 | 0.374062 | 0.187031 | − | 0.982354i | \(-0.440114\pi\) | ||||
0.187031 | + | 0.982354i | \(0.440114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | + | 16.4545i | −0.381837 | + | 0.661361i | −0.991325 | − | 0.131434i | \(-0.958042\pi\) |
0.609488 | + | 0.792796i | \(0.291375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.822876 | − | 1.42526i | −0.0330209 | − | 0.0571938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.8229 | + | 32.6022i | −0.754123 | + | 1.30618i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.82288 | + | 11.8176i | −0.272479 | + | 0.471948i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.06275 | −0.0423745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.7490 | 1.42315 | 0.711573 | − | 0.702612i | \(-0.247983\pi\) | ||||
0.711573 | + | 0.702612i | \(0.247983\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.29150 | + | 7.43310i | −0.170572 | + | 0.295439i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.03137 | − | 1.78639i | −0.0409288 | − | 0.0708907i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.26013 | − | 16.0390i | 0.366900 | − | 0.635489i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.82288 | + | 11.8176i | 0.269909 | + | 0.467496i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.05163 | − | 10.4817i | 0.239025 | − | 0.414004i | −0.721410 | − | 0.692509i | \(-0.756506\pi\) |
0.960435 | + | 0.278505i | \(0.0898388\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8118 | 0.860172 | 0.430086 | − | 0.902788i | \(-0.358483\pi\) | ||||
0.430086 | + | 0.902788i | \(0.358483\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.93725 | −0.233779 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.4686 | − | 19.8642i | 0.450878 | − | 0.780944i | −0.547563 | − | 0.836765i | \(-0.684444\pi\) |
0.998441 | + | 0.0558207i | \(0.0177775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | + | 15.5885i | 0.353281 | + | 0.611900i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.67712 | + | 9.83307i | −0.222504 | + | 0.385388i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.1771 | − | 24.5555i | −0.554794 | − | 0.960931i | −0.997920 | − | 0.0644715i | \(-0.979464\pi\) |
0.443126 | − | 0.896459i | \(-0.353869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.6458 | − | 18.4390i | 0.415964 | − | 0.720471i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.2288 | 0.516103 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.4373 | − | 35.3984i | 0.794917 | − | 1.37684i | −0.127975 | − | 0.991777i | \(-0.540848\pi\) |
0.922892 | − | 0.385059i | \(-0.125819\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.17712 | + | 3.77089i | 0.0845525 | + | 0.146449i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.9373 | 0.850690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.29150 | + | 10.8972i | 0.243608 | + | 0.421941i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.93725 | + | 15.4798i | −0.345534 | + | 0.598483i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.1660 | 0.508268 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.35425 | −0.206391 | −0.103196 | − | 0.994661i | \(-0.532907\pi\) | ||||
−0.103196 | + | 0.994661i | \(0.532907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.1771 | + | 19.3593i | 0.429572 | + | 0.744040i | 0.996835 | − | 0.0794963i | \(-0.0253312\pi\) |
−0.567263 | + | 0.823536i | \(0.691998\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5830 | + | 18.3303i | 0.406138 | + | 0.703452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.82288 | − | 17.0137i | −0.376413 | − | 0.651967i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.46863 | − | 4.27579i | 0.0944594 | − | 0.163608i | −0.814923 | − | 0.579569i | \(-0.803221\pi\) |
0.909383 | + | 0.415960i | \(0.136554\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.2288 | −0.772901 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00000 | 0.267067 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.35425 | − | 7.54178i | 0.165884 | − | 0.287319i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.7915 | + | 20.4235i | 0.448570 | + | 0.776946i | 0.998293 | − | 0.0584009i | \(-0.0186002\pi\) |
−0.549723 | + | 0.835347i | \(0.685267\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.17712 | + | 3.77089i | 0.0827021 | + | 0.143244i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.50000 | + | 4.33013i | 0.0948304 | + | 0.164251i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.06275 | − | 7.03688i | 0.153887 | − | 0.266541i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.2915 | −0.805319 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 34.9373 | 1.31956 | 0.659781 | − | 0.751458i | \(-0.270649\pi\) | ||||
0.659781 | + | 0.751458i | \(0.270649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.67712 | − | 4.63692i | 0.100970 | − | 0.174885i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.00000 | − | 5.19615i | −0.112987 | − | 0.195698i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0627 | 0.491275 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2915 | + | 19.5575i | 0.424061 | + | 0.734496i | 0.996332 | − | 0.0855689i | \(-0.0272708\pi\) |
−0.572271 | + | 0.820065i | \(0.693937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.14575 | − | 1.98450i | 0.0429690 | − | 0.0744245i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.06275 | −0.264502 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.35425 | −0.162840 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.00000 | + | 5.19615i | −0.112037 | + | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.35425 | − | 12.7379i | −0.274267 | − | 0.475045i | 0.695683 | − | 0.718349i | \(-0.255102\pi\) |
−0.969950 | + | 0.243304i | \(0.921769\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3745 | + | 21.4333i | −0.460851 | + | 0.798217i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.35425 | − | 11.0059i | −0.236317 | − | 0.409313i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.82288 | + | 6.62141i | −0.141978 | + | 0.245913i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.8118 | 1.25401 | 0.627004 | − | 0.779016i | \(-0.284281\pi\) | ||||
0.627004 | + | 0.779016i | \(0.284281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.88562 | − | 8.46215i | 0.180701 | − | 0.312984i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.61438 | − | 6.26029i | −0.133500 | − | 0.231229i | 0.791523 | − | 0.611139i | \(-0.209288\pi\) |
−0.925023 | + | 0.379910i | \(0.875955\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.50000 | − | 6.06218i | 0.129099 | − | 0.223607i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.531373 | + | 0.920365i | 0.0195734 | + | 0.0339021i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5000 | − | 25.1147i | 0.533391 | − | 0.923861i | −0.465848 | − | 0.884865i | \(-0.654251\pi\) |
0.999239 | − | 0.0389959i | \(-0.0124159\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.9373 | −0.805885 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.0627 | 0.479226 | 0.239613 | − | 0.970869i | \(-0.422979\pi\) | ||||
0.239613 | + | 0.970869i | \(0.422979\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.29150 | − | 5.70105i | 0.120591 | − | 0.208870i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.46863 | − | 9.47194i | −0.200087 | − | 0.346560i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.4059 | − | 38.8081i | 0.818693 | − | 1.41802i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0830 | + | 20.9284i | 0.440915 | + | 0.763687i | 0.997758 | − | 0.0669307i | \(-0.0213206\pi\) |
−0.556843 | + | 0.830618i | \(0.687987\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.46863 | − | 9.47194i | 0.199288 | − | 0.345177i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.58301 | 0.166793 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.83399 | −0.321077 | −0.160538 | − | 0.987030i | \(-0.551323\pi\) | ||||
−0.160538 | + | 0.987030i | \(0.551323\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.35425 | + | 2.34563i | −0.0491561 | + | 0.0851409i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.05163 | + | 10.4817i | 0.219371 | + | 0.379963i | 0.954616 | − | 0.297839i | \(-0.0962660\pi\) |
−0.735244 | + | 0.677802i | \(0.762933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 34.3948 | 1.24517 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.822876 | + | 1.42526i | 0.0297511 | + | 0.0515305i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.4686 | + | 25.0604i | −0.522432 | + | 0.904878i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.70850 | −0.133732 | −0.0668659 | − | 0.997762i | \(-0.521300\pi\) | ||||
−0.0668659 | + | 0.997762i | \(0.521300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.52026 | −0.198807 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.6974 | + | 23.7246i | −0.492661 | + | 0.853313i | −0.999964 | − | 0.00845413i | \(-0.997309\pi\) |
0.507304 | + | 0.861767i | \(0.330642\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.14575 | − | 3.71655i | −0.0770777 | − | 0.133502i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.854249 | − | 1.47960i | −0.0306460 | − | 0.0530804i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.4686 | + | 35.4527i | 0.733365 | + | 1.27022i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2288 | − | 19.4488i | 0.401796 | − | 0.695932i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.64575 | −0.273237 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.29150 | −0.0460957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.93725 | − | 5.08747i | 0.104702 | − | 0.181349i | −0.808915 | − | 0.587926i | \(-0.799945\pi\) |
0.913616 | + | 0.406577i | \(0.133278\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.2288 | + | 24.6449i | 0.506557 | + | 0.877383i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.93725 | + | 13.7477i | 0.282216 | + | 0.488813i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.5830 | + | 18.3303i | 0.375814 | + | 0.650928i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.64575 | − | 2.85052i | 0.0583688 | − | 0.101098i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.93725 | 0.174887 | 0.0874433 | − | 0.996170i | \(-0.472130\pi\) | ||||
0.0874433 | + | 0.996170i | \(0.472130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.87451 | 0.349335 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.11438 | − | 12.3225i | 0.251374 | − | 0.435393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.8856 | − | 18.8544i | −0.384145 | − | 0.665359i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.35425 | 0.153467 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.9373 | + | 24.1400i | 0.490615 | + | 0.849769i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.58301 | + | 16.5983i | −0.336921 | + | 0.583563i | −0.983852 | − | 0.178985i | \(-0.942719\pi\) |
0.646931 | + | 0.762548i | \(0.276052\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.2915 | −0.607187 | −0.303593 | − | 0.952802i | \(-0.598186\pi\) | ||||
−0.303593 | + | 0.952802i | \(0.598186\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.41699 | 0.260125 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.00000 | + | 13.8564i | −0.280228 | + | 0.485369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.6144 | + | 42.6334i | 0.861148 | + | 1.49155i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.50000 | + | 6.06218i | −0.122300 | + | 0.211830i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.9889 | + | 45.0141i | 0.907018 | + | 1.57100i | 0.818185 | + | 0.574955i | \(0.194981\pi\) |
0.0888337 | + | 0.996046i | \(0.471686\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.22876 | − | 15.9847i | 0.321694 | − | 0.557191i | −0.659144 | − | 0.752017i | \(-0.729081\pi\) |
0.980838 | + | 0.194826i | \(0.0624144\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.64575 | −0.0572977 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.4575 | −0.780924 | −0.390462 | − | 0.920619i | \(-0.627685\pi\) | ||||
−0.390462 | + | 0.920619i | \(0.627685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.85425 | + | 17.0681i | −0.342252 | + | 0.592798i | −0.984851 | − | 0.173405i | \(-0.944523\pi\) |
0.642598 | + | 0.766203i | \(0.277856\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.3229 | − | 17.8797i | −0.358097 | − | 0.620241i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.76013 | + | 9.97684i | 0.199577 | + | 0.345677i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.82288 | + | 17.0137i | 0.339935 | + | 0.588784i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.14575 | − | 3.71655i | 0.0741680 | − | 0.128463i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.3542 | −0.564611 | −0.282306 | − | 0.959325i | \(-0.591099\pi\) | ||||
−0.282306 | + | 0.959325i | \(0.591099\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.4575 | 1.01578 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000 | − | 20.7846i | 0.413302 | − | 0.715860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.00000 | + | 5.19615i | 0.103203 | + | 0.178753i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.9686 | + | 18.9982i | −0.376886 | + | 0.652787i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.32288 | + | 12.6836i | 0.251320 | + | 0.435300i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.531373 | − | 0.920365i | 0.0182152 | − | 0.0315497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.2288 | 1.48012 | 0.740062 | − | 0.672538i | \(-0.234796\pi\) | ||||
0.740062 | + | 0.672538i | \(0.234796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.29150 | −0.283563 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 6.82288 | − | 11.8176i | 0.233065 | − | 0.403680i | −0.725644 | − | 0.688071i | \(-0.758458\pi\) |
0.958709 | + | 0.284390i | \(0.0917912\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.2288 | − | 22.9129i | −0.451359 | − | 0.781777i | 0.547111 | − | 0.837060i | \(-0.315727\pi\) |
−0.998471 | + | 0.0552825i | \(0.982394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.0627 | 0.445177 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.2288 | − | 29.8411i | −0.586474 | − | 1.01580i | −0.994690 | − | 0.102917i | \(-0.967182\pi\) |
0.408216 | − | 0.912885i | \(-0.366151\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.93725 | + | 8.55157i | −0.167872 | + | 0.290762i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.2915 | 0.485365 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.77124 | −0.127931 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.854249 | + | 1.47960i | −0.0289451 | + | 0.0501344i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.00000 | − | 6.92820i | −0.135379 | − | 0.234484i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.32288 | + | 2.29129i | 0.0447214 | + | 0.0774597i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.00000 | − | 12.1244i | −0.236373 | − | 0.409410i | 0.723298 | − | 0.690536i | \(-0.242625\pi\) |
−0.959671 | + | 0.281126i | \(0.909292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.16601 | 0.0392839 | 0.0196419 | − | 0.999807i | \(-0.493747\pi\) | ||||
0.0196419 | + | 0.999807i | \(0.493747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.8118 | 0.734024 | 0.367012 | − | 0.930216i | \(-0.380381\pi\) | ||||
0.367012 | + | 0.930216i | \(0.380381\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.46863 | + | 9.47194i | −0.183826 | + | 0.318396i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.82288 | − | 17.0137i | −0.329820 | − | 0.571265i | 0.652656 | − | 0.757654i | \(-0.273655\pi\) |
−0.982476 | + | 0.186390i | \(0.940321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.72876 | + | 4.72634i | 0.0915196 | + | 0.158517i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.822876 | − | 1.42526i | −0.0275674 | − | 0.0477481i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.8745 | + | 43.0839i | −0.832394 | + | 1.44175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.583005 | −0.0194877 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.35425 | −0.145384 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −16.4059 | + | 28.4158i | −0.547167 | + | 0.947721i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.70850 | + | 4.69126i | 0.0902331 | + | 0.156288i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.7085 | 0.522746 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.14575 | + | 3.71655i | 0.0713272 | + | 0.123542i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.3229 | + | 17.8797i | −0.342765 | + | 0.593687i | −0.984945 | − | 0.172867i | \(-0.944697\pi\) |
0.642180 | + | 0.766554i | \(0.278030\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.93725 | −0.163758 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.52026 | 0.182894 | 0.0914472 | − | 0.995810i | \(-0.470851\pi\) | ||||
0.0914472 | + | 0.995810i | \(0.470851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.00000 | + | 15.5885i | −0.297857 | + | 0.515903i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.00000 | + | 6.92820i | 0.132236 | + | 0.229039i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.1660 | + | 48.7850i | −0.930124 | + | 1.61102i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.20850 | + | 9.02138i | 0.171812 | + | 0.297588i | 0.939054 | − | 0.343771i | \(-0.111704\pi\) |
−0.767241 | + | 0.641359i | \(0.778371\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.9686 | + | 24.1944i | −0.460282 | + | 0.797232i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.1033 | 1.18835 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.645751 | 0.0212322 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.67712 | − | 8.10102i | 0.153617 | − | 0.266072i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7601 | − | 30.7614i | −0.582691 | − | 1.00925i | −0.995159 | − | 0.0982783i | \(-0.968666\pi\) |
0.412468 | − | 0.910972i | \(-0.364667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −58.0405 | −1.90220 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.82288 | − | 11.8176i | −0.223371 | − | 0.386890i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.35425 | − | 2.34563i | 0.0442887 | − | 0.0767102i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.9778 | 1.27335 | 0.636674 | − | 0.771133i | \(-0.280310\pi\) | ||||
0.636674 | + | 0.771133i | \(0.280310\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.2288 | 0.692774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.46863 | − | 9.47194i | 0.178272 | − | 0.308776i | −0.763017 | − | 0.646379i | \(-0.776283\pi\) |
0.941289 | + | 0.337602i | \(0.109616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.06275 | + | 7.03688i | 0.132301 | + | 0.229152i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.32288 | + | 2.29129i | −0.0430331 | + | 0.0745356i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.1771 | − | 34.9478i | −0.655668 | − | 1.13565i | −0.981726 | − | 0.190301i | \(-0.939054\pi\) |
0.326057 | − | 0.945350i | \(-0.394280\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.5000 | − | 30.3109i | 0.568074 | − | 0.983933i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.5203 | −0.762697 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −52.4575 | −1.69927 | −0.849633 | − | 0.527375i | \(-0.823176\pi\) | ||||
−0.849633 | + | 0.527375i | \(0.823176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.58301 | − | 16.5983i | 0.310099 | − | 0.537107i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.29150 | + | 10.8972i | 0.203375 | + | 0.352257i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.5203 | 1.72826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.29150 | + | 10.8972i | 0.202952 | + | 0.351523i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.46863 | + | 14.6681i | −0.272898 | + | 0.472673i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.06275 | −0.259549 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.3948 | 0.913114 | 0.456557 | − | 0.889694i | \(-0.349082\pi\) | ||||
0.456557 | + | 0.889694i | \(0.349082\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.82288 | − | 11.8176i | 0.219182 | − | 0.379635i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.41699 | + | 9.38251i | 0.173840 | + | 0.301099i | 0.939759 | − | 0.341837i | \(-0.111049\pi\) |
−0.765919 | + | 0.642937i | \(0.777716\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.61438 | − | 11.4564i | −0.212047 | − | 0.367277i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.32288 | − | 2.29129i | −0.0423659 | − | 0.0733799i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.5314 | − | 21.7050i | 0.400914 | − | 0.694404i | −0.592922 | − | 0.805260i | \(-0.702026\pi\) |
0.993836 | + | 0.110856i | \(0.0353592\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.4170 | −0.748410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0000 | −0.415058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.3431 | − | 21.3789i | 0.393685 | − | 0.681882i | −0.599247 | − | 0.800564i | \(-0.704533\pi\) |
0.992932 | + | 0.118682i | \(0.0378668\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.46863 | + | 4.27579i | 0.0786570 | + | 0.136238i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.93725 | + | 13.7477i | 0.252646 | + | 0.437595i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.88562 | + | 8.46215i | 0.155354 | + | 0.269081i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.1458 | − | 38.3576i | 0.703483 | − | 1.21847i | −0.263753 | − | 0.964590i | \(-0.584960\pi\) |
0.967236 | − | 0.253878i | \(-0.0817062\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.1660 | −0.639949 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.1660 | 0.734412 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.6144 | + | 37.4372i | −0.684534 | + | 1.18565i | 0.289049 | + | 0.957314i | \(0.406661\pi\) |
−0.973583 | + | 0.228334i | \(0.926672\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.322876 | + | 0.559237i | 0.0102153 | + | 0.0176935i |
(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 | 1680.2.bg.q.1201.2 | 4 | ||
4.3 | odd | 2 | 420.2.q.c.361.1 | yes | 4 | ||
7.2 | even | 3 | inner | 1680.2.bg.q.961.2 | 4 | ||
12.11 | even | 2 | 1260.2.s.f.361.1 | 4 | |||
20.3 | even | 4 | 2100.2.bc.e.949.1 | 8 | |||
20.7 | even | 4 | 2100.2.bc.e.949.4 | 8 | |||
20.19 | odd | 2 | 2100.2.q.h.1201.2 | 4 | |||
28.3 | even | 6 | 2940.2.a.m.1.1 | 2 | |||
28.11 | odd | 6 | 2940.2.a.s.1.1 | 2 | |||
28.19 | even | 6 | 2940.2.q.t.961.2 | 4 | |||
28.23 | odd | 6 | 420.2.q.c.121.1 | ✓ | 4 | ||
28.27 | even | 2 | 2940.2.q.t.361.2 | 4 | |||
84.11 | even | 6 | 8820.2.a.be.1.2 | 2 | |||
84.23 | even | 6 | 1260.2.s.f.541.1 | 4 | |||
84.59 | odd | 6 | 8820.2.a.bj.1.2 | 2 | |||
140.23 | even | 12 | 2100.2.bc.e.1549.4 | 8 | |||
140.79 | odd | 6 | 2100.2.q.h.1801.2 | 4 | |||
140.107 | even | 12 | 2100.2.bc.e.1549.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.c.121.1 | ✓ | 4 | 28.23 | odd | 6 | ||
420.2.q.c.361.1 | yes | 4 | 4.3 | odd | 2 | ||
1260.2.s.f.361.1 | 4 | 12.11 | even | 2 | |||
1260.2.s.f.541.1 | 4 | 84.23 | even | 6 | |||
1680.2.bg.q.961.2 | 4 | 7.2 | even | 3 | inner | ||
1680.2.bg.q.1201.2 | 4 | 1.1 | even | 1 | trivial | ||
2100.2.q.h.1201.2 | 4 | 20.19 | odd | 2 | |||
2100.2.q.h.1801.2 | 4 | 140.79 | odd | 6 | |||
2100.2.bc.e.949.1 | 8 | 20.3 | even | 4 | |||
2100.2.bc.e.949.4 | 8 | 20.7 | even | 4 | |||
2100.2.bc.e.1549.1 | 8 | 140.107 | even | 12 | |||
2100.2.bc.e.1549.4 | 8 | 140.23 | even | 12 | |||
2940.2.a.m.1.1 | 2 | 28.3 | even | 6 | |||
2940.2.a.s.1.1 | 2 | 28.11 | odd | 6 | |||
2940.2.q.t.361.2 | 4 | 28.27 | even | 2 | |||
2940.2.q.t.961.2 | 4 | 28.19 | even | 6 | |||
8820.2.a.be.1.2 | 2 | 84.11 | even | 6 | |||
8820.2.a.bj.1.2 | 2 | 84.59 | odd | 6 |