Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(361,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.s (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.0611506547\) |
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 | 361.1 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.361 |
Dual form | 1260.2.s.f.541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 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 | 0 | ||||||||
\(10\) | 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 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.822876 | + | 1.42526i | −0.199577 | + | 0.345677i | −0.948391 | − | 0.317103i | \(-0.897290\pi\) |
0.748815 | + | 0.662780i | \(0.230623\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.14575 | − | 7.18065i | −0.951101 | − | 1.64735i | −0.743049 | − | 0.669237i | \(-0.766621\pi\) |
−0.208051 | − | 0.978118i | \(-0.566712\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 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 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.64575 | −1.41978 | −0.709890 | − | 0.704312i | \(-0.751255\pi\) | ||||
−0.709890 | + | 0.704312i | \(0.751255\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.14575 | − | 3.71655i | 0.385388 | − | 0.667512i | −0.606435 | − | 0.795133i | \(-0.707401\pi\) |
0.991823 | + | 0.127621i | \(0.0407342\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.93725 | −0.771070 | −0.385535 | − | 0.922693i | \(-0.625983\pi\) | ||||
−0.385535 | + | 0.922693i | \(0.625983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.93725 | −0.905423 | −0.452711 | − | 0.891657i | \(-0.649543\pi\) | ||||
−0.452711 | + | 0.891657i | \(0.649543\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 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 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.64575 | − | 2.85052i | 0.226061 | − | 0.391550i | −0.730576 | − | 0.682831i | \(-0.760748\pi\) |
0.956637 | + | 0.291282i | \(0.0940817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64575 | −0.221913 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.32288 | − | 2.29129i | −0.164083 | − | 0.284199i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.322876 | + | 0.559237i | −0.0394455 | + | 0.0683217i | −0.885074 | − | 0.465450i | \(-0.845892\pi\) |
0.845629 | + | 0.533772i | \(0.179226\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.35425 | 0.496213 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.14575 | − | 1.98450i | −0.128907 | − | 0.223274i | 0.794346 | − | 0.607465i | \(-0.207814\pi\) |
−0.923253 | + | 0.384192i | \(0.874480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.11438 | − | 12.3225i | −0.754123 | − | 1.30618i | −0.945809 | − | 0.324722i | \(-0.894729\pi\) |
0.191687 | − | 0.981456i | \(-0.438604\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50000 | + | 6.06218i | 0.366900 | + | 0.635489i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.46863 | + | 4.27579i | −0.245638 | + | 0.425457i | −0.962311 | − | 0.271953i | \(-0.912331\pi\) |
0.716673 | + | 0.697409i | \(0.245664\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.67712 | − | 8.10102i | −0.460851 | − | 0.798217i | 0.538153 | − | 0.842847i | \(-0.319122\pi\) |
−0.999004 | + | 0.0446304i | \(0.985789\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 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 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.822876 | + | 1.42526i | −0.0767336 | + | 0.132906i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.35425 | 0.399153 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.14575 | + | 7.18065i | 0.376886 | + | 0.652787i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.06275 | −0.183039 | −0.0915196 | − | 0.995803i | \(-0.529172\pi\) | ||||
−0.0915196 | + | 0.995803i | \(0.529172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 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 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.1144 | + | 17.5186i | −0.864130 | + | 1.49672i | 0.00377913 | + | 0.999993i | \(0.498797\pi\) |
−0.867909 | + | 0.496724i | \(0.834536\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.00000 | 0.424094 | 0.212047 | − | 0.977259i | \(-0.431987\pi\) | ||||
0.212047 | + | 0.977259i | \(0.431987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.29150 | − | 5.70105i | −0.269650 | − | 0.467048i | 0.699121 | − | 0.715003i | \(-0.253575\pi\) |
−0.968772 | + | 0.247955i | \(0.920241\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.29150 | − | 3.96900i | 0.186480 | − | 0.322993i | −0.757594 | − | 0.652726i | \(-0.773625\pi\) |
0.944074 | + | 0.329733i | \(0.106959\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 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 | \(0.0488907\pi\) |
−0.361619 | + | 0.932326i | \(0.617776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 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 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.93725 | + | 8.55157i | 0.375372 | + | 0.650164i | 0.990383 | − | 0.138355i | \(-0.0441815\pi\) |
−0.615010 | + | 0.788519i | \(0.710848\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.64575 | 0.200000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.93725 | 0.351765 | 0.175882 | − | 0.984411i | \(-0.443722\pi\) | ||||
0.175882 | + | 0.984411i | \(0.443722\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5830 | − | 20.0624i | 0.821097 | − | 1.42218i | −0.0837682 | − | 0.996485i | \(-0.526696\pi\) |
0.904866 | − | 0.425697i | \(-0.139971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.6458 | 0.943896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.58301 | 0.590878 | 0.295439 | − | 0.955362i | \(-0.404534\pi\) | ||||
0.295439 | + | 0.955362i | \(0.404534\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.96863 | − | 5.14181i | −0.202459 | − | 0.350669i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3542 | −0.770777 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17712 | − | 3.77089i | 0.146449 | − | 0.253658i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.8745 | 1.19697 | 0.598483 | − | 0.801136i | \(-0.295770\pi\) | ||||
0.598483 | + | 0.801136i | \(0.295770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.6458 | + | 18.4390i | 0.697426 | + | 1.20798i | 0.969356 | + | 0.245661i | \(0.0790049\pi\) |
−0.271930 | + | 0.962317i | \(0.587662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | + | 5.19615i | −0.195698 | + | 0.338960i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.00000 | −0.447214 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9686 | + | 18.9982i | 0.697917 | + | 1.20883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.76013 | + | 4.78068i | 0.172172 | + | 0.298211i | 0.939179 | − | 0.343428i | \(-0.111588\pi\) |
−0.767007 | + | 0.641639i | \(0.778255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.854249 | + | 1.47960i | −0.0530804 | + | 0.0919380i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.9373 | − | 24.1400i | 0.849769 | − | 1.47184i | −0.0316446 | − | 0.999499i | \(-0.510074\pi\) |
0.881414 | − | 0.472345i | \(-0.156592\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.70850 | − | 6.42331i | −0.225275 | − | 0.390188i | 0.731127 | − | 0.682242i | \(-0.238995\pi\) |
−0.956402 | + | 0.292054i | \(0.905661\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.32288 | − | 12.6836i | 0.435300 | − | 0.753961i | −0.562020 | − | 0.827123i | \(-0.689976\pi\) |
0.997320 | + | 0.0731621i | \(0.0233091\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 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 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 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 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.00000 | − | 6.92820i | 0.229039 | − | 0.396708i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.9373 | 1.59446 | 0.797232 | − | 0.603674i | \(-0.206297\pi\) | ||||
0.797232 | + | 0.603674i | \(0.206297\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 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 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.7601 | + | 20.3691i | 0.660515 | + | 1.14404i | 0.980481 | + | 0.196616i | \(0.0629952\pi\) |
−0.319966 | + | 0.947429i | \(0.603671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.29150 | − | 10.8972i | 0.352257 | − | 0.610126i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6458 | 0.759270 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.32288 | − | 2.29129i | 0.0733799 | − | 0.127098i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | \(0.0203137\pi\) |
−0.443752 | + | 0.896149i | \(0.646353\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 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 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.53137 | + | 6.11652i | 0.191235 | + | 0.331228i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0516 | + | 31.2663i | −0.960791 | + | 1.66414i | −0.240271 | + | 0.970706i | \(0.577236\pi\) |
−0.720520 | + | 0.693434i | \(0.756097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.82288 | − | 11.8176i | −0.362121 | − | 0.627211i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 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 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.2288 | −0.692425 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.61438 | + | 6.26029i | −0.188669 | + | 0.326784i | −0.944807 | − | 0.327628i | \(-0.893751\pi\) |
0.756138 | + | 0.654413i | \(0.227084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 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 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.2288 | 1.04183 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.7085 | −0.806891 | −0.403446 | − | 0.915004i | \(-0.632188\pi\) | ||||
−0.403446 | + | 0.915004i | \(0.632188\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 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 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.239870 | + | 0.415468i | −0.0121619 | + | 0.0210651i | −0.872042 | − | 0.489430i | \(-0.837205\pi\) |
0.859880 | + | 0.510496i | \(0.170538\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.70850 | −0.136975 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.35425 | + | 7.54178i | 0.217441 | + | 0.376619i | 0.954025 | − | 0.299727i | \(-0.0968958\pi\) |
−0.736584 | + | 0.676346i | \(0.763562\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.67712 | + | 9.83307i | −0.282798 | + | 0.489820i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.9373 | −1.42391 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.46863 | + | 9.47194i | 0.268444 | + | 0.464959i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 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 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 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 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.82288 | − | 11.8176i | 0.326382 | − | 0.565311i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.64575 | − | 4.58258i | −0.126275 | − | 0.218714i | 0.795956 | − | 0.605355i | \(-0.206969\pi\) |
−0.922231 | + | 0.386640i | \(0.873635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.5830 | 0.593829 | 0.296914 | − | 0.954904i | \(-0.404042\pi\) | ||||
0.296914 | + | 0.954904i | \(0.404042\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.06275 | − | 7.03688i | 0.191307 | − | 0.331354i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.6458 | 0.914994 | 0.457497 | − | 0.889211i | \(-0.348746\pi\) | ||||
0.457497 | + | 0.889211i | \(0.348746\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.5203 | 0.488918 | 0.244459 | − | 0.969660i | \(-0.421390\pi\) | ||||
0.244459 | + | 0.969660i | \(0.421390\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.88562 | − | 8.46215i | 0.224641 | − | 0.389090i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.29150 | 0.380440 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.00000 | + | 6.92820i | 0.181631 | + | 0.314594i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.32288 | − | 2.29129i | 0.0599452 | − | 0.103828i | −0.834495 | − | 0.551015i | \(-0.814241\pi\) |
0.894441 | + | 0.447187i | \(0.147574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 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 | 0 | ||||||||
\(496\) | 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 | \(-0.955991\pi\) |
0.375874 | − | 0.926671i | \(-0.377343\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.9373 | − | 24.1400i | −0.617758 | − | 1.06999i | −0.989894 | − | 0.141810i | \(-0.954708\pi\) |
0.372136 | − | 0.928178i | \(-0.378626\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.0000 | 1.54831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.67712 | − | 8.10102i | 0.206099 | − | 0.356973i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.87451 | −0.434280 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.06275 | + | 1.84073i | −0.0465598 | + | 0.0806439i | −0.888366 | − | 0.459136i | \(-0.848159\pi\) |
0.841806 | + | 0.539780i | \(0.181492\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.6144 | − | 27.0449i | −0.682769 | − | 1.18259i | −0.974132 | − | 0.225978i | \(-0.927442\pi\) |
0.291363 | − | 0.956612i | \(-0.405891\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.0627 | 0.565810 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.46863 | − | 14.6681i | 0.366131 | − | 0.634157i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.0000 | 0.556859 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.2915 | −1.85101 | −0.925505 | − | 0.378734i | \(-0.876359\pi\) | ||||
−0.925505 | + | 0.378734i | \(0.876359\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.00000 | + | 15.5885i | −0.381342 | + | 0.660504i | −0.991254 | − | 0.131965i | \(-0.957871\pi\) |
0.609912 | + | 0.792469i | \(0.291205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.7085 | 0.664399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.88562 | − | 3.26599i | −0.0790494 | − | 0.136918i | 0.823791 | − | 0.566894i | \(-0.191855\pi\) |
−0.902840 | + | 0.429977i | \(0.858522\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.1458 | + | 38.3576i | −0.926771 | + | 1.60521i | −0.138083 | + | 0.990421i | \(0.544094\pi\) |
−0.788688 | + | 0.614793i | \(0.789239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 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 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −12.5314 | − | 21.7050i | −0.514602 | − | 0.891316i | −0.999856 | − | 0.0169436i | \(-0.994606\pi\) |
0.485255 | − | 0.874373i | \(-0.338727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.17712 | + | 3.77089i | 0.0892534 | + | 0.154591i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.14575 | + | 7.18065i | −0.168549 | + | 0.291935i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.38562 | + | 14.5243i | 0.340362 | + | 0.589524i | 0.984500 | − | 0.175385i | \(-0.0561171\pi\) |
−0.644138 | + | 0.764909i | \(0.722784\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.29150 | −0.374062 | −0.187031 | − | 0.982354i | \(-0.559886\pi\) | ||||
−0.187031 | + | 0.982354i | \(0.559886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.50000 | − | 16.4545i | 0.381837 | − | 0.661361i | −0.609488 | − | 0.792796i | \(-0.708625\pi\) |
0.991325 | + | 0.131434i | \(0.0419582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.06275 | 0.0423745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.7490 | −1.42315 | −0.711573 | − | 0.702612i | \(-0.752017\pi\) | ||||
−0.711573 | + | 0.702612i | \(0.752017\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.05163 | + | 10.4817i | −0.239025 | + | 0.414004i | −0.960435 | − | 0.278505i | \(-0.910161\pi\) |
0.721410 | + | 0.692509i | \(0.243494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.8118 | −0.860172 | −0.430086 | − | 0.902788i | \(-0.641517\pi\) | ||||
−0.430086 | + | 0.902788i | \(0.641517\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.1771 | + | 24.5555i | 0.554794 | + | 0.960931i | 0.997920 | + | 0.0644715i | \(0.0205362\pi\) |
−0.443126 | + | 0.896459i | \(0.646131\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.6458 | + | 18.4390i | −0.415964 | + | 0.720471i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21.9373 | −0.850690 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.29150 | − | 10.8972i | −0.243608 | − | 0.421941i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 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 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.1771 | − | 19.3593i | −0.429572 | − | 0.744040i | 0.567263 | − | 0.823536i | \(-0.308002\pi\) |
−0.996835 | + | 0.0794963i | \(0.974669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5830 | − | 18.3303i | −0.406138 | − | 0.703452i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 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 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.35425 | + | 7.54178i | −0.165884 | + | 0.287319i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7915 | − | 20.4235i | −0.448570 | − | 0.776946i | 0.549723 | − | 0.835347i | \(-0.314733\pi\) |
−0.998293 | + | 0.0584009i | \(0.981400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.9373 | −1.31956 | −0.659781 | − | 0.751458i | \(-0.729351\pi\) | ||||
−0.659781 | + | 0.751458i | \(0.729351\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.67712 | + | 4.63692i | −0.100970 | + | 0.174885i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.06275 | 0.264502 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.35425 | 0.162840 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.82288 | − | 6.62141i | 0.141978 | − | 0.245913i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.8118 | −1.25401 | −0.627004 | − | 0.779016i | \(-0.715719\pi\) | ||||
−0.627004 | + | 0.779016i | \(0.715719\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 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 | \(0.345749\pi\) |
−0.999239 | + | 0.0389959i | \(0.987584\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 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 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −22.4059 | + | 38.8081i | −0.818693 | + | 1.41802i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.0830 | − | 20.9284i | −0.440915 | − | 0.763687i | 0.556843 | − | 0.830618i | \(-0.312013\pi\) |
−0.997758 | + | 0.0669307i | \(0.978679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.05163 | − | 10.4817i | −0.219371 | − | 0.379963i | 0.735244 | − | 0.677802i | \(-0.237067\pi\) |
−0.954616 | + | 0.297839i | \(0.903734\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.3948 | −1.24517 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.6974 | − | 23.7246i | 0.492661 | − | 0.853313i | −0.507304 | − | 0.861767i | \(-0.669358\pi\) |
0.999964 | + | 0.00845413i | \(0.00269106\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.14575 | + | 3.71655i | 0.0770777 | + | 0.133502i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.29150 | 0.0460957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.93725 | + | 5.08747i | −0.104702 | + | 0.181349i | −0.913616 | − | 0.406577i | \(-0.866722\pi\) |
0.808915 | + | 0.587926i | \(0.200055\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.93725 | −0.174887 | −0.0874433 | − | 0.996170i | \(-0.527870\pi\) | ||||
−0.0874433 | + | 0.996170i | \(0.527870\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.87451 | −0.349335 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.8856 | − | 18.8544i | −0.384145 | − | 0.665359i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.35425 | 0.153467 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.58301 | − | 16.5983i | 0.336921 | − | 0.583563i | −0.646931 | − | 0.762548i | \(-0.723948\pi\) |
0.983852 | + | 0.178985i | \(0.0572813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.2915 | 0.607187 | 0.303593 | − | 0.952802i | \(-0.401814\pi\) | ||||
0.303593 | + | 0.952802i | \(0.401814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.9889 | − | 45.0141i | −0.907018 | − | 1.57100i | −0.818185 | − | 0.574955i | \(-0.805019\pi\) |
−0.0888337 | − | 0.996046i | \(-0.528314\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.22876 | + | 15.9847i | −0.321694 | + | 0.557191i | −0.980838 | − | 0.194826i | \(-0.937586\pi\) |
0.659144 | + | 0.752017i | \(0.270919\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 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 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 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 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 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 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.82288 | + | 11.8176i | −0.233065 | + | 0.403680i | −0.958709 | − | 0.284390i | \(-0.908209\pi\) |
0.725644 | + | 0.688071i | \(0.241542\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.2288 | + | 22.9129i | 0.451359 | + | 0.781777i | 0.998471 | − | 0.0552825i | \(-0.0176059\pi\) |
−0.547111 | + | 0.837060i | \(0.684273\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 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 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.77124 | 0.127931 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.854249 | − | 1.47960i | 0.0289451 | − | 0.0501344i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 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 | \(-0.506253\pi\) | ||||
−0.0196419 | + | 0.999807i | \(0.506253\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.8118 | −0.734024 | −0.367012 | − | 0.930216i | \(-0.619619\pi\) | ||||
−0.367012 | + | 0.930216i | \(0.619619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 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 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.8745 | − | 43.0839i | 0.832394 | − | 1.44175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.583005 | 0.0194877 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.14575 | − | 3.71655i | −0.0713272 | − | 0.123542i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.3229 | − | 17.8797i | 0.342765 | − | 0.593687i | −0.642180 | − | 0.766554i | \(-0.721970\pi\) |
0.984945 | + | 0.172867i | \(0.0553031\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 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 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.1660 | − | 48.7850i | 0.930124 | − | 1.61102i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.20850 | − | 9.02138i | −0.171812 | − | 0.297588i | 0.767241 | − | 0.641359i | \(-0.221629\pi\) |
−0.939054 | + | 0.343771i | \(0.888296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.1033 | 1.18835 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.645751 | 0.0212322 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.7601 | + | 30.7614i | 0.582691 | + | 1.00925i | 0.995159 | + | 0.0982783i | \(0.0313335\pi\) |
−0.412468 | + | 0.910972i | \(0.635333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 58.0405 | 1.90220 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 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 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.46863 | + | 9.47194i | −0.178272 | + | 0.308776i | −0.941289 | − | 0.337602i | \(-0.890384\pi\) |
0.763017 | + | 0.646379i | \(0.223717\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.06275 | − | 7.03688i | −0.132301 | − | 0.229152i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 52.4575 | 1.69927 | 0.849633 | − | 0.527375i | \(-0.176824\pi\) | ||||
0.849633 | + | 0.527375i | \(0.176824\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.58301 | + | 16.5983i | −0.310099 | + | 0.537107i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.5203 | 1.72826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.29150 | + | 10.8972i | 0.202952 | + | 0.351523i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.06275 | 0.259549 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.3948 | −0.913114 | −0.456557 | − | 0.889694i | \(-0.650918\pi\) | ||||
−0.456557 | + | 0.889694i | \(0.650918\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.5314 | + | 21.7050i | −0.400914 | + | 0.694404i | −0.993836 | − | 0.110856i | \(-0.964641\pi\) |
0.592922 | + | 0.805260i | \(0.297974\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.4170 | 0.748410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 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 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | \(0.415040\pi\) |
−0.967236 | + | 0.253878i | \(0.918294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 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 | 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 | 1260.2.s.f.361.1 | 4 | ||
3.2 | odd | 2 | 420.2.q.c.361.1 | yes | 4 | ||
7.2 | even | 3 | inner | 1260.2.s.f.541.1 | 4 | ||
7.3 | odd | 6 | 8820.2.a.bj.1.2 | 2 | |||
7.4 | even | 3 | 8820.2.a.be.1.2 | 2 | |||
12.11 | even | 2 | 1680.2.bg.q.1201.2 | 4 | |||
15.2 | even | 4 | 2100.2.bc.e.949.4 | 8 | |||
15.8 | even | 4 | 2100.2.bc.e.949.1 | 8 | |||
15.14 | odd | 2 | 2100.2.q.h.1201.2 | 4 | |||
21.2 | odd | 6 | 420.2.q.c.121.1 | ✓ | 4 | ||
21.5 | even | 6 | 2940.2.q.t.961.2 | 4 | |||
21.11 | odd | 6 | 2940.2.a.s.1.1 | 2 | |||
21.17 | even | 6 | 2940.2.a.m.1.1 | 2 | |||
21.20 | even | 2 | 2940.2.q.t.361.2 | 4 | |||
84.23 | even | 6 | 1680.2.bg.q.961.2 | 4 | |||
105.2 | even | 12 | 2100.2.bc.e.1549.1 | 8 | |||
105.23 | even | 12 | 2100.2.bc.e.1549.4 | 8 | |||
105.44 | odd | 6 | 2100.2.q.h.1801.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.c.121.1 | ✓ | 4 | 21.2 | odd | 6 | ||
420.2.q.c.361.1 | yes | 4 | 3.2 | odd | 2 | ||
1260.2.s.f.361.1 | 4 | 1.1 | even | 1 | trivial | ||
1260.2.s.f.541.1 | 4 | 7.2 | even | 3 | inner | ||
1680.2.bg.q.961.2 | 4 | 84.23 | even | 6 | |||
1680.2.bg.q.1201.2 | 4 | 12.11 | even | 2 | |||
2100.2.q.h.1201.2 | 4 | 15.14 | odd | 2 | |||
2100.2.q.h.1801.2 | 4 | 105.44 | odd | 6 | |||
2100.2.bc.e.949.1 | 8 | 15.8 | even | 4 | |||
2100.2.bc.e.949.4 | 8 | 15.2 | even | 4 | |||
2100.2.bc.e.1549.1 | 8 | 105.2 | even | 12 | |||
2100.2.bc.e.1549.4 | 8 | 105.23 | even | 12 | |||
2940.2.a.m.1.1 | 2 | 21.17 | even | 6 | |||
2940.2.a.s.1.1 | 2 | 21.11 | odd | 6 | |||
2940.2.q.t.361.2 | 4 | 21.20 | even | 2 | |||
2940.2.q.t.961.2 | 4 | 21.5 | even | 6 | |||
8820.2.a.be.1.2 | 2 | 7.4 | even | 3 | |||
8820.2.a.bj.1.2 | 2 | 7.3 | odd | 6 |