Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(949,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.949");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bc (of order \(6\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1549.4 | ||
Root | \(0.228425 - 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1549 |
Dual form | 2100.2.bc.e.949.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.29129 | + | 1.32288i | 0.866025 | + | 0.500000i | ||||
\(8\) | 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 | \(-0.0868584\pi\) |
−0.714894 | + | 0.699233i | \(0.753525\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.64575i | − | 0.733799i | −0.930261 | − | 0.366900i | \(-0.880419\pi\) | ||
0.930261 | − | 0.366900i | \(-0.119581\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.42526 | − | 0.822876i | 0.345677 | − | 0.199577i | −0.317103 | − | 0.948391i | \(-0.602710\pi\) |
0.662780 | + | 0.748815i | \(0.269377\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.14575 | − | 7.18065i | 0.951101 | − | 1.64735i | 0.208051 | − | 0.978118i | \(-0.433288\pi\) |
0.743049 | − | 0.669237i | \(-0.233379\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.64575 | 0.577350 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.42526 | − | 0.822876i | −0.297188 | − | 0.171581i | 0.343991 | − | 0.938973i | \(-0.388221\pi\) |
−0.641179 | + | 0.767391i | \(0.721554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 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 | 0.991823 | − | 0.127621i | \(-0.0407342\pi\) |
−0.606435 | + | 0.795133i | \(0.707401\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.42526 | + | 0.822876i | 0.248106 | + | 0.143244i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.559237 | + | 0.322876i | 0.0919380 | + | 0.0530804i | 0.545264 | − | 0.838264i | \(-0.316429\pi\) |
−0.453326 | + | 0.891345i | \(0.649763\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | − | 5.93725i | − | 0.905423i | −0.891657 | − | 0.452711i | \(-0.850457\pi\) | ||
0.891657 | − | 0.452711i | \(-0.149543\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.19615 | + | 3.00000i | 0.757937 | + | 0.437595i | 0.828554 | − | 0.559908i | \(-0.189164\pi\) |
−0.0706177 | + | 0.997503i | \(0.522497\pi\) | |||||||
\(48\) | 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 | ||||||||
\(53\) | 2.85052 | − | 1.64575i | 0.391550 | − | 0.226061i | −0.291282 | − | 0.956637i | \(-0.594082\pi\) |
0.682831 | + | 0.730576i | \(0.260748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.29150i | − | 1.09824i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.46863 | + | 9.47194i | 0.711955 | + | 1.23314i | 0.964122 | + | 0.265458i | \(0.0855232\pi\) |
−0.252168 | + | 0.967684i | \(0.581144\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.29129 | − | 1.32288i | 0.288675 | − | 0.166667i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.559237 | + | 0.322876i | −0.0683217 | + | 0.0394455i | −0.533772 | − | 0.845629i | \(-0.679226\pi\) |
0.465450 | + | 0.885074i | \(0.345892\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.64575 | −0.198125 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6458 | 1.61945 | 0.809726 | − | 0.586808i | \(-0.199616\pi\) | ||||
0.809726 | + | 0.586808i | \(0.199616\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4564 | − | 6.61438i | 1.34087 | − | 0.774154i | 0.353939 | − | 0.935269i | \(-0.384842\pi\) |
0.986936 | + | 0.161114i | \(0.0515087\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.35425i | 0.496213i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.14575 | − | 1.98450i | 0.128907 | − | 0.223274i | −0.794346 | − | 0.607465i | \(-0.792186\pi\) |
0.923253 | + | 0.384192i | \(0.125520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 10.9373i | − | 1.20052i | −0.799805 | − | 0.600260i | \(-0.795064\pi\) | ||
0.799805 | − | 0.600260i | \(-0.204936\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.62141 | + | 3.82288i | −0.709890 | + | 0.409855i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.11438 | + | 12.3225i | −0.754123 | + | 1.30618i | 0.191687 | + | 0.981456i | \(0.438604\pi\) |
−0.945809 | + | 0.324722i | \(0.894729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.50000 | − | 6.06218i | 0.366900 | − | 0.635489i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.71655 | + | 2.14575i | 0.385388 | + | 0.222504i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.00000i | − | 0.812277i | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||
0.913812 | − | 0.406138i | \(-0.133125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.64575 | 0.165404 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.46863 | + | 4.27579i | 0.245638 | + | 0.425457i | 0.962311 | − | 0.271953i | \(-0.0876694\pi\) |
−0.716673 | + | 0.697409i | \(0.754336\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.10102 | − | 4.67712i | −0.798217 | − | 0.460851i | 0.0446304 | − | 0.999004i | \(-0.485789\pi\) |
−0.842847 | + | 0.538153i | \(0.819122\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.6681 | − | 8.46863i | −1.41802 | − | 0.818693i | −0.421893 | − | 0.906645i | \(-0.638634\pi\) |
−0.996125 | + | 0.0879524i | \(0.971968\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.50000 | − | 11.2583i | −0.622587 | − | 1.07835i | −0.989002 | − | 0.147901i | \(-0.952748\pi\) |
0.366415 | − | 0.930451i | \(-0.380585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.645751 | 0.0612920 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.29129 | − | 1.32288i | −0.211830 | − | 0.122300i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.35425 | 0.399153 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.14575 | − | 7.18065i | 0.376886 | − | 0.652787i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.27579 | − | 2.46863i | 0.385535 | − | 0.222589i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.06275i | 0.183039i | 0.995803 | + | 0.0915196i | \(0.0291724\pi\) | ||||
−0.995803 | + | 0.0915196i | \(0.970828\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.96863 | − | 5.14181i | −0.261373 | − | 0.452711i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.6458 | + | 18.4390i | −0.930124 | + | 1.61102i | −0.147017 | + | 0.989134i | \(0.546967\pi\) |
−0.783107 | + | 0.621887i | \(0.786366\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.9982 | − | 10.9686i | 1.64735 | − | 0.951101i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.5186 | − | 10.1144i | 1.49672 | − | 0.864130i | 0.496724 | − | 0.867909i | \(-0.334536\pi\) |
0.999993 | + | 0.00377913i | \(0.00120294\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | 3.77089 | − | 2.17712i | 0.315338 | − | 0.182060i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.06218 | + | 3.50000i | 0.500000 | + | 0.288675i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.29150 | + | 5.70105i | −0.269650 | + | 0.467048i | −0.968772 | − | 0.247955i | \(-0.920241\pi\) |
0.699121 | + | 0.715003i | \(0.253575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.29150 | + | 3.96900i | 0.186480 | + | 0.322993i | 0.944074 | − | 0.329733i | \(-0.106959\pi\) |
−0.757594 | + | 0.652726i | \(0.773625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.64575i | − | 0.133051i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.11847 | − | 0.645751i | 0.0892639 | − | 0.0515366i | −0.454704 | − | 0.890643i | \(-0.650255\pi\) |
0.543968 | + | 0.839106i | \(0.316921\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | 13.8564 | + | 8.00000i | 1.08532 | + | 0.626608i | 0.932326 | − | 0.361619i | \(-0.117776\pi\) |
0.152992 | + | 0.988227i | \(0.451109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 19.6458i | − | 1.52023i | −0.649786 | − | 0.760117i | \(-0.725142\pi\) | ||
0.649786 | − | 0.760117i | \(-0.274858\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | 0.461538 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.14575 | − | 7.18065i | −0.317034 | − | 0.549118i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.55157 | − | 4.93725i | −0.650164 | − | 0.375372i | 0.138355 | − | 0.990383i | \(-0.455819\pi\) |
−0.788519 | + | 0.615010i | \(0.789152\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.47194 | + | 5.46863i | 0.711955 | + | 0.411047i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.291503 | + | 0.504897i | 0.0217879 | + | 0.0377378i | 0.876714 | − | 0.481012i | \(-0.159731\pi\) |
−0.854926 | + | 0.518750i | \(0.826397\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29150 | −0.318985 | −0.159492 | − | 0.987199i | \(-0.550986\pi\) | ||||
−0.159492 | + | 0.987199i | \(0.550986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.34563 | + | 1.35425i | 0.171529 | + | 0.0990325i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.32288 | − | 2.29129i | 0.0962250 | − | 0.166667i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.58301 | + | 16.5983i | −0.693402 | + | 1.20101i | 0.277315 | + | 0.960779i | \(0.410556\pi\) |
−0.970716 | + | 0.240228i | \(0.922778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.98254 | + | 4.03137i | −0.502614 | + | 0.290185i | −0.729793 | − | 0.683669i | \(-0.760383\pi\) |
0.227178 | + | 0.973853i | \(0.427050\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.93725i | 0.351765i | 0.984411 | + | 0.175882i | \(0.0562778\pi\) | ||||
−0.984411 | + | 0.175882i | \(0.943722\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5830 | − | 20.0624i | −0.821097 | − | 1.42218i | −0.904866 | − | 0.425697i | \(-0.860029\pi\) |
0.0837682 | − | 0.996485i | \(-0.473304\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.322876 | + | 0.559237i | −0.0227739 | + | 0.0394455i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.5186 | − | 10.1144i | −1.22957 | − | 0.709890i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.42526 | + | 0.822876i | −0.0990626 | + | 0.0571938i | ||||
\(208\) | 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 | ||||||||
\(213\) | 11.8176 | − | 6.82288i | 0.809726 | − | 0.467496i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3542i | 0.770777i | ||||||||
\(218\) | 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 | ||||||||
\(223\) | 17.8745i | 1.19697i | 0.801136 | + | 0.598483i | \(0.204230\pi\) | ||||
−0.801136 | + | 0.598483i | \(0.795770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −17.0137 | + | 9.82288i | −1.12924 | + | 0.651967i | −0.943744 | − | 0.330678i | \(-0.892723\pi\) |
−0.185497 | + | 0.982645i | \(0.559389\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.50000 | + | 6.06218i | −0.231287 | + | 0.400600i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.17712 | + | 3.77089i | 0.143244 | + | 0.248106i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.4390 | − | 10.6458i | −1.20798 | − | 0.697426i | −0.245661 | − | 0.969356i | \(-0.579005\pi\) |
−0.962317 | + | 0.271930i | \(0.912338\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 2.29150i | − | 0.148849i | ||||||
\(238\) | 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 | 0.994813 | − | 0.101721i | \(-0.0324350\pi\) |
−0.585500 | + | 0.810673i | \(0.699102\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.9982 | − | 10.9686i | −1.20883 | − | 0.697917i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.46863 | − | 9.47194i | −0.346560 | − | 0.600260i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.9373 | −0.690353 | −0.345177 | − | 0.938538i | \(-0.612181\pi\) | ||||
−0.345177 | + | 0.938538i | \(0.612181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.70850i | − | 0.170282i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.78068 | + | 2.76013i | 0.298211 | + | 0.172172i | 0.641639 | − | 0.767007i | \(-0.278255\pi\) |
−0.343428 | + | 0.939179i | \(0.611588\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | −24.6449 | + | 14.2288i | −1.51967 | + | 0.877383i | −0.519940 | + | 0.854203i | \(0.674046\pi\) |
−0.999731 | + | 0.0231800i | \(0.992621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.2288i | 0.870786i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.9373 | + | 24.1400i | 0.849769 | + | 1.47184i | 0.881414 | + | 0.472345i | \(0.156592\pi\) |
−0.0316446 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.70850 | + | 6.42331i | −0.225275 | + | 0.390188i | −0.956402 | − | 0.292054i | \(-0.905661\pi\) |
0.731127 | + | 0.682242i | \(0.238995\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 7.00000i | − | 0.423659i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.8797 | − | 10.3229i | 1.07429 | − | 0.620241i | 0.144939 | − | 0.989441i | \(-0.453701\pi\) |
0.929350 | + | 0.369199i | \(0.120368\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −12.6836 | + | 7.32288i | −0.753961 | + | 0.435300i | −0.827123 | − | 0.562020i | \(-0.810024\pi\) |
0.0731621 | + | 0.997320i | \(0.476691\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3127 | + | 6.53137i | 0.667766 | + | 0.385535i | ||||
\(288\) | 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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.42526 | − | 0.822876i | 0.0827021 | − | 0.0477481i | ||||
\(298\) | 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 | ||||||||
\(303\) | 4.27579 | + | 2.46863i | 0.245638 | + | 0.141819i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 27.9373i | − | 1.59446i | −0.603674 | − | 0.797232i | \(-0.706297\pi\) | ||
0.603674 | − | 0.797232i | \(-0.293703\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.35425 | −0.532145 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.82288 | − | 11.8176i | −0.386890 | − | 0.670113i | 0.605140 | − | 0.796119i | \(-0.293117\pi\) |
−0.992029 | + | 0.126007i | \(0.959784\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.3846 | + | 10.6144i | 1.03916 | + | 0.599960i | 0.919596 | − | 0.392866i | \(-0.128516\pi\) |
0.119566 | + | 0.992826i | \(0.461850\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.3691 | + | 11.7601i | 1.14404 | + | 0.660515i | 0.947429 | − | 0.319966i | \(-0.103671\pi\) |
0.196616 | + | 0.980481i | \(0.437005\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.29150 | − | 10.8972i | −0.352257 | − | 0.610126i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.9373 | −0.945345 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 13.6458i | − | 0.759270i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.2583 | − | 6.50000i | −0.622587 | − | 0.359451i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.93725 | + | 13.7477i | 0.437595 | + | 0.757937i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0830 | − | 17.4643i | 0.554212 | − | 0.959923i | −0.443752 | − | 0.896149i | \(-0.646353\pi\) |
0.997964 | − | 0.0637740i | \(-0.0203137\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.559237 | − | 0.322876i | 0.0306460 | − | 0.0176935i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.2288i | 1.81009i | 0.425320 | + | 0.905043i | \(0.360161\pi\) | ||||
−0.425320 | + | 0.905043i | \(0.639839\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | 18.5203i | 1.00000i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.4021 | + | 6.58301i | −0.612097 | + | 0.353394i | −0.773786 | − | 0.633448i | \(-0.781639\pi\) |
0.161689 | + | 0.986842i | \(0.448306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.64575 | −0.141220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −31.2663 | + | 18.0516i | −1.66414 | + | 0.960791i | −0.693434 | + | 0.720520i | \(0.743903\pi\) |
−0.970706 | + | 0.240271i | \(0.922764\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.77089 | − | 2.17712i | 0.199577 | − | 0.115226i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4059 | + | 18.0235i | −0.549201 | + | 0.951245i | 0.449128 | + | 0.893467i | \(0.351735\pi\) |
−0.998329 | + | 0.0577773i | \(0.981599\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −24.8745 | − | 43.0839i | −1.30918 | − | 2.26757i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 8.29150i | − | 0.435191i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.26029 | + | 3.61438i | −0.326784 | + | 0.188669i | −0.654413 | − | 0.756138i | \(-0.727084\pi\) |
0.327628 | + | 0.944807i | \(0.393751\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.46863 | − | 4.27579i | 0.128512 | − | 0.222589i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.70850 | 0.452123 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.0543397 | − | 0.0313730i | −0.00281360 | − | 0.00162443i | 0.498593 | − | 0.866836i | \(-0.333850\pi\) |
−0.501406 | + | 0.865212i | \(0.667184\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.2288i | 1.04183i | ||||||||
\(378\) | 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 | ||||||||
\(383\) | 23.6351 | + | 13.6458i | 1.20770 | + | 0.697265i | 0.962256 | − | 0.272146i | \(-0.0877333\pi\) |
0.245443 | + | 0.969411i | \(0.421067\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.14181 | − | 2.96863i | −0.261373 | − | 0.150904i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.239870 | − | 0.415468i | −0.0121619 | − | 0.0210651i | 0.859880 | − | 0.510496i | \(-0.170538\pi\) |
−0.872042 | + | 0.489430i | \(0.837205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.70850 | −0.136975 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.2915i | 1.07401i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.83307 | − | 5.67712i | −0.493508 | − | 0.284927i | 0.232521 | − | 0.972591i | \(-0.425303\pi\) |
−0.726028 | + | 0.687665i | \(0.758636\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.9686 | − | 18.9982i | 0.549118 | − | 0.951101i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.35425 | + | 7.54178i | −0.217441 | + | 0.376619i | −0.954025 | − | 0.299727i | \(-0.903104\pi\) |
0.736584 | + | 0.676346i | \(0.236438\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.83307 | − | 5.67712i | 0.489820 | − | 0.282798i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.06275i | 0.0526784i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.08301 | + | 5.33992i | 0.152445 | + | 0.264042i | 0.932126 | − | 0.362135i | \(-0.117952\pi\) |
−0.779681 | + | 0.626177i | \(0.784619\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.1144 | − | 17.5186i | 0.498905 | − | 0.864130i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.9373i | 1.42391i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.33013 | + | 2.50000i | −0.212047 | + | 0.122426i | ||||
\(418\) | 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 | ||||||||
\(423\) | 5.19615 | − | 3.00000i | 0.252646 | − | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.3303 | + | 10.5830i | −0.887066 | + | 0.512148i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.17712 | − | 3.77089i | 0.105113 | − | 0.182060i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.9373 | − | 34.5323i | −0.960344 | − | 1.66336i | −0.721636 | − | 0.692273i | \(-0.756610\pi\) |
−0.238708 | − | 0.971091i | \(-0.576724\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.35425i | 0.161195i | 0.996747 | + | 0.0805975i | \(0.0256828\pi\) | ||||
−0.996747 | + | 0.0805975i | \(0.974317\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.8176 | + | 6.82288i | −0.565311 | + | 0.326382i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.64575 | − | 4.58258i | 0.126275 | − | 0.218714i | −0.795956 | − | 0.605355i | \(-0.793031\pi\) |
0.922231 | + | 0.386640i | \(0.126365\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.00000 | 0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.55157 | − | 4.93725i | −0.406298 | − | 0.234576i | 0.282900 | − | 0.959149i | \(-0.408704\pi\) |
−0.689198 | + | 0.724573i | \(0.742037\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.58301i | 0.311365i | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 3.96900 | + | 2.29150i | 0.186480 | + | 0.107664i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.6836 | − | 7.32288i | −0.593313 | − | 0.342550i | 0.173093 | − | 0.984905i | \(-0.444624\pi\) |
−0.766407 | + | 0.642356i | \(0.777957\pi\) | |||||||
\(458\) | 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 | ||||||||
\(463\) | 10.5203i | 0.488918i | 0.969660 | + | 0.244459i | \(0.0786103\pi\) | ||||
−0.969660 | + | 0.244459i | \(0.921390\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.6916 | − | 18.8745i | −1.51279 | − | 0.873408i | −0.999888 | − | 0.0149591i | \(-0.995238\pi\) |
−0.512899 | − | 0.858449i | \(-0.671428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.70850 | −0.0788911 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.645751 | − | 1.11847i | 0.0297546 | − | 0.0515366i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.46215 | − | 4.88562i | 0.389090 | − | 0.224641i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.29150i | − | 0.150708i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.29150 | − | 5.70105i | −0.150393 | − | 0.260488i | 0.780979 | − | 0.624557i | \(-0.214720\pi\) |
−0.931372 | + | 0.364069i | \(0.881387\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.854249 | − | 1.47960i | 0.0389504 | − | 0.0674641i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.77089 | − | 2.17712i | −0.171581 | − | 0.0990626i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.29129 | − | 1.32288i | 0.103828 | − | 0.0599452i | −0.447187 | − | 0.894441i | \(-0.647574\pi\) |
0.551015 | + | 0.834495i | \(0.314241\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.0000 | 0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.12549 | 0.0959221 | 0.0479611 | − | 0.998849i | \(-0.484728\pi\) | ||||
0.0479611 | + | 0.998849i | \(0.484728\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.8972 | + | 6.29150i | −0.490785 | + | 0.283355i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.2663 | + | 18.0516i | 1.40249 | + | 0.809726i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7288 | − | 23.7789i | 0.614584 | − | 1.06449i | −0.375874 | − | 0.926671i | \(-0.622657\pi\) |
0.990457 | − | 0.137819i | \(-0.0440093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.82288 | − | 17.0137i | −0.438854 | − | 0.760117i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.4575i | 1.00133i | 0.865641 | + | 0.500666i | \(0.166911\pi\) | ||||
−0.865641 | + | 0.500666i | \(0.833089\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.19615 | − | 3.00000i | 0.230769 | − | 0.133235i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.9373 | + | 24.1400i | −0.617758 | + | 1.06999i | 0.372136 | + | 0.928178i | \(0.378626\pi\) |
−0.989894 | + | 0.141810i | \(0.954708\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 35.0000 | 1.54831 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.18065 | − | 4.14575i | −0.317034 | − | 0.183039i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.87451i | 0.434280i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.87451 | −0.433443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.06275 | + | 1.84073i | 0.0465598 | + | 0.0806439i | 0.888366 | − | 0.459136i | \(-0.151841\pi\) |
−0.841806 | + | 0.539780i | \(0.818508\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.0449 | − | 15.6144i | −1.18259 | − | 0.682769i | −0.225978 | − | 0.974132i | \(-0.572558\pi\) |
−0.956612 | + | 0.291363i | \(0.905891\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.11652 | + | 3.53137i | 0.266440 | + | 0.153829i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.1458 | − | 17.5730i | −0.441120 | − | 0.764042i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.9373 | 0.474636 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 13.0627i | − | 0.565810i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.504897 | + | 0.291503i | 0.0217879 | + | 0.0125793i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.76013 | + | 9.97684i | −0.248106 | + | 0.429733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.3745 | + | 31.8256i | −0.789982 | + | 1.36829i | 0.135996 | + | 0.990709i | \(0.456577\pi\) |
−0.925977 | + | 0.377579i | \(0.876757\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.71655 | + | 2.14575i | −0.159492 | + | 0.0920830i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.2915i | 1.85101i | 0.378734 | + | 0.925505i | \(0.376359\pi\) | ||||
−0.378734 | + | 0.925505i | \(0.623641\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 5.25049 | − | 3.03137i | 0.223274 | − | 0.128907i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.5885 | − | 9.00000i | 0.660504 | − | 0.381342i | −0.131965 | − | 0.991254i | \(-0.542129\pi\) |
0.792469 | + | 0.609912i | \(0.208795\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.7085 | −0.664399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.70850 | 0.114353 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −31.6818 | + | 18.2915i | −1.33523 | + | 0.770895i | −0.986096 | − | 0.166178i | \(-0.946857\pi\) |
−0.349133 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.64575i | − | 0.111111i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.88562 | + | 3.26599i | −0.0790494 | + | 0.136918i | −0.902840 | − | 0.429977i | \(-0.858522\pi\) |
0.823791 | + | 0.566894i | \(0.191855\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.1458 | − | 38.3576i | −0.926771 | − | 1.60521i | −0.788688 | − | 0.614793i | \(-0.789239\pi\) |
−0.138083 | − | 0.990421i | \(-0.544094\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.1660i | 0.800672i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.8236 | − | 21.2601i | 1.53299 | − | 0.885071i | 0.533766 | − | 0.845633i | \(-0.320776\pi\) |
0.999222 | − | 0.0394383i | \(-0.0125568\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | 4.69126 | + | 2.70850i | 0.194292 | + | 0.112174i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 16.9373i | − | 0.699075i | −0.936922 | − | 0.349538i | \(-0.886339\pi\) | ||
0.936922 | − | 0.349538i | \(-0.113661\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.5830 | 1.46617 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.46863 | + | 4.27579i | 0.101546 | + | 0.175882i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.7050 | + | 12.5314i | 0.891316 | + | 0.514602i | 0.874373 | − | 0.485255i | \(-0.161273\pi\) |
0.0169436 | + | 0.999856i | \(0.494606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.0624 | − | 11.5830i | −0.821097 | − | 0.474061i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.06275 | + | 1.84073i | 0.0434226 | + | 0.0752102i | 0.886920 | − | 0.461923i | \(-0.152840\pi\) |
−0.843497 | + | 0.537133i | \(0.819507\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.5830 | −1.53304 | −0.766521 | − | 0.642219i | \(-0.778014\pi\) | ||||
−0.766521 | + | 0.642219i | \(0.778014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.645751i | 0.0262970i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.5243 | − | 8.38562i | −0.589524 | − | 0.340362i | 0.175385 | − | 0.984500i | \(-0.443883\pi\) |
−0.764909 | + | 0.644138i | \(0.777216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.2288 | −0.819711 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.93725 | − | 13.7477i | 0.321107 | − | 0.556174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.6508 | + | 20.5830i | −1.43992 | + | 0.831340i | −0.997844 | − | 0.0656363i | \(-0.979092\pi\) |
−0.442079 | + | 0.896976i | \(0.645759\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.29150i | − | 0.374062i | −0.982354 | − | 0.187031i | \(-0.940114\pi\) | ||
0.982354 | − | 0.187031i | \(-0.0598865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | − | 16.4545i | −0.381837 | − | 0.661361i | 0.609488 | − | 0.792796i | \(-0.291375\pi\) |
−0.991325 | + | 0.131434i | \(0.958042\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.822876 | + | 1.42526i | −0.0330209 | + | 0.0571938i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.6022 | + | 18.8229i | −1.30618 | + | 0.754123i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.8176 | − | 6.82288i | 0.471948 | − | 0.272479i | ||||
\(628\) | 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 | ||||||||
\(633\) | 7.43310 | − | 4.29150i | 0.295439 | − | 0.170572i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.0390 | − | 9.26013i | 0.635489 | − | 0.366900i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.82288 | − | 11.8176i | 0.269909 | − | 0.467496i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.05163 | + | 10.4817i | 0.239025 | + | 0.414004i | 0.960435 | − | 0.278505i | \(-0.0898388\pi\) |
−0.721410 | + | 0.692509i | \(0.756506\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 21.8118i | − | 0.860172i | −0.902788 | − | 0.430086i | \(-0.858483\pi\) | ||
0.902788 | − | 0.430086i | \(-0.141517\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.8642 | + | 11.4686i | −0.780944 | + | 0.450878i | −0.836765 | − | 0.547563i | \(-0.815556\pi\) |
0.0558207 | + | 0.998441i | \(0.482222\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | −24.5555 | − | 14.1771i | −0.960931 | − | 0.554794i | −0.0644715 | − | 0.997920i | \(-0.520536\pi\) |
−0.896459 | + | 0.443126i | \(0.853869\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 13.2288i | − | 0.516103i | ||||||
\(658\) | 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 | 0.922892 | + | 0.385059i | \(0.125819\pi\) |
−0.127975 | + | 0.991777i | \(0.540848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.77089 | − | 2.17712i | −0.146449 | − | 0.0845525i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.8972 | + | 6.29150i | 0.421941 | + | 0.243608i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.93725 | + | 15.4798i | 0.345534 | + | 0.598483i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.1660 | −0.508268 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.35425i | − | 0.206391i | −0.994661 | − | 0.103196i | \(-0.967093\pi\) | ||
0.994661 | − | 0.103196i | \(-0.0329067\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.3593 | − | 11.1771i | −0.744040 | − | 0.429572i | 0.0794963 | − | 0.996835i | \(-0.474669\pi\) |
−0.823536 | + | 0.567263i | \(0.808002\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | 4.27579 | − | 2.46863i | 0.163608 | − | 0.0944594i | −0.415960 | − | 0.909383i | \(-0.636554\pi\) |
0.579569 | + | 0.814923i | \(0.303221\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.00000i | 0.267067i | ||||||||
\(688\) | 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 | \(-0.981400\pi\) |
0.549723 | + | 0.835347i | \(0.314733\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.77089 | + | 2.17712i | 0.143244 | + | 0.0827021i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.03688 | − | 4.06275i | 0.266541 | − | 0.153887i | ||||
\(698\) | 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 | ||||||||
\(703\) | 4.63692 | − | 2.67712i | 0.174885 | − | 0.100970i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0627i | 0.491275i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.2915 | + | 19.5575i | −0.424061 | + | 0.734496i | −0.996332 | − | 0.0855689i | \(-0.972729\pi\) |
0.572271 | + | 0.820065i | \(0.306063\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.14575 | − | 1.98450i | −0.0429690 | − | 0.0744245i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 7.06275i | − | 0.264502i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.19615 | + | 3.00000i | −0.194054 | + | 0.112037i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.35425 | + | 12.7379i | −0.274267 | + | 0.475045i | −0.969950 | − | 0.243304i | \(-0.921769\pi\) |
0.695683 | + | 0.718349i | \(0.255102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.3745 | − | 21.4333i | −0.460851 | − | 0.798217i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.0059 | + | 6.35425i | 0.409313 | + | 0.236317i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.8118i | 1.25401i | 0.779016 | + | 0.627004i | \(0.215719\pi\) | ||||
−0.779016 | + | 0.627004i | \(0.784281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.88562 | − | 8.46215i | −0.180701 | − | 0.312984i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.26029 | − | 3.61438i | −0.231229 | − | 0.133500i | 0.379910 | − | 0.925023i | \(-0.375955\pi\) |
−0.611139 | + | 0.791523i | \(0.709288\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.920365 | − | 0.531373i | −0.0339021 | − | 0.0195734i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.5000 | + | 25.1147i | 0.533391 | + | 0.923861i | 0.999239 | + | 0.0389959i | \(0.0124159\pi\) |
−0.465848 | + | 0.884865i | \(0.654251\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.9373 | −0.805885 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 13.0627i | − | 0.479226i | −0.970869 | − | 0.239613i | \(-0.922979\pi\) | ||
0.970869 | − | 0.239613i | \(-0.0770205\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.47194 | − | 5.46863i | −0.346560 | − | 0.200087i | ||||
\(748\) | 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 | \(-0.978679\pi\) |
0.556843 | + | 0.830618i | \(0.312013\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.47194 | + | 5.46863i | −0.345177 | + | 0.199288i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.83399i | 0.321077i | 0.987030 | + | 0.160538i | \(0.0513230\pi\) | ||||
−0.987030 | + | 0.160538i | \(0.948677\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.35425 | − | 2.34563i | −0.0491561 | − | 0.0851409i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.05163 | − | 10.4817i | 0.219371 | − | 0.379963i | −0.735244 | − | 0.677802i | \(-0.762933\pi\) |
0.954616 | + | 0.297839i | \(0.0962660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 34.3948i | − | 1.24517i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.0604 | − | 14.4686i | 0.904878 | − | 0.522432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.70850 | 0.133732 | 0.0668659 | − | 0.997762i | \(-0.478700\pi\) | ||||
0.0668659 | + | 0.997762i | \(0.478700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.52026 | 0.198807 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.7246 | − | 13.6974i | 0.853313 | − | 0.492661i | −0.00845413 | − | 0.999964i | \(-0.502691\pi\) |
0.861767 | + | 0.507304i | \(0.169358\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.47960 | + | 0.854249i | 0.0530804 | + | 0.0306460i | ||||
\(778\) | 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 | ||||||||
\(783\) | 7.64575i | 0.273237i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.08747 | + | 2.93725i | −0.181349 | + | 0.104702i | −0.587926 | − | 0.808915i | \(-0.700055\pi\) |
0.406577 | + | 0.913616i | \(0.366722\pi\) | |||||||
\(788\) | 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 | ||||||||
\(793\) | 18.3303 | + | 10.5830i | 0.650928 | + | 0.375814i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.93725i | − | 0.174887i | −0.996170 | − | 0.0874433i | \(-0.972130\pi\) | ||
0.996170 | − | 0.0874433i | \(-0.0278696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.87451 | 0.349335 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.11438 | + | 12.3225i | 0.251374 | + | 0.435393i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.8544 | + | 10.8856i | 0.665359 | + | 0.384145i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.1400 | + | 13.9373i | 0.849769 | + | 0.490615i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.58301 | + | 16.5983i | 0.336921 | + | 0.583563i | 0.983852 | − | 0.178985i | \(-0.0572813\pi\) |
−0.646931 | + | 0.762548i | \(0.723948\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.2915 | 0.607187 | 0.303593 | − | 0.952802i | \(-0.401814\pi\) | ||||
0.303593 | + | 0.952802i | \(0.401814\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.41699i | 0.260125i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.6334 | − | 24.6144i | −1.49155 | − | 0.861148i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.50000 | − | 6.06218i | −0.122300 | − | 0.211830i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.9889 | − | 45.0141i | 0.907018 | − | 1.57100i | 0.0888337 | − | 0.996046i | \(-0.471686\pi\) |
0.818185 | − | 0.574955i | \(-0.194981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.9847 | − | 9.22876i | 0.557191 | − | 0.321694i | −0.194826 | − | 0.980838i | \(-0.562414\pi\) |
0.752017 | + | 0.659144i | \(0.229081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.4575i | − | 0.780924i | −0.920619 | − | 0.390462i | \(-0.872315\pi\) | ||
0.920619 | − | 0.390462i | \(-0.127685\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.85425 | + | 17.0681i | 0.342252 | + | 0.592798i | 0.984851 | − | 0.173405i | \(-0.0554769\pi\) |
−0.642598 | + | 0.766203i | \(0.722144\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.3229 | − | 17.8797i | 0.358097 | − | 0.620241i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.97684 | + | 5.76013i | 0.345677 | + | 0.199577i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.71655 | − | 2.14575i | 0.128463 | − | 0.0741680i | ||||
\(838\) | 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 | ||||||||
\(843\) | 20.7846 | − | 12.0000i | 0.715860 | − | 0.413302i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.9982 | − | 10.9686i | 0.652787 | − | 0.376886i | ||||
\(848\) | 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 | ||||||||
\(853\) | 43.2288i | 1.48012i | 0.672538 | + | 0.740062i | \(0.265204\pi\) | ||||
−0.672538 | + | 0.740062i | \(0.734796\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.8176 | − | 6.82288i | 0.403680 | − | 0.233065i | −0.284390 | − | 0.958709i | \(-0.591791\pi\) |
0.688071 | + | 0.725644i | \(0.258458\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.2288 | + | 22.9129i | −0.451359 | + | 0.781777i | −0.998471 | − | 0.0552825i | \(-0.982394\pi\) |
0.547111 | + | 0.837060i | \(0.315727\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.0627 | 0.445177 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.8411 | + | 17.2288i | 1.01580 | + | 0.586474i | 0.912885 | − | 0.408216i | \(-0.133849\pi\) |
0.102917 | + | 0.994690i | \(0.467182\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.2915i | 0.485365i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.77124 | 0.127931 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.854249 | + | 1.47960i | 0.0289451 | + | 0.0501344i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.92820 | − | 4.00000i | −0.234484 | − | 0.135379i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.1244 | + | 7.00000i | 0.409410 | + | 0.236373i | 0.690536 | − | 0.723298i | \(-0.257375\pi\) |
−0.281126 | + | 0.959671i | \(0.590708\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 21.8118i | − | 0.734024i | −0.930216 | − | 0.367012i | \(-0.880381\pi\) | ||
0.930216 | − | 0.367012i | \(-0.119619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0137 | − | 9.82288i | −0.571265 | − | 0.329820i | 0.186390 | − | 0.982476i | \(-0.440321\pi\) |
−0.757654 | + | 0.652656i | \(0.773655\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | 43.0839 | − | 24.8745i | 1.44175 | − | 0.832394i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.35425i | 0.145384i | ||||||||
\(898\) | 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 | ||||||||
\(903\) | − | 15.7085i | − | 0.522746i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8797 | − | 10.3229i | 0.593687 | − | 0.342765i | −0.172867 | − | 0.984945i | \(-0.555303\pi\) |
0.766554 | + | 0.642180i | \(0.221970\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.93725 | 0.163758 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.52026 | −0.182894 | −0.0914472 | − | 0.995810i | \(-0.529149\pi\) | ||||
−0.0914472 | + | 0.995810i | \(0.529149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.5885 | − | 9.00000i | 0.515903 | − | 0.297857i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.7850 | + | 28.1660i | −1.61102 | + | 0.930124i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.20850 | − | 9.02138i | 0.171812 | − | 0.297588i | −0.767241 | − | 0.641359i | \(-0.778371\pi\) |
0.939054 | + | 0.343771i | \(0.111704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.9686 | − | 24.1944i | −0.460282 | − | 0.797232i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 36.1033i | − | 1.18835i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.10102 | + | 4.67712i | −0.266072 | + | 0.153617i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.7601 | − | 30.7614i | 0.582691 | − | 1.00925i | −0.412468 | − | 0.910972i | \(-0.635333\pi\) |
0.995159 | − | 0.0982783i | \(-0.0313335\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 58.0405 | 1.90220 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.8176 | − | 6.82288i | −0.386890 | − | 0.223371i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 38.9778i | − | 1.27335i | −0.771133 | − | 0.636674i | \(-0.780310\pi\) | ||
0.771133 | − | 0.636674i | \(-0.219690\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.2288 | 0.692774 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.46863 | + | 9.47194i | 0.178272 | + | 0.308776i | 0.941289 | − | 0.337602i | \(-0.109616\pi\) |
−0.763017 | + | 0.646379i | \(0.776283\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.03688 | − | 4.06275i | −0.229152 | − | 0.132301i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.9478 | − | 20.1771i | −1.13565 | − | 0.655668i | −0.190301 | − | 0.981726i | \(-0.560946\pi\) |
−0.945350 | + | 0.326057i | \(0.894280\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17.5000 | − | 30.3109i | −0.568074 | − | 0.983933i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.5203 | 0.762697 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 52.4575i | − | 1.69927i | −0.527375 | − | 0.849633i | \(-0.676824\pi\) | ||
0.527375 | − | 0.849633i | \(-0.323176\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.8972 | − | 6.29150i | −0.352257 | − | 0.203375i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.5203 | 1.72826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.29150 | − | 10.8972i | 0.202952 | − | 0.351523i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6681 | + | 8.46863i | −0.472673 | + | 0.272898i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.3948i | 0.913114i | 0.889694 | + | 0.456557i | \(0.150918\pi\) | ||||
−0.889694 | + | 0.456557i | \(0.849082\pi\) | |||||||
\(968\) | 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 | \(-0.888951\pi\) |
0.765919 | + | 0.642937i | \(0.222284\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.4564 | − | 6.61438i | −0.367277 | − | 0.212047i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.7050 | − | 12.5314i | 0.694404 | − | 0.400914i | −0.110856 | − | 0.993836i | \(-0.535359\pi\) |
0.805260 | + | 0.592922i | \(0.202026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.4170 | −0.748410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.0000 | −0.415058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.3789 | − | 12.3431i | 0.681882 | − | 0.393685i | −0.118682 | − | 0.992932i | \(-0.537867\pi\) |
0.800564 | + | 0.599247i | \(0.204533\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13.7477 | + | 7.93725i | 0.437595 | + | 0.252646i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.88562 | + | 8.46215i | −0.155354 | + | 0.269081i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.1458 | − | 38.3576i | −0.703483 | − | 1.21847i | −0.967236 | − | 0.253878i | \(-0.918294\pi\) |
0.263753 | − | 0.964590i | \(-0.415040\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 20.1660i | − | 0.639949i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.4372 | + | 21.6144i | −1.18565 | + | 0.684534i | −0.957314 | − | 0.289049i | \(-0.906661\pi\) |
−0.228334 | + | 0.973583i | \(0.573328\pi\) | |||||||
\(998\) | 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 | 2100.2.bc.e.1549.4 | 8 | ||
5.2 | odd | 4 | 420.2.q.c.121.1 | ✓ | 4 | ||
5.3 | odd | 4 | 2100.2.q.h.1801.2 | 4 | |||
5.4 | even | 2 | inner | 2100.2.bc.e.1549.1 | 8 | ||
7.4 | even | 3 | inner | 2100.2.bc.e.949.1 | 8 | ||
15.2 | even | 4 | 1260.2.s.f.541.1 | 4 | |||
20.7 | even | 4 | 1680.2.bg.q.961.2 | 4 | |||
35.2 | odd | 12 | 2940.2.a.s.1.1 | 2 | |||
35.4 | even | 6 | inner | 2100.2.bc.e.949.4 | 8 | ||
35.12 | even | 12 | 2940.2.a.m.1.1 | 2 | |||
35.17 | even | 12 | 2940.2.q.t.361.2 | 4 | |||
35.18 | odd | 12 | 2100.2.q.h.1201.2 | 4 | |||
35.27 | even | 4 | 2940.2.q.t.961.2 | 4 | |||
35.32 | odd | 12 | 420.2.q.c.361.1 | yes | 4 | ||
105.2 | even | 12 | 8820.2.a.be.1.2 | 2 | |||
105.32 | even | 12 | 1260.2.s.f.361.1 | 4 | |||
105.47 | odd | 12 | 8820.2.a.bj.1.2 | 2 | |||
140.67 | even | 12 | 1680.2.bg.q.1201.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.q.c.121.1 | ✓ | 4 | 5.2 | odd | 4 | ||
420.2.q.c.361.1 | yes | 4 | 35.32 | odd | 12 | ||
1260.2.s.f.361.1 | 4 | 105.32 | even | 12 | |||
1260.2.s.f.541.1 | 4 | 15.2 | even | 4 | |||
1680.2.bg.q.961.2 | 4 | 20.7 | even | 4 | |||
1680.2.bg.q.1201.2 | 4 | 140.67 | even | 12 | |||
2100.2.q.h.1201.2 | 4 | 35.18 | odd | 12 | |||
2100.2.q.h.1801.2 | 4 | 5.3 | odd | 4 | |||
2100.2.bc.e.949.1 | 8 | 7.4 | even | 3 | inner | ||
2100.2.bc.e.949.4 | 8 | 35.4 | even | 6 | inner | ||
2100.2.bc.e.1549.1 | 8 | 5.4 | even | 2 | inner | ||
2100.2.bc.e.1549.4 | 8 | 1.1 | even | 1 | trivial | ||
2940.2.a.m.1.1 | 2 | 35.12 | even | 12 | |||
2940.2.a.s.1.1 | 2 | 35.2 | odd | 12 | |||
2940.2.q.t.361.2 | 4 | 35.17 | even | 12 | |||
2940.2.q.t.961.2 | 4 | 35.27 | even | 4 | |||
8820.2.a.be.1.2 | 2 | 105.2 | even | 12 | |||
8820.2.a.bj.1.2 | 2 | 105.47 | odd | 12 |