Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,2,Mod(45,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.45");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.e (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: | \(0.606863055362\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 45.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.45 |
Dual form | 76.2.e.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.500000 | + | 0.866025i | −0.129099 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.50000 | + | 4.33013i | −0.521286 | + | 0.902894i | 0.478407 | + | 0.878138i | \(0.341214\pi\) |
−0.999694 | + | 0.0247559i | \(0.992119\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.50000 | + | 6.06218i | −0.649934 | + | 1.12572i | 0.333205 | + | 0.942855i | \(0.391870\pi\) |
−0.983138 | + | 0.182864i | \(0.941463\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00000 | − | 3.46410i | −0.348155 | − | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | 1.64399 | 0.821995 | − | 0.569495i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50000 | + | 4.33013i | 0.390434 | + | 0.676252i | 0.992507 | − | 0.122189i | \(-0.0389915\pi\) |
−0.602072 | + | 0.798441i | \(0.705658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.50000 | + | 4.33013i | 0.381246 | + | 0.660338i | 0.991241 | − | 0.132068i | \(-0.0421616\pi\) |
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.50000 | − | 6.06218i | 0.510527 | − | 0.884260i | −0.489398 | − | 0.872060i | \(-0.662783\pi\) |
0.999926 | − | 0.0121990i | \(-0.00388317\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50000 | − | 2.59808i | 0.210042 | − | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.50000 | + | 9.52628i | −0.755483 | + | 1.30854i | 0.189651 | + | 0.981852i | \(0.439264\pi\) |
−0.945134 | + | 0.326683i | \(0.894069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | − | 3.46410i | −0.269680 | − | 0.467099i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.500000 | − | 4.33013i | −0.0662266 | − | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.50000 | − | 2.59808i | −0.195283 | − | 0.338241i | 0.751710 | − | 0.659494i | \(-0.229229\pi\) |
−0.946993 | + | 0.321253i | \(0.895896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.50000 | + | 9.52628i | −0.704203 | + | 1.21972i | 0.262776 | + | 0.964857i | \(0.415362\pi\) |
−0.966978 | + | 0.254858i | \(0.917971\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | − | 2.59808i | 0.183254 | − | 0.317406i | −0.759733 | − | 0.650236i | \(-0.774670\pi\) |
0.942987 | + | 0.332830i | \(0.108004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.00000 | −0.601929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.50000 | − | 9.52628i | −0.652730 | − | 1.13056i | −0.982458 | − | 0.186485i | \(-0.940290\pi\) |
0.329728 | − | 0.944076i | \(-0.393043\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.50000 | − | 12.9904i | −0.877809 | − | 1.52041i | −0.853740 | − | 0.520699i | \(-0.825671\pi\) |
−0.0240681 | − | 0.999710i | \(-0.507662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.50000 | + | 11.2583i | 0.731307 | + | 1.26666i | 0.956325 | + | 0.292306i | \(0.0944227\pi\) |
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | − | 2.59808i | 0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.00000 | −0.750479 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.50000 | + | 2.59808i | −0.159000 | + | 0.275396i | −0.934508 | − | 0.355942i | \(-0.884160\pi\) |
0.775509 | + | 0.631337i | \(0.217494\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | + | 3.46410i | 0.207390 | + | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.500000 | − | 4.33013i | −0.0512989 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | + | 6.92820i | −0.402015 | + | 0.696311i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.500000 | − | 0.866025i | 0.0497519 | − | 0.0861727i | −0.840077 | − | 0.542467i | \(-0.817490\pi\) |
0.889829 | + | 0.456294i | \(0.150824\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 20.0000 | 1.93347 | 0.966736 | − | 0.255774i | \(-0.0823304\pi\) | ||||
0.966736 | + | 0.255774i | \(0.0823304\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.50000 | − | 2.59808i | −0.143674 | − | 0.248851i | 0.785203 | − | 0.619238i | \(-0.212558\pi\) |
−0.928877 | + | 0.370387i | \(0.879225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.00000 | + | 8.66025i | 0.474579 | + | 0.821995i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.00000 | −0.466252 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | − | 1.73205i | −0.0924500 | − | 0.160128i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.50000 | + | 4.33013i | −0.225417 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.50000 | − | 2.59808i | 0.133103 | − | 0.230542i | −0.791768 | − | 0.610822i | \(-0.790839\pi\) |
0.924871 | + | 0.380280i | \(0.124172\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.50000 | + | 4.33013i | −0.220113 | + | 0.381246i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.50000 | − | 12.9904i | −0.655278 | − | 1.13497i | −0.981824 | − | 0.189794i | \(-0.939218\pi\) |
0.326546 | − | 0.945181i | \(-0.394115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.50000 | + | 4.33013i | 0.215166 | + | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.50000 | − | 4.33013i | 0.213589 | − | 0.369948i | −0.739246 | − | 0.673436i | \(-0.764818\pi\) |
0.952835 | + | 0.303488i | \(0.0981512\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.50000 | + | 7.79423i | −0.381685 | + | 0.661098i | −0.991303 | − | 0.131597i | \(-0.957989\pi\) |
0.609618 | + | 0.792695i | \(0.291323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.00000 | 0.589506 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.00000 | + | 3.46410i | −0.167248 | + | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.00000 | −0.581318 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.50000 | − | 6.06218i | −0.288675 | − | 0.500000i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.50000 | − | 2.59808i | −0.122885 | − | 0.212843i | 0.798019 | − | 0.602632i | \(-0.205881\pi\) |
−0.920904 | + | 0.389789i | \(0.872548\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.00000 | + | 3.46410i | 0.160644 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | − | 6.06218i | −0.279330 | − | 0.483814i | 0.691888 | − | 0.722005i | \(-0.256779\pi\) |
−0.971219 | + | 0.238190i | \(0.923446\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.0000 | −0.872357 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.00000 | − | 3.46410i | 0.155700 | − | 0.269680i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.50000 | − | 12.9904i | 0.580367 | − | 1.00523i | −0.415068 | − | 0.909790i | \(-0.636242\pi\) |
0.995436 | − | 0.0954356i | \(-0.0304244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.00000 | + | 5.19615i | −0.535303 | + | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.50000 | − | 12.9904i | −0.570214 | − | 0.987640i | −0.996544 | − | 0.0830722i | \(-0.973527\pi\) |
0.426329 | − | 0.904568i | \(-0.359807\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.50000 | − | 2.59808i | 0.112747 | − | 0.195283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.50000 | − | 4.33013i | 0.185824 | − | 0.321856i | −0.758030 | − | 0.652219i | \(-0.773838\pi\) |
0.943854 | + | 0.330364i | \(0.107171\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.0000 | −0.813143 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.00000 | + | 8.66025i | 0.367607 | + | 0.636715i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000 | + | 10.3923i | 0.438763 | + | 0.759961i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.0000 | 1.15772 | 0.578860 | − | 0.815427i | \(-0.303498\pi\) | ||||
0.578860 | + | 0.815427i | \(0.303498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.50000 | − | 12.9904i | −0.539862 | − | 0.935068i | −0.998911 | − | 0.0466572i | \(-0.985143\pi\) |
0.459049 | − | 0.888411i | \(-0.348190\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.500000 | + | 0.866025i | 0.0358057 | + | 0.0620174i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.00000 | 0.211604 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.50000 | + | 4.33013i | −0.174608 | + | 0.302429i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.00000 | + | 8.66025i | 0.347524 | + | 0.601929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | + | 6.92820i | 1.10674 | + | 0.479234i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.50000 | + | 7.79423i | 0.309793 | + | 0.536577i | 0.978317 | − | 0.207114i | \(-0.0664070\pi\) |
−0.668524 | + | 0.743690i | \(0.733074\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.50000 | − | 9.52628i | 0.376854 | − | 0.652730i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.50000 | + | 4.33013i | −0.170499 | + | 0.295312i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.50000 | − | 12.9904i | 0.506803 | − | 0.877809i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | −0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5000 | + | 21.6506i | 0.837062 | + | 1.44983i | 0.892341 | + | 0.451363i | \(0.149062\pi\) |
−0.0552786 | + | 0.998471i | \(0.517605\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | − | 6.92820i | −0.266667 | − | 0.461880i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0000 | −1.32745 | −0.663723 | − | 0.747978i | \(-0.731025\pi\) | ||||
−0.663723 | + | 0.747978i | \(0.731025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00000 | 0.132164 | 0.0660819 | − | 0.997814i | \(-0.478950\pi\) | ||||
0.0660819 | + | 0.997814i | \(0.478950\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5000 | + | 18.1865i | 0.687878 | + | 1.19144i | 0.972523 | + | 0.232806i | \(0.0747909\pi\) |
−0.284645 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00000 | 0.456630 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.50000 | + | 11.2583i | −0.422220 | + | 0.731307i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.50000 | + | 16.4545i | −0.611949 | + | 1.05993i | 0.378963 | + | 0.925412i | \(0.376281\pi\) |
−0.990912 | + | 0.134515i | \(0.957053\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.50000 | − | 6.06218i | −0.223607 | − | 0.387298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.50000 | + | 2.59808i | −0.222700 | + | 0.165312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.5000 | − | 26.8468i | 0.978351 | − | 1.69455i | 0.309951 | − | 0.950753i | \(-0.399687\pi\) |
0.668400 | − | 0.743802i | \(-0.266979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | − | 17.3205i | 0.628695 | − | 1.08893i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.00000 | 0.187867 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.5000 | + | 19.9186i | −0.717350 | + | 1.24249i | 0.244696 | + | 0.969600i | \(0.421312\pi\) |
−0.962046 | + | 0.272887i | \(0.912021\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.00000 | + | 12.1244i | 0.433289 | + | 0.750479i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.50000 | + | 7.79423i | 0.277482 | + | 0.480613i | 0.970758 | − | 0.240059i | \(-0.0771668\pi\) |
−0.693276 | + | 0.720672i | \(0.743833\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.0000 | −0.675725 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.00000 | −0.183597 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5000 | − | 23.3827i | −0.823110 | − | 1.42567i | −0.903356 | − | 0.428892i | \(-0.858904\pi\) |
0.0802460 | − | 0.996775i | \(-0.474429\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5000 | − | 26.8468i | −0.941558 | − | 1.63083i | −0.762501 | − | 0.646988i | \(-0.776029\pi\) |
−0.179057 | − | 0.983839i | \(-0.557305\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.00000 | + | 13.8564i | −0.482418 | + | 0.835573i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0000 | 0.600842 | 0.300421 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300421 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.00000 | − | 6.92820i | 0.239474 | − | 0.414781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.50000 | + | 6.06218i | −0.208792 | + | 0.361639i | −0.951334 | − | 0.308160i | \(-0.900287\pi\) |
0.742542 | + | 0.669800i | \(0.233620\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.50000 | + | 7.79423i | 0.267497 | + | 0.463319i | 0.968215 | − | 0.250120i | \(-0.0804700\pi\) |
−0.700718 | + | 0.713439i | \(0.747137\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.50000 | − | 2.59808i | 0.207322 | − | 0.153897i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.50000 | + | 4.33013i | −0.146553 | + | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.50000 | − | 2.59808i | 0.0873334 | − | 0.151266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.0000 | −1.16052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.50000 | + | 4.33013i | 0.144579 | + | 0.250418i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.00000 | 0.0574485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.0000 | −0.629858 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5000 | − | 23.3827i | −0.770486 | − | 1.33452i | −0.937297 | − | 0.348532i | \(-0.886680\pi\) |
0.166811 | − | 0.985989i | \(-0.446653\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.0000 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691915\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.50000 | + | 9.52628i | −0.310878 | + | 0.538457i | −0.978553 | − | 0.205996i | \(-0.933957\pi\) |
0.667674 | + | 0.744453i | \(0.267290\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.50000 | + | 12.9904i | −0.421242 | + | 0.729612i | −0.996061 | − | 0.0886679i | \(-0.971739\pi\) |
0.574819 | + | 0.818280i | \(0.305072\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0000 | − | 24.2487i | 0.783850 | − | 1.35767i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.0000 | + | 17.3205i | 0.558146 | + | 0.966736i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.50000 | + | 12.9904i | 0.0834622 | + | 0.722804i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | − | 3.46410i | −0.110940 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.50000 | − | 2.59808i | 0.0829502 | − | 0.143674i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0000 | − | 17.3205i | 0.547997 | − | 0.949158i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.00000 | 0.163908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.50000 | + | 4.33013i | 0.136184 | + | 0.235877i | 0.926049 | − | 0.377403i | \(-0.123183\pi\) |
−0.789865 | + | 0.613280i | \(0.789850\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.00000 | + | 12.1244i | 0.380188 | + | 0.658505i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.0000 | −0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.50000 | − | 4.33013i | −0.134595 | − | 0.233126i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.50000 | + | 4.33013i | 0.134207 | + | 0.232453i | 0.925294 | − | 0.379250i | \(-0.123818\pi\) |
−0.791087 | + | 0.611703i | \(0.790485\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.50000 | − | 4.33013i | 0.133440 | − | 0.231125i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0000 | 1.59674 | 0.798369 | − | 0.602168i | \(-0.205696\pi\) | ||||
0.798369 | + | 0.602168i | \(0.205696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.50000 | − | 9.52628i | 0.291910 | − | 0.505602i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.50000 | − | 12.9904i | −0.395835 | − | 0.685606i | 0.597372 | − | 0.801964i | \(-0.296211\pi\) |
−0.993207 | + | 0.116358i | \(0.962878\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.50000 | + | 4.33013i | 0.131216 | + | 0.227273i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.50000 | − | 12.9904i | 0.392568 | − | 0.679948i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.5000 | + | 21.6506i | −0.652495 | + | 1.13015i | 0.330021 | + | 0.943974i | \(0.392944\pi\) |
−0.982516 | + | 0.186180i | \(0.940389\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.50000 | + | 7.79423i | 0.232379 | + | 0.402492i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.50000 | + | 6.06218i | 0.180259 | + | 0.312218i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.0000 | −0.616399 | −0.308199 | − | 0.951322i | \(-0.599726\pi\) | ||||
−0.308199 | + | 0.951322i | \(0.599726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.00000 | 0.153695 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.5000 | + | 25.1147i | 0.740915 | + | 1.28330i | 0.952079 | + | 0.305852i | \(0.0989414\pi\) |
−0.211164 | + | 0.977451i | \(0.567725\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.0000 | 0.508329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.50000 | + | 2.59808i | −0.0760530 | + | 0.131728i | −0.901544 | − | 0.432688i | \(-0.857565\pi\) |
0.825491 | + | 0.564416i | \(0.190898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0000 | 0.758583 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.50000 | − | 12.9904i | 0.378325 | − | 0.655278i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.50000 | + | 11.2583i | −0.327050 | + | 0.566468i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.5000 | + | 21.6506i | 0.627357 | + | 1.08661i | 0.988080 | + | 0.153941i | \(0.0491966\pi\) |
−0.360723 | + | 0.932673i | \(0.617470\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.50000 | − | 16.4545i | −0.474407 | − | 0.821698i | 0.525163 | − | 0.851002i | \(-0.324004\pi\) |
−0.999571 | + | 0.0293039i | \(0.990671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.00000 | − | 3.46410i | 0.0996271 | − | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.500000 | − | 0.866025i | 0.0248452 | − | 0.0430331i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −40.0000 | −1.98273 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.50000 | − | 14.7224i | 0.420298 | − | 0.727977i | −0.575670 | − | 0.817682i | \(-0.695259\pi\) |
0.995968 | + | 0.0897044i | \(0.0285922\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.00000 | 0.246632 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.00000 | −0.440732 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.500000 | + | 0.866025i | 0.0243685 | + | 0.0422075i | 0.877952 | − | 0.478748i | \(-0.158909\pi\) |
−0.853584 | + | 0.520955i | \(0.825576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.00000 | − | 12.1244i | −0.340352 | − | 0.589506i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0000 | −0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.00000 | −0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5000 | + | 18.1865i | −0.505767 | + | 0.876014i | 0.494211 | + | 0.869342i | \(0.335457\pi\) |
−0.999978 | + | 0.00667224i | \(0.997876\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.5000 | − | 21.6506i | 0.600712 | − | 1.04046i | −0.392002 | − | 0.919964i | \(-0.628217\pi\) |
0.992713 | − | 0.120499i | \(-0.0384494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.50000 | − | 6.06218i | −0.167812 | − | 0.290659i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.5000 | − | 12.9904i | 0.837139 | − | 0.621414i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.50000 | + | 11.2583i | 0.310228 | + | 0.537331i | 0.978412 | − | 0.206666i | \(-0.0662612\pi\) |
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | + | 12.1244i | −0.333333 | + | 0.577350i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.5000 | + | 21.6506i | −0.593893 | + | 1.02865i | 0.399809 | + | 0.916598i | \(0.369076\pi\) |
−0.993702 | + | 0.112054i | \(0.964257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00000 | −0.142214 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.50000 | − | 2.59808i | 0.0709476 | − | 0.122885i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.0000 | 1.03824 | 0.519122 | − | 0.854700i | \(-0.326259\pi\) | ||||
0.519122 | + | 0.854700i | \(0.326259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.0000 | − | 17.3205i | −0.470882 | − | 0.815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.00000 | − | 13.8564i | −0.375873 | − | 0.651031i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.50000 | − | 12.9904i | −0.350070 | − | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.50000 | − | 9.52628i | −0.256161 | − | 0.443683i | 0.709050 | − | 0.705159i | \(-0.249124\pi\) |
−0.965210 | + | 0.261476i | \(0.915791\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | + | 3.46410i | −0.0927478 | + | 0.160644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.0000 | −0.925490 | −0.462745 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462745 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.50000 | − | 6.06218i | 0.161271 | − | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0000 | − | 17.3205i | −0.459800 | − | 0.796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.0000 | + | 10.3923i | −0.642364 | + | 0.476832i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.0000 | + | 19.0526i | 0.503655 | + | 0.872357i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.5000 | − | 19.9186i | 0.525448 | − | 0.910103i | −0.474112 | − | 0.880464i | \(-0.657231\pi\) |
0.999561 | − | 0.0296389i | \(-0.00943575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | − | 8.66025i | 0.227980 | − | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.50000 | + | 4.33013i | −0.113519 | + | 0.196621i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.00000 | − | 3.46410i | −0.0904431 | − | 0.156652i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.500000 | + | 0.866025i | 0.0225647 | + | 0.0390832i | 0.877087 | − | 0.480331i | \(-0.159483\pi\) |
−0.854523 | + | 0.519414i | \(0.826150\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.0000 | 0.945792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −8.00000 | −0.359573 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | + | 4.33013i | 0.111915 | + | 0.193843i | 0.916542 | − | 0.399937i | \(-0.130968\pi\) |
−0.804627 | + | 0.593780i | \(0.797635\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.0000 | 0.670151 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5000 | + | 18.1865i | −0.468172 | + | 0.810897i | −0.999338 | − | 0.0363700i | \(-0.988421\pi\) |
0.531167 | + | 0.847267i | \(0.321754\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.00000 | 0.0444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.50000 | + | 12.9904i | −0.332432 | + | 0.575789i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −20.0000 | − | 8.66025i | −0.883022 | − | 0.382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.0000 | + | 24.2487i | −0.615719 | + | 1.06646i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.50000 | − | 12.9904i | 0.329213 | − | 0.570214i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.0000 | 1.13908 | 0.569540 | − | 0.821963i | \(-0.307121\pi\) | ||||
0.569540 | + | 0.821963i | \(0.307121\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.50000 | − | 16.4545i | 0.415406 | − | 0.719504i | −0.580065 | − | 0.814570i | \(-0.696973\pi\) |
0.995471 | + | 0.0950659i | \(0.0303062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.00000 | − | 10.3923i | −0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | − | 1.73205i | −0.0434783 | − | 0.0753066i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.00000 | 0.216574 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.0000 | + | 17.3205i | 0.432338 | + | 0.748831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | − | 10.3923i | −0.258919 | − | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.0000 | 1.20605 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.500000 | − | 0.866025i | 0.0214967 | − | 0.0372333i | −0.855077 | − | 0.518501i | \(-0.826490\pi\) |
0.876574 | + | 0.481268i | \(0.159824\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.00000 | 0.214571 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.50000 | − | 2.59808i | 0.0642529 | − | 0.111289i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.5000 | + | 21.6506i | −0.534461 | + | 0.925714i | 0.464728 | + | 0.885454i | \(0.346152\pi\) |
−0.999189 | + | 0.0402607i | \(0.987181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.0000 | + | 19.0526i | 0.469469 | + | 0.813143i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.5000 | − | 18.1865i | 1.04374 | − | 0.774772i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.00000 | + | 8.66025i | −0.212238 | + | 0.367607i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.50000 | − | 4.33013i | 0.105928 | − | 0.183473i | −0.808189 | − | 0.588924i | \(-0.799552\pi\) |
0.914117 | + | 0.405450i | \(0.132885\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.00000 | 0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | + | 10.3923i | −0.253320 | + | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.0000 | 1.51722 | 0.758610 | − | 0.651546i | \(-0.225879\pi\) | ||||
0.758610 | + | 0.651546i | \(0.225879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00000 | + | 12.1244i | 0.294492 | + | 0.510075i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | + | 13.8564i | 0.334205 | + | 0.578860i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 10.0000 | + | 17.3205i | 0.417029 | + | 0.722315i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.50000 | − | 12.9904i | 0.311689 | − | 0.539862i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.0000 | − | 38.1051i | 0.911147 | − | 1.57815i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.00000 | − | 1.73205i | 0.0413449 | − | 0.0716115i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.50000 | − | 12.9904i | −0.309558 | − | 0.536170i | 0.668708 | − | 0.743525i | \(-0.266848\pi\) |
−0.978266 | + | 0.207355i | \(0.933514\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | − | 6.92820i | −0.659269 | − | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.00000 | + | 1.73205i | 0.0411345 | + | 0.0712470i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.50000 | − | 4.33013i | 0.102663 | − | 0.177817i | −0.810118 | − | 0.586267i | \(-0.800597\pi\) |
0.912781 | + | 0.408450i | \(0.133930\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.00000 | 0.286491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.5000 | + | 38.9711i | −0.919325 | + | 1.59232i | −0.118882 | + | 0.992908i | \(0.537931\pi\) |
−0.800443 | + | 0.599409i | \(0.795402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.00000 | − | 5.19615i | −0.122169 | − | 0.211604i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50000 | + | 4.33013i | 0.101639 | + | 0.176045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.50000 | − | 6.06218i | −0.141595 | − | 0.245249i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5000 | + | 25.1147i | 0.585649 | + | 1.01437i | 0.994794 | + | 0.101905i | \(0.0324938\pi\) |
−0.409145 | + | 0.912470i | \(0.634173\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.00000 | −0.201619 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.5000 | − | 38.9711i | 0.905816 | − | 1.56892i | 0.0859976 | − | 0.996295i | \(-0.472592\pi\) |
0.819818 | − | 0.572624i | \(-0.194074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.5000 | + | 21.6506i | −0.501608 | + | 0.868810i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.00000 | + | 17.3205i | 0.0798723 | + | 0.691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.0000 | − | 25.9808i | −0.598089 | − | 1.03592i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.5000 | + | 35.5070i | −0.816092 | + | 1.41351i | 0.0924489 | + | 0.995717i | \(0.470531\pi\) |
−0.908541 | + | 0.417796i | \(0.862803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.50000 | + | 7.79423i | −0.178859 | + | 0.309793i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.00000 | 0.119051 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.50000 | + | 6.06218i | −0.138675 | + | 0.240192i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −22.0000 | −0.870307 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.5000 | − | 33.7750i | −0.770204 | − | 1.33403i | −0.937451 | − | 0.348117i | \(-0.886821\pi\) |
0.167247 | − | 0.985915i | \(-0.446512\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.50000 | − | 16.4545i | −0.374643 | − | 0.648901i | 0.615630 | − | 0.788035i | \(-0.288902\pi\) |
−0.990274 | + | 0.139134i | \(0.955568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.00000 | −0.196875 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.0000 | 1.25805 | 0.629025 | − | 0.777385i | \(-0.283454\pi\) | ||||
0.629025 | + | 0.777385i | \(0.283454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | + | 10.3923i | 0.235521 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.0000 | −1.17399 | −0.586995 | − | 0.809590i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809590i | \(0.699689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.50000 | − | 12.9904i | 0.293049 | − | 0.507576i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.0000 | −1.17041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.50000 | + | 4.33013i | −0.0973862 | + | 0.168678i | −0.910602 | − | 0.413284i | \(-0.864382\pi\) |
0.813216 | + | 0.581962i | \(0.197715\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.5000 | + | 26.8468i | −0.602880 | + | 1.04422i | 0.389503 | + | 0.921025i | \(0.372647\pi\) |
−0.992383 | + | 0.123194i | \(0.960686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.50000 | − | 2.59808i | −0.0582552 | − | 0.100901i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.5000 | − | 30.3109i | −0.677603 | − | 1.17364i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.5000 | + | 21.6506i | −0.483278 | + | 0.837062i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.0000 | − | 38.1051i | 0.849301 | − | 1.47103i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.0000 | −0.385472 | −0.192736 | − | 0.981251i | \(-0.561736\pi\) | ||||
−0.192736 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | − | 17.3205i | 0.384900 | − | 0.666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0000 | 0.384331 | 0.192166 | − | 0.981363i | \(-0.438449\pi\) | ||||
0.192166 | + | 0.981363i | \(0.438449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.0000 | − | 17.3205i | −0.383201 | − | 0.663723i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.0000 | 0.612223 | 0.306111 | − | 0.951996i | \(-0.400972\pi\) | ||||
0.306111 | + | 0.951996i | \(0.400972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.00000 | 0.191040 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.00000 | + | 1.73205i | 0.0381524 | + | 0.0660819i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.50000 | + | 9.52628i | 0.209533 | + | 0.362922i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.0000 | 1.36950 | 0.684752 | − | 0.728776i | \(-0.259910\pi\) | ||||
0.684752 | + | 0.728776i | \(0.259910\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.00000 | −0.341389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.50000 | − | 12.9904i | 0.284083 | − | 0.492046i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.5000 | + | 18.1865i | −0.397146 | + | 0.687878i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.5000 | − | 30.3109i | −0.660966 | − | 1.14483i | −0.980362 | − | 0.197205i | \(-0.936813\pi\) |
0.319396 | − | 0.947621i | \(-0.396520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.0000 | − | 17.3205i | −1.50863 | − | 0.653255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.50000 | + | 6.06218i | 0.131818 | + | 0.228315i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.50000 | + | 2.59808i | −0.0563337 | + | 0.0975728i | −0.892817 | − | 0.450420i | \(-0.851274\pi\) |
0.836483 | + | 0.547992i | \(0.184608\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.0000 | 0.975076 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.0000 | + | 17.3205i | −0.374503 | + | 0.648658i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.00000 | −0.149592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.00000 | + | 10.3923i | 0.224074 | + | 0.388108i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.50000 | − | 6.06218i | −0.130528 | − | 0.226081i | 0.793352 | − | 0.608763i | \(-0.208334\pi\) |
−0.923880 | + | 0.382682i | \(0.875001\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.0000 | −0.706618 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.0000 | + | 24.2487i | 0.519947 | + | 0.900575i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.50000 | − | 6.06218i | −0.129808 | − | 0.224834i | 0.793794 | − | 0.608186i | \(-0.208103\pi\) |
−0.923602 | + | 0.383353i | \(0.874769\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.50000 | − | 12.9904i | 0.277398 | − | 0.480467i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.0000 | −1.10808 | −0.554038 | − | 0.832492i | \(-0.686914\pi\) | ||||
−0.554038 | + | 0.832492i | \(0.686914\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.50000 | − | 6.06218i | 0.129099 | − | 0.223607i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.00000 | + | 10.3923i | −0.221013 | + | 0.382805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.50000 | + | 11.2583i | 0.239106 | + | 0.414144i | 0.960458 | − | 0.278425i | \(-0.0898122\pi\) |
−0.721352 | + | 0.692569i | \(0.756479\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.00000 | − | 1.73205i | −0.146944 | − | 0.0636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.5000 | + | 21.6506i | 0.458581 | + | 0.794285i | 0.998886 | − | 0.0471840i | \(-0.0150247\pi\) |
−0.540306 | + | 0.841469i | \(0.681691\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50000 | − | 2.59808i | 0.0549557 | − | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.5000 | + | 25.1147i | −0.529113 | + | 0.916450i | 0.470311 | + | 0.882501i | \(0.344142\pi\) |
−0.999424 | + | 0.0339490i | \(0.989192\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.0000 | 1.12970 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.00000 | − | 13.8564i | −0.291150 | − | 0.504286i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.50000 | + | 14.7224i | 0.308938 | + | 0.535096i | 0.978130 | − | 0.207993i | \(-0.0666932\pi\) |
−0.669193 | + | 0.743089i | \(0.733360\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.0000 | 0.725954 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.00000 | − | 5.19615i | −0.108465 | − | 0.187867i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.00000 | −0.108324 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.50000 | + | 6.06218i | −0.126213 | + | 0.218608i | −0.922207 | − | 0.386698i | \(-0.873616\pi\) |
0.795993 | + | 0.605305i | \(0.206949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.0000 | −0.828325 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5000 | − | 18.1865i | 0.377659 | − | 0.654124i | −0.613062 | − | 0.790034i | \(-0.710063\pi\) |
0.990721 | + | 0.135910i | \(0.0433959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | − | 13.8564i | 0.287368 | − | 0.497737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.50000 | − | 21.6506i | −0.0895718 | − | 0.775715i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.0000 | + | 38.1051i | 0.787222 | + | 1.36351i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −17.5000 | + | 30.3109i | −0.625399 | + | 1.08322i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.50000 | − | 6.06218i | 0.124920 | − | 0.216368i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.0000 | 1.85360 | 0.926800 | − | 0.375555i | \(-0.122548\pi\) | ||||
0.926800 | + | 0.375555i | \(0.122548\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.50000 | + | 7.79423i | −0.160204 | + | 0.277482i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.50000 | + | 9.52628i | 0.195311 | + | 0.338288i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.50000 | − | 9.52628i | −0.195065 | − | 0.337862i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.0000 | 0.637593 | 0.318796 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318796 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.0000 | −0.742927 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.0000 | + | 51.9615i | 1.05868 | + | 1.83368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.5000 | − | 23.3827i | 0.475223 | − | 0.823110i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.0000 | −0.632846 | −0.316423 | − | 0.948618i | \(-0.602482\pi\) | ||||
−0.316423 | + | 0.948618i | \(0.602482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.5000 | + | 18.1865i | −0.368705 | + | 0.638616i | −0.989363 | − | 0.145465i | \(-0.953532\pi\) |
0.620658 | + | 0.784081i | \(0.286865\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.5000 | − | 26.8468i | 0.543609 | − | 0.941558i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.50000 | − | 21.6506i | −0.0874639 | − | 0.757460i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.50000 | − | 7.79423i | 0.157051 | − | 0.272020i | −0.776753 | − | 0.629805i | \(-0.783135\pi\) |
0.933804 | + | 0.357785i | \(0.116468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5000 | − | 26.8468i | 0.540296 | − | 0.935820i | −0.458591 | − | 0.888648i | \(-0.651646\pi\) |
0.998887 | − | 0.0471726i | \(-0.0150211\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −16.0000 | −0.557048 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.50000 | − | 6.06218i | 0.121707 | − | 0.210803i | −0.798734 | − | 0.601684i | \(-0.794497\pi\) |
0.920441 | + | 0.390882i | \(0.127830\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00000 | + | 8.66025i | 0.173448 | + | 0.300421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5000 | + | 18.1865i | 0.363803 | + | 0.630126i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.0000 | 0.519096 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.0000 | 0.691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.5000 | + | 21.6506i | 0.431548 | + | 0.747463i | 0.997007 | − | 0.0773135i | \(-0.0246342\pi\) |
−0.565459 | + | 0.824776i | \(0.691301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0000 | − | 17.3205i | −0.344828 | − | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.00000 | −0.241093 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.50000 | + | 7.79423i | −0.154440 | + | 0.267497i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.0000 | + | 43.3013i | −0.856989 | + | 1.48435i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.5000 | − | 33.7750i | −0.667667 | − | 1.15643i | −0.978555 | − | 0.205987i | \(-0.933960\pi\) |
0.310887 | − | 0.950447i | \(-0.399374\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.00000 | − | 3.46410i | −0.273594 | − | 0.118470i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.50000 | − | 12.9904i | −0.256195 | − | 0.443743i | 0.709024 | − | 0.705184i | \(-0.249136\pi\) |
−0.965219 | + | 0.261441i | \(0.915802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.50000 | + | 11.2583i | −0.221777 | + | 0.384129i | −0.955348 | − | 0.295484i | \(-0.904519\pi\) |
0.733571 | + | 0.679613i | \(0.237852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.0000 | −1.22545 | −0.612727 | − | 0.790295i | \(-0.709928\pi\) | ||||
−0.612727 | + | 0.790295i | \(0.709928\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.50000 | − | 12.9904i | 0.255008 | − | 0.441686i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.00000 | 0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.0000 | − | 45.0333i | −0.881990 | − | 1.52765i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.50000 | − | 2.59808i | −0.0508256 | − | 0.0880325i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.0000 | 0.338449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.50000 | + | 4.33013i | 0.0844190 | + | 0.146218i | 0.905143 | − | 0.425106i | \(-0.139763\pi\) |
−0.820724 | + | 0.571324i | \(0.806430\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.0000 | − | 25.9808i | −0.505937 | − | 0.876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.5000 | + | 21.6506i | −0.420658 | + | 0.728602i | −0.996004 | − | 0.0893086i | \(-0.971534\pi\) |
0.575346 | + | 0.817910i | \(0.304868\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.00000 | 0.100844 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.5000 | + | 21.6506i | −0.419709 | + | 0.726957i | −0.995910 | − | 0.0903508i | \(-0.971201\pi\) |
0.576201 | + | 0.817308i | \(0.304535\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.00000 | + | 3.46410i | 0.0670025 | + | 0.116052i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −24.5000 | + | 18.1865i | −0.819861 | + | 0.608589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.00000 | − | 10.3923i | −0.200558 | − | 0.347376i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.50000 | + | 4.33013i | −0.0834726 | + | 0.144579i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.0000 | + | 24.2487i | −0.466926 | + | 0.808740i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 33.0000 | 1.09939 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.00000 | 0.166206 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.5000 | − | 30.3109i | −0.581078 | − | 1.00646i | −0.995352 | − | 0.0963043i | \(-0.969298\pi\) |
0.414274 | − | 0.910152i | \(-0.364036\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.00000 | − | 1.73205i | −0.0331679 | − | 0.0574485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.50000 | − | 9.52628i | −0.181824 | − | 0.314929i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.5000 | − | 23.3827i | 0.444840 | − | 0.770486i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.0000 | −0.362069 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | − | 34.6410i | 0.657596 | − | 1.13899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.5000 | − | 19.9186i | −0.377303 | − | 0.653508i | 0.613366 | − | 0.789799i | \(-0.289815\pi\) |
−0.990669 | + | 0.136291i | \(0.956482\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.0000 | + | 12.1244i | 0.917663 | + | 0.397360i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.0000 | − | 17.3205i | −0.327385 | − | 0.567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.00000 | + | 10.3923i | −0.196221 | + | 0.339865i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.5000 | + | 19.9186i | −0.375689 | + | 0.650712i | −0.990430 | − | 0.138017i | \(-0.955927\pi\) |
0.614741 | + | 0.788729i | \(0.289260\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.0000 | −0.358971 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.50000 | + | 16.4545i | −0.309691 | + | 0.536401i | −0.978295 | − | 0.207218i | \(-0.933559\pi\) |
0.668604 | + | 0.743619i | \(0.266892\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.0000 | −0.814112 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.5000 | − | 23.3827i | −0.438691 | − | 0.759835i | 0.558898 | − | 0.829237i | \(-0.311224\pi\) |
−0.997589 | + | 0.0694014i | \(0.977891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | −0.486921 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.0000 | −0.486408 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5000 | + | 21.6506i | 0.404915 | + | 0.701333i | 0.994312 | − | 0.106511i | \(-0.0339679\pi\) |
−0.589397 | + | 0.807844i | \(0.700635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | + | 13.8564i | 0.258874 | + | 0.448383i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 28.0000 | 0.905111 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.0000 | − | 34.6410i | 0.644491 | − | 1.11629i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.50000 | − | 12.9904i | 0.241434 | − | 0.418175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.5000 | + | 38.9711i | 0.723551 | + | 1.25323i | 0.959568 | + | 0.281478i | \(0.0908248\pi\) |
−0.236016 | + | 0.971749i | \(0.575842\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.5000 | + | 7.79423i | −0.337309 | + | 0.250387i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.5000 | − | 30.3109i | −0.561602 | − | 0.972723i | −0.997357 | − | 0.0726575i | \(-0.976852\pi\) |
0.435755 | − | 0.900065i | \(-0.356481\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.00000 | − | 3.46410i | 0.0640513 | − | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −10.0000 | −0.319928 | −0.159964 | − | 0.987123i | \(-0.551138\pi\) | ||||
−0.159964 | + | 0.987123i | \(0.551138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | − | 10.3923i | 0.191761 | − | 0.332140i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.5000 | + | 38.9711i | 0.717639 | + | 1.24299i | 0.961933 | + | 0.273285i | \(0.0881103\pi\) |
−0.244294 | + | 0.969701i | \(0.578556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | + | 1.73205i | 0.0318626 | + | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.0000 | −0.794954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.50000 | + | 4.33013i | 0.0794151 | + | 0.137551i | 0.902998 | − | 0.429645i | \(-0.141361\pi\) |
−0.823583 | + | 0.567196i | \(0.808028\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.0000 | + | 17.3205i | 0.317340 | + | 0.549650i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.00000 | 0.221915 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5000 | − | 45.8993i | 0.839263 | − | 1.45365i | −0.0512480 | − | 0.998686i | \(-0.516320\pi\) |
0.890511 | − | 0.454961i | \(-0.150347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 50.0000 | 1.58193 |
(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 | 76.2.e.a.45.1 | ✓ | 2 | |
3.2 | odd | 2 | 684.2.k.b.577.1 | 2 | |||
4.3 | odd | 2 | 304.2.i.a.273.1 | 2 | |||
5.2 | odd | 4 | 1900.2.s.a.349.2 | 4 | |||
5.3 | odd | 4 | 1900.2.s.a.349.1 | 4 | |||
5.4 | even | 2 | 1900.2.i.a.501.1 | 2 | |||
8.3 | odd | 2 | 1216.2.i.g.577.1 | 2 | |||
8.5 | even | 2 | 1216.2.i.c.577.1 | 2 | |||
12.11 | even | 2 | 2736.2.s.g.577.1 | 2 | |||
19.7 | even | 3 | 1444.2.a.b.1.1 | 1 | |||
19.8 | odd | 6 | 1444.2.e.b.429.1 | 2 | |||
19.11 | even | 3 | inner | 76.2.e.a.49.1 | yes | 2 | |
19.12 | odd | 6 | 1444.2.a.c.1.1 | 1 | |||
19.18 | odd | 2 | 1444.2.e.b.653.1 | 2 | |||
57.11 | odd | 6 | 684.2.k.b.505.1 | 2 | |||
76.7 | odd | 6 | 5776.2.a.k.1.1 | 1 | |||
76.11 | odd | 6 | 304.2.i.a.49.1 | 2 | |||
76.31 | even | 6 | 5776.2.a.f.1.1 | 1 | |||
95.49 | even | 6 | 1900.2.i.a.201.1 | 2 | |||
95.68 | odd | 12 | 1900.2.s.a.49.2 | 4 | |||
95.87 | odd | 12 | 1900.2.s.a.49.1 | 4 | |||
152.11 | odd | 6 | 1216.2.i.g.961.1 | 2 | |||
152.125 | even | 6 | 1216.2.i.c.961.1 | 2 | |||
228.11 | even | 6 | 2736.2.s.g.1873.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.2.e.a.45.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
76.2.e.a.49.1 | yes | 2 | 19.11 | even | 3 | inner | |
304.2.i.a.49.1 | 2 | 76.11 | odd | 6 | |||
304.2.i.a.273.1 | 2 | 4.3 | odd | 2 | |||
684.2.k.b.505.1 | 2 | 57.11 | odd | 6 | |||
684.2.k.b.577.1 | 2 | 3.2 | odd | 2 | |||
1216.2.i.c.577.1 | 2 | 8.5 | even | 2 | |||
1216.2.i.c.961.1 | 2 | 152.125 | even | 6 | |||
1216.2.i.g.577.1 | 2 | 8.3 | odd | 2 | |||
1216.2.i.g.961.1 | 2 | 152.11 | odd | 6 | |||
1444.2.a.b.1.1 | 1 | 19.7 | even | 3 | |||
1444.2.a.c.1.1 | 1 | 19.12 | odd | 6 | |||
1444.2.e.b.429.1 | 2 | 19.8 | odd | 6 | |||
1444.2.e.b.653.1 | 2 | 19.18 | odd | 2 | |||
1900.2.i.a.201.1 | 2 | 95.49 | even | 6 | |||
1900.2.i.a.501.1 | 2 | 5.4 | even | 2 | |||
1900.2.s.a.49.1 | 4 | 95.87 | odd | 12 | |||
1900.2.s.a.49.2 | 4 | 95.68 | odd | 12 | |||
1900.2.s.a.349.1 | 4 | 5.3 | odd | 4 | |||
1900.2.s.a.349.2 | 4 | 5.2 | odd | 4 | |||
2736.2.s.g.577.1 | 2 | 12.11 | even | 2 | |||
2736.2.s.g.1873.1 | 2 | 228.11 | even | 6 | |||
5776.2.a.f.1.1 | 1 | 76.31 | even | 6 | |||
5776.2.a.k.1.1 | 1 | 76.7 | odd | 6 |