Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,3,Mod(23,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.23");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.899184872389\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 23.2 | ||
Root | \(0.500000 - 1.65831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.3.b.a.23.1 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.31662i | 1.65831i | 0.559017 | + | 0.829156i | \(0.311179\pi\) | ||||
−0.559017 | + | 0.829156i | \(0.688821\pi\) | |||||||
\(3\) | 3.00000 | 1.00000 | ||||||||
\(4\) | −7.00000 | −1.75000 | ||||||||
\(5\) | − 6.63325i | − 1.32665i | −0.748331 | − | 0.663325i | \(-0.769145\pi\) | ||||
0.748331 | − | 0.663325i | \(-0.230855\pi\) | |||||||
\(6\) | 9.94987i | 1.65831i | ||||||||
\(7\) | −8.00000 | −1.14286 | −0.571429 | − | 0.820652i | \(-0.693611\pi\) | ||||
−0.571429 | + | 0.820652i | \(0.693611\pi\) | |||||||
\(8\) | − 9.94987i | − 1.24373i | ||||||||
\(9\) | 9.00000 | 1.00000 | ||||||||
\(10\) | 22.0000 | 2.20000 | ||||||||
\(11\) | 3.31662i | 0.301511i | ||||||||
\(12\) | −21.0000 | −1.75000 | ||||||||
\(13\) | 4.00000 | 0.307692 | 0.153846 | − | 0.988095i | \(-0.450834\pi\) | ||||
0.153846 | + | 0.988095i | \(0.450834\pi\) | |||||||
\(14\) | − 26.5330i | − 1.89521i | ||||||||
\(15\) | − 19.8997i | − 1.32665i | ||||||||
\(16\) | 5.00000 | 0.312500 | ||||||||
\(17\) | 13.2665i | 0.780382i | 0.920734 | + | 0.390191i | \(0.127591\pi\) | ||||
−0.920734 | + | 0.390191i | \(0.872409\pi\) | |||||||
\(18\) | 29.8496i | 1.65831i | ||||||||
\(19\) | −6.00000 | −0.315789 | −0.157895 | − | 0.987456i | \(-0.550471\pi\) | ||||
−0.157895 | + | 0.987456i | \(0.550471\pi\) | |||||||
\(20\) | 46.4327i | 2.32164i | ||||||||
\(21\) | −24.0000 | −1.14286 | ||||||||
\(22\) | −11.0000 | −0.500000 | ||||||||
\(23\) | 6.63325i | 0.288402i | 0.989548 | + | 0.144201i | \(0.0460612\pi\) | ||||
−0.989548 | + | 0.144201i | \(0.953939\pi\) | |||||||
\(24\) | − 29.8496i | − 1.24373i | ||||||||
\(25\) | −19.0000 | −0.760000 | ||||||||
\(26\) | 13.2665i | 0.510250i | ||||||||
\(27\) | 27.0000 | 1.00000 | ||||||||
\(28\) | 56.0000 | 2.00000 | ||||||||
\(29\) | − 39.7995i | − 1.37240i | −0.727415 | − | 0.686198i | \(-0.759278\pi\) | ||||
0.727415 | − | 0.686198i | \(-0.240722\pi\) | |||||||
\(30\) | 66.0000 | 2.20000 | ||||||||
\(31\) | −26.0000 | −0.838710 | −0.419355 | − | 0.907822i | \(-0.637744\pi\) | ||||
−0.419355 | + | 0.907822i | \(0.637744\pi\) | |||||||
\(32\) | − 23.2164i | − 0.725512i | ||||||||
\(33\) | 9.94987i | 0.301511i | ||||||||
\(34\) | −44.0000 | −1.29412 | ||||||||
\(35\) | 53.0660i | 1.51617i | ||||||||
\(36\) | −63.0000 | −1.75000 | ||||||||
\(37\) | 30.0000 | 0.810811 | 0.405405 | − | 0.914137i | \(-0.367130\pi\) | ||||
0.405405 | + | 0.914137i | \(0.367130\pi\) | |||||||
\(38\) | − 19.8997i | − 0.523678i | ||||||||
\(39\) | 12.0000 | 0.307692 | ||||||||
\(40\) | −66.0000 | −1.65000 | ||||||||
\(41\) | 13.2665i | 0.323573i | 0.986826 | + | 0.161787i | \(0.0517256\pi\) | ||||
−0.986826 | + | 0.161787i | \(0.948274\pi\) | |||||||
\(42\) | − 79.5990i | − 1.89521i | ||||||||
\(43\) | 42.0000 | 0.976744 | 0.488372 | − | 0.872635i | \(-0.337591\pi\) | ||||
0.488372 | + | 0.872635i | \(0.337591\pi\) | |||||||
\(44\) | − 23.2164i | − 0.527645i | ||||||||
\(45\) | − 59.6992i | − 1.32665i | ||||||||
\(46\) | −22.0000 | −0.478261 | ||||||||
\(47\) | 86.2322i | 1.83473i | 0.398049 | + | 0.917364i | \(0.369688\pi\) | ||||
−0.398049 | + | 0.917364i | \(0.630312\pi\) | |||||||
\(48\) | 15.0000 | 0.312500 | ||||||||
\(49\) | 15.0000 | 0.306122 | ||||||||
\(50\) | − 63.0159i | − 1.26032i | ||||||||
\(51\) | 39.7995i | 0.780382i | ||||||||
\(52\) | −28.0000 | −0.538462 | ||||||||
\(53\) | − 59.6992i | − 1.12640i | −0.826320 | − | 0.563200i | \(-0.809570\pi\) | ||||
0.826320 | − | 0.563200i | \(-0.190430\pi\) | |||||||
\(54\) | 89.5489i | 1.65831i | ||||||||
\(55\) | 22.0000 | 0.400000 | ||||||||
\(56\) | 79.5990i | 1.42141i | ||||||||
\(57\) | −18.0000 | −0.315789 | ||||||||
\(58\) | 132.000 | 2.27586 | ||||||||
\(59\) | 66.3325i | 1.12428i | 0.827042 | + | 0.562140i | \(0.190022\pi\) | ||||
−0.827042 | + | 0.562140i | \(0.809978\pi\) | |||||||
\(60\) | 139.298i | 2.32164i | ||||||||
\(61\) | 12.0000 | 0.196721 | 0.0983607 | − | 0.995151i | \(-0.468640\pi\) | ||||
0.0983607 | + | 0.995151i | \(0.468640\pi\) | |||||||
\(62\) | − 86.2322i | − 1.39084i | ||||||||
\(63\) | −72.0000 | −1.14286 | ||||||||
\(64\) | 97.0000 | 1.51562 | ||||||||
\(65\) | − 26.5330i | − 0.408200i | ||||||||
\(66\) | −33.0000 | −0.500000 | ||||||||
\(67\) | 2.00000 | 0.0298507 | 0.0149254 | − | 0.999889i | \(-0.495249\pi\) | ||||
0.0149254 | + | 0.999889i | \(0.495249\pi\) | |||||||
\(68\) | − 92.8655i | − 1.36567i | ||||||||
\(69\) | 19.8997i | 0.288402i | ||||||||
\(70\) | −176.000 | −2.51429 | ||||||||
\(71\) | − 59.6992i | − 0.840834i | −0.907331 | − | 0.420417i | \(-0.861884\pi\) | ||||
0.907331 | − | 0.420417i | \(-0.138116\pi\) | |||||||
\(72\) | − 89.5489i | − 1.24373i | ||||||||
\(73\) | −74.0000 | −1.01370 | −0.506849 | − | 0.862035i | \(-0.669190\pi\) | ||||
−0.506849 | + | 0.862035i | \(0.669190\pi\) | |||||||
\(74\) | 99.4987i | 1.34458i | ||||||||
\(75\) | −57.0000 | −0.760000 | ||||||||
\(76\) | 42.0000 | 0.552632 | ||||||||
\(77\) | − 26.5330i | − 0.344584i | ||||||||
\(78\) | 39.7995i | 0.510250i | ||||||||
\(79\) | −40.0000 | −0.506329 | −0.253165 | − | 0.967423i | \(-0.581471\pi\) | ||||
−0.253165 | + | 0.967423i | \(0.581471\pi\) | |||||||
\(80\) | − 33.1662i | − 0.414578i | ||||||||
\(81\) | 81.0000 | 1.00000 | ||||||||
\(82\) | −44.0000 | −0.536585 | ||||||||
\(83\) | − 39.7995i | − 0.479512i | −0.970833 | − | 0.239756i | \(-0.922933\pi\) | ||||
0.970833 | − | 0.239756i | \(-0.0770674\pi\) | |||||||
\(84\) | 168.000 | 2.00000 | ||||||||
\(85\) | 88.0000 | 1.03529 | ||||||||
\(86\) | 139.298i | 1.61975i | ||||||||
\(87\) | − 119.398i | − 1.37240i | ||||||||
\(88\) | 33.0000 | 0.375000 | ||||||||
\(89\) | − 119.398i | − 1.34156i | −0.741658 | − | 0.670778i | \(-0.765960\pi\) | ||||
0.741658 | − | 0.670778i | \(-0.234040\pi\) | |||||||
\(90\) | 198.000 | 2.20000 | ||||||||
\(91\) | −32.0000 | −0.351648 | ||||||||
\(92\) | − 46.4327i | − 0.504704i | ||||||||
\(93\) | −78.0000 | −0.838710 | ||||||||
\(94\) | −286.000 | −3.04255 | ||||||||
\(95\) | 39.7995i | 0.418942i | ||||||||
\(96\) | − 69.6491i | − 0.725512i | ||||||||
\(97\) | 62.0000 | 0.639175 | 0.319588 | − | 0.947557i | \(-0.396456\pi\) | ||||
0.319588 | + | 0.947557i | \(0.396456\pi\) | |||||||
\(98\) | 49.7494i | 0.507647i | ||||||||
\(99\) | 29.8496i | 0.301511i | ||||||||
\(100\) | 133.000 | 1.33000 | ||||||||
\(101\) | 106.132i | 1.05081i | 0.850852 | + | 0.525406i | \(0.176087\pi\) | ||||
−0.850852 | + | 0.525406i | \(0.823913\pi\) | |||||||
\(102\) | −132.000 | −1.29412 | ||||||||
\(103\) | 74.0000 | 0.718447 | 0.359223 | − | 0.933252i | \(-0.383042\pi\) | ||||
0.359223 | + | 0.933252i | \(0.383042\pi\) | |||||||
\(104\) | − 39.7995i | − 0.382687i | ||||||||
\(105\) | 159.198i | 1.51617i | ||||||||
\(106\) | 198.000 | 1.86792 | ||||||||
\(107\) | − 39.7995i | − 0.371958i | −0.982554 | − | 0.185979i | \(-0.940454\pi\) | ||||
0.982554 | − | 0.185979i | \(-0.0595456\pi\) | |||||||
\(108\) | −189.000 | −1.75000 | ||||||||
\(109\) | −200.000 | −1.83486 | −0.917431 | − | 0.397894i | \(-0.869741\pi\) | ||||
−0.917431 | + | 0.397894i | \(0.869741\pi\) | |||||||
\(110\) | 72.9657i | 0.663325i | ||||||||
\(111\) | 90.0000 | 0.810811 | ||||||||
\(112\) | −40.0000 | −0.357143 | ||||||||
\(113\) | − 39.7995i | − 0.352208i | −0.984372 | − | 0.176104i | \(-0.943651\pi\) | ||||
0.984372 | − | 0.176104i | \(-0.0563495\pi\) | |||||||
\(114\) | − 59.6992i | − 0.523678i | ||||||||
\(115\) | 44.0000 | 0.382609 | ||||||||
\(116\) | 278.596i | 2.40169i | ||||||||
\(117\) | 36.0000 | 0.307692 | ||||||||
\(118\) | −220.000 | −1.86441 | ||||||||
\(119\) | − 106.132i | − 0.891865i | ||||||||
\(120\) | −198.000 | −1.65000 | ||||||||
\(121\) | −11.0000 | −0.0909091 | ||||||||
\(122\) | 39.7995i | 0.326225i | ||||||||
\(123\) | 39.7995i | 0.323573i | ||||||||
\(124\) | 182.000 | 1.46774 | ||||||||
\(125\) | − 39.7995i | − 0.318396i | ||||||||
\(126\) | − 238.797i | − 1.89521i | ||||||||
\(127\) | 188.000 | 1.48031 | 0.740157 | − | 0.672434i | \(-0.234751\pi\) | ||||
0.740157 | + | 0.672434i | \(0.234751\pi\) | |||||||
\(128\) | 228.847i | 1.78787i | ||||||||
\(129\) | 126.000 | 0.976744 | ||||||||
\(130\) | 88.0000 | 0.676923 | ||||||||
\(131\) | 39.7995i | 0.303813i | 0.988395 | + | 0.151906i | \(0.0485413\pi\) | ||||
−0.988395 | + | 0.151906i | \(0.951459\pi\) | |||||||
\(132\) | − 69.6491i | − 0.527645i | ||||||||
\(133\) | 48.0000 | 0.360902 | ||||||||
\(134\) | 6.63325i | 0.0495019i | ||||||||
\(135\) | − 179.098i | − 1.32665i | ||||||||
\(136\) | 132.000 | 0.970588 | ||||||||
\(137\) | 106.132i | 0.774686i | 0.921936 | + | 0.387343i | \(0.126607\pi\) | ||||
−0.921936 | + | 0.387343i | \(0.873393\pi\) | |||||||
\(138\) | −66.0000 | −0.478261 | ||||||||
\(139\) | −74.0000 | −0.532374 | −0.266187 | − | 0.963921i | \(-0.585764\pi\) | ||||
−0.266187 | + | 0.963921i | \(0.585764\pi\) | |||||||
\(140\) | − 371.462i | − 2.65330i | ||||||||
\(141\) | 258.697i | 1.83473i | ||||||||
\(142\) | 198.000 | 1.39437 | ||||||||
\(143\) | 13.2665i | 0.0927727i | ||||||||
\(144\) | 45.0000 | 0.312500 | ||||||||
\(145\) | −264.000 | −1.82069 | ||||||||
\(146\) | − 245.430i | − 1.68103i | ||||||||
\(147\) | 45.0000 | 0.306122 | ||||||||
\(148\) | −210.000 | −1.41892 | ||||||||
\(149\) | − 92.8655i | − 0.623258i | −0.950204 | − | 0.311629i | \(-0.899125\pi\) | ||||
0.950204 | − | 0.311629i | \(-0.100875\pi\) | |||||||
\(150\) | − 189.048i | − 1.26032i | ||||||||
\(151\) | −160.000 | −1.05960 | −0.529801 | − | 0.848122i | \(-0.677734\pi\) | ||||
−0.529801 | + | 0.848122i | \(0.677734\pi\) | |||||||
\(152\) | 59.6992i | 0.392758i | ||||||||
\(153\) | 119.398i | 0.780382i | ||||||||
\(154\) | 88.0000 | 0.571429 | ||||||||
\(155\) | 172.464i | 1.11267i | ||||||||
\(156\) | −84.0000 | −0.538462 | ||||||||
\(157\) | 182.000 | 1.15924 | 0.579618 | − | 0.814888i | \(-0.303202\pi\) | ||||
0.579618 | + | 0.814888i | \(0.303202\pi\) | |||||||
\(158\) | − 132.665i | − 0.839652i | ||||||||
\(159\) | − 179.098i | − 1.12640i | ||||||||
\(160\) | −154.000 | −0.962500 | ||||||||
\(161\) | − 53.0660i | − 0.329602i | ||||||||
\(162\) | 268.647i | 1.65831i | ||||||||
\(163\) | −290.000 | −1.77914 | −0.889571 | − | 0.456798i | \(-0.848996\pi\) | ||||
−0.889571 | + | 0.456798i | \(0.848996\pi\) | |||||||
\(164\) | − 92.8655i | − 0.566253i | ||||||||
\(165\) | 66.0000 | 0.400000 | ||||||||
\(166\) | 132.000 | 0.795181 | ||||||||
\(167\) | − 238.797i | − 1.42992i | −0.699164 | − | 0.714961i | \(-0.746444\pi\) | ||||
0.699164 | − | 0.714961i | \(-0.253556\pi\) | |||||||
\(168\) | 238.797i | 1.42141i | ||||||||
\(169\) | −153.000 | −0.905325 | ||||||||
\(170\) | 291.863i | 1.71684i | ||||||||
\(171\) | −54.0000 | −0.315789 | ||||||||
\(172\) | −294.000 | −1.70930 | ||||||||
\(173\) | 198.997i | 1.15027i | 0.818057 | + | 0.575137i | \(0.195051\pi\) | ||||
−0.818057 | + | 0.575137i | \(0.804949\pi\) | |||||||
\(174\) | 396.000 | 2.27586 | ||||||||
\(175\) | 152.000 | 0.868571 | ||||||||
\(176\) | 16.5831i | 0.0942223i | ||||||||
\(177\) | 198.997i | 1.12428i | ||||||||
\(178\) | 396.000 | 2.22472 | ||||||||
\(179\) | 198.997i | 1.11172i | 0.831277 | + | 0.555859i | \(0.187611\pi\) | ||||
−0.831277 | + | 0.555859i | \(0.812389\pi\) | |||||||
\(180\) | 417.895i | 2.32164i | ||||||||
\(181\) | 10.0000 | 0.0552486 | 0.0276243 | − | 0.999618i | \(-0.491206\pi\) | ||||
0.0276243 | + | 0.999618i | \(0.491206\pi\) | |||||||
\(182\) | − 106.132i | − 0.583143i | ||||||||
\(183\) | 36.0000 | 0.196721 | ||||||||
\(184\) | 66.0000 | 0.358696 | ||||||||
\(185\) | − 198.997i | − 1.07566i | ||||||||
\(186\) | − 258.697i | − 1.39084i | ||||||||
\(187\) | −44.0000 | −0.235294 | ||||||||
\(188\) | − 603.626i | − 3.21078i | ||||||||
\(189\) | −216.000 | −1.14286 | ||||||||
\(190\) | −132.000 | −0.694737 | ||||||||
\(191\) | − 112.765i | − 0.590394i | −0.955436 | − | 0.295197i | \(-0.904615\pi\) | ||||
0.955436 | − | 0.295197i | \(-0.0953853\pi\) | |||||||
\(192\) | 291.000 | 1.51562 | ||||||||
\(193\) | 298.000 | 1.54404 | 0.772021 | − | 0.635597i | \(-0.219246\pi\) | ||||
0.772021 | + | 0.635597i | \(0.219246\pi\) | |||||||
\(194\) | 205.631i | 1.05995i | ||||||||
\(195\) | − 79.5990i | − 0.408200i | ||||||||
\(196\) | −105.000 | −0.535714 | ||||||||
\(197\) | 132.665i | 0.673426i | 0.941607 | + | 0.336713i | \(0.109315\pi\) | ||||
−0.941607 | + | 0.336713i | \(0.890685\pi\) | |||||||
\(198\) | −99.0000 | −0.500000 | ||||||||
\(199\) | −42.0000 | −0.211055 | −0.105528 | − | 0.994416i | \(-0.533653\pi\) | ||||
−0.105528 | + | 0.994416i | \(0.533653\pi\) | |||||||
\(200\) | 189.048i | 0.945238i | ||||||||
\(201\) | 6.00000 | 0.0298507 | ||||||||
\(202\) | −352.000 | −1.74257 | ||||||||
\(203\) | 318.396i | 1.56845i | ||||||||
\(204\) | − 278.596i | − 1.36567i | ||||||||
\(205\) | 88.0000 | 0.429268 | ||||||||
\(206\) | 245.430i | 1.19141i | ||||||||
\(207\) | 59.6992i | 0.288402i | ||||||||
\(208\) | 20.0000 | 0.0961538 | ||||||||
\(209\) | − 19.8997i | − 0.0952141i | ||||||||
\(210\) | −528.000 | −2.51429 | ||||||||
\(211\) | 246.000 | 1.16588 | 0.582938 | − | 0.812516i | \(-0.301903\pi\) | ||||
0.582938 | + | 0.812516i | \(0.301903\pi\) | |||||||
\(212\) | 417.895i | 1.97120i | ||||||||
\(213\) | − 179.098i | − 0.840834i | ||||||||
\(214\) | 132.000 | 0.616822 | ||||||||
\(215\) | − 278.596i | − 1.29580i | ||||||||
\(216\) | − 268.647i | − 1.24373i | ||||||||
\(217\) | 208.000 | 0.958525 | ||||||||
\(218\) | − 663.325i | − 3.04278i | ||||||||
\(219\) | −222.000 | −1.01370 | ||||||||
\(220\) | −154.000 | −0.700000 | ||||||||
\(221\) | 53.0660i | 0.240118i | ||||||||
\(222\) | 298.496i | 1.34458i | ||||||||
\(223\) | −302.000 | −1.35426 | −0.677130 | − | 0.735863i | \(-0.736777\pi\) | ||||
−0.677130 | + | 0.735863i | \(0.736777\pi\) | |||||||
\(224\) | 185.731i | 0.829156i | ||||||||
\(225\) | −171.000 | −0.760000 | ||||||||
\(226\) | 132.000 | 0.584071 | ||||||||
\(227\) | − 198.997i | − 0.876641i | −0.898819 | − | 0.438320i | \(-0.855574\pi\) | ||||
0.898819 | − | 0.438320i | \(-0.144426\pi\) | |||||||
\(228\) | 126.000 | 0.552632 | ||||||||
\(229\) | 150.000 | 0.655022 | 0.327511 | − | 0.944847i | \(-0.393790\pi\) | ||||
0.327511 | + | 0.944847i | \(0.393790\pi\) | |||||||
\(230\) | 145.931i | 0.634485i | ||||||||
\(231\) | − 79.5990i | − 0.344584i | ||||||||
\(232\) | −396.000 | −1.70690 | ||||||||
\(233\) | − 437.794i | − 1.87895i | −0.342623 | − | 0.939473i | \(-0.611315\pi\) | ||||
0.342623 | − | 0.939473i | \(-0.388685\pi\) | |||||||
\(234\) | 119.398i | 0.510250i | ||||||||
\(235\) | 572.000 | 2.43404 | ||||||||
\(236\) | − 464.327i | − 1.96749i | ||||||||
\(237\) | −120.000 | −0.506329 | ||||||||
\(238\) | 352.000 | 1.47899 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | − 99.4987i | − 0.414578i | ||||||||
\(241\) | 130.000 | 0.539419 | 0.269710 | − | 0.962942i | \(-0.413072\pi\) | ||||
0.269710 | + | 0.962942i | \(0.413072\pi\) | |||||||
\(242\) | − 36.4829i | − 0.150756i | ||||||||
\(243\) | 243.000 | 1.00000 | ||||||||
\(244\) | −84.0000 | −0.344262 | ||||||||
\(245\) | − 99.4987i | − 0.406117i | ||||||||
\(246\) | −132.000 | −0.536585 | ||||||||
\(247\) | −24.0000 | −0.0971660 | ||||||||
\(248\) | 258.697i | 1.04313i | ||||||||
\(249\) | − 119.398i | − 0.479512i | ||||||||
\(250\) | 132.000 | 0.528000 | ||||||||
\(251\) | 291.863i | 1.16280i | 0.813618 | + | 0.581400i | \(0.197495\pi\) | ||||
−0.813618 | + | 0.581400i | \(0.802505\pi\) | |||||||
\(252\) | 504.000 | 2.00000 | ||||||||
\(253\) | −22.0000 | −0.0869565 | ||||||||
\(254\) | 623.525i | 2.45482i | ||||||||
\(255\) | 264.000 | 1.03529 | ||||||||
\(256\) | −371.000 | −1.44922 | ||||||||
\(257\) | 490.860i | 1.90996i | 0.296665 | + | 0.954981i | \(0.404125\pi\) | ||||
−0.296665 | + | 0.954981i | \(0.595875\pi\) | |||||||
\(258\) | 417.895i | 1.61975i | ||||||||
\(259\) | −240.000 | −0.926641 | ||||||||
\(260\) | 185.731i | 0.714350i | ||||||||
\(261\) | − 358.195i | − 1.37240i | ||||||||
\(262\) | −132.000 | −0.503817 | ||||||||
\(263\) | 225.530i | 0.857530i | 0.903416 | + | 0.428765i | \(0.141051\pi\) | ||||
−0.903416 | + | 0.428765i | \(0.858949\pi\) | |||||||
\(264\) | 99.0000 | 0.375000 | ||||||||
\(265\) | −396.000 | −1.49434 | ||||||||
\(266\) | 159.198i | 0.598489i | ||||||||
\(267\) | − 358.195i | − 1.34156i | ||||||||
\(268\) | −14.0000 | −0.0522388 | ||||||||
\(269\) | 72.9657i | 0.271248i | 0.990760 | + | 0.135624i | \(0.0433039\pi\) | ||||
−0.990760 | + | 0.135624i | \(0.956696\pi\) | |||||||
\(270\) | 594.000 | 2.20000 | ||||||||
\(271\) | −448.000 | −1.65314 | −0.826568 | − | 0.562836i | \(-0.809710\pi\) | ||||
−0.826568 | + | 0.562836i | \(0.809710\pi\) | |||||||
\(272\) | 66.3325i | 0.243869i | ||||||||
\(273\) | −96.0000 | −0.351648 | ||||||||
\(274\) | −352.000 | −1.28467 | ||||||||
\(275\) | − 63.0159i | − 0.229149i | ||||||||
\(276\) | − 139.298i | − 0.504704i | ||||||||
\(277\) | −260.000 | −0.938628 | −0.469314 | − | 0.883031i | \(-0.655499\pi\) | ||||
−0.469314 | + | 0.883031i | \(0.655499\pi\) | |||||||
\(278\) | − 245.430i | − 0.882843i | ||||||||
\(279\) | −234.000 | −0.838710 | ||||||||
\(280\) | 528.000 | 1.88571 | ||||||||
\(281\) | − 198.997i | − 0.708176i | −0.935212 | − | 0.354088i | \(-0.884791\pi\) | ||||
0.935212 | − | 0.354088i | \(-0.115209\pi\) | |||||||
\(282\) | −858.000 | −3.04255 | ||||||||
\(283\) | −50.0000 | −0.176678 | −0.0883392 | − | 0.996090i | \(-0.528156\pi\) | ||||
−0.0883392 | + | 0.996090i | \(0.528156\pi\) | |||||||
\(284\) | 417.895i | 1.47146i | ||||||||
\(285\) | 119.398i | 0.418942i | ||||||||
\(286\) | −44.0000 | −0.153846 | ||||||||
\(287\) | − 106.132i | − 0.369798i | ||||||||
\(288\) | − 208.947i | − 0.725512i | ||||||||
\(289\) | 113.000 | 0.391003 | ||||||||
\(290\) | − 875.589i | − 3.01927i | ||||||||
\(291\) | 186.000 | 0.639175 | ||||||||
\(292\) | 518.000 | 1.77397 | ||||||||
\(293\) | 477.594i | 1.63001i | 0.579451 | + | 0.815007i | \(0.303267\pi\) | ||||
−0.579451 | + | 0.815007i | \(0.696733\pi\) | |||||||
\(294\) | 149.248i | 0.507647i | ||||||||
\(295\) | 440.000 | 1.49153 | ||||||||
\(296\) | − 298.496i | − 1.00843i | ||||||||
\(297\) | 89.5489i | 0.301511i | ||||||||
\(298\) | 308.000 | 1.03356 | ||||||||
\(299\) | 26.5330i | 0.0887391i | ||||||||
\(300\) | 399.000 | 1.33000 | ||||||||
\(301\) | −336.000 | −1.11628 | ||||||||
\(302\) | − 530.660i | − 1.75715i | ||||||||
\(303\) | 318.396i | 1.05081i | ||||||||
\(304\) | −30.0000 | −0.0986842 | ||||||||
\(305\) | − 79.5990i | − 0.260980i | ||||||||
\(306\) | −396.000 | −1.29412 | ||||||||
\(307\) | 86.0000 | 0.280130 | 0.140065 | − | 0.990142i | \(-0.455269\pi\) | ||||
0.140065 | + | 0.990142i | \(0.455269\pi\) | |||||||
\(308\) | 185.731i | 0.603023i | ||||||||
\(309\) | 222.000 | 0.718447 | ||||||||
\(310\) | −572.000 | −1.84516 | ||||||||
\(311\) | 19.8997i | 0.0639863i | 0.999488 | + | 0.0319932i | \(0.0101855\pi\) | ||||
−0.999488 | + | 0.0319932i | \(0.989815\pi\) | |||||||
\(312\) | − 119.398i | − 0.382687i | ||||||||
\(313\) | 98.0000 | 0.313099 | 0.156550 | − | 0.987670i | \(-0.449963\pi\) | ||||
0.156550 | + | 0.987670i | \(0.449963\pi\) | |||||||
\(314\) | 603.626i | 1.92237i | ||||||||
\(315\) | 477.594i | 1.51617i | ||||||||
\(316\) | 280.000 | 0.886076 | ||||||||
\(317\) | 311.763i | 0.983479i | 0.870742 | + | 0.491739i | \(0.163639\pi\) | ||||
−0.870742 | + | 0.491739i | \(0.836361\pi\) | |||||||
\(318\) | 594.000 | 1.86792 | ||||||||
\(319\) | 132.000 | 0.413793 | ||||||||
\(320\) | − 643.425i | − 2.01070i | ||||||||
\(321\) | − 119.398i | − 0.371958i | ||||||||
\(322\) | 176.000 | 0.546584 | ||||||||
\(323\) | − 79.5990i | − 0.246437i | ||||||||
\(324\) | −567.000 | −1.75000 | ||||||||
\(325\) | −76.0000 | −0.233846 | ||||||||
\(326\) | − 961.821i | − 2.95037i | ||||||||
\(327\) | −600.000 | −1.83486 | ||||||||
\(328\) | 132.000 | 0.402439 | ||||||||
\(329\) | − 689.858i | − 2.09683i | ||||||||
\(330\) | 218.897i | 0.663325i | ||||||||
\(331\) | −218.000 | −0.658610 | −0.329305 | − | 0.944224i | \(-0.606814\pi\) | ||||
−0.329305 | + | 0.944224i | \(0.606814\pi\) | |||||||
\(332\) | 278.596i | 0.839146i | ||||||||
\(333\) | 270.000 | 0.810811 | ||||||||
\(334\) | 792.000 | 2.37126 | ||||||||
\(335\) | − 13.2665i | − 0.0396015i | ||||||||
\(336\) | −120.000 | −0.357143 | ||||||||
\(337\) | 278.000 | 0.824926 | 0.412463 | − | 0.910974i | \(-0.364669\pi\) | ||||
0.412463 | + | 0.910974i | \(0.364669\pi\) | |||||||
\(338\) | − 507.444i | − 1.50131i | ||||||||
\(339\) | − 119.398i | − 0.352208i | ||||||||
\(340\) | −616.000 | −1.81176 | ||||||||
\(341\) | − 86.2322i | − 0.252880i | ||||||||
\(342\) | − 179.098i | − 0.523678i | ||||||||
\(343\) | 272.000 | 0.793003 | ||||||||
\(344\) | − 417.895i | − 1.21481i | ||||||||
\(345\) | 132.000 | 0.382609 | ||||||||
\(346\) | −660.000 | −1.90751 | ||||||||
\(347\) | 331.662i | 0.955800i | 0.878414 | + | 0.477900i | \(0.158602\pi\) | ||||
−0.878414 | + | 0.477900i | \(0.841398\pi\) | |||||||
\(348\) | 835.789i | 2.40169i | ||||||||
\(349\) | 324.000 | 0.928367 | 0.464183 | − | 0.885739i | \(-0.346348\pi\) | ||||
0.464183 | + | 0.885739i | \(0.346348\pi\) | |||||||
\(350\) | 504.127i | 1.44036i | ||||||||
\(351\) | 108.000 | 0.307692 | ||||||||
\(352\) | 77.0000 | 0.218750 | ||||||||
\(353\) | 397.995i | 1.12746i | 0.825958 | + | 0.563732i | \(0.190635\pi\) | ||||
−0.825958 | + | 0.563732i | \(0.809365\pi\) | |||||||
\(354\) | −660.000 | −1.86441 | ||||||||
\(355\) | −396.000 | −1.11549 | ||||||||
\(356\) | 835.789i | 2.34772i | ||||||||
\(357\) | − 318.396i | − 0.891865i | ||||||||
\(358\) | −660.000 | −1.84358 | ||||||||
\(359\) | − 305.129i | − 0.849943i | −0.905207 | − | 0.424971i | \(-0.860284\pi\) | ||||
0.905207 | − | 0.424971i | \(-0.139716\pi\) | |||||||
\(360\) | −594.000 | −1.65000 | ||||||||
\(361\) | −325.000 | −0.900277 | ||||||||
\(362\) | 33.1662i | 0.0916195i | ||||||||
\(363\) | −33.0000 | −0.0909091 | ||||||||
\(364\) | 224.000 | 0.615385 | ||||||||
\(365\) | 490.860i | 1.34482i | ||||||||
\(366\) | 119.398i | 0.326225i | ||||||||
\(367\) | −278.000 | −0.757493 | −0.378747 | − | 0.925500i | \(-0.623645\pi\) | ||||
−0.378747 | + | 0.925500i | \(0.623645\pi\) | |||||||
\(368\) | 33.1662i | 0.0901257i | ||||||||
\(369\) | 119.398i | 0.323573i | ||||||||
\(370\) | 660.000 | 1.78378 | ||||||||
\(371\) | 477.594i | 1.28732i | ||||||||
\(372\) | 546.000 | 1.46774 | ||||||||
\(373\) | −68.0000 | −0.182306 | −0.0911528 | − | 0.995837i | \(-0.529055\pi\) | ||||
−0.0911528 | + | 0.995837i | \(0.529055\pi\) | |||||||
\(374\) | − 145.931i | − 0.390191i | ||||||||
\(375\) | − 119.398i | − 0.318396i | ||||||||
\(376\) | 858.000 | 2.28191 | ||||||||
\(377\) | − 159.198i | − 0.422276i | ||||||||
\(378\) | − 716.391i | − 1.89521i | ||||||||
\(379\) | 670.000 | 1.76781 | 0.883905 | − | 0.467666i | \(-0.154905\pi\) | ||||
0.883905 | + | 0.467666i | \(0.154905\pi\) | |||||||
\(380\) | − 278.596i | − 0.733149i | ||||||||
\(381\) | 564.000 | 1.48031 | ||||||||
\(382\) | 374.000 | 0.979058 | ||||||||
\(383\) | − 33.1662i | − 0.0865959i | −0.999062 | − | 0.0432980i | \(-0.986214\pi\) | ||||
0.999062 | − | 0.0432980i | \(-0.0137865\pi\) | |||||||
\(384\) | 686.541i | 1.78787i | ||||||||
\(385\) | −176.000 | −0.457143 | ||||||||
\(386\) | 988.354i | 2.56050i | ||||||||
\(387\) | 378.000 | 0.976744 | ||||||||
\(388\) | −434.000 | −1.11856 | ||||||||
\(389\) | − 417.895i | − 1.07428i | −0.843493 | − | 0.537140i | \(-0.819505\pi\) | ||||
0.843493 | − | 0.537140i | \(-0.180495\pi\) | |||||||
\(390\) | 264.000 | 0.676923 | ||||||||
\(391\) | −88.0000 | −0.225064 | ||||||||
\(392\) | − 149.248i | − 0.380735i | ||||||||
\(393\) | 119.398i | 0.303813i | ||||||||
\(394\) | −440.000 | −1.11675 | ||||||||
\(395\) | 265.330i | 0.671721i | ||||||||
\(396\) | − 208.947i | − 0.527645i | ||||||||
\(397\) | −86.0000 | −0.216625 | −0.108312 | − | 0.994117i | \(-0.534545\pi\) | ||||
−0.108312 | + | 0.994117i | \(0.534545\pi\) | |||||||
\(398\) | − 139.298i | − 0.349996i | ||||||||
\(399\) | 144.000 | 0.360902 | ||||||||
\(400\) | −95.0000 | −0.237500 | ||||||||
\(401\) | − 252.063i | − 0.628587i | −0.949326 | − | 0.314294i | \(-0.898232\pi\) | ||||
0.949326 | − | 0.314294i | \(-0.101768\pi\) | |||||||
\(402\) | 19.8997i | 0.0495019i | ||||||||
\(403\) | −104.000 | −0.258065 | ||||||||
\(404\) | − 742.924i | − 1.83892i | ||||||||
\(405\) | − 537.293i | − 1.32665i | ||||||||
\(406\) | −1056.00 | −2.60099 | ||||||||
\(407\) | 99.4987i | 0.244469i | ||||||||
\(408\) | 396.000 | 0.970588 | ||||||||
\(409\) | 510.000 | 1.24694 | 0.623472 | − | 0.781846i | \(-0.285722\pi\) | ||||
0.623472 | + | 0.781846i | \(0.285722\pi\) | |||||||
\(410\) | 291.863i | 0.711861i | ||||||||
\(411\) | 318.396i | 0.774686i | ||||||||
\(412\) | −518.000 | −1.25728 | ||||||||
\(413\) | − 530.660i | − 1.28489i | ||||||||
\(414\) | −198.000 | −0.478261 | ||||||||
\(415\) | −264.000 | −0.636145 | ||||||||
\(416\) | − 92.8655i | − 0.223234i | ||||||||
\(417\) | −222.000 | −0.532374 | ||||||||
\(418\) | 66.0000 | 0.157895 | ||||||||
\(419\) | − 530.660i | − 1.26649i | −0.773951 | − | 0.633246i | \(-0.781722\pi\) | ||||
0.773951 | − | 0.633246i | \(-0.218278\pi\) | |||||||
\(420\) | − 1114.39i | − 2.65330i | ||||||||
\(421\) | −170.000 | −0.403800 | −0.201900 | − | 0.979406i | \(-0.564712\pi\) | ||||
−0.201900 | + | 0.979406i | \(0.564712\pi\) | |||||||
\(422\) | 815.890i | 1.93339i | ||||||||
\(423\) | 776.090i | 1.83473i | ||||||||
\(424\) | −594.000 | −1.40094 | ||||||||
\(425\) | − 252.063i | − 0.593091i | ||||||||
\(426\) | 594.000 | 1.39437 | ||||||||
\(427\) | −96.0000 | −0.224824 | ||||||||
\(428\) | 278.596i | 0.650926i | ||||||||
\(429\) | 39.7995i | 0.0927727i | ||||||||
\(430\) | 924.000 | 2.14884 | ||||||||
\(431\) | 278.596i | 0.646396i | 0.946331 | + | 0.323198i | \(0.104758\pi\) | ||||
−0.946331 | + | 0.323198i | \(0.895242\pi\) | |||||||
\(432\) | 135.000 | 0.312500 | ||||||||
\(433\) | −542.000 | −1.25173 | −0.625866 | − | 0.779931i | \(-0.715254\pi\) | ||||
−0.625866 | + | 0.779931i | \(0.715254\pi\) | |||||||
\(434\) | 689.858i | 1.58953i | ||||||||
\(435\) | −792.000 | −1.82069 | ||||||||
\(436\) | 1400.00 | 3.21101 | ||||||||
\(437\) | − 39.7995i | − 0.0910744i | ||||||||
\(438\) | − 736.291i | − 1.68103i | ||||||||
\(439\) | 328.000 | 0.747153 | 0.373576 | − | 0.927599i | \(-0.378131\pi\) | ||||
0.373576 | + | 0.927599i | \(0.378131\pi\) | |||||||
\(440\) | − 218.897i | − 0.497494i | ||||||||
\(441\) | 135.000 | 0.306122 | ||||||||
\(442\) | −176.000 | −0.398190 | ||||||||
\(443\) | 132.665i | 0.299470i | 0.988726 | + | 0.149735i | \(0.0478420\pi\) | ||||
−0.988726 | + | 0.149735i | \(0.952158\pi\) | |||||||
\(444\) | −630.000 | −1.41892 | ||||||||
\(445\) | −792.000 | −1.77978 | ||||||||
\(446\) | − 1001.62i | − 2.24579i | ||||||||
\(447\) | − 278.596i | − 0.623258i | ||||||||
\(448\) | −776.000 | −1.73214 | ||||||||
\(449\) | − 451.061i | − 1.00459i | −0.864696 | − | 0.502295i | \(-0.832489\pi\) | ||||
0.864696 | − | 0.502295i | \(-0.167511\pi\) | |||||||
\(450\) | − 567.143i | − 1.26032i | ||||||||
\(451\) | −44.0000 | −0.0975610 | ||||||||
\(452\) | 278.596i | 0.616364i | ||||||||
\(453\) | −480.000 | −1.05960 | ||||||||
\(454\) | 660.000 | 1.45374 | ||||||||
\(455\) | 212.264i | 0.466514i | ||||||||
\(456\) | 179.098i | 0.392758i | ||||||||
\(457\) | 342.000 | 0.748359 | 0.374179 | − | 0.927356i | \(-0.377924\pi\) | ||||
0.374179 | + | 0.927356i | \(0.377924\pi\) | |||||||
\(458\) | 497.494i | 1.08623i | ||||||||
\(459\) | 358.195i | 0.780382i | ||||||||
\(460\) | −308.000 | −0.669565 | ||||||||
\(461\) | − 79.5990i | − 0.172666i | −0.996266 | − | 0.0863330i | \(-0.972485\pi\) | ||||
0.996266 | − | 0.0863330i | \(-0.0275149\pi\) | |||||||
\(462\) | 264.000 | 0.571429 | ||||||||
\(463\) | −86.0000 | −0.185745 | −0.0928726 | − | 0.995678i | \(-0.529605\pi\) | ||||
−0.0928726 | + | 0.995678i | \(0.529605\pi\) | |||||||
\(464\) | − 198.997i | − 0.428874i | ||||||||
\(465\) | 517.393i | 1.11267i | ||||||||
\(466\) | 1452.00 | 3.11588 | ||||||||
\(467\) | − 596.992i | − 1.27836i | −0.769059 | − | 0.639178i | \(-0.779275\pi\) | ||||
0.769059 | − | 0.639178i | \(-0.220725\pi\) | |||||||
\(468\) | −252.000 | −0.538462 | ||||||||
\(469\) | −16.0000 | −0.0341151 | ||||||||
\(470\) | 1897.11i | 4.03640i | ||||||||
\(471\) | 546.000 | 1.15924 | ||||||||
\(472\) | 660.000 | 1.39831 | ||||||||
\(473\) | 139.298i | 0.294499i | ||||||||
\(474\) | − 397.995i | − 0.839652i | ||||||||
\(475\) | 114.000 | 0.240000 | ||||||||
\(476\) | 742.924i | 1.56076i | ||||||||
\(477\) | − 537.293i | − 1.12640i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 225.530i | 0.470836i | 0.971894 | + | 0.235418i | \(0.0756459\pi\) | ||||
−0.971894 | + | 0.235418i | \(0.924354\pi\) | |||||||
\(480\) | −462.000 | −0.962500 | ||||||||
\(481\) | 120.000 | 0.249480 | ||||||||
\(482\) | 431.161i | 0.894525i | ||||||||
\(483\) | − 159.198i | − 0.329602i | ||||||||
\(484\) | 77.0000 | 0.159091 | ||||||||
\(485\) | − 411.261i | − 0.847962i | ||||||||
\(486\) | 805.940i | 1.65831i | ||||||||
\(487\) | 446.000 | 0.915811 | 0.457906 | − | 0.889001i | \(-0.348600\pi\) | ||||
0.457906 | + | 0.889001i | \(0.348600\pi\) | |||||||
\(488\) | − 119.398i | − 0.244669i | ||||||||
\(489\) | −870.000 | −1.77914 | ||||||||
\(490\) | 330.000 | 0.673469 | ||||||||
\(491\) | − 703.124i | − 1.43203i | −0.698087 | − | 0.716013i | \(-0.745965\pi\) | ||||
0.698087 | − | 0.716013i | \(-0.254035\pi\) | |||||||
\(492\) | − 278.596i | − 0.566253i | ||||||||
\(493\) | 528.000 | 1.07099 | ||||||||
\(494\) | − 79.5990i | − 0.161132i | ||||||||
\(495\) | 198.000 | 0.400000 | ||||||||
\(496\) | −130.000 | −0.262097 | ||||||||
\(497\) | 477.594i | 0.960954i | ||||||||
\(498\) | 396.000 | 0.795181 | ||||||||
\(499\) | −58.0000 | −0.116232 | −0.0581162 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581162 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(500\) | 278.596i | 0.557193i | ||||||||
\(501\) | − 716.391i | − 1.42992i | ||||||||
\(502\) | −968.000 | −1.92829 | ||||||||
\(503\) | − 504.127i | − 1.00224i | −0.865378 | − | 0.501120i | \(-0.832921\pi\) | ||||
0.865378 | − | 0.501120i | \(-0.167079\pi\) | |||||||
\(504\) | 716.391i | 1.42141i | ||||||||
\(505\) | 704.000 | 1.39406 | ||||||||
\(506\) | − 72.9657i | − 0.144201i | ||||||||
\(507\) | −459.000 | −0.905325 | ||||||||
\(508\) | −1316.00 | −2.59055 | ||||||||
\(509\) | 736.291i | 1.44654i | 0.690563 | + | 0.723272i | \(0.257363\pi\) | ||||
−0.690563 | + | 0.723272i | \(0.742637\pi\) | |||||||
\(510\) | 875.589i | 1.71684i | ||||||||
\(511\) | 592.000 | 1.15851 | ||||||||
\(512\) | − 315.079i | − 0.615389i | ||||||||
\(513\) | −162.000 | −0.315789 | ||||||||
\(514\) | −1628.00 | −3.16732 | ||||||||
\(515\) | − 490.860i | − 0.953127i | ||||||||
\(516\) | −882.000 | −1.70930 | ||||||||
\(517\) | −286.000 | −0.553191 | ||||||||
\(518\) | − 795.990i | − 1.53666i | ||||||||
\(519\) | 596.992i | 1.15027i | ||||||||
\(520\) | −264.000 | −0.507692 | ||||||||
\(521\) | 278.596i | 0.534734i | 0.963595 | + | 0.267367i | \(0.0861536\pi\) | ||||
−0.963595 | + | 0.267367i | \(0.913846\pi\) | |||||||
\(522\) | 1188.00 | 2.27586 | ||||||||
\(523\) | −142.000 | −0.271511 | −0.135755 | − | 0.990742i | \(-0.543346\pi\) | ||||
−0.135755 | + | 0.990742i | \(0.543346\pi\) | |||||||
\(524\) | − 278.596i | − 0.531673i | ||||||||
\(525\) | 456.000 | 0.868571 | ||||||||
\(526\) | −748.000 | −1.42205 | ||||||||
\(527\) | − 344.929i | − 0.654514i | ||||||||
\(528\) | 49.7494i | 0.0942223i | ||||||||
\(529\) | 485.000 | 0.916824 | ||||||||
\(530\) | − 1313.38i | − 2.47808i | ||||||||
\(531\) | 596.992i | 1.12428i | ||||||||
\(532\) | −336.000 | −0.631579 | ||||||||
\(533\) | 53.0660i | 0.0995610i | ||||||||
\(534\) | 1188.00 | 2.22472 | ||||||||
\(535\) | −264.000 | −0.493458 | ||||||||
\(536\) | − 19.8997i | − 0.0371264i | ||||||||
\(537\) | 596.992i | 1.11172i | ||||||||
\(538\) | −242.000 | −0.449814 | ||||||||
\(539\) | 49.7494i | 0.0922994i | ||||||||
\(540\) | 1253.68i | 2.32164i | ||||||||
\(541\) | 400.000 | 0.739372 | 0.369686 | − | 0.929157i | \(-0.379465\pi\) | ||||
0.369686 | + | 0.929157i | \(0.379465\pi\) | |||||||
\(542\) | − 1485.85i | − 2.74142i | ||||||||
\(543\) | 30.0000 | 0.0552486 | ||||||||
\(544\) | 308.000 | 0.566176 | ||||||||
\(545\) | 1326.65i | 2.43422i | ||||||||
\(546\) | − 318.396i | − 0.583143i | ||||||||
\(547\) | 170.000 | 0.310786 | 0.155393 | − | 0.987853i | \(-0.450336\pi\) | ||||
0.155393 | + | 0.987853i | \(0.450336\pi\) | |||||||
\(548\) | − 742.924i | − 1.35570i | ||||||||
\(549\) | 108.000 | 0.196721 | ||||||||
\(550\) | 209.000 | 0.380000 | ||||||||
\(551\) | 238.797i | 0.433388i | ||||||||
\(552\) | 198.000 | 0.358696 | ||||||||
\(553\) | 320.000 | 0.578662 | ||||||||
\(554\) | − 862.322i | − 1.55654i | ||||||||
\(555\) | − 596.992i | − 1.07566i | ||||||||
\(556\) | 518.000 | 0.931655 | ||||||||
\(557\) | 849.056i | 1.52434i | 0.647378 | + | 0.762169i | \(0.275865\pi\) | ||||
−0.647378 | + | 0.762169i | \(0.724135\pi\) | |||||||
\(558\) | − 776.090i | − 1.39084i | ||||||||
\(559\) | 168.000 | 0.300537 | ||||||||
\(560\) | 265.330i | 0.473804i | ||||||||
\(561\) | −132.000 | −0.235294 | ||||||||
\(562\) | 660.000 | 1.17438 | ||||||||
\(563\) | − 703.124i | − 1.24889i | −0.781069 | − | 0.624444i | \(-0.785325\pi\) | ||||
0.781069 | − | 0.624444i | \(-0.214675\pi\) | |||||||
\(564\) | − 1810.88i | − 3.21078i | ||||||||
\(565\) | −264.000 | −0.467257 | ||||||||
\(566\) | − 165.831i | − 0.292988i | ||||||||
\(567\) | −648.000 | −1.14286 | ||||||||
\(568\) | −594.000 | −1.04577 | ||||||||
\(569\) | − 119.398i | − 0.209839i | −0.994481 | − | 0.104920i | \(-0.966541\pi\) | ||||
0.994481 | − | 0.104920i | \(-0.0334585\pi\) | |||||||
\(570\) | −396.000 | −0.694737 | ||||||||
\(571\) | −706.000 | −1.23643 | −0.618214 | − | 0.786010i | \(-0.712143\pi\) | ||||
−0.618214 | + | 0.786010i | \(0.712143\pi\) | |||||||
\(572\) | − 92.8655i | − 0.162352i | ||||||||
\(573\) | − 338.296i | − 0.590394i | ||||||||
\(574\) | 352.000 | 0.613240 | ||||||||
\(575\) | − 126.032i | − 0.219186i | ||||||||
\(576\) | 873.000 | 1.51562 | ||||||||
\(577\) | −738.000 | −1.27903 | −0.639515 | − | 0.768779i | \(-0.720865\pi\) | ||||
−0.639515 | + | 0.768779i | \(0.720865\pi\) | |||||||
\(578\) | 374.779i | 0.648406i | ||||||||
\(579\) | 894.000 | 1.54404 | ||||||||
\(580\) | 1848.00 | 3.18621 | ||||||||
\(581\) | 318.396i | 0.548014i | ||||||||
\(582\) | 616.892i | 1.05995i | ||||||||
\(583\) | 198.000 | 0.339623 | ||||||||
\(584\) | 736.291i | 1.26077i | ||||||||
\(585\) | − 238.797i | − 0.408200i | ||||||||
\(586\) | −1584.00 | −2.70307 | ||||||||
\(587\) | − 941.921i | − 1.60464i | −0.596897 | − | 0.802318i | \(-0.703600\pi\) | ||||
0.596897 | − | 0.802318i | \(-0.296400\pi\) | |||||||
\(588\) | −315.000 | −0.535714 | ||||||||
\(589\) | 156.000 | 0.264856 | ||||||||
\(590\) | 1459.31i | 2.47342i | ||||||||
\(591\) | 397.995i | 0.673426i | ||||||||
\(592\) | 150.000 | 0.253378 | ||||||||
\(593\) | 543.926i | 0.917245i | 0.888631 | + | 0.458623i | \(0.151657\pi\) | ||||
−0.888631 | + | 0.458623i | \(0.848343\pi\) | |||||||
\(594\) | −297.000 | −0.500000 | ||||||||
\(595\) | −704.000 | −1.18319 | ||||||||
\(596\) | 650.058i | 1.09070i | ||||||||
\(597\) | −126.000 | −0.211055 | ||||||||
\(598\) | −88.0000 | −0.147157 | ||||||||
\(599\) | − 46.4327i | − 0.0775171i | −0.999249 | − | 0.0387586i | \(-0.987660\pi\) | ||||
0.999249 | − | 0.0387586i | \(-0.0123403\pi\) | |||||||
\(600\) | 567.143i | 0.945238i | ||||||||
\(601\) | 542.000 | 0.901830 | 0.450915 | − | 0.892567i | \(-0.351098\pi\) | ||||
0.450915 | + | 0.892567i | \(0.351098\pi\) | |||||||
\(602\) | − 1114.39i | − 1.85114i | ||||||||
\(603\) | 18.0000 | 0.0298507 | ||||||||
\(604\) | 1120.00 | 1.85430 | ||||||||
\(605\) | 72.9657i | 0.120605i | ||||||||
\(606\) | −1056.00 | −1.74257 | ||||||||
\(607\) | −700.000 | −1.15321 | −0.576606 | − | 0.817022i | \(-0.695623\pi\) | ||||
−0.576606 | + | 0.817022i | \(0.695623\pi\) | |||||||
\(608\) | 139.298i | 0.229109i | ||||||||
\(609\) | 955.188i | 1.56845i | ||||||||
\(610\) | 264.000 | 0.432787 | ||||||||
\(611\) | 344.929i | 0.564532i | ||||||||
\(612\) | − 835.789i | − 1.36567i | ||||||||
\(613\) | 764.000 | 1.24633 | 0.623165 | − | 0.782091i | \(-0.285847\pi\) | ||||
0.623165 | + | 0.782091i | \(0.285847\pi\) | |||||||
\(614\) | 285.230i | 0.464544i | ||||||||
\(615\) | 264.000 | 0.429268 | ||||||||
\(616\) | −264.000 | −0.428571 | ||||||||
\(617\) | 39.7995i | 0.0645049i | 0.999480 | + | 0.0322524i | \(0.0102680\pi\) | ||||
−0.999480 | + | 0.0322524i | \(0.989732\pi\) | |||||||
\(618\) | 736.291i | 1.19141i | ||||||||
\(619\) | −742.000 | −1.19871 | −0.599354 | − | 0.800484i | \(-0.704576\pi\) | ||||
−0.599354 | + | 0.800484i | \(0.704576\pi\) | |||||||
\(620\) | − 1207.25i | − 1.94718i | ||||||||
\(621\) | 179.098i | 0.288402i | ||||||||
\(622\) | −66.0000 | −0.106109 | ||||||||
\(623\) | 955.188i | 1.53321i | ||||||||
\(624\) | 60.0000 | 0.0961538 | ||||||||
\(625\) | −739.000 | −1.18240 | ||||||||
\(626\) | 325.029i | 0.519216i | ||||||||
\(627\) | − 59.6992i | − 0.0952141i | ||||||||
\(628\) | −1274.00 | −2.02866 | ||||||||
\(629\) | 397.995i | 0.632742i | ||||||||
\(630\) | −1584.00 | −2.51429 | ||||||||
\(631\) | −410.000 | −0.649762 | −0.324881 | − | 0.945755i | \(-0.605324\pi\) | ||||
−0.324881 | + | 0.945755i | \(0.605324\pi\) | |||||||
\(632\) | 397.995i | 0.629739i | ||||||||
\(633\) | 738.000 | 1.16588 | ||||||||
\(634\) | −1034.00 | −1.63091 | ||||||||
\(635\) | − 1247.05i | − 1.96386i | ||||||||
\(636\) | 1253.68i | 1.97120i | ||||||||
\(637\) | 60.0000 | 0.0941915 | ||||||||
\(638\) | 437.794i | 0.686198i | ||||||||
\(639\) | − 537.293i | − 0.840834i | ||||||||
\(640\) | 1518.00 | 2.37188 | ||||||||
\(641\) | − 756.190i | − 1.17970i | −0.807511 | − | 0.589852i | \(-0.799186\pi\) | ||||
0.807511 | − | 0.589852i | \(-0.200814\pi\) | |||||||
\(642\) | 396.000 | 0.616822 | ||||||||
\(643\) | 890.000 | 1.38414 | 0.692068 | − | 0.721832i | \(-0.256700\pi\) | ||||
0.692068 | + | 0.721832i | \(0.256700\pi\) | |||||||
\(644\) | 371.462i | 0.576804i | ||||||||
\(645\) | − 835.789i | − 1.29580i | ||||||||
\(646\) | 264.000 | 0.408669 | ||||||||
\(647\) | 484.227i | 0.748419i | 0.927344 | + | 0.374210i | \(0.122086\pi\) | ||||
−0.927344 | + | 0.374210i | \(0.877914\pi\) | |||||||
\(648\) | − 805.940i | − 1.24373i | ||||||||
\(649\) | −220.000 | −0.338983 | ||||||||
\(650\) | − 252.063i | − 0.387790i | ||||||||
\(651\) | 624.000 | 0.958525 | ||||||||
\(652\) | 2030.00 | 3.11350 | ||||||||
\(653\) | 391.362i | 0.599329i | 0.954045 | + | 0.299664i | \(0.0968747\pi\) | ||||
−0.954045 | + | 0.299664i | \(0.903125\pi\) | |||||||
\(654\) | − 1989.97i | − 3.04278i | ||||||||
\(655\) | 264.000 | 0.403053 | ||||||||
\(656\) | 66.3325i | 0.101117i | ||||||||
\(657\) | −666.000 | −1.01370 | ||||||||
\(658\) | 2288.00 | 3.47720 | ||||||||
\(659\) | − 384.728i | − 0.583806i | −0.956448 | − | 0.291903i | \(-0.905711\pi\) | ||||
0.956448 | − | 0.291903i | \(-0.0942885\pi\) | |||||||
\(660\) | −462.000 | −0.700000 | ||||||||
\(661\) | −746.000 | −1.12859 | −0.564297 | − | 0.825572i | \(-0.690853\pi\) | ||||
−0.564297 | + | 0.825572i | \(0.690853\pi\) | |||||||
\(662\) | − 723.024i | − 1.09218i | ||||||||
\(663\) | 159.198i | 0.240118i | ||||||||
\(664\) | −396.000 | −0.596386 | ||||||||
\(665\) | − 318.396i | − 0.478791i | ||||||||
\(666\) | 895.489i | 1.34458i | ||||||||
\(667\) | 264.000 | 0.395802 | ||||||||
\(668\) | 1671.58i | 2.50236i | ||||||||
\(669\) | −906.000 | −1.35426 | ||||||||
\(670\) | 44.0000 | 0.0656716 | ||||||||
\(671\) | 39.7995i | 0.0593137i | ||||||||
\(672\) | 557.193i | 0.829156i | ||||||||
\(673\) | −634.000 | −0.942051 | −0.471025 | − | 0.882120i | \(-0.656116\pi\) | ||||
−0.471025 | + | 0.882120i | \(0.656116\pi\) | |||||||
\(674\) | 922.022i | 1.36798i | ||||||||
\(675\) | −513.000 | −0.760000 | ||||||||
\(676\) | 1071.00 | 1.58432 | ||||||||
\(677\) | 795.990i | 1.17576i | 0.808948 | + | 0.587880i | \(0.200037\pi\) | ||||
−0.808948 | + | 0.587880i | \(0.799963\pi\) | |||||||
\(678\) | 396.000 | 0.584071 | ||||||||
\(679\) | −496.000 | −0.730486 | ||||||||
\(680\) | − 875.589i | − 1.28763i | ||||||||
\(681\) | − 596.992i | − 0.876641i | ||||||||
\(682\) | 286.000 | 0.419355 | ||||||||
\(683\) | − 451.061i | − 0.660411i | −0.943909 | − | 0.330206i | \(-0.892882\pi\) | ||||
0.943909 | − | 0.330206i | \(-0.107118\pi\) | |||||||
\(684\) | 378.000 | 0.552632 | ||||||||
\(685\) | 704.000 | 1.02774 | ||||||||
\(686\) | 902.122i | 1.31505i | ||||||||
\(687\) | 450.000 | 0.655022 | ||||||||
\(688\) | 210.000 | 0.305233 | ||||||||
\(689\) | − 238.797i | − 0.346585i | ||||||||
\(690\) | 437.794i | 0.634485i | ||||||||
\(691\) | 458.000 | 0.662808 | 0.331404 | − | 0.943489i | \(-0.392478\pi\) | ||||
0.331404 | + | 0.943489i | \(0.392478\pi\) | |||||||
\(692\) | − 1392.98i | − 2.01298i | ||||||||
\(693\) | − 238.797i | − 0.344584i | ||||||||
\(694\) | −1100.00 | −1.58501 | ||||||||
\(695\) | 490.860i | 0.706274i | ||||||||
\(696\) | −1188.00 | −1.70690 | ||||||||
\(697\) | −176.000 | −0.252511 | ||||||||
\(698\) | 1074.59i | 1.53952i | ||||||||
\(699\) | − 1313.38i | − 1.87895i | ||||||||
\(700\) | −1064.00 | −1.52000 | ||||||||
\(701\) | 504.127i | 0.719154i | 0.933115 | + | 0.359577i | \(0.117079\pi\) | ||||
−0.933115 | + | 0.359577i | \(0.882921\pi\) | |||||||
\(702\) | 358.195i | 0.510250i | ||||||||
\(703\) | −180.000 | −0.256046 | ||||||||
\(704\) | 321.713i | 0.456978i | ||||||||
\(705\) | 1716.00 | 2.43404 | ||||||||
\(706\) | −1320.00 | −1.86969 | ||||||||
\(707\) | − 849.056i | − 1.20093i | ||||||||
\(708\) | − 1392.98i | − 1.96749i | ||||||||
\(709\) | −562.000 | −0.792666 | −0.396333 | − | 0.918107i | \(-0.629717\pi\) | ||||
−0.396333 | + | 0.918107i | \(0.629717\pi\) | |||||||
\(710\) | − 1313.38i | − 1.84984i | ||||||||
\(711\) | −360.000 | −0.506329 | ||||||||
\(712\) | −1188.00 | −1.66854 | ||||||||
\(713\) | − 172.464i | − 0.241886i | ||||||||
\(714\) | 1056.00 | 1.47899 | ||||||||
\(715\) | 88.0000 | 0.123077 | ||||||||
\(716\) | − 1392.98i | − 1.94551i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1012.00 | 1.40947 | ||||||||
\(719\) | 338.296i | 0.470509i | 0.971934 | + | 0.235254i | \(0.0755923\pi\) | ||||
−0.971934 | + | 0.235254i | \(0.924408\pi\) | |||||||
\(720\) | − 298.496i | − 0.414578i | ||||||||
\(721\) | −592.000 | −0.821082 | ||||||||
\(722\) | − 1077.90i | − 1.49294i | ||||||||
\(723\) | 390.000 | 0.539419 | ||||||||
\(724\) | −70.0000 | −0.0966851 | ||||||||
\(725\) | 756.190i | 1.04302i | ||||||||
\(726\) | − 109.449i | − 0.150756i | ||||||||
\(727\) | −42.0000 | −0.0577717 | −0.0288858 | − | 0.999583i | \(-0.509196\pi\) | ||||
−0.0288858 | + | 0.999583i | \(0.509196\pi\) | |||||||
\(728\) | 318.396i | 0.437357i | ||||||||
\(729\) | 729.000 | 1.00000 | ||||||||
\(730\) | −1628.00 | −2.23014 | ||||||||
\(731\) | 557.193i | 0.762234i | ||||||||
\(732\) | −252.000 | −0.344262 | ||||||||
\(733\) | −624.000 | −0.851296 | −0.425648 | − | 0.904889i | \(-0.639954\pi\) | ||||
−0.425648 | + | 0.904889i | \(0.639954\pi\) | |||||||
\(734\) | − 922.022i | − 1.25616i | ||||||||
\(735\) | − 298.496i | − 0.406117i | ||||||||
\(736\) | 154.000 | 0.209239 | ||||||||
\(737\) | 6.63325i | 0.00900034i | ||||||||
\(738\) | −396.000 | −0.536585 | ||||||||
\(739\) | 686.000 | 0.928281 | 0.464141 | − | 0.885761i | \(-0.346363\pi\) | ||||
0.464141 | + | 0.885761i | \(0.346363\pi\) | |||||||
\(740\) | 1392.98i | 1.88241i | ||||||||
\(741\) | −72.0000 | −0.0971660 | ||||||||
\(742\) | −1584.00 | −2.13477 | ||||||||
\(743\) | − 862.322i | − 1.16060i | −0.814404 | − | 0.580298i | \(-0.802936\pi\) | ||||
0.814404 | − | 0.580298i | \(-0.197064\pi\) | |||||||
\(744\) | 776.090i | 1.04313i | ||||||||
\(745\) | −616.000 | −0.826846 | ||||||||
\(746\) | − 225.530i | − 0.302320i | ||||||||
\(747\) | − 358.195i | − 0.479512i | ||||||||
\(748\) | 308.000 | 0.411765 | ||||||||
\(749\) | 318.396i | 0.425095i | ||||||||
\(750\) | 396.000 | 0.528000 | ||||||||
\(751\) | 94.0000 | 0.125166 | 0.0625832 | − | 0.998040i | \(-0.480066\pi\) | ||||
0.0625832 | + | 0.998040i | \(0.480066\pi\) | |||||||
\(752\) | 431.161i | 0.573353i | ||||||||
\(753\) | 875.589i | 1.16280i | ||||||||
\(754\) | 528.000 | 0.700265 | ||||||||
\(755\) | 1061.32i | 1.40572i | ||||||||
\(756\) | 1512.00 | 2.00000 | ||||||||
\(757\) | 1118.00 | 1.47688 | 0.738441 | − | 0.674318i | \(-0.235562\pi\) | ||||
0.738441 | + | 0.674318i | \(0.235562\pi\) | |||||||
\(758\) | 2222.14i | 2.93158i | ||||||||
\(759\) | −66.0000 | −0.0869565 | ||||||||
\(760\) | 396.000 | 0.521053 | ||||||||
\(761\) | − 1154.19i | − 1.51667i | −0.651865 | − | 0.758335i | \(-0.726013\pi\) | ||||
0.651865 | − | 0.758335i | \(-0.273987\pi\) | |||||||
\(762\) | 1870.58i | 2.45482i | ||||||||
\(763\) | 1600.00 | 2.09699 | ||||||||
\(764\) | 789.357i | 1.03319i | ||||||||
\(765\) | 792.000 | 1.03529 | ||||||||
\(766\) | 110.000 | 0.143603 | ||||||||
\(767\) | 265.330i | 0.345932i | ||||||||
\(768\) | −1113.00 | −1.44922 | ||||||||
\(769\) | 1274.00 | 1.65670 | 0.828349 | − | 0.560213i | \(-0.189281\pi\) | ||||
0.828349 | + | 0.560213i | \(0.189281\pi\) | |||||||
\(770\) | − 583.726i | − 0.758086i | ||||||||
\(771\) | 1472.58i | 1.90996i | ||||||||
\(772\) | −2086.00 | −2.70207 | ||||||||
\(773\) | − 935.288i | − 1.20995i | −0.796246 | − | 0.604973i | \(-0.793184\pi\) | ||||
0.796246 | − | 0.604973i | \(-0.206816\pi\) | |||||||
\(774\) | 1253.68i | 1.61975i | ||||||||
\(775\) | 494.000 | 0.637419 | ||||||||
\(776\) | − 616.892i | − 0.794964i | ||||||||
\(777\) | −720.000 | −0.926641 | ||||||||
\(778\) | 1386.00 | 1.78149 | ||||||||
\(779\) | − 79.5990i | − 0.102181i | ||||||||
\(780\) | 557.193i | 0.714350i | ||||||||
\(781\) | 198.000 | 0.253521 | ||||||||
\(782\) | − 291.863i | − 0.373226i | ||||||||
\(783\) | − 1074.59i | − 1.37240i | ||||||||
\(784\) | 75.0000 | 0.0956633 | ||||||||
\(785\) | − 1207.25i | − 1.53790i | ||||||||
\(786\) | −396.000 | −0.503817 | ||||||||
\(787\) | 298.000 | 0.378653 | 0.189327 | − | 0.981914i | \(-0.439370\pi\) | ||||
0.189327 | + | 0.981914i | \(0.439370\pi\) | |||||||
\(788\) | − 928.655i | − 1.17850i | ||||||||
\(789\) | 676.591i | 0.857530i | ||||||||
\(790\) | −880.000 | −1.11392 | ||||||||
\(791\) | 318.396i | 0.402523i | ||||||||
\(792\) | 297.000 | 0.375000 | ||||||||
\(793\) | 48.0000 | 0.0605296 | ||||||||
\(794\) | − 285.230i | − 0.359231i | ||||||||
\(795\) | −1188.00 | −1.49434 | ||||||||
\(796\) | 294.000 | 0.369347 | ||||||||
\(797\) | 524.027i | 0.657499i | 0.944417 | + | 0.328750i | \(0.106627\pi\) | ||||
−0.944417 | + | 0.328750i | \(0.893373\pi\) | |||||||
\(798\) | 477.594i | 0.598489i | ||||||||
\(799\) | −1144.00 | −1.43179 | ||||||||
\(800\) | 441.111i | 0.551389i | ||||||||
\(801\) | − 1074.59i | − 1.34156i | ||||||||
\(802\) | 836.000 | 1.04239 | ||||||||
\(803\) | − 245.430i | − 0.305642i | ||||||||
\(804\) | −42.0000 | −0.0522388 | ||||||||
\(805\) | −352.000 | −0.437267 | ||||||||
\(806\) | − 344.929i | − 0.427952i | ||||||||
\(807\) | 218.897i | 0.271248i | ||||||||
\(808\) | 1056.00 | 1.30693 | ||||||||
\(809\) | − 915.388i | − 1.13151i | −0.824575 | − | 0.565753i | \(-0.808586\pi\) | ||||
0.824575 | − | 0.565753i | \(-0.191414\pi\) | |||||||
\(810\) | 1782.00 | 2.20000 | ||||||||
\(811\) | −182.000 | −0.224414 | −0.112207 | − | 0.993685i | \(-0.535792\pi\) | ||||
−0.112207 | + | 0.993685i | \(0.535792\pi\) | |||||||
\(812\) | − 2228.77i | − 2.74479i | ||||||||
\(813\) | −1344.00 | −1.65314 | ||||||||
\(814\) | −330.000 | −0.405405 | ||||||||
\(815\) | 1923.64i | 2.36030i | ||||||||
\(816\) | 198.997i | 0.243869i | ||||||||
\(817\) | −252.000 | −0.308446 | ||||||||
\(818\) | 1691.48i | 2.06782i | ||||||||
\(819\) | −288.000 | −0.351648 | ||||||||
\(820\) | −616.000 | −0.751220 | ||||||||
\(821\) | − 822.523i | − 1.00185i | −0.865489 | − | 0.500927i | \(-0.832992\pi\) | ||||
0.865489 | − | 0.500927i | \(-0.167008\pi\) | |||||||
\(822\) | −1056.00 | −1.28467 | ||||||||
\(823\) | −246.000 | −0.298906 | −0.149453 | − | 0.988769i | \(-0.547751\pi\) | ||||
−0.149453 | + | 0.988769i | \(0.547751\pi\) | |||||||
\(824\) | − 736.291i | − 0.893557i | ||||||||
\(825\) | − 189.048i | − 0.229149i | ||||||||
\(826\) | 1760.00 | 2.13075 | ||||||||
\(827\) | 543.926i | 0.657710i | 0.944380 | + | 0.328855i | \(0.106663\pi\) | ||||
−0.944380 | + | 0.328855i | \(0.893337\pi\) | |||||||
\(828\) | − 417.895i | − 0.504704i | ||||||||
\(829\) | 250.000 | 0.301568 | 0.150784 | − | 0.988567i | \(-0.451820\pi\) | ||||
0.150784 | + | 0.988567i | \(0.451820\pi\) | |||||||
\(830\) | − 875.589i | − 1.05493i | ||||||||
\(831\) | −780.000 | −0.938628 | ||||||||
\(832\) | 388.000 | 0.466346 | ||||||||
\(833\) | 198.997i | 0.238893i | ||||||||
\(834\) | − 736.291i | − 0.882843i | ||||||||
\(835\) | −1584.00 | −1.89701 | ||||||||
\(836\) | 139.298i | 0.166625i | ||||||||
\(837\) | −702.000 | −0.838710 | ||||||||
\(838\) | 1760.00 | 2.10024 | ||||||||
\(839\) | 470.961i | 0.561336i | 0.959805 | + | 0.280668i | \(0.0905559\pi\) | ||||
−0.959805 | + | 0.280668i | \(0.909444\pi\) | |||||||
\(840\) | 1584.00 | 1.88571 | ||||||||
\(841\) | −743.000 | −0.883472 | ||||||||
\(842\) | − 563.826i | − 0.669627i | ||||||||
\(843\) | − 596.992i | − 0.708176i | ||||||||
\(844\) | −1722.00 | −2.04028 | ||||||||
\(845\) | 1014.89i | 1.20105i | ||||||||
\(846\) | −2574.00 | −3.04255 | ||||||||
\(847\) | 88.0000 | 0.103896 | ||||||||
\(848\) | − 298.496i | − 0.352000i | ||||||||
\(849\) | −150.000 | −0.176678 | ||||||||
\(850\) | 836.000 | 0.983529 | ||||||||
\(851\) | 198.997i | 0.233840i | ||||||||
\(852\) | 1253.68i | 1.47146i | ||||||||
\(853\) | 56.0000 | 0.0656506 | 0.0328253 | − | 0.999461i | \(-0.489549\pi\) | ||||
0.0328253 | + | 0.999461i | \(0.489549\pi\) | |||||||
\(854\) | − 318.396i | − 0.372829i | ||||||||
\(855\) | 358.195i | 0.418942i | ||||||||
\(856\) | −396.000 | −0.462617 | ||||||||
\(857\) | − 252.063i | − 0.294123i | −0.989127 | − | 0.147062i | \(-0.953018\pi\) | ||||
0.989127 | − | 0.147062i | \(-0.0469815\pi\) | |||||||
\(858\) | −132.000 | −0.153846 | ||||||||
\(859\) | 1278.00 | 1.48778 | 0.743888 | − | 0.668304i | \(-0.232979\pi\) | ||||
0.743888 | + | 0.668304i | \(0.232979\pi\) | |||||||
\(860\) | 1950.18i | 2.26765i | ||||||||
\(861\) | − 318.396i | − 0.369798i | ||||||||
\(862\) | −924.000 | −1.07193 | ||||||||
\(863\) | − 1134.29i | − 1.31435i | −0.753737 | − | 0.657176i | \(-0.771751\pi\) | ||||
0.753737 | − | 0.657176i | \(-0.228249\pi\) | |||||||
\(864\) | − 626.842i | − 0.725512i | ||||||||
\(865\) | 1320.00 | 1.52601 | ||||||||
\(866\) | − 1797.61i | − 2.07576i | ||||||||
\(867\) | 339.000 | 0.391003 | ||||||||
\(868\) | −1456.00 | −1.67742 | ||||||||
\(869\) | − 132.665i | − 0.152664i | ||||||||
\(870\) | − 2626.77i | − 3.01927i | ||||||||
\(871\) | 8.00000 | 0.00918485 | ||||||||
\(872\) | 1989.97i | 2.28208i | ||||||||
\(873\) | 558.000 | 0.639175 | ||||||||
\(874\) | 132.000 | 0.151030 | ||||||||
\(875\) | 318.396i | 0.363881i | ||||||||
\(876\) | 1554.00 | 1.77397 | ||||||||
\(877\) | 456.000 | 0.519954 | 0.259977 | − | 0.965615i | \(-0.416285\pi\) | ||||
0.259977 | + | 0.965615i | \(0.416285\pi\) | |||||||
\(878\) | 1087.85i | 1.23901i | ||||||||
\(879\) | 1432.78i | 1.63001i | ||||||||
\(880\) | 110.000 | 0.125000 | ||||||||
\(881\) | − 610.259i | − 0.692689i | −0.938107 | − | 0.346344i | \(-0.887423\pi\) | ||||
0.938107 | − | 0.346344i | \(-0.112577\pi\) | |||||||
\(882\) | 447.744i | 0.507647i | ||||||||
\(883\) | −1094.00 | −1.23896 | −0.619479 | − | 0.785013i | \(-0.712656\pi\) | ||||
−0.619479 | + | 0.785013i | \(0.712656\pi\) | |||||||
\(884\) | − 371.462i | − 0.420206i | ||||||||
\(885\) | 1320.00 | 1.49153 | ||||||||
\(886\) | −440.000 | −0.496614 | ||||||||
\(887\) | 145.931i | 0.164523i | 0.996611 | + | 0.0822613i | \(0.0262142\pi\) | ||||
−0.996611 | + | 0.0822613i | \(0.973786\pi\) | |||||||
\(888\) | − 895.489i | − 1.00843i | ||||||||
\(889\) | −1504.00 | −1.69179 | ||||||||
\(890\) | − 2626.77i | − 2.95142i | ||||||||
\(891\) | 268.647i | 0.301511i | ||||||||
\(892\) | 2114.00 | 2.36996 | ||||||||
\(893\) | − 517.393i | − 0.579388i | ||||||||
\(894\) | 924.000 | 1.03356 | ||||||||
\(895\) | 1320.00 | 1.47486 | ||||||||
\(896\) | − 1830.78i | − 2.04328i | ||||||||
\(897\) | 79.5990i | 0.0887391i | ||||||||
\(898\) | 1496.00 | 1.66592 | ||||||||
\(899\) | 1034.79i | 1.15104i | ||||||||
\(900\) | 1197.00 | 1.33000 | ||||||||
\(901\) | 792.000 | 0.879023 | ||||||||
\(902\) | − 145.931i | − 0.161787i | ||||||||
\(903\) | −1008.00 | −1.11628 | ||||||||
\(904\) | −396.000 | −0.438053 | ||||||||
\(905\) | − 66.3325i | − 0.0732956i | ||||||||
\(906\) | − 1591.98i | − 1.75715i | ||||||||
\(907\) | 186.000 | 0.205072 | 0.102536 | − | 0.994729i | \(-0.467304\pi\) | ||||
0.102536 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(908\) | 1392.98i | 1.53412i | ||||||||
\(909\) | 955.188i | 1.05081i | ||||||||
\(910\) | −704.000 | −0.773626 | ||||||||
\(911\) | 855.689i | 0.939286i | 0.882857 | + | 0.469643i | \(0.155617\pi\) | ||||
−0.882857 | + | 0.469643i | \(0.844383\pi\) | |||||||
\(912\) | −90.0000 | −0.0986842 | ||||||||
\(913\) | 132.000 | 0.144578 | ||||||||
\(914\) | 1134.29i | 1.24101i | ||||||||
\(915\) | − 238.797i | − 0.260980i | ||||||||
\(916\) | −1050.00 | −1.14629 | ||||||||
\(917\) | − 318.396i | − 0.347215i | ||||||||
\(918\) | −1188.00 | −1.29412 | ||||||||
\(919\) | −428.000 | −0.465724 | −0.232862 | − | 0.972510i | \(-0.574809\pi\) | ||||
−0.232862 | + | 0.972510i | \(0.574809\pi\) | |||||||
\(920\) | − 437.794i | − 0.475864i | ||||||||
\(921\) | 258.000 | 0.280130 | ||||||||
\(922\) | 264.000 | 0.286334 | ||||||||
\(923\) | − 238.797i | − 0.258718i | ||||||||
\(924\) | 557.193i | 0.603023i | ||||||||
\(925\) | −570.000 | −0.616216 | ||||||||
\(926\) | − 285.230i | − 0.308023i | ||||||||
\(927\) | 666.000 | 0.718447 | ||||||||
\(928\) | −924.000 | −0.995690 | ||||||||
\(929\) | 636.792i | 0.685460i | 0.939434 | + | 0.342730i | \(0.111352\pi\) | ||||
−0.939434 | + | 0.342730i | \(0.888648\pi\) | |||||||
\(930\) | −1716.00 | −1.84516 | ||||||||
\(931\) | −90.0000 | −0.0966702 | ||||||||
\(932\) | 3064.56i | 3.28816i | ||||||||
\(933\) | 59.6992i | 0.0639863i | ||||||||
\(934\) | 1980.00 | 2.11991 | ||||||||
\(935\) | 291.863i | 0.312153i | ||||||||
\(936\) | − 358.195i | − 0.382687i | ||||||||
\(937\) | 290.000 | 0.309498 | 0.154749 | − | 0.987954i | \(-0.450543\pi\) | ||||
0.154749 | + | 0.987954i | \(0.450543\pi\) | |||||||
\(938\) | − 53.0660i | − 0.0565736i | ||||||||
\(939\) | 294.000 | 0.313099 | ||||||||
\(940\) | −4004.00 | −4.25957 | ||||||||
\(941\) | 875.589i | 0.930488i | 0.885183 | + | 0.465244i | \(0.154033\pi\) | ||||
−0.885183 | + | 0.465244i | \(0.845967\pi\) | |||||||
\(942\) | 1810.88i | 1.92237i | ||||||||
\(943\) | −88.0000 | −0.0933192 | ||||||||
\(944\) | 331.662i | 0.351337i | ||||||||
\(945\) | 1432.78i | 1.51617i | ||||||||
\(946\) | −462.000 | −0.488372 | ||||||||
\(947\) | − 79.5990i | − 0.0840538i | −0.999116 | − | 0.0420269i | \(-0.986618\pi\) | ||||
0.999116 | − | 0.0420269i | \(-0.0133815\pi\) | |||||||
\(948\) | 840.000 | 0.886076 | ||||||||
\(949\) | −296.000 | −0.311907 | ||||||||
\(950\) | 378.095i | 0.397995i | ||||||||
\(951\) | 935.288i | 0.983479i | ||||||||
\(952\) | −1056.00 | −1.10924 | ||||||||
\(953\) | − 782.723i | − 0.821326i | −0.911787 | − | 0.410663i | \(-0.865297\pi\) | ||||
0.911787 | − | 0.410663i | \(-0.134703\pi\) | |||||||
\(954\) | 1782.00 | 1.86792 | ||||||||
\(955\) | −748.000 | −0.783246 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 396.000 | 0.413793 | ||||||||
\(958\) | −748.000 | −0.780793 | ||||||||
\(959\) | − 849.056i | − 0.885356i | ||||||||
\(960\) | − 1930.28i | − 2.01070i | ||||||||
\(961\) | −285.000 | −0.296566 | ||||||||
\(962\) | 397.995i | 0.413716i | ||||||||
\(963\) | − 358.195i | − 0.371958i | ||||||||
\(964\) | −910.000 | −0.943983 | ||||||||
\(965\) | − 1976.71i | − 2.04840i | ||||||||
\(966\) | 528.000 | 0.546584 | ||||||||
\(967\) | 460.000 | 0.475698 | 0.237849 | − | 0.971302i | \(-0.423558\pi\) | ||||
0.237849 | + | 0.971302i | \(0.423558\pi\) | |||||||
\(968\) | 109.449i | 0.113067i | ||||||||
\(969\) | − 238.797i | − 0.246437i | ||||||||
\(970\) | 1364.00 | 1.40619 | ||||||||
\(971\) | − 1167.45i | − 1.20232i | −0.799129 | − | 0.601160i | \(-0.794706\pi\) | ||||
0.799129 | − | 0.601160i | \(-0.205294\pi\) | |||||||
\(972\) | −1701.00 | −1.75000 | ||||||||
\(973\) | 592.000 | 0.608428 | ||||||||
\(974\) | 1479.21i | 1.51870i | ||||||||
\(975\) | −228.000 | −0.233846 | ||||||||
\(976\) | 60.0000 | 0.0614754 | ||||||||
\(977\) | 1313.38i | 1.34430i | 0.740414 | + | 0.672151i | \(0.234630\pi\) | ||||
−0.740414 | + | 0.672151i | \(0.765370\pi\) | |||||||
\(978\) | − 2885.46i | − 2.95037i | ||||||||
\(979\) | 396.000 | 0.404494 | ||||||||
\(980\) | 696.491i | 0.710705i | ||||||||
\(981\) | −1800.00 | −1.83486 | ||||||||
\(982\) | 2332.00 | 2.37475 | ||||||||
\(983\) | 417.895i | 0.425122i | 0.977148 | + | 0.212561i | \(0.0681804\pi\) | ||||
−0.977148 | + | 0.212561i | \(0.931820\pi\) | |||||||
\(984\) | 396.000 | 0.402439 | ||||||||
\(985\) | 880.000 | 0.893401 | ||||||||
\(986\) | 1751.18i | 1.77604i | ||||||||
\(987\) | − 2069.57i | − 2.09683i | ||||||||
\(988\) | 168.000 | 0.170040 | ||||||||
\(989\) | 278.596i | 0.281695i | ||||||||
\(990\) | 656.692i | 0.663325i | ||||||||
\(991\) | 838.000 | 0.845610 | 0.422805 | − | 0.906221i | \(-0.361045\pi\) | ||||
0.422805 | + | 0.906221i | \(0.361045\pi\) | |||||||
\(992\) | 603.626i | 0.608494i | ||||||||
\(993\) | −654.000 | −0.658610 | ||||||||
\(994\) | −1584.00 | −1.59356 | ||||||||
\(995\) | 278.596i | 0.279996i | ||||||||
\(996\) | 835.789i | 0.839146i | ||||||||
\(997\) | −52.0000 | −0.0521565 | −0.0260782 | − | 0.999660i | \(-0.508302\pi\) | ||||
−0.0260782 | + | 0.999660i | \(0.508302\pi\) | |||||||
\(998\) | − 192.364i | − 0.192750i | ||||||||
\(999\) | 810.000 | 0.810811 |
(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 | 33.3.b.a.23.2 | yes | 2 | |
3.2 | odd | 2 | inner | 33.3.b.a.23.1 | ✓ | 2 | |
4.3 | odd | 2 | 528.3.i.a.353.1 | 2 | |||
11.2 | odd | 10 | 363.3.h.d.323.1 | 8 | |||
11.3 | even | 5 | 363.3.h.e.251.2 | 8 | |||
11.4 | even | 5 | 363.3.h.e.269.1 | 8 | |||
11.5 | even | 5 | 363.3.h.e.245.1 | 8 | |||
11.6 | odd | 10 | 363.3.h.d.245.2 | 8 | |||
11.7 | odd | 10 | 363.3.h.d.269.2 | 8 | |||
11.8 | odd | 10 | 363.3.h.d.251.1 | 8 | |||
11.9 | even | 5 | 363.3.h.e.323.2 | 8 | |||
11.10 | odd | 2 | 363.3.b.d.122.1 | 2 | |||
12.11 | even | 2 | 528.3.i.a.353.2 | 2 | |||
33.2 | even | 10 | 363.3.h.d.323.2 | 8 | |||
33.5 | odd | 10 | 363.3.h.e.245.2 | 8 | |||
33.8 | even | 10 | 363.3.h.d.251.2 | 8 | |||
33.14 | odd | 10 | 363.3.h.e.251.1 | 8 | |||
33.17 | even | 10 | 363.3.h.d.245.1 | 8 | |||
33.20 | odd | 10 | 363.3.h.e.323.1 | 8 | |||
33.26 | odd | 10 | 363.3.h.e.269.2 | 8 | |||
33.29 | even | 10 | 363.3.h.d.269.1 | 8 | |||
33.32 | even | 2 | 363.3.b.d.122.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.b.a.23.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
33.3.b.a.23.2 | yes | 2 | 1.1 | even | 1 | trivial | |
363.3.b.d.122.1 | 2 | 11.10 | odd | 2 | |||
363.3.b.d.122.2 | 2 | 33.32 | even | 2 | |||
363.3.h.d.245.1 | 8 | 33.17 | even | 10 | |||
363.3.h.d.245.2 | 8 | 11.6 | odd | 10 | |||
363.3.h.d.251.1 | 8 | 11.8 | odd | 10 | |||
363.3.h.d.251.2 | 8 | 33.8 | even | 10 | |||
363.3.h.d.269.1 | 8 | 33.29 | even | 10 | |||
363.3.h.d.269.2 | 8 | 11.7 | odd | 10 | |||
363.3.h.d.323.1 | 8 | 11.2 | odd | 10 | |||
363.3.h.d.323.2 | 8 | 33.2 | even | 10 | |||
363.3.h.e.245.1 | 8 | 11.5 | even | 5 | |||
363.3.h.e.245.2 | 8 | 33.5 | odd | 10 | |||
363.3.h.e.251.1 | 8 | 33.14 | odd | 10 | |||
363.3.h.e.251.2 | 8 | 11.3 | even | 5 | |||
363.3.h.e.269.1 | 8 | 11.4 | even | 5 | |||
363.3.h.e.269.2 | 8 | 33.26 | odd | 10 | |||
363.3.h.e.323.1 | 8 | 33.20 | odd | 10 | |||
363.3.h.e.323.2 | 8 | 11.9 | even | 5 | |||
528.3.i.a.353.1 | 2 | 4.3 | odd | 2 | |||
528.3.i.a.353.2 | 2 | 12.11 | even | 2 |