Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(65,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bn (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 57) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.1 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.65 |
Dual form | 912.2.bn.m.449.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.57313 | + | 0.724745i | −0.908248 | + | 0.418432i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | + | 0.707107i | 0.547723 | + | 0.316228i | 0.748203 | − | 0.663470i | \(-0.230917\pi\) |
−0.200480 | + | 0.979698i | \(0.564250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.73205 | 1.41058 | 0.705291 | − | 0.708918i | \(-0.250816\pi\) | ||||
0.705291 | + | 0.708918i | \(0.250816\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.94949 | − | 2.28024i | 0.649830 | − | 0.760080i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.378937i | 0.114254i | 0.998367 | + | 0.0571270i | \(0.0181940\pi\) | ||||
−0.998367 | + | 0.0571270i | \(0.981806\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23205 | − | 1.86603i | 0.896410 | − | 0.517542i | 0.0203760 | − | 0.999792i | \(-0.493514\pi\) |
0.876034 | + | 0.482250i | \(0.160180\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.43916 | − | 0.224745i | −0.629788 | − | 0.0580289i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.24264 | − | 2.44949i | −1.02899 | − | 0.594089i | −0.112296 | − | 0.993675i | \(-0.535820\pi\) |
−0.916696 | + | 0.399586i | \(0.869154\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205 | − | 4.00000i | 0.397360 | − | 0.917663i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.87101 | + | 2.70478i | −1.28116 | + | 0.590232i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.328169 | − | 0.189469i | 0.0684280 | − | 0.0395070i | −0.465396 | − | 0.885103i | \(-0.654088\pi\) |
0.533824 | + | 0.845596i | \(0.320755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.41421 | + | 5.00000i | −0.272166 | + | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.86370 | + | 6.69213i | 0.717472 | + | 1.24270i | 0.961998 | + | 0.273055i | \(0.0880341\pi\) |
−0.244527 | + | 0.969643i | \(0.578633\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.46410i | − | 0.801776i | −0.916127 | − | 0.400888i | \(-0.868702\pi\) | ||
0.916127 | − | 0.400888i | \(-0.131298\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.274633 | − | 0.596119i | −0.0478075 | − | 0.103771i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.57081 | + | 2.63896i | 0.772608 | + | 0.446065i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.26795i | 0.701647i | 0.936442 | + | 0.350823i | \(0.114098\pi\) | ||||
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.73205 | + | 5.27792i | −0.597606 | + | 0.845143i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.82843 | − | 4.89898i | 0.441726 | − | 0.765092i | −0.556092 | − | 0.831121i | \(-0.687700\pi\) |
0.997818 | + | 0.0660290i | \(0.0210330\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.13397 | − | 1.96410i | 0.172930 | − | 0.299523i | −0.766513 | − | 0.642228i | \(-0.778010\pi\) |
0.939443 | + | 0.342706i | \(0.111343\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.00000 | − | 1.41421i | 0.596285 | − | 0.210819i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.14162 | − | 5.27792i | 1.33344 | − | 0.769863i | 0.347617 | − | 0.937637i | \(-0.386991\pi\) |
0.985826 | + | 0.167773i | \(0.0536577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.44949 | + | 0.778539i | 1.18317 | + | 0.109017i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.01790 | + | 5.22715i | 0.414540 | + | 0.718004i | 0.995380 | − | 0.0960135i | \(-0.0306092\pi\) |
−0.580840 | + | 0.814018i | \(0.697276\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.267949 | + | 0.464102i | −0.0361303 | + | 0.0625794i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.174235 | + | 7.54782i | 0.0230779 | + | 0.999734i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.19187 | + | 7.26054i | −0.545735 | + | 0.945241i | 0.452825 | + | 0.891599i | \(0.350416\pi\) |
−0.998560 | + | 0.0536419i | \(0.982917\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.76795 | + | 3.06218i | 0.226363 | + | 0.392072i | 0.956727 | − | 0.290986i | \(-0.0939832\pi\) |
−0.730365 | + | 0.683057i | \(0.760650\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.27559 | − | 8.50997i | 0.916639 | − | 1.07216i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.27792 | 0.654645 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.866025 | + | 0.500000i | −0.105802 | + | 0.0610847i | −0.551967 | − | 0.833866i | \(-0.686123\pi\) |
0.446165 | + | 0.894951i | \(0.352789\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.378937 | + | 0.535898i | −0.0456187 | + | 0.0645146i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.79315 | + | 3.10583i | −0.212808 | + | 0.368594i | −0.952592 | − | 0.304250i | \(-0.901594\pi\) |
0.739784 | + | 0.672844i | \(0.234928\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | − | 2.59808i | 0.175562 | − | 0.304082i | −0.764794 | − | 0.644275i | \(-0.777159\pi\) |
0.940356 | + | 0.340193i | \(0.110493\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.24264 | + | 3.00000i | 0.489898 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41421i | 0.161165i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.06218 | + | 1.76795i | 0.344522 | + | 0.198910i | 0.662270 | − | 0.749265i | \(-0.269593\pi\) |
−0.317748 | + | 0.948175i | \(0.602927\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.39898 | − | 8.89060i | −0.155442 | − | 0.987845i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.72741i | 0.848193i | 0.905617 | + | 0.424097i | \(0.139408\pi\) | ||||
−0.905617 | + | 0.424097i | \(0.860592\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.46410 | − | 6.00000i | −0.375735 | − | 0.650791i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.9282 | − | 7.72741i | −1.17163 | − | 0.828465i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.67423 | + | 6.36396i | 0.389468 | + | 0.674579i | 0.992378 | − | 0.123231i | \(-0.0393255\pi\) |
−0.602910 | + | 0.797809i | \(0.705992\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0622 | − | 6.96410i | 1.26446 | − | 0.730036i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.23533 | + | 7.02262i | 0.335489 | + | 0.728212i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.94975 | − | 3.67423i | 0.507833 | − | 0.376969i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.46410 | + | 3.73205i | 0.656330 | + | 0.378932i | 0.790877 | − | 0.611975i | \(-0.209625\pi\) |
−0.134547 | + | 0.990907i | \(0.542958\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.864068 | + | 0.738735i | 0.0868421 | + | 0.0742456i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.69213 | − | 3.86370i | 0.665892 | − | 0.384453i | −0.128626 | − | 0.991693i | \(-0.541057\pi\) |
0.794518 | + | 0.607240i | \(0.207723\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4641i | 1.03106i | 0.856872 | + | 0.515529i | \(0.172405\pi\) | ||||
−0.856872 | + | 0.515529i | \(0.827595\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.10306 | − | 0.838759i | −0.888368 | − | 0.0818545i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.89898 | −0.473602 | −0.236801 | − | 0.971558i | \(-0.576099\pi\) | ||||
−0.236801 | + | 0.971558i | \(0.576099\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4641 | − | 7.19615i | −1.19384 | − | 0.689266i | −0.234668 | − | 0.972076i | \(-0.575400\pi\) |
−0.959176 | + | 0.282809i | \(0.908734\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.09317 | − | 6.71405i | −0.293591 | − | 0.637269i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.6622 | −1.75559 | −0.877795 | − | 0.479036i | \(-0.840986\pi\) | ||||
−0.877795 | + | 0.479036i | \(0.840986\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.535898 | 0.0499728 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.04587 | − | 11.0076i | 0.189140 | − | 1.01766i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.8338 | − | 9.14162i | −1.45148 | − | 0.838011i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8564 | 0.986946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.898979 | + | 9.75663i | −0.0810583 | + | 0.879726i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.80385 | + | 3.92820i | −0.603744 | + | 0.348572i | −0.770513 | − | 0.637424i | \(-0.780000\pi\) |
0.166769 | + | 0.985996i | \(0.446667\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.360419 | + | 3.91163i | −0.0317332 | + | 0.344400i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.03579 | − | 3.48477i | −0.527350 | − | 0.304465i | 0.212587 | − | 0.977142i | \(-0.431811\pi\) |
−0.739936 | + | 0.672677i | \(0.765144\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.46410 | − | 14.9282i | 0.560509 | − | 1.29444i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.26758 | + | 5.12372i | −0.453362 | + | 0.440980i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.656339 | − | 0.378937i | 0.0560748 | − | 0.0323748i | −0.471700 | − | 0.881759i | \(-0.656360\pi\) |
0.527775 | + | 0.849384i | \(0.323026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.59808 | + | 11.4282i | 0.559642 | + | 0.969328i | 0.997526 | + | 0.0702964i | \(0.0223945\pi\) |
−0.437885 | + | 0.899031i | \(0.644272\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5558 | + | 14.9282i | −0.888962 | + | 1.25718i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.707107 | + | 1.22474i | 0.0591312 | + | 0.102418i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.9282i | 0.907538i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −10.8990 | + | 5.02118i | −0.898933 | + | 0.414140i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.6090 | − | 8.43451i | −1.19682 | − | 0.690982i | −0.236972 | − | 0.971516i | \(-0.576155\pi\) |
−0.959844 | + | 0.280534i | \(0.909488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.00000i | − | 0.162758i | −0.996683 | − | 0.0813788i | \(-0.974068\pi\) | ||
0.996683 | − | 0.0813788i | \(-0.0259324\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.8564 | + | 4.89898i | −1.12022 | + | 0.396059i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.15660 | − | 5.46739i | 0.253544 | − | 0.439151i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.76795 | + | 3.06218i | −0.141098 | + | 0.244388i | −0.927910 | − | 0.372804i | \(-0.878397\pi\) |
0.786813 | + | 0.617192i | \(0.211730\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.53590 | − | 6.03579i | −0.676941 | − | 0.478669i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.22474 | − | 0.707107i | 0.0965234 | − | 0.0557278i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.19615 | −0.406994 | −0.203497 | − | 0.979076i | \(-0.565231\pi\) | ||||
−0.203497 | + | 0.979076i | \(0.565231\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0851642 | − | 0.924288i | 0.00663003 | − | 0.0719557i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.81294 | − | 6.60420i | −0.295054 | − | 0.511048i | 0.679944 | − | 0.733264i | \(-0.262004\pi\) |
−0.974997 | + | 0.222216i | \(0.928671\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.464102 | − | 0.803848i | 0.0357001 | − | 0.0618344i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.74434 | − | 11.7474i | −0.439281 | − | 0.898350i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.93426 | + | 10.2784i | −0.451173 | + | 0.781455i | −0.998459 | − | 0.0554909i | \(-0.982328\pi\) |
0.547286 | + | 0.836946i | \(0.315661\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.59808 | − | 9.69615i | −0.423175 | − | 0.732960i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.33233 | − | 14.4598i | 0.100144 | − | 1.08687i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.41421 | 0.105703 | 0.0528516 | − | 0.998602i | \(-0.483169\pi\) | ||||
0.0528516 | + | 0.998602i | \(0.483169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00000 | + | 1.73205i | −0.222988 | + | 0.128742i | −0.607333 | − | 0.794447i | \(-0.707761\pi\) |
0.384345 | + | 0.923190i | \(0.374427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.00052 | − | 3.53590i | −0.369649 | − | 0.261381i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.01790 | + | 5.22715i | −0.221880 | + | 0.384308i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.928203 | − | 1.60770i | 0.0678769 | − | 0.117566i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.27792 | + | 18.6603i | −0.383912 | + | 1.35733i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.69161i | − | 0.122401i | −0.998125 | − | 0.0612005i | \(-0.980507\pi\) | ||
0.998125 | − | 0.0612005i | \(-0.0194929\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4282 | + | 6.59808i | 0.822620 | + | 0.474940i | 0.851319 | − | 0.524648i | \(-0.175803\pi\) |
−0.0286991 | + | 0.999588i | \(0.509136\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.30286 | + | 3.82514i | −0.594580 | + | 0.273924i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.14162i | − | 0.651313i | −0.945488 | − | 0.325657i | \(-0.894415\pi\) | ||
0.945488 | − | 0.325657i | \(-0.105585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.40192 | − | 11.0885i | −0.453820 | − | 0.786040i | 0.544799 | − | 0.838567i | \(-0.316606\pi\) |
−0.998620 | + | 0.0525267i | \(0.983273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00000 | − | 1.41421i | 0.0705346 | − | 0.0997509i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.4195 | + | 24.9754i | 1.01205 | + | 1.75293i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.92820 | − | 4.00000i | 0.483887 | − | 0.279372i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.207729 | − | 1.11767i | 0.0144382 | − | 0.0776836i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.51575 | + | 0.656339i | 0.104847 | + | 0.0453999i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.52628 | + | 5.50000i | 0.655816 | + | 0.378636i | 0.790681 | − | 0.612228i | \(-0.209727\pi\) |
−0.134865 | + | 0.990864i | \(0.543060\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.569930 | − | 6.18546i | 0.0390510 | − | 0.423820i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.77766 | − | 1.60368i | 0.189435 | − | 0.109370i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.6603i | − | 1.13097i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.476756 | + | 5.17423i | −0.0322162 | + | 0.349642i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.2832 | −1.22986 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.13397 | + | 4.69615i | 0.544691 | + | 0.314478i | 0.746978 | − | 0.664849i | \(-0.231504\pi\) |
−0.202287 | + | 0.979326i | \(0.564837\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.84847 | − | 1.64456i | −0.589898 | − | 0.109638i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.5964 | −1.63252 | −0.816261 | − | 0.577683i | \(-0.803957\pi\) | ||||
−0.816261 | + | 0.577683i | \(0.803957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.39230 | 0.620661 | 0.310330 | − | 0.950629i | \(-0.399560\pi\) | ||||
0.310330 | + | 0.950629i | \(0.399560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.02494 | − | 2.22474i | −0.0674364 | − | 0.146377i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.10583 | − | 1.79315i | −0.203470 | − | 0.117473i | 0.394803 | − | 0.918766i | \(-0.370813\pi\) |
−0.598273 | + | 0.801292i | \(0.704146\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.9282 | 0.973809 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.09852 | − | 0.561920i | −0.396142 | − | 0.0365006i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 29.9759i | − | 1.93898i | −0.245133 | − | 0.969489i | \(-0.578832\pi\) | ||
0.245133 | − | 0.969489i | \(-0.421168\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.8205 | + | 14.3301i | −1.59883 | + | 0.923085i | −0.607116 | + | 0.794613i | \(0.707674\pi\) |
−0.991713 | + | 0.128472i | \(0.958993\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.64420 | + | 12.9722i | 0.554526 | + | 0.832167i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 8.48528 | + | 4.89898i | 0.542105 | + | 0.312984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.86603 | − | 16.1603i | −0.118732 | − | 1.02825i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.60040 | − | 12.1562i | −0.354911 | − | 0.770370i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7279 | − | 7.34847i | 0.803379 | − | 0.463831i | −0.0412721 | − | 0.999148i | \(-0.513141\pi\) |
0.844651 | + | 0.535317i | \(0.179808\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0717968 | + | 0.124356i | 0.00451382 | + | 0.00781817i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.79796 | + | 6.92820i | 0.613572 | + | 0.433861i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.60368 | + | 2.77766i | 0.100035 | + | 0.173266i | 0.911699 | − | 0.410859i | \(-0.134771\pi\) |
−0.811664 | + | 0.584125i | \(0.801438\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.9282i | 0.989730i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.7919 | + | 4.23607i | 1.41078 | + | 0.262206i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.480473 | + | 0.277401i | 0.0296273 | + | 0.0171053i | 0.514740 | − | 0.857346i | \(-0.327888\pi\) |
−0.485113 | + | 0.874451i | \(0.661222\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.53590i | 0.524356i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3923 | − | 7.34847i | −0.635999 | − | 0.449719i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.01790 | − | 5.22715i | 0.184004 | − | 0.318705i | −0.759236 | − | 0.650815i | \(-0.774427\pi\) |
0.943241 | + | 0.332110i | \(0.107761\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.46410 | + | 6.00000i | −0.210429 | + | 0.364474i | −0.951849 | − | 0.306568i | \(-0.900819\pi\) |
0.741420 | + | 0.671042i | \(0.234153\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.9282 | + | 19.6975i | −0.842973 | + | 1.19214i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.984508 | − | 0.568406i | 0.0593681 | − | 0.0342762i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.85641 | −0.592214 | −0.296107 | − | 0.955155i | \(-0.595689\pi\) | ||||
−0.296107 | + | 0.955155i | \(0.595689\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.1792 | − | 8.70272i | −0.609414 | − | 0.521018i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.53794 | − | 13.0561i | −0.449676 | − | 0.778861i | 0.548689 | − | 0.836027i | \(-0.315127\pi\) |
−0.998365 | + | 0.0571654i | \(0.981794\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9282 | + | 18.9282i | −0.649614 | + | 1.12516i | 0.333601 | + | 0.942714i | \(0.391736\pi\) |
−0.983215 | + | 0.182450i | \(0.941597\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.12372 | + | 9.36736i | −0.303503 | + | 0.554875i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.5558 | − | 18.2832i | 0.623091 | − | 1.07923i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.50000 | + | 6.06218i | 0.205882 | + | 0.356599i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.8737 | − | 1.18618i | −0.754668 | − | 0.0695354i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.2528 | 1.47528 | 0.737641 | − | 0.675193i | \(-0.235940\pi\) | ||||
0.737641 | + | 0.675193i | \(0.235940\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.2679 | + | 5.92820i | −0.597823 | + | 0.345153i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.89469 | − | 0.535898i | −0.109941 | − | 0.0310960i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.707107 | − | 1.22474i | 0.0408930 | − | 0.0708288i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.23205 | − | 7.33013i | 0.243931 | − | 0.422501i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.72741 | + | 10.9282i | −0.443928 | + | 0.627809i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.00052i | 0.286329i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | + | 6.92820i | 0.684876 | + | 0.395413i | 0.801690 | − | 0.597740i | \(-0.203935\pi\) |
−0.116814 | + | 0.993154i | \(0.537268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.58380 | − | 16.4614i | −0.431428 | − | 0.936457i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 27.1475i | 1.53939i | 0.638411 | + | 0.769696i | \(0.279592\pi\) | ||||
−0.638411 | + | 0.769696i | \(0.720408\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3923 | + | 21.4641i | 0.700454 | + | 1.21322i | 0.968307 | + | 0.249763i | \(0.0803527\pi\) |
−0.267853 | + | 0.963460i | \(0.586314\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.9282 | − | 5.27792i | 0.841109 | − | 0.297377i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.88160 | − | 11.9193i | −0.386509 | − | 0.669453i | 0.605468 | − | 0.795870i | \(-0.292986\pi\) |
−0.991977 | + | 0.126416i | \(0.959653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.53590 | + | 1.46410i | −0.141983 | + | 0.0819740i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.70674 | − | 3.55051i | 0.430148 | − | 0.198170i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.1464 | + | 12.7279i | −0.954053 | + | 0.708201i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.69615 | − | 5.59808i | −0.537846 | − | 0.310525i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 24.8231 | + | 2.28721i | 1.37272 | + | 0.126483i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.1170 | − | 19.6975i | 1.88093 | − | 1.08596i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 31.9282i | − | 1.75493i | −0.479638 | − | 0.877466i | \(-0.659232\pi\) | ||
0.479638 | − | 0.877466i | \(-0.340768\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.73194 | + | 8.32032i | 0.533307 | + | 0.455951i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.41421 | −0.0772667 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.35641 | + | 3.66987i | 0.346256 | + | 0.199911i | 0.663035 | − | 0.748589i | \(-0.269268\pi\) |
−0.316779 | + | 0.948499i | \(0.602601\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.3581 | − | 13.5253i | 1.59451 | − | 0.734594i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.69161 | 0.0916061 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.267949 | −0.0144679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.843039 | + | 0.388390i | −0.0453877 | + | 0.0209102i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.5414 | − | 12.4369i | −1.15640 | − | 0.667649i | −0.205963 | − | 0.978560i | \(-0.566032\pi\) |
−0.950439 | + | 0.310911i | \(0.899366\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3923 | −0.609816 | −0.304908 | − | 0.952382i | \(-0.598626\pi\) | ||||
−0.304908 | + | 0.952382i | \(0.598626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.75932 | + | 18.7992i | 0.254034 | + | 1.00343i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.9700i | 0.637101i | 0.947906 | + | 0.318551i | \(0.103196\pi\) | ||||
−0.947906 | + | 0.318551i | \(0.896804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.39230 | + | 2.53590i | −0.233119 | + | 0.134592i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 31.5339 | + | 2.90555i | 1.66895 | + | 0.153778i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.1822 | + | 13.3843i | 1.22351 | + | 0.706394i | 0.965665 | − | 0.259792i | \(-0.0836539\pi\) |
0.257846 | + | 0.966186i | \(0.416987\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | − | 13.8564i | −0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.0786 | + | 7.86812i | −0.896392 | + | 0.412969i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.67423 | − | 2.12132i | 0.192318 | − | 0.111035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.52628 | − | 14.7679i | −0.445068 | − | 0.770881i | 0.552989 | − | 0.833189i | \(-0.313487\pi\) |
−0.998057 | + | 0.0623080i | \(0.980154\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.65685 | − | 16.0000i | −0.294484 | − | 0.832927i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2629 | + | 19.5080i | 0.584743 | + | 1.01280i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5359i | 0.649084i | 0.945871 | + | 0.324542i | \(0.105210\pi\) | ||||
−0.945871 | + | 0.324542i | \(0.894790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.19955 | + | 17.7980i | 0.423423 | + | 0.919083i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.9754 | + | 14.4195i | 1.28630 | + | 0.742644i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 17.7846i | − | 0.913534i | −0.889586 | − | 0.456767i | \(-0.849007\pi\) | ||
0.889586 | − | 0.456767i | \(-0.150993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.85641 | − | 11.1106i | 0.402496 | − | 0.569215i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.3335 | + | 23.0943i | −0.681310 | + | 1.18006i | 0.293272 | + | 0.956029i | \(0.405256\pi\) |
−0.974581 | + | 0.224034i | \(0.928077\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | + | 1.73205i | −0.0509647 | + | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.26795 | − | 6.41473i | −0.115286 | − | 0.326079i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.33057 | − | 2.50026i | 0.219569 | − | 0.126768i | −0.386182 | − | 0.922423i | \(-0.626206\pi\) |
0.605751 | + | 0.795655i | \(0.292873\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85641 | −0.0938825 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.0207 | + | 1.10759i | 0.606362 | + | 0.0558704i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.50026 | + | 4.33057i | 0.125802 | + | 0.217895i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.16025 | + | 7.20577i | −0.208797 | + | 0.361647i | −0.951336 | − | 0.308156i | \(-0.900288\pi\) |
0.742539 | + | 0.669803i | \(0.233622\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.650252 | + | 28.1689i | 0.0325533 | + | 1.41021i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.74479 | + | 9.95026i | −0.286881 | + | 0.496892i | −0.973064 | − | 0.230537i | \(-0.925952\pi\) |
0.686183 | + | 0.727429i | \(0.259285\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.33013 | − | 14.4282i | −0.414953 | − | 0.718720i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.57321 | − | 11.8780i | 0.227245 | − | 0.590220i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.61729 | −0.0801659 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.4641 | − | 14.1244i | 1.20967 | − | 0.698404i | 0.246984 | − | 0.969019i | \(-0.420560\pi\) |
0.962688 | + | 0.270615i | \(0.0872270\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.757875 | + | 1.07180i | −0.0373832 | + | 0.0528678i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.6443 | + | 27.0967i | −0.769805 | + | 1.33334i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.46410 | + | 9.46410i | −0.268222 | + | 0.464574i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.6622 | − | 13.1962i | −0.913891 | − | 0.646218i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 32.0464i | − | 1.56557i | −0.622292 | − | 0.782785i | \(-0.713798\pi\) | ||
0.622292 | − | 0.782785i | \(-0.286202\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.7128 | − | 17.7321i | −1.49685 | − | 0.864207i | −0.496857 | − | 0.867832i | \(-0.665513\pi\) |
−0.999993 | + | 0.00362487i | \(0.998846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.78658 | − | 31.1343i | 0.281353 | − | 1.51380i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.6969i | 0.712906i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.59808 | + | 11.4282i | 0.319303 | + | 0.553050i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.00000 | − | 1.41421i | −0.0965609 | − | 0.0682789i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.7279 | − | 22.0454i | −0.613082 | − | 1.06189i | −0.990718 | − | 0.135935i | \(-0.956596\pi\) |
0.377635 | − | 0.925954i | \(-0.376737\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.89230 | − | 1.66987i | 0.138995 | − | 0.0802490i | −0.428890 | − | 0.903357i | \(-0.641095\pi\) |
0.567885 | + | 0.823108i | \(0.307762\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.92016 | − | 17.1915i | −0.379743 | − | 0.824270i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.189469 | − | 1.64085i | −0.00906352 | − | 0.0784924i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4545 | − | 11.2321i | −0.928512 | − | 0.536077i | −0.0421712 | − | 0.999110i | \(-0.513427\pi\) |
−0.886341 | + | 0.463034i | \(0.846761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.5065 | − | 15.7980i | 0.643165 | − | 0.752284i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.4607 | − | 19.3185i | 1.58976 | − | 0.917850i | 0.596419 | − | 0.802674i | \(-0.296590\pi\) |
0.993345 | − | 0.115177i | \(-0.0367435\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.3923i | 0.492642i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 29.0948 | + | 2.68080i | 1.37614 | + | 0.126798i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.4959 | −1.62796 | −0.813982 | − | 0.580890i | \(-0.802704\pi\) | ||||
−0.813982 | + | 0.580890i | \(0.802704\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.85641 | + | 1.07180i | 0.0874148 | + | 0.0504689i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.44949 | + | 3.14626i | 0.0681030 | + | 0.147824i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.6975 | 0.923431 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7128 | −0.968905 | −0.484452 | − | 0.874818i | \(-0.660981\pi\) | ||||
−0.484452 | + | 0.874818i | \(0.660981\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.2474 | − | 17.7491i | 0.851718 | − | 0.828457i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.4737 | − | 16.4393i | −1.32615 | − | 0.765656i | −0.341452 | − | 0.939899i | \(-0.610919\pi\) |
−0.984703 | + | 0.174244i | \(0.944252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.5885 | 1.37509 | 0.687546 | − | 0.726141i | \(-0.258688\pi\) | ||||
0.687546 | + | 0.726141i | \(0.258688\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00328 | + | 10.8886i | −0.0465262 | + | 0.504949i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.6274i | 1.04707i | 0.852004 | + | 0.523536i | \(0.175387\pi\) | ||||
−0.852004 | + | 0.523536i | \(0.824613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.23205 | + | 1.86603i | −0.149242 | + | 0.0861650i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.561920 | − | 6.09852i | 0.0258919 | − | 0.281005i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.744272 | + | 0.429705i | 0.0342216 | + | 0.0197579i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.9904 | + | 1.50000i | −0.596040 | + | 0.0688247i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.8025 | + | 3.30875i | 0.815121 | + | 0.151497i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2784 | + | 5.93426i | −0.469634 | + | 0.271143i | −0.716086 | − | 0.698012i | \(-0.754068\pi\) |
0.246453 | + | 0.969155i | \(0.420735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.96410 | + | 13.7942i | 0.363132 | + | 0.628963i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.41421 | + | 2.00000i | −0.0643489 | + | 0.0910032i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.27792 | + | 9.14162i | 0.239658 | + | 0.415100i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.9282i | 1.12960i | 0.825226 | + | 0.564802i | \(0.191048\pi\) | ||||
−0.825226 | + | 0.564802i | \(0.808952\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.17423 | − | 3.76588i | 0.369652 | − | 0.170299i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.66115 | + | 5.00052i | 0.390872 | + | 0.225670i | 0.682538 | − | 0.730850i | \(-0.260876\pi\) |
−0.291666 | + | 0.956520i | \(0.594210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 37.8564i | − | 1.70497i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.535898 | + | 1.51575i | 0.0240868 | + | 0.0681279i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.69213 | + | 11.5911i | −0.300183 | + | 0.519932i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.06218 | + | 13.9641i | −0.360913 | + | 0.625119i | −0.988111 | − | 0.153740i | \(-0.950868\pi\) |
0.627199 | + | 0.778859i | \(0.284201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.7846 | + | 7.62587i | 0.481821 | + | 0.340699i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.8338 | + | 9.14162i | −0.705992 | + | 0.407605i | −0.809575 | − | 0.587016i | \(-0.800303\pi\) |
0.103583 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9282 | 0.486299 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.147509 | + | 1.60091i | −0.00655109 | + | 0.0710991i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.79367 | + | 11.7670i | 0.301124 | + | 0.521562i | 0.976391 | − | 0.216011i | \(-0.0693049\pi\) |
−0.675267 | + | 0.737574i | \(0.735972\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.59808 | − | 9.69615i | 0.247644 | − | 0.428933i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.5505 | + | 14.3171i | 0.774874 | + | 0.632116i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.39924 | + | 12.8159i | −0.326049 | + | 0.564734i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00000 | + | 3.46410i | 0.0879599 | + | 0.152351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.88613 | − | 20.4702i | 0.0827918 | − | 0.898540i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.52004 | 0.198027 | 0.0990133 | − | 0.995086i | \(-0.468431\pi\) | ||||
0.0990133 | + | 0.995086i | \(0.468431\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5981 | − | 8.42820i | 0.638329 | − | 0.368540i | −0.145641 | − | 0.989337i | \(-0.546525\pi\) |
0.783971 | + | 0.620798i | \(0.213191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.8338 | + | 11.1962i | 0.691042 | + | 0.488640i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.9348 | + | 18.9396i | −0.476326 | + | 0.825021i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4282 | + | 19.7942i | −0.496878 | + | 0.860619i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.38375 | + | 23.7128i | 0.363824 | + | 1.02905i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21.1117i | − | 0.914448i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 3.46410i | −0.259403 | − | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.22474 | + | 1.02494i | −0.0960048 | + | 0.0442296i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.62536i | 0.113082i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.76795 | + | 15.1865i | 0.376964 | + | 0.652920i | 0.990619 | − | 0.136654i | \(-0.0436349\pi\) |
−0.613655 | + | 0.789574i | \(0.710302\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.46410 | − | 4.89898i | 0.148659 | − | 0.210235i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.1769 | − | 17.6269i | −0.435930 | − | 0.755054i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1340 | − | 6.42820i | 0.476054 | − | 0.274850i | −0.242716 | − | 0.970097i | \(-0.578038\pi\) |
0.718771 | + | 0.695247i | \(0.244705\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.4291 | + | 1.93834i | 0.445103 | + | 0.0827262i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.4607 | − | 3.86370i | 1.42547 | − | 0.164599i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4282 | + | 6.59808i | 0.485977 | + | 0.280579i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.959200 | − | 10.4102i | 0.0407158 | − | 0.441888i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.92996 | − | 1.69161i | 0.124147 | − | 0.0716760i | −0.436641 | − | 0.899636i | \(-0.643832\pi\) |
0.560787 | + | 0.827960i | \(0.310499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.46410i | − | 0.357993i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.295018 | + | 3.20183i | −0.0124557 | + | 0.135181i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.38323 | 0.142586 | 0.0712931 | − | 0.997455i | \(-0.477287\pi\) | ||||
0.0712931 | + | 0.997455i | \(0.477287\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.8564 | − | 13.1962i | −0.961576 | − | 0.555166i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.22106 | − | 33.1802i | −0.219264 | − | 1.39344i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.9391 | 0.584356 | 0.292178 | − | 0.956364i | \(-0.405620\pi\) | ||||
0.292178 | + | 0.956364i | \(0.405620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.1962 | −1.05443 | −0.527213 | − | 0.849733i | \(-0.676763\pi\) | ||||
−0.527213 | + | 0.849733i | \(0.676763\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.22599 | + | 2.66113i | 0.0512164 | + | 0.111170i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.984508 | − | 0.568406i | −0.0410568 | − | 0.0237042i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.9282 | 1.78712 | 0.893562 | − | 0.448939i | \(-0.148198\pi\) | ||||
0.893562 | + | 0.448939i | \(0.148198\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.7600 | − | 2.09711i | −0.945873 | − | 0.0871531i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.8391i | 1.19645i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.98076 | + | 1.14359i | −0.0820348 | + | 0.0473628i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.2892 | − | 12.0349i | 0.425408 | − | 0.497582i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.29392 | + | 5.36585i | 0.383601 | + | 0.221472i | 0.679384 | − | 0.733783i | \(-0.262247\pi\) |
−0.295783 | + | 0.955255i | \(0.595580\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.8564 | − | 7.73205i | −0.735760 | − | 0.318594i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.62534 | + | 14.3810i | 0.272530 | + | 0.591554i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.7816 | − | 12.5756i | 0.894463 | − | 0.516419i | 0.0190636 | − | 0.999818i | \(-0.493931\pi\) |
0.875400 | + | 0.483400i | \(0.160598\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.9282 | − | 22.3923i | −0.530005 | − | 0.917995i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.1074 | + | 12.8038i | 0.741086 | + | 0.524027i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.43451 | − | 14.6090i | −0.344625 | − | 0.596908i | 0.640661 | − | 0.767824i | \(-0.278661\pi\) |
−0.985286 | + | 0.170916i | \(0.945327\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 44.3731i | − | 1.81002i | −0.425395 | − | 0.905008i | \(-0.639865\pi\) | ||
0.425395 | − | 0.905008i | \(-0.360135\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.548188 | + | 2.94949i | −0.0223239 | + | 0.120113i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.2963 | + | 7.67664i | 0.540573 | + | 0.312100i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 13.2487i | − | 0.537749i | −0.963175 | − | 0.268874i | \(-0.913348\pi\) | ||
0.963175 | − | 0.268874i | \(-0.0866516\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −40.7846 | − | 28.8391i | −1.65268 | − | 1.16862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.6975 | − | 34.1170i | 0.796874 | − | 1.38023i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.3205 | + | 19.6077i | −0.457231 | + | 0.791947i | −0.998813 | − | 0.0487003i | \(-0.984492\pi\) |
0.541582 | + | 0.840648i | \(0.317825\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.00000 | + | 11.3137i | −0.322591 | + | 0.456213i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.4379 | + | 12.9546i | −0.903318 | + | 0.521531i | −0.878275 | − | 0.478156i | \(-0.841305\pi\) |
−0.0250427 | + | 0.999686i | \(0.507972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.80385 | −0.112696 | −0.0563481 | − | 0.998411i | \(-0.517946\pi\) | ||||
−0.0563481 | + | 0.998411i | \(0.517946\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.483242 | + | 1.90880i | 0.0193918 | + | 0.0765974i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.7124 | + | 23.7506i | 0.549377 | + | 0.951549i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.86015 | + | 0.0660240i | −0.114223 | + | 0.00263674i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.4543 | − | 18.1074i | 0.416840 | − | 0.721988i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.5263 | + | 42.4808i | 0.976376 | + | 1.69113i | 0.675318 | + | 0.737526i | \(0.264006\pi\) |
0.301058 | + | 0.953606i | \(0.402660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.9722 | − | 1.74810i | −0.754077 | − | 0.0694809i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.1106 | −0.440912 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.3923 | − | 12.9282i | 0.887215 | − | 0.512234i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.58630 | + | 10.1436i | 0.141872 | + | 0.401274i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.41473 | − | 11.1106i | 0.253367 | − | 0.438844i | −0.711084 | − | 0.703107i | \(-0.751795\pi\) |
0.964451 | + | 0.264263i | \(0.0851288\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.7942 | + | 37.7487i | −0.859480 | + | 1.48866i | 0.0129447 | + | 0.999916i | \(0.495879\pi\) |
−0.872425 | + | 0.488748i | \(0.837454\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.20736 | + | 4.53590i | −0.126290 | + | 0.178601i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.5569i | 0.808174i | 0.914721 | + | 0.404087i | \(0.132411\pi\) | ||||
−0.914721 | + | 0.404087i | \(0.867589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.75129 | − | 1.58846i | −0.107998 | − | 0.0623524i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0744 | + | 26.2088i | 0.473234 | + | 1.02720i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.1223i | 1.84404i | 0.387144 | + | 0.922019i | \(0.373462\pi\) | ||||
−0.387144 | + | 0.922019i | \(0.626538\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.92820 | − | 8.53590i | −0.192561 | − | 0.333525i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00000 | − | 8.48528i | −0.117041 | − | 0.331042i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.5409 | − | 28.6496i | −0.644340 | − | 1.11603i | −0.984453 | − | 0.175646i | \(-0.943799\pi\) |
0.340113 | − | 0.940385i | \(-0.389535\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.32051 | − | 3.07180i | 0.206944 | − | 0.119479i | −0.392946 | − | 0.919561i | \(-0.628544\pi\) |
0.599890 | + | 0.800082i | \(0.295211\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.7620 | − | 13.2507i | 1.11702 | − | 0.514614i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.4727 | − | 13.7124i | 0.716341 | − | 0.531745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53590 | + | 1.46410i | 0.0981904 | + | 0.0566902i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.1993 | − | 1.49261i | −0.626302 | − | 0.0577077i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.16037 | + | 0.669942i | −0.0447957 | + | 0.0258628i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.9808i | 0.847296i | 0.905827 | + | 0.423648i | \(0.139251\pi\) | ||||
−0.905827 | + | 0.423648i | \(0.860749\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.1117 | − | 3.82577i | 0.581650 | − | 0.147254i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.8380 | 0.724005 | 0.362002 | − | 0.932177i | \(-0.382093\pi\) | ||||
0.362002 | + | 0.932177i | \(0.382093\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.1244 | + | 13.9282i | 0.925808 | + | 0.534515i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.6934 | − | 17.8261i | 1.48274 | − | 0.683099i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.3142 | −0.624246 | −0.312123 | − | 0.950042i | \(-0.601040\pi\) | ||||
−0.312123 | + | 0.950042i | \(0.601040\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.07180 | 0.0409512 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.7753 | + | 6.80702i | −0.563714 | + | 0.259704i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 19.5080 | + | 11.2629i | 0.743195 | + | 0.429084i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.85641 | −0.374955 | −0.187478 | − | 0.982269i | \(-0.560031\pi\) | ||||
−0.187478 | + | 0.982269i | \(0.560031\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.22474 | + | 2.75699i | 0.122498 | + | 0.104730i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 18.6622i | 0.707897i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | + | 13.8564i | −0.909065 | + | 0.524849i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.18546 | + | 0.569930i | 0.233955 | + | 0.0215567i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.2344 | − | 9.95026i | −0.650933 | − | 0.375816i | 0.137881 | − | 0.990449i | \(-0.455971\pi\) |
−0.788814 | + | 0.614633i | \(0.789304\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.0718 | + | 7.39230i | 0.643875 | + | 0.278806i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.4840 | + | 10.8191i | −0.884460 | + | 0.407472i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.9754 | − | 14.4195i | 0.939295 | − | 0.542303i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.1603 | − | 36.6506i | −0.794690 | − | 1.37644i | −0.923036 | − | 0.384714i | \(-0.874300\pi\) |
0.128346 | − | 0.991729i | \(-0.459033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0010 | − | 3.53590i | 0.375068 | − | 0.132607i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.845807 | − | 1.46498i | −0.0316757 | − | 0.0548640i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000i | 0.0747958i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.7249 | + | 47.1560i | 0.811330 | + | 1.76107i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.22715 | − | 3.01790i | −0.194940 | − | 0.112549i | 0.399353 | − | 0.916797i | \(-0.369235\pi\) |
−0.594293 | + | 0.804249i | \(0.702568\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 39.0526i | 1.45439i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 28.6603 | − | 40.5317i | 1.06589 | − | 1.50739i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.5911 | − | 20.0764i | 0.430483 | − | 0.745618i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.79423 | + | 11.7679i | −0.251984 | + | 0.436449i | −0.964072 | − | 0.265641i | \(-0.914416\pi\) |
0.712088 | + | 0.702090i | \(0.247750\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.62209 | + | 5.55532i | −0.355886 | + | 0.205471i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.7128 | −1.31908 | −0.659541 | − | 0.751668i | \(-0.729249\pi\) | ||||
−0.659541 | + | 0.751668i | \(0.729249\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.8990 | − | 1.55708i | −0.623328 | − | 0.0574337i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.189469 | − | 0.328169i | −0.00697917 | − | 0.0120883i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.4019 | + | 30.1410i | −0.640140 | + | 1.10876i | 0.345261 | + | 0.938507i | \(0.387790\pi\) |
−0.985401 | + | 0.170249i | \(0.945543\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.6476 | + | 24.0698i | 0.538092 | + | 0.884227i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.53553 | − | 6.12372i | 0.129706 | − | 0.224658i | −0.793857 | − | 0.608105i | \(-0.791930\pi\) |
0.923563 | + | 0.383447i | \(0.125263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.9282 | − | 20.6603i | −0.437016 | − | 0.756933i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.6203 | + | 15.0645i | 0.644694 | + | 0.551181i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.2832 | −0.668055 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.45448 | − | 4.30385i | 0.272018 | − | 0.157050i | −0.357786 | − | 0.933803i | \(-0.616468\pi\) |
0.629804 | + | 0.776754i | \(0.283135\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.6969 | + | 20.7846i | −0.535586 | + | 0.757433i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.41421 | − | 2.44949i | 0.0514685 | − | 0.0891461i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.30385 | + | 3.99038i | −0.0837348 | + | 0.145033i | −0.904851 | − | 0.425728i | \(-0.860018\pi\) |
0.821117 | + | 0.570760i | \(0.193352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.203072 | − | 0.143594i | −0.00737104 | − | 0.00521212i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 46.2629i | − | 1.67703i | −0.544879 | − | 0.838514i | \(-0.683425\pi\) | ||
0.544879 | − | 0.838514i | \(-0.316575\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −46.5167 | − | 26.8564i | −1.68402 | − | 0.972267i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.4347 | − | 3.79796i | −0.738817 | − | 0.137315i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.2886i | 1.12976i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.428203 | + | 0.741670i | 0.0154414 | + | 0.0267453i | 0.873643 | − | 0.486568i | \(-0.161751\pi\) |
−0.858201 | + | 0.513313i | \(0.828418\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.53590 | − | 3.20736i | −0.163356 | − | 0.115510i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.04008 | + | 15.6579i | 0.325149 | + | 0.563175i | 0.981543 | − | 0.191244i | \(-0.0612521\pi\) |
−0.656393 | + | 0.754419i | \(0.727919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.5981 | + | 6.69615i | −0.416615 | + | 0.240533i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.5439 | − | 25.0572i | −0.414135 | − | 0.898921i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.6969 | − | 19.7990i | −0.526572 | − | 0.709372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.17691 | − | 0.679492i | −0.0421133 | − | 0.0243141i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −38.9248 | + | 9.85441i | −1.39106 | + | 0.352168i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.33057 | + | 2.50026i | −0.154565 | + | 0.0892380i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.0718i | 0.858067i | 0.903289 | + | 0.429033i | \(0.141146\pi\) | ||||
−0.903289 | + | 0.429033i | \(0.858854\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.956893 | − | 0.0881685i | −0.0340663 | − | 0.00313888i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −69.6482 | −2.47640 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.4282 | + | 6.59808i | 0.405827 | + | 0.234305i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.18635 | − | 13.4281i | −0.219407 | − | 0.476246i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.4939 | −0.513399 | −0.256700 | − | 0.966491i | \(-0.582635\pi\) | ||||
−0.256700 | + | 0.966491i | \(0.582635\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51.7128 | −1.82947 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.6742 | + | 4.02834i | 0.765821 | + | 0.142335i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.984508 | + | 0.568406i | 0.0347425 | + | 0.0200586i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.959200 | + | 10.4102i | −0.0337654 | + | 0.366456i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 51.1619i | − | 1.79876i | −0.437172 | − | 0.899378i | \(-0.644020\pi\) | ||
0.437172 | − | 0.899378i | \(-0.355980\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.8038 | + | 10.8564i | −0.660292 | + | 0.381220i | −0.792388 | − | 0.610017i | \(-0.791163\pi\) |
0.132096 | + | 0.991237i | \(0.457829\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.10102 | − | 11.9494i | 0.0386145 | − | 0.419083i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.36396 | − | 3.67423i | −0.222920 | − | 0.128703i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.89230 | − | 7.93782i | −0.206146 | − | 0.277709i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.63528 | − | 41.0811i | 0.266798 | − | 1.43549i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.8744 | + | 17.2480i | −1.04262 | + | 0.601958i | −0.920575 | − | 0.390566i | \(-0.872279\pi\) |
−0.122047 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | − | 6.92820i | −0.139431 | − | 0.241502i | 0.787850 | − | 0.615867i | \(-0.211194\pi\) |
−0.927281 | + | 0.374365i | \(0.877861\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.13681 | + | 1.60770i | −0.0395787 | + | 0.0559728i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.2474 | − | 21.2132i | −0.425886 | − | 0.737655i | 0.570617 | − | 0.821216i | \(-0.306704\pi\) |
−0.996503 | + | 0.0835608i | \(0.973371\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.6603i | 1.34273i | 0.741129 | + | 0.671363i | \(0.234291\pi\) | ||||
−0.741129 | + | 0.671363i | \(0.765709\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.5054 | − | 7.14338i | 0.537877 | − | 0.247801i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −29.3939 | − | 16.9706i | −1.01844 | − | 0.587995i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 10.7846i | − | 0.373217i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3205 | + | 6.31319i | 0.771510 | + | 0.218216i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.87920 | − | 4.98691i | 0.0994009 | − | 0.172167i | −0.812036 | − | 0.583607i | \(-0.801641\pi\) |
0.911437 | + | 0.411440i | \(0.134974\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3564 | + | 26.5981i | −0.529531 | + | 0.917175i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.3205 | + | 15.0759i | 0.734317 | + | 0.519241i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.13681 | − | 0.656339i | 0.0391075 | − | 0.0225787i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.5167 | 1.39217 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.47339 | − | 37.6967i | 0.119206 | − | 1.29375i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.808643 | + | 1.40061i | 0.0277199 | + | 0.0480123i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.83975 | + | 17.0429i | −0.336906 | + | 0.583539i | −0.983849 | − | 0.178999i | \(-0.942714\pi\) |
0.646943 | + | 0.762539i | \(0.276047\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.27135 | − | 18.4495i | 0.0434792 | − | 0.630959i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.51575 | + | 2.62536i | −0.0517770 | + | 0.0896804i | −0.890752 | − | 0.454489i | \(-0.849822\pi\) |
0.838975 | + | 0.544170i | \(0.183155\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.33013 | − | 4.03590i | −0.0795029 | − | 0.137703i | 0.823533 | − | 0.567269i | \(-0.192000\pi\) |
−0.903036 | + | 0.429566i | \(0.858667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.35504 | + | 36.4122i | −0.114339 | + | 1.24093i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2832 | 0.622369 | 0.311184 | − | 0.950350i | \(-0.399274\pi\) | ||||
0.311184 | + | 0.950350i | \(0.399274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.5359 | + | 8.39230i | −0.494235 | + | 0.285347i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.89949 | − | 7.00000i | −0.336204 | − | 0.237732i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.669942 | + | 1.16037i | −0.0227262 | + | 0.0393630i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.86603 | + | 3.23205i | −0.0632279 | + | 0.109514i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.1117 | − | 7.46410i | 0.714522 | − | 0.252622i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 42.2233i | − | 1.42741i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.23205 | − | 1.86603i | −0.109139 | − | 0.0630112i | 0.444437 | − | 0.895810i | \(-0.353404\pi\) |
−0.553576 | + | 0.832799i | \(0.686737\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −39.7259 | + | 18.3018i | −1.33992 | + | 0.617305i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.8482i | 1.34252i | 0.741222 | + | 0.671260i | \(0.234246\pi\) | ||||
−0.741222 | + | 0.671260i | \(0.765754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.1340 | − | 19.2846i | −0.374688 | − | 0.648979i | 0.615592 | − | 0.788065i | \(-0.288917\pi\) |
−0.990280 | + | 0.139086i | \(0.955584\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.8564 | − | 16.7675i | 0.398549 | − | 0.563633i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.98502 | − | 10.3664i | −0.200957 | − | 0.348068i | 0.747880 | − | 0.663834i | \(-0.231072\pi\) |
−0.948837 | + | 0.315766i | \(0.897739\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.3923 | + | 14.6603i | −0.851631 | + | 0.491689i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.36898 | − | 0.530126i | 0.112865 | − | 0.0177599i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.27792 | − | 45.7081i | −0.176619 | − | 1.52956i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.73205 | + | 1.00000i | 0.0578961 | + | 0.0334263i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.224745 | + | 2.43916i | −0.00750401 | + | 0.0814411i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.8744 | − | 17.2480i | 0.996365 | − | 0.575252i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 29.5692i | − | 0.985094i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.34510 | + | 14.5984i | −0.0447622 | + | 0.485805i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.89898 | −0.162848 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.4449 | − | 20.4641i | −1.17693 | − | 0.679499i | −0.221626 | − | 0.975132i | \(-0.571136\pi\) |
−0.955302 | + | 0.295632i | \(0.904470\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.23607 | − | 22.7919i | 0.140502 | − | 0.755960i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40.9107 | −1.35543 | −0.677715 | − | 0.735324i | \(-0.737030\pi\) | ||||
−0.677715 | + | 0.735324i | \(0.737030\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.92820 | −0.0969094 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.62410 | − | 7.86647i | −0.119809 | − | 0.260058i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.5259 | − | 13.0053i | −0.743870 | − | 0.429474i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.9808 | 1.05495 | 0.527474 | − | 0.849571i | \(-0.323139\pi\) | ||||
0.527474 | + | 0.849571i | \(0.323139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.8988 | − | 2.20204i | −0.787491 | − | 0.0725597i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.3843i | 0.440548i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0885 | − | 6.40192i | 0.364586 | − | 0.210494i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.8607 | + | 20.3997i | 0.783687 | + | 0.670013i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.7148 | − | 10.2277i | −0.581205 | − | 0.335559i | 0.180407 | − | 0.983592i | \(-0.442258\pi\) |
−0.761612 | + | 0.648033i | \(0.775592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000 | − | 27.7128i | 0.393284 | − | 0.908251i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −19.6750 | − | 42.7065i | −0.644130 | − | 1.39815i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.27362 | − | 1.31268i | 0.0743555 | − | 0.0429291i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.89230 | − | 5.00962i | −0.0944875 | − | 0.163657i | 0.814907 | − | 0.579592i | \(-0.196788\pi\) |
−0.909395 | + | 0.415934i | \(0.863455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.0507 | − | 24.7846i | −1.14384 | − | 0.808815i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.96953 | + | 12.0716i | 0.227200 | + | 0.393522i | 0.956977 | − | 0.290163i | \(-0.0937095\pi\) |
−0.729777 | + | 0.683685i | \(0.760376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.14359i | − | 0.0698050i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19.6589 | + | 19.1220i | −0.639504 | + | 0.622039i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 38.3596 | + | 22.1469i | 1.24652 | + | 0.719679i | 0.970414 | − | 0.241448i | \(-0.0776223\pi\) |
0.276107 | + | 0.961127i | \(0.410956\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 11.1962i | − | 0.363442i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.4641 | + | 13.7632i | 0.631167 | + | 0.446302i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.3011 | + | 36.8947i | −0.690011 | + | 1.19513i | 0.281822 | + | 0.959467i | \(0.409061\pi\) |
−0.971834 | + | 0.235668i | \(0.924272\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.19615 | − | 2.07180i | 0.0387066 | − | 0.0670418i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.92820 | − | 4.14110i | 0.0946554 | − | 0.133863i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.44949 | − | 1.41421i | 0.0790981 | − | 0.0456673i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0718 | 0.357155 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.55051 | + | 11.1708i | −0.307761 | + | 0.359975i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.33109 | + | 16.1619i | 0.300378 | + | 0.520271i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.40192 | + | 7.62436i | −0.141556 | + | 0.245183i | −0.928083 | − | 0.372374i | \(-0.878544\pi\) |
0.786527 | + | 0.617556i | \(0.211877\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.7491 | − | 32.4495i | 0.570183 | − | 1.04243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.17260 | + | 12.4233i | −0.230180 | + | 0.398683i | −0.957861 | − | 0.287232i | \(-0.907265\pi\) |
0.727681 | + | 0.685916i | \(0.240598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.6244 | + | 42.6506i | 0.789421 | + | 1.36732i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19.3105 | + | 1.77928i | 0.618431 | + | 0.0569825i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.3538 | −0.651176 | −0.325588 | − | 0.945512i | \(-0.605562\pi\) | ||||
−0.325588 | + | 0.945512i | \(0.605562\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.41154 | + | 1.39230i | −0.0770732 | + | 0.0444983i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −40.7076 | + | 14.3923i | −1.29969 | + | 0.459511i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.2635 | − | 28.1691i | 0.518724 | − | 0.898456i | −0.481040 | − | 0.876699i | \(-0.659741\pi\) |
0.999763 | − | 0.0217569i | \(-0.00692599\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.46410 | − | 11.1962i | 0.205963 | − | 0.356739i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −39.3949 | + | 55.7128i | −1.25395 | + | 1.77336i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 0.859411i | − | 0.0273277i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.61731 | + | 2.08846i | 0.114908 | + | 0.0663420i | 0.556352 | − | 0.830946i | \(-0.312200\pi\) |
−0.441445 | + | 0.897289i | \(0.645534\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.1398 | + | 50.2273i | 0.734319 | + | 1.59391i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 18.1074i | − | 0.574042i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.0885 | − | 43.4545i | −0.794559 | − | 1.37622i | −0.923119 | − | 0.384515i | \(-0.874369\pi\) |
0.128559 | − | 0.991702i | \(-0.458965\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.3397 | − | 6.03579i | −0.675160 | − | 0.190964i |
(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 | 912.2.bn.m.65.1 | 8 | ||
3.2 | odd | 2 | inner | 912.2.bn.m.65.2 | 8 | ||
4.3 | odd | 2 | 57.2.f.a.8.1 | ✓ | 8 | ||
12.11 | even | 2 | 57.2.f.a.8.4 | yes | 8 | ||
19.12 | odd | 6 | inner | 912.2.bn.m.449.2 | 8 | ||
57.50 | even | 6 | inner | 912.2.bn.m.449.1 | 8 | ||
76.11 | odd | 6 | 1083.2.d.b.1082.7 | 8 | |||
76.27 | even | 6 | 1083.2.d.b.1082.2 | 8 | |||
76.31 | even | 6 | 57.2.f.a.50.4 | yes | 8 | ||
228.11 | even | 6 | 1083.2.d.b.1082.1 | 8 | |||
228.107 | odd | 6 | 57.2.f.a.50.1 | yes | 8 | ||
228.179 | odd | 6 | 1083.2.d.b.1082.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.2.f.a.8.1 | ✓ | 8 | 4.3 | odd | 2 | ||
57.2.f.a.8.4 | yes | 8 | 12.11 | even | 2 | ||
57.2.f.a.50.1 | yes | 8 | 228.107 | odd | 6 | ||
57.2.f.a.50.4 | yes | 8 | 76.31 | even | 6 | ||
912.2.bn.m.65.1 | 8 | 1.1 | even | 1 | trivial | ||
912.2.bn.m.65.2 | 8 | 3.2 | odd | 2 | inner | ||
912.2.bn.m.449.1 | 8 | 57.50 | even | 6 | inner | ||
912.2.bn.m.449.2 | 8 | 19.12 | odd | 6 | inner | ||
1083.2.d.b.1082.1 | 8 | 228.11 | even | 6 | |||
1083.2.d.b.1082.2 | 8 | 76.27 | even | 6 | |||
1083.2.d.b.1082.7 | 8 | 76.11 | odd | 6 | |||
1083.2.d.b.1082.8 | 8 | 228.179 | odd | 6 |