Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,2,Mod(49,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.bb (of order \(12\), degree \(4\), 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: | \(4.59938315643\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.49 |
Dual form | 576.2.bb.a.529.1 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.86603 | + | 0.500000i | −0.834512 | + | 0.223607i | −0.650681 | − | 0.759351i | \(-0.725517\pi\) |
−0.183831 | + | 0.982958i | \(0.558850\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.86603 | + | 2.23205i | −1.46122 | + | 0.843636i | −0.999068 | − | 0.0431647i | \(-0.986256\pi\) |
−0.462152 | + | 0.886801i | \(0.652923\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 1.86603i | 0.150756 | − | 0.562628i | −0.848676 | − | 0.528913i | \(-0.822600\pi\) |
0.999432 | − | 0.0337145i | \(-0.0107337\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.598076 | − | 2.23205i | −0.165876 | − | 0.619060i | −0.997927 | − | 0.0643593i | \(-0.979500\pi\) |
0.832050 | − | 0.554700i | \(-0.187167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.23205 | − | 0.866025i | 0.834512 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 3.00000i | 0.688247 | − | 0.688247i | −0.273597 | − | 0.961844i | \(-0.588214\pi\) |
0.961844 | + | 0.273597i | \(0.0882135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.69615 | − | 3.86603i | 1.46122 | − | 0.843636i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.59808 | + | 3.23205i | 1.16728 | + | 0.673929i | 0.953038 | − | 0.302851i | \(-0.0979386\pi\) |
0.214242 | + | 0.976781i | \(0.431272\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.09808 | + | 0.633975i | −0.219615 | + | 0.126795i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.866025 | − | 0.232051i | −0.160817 | − | 0.0430908i | 0.177512 | − | 0.984119i | \(-0.443195\pi\) |
−0.338329 | + | 0.941028i | \(0.609862\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.59808 | − | 7.96410i | 0.825839 | − | 1.43039i | −0.0754376 | − | 0.997151i | \(-0.524035\pi\) |
0.901277 | − | 0.433244i | \(-0.142631\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.866025 | + | 3.23205i | −0.150756 | + | 0.562628i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.09808 | − | 6.09808i | 1.03076 | − | 1.03076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26795 | − | 4.26795i | −0.701647 | − | 0.701647i | 0.263117 | − | 0.964764i | \(-0.415249\pi\) |
−0.964764 | + | 0.263117i | \(0.915249\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.03590 | + | 3.86603i | 0.165876 | + | 0.619060i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.696152 | + | 0.401924i | 0.108721 | + | 0.0627700i | 0.553374 | − | 0.832933i | \(-0.313340\pi\) |
−0.444654 | + | 0.895703i | \(0.646673\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.69615 | − | 6.33013i | 0.258661 | − | 0.965335i | −0.707356 | − | 0.706857i | \(-0.750112\pi\) |
0.966017 | − | 0.258478i | \(-0.0832210\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.59808 | + | 1.50000i | −0.834512 | + | 0.223607i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.598076 | + | 1.03590i | 0.0872384 | + | 0.151101i | 0.906343 | − | 0.422543i | \(-0.138862\pi\) |
−0.819104 | + | 0.573644i | \(0.805529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.46410 | − | 11.1962i | 0.923443 | − | 1.59945i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.92820 | −0.970143 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.73205 | + | 5.73205i | 0.787358 | + | 0.787358i | 0.981060 | − | 0.193703i | \(-0.0620497\pi\) |
−0.193703 | + | 0.981060i | \(0.562050\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.73205i | 0.503230i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.19615 | + | 5.19615i | −0.688247 | + | 0.688247i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | − | 0.401924i | 0.195283 | − | 0.0523260i | −0.159852 | − | 0.987141i | \(-0.551102\pi\) |
0.355135 | + | 0.934815i | \(0.384435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.13397 | − | 0.571797i | −0.273227 | − | 0.0732111i | 0.119604 | − | 0.992822i | \(-0.461838\pi\) |
−0.392831 | + | 0.919611i | \(0.628504\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.5981 | + | 6.69615i | −1.46122 | + | 0.843636i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.23205 | + | 3.86603i | 0.276852 | + | 0.479521i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.23205 | + | 8.33013i | 0.272688 | + | 1.01769i | 0.957375 | + | 0.288849i | \(0.0932726\pi\) |
−0.684686 | + | 0.728838i | \(0.740061\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.69615 | − | 5.59808i | −1.16728 | − | 0.673929i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 2.92820i | − | 0.347514i | −0.984789 | − | 0.173757i | \(-0.944409\pi\) | ||
0.984789 | − | 0.173757i | \(-0.0555907\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.46410i | − | 0.873607i | −0.899557 | − | 0.436804i | \(-0.856111\pi\) | ||
0.899557 | − | 0.436804i | \(-0.143889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.90192 | − | 1.09808i | 0.219615 | − | 0.126795i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.23205 | + | 8.33013i | 0.254366 | + | 0.949306i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.866025 | + | 1.50000i | 0.0974355 | + | 0.168763i | 0.910622 | − | 0.413239i | \(-0.135603\pi\) |
−0.813187 | + | 0.582003i | \(0.802269\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1603 | + | 3.79423i | 1.55429 | + | 0.416471i | 0.930850 | − | 0.365401i | \(-0.119068\pi\) |
0.623440 | + | 0.781872i | \(0.285735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.46410 | + | 2.00000i | −0.809595 | + | 0.216930i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.50000 | + | 0.401924i | 0.160817 | + | 0.0430908i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.8564i | − | 1.68078i | −0.541985 | − | 0.840388i | \(-0.682327\pi\) | ||
0.541985 | − | 0.840388i | \(-0.317673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.29423 | + | 7.29423i | 0.764643 | + | 0.764643i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.96410 | + | 13.7942i | −0.825839 | + | 1.43039i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.09808 | + | 7.09808i | −0.420454 | + | 0.728247i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.50000 | − | 5.59808i | 0.150756 | − | 0.562628i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.133975 | + | 0.500000i | −0.0133310 | + | 0.0497519i | −0.972271 | − | 0.233857i | \(-0.924865\pi\) |
0.958940 | + | 0.283609i | \(0.0915318\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.7942 | − | 7.96410i | −1.35919 | − | 0.784726i | −0.369672 | − | 0.929162i | \(-0.620530\pi\) |
−0.989514 | + | 0.144436i | \(0.953863\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.5622 | + | 10.5622i | −1.03076 | + | 1.03076i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.39230 | − | 9.39230i | −0.907988 | − | 0.907988i | 0.0881214 | − | 0.996110i | \(-0.471914\pi\) |
−0.996110 | + | 0.0881214i | \(0.971914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.73205 | + | 1.73205i | −0.165900 | + | 0.165900i | −0.785175 | − | 0.619274i | \(-0.787427\pi\) |
0.619274 | + | 0.785175i | \(0.287427\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.39230 | + | 7.39230i | 0.701647 | + | 0.701647i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.23205 | + | 10.7942i | −0.586262 | + | 1.01544i | 0.408455 | + | 0.912779i | \(0.366068\pi\) |
−0.994717 | + | 0.102657i | \(0.967266\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0622 | − | 3.23205i | −1.12480 | − | 0.301390i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.79423 | − | 6.69615i | −0.165876 | − | 0.619060i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.4641 | + | 8.92820i | −1.41759 | + | 0.818447i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.29423 | + | 3.63397i | 0.572203 | + | 0.330361i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.20577 | − | 0.696152i | −0.108721 | − | 0.0627700i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.56218 | − | 8.56218i | 0.765824 | − | 0.765824i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.392305 | −0.0348114 | −0.0174057 | − | 0.999849i | \(-0.505541\pi\) | ||||
−0.0174057 | + | 0.999849i | \(0.505541\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.93782 | + | 10.9641i | −0.258661 | + | 0.965335i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.30385 | − | 4.86603i | −0.113918 | − | 0.425147i | 0.885286 | − | 0.465047i | \(-0.153963\pi\) |
−0.999204 | + | 0.0399004i | \(0.987296\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.90192 | + | 18.2942i | −0.425051 | + | 1.58631i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.69615 | − | 2.59808i | 0.834512 | − | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.571797 | + | 0.330127i | −0.0488519 | + | 0.0282047i | −0.524227 | − | 0.851579i | \(-0.675646\pi\) |
0.475375 | + | 0.879783i | \(0.342312\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.1603 | + | 4.33013i | −1.37069 | + | 0.367277i | −0.867732 | − | 0.497032i | \(-0.834423\pi\) |
−0.502962 | + | 0.864308i | \(0.667757\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.03590 | − | 1.79423i | −0.0872384 | − | 0.151101i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.46410 | −0.373307 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.73205 | 0.143839 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.1962 | + | 19.3923i | −0.923443 | + | 1.59945i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.0622 | − | 4.30385i | 1.31586 | − | 0.352585i | 0.468438 | − | 0.883497i | \(-0.344817\pi\) |
0.847427 | + | 0.530912i | \(0.178150\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.06218 | − | 3.50000i | 0.493333 | − | 0.284826i | −0.232623 | − | 0.972567i | \(-0.574731\pi\) |
0.725956 | + | 0.687741i | \(0.241398\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.0000 | 0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.59808 | + | 17.1603i | −0.369326 | + | 1.37834i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.866025 | − | 3.23205i | −0.0691164 | − | 0.257946i | 0.922719 | − | 0.385474i | \(-0.125962\pi\) |
−0.991835 | + | 0.127529i | \(0.959296\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.92820 | − | 9.92820i | −0.787358 | − | 0.787358i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −28.8564 | −2.27420 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.92820 | − | 1.92820i | 0.151029 | − | 0.151029i | −0.627549 | − | 0.778577i | \(-0.715942\pi\) |
0.778577 | + | 0.627549i | \(0.215942\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 6.46410i | − | 0.503230i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.2583 | + | 8.23205i | 1.10334 | + | 0.637015i | 0.937097 | − | 0.349069i | \(-0.113502\pi\) |
0.166246 | + | 0.986084i | \(0.446835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.63397 | − | 3.83013i | 0.510306 | − | 0.294625i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.00000 | − | 9.00000i | 0.688247 | − | 0.688247i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.59808 | + | 2.03590i | 0.577671 | + | 0.154786i | 0.535812 | − | 0.844337i | \(-0.320005\pi\) |
0.0418586 | + | 0.999124i | \(0.486672\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.83013 | − | 4.90192i | 0.213937 | − | 0.370551i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.59808 | + | 0.696152i | −0.195283 | + | 0.0523260i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.92820 | − | 5.92820i | 0.443095 | − | 0.443095i | −0.449956 | − | 0.893051i | \(-0.648560\pi\) |
0.893051 | + | 0.449956i | \(0.148560\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.73205 | − | 7.73205i | −0.574719 | − | 0.574719i | 0.358725 | − | 0.933443i | \(-0.383212\pi\) |
−0.933443 | + | 0.358725i | \(0.883212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.69615 | + | 0.990381i | 0.273227 | + | 0.0732111i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0981 | + | 5.83013i | 0.742425 | + | 0.428639i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 7.46410i | 0.146254 | − | 0.545829i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.0885 | − | 11.5981i | 1.46122 | − | 0.843636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.40192 | − | 2.42820i | −0.101440 | − | 0.175699i | 0.810838 | − | 0.585270i | \(-0.199012\pi\) |
−0.912278 | + | 0.409572i | \(0.865678\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23205 | − | 3.86603i | 0.160667 | − | 0.278283i | −0.774441 | − | 0.632646i | \(-0.781969\pi\) |
0.935108 | + | 0.354363i | \(0.115302\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.86603 | − | 6.69615i | −0.276852 | − | 0.479521i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.53590 | + | 3.53590i | 0.251922 | + | 0.251922i | 0.821758 | − | 0.569836i | \(-0.192993\pi\) |
−0.569836 | + | 0.821758i | \(0.692993\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.8564i | − | 1.54936i | −0.632354 | − | 0.774680i | \(-0.717911\pi\) | ||
0.632354 | − | 0.774680i | \(-0.282089\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.86603 | − | 14.4282i | −0.272688 | − | 1.01769i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.86603 | − | 1.03590i | 0.271342 | − | 0.0727058i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50000 | − | 0.401924i | −0.104765 | − | 0.0280716i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 16.7942 | + | 9.69615i | 1.16728 | + | 0.673929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.09808 | − | 7.09808i | −0.283470 | − | 0.490984i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.96410 | + | 18.5263i | 0.341743 | + | 1.27540i | 0.896371 | + | 0.443304i | \(0.146194\pi\) |
−0.554629 | + | 0.832098i | \(0.687140\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.07180i | 0.347514i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.6603i | 0.863422i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 41.0526i | 2.78683i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.9282i | 0.873607i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.39230 | − | 8.92820i | −0.160924 | − | 0.600576i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.79423 | − | 13.5000i | −0.521940 | − | 0.904027i | −0.999674 | − | 0.0255224i | \(-0.991875\pi\) |
0.477734 | − | 0.878504i | \(-0.341458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.29423 | + | 1.90192i | −0.219615 | + | 0.126795i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.6244 | − | 5.25833i | −1.30251 | − | 0.349008i | −0.460114 | − | 0.887860i | \(-0.652191\pi\) |
−0.842400 | + | 0.538852i | \(0.818858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.5263 | − | 4.42820i | 1.09209 | − | 0.292624i | 0.332549 | − | 0.943086i | \(-0.392091\pi\) |
0.759539 | + | 0.650462i | \(0.225425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.86603 | − | 14.4282i | −0.254366 | − | 0.949306i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.07180i | − | 0.594313i | −0.954829 | − | 0.297157i | \(-0.903962\pi\) | ||
0.954829 | − | 0.297157i | \(-0.0960383\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.63397 | − | 1.63397i | −0.106589 | − | 0.106589i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.50000 | − | 2.59808i | −0.0974355 | − | 0.168763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.401924 | − | 0.696152i | 0.0259983 | − | 0.0450304i | −0.852734 | − | 0.522346i | \(-0.825057\pi\) |
0.878732 | + | 0.477316i | \(0.158390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.76795 | − | 4.79423i | −0.178299 | − | 0.308823i | 0.762999 | − | 0.646400i | \(-0.223726\pi\) |
−0.941298 | + | 0.337576i | \(0.890393\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.46410 | + | 24.1244i | −0.412976 | + | 1.54125i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.49038 | − | 4.90192i | −0.540230 | − | 0.311902i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −24.5263 | − | 6.57180i | −1.55429 | − | 0.416471i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.3923 | + | 13.3923i | 0.845315 | + | 0.845315i | 0.989544 | − | 0.144229i | \(-0.0460703\pi\) |
−0.144229 | + | 0.989544i | \(0.546070\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.83013 | − | 8.83013i | 0.555145 | − | 0.555145i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.9282 | − | 3.46410i | 0.809595 | − | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.1603 | − | 21.0622i | 0.758536 | − | 1.31382i | −0.185061 | − | 0.982727i | \(-0.559248\pi\) |
0.943597 | − | 0.331096i | \(-0.107418\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.0263 | + | 6.97372i | 1.61719 | + | 0.433326i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.59808 | − | 0.696152i | −0.160817 | − | 0.0430908i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.59808 | − | 4.96410i | 0.530180 | − | 0.306100i | −0.210910 | − | 0.977506i | \(-0.567643\pi\) |
0.741090 | + | 0.671406i | \(0.234309\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.5622 | − | 7.83013i | −0.833118 | − | 0.481001i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.4641i | 1.68078i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.26795 | − | 4.26795i | 0.260221 | − | 0.260221i | −0.564923 | − | 0.825144i | \(-0.691094\pi\) |
0.825144 | + | 0.564923i | \(0.191094\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.07180 | 0.0651070 | 0.0325535 | − | 0.999470i | \(-0.489636\pi\) | ||||
0.0325535 | + | 0.999470i | \(0.489636\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.6340 | − | 12.6340i | −0.764643 | − | 0.764643i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.633975 | + | 2.36603i | 0.0382301 | + | 0.142677i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.79423 | + | 6.69615i | −0.107805 | + | 0.402333i | −0.998648 | − | 0.0519775i | \(-0.983448\pi\) |
0.890844 | + | 0.454310i | \(0.150114\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.7942 | − | 23.8923i | 0.825839 | − | 1.43039i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0359 | + | 5.79423i | −0.598692 | + | 0.345655i | −0.768527 | − | 0.639818i | \(-0.779010\pi\) |
0.169835 | + | 0.985472i | \(0.445676\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1603 | − | 3.52628i | 0.782296 | − | 0.209616i | 0.154499 | − | 0.987993i | \(-0.450624\pi\) |
0.627797 | + | 0.778377i | \(0.283957\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.09808 | − | 12.2942i | 0.420454 | − | 0.728247i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.58846 | −0.211820 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.866025 | + | 1.50000i | 0.0507673 | + | 0.0879316i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.13397 | − | 0.571797i | 0.124668 | − | 0.0334047i | −0.195945 | − | 0.980615i | \(-0.562778\pi\) |
0.320614 | + | 0.947210i | \(0.396111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.59808 | + | 1.50000i | −0.151266 | + | 0.0873334i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.59808 | + | 9.69615i | −0.150756 | + | 0.562628i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.86603 | − | 14.4282i | 0.223578 | − | 0.834405i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.57180 | + | 28.2583i | 0.436431 | + | 1.62878i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.232051 | − | 0.866025i | 0.0133310 | − | 0.0497519i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.26795 | 0.244382 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.92820 | + | 7.92820i | −0.452486 | + | 0.452486i | −0.896179 | − | 0.443693i | \(-0.853668\pi\) |
0.443693 | + | 0.896179i | \(0.353668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.8923 | + | 13.7942i | 1.35919 | + | 0.784726i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.18653 | − | 5.30385i | −0.520921 | − | 0.300754i | 0.216391 | − | 0.976307i | \(-0.430572\pi\) |
−0.737311 | + | 0.675553i | \(0.763905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.1603 | − | 14.5263i | 1.42214 | − | 0.821074i | 0.425660 | − | 0.904883i | \(-0.360042\pi\) |
0.996482 | + | 0.0838094i | \(0.0267087\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.2942 | − | 18.2942i | 1.03076 | − | 1.03076i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −33.4545 | − | 8.96410i | −1.87899 | − | 0.503474i | −0.999627 | − | 0.0273246i | \(-0.991301\pi\) |
−0.879364 | − | 0.476150i | \(-0.842032\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.866025 | + | 1.50000i | −0.0484881 | + | 0.0839839i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.2679 | + | 16.2679i | 0.907988 | + | 0.907988i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | − | 12.0000i | 0.667698 | − | 0.667698i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.07180 | + | 2.07180i | 0.114923 | + | 0.114923i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.00000 | − | 3.00000i | 0.165900 | − | 0.165900i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.62436 | − | 2.66987i | −0.254949 | − | 0.147195i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.35641 | + | 5.06218i | −0.0745548 | + | 0.278242i | −0.993132 | − | 0.116999i | \(-0.962672\pi\) |
0.918577 | + | 0.395242i | \(0.129339\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.8038 | − | 12.8038i | −0.701647 | − | 0.701647i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.33013 | − | 14.4282i | −0.455123 | − | 0.788297i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.69615 | + | 16.7942i | −0.528183 | + | 0.914840i | 0.471277 | + | 0.881985i | \(0.343793\pi\) |
−0.999460 | + | 0.0328547i | \(0.989540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.7942 | − | 18.6962i | 0.586262 | − | 1.01544i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.5622 | − | 12.5622i | −0.680280 | − | 0.680280i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 26.4641i | 1.42893i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.8923 | + | 5.59808i | 1.12480 | + | 0.301390i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.76795 | − | 0.473721i | 0.0949085 | − | 0.0254307i | −0.211052 | − | 0.977475i | \(-0.567689\pi\) |
0.305961 | + | 0.952044i | \(0.401022\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.86603 | − | 1.03590i | −0.206944 | − | 0.0554504i | 0.153858 | − | 0.988093i | \(-0.450830\pi\) |
−0.360802 | + | 0.932643i | \(0.617497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.10770 | + | 11.5981i | 0.165876 | + | 0.619060i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.7679 | − | 20.3827i | −0.626345 | − | 1.08486i | −0.988279 | − | 0.152657i | \(-0.951217\pi\) |
0.361934 | − | 0.932204i | \(-0.382116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.46410 | + | 5.46410i | 0.0777064 | + | 0.290004i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 26.7846 | − | 15.4641i | 1.41759 | − | 0.818447i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 28.9282i | − | 1.52677i | −0.645942 | − | 0.763386i | \(-0.723535\pi\) | ||
0.645942 | − | 0.763386i | \(-0.276465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000i | 0.0526316i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.9019 | − | 6.29423i | −0.572203 | − | 0.330361i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.73205 | + | 13.9282i | 0.195344 | + | 0.729035i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4545 | + | 30.2321i | 0.911117 | + | 1.57810i | 0.812490 | + | 0.582976i | \(0.198112\pi\) |
0.0986270 | + | 0.995124i | \(0.468555\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.08846 | + | 1.20577i | 0.108721 | + | 0.0627700i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −34.9545 | − | 9.36603i | −1.81475 | − | 0.486260i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.59808 | + | 0.428203i | −0.0827452 | + | 0.0221715i | −0.299954 | − | 0.953954i | \(-0.596971\pi\) |
0.217209 | + | 0.976125i | \(0.430305\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.8301 | + | 14.8301i | −0.765824 | + | 0.765824i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.07180i | 0.106703i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.5885 | + | 15.5885i | 0.800725 | + | 0.800725i | 0.983209 | − | 0.182484i | \(-0.0584137\pi\) |
−0.182484 | + | 0.983209i | \(0.558414\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.679492 | 0.0348114 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.66987 | + | 6.35641i | −0.187522 | + | 0.324797i | −0.944423 | − | 0.328732i | \(-0.893379\pi\) |
0.756902 | + | 0.653529i | \(0.226712\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.33013 | − | 14.4282i | −0.424543 | − | 0.735329i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.08846 | − | 18.9904i | 0.258661 | − | 0.965335i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.40192 | − | 8.96410i | 0.121782 | − | 0.454498i | −0.877922 | − | 0.478803i | \(-0.841071\pi\) |
0.999705 | + | 0.0243053i | \(0.00773738\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.3923 | + | 12.9282i | 1.13243 | + | 0.653807i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.25833 | + | 8.42820i | 0.113918 | + | 0.425147i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.36603 | − | 2.36603i | −0.119048 | − | 0.119048i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.0526 | − | 17.0526i | 0.855843 | − | 0.855843i | −0.135002 | − | 0.990845i | \(-0.543104\pi\) |
0.990845 | + | 0.135002i | \(0.0431041\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.49038 | − | 31.6865i | 0.425051 | − | 1.58631i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.1603 | + | 27.9904i | −0.807005 | + | 1.39777i | 0.107925 | + | 0.994159i | \(0.465579\pi\) |
−0.914929 | + | 0.403614i | \(0.867754\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.5263 | − | 5.50000i | −1.02249 | − | 0.273975i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.7942 | + | 4.50000i | −0.834512 | + | 0.223607i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.0981 | + | 5.83013i | −0.500543 | + | 0.288989i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.6244 | − | 11.3301i | −0.970362 | − | 0.560239i | −0.0710154 | − | 0.997475i | \(-0.522624\pi\) |
−0.899347 | + | 0.437236i | \(0.855957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.990381 | − | 0.571797i | 0.0488519 | − | 0.0282047i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.90192 | + | 4.90192i | −0.241208 | + | 0.241208i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.3205 | −1.39020 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.9904 | − | 7.50000i | 1.37069 | − | 0.367277i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.96410 | + | 18.5263i | 0.242512 | + | 0.905068i | 0.974618 | + | 0.223876i | \(0.0718712\pi\) |
−0.732105 | + | 0.681191i | \(0.761462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.79423 | + | 17.8923i | −0.233656 | + | 0.872018i | 0.745094 | + | 0.666960i | \(0.232405\pi\) |
−0.978750 | + | 0.205058i | \(0.934262\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.79423 | + | 3.10770i | 0.0872384 | + | 0.151101i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.39230 | + | 2.53590i | −0.213058 | + | 0.123009i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.52628 | − | 2.55256i | 0.461009 | − | 0.123527i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.73205 | 0.373307 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.32051 | 0.159943 | 0.0799716 | − | 0.996797i | \(-0.474517\pi\) | ||||
0.0799716 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.60770 | 0.173375 | 0.0866874 | − | 0.996236i | \(-0.472372\pi\) | ||||
0.0866874 | + | 0.996236i | \(0.472372\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00000 | −0.143839 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.4904 | − | 7.09808i | 1.26721 | − | 0.339547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.93782 | + | 3.42820i | −0.283397 | + | 0.163619i | −0.634960 | − | 0.772545i | \(-0.718984\pi\) |
0.351563 | + | 0.936164i | \(0.385650\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.3923 | − | 33.5885i | 0.923443 | − | 1.59945i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.16025 | − | 4.33013i | 0.0551253 | − | 0.205731i | −0.932870 | − | 0.360213i | \(-0.882704\pi\) |
0.987996 | + | 0.154482i | \(0.0493708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.92820 | + | 29.5885i | 0.375833 | + | 1.40263i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.8205 | + | 7.45448i | −1.31586 | + | 0.352585i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.3205 | 1.66688 | 0.833439 | − | 0.552612i | \(-0.186369\pi\) | ||||
0.833439 | + | 0.552612i | \(0.186369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.09808 | − | 1.09808i | 0.0517064 | − | 0.0517064i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.5000 | + | 6.06218i | −0.493333 | + | 0.284826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.2583 | − | 9.96410i | −0.809083 | − | 0.467124i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.9641 | − | 14.9904i | 1.21455 | − | 0.701220i | 0.250802 | − | 0.968038i | \(-0.419306\pi\) |
0.963747 | + | 0.266818i | \(0.0859722\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −20.7846 | −0.970143 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.59808 | + | 1.23205i | 0.214154 | + | 0.0573823i | 0.364301 | − | 0.931281i | \(-0.381308\pi\) |
−0.150147 | + | 0.988664i | \(0.547975\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.33013 | − | 9.23205i | 0.247712 | − | 0.429050i | −0.715179 | − | 0.698942i | \(-0.753655\pi\) |
0.962891 | + | 0.269892i | \(0.0869880\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.96410 | − | 29.7224i | 0.369326 | − | 1.37834i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.7846 | + | 21.7846i | −1.00807 | + | 1.00807i | −0.00810436 | + | 0.999967i | \(0.502580\pi\) |
−0.999967 | + | 0.00810436i | \(0.997420\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.2224 | − | 27.2224i | −1.25702 | − | 1.25702i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.50000 | + | 5.59808i | 0.0691164 | + | 0.257946i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.9641 | − | 6.33013i | −0.504130 | − | 0.291060i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.39230 | + | 5.19615i | −0.0638833 | + | 0.238416i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.1962 | + | 17.1962i | 0.787358 | + | 0.787358i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.33013 | − | 16.1603i | −0.426304 | − | 0.738381i | 0.570237 | − | 0.821480i | \(-0.306851\pi\) |
−0.996541 | + | 0.0830995i | \(0.973518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.97372 | + | 12.0788i | −0.317974 | + | 0.550748i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 49.9808 | 2.27420 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.36603 | + | 1.36603i | 0.0620280 | + | 0.0620280i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.78461i | − | 0.307440i | −0.988114 | − | 0.153720i | \(-0.950875\pi\) | ||
0.988114 | − | 0.153720i | \(-0.0491254\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.33975 | + | 3.33975i | −0.151029 | + | 0.151029i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.500000 | + | 0.133975i | −0.0225647 | + | 0.00604619i | −0.270084 | − | 0.962837i | \(-0.587051\pi\) |
0.247519 | + | 0.968883i | \(0.420385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.46410 | − | 0.928203i | −0.156015 | − | 0.0418042i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.1962i | 0.503230i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.53590 | + | 11.3205i | 0.293175 | + | 0.507794i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.50000 | + | 9.33013i | 0.111915 | + | 0.417674i | 0.999038 | − | 0.0438606i | \(-0.0139657\pi\) |
−0.887122 | + | 0.461534i | \(0.847299\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.6962 | − | 14.2583i | −1.10334 | − | 0.637015i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8564i | 0.617827i | 0.951090 | + | 0.308913i | \(0.0999653\pi\) | ||||
−0.951090 | + | 0.308913i | \(0.900035\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.00000i | − | 0.0444994i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −11.4904 | + | 6.63397i | −0.510306 | + | 0.294625i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.25833 | + | 4.69615i | 0.0557745 | + | 0.208153i | 0.988190 | − | 0.153236i | \(-0.0489693\pi\) |
−0.932415 | + | 0.361389i | \(0.882303\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.6603 | + | 28.8564i | 0.737006 | + | 1.27653i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.5885 | + | 15.5885i | −0.688247 | + | 0.688247i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.7224 | + | 7.96410i | 1.30973 | + | 0.350940i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.23205 | − | 0.598076i | 0.0981655 | − | 0.0263034i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13.1603 | − | 3.52628i | −0.577671 | − | 0.154786i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.8564i | 1.83376i | 0.399160 | + | 0.916881i | \(0.369302\pi\) | ||||
−0.399160 | + | 0.916881i | \(0.630698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.1244 | − | 22.1244i | −0.967431 | − | 0.967431i | 0.0320556 | − | 0.999486i | \(-0.489795\pi\) |
−0.999486 | + | 0.0320556i | \(0.989795\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.90192 | + | 8.49038i | −0.213937 | + | 0.370551i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.3923 | − | 31.8564i | 0.801181 | − | 1.38769i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.39230 | + | 16.2679i | 0.408361 | + | 0.707302i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.50000 | − | 1.20577i | 0.195283 | − | 0.0523260i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.480762 | − | 1.79423i | 0.0208241 | − | 0.0777167i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.2224 | + | 12.8301i | 0.960760 | + | 0.554695i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.2679 | + | 10.2679i | −0.443095 | + | 0.443095i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.6603 | − | 17.6603i | −0.760681 | − | 0.760681i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.0000 | + | 15.0000i | −0.644900 | + | 0.644900i | −0.951756 | − | 0.306856i | \(-0.900723\pi\) |
0.306856 | + | 0.951756i | \(0.400723\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.3923 | + | 13.3923i | 0.574719 | + | 0.574719i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.36603 | − | 4.09808i | 0.101349 | − | 0.175542i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.4282 | − | 5.74167i | −0.916204 | − | 0.245496i | −0.230242 | − | 0.973133i | \(-0.573952\pi\) |
−0.685962 | + | 0.727637i | \(0.740618\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.40192 | − | 1.71539i | −0.273227 | − | 0.0732111i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.29423 | + | 1.90192i | −0.140339 | + | 0.0810247i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.69615 | − | 3.86603i | −0.284749 | − | 0.164400i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17.4904 | − | 10.0981i | −0.742425 | − | 0.428639i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −23.9808 | + | 23.9808i | −1.01610 | + | 1.01610i | −0.0162292 | + | 0.999868i | \(0.505166\pi\) |
−0.999868 | + | 0.0162292i | \(0.994834\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.1436 | −0.640506 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.46410 | + | 12.9282i | −0.146254 | + | 0.545829i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.64359 | + | 6.13397i | 0.0692692 | + | 0.258516i | 0.991873 | − | 0.127233i | \(-0.0406096\pi\) |
−0.922604 | + | 0.385749i | \(0.873943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.23205 | − | 23.2583i | 0.262184 | − | 0.978485i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −34.7942 | + | 20.0885i | −1.46122 | + | 0.843636i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.4808 | + | 15.8660i | −1.15205 | + | 0.665138i | −0.949387 | − | 0.314109i | \(-0.898294\pi\) |
−0.202667 | + | 0.979248i | \(0.564961\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.5526 | + | 10.5981i | −1.65522 | + | 0.443516i | −0.961068 | − | 0.276310i | \(-0.910888\pi\) |
−0.694155 | + | 0.719826i | \(0.744222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.42820 | + | 4.20577i | 0.101440 | + | 0.175699i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.19615 | −0.341803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.1769 | −1.04813 | −0.524064 | − | 0.851679i | \(-0.675585\pi\) | ||||
−0.524064 | + | 0.851679i | \(0.675585\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.86603 | + | 6.69615i | −0.160667 | + | 0.278283i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −63.2128 | + | 16.9378i | −2.62251 | + | 0.702699i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.5622 | − | 7.83013i | 0.561688 | − | 0.324291i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6.69615 | + | 11.5981i | 0.276852 | + | 0.479521i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.96410 | + | 14.7942i | −0.163616 | + | 0.610623i | 0.834597 | + | 0.550861i | \(0.185701\pi\) |
−0.998213 | + | 0.0597617i | \(0.980966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0981 | − | 37.6865i | −0.416084 | − | 1.55285i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.12436 | − | 6.12436i | −0.251922 | − | 0.251922i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.46410 | −0.224384 | −0.112192 | − | 0.993687i | \(-0.535787\pi\) | ||||
−0.112192 | + | 0.993687i | \(0.535787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.3923 | − | 24.3923i | 0.999987 | − | 0.999987i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.8564i | 1.54936i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.3109 | + | 17.5000i | 1.23847 | + | 0.715031i | 0.968781 | − | 0.247917i | \(-0.0797461\pi\) |
0.269688 | + | 0.962948i | \(0.413079\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.7679 | + | 15.4545i | −1.09189 | + | 0.630401i | −0.934078 | − | 0.357068i | \(-0.883776\pi\) |
−0.157809 | + | 0.987470i | \(0.550443\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.69615 | + | 24.9904i | 0.272688 | + | 1.01769i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −13.5622 | − | 3.63397i | −0.551381 | − | 0.147742i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.598076 | + | 1.03590i | −0.0242752 | + | 0.0420458i | −0.877908 | − | 0.478830i | \(-0.841061\pi\) |
0.853633 | + | 0.520876i | \(0.174394\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.69615 | + | 1.79423i | −0.271342 | + | 0.0727058i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.95448 | − | 1.95448i | 0.0790699 | − | 0.0790699i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5885 | + | 23.5885i | 0.952729 | + | 0.952729i | 0.998932 | − | 0.0462032i | \(-0.0147122\pi\) |
−0.0462032 | + | 0.998932i | \(0.514712\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.59808 | + | 0.696152i | 0.104765 | + | 0.0280716i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.0885 | + | 13.3301i | 0.929506 | + | 0.536651i | 0.886655 | − | 0.462431i | \(-0.153023\pi\) |
0.0428509 | + | 0.999081i | \(0.486356\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.91154 | − | 7.13397i | 0.0768314 | − | 0.286739i | −0.916811 | − | 0.399322i | \(-0.869246\pi\) |
0.993642 | + | 0.112583i | \(0.0359124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29.0885 | − | 16.7942i | −1.16728 | − | 0.673929i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.3923 | + | 61.3013i | 1.41796 | + | 2.45598i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.52628 | + | 14.7679i | −0.341051 | + | 0.590718i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.09808 | + | 12.2942i | 0.283470 | + | 0.490984i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −17.0718 | − | 17.0718i | −0.680697 | − | 0.680697i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.2487i | 0.646851i | 0.946254 | + | 0.323425i | \(0.104835\pi\) | ||||
−0.946254 | + | 0.323425i | \(0.895165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.59808 | − | 32.0885i | −0.341743 | − | 1.27540i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.732051 | − | 0.196152i | 0.0290506 | − | 0.00778407i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.8564 | − | 7.73205i | −1.14333 | − | 0.306355i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 8.78461i | − | 0.347514i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.23205 | + | 15.9904i | 0.364644 | + | 0.631582i | 0.988719 | − | 0.149782i | \(-0.0478573\pi\) |
−0.624075 | + | 0.781365i | \(0.714524\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.96410 | − | 29.7224i | −0.314074 | − | 1.17214i | −0.924849 | − | 0.380334i | \(-0.875809\pi\) |
0.610776 | − | 0.791804i | \(-0.290858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 21.9282i | − | 0.863422i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.6077i | 1.00674i | 0.864070 | + | 0.503371i | \(0.167907\pi\) | ||||
−0.864070 | + | 0.503371i | \(0.832093\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 3.00000i | − | 0.117760i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 71.1051i | − | 2.78683i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.6699 | − | 47.2846i | −0.495810 | − | 1.85039i | −0.525443 | − | 0.850829i | \(-0.676100\pi\) |
0.0296324 | − | 0.999561i | \(-0.490566\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.86603 | + | 8.42820i | 0.190131 | + | 0.329317i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 22.3923i | − | 0.873607i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.23205 | − | 0.330127i | −0.0479939 | − | 0.0128599i | 0.234742 | − | 0.972058i | \(-0.424575\pi\) |
−0.282736 | + | 0.959198i | \(0.591242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.7942 | − | 5.30385i | 0.769906 | − | 0.206296i | 0.147576 | − | 0.989051i | \(-0.452853\pi\) |
0.622330 | + | 0.782755i | \(0.286186\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.14359 | + | 15.4641i | 0.160924 | + | 0.600576i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 36.5885i | − | 1.41884i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.09808 | − | 4.09808i | −0.158678 | − | 0.158678i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.5000 | + | 23.3827i | 0.521940 | + | 0.904027i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.13397 | + | 3.69615i | −0.0823812 | + | 0.142688i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.1603 | + | 36.6506i | 0.815668 | + | 1.41278i | 0.908847 | + | 0.417129i | \(0.136964\pi\) |
−0.0931795 | + | 0.995649i | \(0.529703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.70577 | − | 3.29423i | 0.219615 | − | 0.126795i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.34936 | − | 8.76795i | 0.0902934 | − | 0.336980i | −0.905970 | − | 0.423341i | \(-0.860857\pi\) |
0.996264 | + | 0.0863612i | \(0.0275239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.86603 | + | 2.23205i | 0.148364 | + | 0.0856582i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.9904 | + | 9.10770i | 1.30251 | + | 0.349008i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.3923 | − | 15.3923i | −0.588970 | − | 0.588970i | 0.348382 | − | 0.937353i | \(-0.386731\pi\) |
−0.937353 | + | 0.348382i | \(0.886731\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.901924 | − | 0.901924i | 0.0344607 | − | 0.0344607i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.6244 | + | 7.66987i | −1.09209 | + | 0.292624i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.36603 | − | 16.2224i | 0.356817 | − | 0.618025i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.96410 | + | 0.526279i | 0.0747179 | + | 0.0200206i | 0.295984 | − | 0.955193i | \(-0.404352\pi\) |
−0.221266 | + | 0.975213i | \(0.571019\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.69615 | + | 24.9904i | 0.254366 | + | 0.949306i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.9904 | − | 16.1603i | 1.06174 | − | 0.612993i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.78461 | + | 1.60770i | 0.105475 | + | 0.0608958i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.7128i | 0.594313i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.0526 | − | 17.0526i | 0.644066 | − | 0.644066i | −0.307486 | − | 0.951553i | \(-0.599488\pi\) |
0.951553 | + | 0.307486i | \(0.0994878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.6077 | −0.965813 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.83013 | + | 2.83013i | 0.106589 | + | 0.106589i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.598076 | − | 2.23205i | −0.0224930 | − | 0.0839449i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.1147 | − | 37.7487i | 0.379867 | − | 1.41768i | −0.466235 | − | 0.884661i | \(-0.654390\pi\) |
0.846102 | − | 0.533022i | \(-0.178944\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.59808 | + | 4.50000i | 0.0974355 | + | 0.168763i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 51.4808 | − | 29.7224i | 1.92797 | − | 1.11311i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.33013 | − | 2.23205i | 0.311529 | − | 0.0834740i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.696152 | + | 1.20577i | −0.0259983 | + | 0.0450304i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.3205 | 0.422184 | 0.211092 | − | 0.977466i | \(-0.432298\pi\) | ||||
0.211092 | + | 0.977466i | \(0.432298\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 71.1051 | 2.64809 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.79423 | + | 8.30385i | 0.178299 | + | 0.308823i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.09808 | − | 0.294229i | 0.0407815 | − | 0.0109274i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.06218 | + | 1.76795i | −0.113570 | + | 0.0655696i | −0.555709 | − | 0.831377i | \(-0.687553\pi\) |
0.442139 | + | 0.896947i | \(0.354220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.78461 | − | 25.3205i | 0.250938 | − | 0.936513i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.47372 | + | 31.6244i | 0.312984 | + | 1.16807i | 0.925852 | + | 0.377887i | \(0.123349\pi\) |
−0.612868 | + | 0.790185i | \(0.709984\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 11.1962 | − | 41.7846i | 0.412976 | − | 1.54125i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.6603 | 0.613688 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.2679 | − | 26.2679i | 0.966282 | − | 0.966282i | −0.0331677 | − | 0.999450i | \(-0.510560\pi\) |
0.999450 | + | 0.0331677i | \(0.0105595\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.7058 | + | 8.49038i | 0.540230 | + | 0.311902i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1147 | − | 14.5000i | −0.921370 | − | 0.531953i | −0.0372984 | − | 0.999304i | \(-0.511875\pi\) |
−0.884072 | + | 0.467351i | \(0.845209\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.8205 | + | 16.0622i | −1.01926 | + | 0.588473i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.4808 | + | 11.3827i | 1.55429 | + | 0.416471i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57.2750 | + | 15.3468i | 2.09278 | + | 0.560759i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.7224 | − | 42.8205i | 0.902134 | − | 1.56254i | 0.0774160 | − | 0.996999i | \(-0.475333\pi\) |
0.824718 | − | 0.565544i | \(-0.191334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −23.1962 | − | 23.1962i | −0.845315 | − | 0.845315i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.56218 | + | 9.56218i | −0.348003 | + | 0.348003i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.53590 | + | 1.53590i | 0.0558232 | + | 0.0558232i | 0.734467 | − | 0.678644i | \(-0.237432\pi\) |
−0.678644 | + | 0.734467i | \(0.737432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.2942 | + | 15.2942i | −0.555145 | + | 0.555145i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.2846 | − | 9.40192i | −0.590317 | − | 0.340819i | 0.174906 | − | 0.984585i | \(-0.444038\pi\) |
−0.765223 | + | 0.643766i | \(0.777371\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.83013 | − | 10.5622i | 0.102457 | − | 0.382377i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.3923 | + | 6.00000i | −0.809595 | + | 0.216930i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.79423 | − | 3.10770i | −0.0647858 | − | 0.112212i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.50000 | + | 6.06218i | −0.126213 | + | 0.218608i | −0.922207 | − | 0.386698i | \(-0.873616\pi\) |
0.795993 | + | 0.605305i | \(0.206949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.0622 | + | 36.4808i | −0.758536 | + | 1.31382i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.5885 | − | 23.5885i | −0.848418 | − | 0.848418i | 0.141518 | − | 0.989936i | \(-0.454802\pi\) |
−0.989936 | + | 0.141518i | \(0.954802\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.6603i | 0.418849i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −45.0788 | − | 12.0788i | −1.61719 | − | 0.433326i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.29423 | − | 0.882686i | 0.118028 | − | 0.0316255i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.46410 | − | 1.46410i | −0.195521 | − | 0.0523897i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.50000 | + | 1.20577i | 0.160817 | + | 0.0430908i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.23205 | + | 5.59808i | 0.115357 | + | 0.199804i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.820508 | − | 3.06218i | −0.0292480 | − | 0.109155i | 0.949759 | − | 0.312983i | \(-0.101328\pi\) |
−0.979007 | + | 0.203828i | \(0.934662\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.8923 | + | 8.59808i | −0.530180 | + | 0.306100i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 55.6410i | − | 1.97837i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.10512i | 0.181288i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.4904 | + | 13.5622i | 0.833118 | + | 0.481001i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.0622 | + | 41.2846i | 0.391842 | + | 1.46238i | 0.827092 | + | 0.562066i | \(0.189993\pi\) |
−0.435250 | + | 0.900310i | \(0.643340\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.39230 | + | 4.14359i | 0.0846337 | + | 0.146590i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 47.5692i | − | 1.68078i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.9282 | − | 3.73205i | −0.491516 | − | 0.131701i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 53.8468 | − | 14.4282i | 1.89785 | − | 0.508527i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.39230 | + | 7.39230i | −0.260221 | + | 0.260221i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.6410i | 1.28823i | 0.764929 | + | 0.644115i | \(0.222774\pi\) | ||||
−0.764929 | + | 0.644115i | \(0.777226\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.4641 | + | 18.4641i | 0.648362 | + | 0.648362i | 0.952597 | − | 0.304235i | \(-0.0984007\pi\) |
−0.304235 | + | 0.952597i | \(0.598401\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.85641 | −0.0651070 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.63397 | + | 4.56218i | −0.0922641 | + | 0.159806i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.9019 | − | 24.0788i | −0.486367 | − | 0.842412i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.8827 | + | 21.8827i | 0.764643 | + | 0.764643i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.7224 | − | 40.0167i | 0.374215 | − | 1.39659i | −0.480272 | − | 0.877119i | \(-0.659462\pi\) |
0.854488 | − | 0.519472i | \(-0.173871\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.6506 | − | 21.1603i | −1.27756 | − | 0.737600i | −0.301162 | − | 0.953573i | \(-0.597374\pi\) |
−0.976399 | + | 0.215973i | \(0.930708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.09808 | − | 4.09808i | −0.0382301 | − | 0.142677i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.3923 | + | 31.3923i | 1.09162 | + | 1.09162i | 0.995356 | + | 0.0962613i | \(0.0306884\pi\) |
0.0962613 | + | 0.995356i | \(0.469312\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.2679 | + | 14.2679i | −0.495546 | + | 0.495546i | −0.910048 | − | 0.414502i | \(-0.863956\pi\) |
0.414502 | + | 0.910048i | \(0.363956\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.10770 | − | 11.5981i | 0.107805 | − | 0.402333i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.8564 | − | 44.7846i | 0.895871 | − | 1.55169i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.7224 | − | 8.23205i | −1.06319 | − | 0.284882i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.8923 | + | 41.3827i | −0.825839 | + | 1.43039i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.74167 | + | 3.89230i | −0.232748 | + | 0.134377i | −0.611839 | − | 0.790982i | \(-0.709570\pi\) |
0.379091 | + | 0.925359i | \(0.376237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.4186 | − | 14.0981i | −0.842020 | − | 0.486141i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.3827 | − | 10.0359i | 0.598692 | − | 0.345655i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −10.4641 | + | 10.4641i | −0.359976 | + | 0.359976i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.4449 | −1.11482 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −22.7942 | + | 6.10770i | −0.782296 | + | 0.209616i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0981 | − | 37.6865i | −0.346158 | − | 1.29188i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.06218 | + | 7.69615i | −0.0706076 | + | 0.263511i | −0.992201 | − | 0.124644i | \(-0.960221\pi\) |
0.921594 | + | 0.388156i | \(0.126888\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.2942 | + | 21.2942i | −0.420454 | + | 0.728247i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.6436 | − | 8.45448i | 0.500216 | − | 0.288800i | −0.228587 | − | 0.973523i | \(-0.573411\pi\) |
0.728803 | + | 0.684724i | \(0.240077\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.50000 | − | 1.20577i | 0.153538 | − | 0.0411404i | −0.181231 | − | 0.983440i | \(-0.558008\pi\) |
0.334769 | + | 0.942300i | \(0.391342\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.21539 | 0.211820 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.5359 | 0.903292 | 0.451646 | − | 0.892197i | \(-0.350837\pi\) | ||||
0.451646 | + | 0.892197i | \(0.350837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.1962 | −0.516685 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.73205 | 0.0588235 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.23205 | − | 0.866025i | 0.109640 | − | 0.0293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.2583 | − | 9.96410i | 0.584776 | − | 0.337621i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.50000 | − | 2.59808i | −0.0507673 | − | 0.0879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.9904 | + | 52.2128i | −0.472961 | + | 1.76512i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3827 | − | 49.9449i | −0.451901 | − | 1.68652i | −0.697042 | − | 0.717031i | \(-0.745501\pi\) |
0.245140 | − | 0.969488i | \(-0.421166\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.69615 | + | 0.990381i | −0.124668 | + | 0.0334047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.3205 | 1.05521 | 0.527607 | − | 0.849488i | \(-0.323089\pi\) | ||||
0.527607 | + | 0.849488i | \(0.323089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.00000 | − | 3.00000i | 0.100958 | − | 0.100958i | −0.654824 | − | 0.755782i | \(-0.727257\pi\) |
0.755782 | + | 0.654824i | \(0.227257\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.50000 | − | 2.59808i | 0.151266 | − | 0.0873334i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.93782 | − | 5.16025i | −0.300103 | − | 0.173264i | 0.342386 | − | 0.939559i | \(-0.388765\pi\) |
−0.642489 | + | 0.766295i | \(0.722098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51666 | − | 0.875644i | 0.0508672 | − | 0.0293682i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.50000 | − | 16.7942i | 0.150756 | − | 0.562628i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.90192 | + | 1.31347i | 0.164037 | + | 0.0439535i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.09808 | + | 14.0263i | −0.270689 | + | 0.468847i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.69615 | + | 24.9904i | −0.223578 | + | 0.834405i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.83013 | + | 5.83013i | −0.194446 | + | 0.194446i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.9282 | + | 22.9282i | 0.763849 | + | 0.763849i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.1147 | − | 48.9449i | −0.436431 | − | 1.62878i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.2942 | + | 10.5622i | 0.608121 | + | 0.351099i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.42820 | − | 9.06218i | 0.0806272 | − | 0.300905i | −0.913823 | − | 0.406112i | \(-0.866884\pi\) |
0.994450 | + | 0.105208i | \(0.0335508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.401924 | + | 1.50000i | −0.0133310 | + | 0.0497519i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.13397 | + | 7.16025i | 0.136965 | + | 0.237230i | 0.926346 | − | 0.376673i | \(-0.122932\pi\) |
−0.789382 | + | 0.613903i | \(0.789599\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.1603 | − | 24.5263i | 0.468636 | − | 0.811701i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.39230 | −0.244382 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.9019 | + | 15.9019i | 0.525128 | + | 0.525128i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 36.5359i | − | 1.20521i | −0.798040 | − | 0.602604i | \(-0.794130\pi\) | ||
0.798040 | − | 0.602604i | \(-0.205870\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.7321 | − | 13.7321i | 0.452486 | − | 0.452486i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.53590 | + | 1.75129i | −0.215132 | + | 0.0576444i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.39230 | + | 1.98076i | 0.243057 | + | 0.0651271i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.3827 | − | 23.8923i | −1.35919 | − | 0.784726i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.35641 | + | 16.2058i | 0.306974 | + | 0.531694i | 0.977699 | − | 0.210012i | \(-0.0673503\pi\) |
−0.670725 | + | 0.741706i | \(0.734017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.1962 | − | 52.9808i | −0.465260 | − | 1.73637i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.9115 | + | 9.18653i | 0.520921 | + | 0.300754i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.9282i | 0.488204i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 19.0718i | − | 0.623048i | −0.950238 | − | 0.311524i | \(-0.899160\pi\) | ||
0.950238 | − | 0.311524i | \(-0.100840\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.5788 | + | 25.1603i | −1.42214 | + | 0.821074i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.13397 | + | 34.0885i | 0.297759 | + | 1.11125i | 0.939001 | + | 0.343913i | \(0.111753\pi\) |
−0.641242 | + | 0.767338i | \(0.721581\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.59808 | + | 4.50000i | 0.0846050 | + | 0.146540i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −31.6865 | + | 31.6865i | −1.03076 | + | 1.03076i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.0167 | + | 10.9904i | 1.33286 | + | 0.357139i | 0.853782 | − | 0.520631i | \(-0.174303\pi\) |
0.479081 | + | 0.877771i | \(0.340970\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.6603 | + | 4.46410i | −0.540815 | + | 0.144911i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.9449 | + | 15.5263i | 1.87899 | + | 0.503474i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.5359i | 1.05394i | 0.849884 | + | 0.526971i | \(0.176672\pi\) | ||||
−0.849884 | + | 0.526971i | \(0.823328\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.83013 | + | 3.83013i | 0.123940 | + | 0.123940i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.50000 | − | 2.59808i | 0.0484881 | − | 0.0839839i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.47372 | − | 2.55256i | 0.0475889 | − | 0.0824264i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7846 | − | 46.3923i | −0.864020 | − | 1.49653i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.1769 | − | 28.1769i | −0.907988 | − | 0.907988i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.23205 | + | 8.33013i | −0.0718523 | + | 0.268156i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.0622 | + | 15.6244i | 0.870261 | + | 0.502445i | 0.867435 | − | 0.497551i | \(-0.165767\pi\) |
0.00282602 | + | 0.999996i | \(0.499100\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.7846 | + | 20.7846i | −0.667698 | + | 0.667698i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.9808 | + | 23.9808i | 0.769579 | + | 0.769579i | 0.978032 | − | 0.208453i | \(-0.0668429\pi\) |
−0.208453 | + | 0.978032i | \(0.566843\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 52.8109 | − | 52.8109i | 1.69304 | − | 1.69304i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.58846 | − | 3.58846i | −0.114923 | − | 0.114923i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.2846 | + | 42.0622i | −0.776933 | + | 1.34569i | 0.156768 | + | 0.987635i | \(0.449893\pi\) |
−0.933701 | + | 0.358053i | \(0.883441\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −29.5885 | − | 7.92820i | −0.945651 | − | 0.253386i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.19615 | + | 5.19615i | −0.165900 | + | 0.165900i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.08142 | − | 0.624356i | 0.0344918 | − | 0.0199139i | −0.482655 | − | 0.875811i | \(-0.660327\pi\) |
0.517147 | + | 0.855897i | \(0.326994\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.36603 | − | 4.83013i | −0.266564 | − | 0.153901i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00962 | + | 4.62436i | 0.254949 | + | 0.147195i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.9545 | − | 29.9545i | 0.952497 | − | 0.952497i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.3923 | 1.41017 | 0.705084 | − | 0.709124i | \(-0.250909\pi\) | ||||
0.705084 | + | 0.709124i | \(0.250909\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.34936 | − | 8.76795i | 0.0745548 | − | 0.278242i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.9282 | + | 40.7846i | 0.346447 | + | 1.29296i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.06218 | + | 3.96410i | −0.0336395 | + | 0.125544i | −0.980704 | − | 0.195500i | \(-0.937367\pi\) |
0.947064 | + | 0.321044i | \(0.104034\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 22.1769 | + | 22.1769i | 0.701647 | + | 0.701647i |
(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 | 576.2.bb.a.49.1 | 4 | ||
3.2 | odd | 2 | 1728.2.bc.c.1009.1 | 4 | |||
4.3 | odd | 2 | 144.2.x.a.85.1 | yes | 4 | ||
9.2 | odd | 6 | 1728.2.bc.b.1585.1 | 4 | |||
9.7 | even | 3 | 576.2.bb.b.241.1 | 4 | |||
12.11 | even | 2 | 432.2.y.d.37.1 | 4 | |||
16.3 | odd | 4 | 144.2.x.d.13.1 | yes | 4 | ||
16.13 | even | 4 | 576.2.bb.b.337.1 | 4 | |||
36.7 | odd | 6 | 144.2.x.d.133.1 | yes | 4 | ||
36.11 | even | 6 | 432.2.y.a.181.1 | 4 | |||
48.29 | odd | 4 | 1728.2.bc.b.145.1 | 4 | |||
48.35 | even | 4 | 432.2.y.a.253.1 | 4 | |||
144.29 | odd | 12 | 1728.2.bc.c.721.1 | 4 | |||
144.61 | even | 12 | inner | 576.2.bb.a.529.1 | 4 | ||
144.83 | even | 12 | 432.2.y.d.397.1 | 4 | |||
144.115 | odd | 12 | 144.2.x.a.61.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.a.61.1 | ✓ | 4 | 144.115 | odd | 12 | ||
144.2.x.a.85.1 | yes | 4 | 4.3 | odd | 2 | ||
144.2.x.d.13.1 | yes | 4 | 16.3 | odd | 4 | ||
144.2.x.d.133.1 | yes | 4 | 36.7 | odd | 6 | ||
432.2.y.a.181.1 | 4 | 36.11 | even | 6 | |||
432.2.y.a.253.1 | 4 | 48.35 | even | 4 | |||
432.2.y.d.37.1 | 4 | 12.11 | even | 2 | |||
432.2.y.d.397.1 | 4 | 144.83 | even | 12 | |||
576.2.bb.a.49.1 | 4 | 1.1 | even | 1 | trivial | ||
576.2.bb.a.529.1 | 4 | 144.61 | even | 12 | inner | ||
576.2.bb.b.241.1 | 4 | 9.7 | even | 3 | |||
576.2.bb.b.337.1 | 4 | 16.13 | even | 4 | |||
1728.2.bc.b.145.1 | 4 | 48.29 | odd | 4 | |||
1728.2.bc.b.1585.1 | 4 | 9.2 | odd | 6 | |||
1728.2.bc.c.721.1 | 4 | 144.29 | odd | 12 | |||
1728.2.bc.c.1009.1 | 4 | 3.2 | odd | 2 |