Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,2,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), 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: | \(2.04417029174\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 225.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 256.225 |
Dual form | 256.2.g.a.33.1 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 1.70711i | 0.408248 | + | 0.985599i | 0.985599 | + | 0.169102i | \(0.0540867\pi\) |
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.12132 | + | 1.29289i | 1.39590 | + | 0.578199i | 0.948683 | − | 0.316228i | \(-0.102416\pi\) |
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 1.00000i | −0.377964 | − | 0.377964i | 0.492403 | − | 0.870367i | \(-0.336119\pi\) |
−0.870367 | + | 0.492403i | \(0.836119\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.292893 | + | 0.292893i | −0.0976311 | + | 0.0976311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.121320 | − | 0.292893i | 0.0365795 | − | 0.0883106i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) |
0.941113 | + | 0.338091i | \(0.109781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.70711 | + | 0.707107i | −0.473466 | + | 0.196116i | −0.606640 | − | 0.794977i | \(-0.707483\pi\) |
0.133174 | + | 0.991093i | \(0.457483\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.24264i | 1.61184i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.82843i | − | 0.685994i | −0.939336 | − | 0.342997i | \(-0.888558\pi\) | ||
0.939336 | − | 0.342997i | \(-0.111442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.53553 | + | 2.29289i | −1.26994 | + | 0.526026i | −0.912946 | − | 0.408081i | \(-0.866198\pi\) |
−0.356993 | + | 0.934107i | \(0.616198\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 2.41421i | 0.218218 | − | 0.526825i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.171573 | + | 0.171573i | −0.0357754 | + | 0.0357754i | −0.724768 | − | 0.688993i | \(-0.758053\pi\) |
0.688993 | + | 0.724768i | \(0.258053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.53553 | + | 4.53553i | 0.907107 | + | 0.907107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.41421 | + | 1.82843i | 0.849516 | + | 0.351881i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.12132 | − | 2.70711i | −0.208224 | − | 0.502697i | 0.784920 | − | 0.619598i | \(-0.212704\pi\) |
−0.993144 | + | 0.116900i | \(0.962704\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.585786 | 0.101972 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.82843 | − | 4.41421i | −0.309061 | − | 0.746138i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.70711 | − | 0.707107i | −0.280647 | − | 0.116248i | 0.237920 | − | 0.971285i | \(-0.423534\pi\) |
−0.518567 | + | 0.855037i | \(0.673534\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.41421 | − | 2.41421i | −0.386584 | − | 0.386584i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.82843 | + | 5.82843i | −0.910247 | + | 0.910247i | −0.996291 | − | 0.0860440i | \(-0.972577\pi\) |
0.0860440 | + | 0.996291i | \(0.472577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.29289 | − | 7.94975i | 0.502162 | − | 1.21233i | −0.446143 | − | 0.894962i | \(-0.647203\pi\) |
0.948304 | − | 0.317363i | \(-0.102797\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.29289 | + | 0.535534i | −0.192733 | + | 0.0798327i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 11.6569i | − | 1.70033i | −0.526519 | − | 0.850163i | \(-0.676503\pi\) | ||
0.526519 | − | 0.850163i | \(-0.323497\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.82843 | − | 2.00000i | 0.676115 | − | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.12132 | + | 7.53553i | −0.428746 | + | 1.03509i | 0.550939 | + | 0.834545i | \(0.314270\pi\) |
−0.979686 | + | 0.200540i | \(0.935730\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.757359 | − | 0.757359i | 0.102122 | − | 0.102122i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.82843 | − | 7.82843i | −1.03690 | − | 1.03690i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.12132 | − | 2.53553i | −0.796928 | − | 0.330098i | −0.0532027 | − | 0.998584i | \(-0.516943\pi\) |
−0.743725 | + | 0.668485i | \(0.766943\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.292893 | − | 0.707107i | −0.0375011 | − | 0.0905357i | 0.904019 | − | 0.427492i | \(-0.140603\pi\) |
−0.941520 | + | 0.336956i | \(0.890603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.585786 | 0.0738022 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.24264 | −0.774304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.53553 | + | 3.70711i | 0.187595 | + | 0.452895i | 0.989496 | − | 0.144563i | \(-0.0461775\pi\) |
−0.801900 | + | 0.597458i | \(0.796178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.414214 | − | 0.171573i | −0.0498655 | − | 0.0206549i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.171573 | + | 0.171573i | 0.0203620 | + | 0.0203620i | 0.717214 | − | 0.696853i | \(-0.245417\pi\) |
−0.696853 | + | 0.717214i | \(0.745417\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.00000 | − | 7.00000i | 0.819288 | − | 0.819288i | −0.166717 | − | 0.986005i | \(-0.553317\pi\) |
0.986005 | + | 0.166717i | \(0.0533166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.53553 | + | 10.9497i | −0.523718 | + | 1.26437i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.414214 | + | 0.171573i | −0.0472040 | + | 0.0195525i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000i | 0.675053i | 0.941316 | + | 0.337526i | \(0.109590\pi\) | ||||
−0.941316 | + | 0.337526i | \(0.890410\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.0711i | 1.11901i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.12132 | − | 2.53553i | 0.671902 | − | 0.278311i | −0.0205350 | − | 0.999789i | \(-0.506537\pi\) |
0.692437 | + | 0.721478i | \(0.256537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | − | 8.82843i | 0.396642 | − | 0.957577i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.82843 | − | 3.82843i | 0.410450 | − | 0.410450i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.65685 | − | 2.65685i | −0.281626 | − | 0.281626i | 0.552131 | − | 0.833757i | \(-0.313815\pi\) |
−0.833757 | + | 0.552131i | \(0.813815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.41421 | + | 1.00000i | 0.253078 | + | 0.104828i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.82843 | + | 6.82843i | 0.293294 | + | 0.708075i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −20.2426 | −2.07685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.51472 | −0.153796 | −0.0768982 | − | 0.997039i | \(-0.524502\pi\) | ||||
−0.0768982 | + | 0.997039i | \(0.524502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0502525 | + | 0.121320i | 0.00505057 | + | 0.0121932i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.3640 | − | 4.70711i | −1.13076 | − | 0.468375i | −0.262718 | − | 0.964873i | \(-0.584619\pi\) |
−0.868038 | + | 0.496498i | \(0.834619\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.48528 | + | 7.48528i | 0.737547 | + | 0.737547i | 0.972103 | − | 0.234556i | \(-0.0753636\pi\) |
−0.234556 | + | 0.972103i | \(0.575364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.24264 | − | 6.24264i | 0.609219 | − | 0.609219i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.121320 | − | 0.292893i | 0.0117285 | − | 0.0283151i | −0.917907 | − | 0.396796i | \(-0.870122\pi\) |
0.929635 | + | 0.368481i | \(0.120122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.29289 | − | 1.77817i | 0.411185 | − | 0.170318i | −0.167496 | − | 0.985873i | \(-0.553568\pi\) |
0.578680 | + | 0.815555i | \(0.303568\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.41421i | − | 0.324063i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.6569i | 1.66102i | 0.557006 | + | 0.830509i | \(0.311950\pi\) | ||||
−0.557006 | + | 0.830509i | \(0.688050\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.757359 | + | 0.313708i | −0.0706241 | + | 0.0292535i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.292893 | − | 0.707107i | 0.0270780 | − | 0.0653720i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.82843 | + | 2.82843i | −0.259281 | + | 0.259281i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.70711 | + | 7.70711i | 0.700646 | + | 0.700646i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −14.0711 | − | 5.82843i | −1.26875 | − | 0.525532i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.82843 | + | 4.41421i | 0.163539 | + | 0.394819i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9706 | 1.86084 | 0.930418 | − | 0.366499i | \(-0.119444\pi\) | ||||
0.930418 | + | 0.366499i | \(0.119444\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.8995 | 1.39987 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.63604 | − | 8.77817i | −0.317682 | − | 0.766953i | −0.999376 | − | 0.0353153i | \(-0.988756\pi\) |
0.681694 | − | 0.731637i | \(-0.261244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.82843 | + | 3.24264i | 0.678811 | + | 0.281173i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.4142 | + | 11.4142i | 0.982379 | + | 0.982379i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.65685 | − | 2.65685i | 0.226990 | − | 0.226990i | −0.584444 | − | 0.811434i | \(-0.698687\pi\) |
0.811434 | + | 0.584444i | \(0.198687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.19239 | + | 12.5355i | −0.440413 | + | 1.06325i | 0.535392 | + | 0.844604i | \(0.320164\pi\) |
−0.975804 | + | 0.218646i | \(0.929836\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 19.8995 | − | 8.24264i | 1.67584 | − | 0.694156i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.585786i | 0.0489859i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.89949i | − | 0.822108i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.53553 | − | 3.53553i | 0.703999 | − | 0.291606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.60660 | + | 13.5355i | −0.459311 | + | 1.10887i | 0.509366 | + | 0.860550i | \(0.329880\pi\) |
−0.968677 | + | 0.248324i | \(0.920120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.4853 | + | 15.4853i | −1.26017 | + | 1.26017i | −0.309166 | + | 0.951008i | \(0.600050\pi\) |
−0.951008 | + | 0.309166i | \(0.899950\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.828427 | + | 0.828427i | 0.0669744 | + | 0.0669744i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.4853 | + | 5.17157i | 1.00284 | + | 0.415391i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.292893 | − | 0.707107i | −0.0233754 | − | 0.0564333i | 0.911761 | − | 0.410722i | \(-0.134723\pi\) |
−0.935136 | + | 0.354288i | \(0.884723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.0711 | −1.19521 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.343146 | 0.0270437 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.53553 | + | 18.1924i | 0.590229 | + | 1.42494i | 0.883282 | + | 0.468842i | \(0.155329\pi\) |
−0.293054 | + | 0.956096i | \(0.594671\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.82843 | + | 0.757359i | 0.142343 | + | 0.0589603i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.34315 | − | 3.34315i | −0.258700 | − | 0.258700i | 0.565825 | − | 0.824525i | \(-0.308558\pi\) |
−0.824525 | + | 0.565825i | \(0.808558\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.77817 | + | 6.77817i | −0.521398 | + | 0.521398i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.949747 | − | 2.29289i | 0.0726290 | − | 0.175342i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.12132 | − | 0.464466i | 0.0852524 | − | 0.0353127i | −0.339650 | − | 0.940552i | \(-0.610309\pi\) |
0.424902 | + | 0.905239i | \(0.360309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 9.07107i | − | 0.685708i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.2426i | − | 0.920213i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.3640 | + | 5.94975i | −1.07361 | + | 0.444705i | −0.848264 | − | 0.529573i | \(-0.822352\pi\) |
−0.225349 | + | 0.974278i | \(0.572352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.19239 | − | 5.29289i | 0.162959 | − | 0.393418i | −0.821216 | − | 0.570618i | \(-0.806704\pi\) |
0.984175 | + | 0.177200i | \(0.0567039\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.00000 | − | 1.00000i | 0.0739221 | − | 0.0739221i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.41421 | − | 4.41421i | −0.324539 | − | 0.324539i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.828427 | − | 0.343146i | −0.0605806 | − | 0.0250933i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.58579 | − | 6.24264i | −0.188088 | − | 0.454085i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4853 | −1.33060 | −0.665300 | − | 0.746576i | \(-0.731696\pi\) | ||||
−0.665300 | + | 0.746576i | \(0.731696\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.41421 | − | 10.6569i | −0.316108 | − | 0.763153i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.3640 | − | 7.19239i | −1.23713 | − | 0.512436i | −0.334314 | − | 0.942462i | \(-0.608505\pi\) |
−0.902817 | + | 0.430025i | \(0.858505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.9706 | − | 17.9706i | −1.27390 | − | 1.27390i | −0.944025 | − | 0.329875i | \(-0.892994\pi\) |
−0.329875 | − | 0.944025i | \(-0.607006\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.24264 | + | 5.24264i | −0.369787 | + | 0.369787i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.58579 | + | 3.82843i | −0.111300 | + | 0.268703i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.7279 | + | 10.6569i | −1.79692 | + | 0.744307i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.100505i | − | 0.00698558i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.89949i | 0.131391i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.464466 | − | 0.192388i | 0.0319752 | − | 0.0132445i | −0.366639 | − | 0.930363i | \(-0.619491\pi\) |
0.398614 | + | 0.917119i | \(0.369491\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.171573 | + | 0.414214i | −0.0117560 | + | 0.0283814i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.5563 | − | 20.5563i | 1.40193 | − | 1.40193i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | − | 4.00000i | −0.271538 | − | 0.271538i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.8995 | + | 7.00000i | 1.14196 | + | 0.473016i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | + | 4.82843i | 0.134535 | + | 0.324795i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.9706 | −0.868573 | −0.434287 | − | 0.900775i | \(-0.642999\pi\) | ||||
−0.434287 | + | 0.900775i | \(0.642999\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.65685 | −0.177124 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.60660 | − | 6.29289i | −0.173006 | − | 0.417674i | 0.813464 | − | 0.581616i | \(-0.197579\pi\) |
−0.986470 | + | 0.163942i | \(0.947579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.7782 | + | 10.2635i | 1.63739 | + | 0.678228i | 0.996030 | − | 0.0890139i | \(-0.0283716\pi\) |
0.641357 | + | 0.767242i | \(0.278372\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.585786 | − | 0.585786i | −0.0385419 | − | 0.0385419i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.65685 | − | 8.65685i | 0.567129 | − | 0.567129i | −0.364194 | − | 0.931323i | \(-0.618655\pi\) |
0.931323 | + | 0.364194i | \(0.118655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.0711 | − | 36.3848i | 0.983128 | − | 2.37348i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.2426 | + | 4.24264i | −0.665331 | + | 0.275589i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3137i | 1.11993i | 0.828516 | + | 0.559965i | \(0.189186\pi\) | ||||
−0.828516 | + | 0.559965i | \(0.810814\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 8.48528i | − | 0.546585i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) | ||
0.961931 | − | 0.273293i | \(-0.0881127\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.94975 | + | 1.63604i | −0.253376 | + | 0.104952i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.46447 | − | 15.6066i | 0.413000 | − | 0.997069i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.82843 | − | 7.82843i | 0.498111 | − | 0.498111i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.65685 | + | 8.65685i | 0.548606 | + | 0.548606i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6066 | − | 6.05025i | −0.921961 | − | 0.381889i | −0.129338 | − | 0.991601i | \(-0.541285\pi\) |
−0.792623 | + | 0.609712i | \(0.791285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0294373 | + | 0.0710678i | 0.00185070 | + | 0.00446800i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.6569 | 1.10572 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000 | 0.374270 | 0.187135 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187135 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | + | 2.41421i | 0.0621370 | + | 0.150012i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.12132 | + | 0.464466i | 0.0694080 | + | 0.0287497i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.171573 | + | 0.171573i | 0.0105796 | + | 0.0105796i | 0.712377 | − | 0.701797i | \(-0.247619\pi\) |
−0.701797 | + | 0.712377i | \(0.747619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.4853 | + | 19.4853i | −1.19697 | + | 1.19697i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.65685 | − | 6.41421i | 0.162597 | − | 0.392543i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.87868 | + | 2.02082i | −0.297458 | + | 0.123211i | −0.526421 | − | 0.850224i | \(-0.676467\pi\) |
0.228963 | + | 0.973435i | \(0.426467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0000i | 1.09342i | 0.837321 | + | 0.546711i | \(0.184120\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.82843i | 0.292230i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.87868 | − | 0.778175i | 0.113289 | − | 0.0469257i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.292893 | + | 0.707107i | −0.0175982 | + | 0.0424859i | −0.932434 | − | 0.361339i | \(-0.882320\pi\) |
0.914836 | + | 0.403825i | \(0.132320\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.17157 | + | 1.17157i | −0.0701402 | + | 0.0701402i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.17157 | − | 6.17157i | −0.368165 | − | 0.368165i | 0.498643 | − | 0.866808i | \(-0.333832\pi\) |
−0.866808 | + | 0.498643i | \(0.833832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.77817 | − | 4.05025i | −0.581252 | − | 0.240763i | 0.0726300 | − | 0.997359i | \(-0.476861\pi\) |
−0.653882 | + | 0.756596i | \(0.726861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14.3137 | − | 34.5563i | −0.847871 | − | 2.04694i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6569 | 0.688082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.07107 | − | 2.58579i | −0.0627871 | − | 0.151581i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.6066 | + | 4.80761i | 0.678065 | + | 0.280864i | 0.695018 | − | 0.718993i | \(-0.255397\pi\) |
−0.0169528 | + | 0.999856i | \(0.505397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.8284 | − | 15.8284i | −0.921567 | − | 0.921567i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.07107 | − | 1.07107i | 0.0621497 | − | 0.0621497i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.171573 | − | 0.414214i | 0.00992232 | − | 0.0239546i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.2426 | + | 4.65685i | −0.648015 | + | 0.268417i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 22.7279i | − | 1.30569i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.58579i | − | 0.148062i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.94975 | − | 1.22183i | 0.168351 | − | 0.0697333i | −0.296916 | − | 0.954904i | \(-0.595958\pi\) |
0.465267 | + | 0.885170i | \(0.345958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.48528 | + | 18.0711i | −0.425823 | + | 1.02803i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.65685 | + | 8.65685i | −0.490885 | + | 0.490885i | −0.908585 | − | 0.417700i | \(-0.862836\pi\) |
0.417700 | + | 0.908585i | \(0.362836\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.48528 | + | 9.48528i | 0.536140 | + | 0.536140i | 0.922393 | − | 0.386253i | \(-0.126231\pi\) |
−0.386253 | + | 0.922393i | \(0.626231\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.82843 | + | 0.757359i | 0.103020 | + | 0.0426724i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.63604 | − | 11.1924i | −0.260386 | − | 0.628627i | 0.738577 | − | 0.674170i | \(-0.235498\pi\) |
−0.998962 | + | 0.0455425i | \(0.985498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.928932 | −0.0520102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.585786 | 0.0326954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.48528 | + | 15.6569i | 0.360851 | + | 0.871171i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.9497 | − | 4.53553i | −0.607383 | − | 0.251586i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.07107 | + | 6.07107i | 0.335731 | + | 0.335731i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.6569 | + | 11.6569i | −0.642663 | + | 0.642663i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.70711 | + | 6.53553i | −0.148796 | + | 0.359225i | −0.980650 | − | 0.195769i | \(-0.937280\pi\) |
0.831854 | + | 0.554995i | \(0.187280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.707107 | − | 0.292893i | 0.0387492 | − | 0.0160504i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.5563i | 0.740662i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.9706i | − | 0.924445i | −0.886764 | − | 0.462223i | \(-0.847052\pi\) | ||
0.886764 | − | 0.462223i | \(-0.152948\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −30.1421 | + | 12.4853i | −1.63710 | + | 0.678107i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.485281 | − | 1.17157i | 0.0262795 | − | 0.0634442i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.07107 | − | 1.07107i | −0.0576644 | − | 0.0576644i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.3640 | + | 5.94975i | 0.771098 | + | 0.319399i | 0.733317 | − | 0.679887i | \(-0.237971\pi\) |
0.0377808 | + | 0.999286i | \(0.487971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.6777 | + | 25.7782i | 0.571563 | + | 1.37987i | 0.900224 | + | 0.435426i | \(0.143402\pi\) |
−0.328662 | + | 0.944448i | \(0.606598\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.82843 | −0.471227 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.313708 | + | 0.757359i | 0.0166499 | + | 0.0401965i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.82843 | − | 2.82843i | −0.361399 | − | 0.149696i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1716 | + | 12.1716i | 0.642391 | + | 0.642391i | 0.951143 | − | 0.308752i | \(-0.0999112\pi\) |
−0.308752 | + | 0.951143i | \(0.599911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9497 | − | 11.9497i | 0.628934 | − | 0.628934i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.70711 | + | 18.6066i | −0.404518 | + | 0.976593i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.8995 | − | 12.7990i | 1.61735 | − | 0.669930i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 6.00000i | − | 0.313197i | −0.987662 | − | 0.156599i | \(-0.949947\pi\) | ||
0.987662 | − | 0.156599i | \(-0.0500529\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 3.41421i | − | 0.177737i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.6569 | − | 4.41421i | 0.553276 | − | 0.229175i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.7071 | − | 28.2635i | 0.606171 | − | 1.46343i | −0.260962 | − | 0.965349i | \(-0.584040\pi\) |
0.867133 | − | 0.498077i | \(-0.165960\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.24264 | + | 6.24264i | −0.322369 | + | 0.322369i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.82843 | + | 3.82843i | 0.197174 | + | 0.197174i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.6777 | + | 8.97918i | 1.11351 | + | 0.461230i | 0.862144 | − | 0.506663i | \(-0.169121\pi\) |
0.251363 | + | 0.967893i | \(0.419121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.8284 | + | 35.7990i | 0.759683 | + | 1.83404i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.9706 | −0.867155 | −0.433578 | − | 0.901116i | \(-0.642749\pi\) | ||||
−0.433578 | + | 0.901116i | \(0.642749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.51472 | −0.0771972 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.36396 | + | 3.29289i | 0.0693340 | + | 0.167387i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 29.6066 | + | 12.2635i | 1.50111 | + | 0.621782i | 0.973702 | − | 0.227827i | \(-0.0731622\pi\) |
0.527413 | + | 0.849609i | \(0.323162\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.485281 | + | 0.485281i | 0.0245417 | + | 0.0245417i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4142 | − | 12.4142i | 0.626214 | − | 0.626214i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.75736 | + | 18.7279i | −0.390315 | + | 0.942304i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.7782 | − | 10.2635i | 1.24358 | − | 0.515108i | 0.338749 | − | 0.940877i | \(-0.389996\pi\) |
0.904832 | + | 0.425769i | \(0.139996\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.6569i | 0.783823i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.82843i | − | 0.141245i | −0.997503 | − | 0.0706225i | \(-0.977501\pi\) | ||
0.997503 | − | 0.0706225i | \(-0.0224986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.82843 | + | 2.82843i | −0.340148 | + | 0.140894i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −13.0208 | + | 31.4350i | −0.647010 | + | 1.56202i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.414214 | + | 0.414214i | −0.0205318 | + | 0.0205318i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.51472 | + | 4.51472i | 0.223238 | + | 0.223238i | 0.809861 | − | 0.586622i | \(-0.199543\pi\) |
−0.586622 | + | 0.809861i | \(0.699543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.41421 | + | 2.65685i | 0.316390 | + | 0.131053i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.58579 | + | 8.65685i | 0.176445 | + | 0.425976i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.3848 | 1.09883 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.0711 | −1.22774 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.60660 | − | 20.7782i | −0.420460 | − | 1.01508i | −0.982212 | − | 0.187775i | \(-0.939873\pi\) |
0.561752 | − | 0.827306i | \(-0.310127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.70711 | − | 3.19239i | −0.375621 | − | 0.155587i | 0.186882 | − | 0.982382i | \(-0.440162\pi\) |
−0.562504 | + | 0.826795i | \(0.690162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.41421 | + | 3.41421i | 0.166005 | + | 0.166005i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.8284 | − | 12.8284i | 0.622270 | − | 0.622270i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.414214 | + | 1.00000i | −0.0200452 | + | 0.0483934i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.00000 | + | 0.414214i | −0.0482805 | + | 0.0199984i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.6569i | − | 1.13951i | −0.821814 | − | 0.569755i | \(-0.807038\pi\) | ||
0.821814 | − | 0.569755i | \(-0.192962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.4853i | 1.56114i | 0.625067 | + | 0.780571i | \(0.285072\pi\) | ||||
−0.625067 | + | 0.780571i | \(0.714928\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.8995 | − | 7.00000i | 0.810269 | − | 0.335624i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.556349 | − | 1.34315i | 0.0266138 | − | 0.0642514i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.0000 | − | 17.0000i | 0.811366 | − | 0.811366i | −0.173473 | − | 0.984839i | \(-0.555499\pi\) |
0.984839 | + | 0.173473i | \(0.0554989\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.46447 | + | 1.46447i | 0.0697365 | + | 0.0697365i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.6066 | − | 8.53553i | −0.979049 | − | 0.405535i | −0.164976 | − | 0.986298i | \(-0.552755\pi\) |
−0.814073 | + | 0.580762i | \(0.802755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.85786 | − | 11.7279i | −0.230285 | − | 0.555957i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −27.0711 | −1.28042 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.4558 | 1.48449 | 0.742247 | − | 0.670127i | \(-0.233760\pi\) | ||||
0.742247 | + | 0.670127i | \(0.233760\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00000 | + | 2.41421i | 0.0470882 | + | 0.113681i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.3848 | − | 15.4853i | −1.75649 | − | 0.727562i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.24264 | + | 6.24264i | 0.292660 | + | 0.292660i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.48528 | − | 9.48528i | 0.443703 | − | 0.443703i | −0.449552 | − | 0.893254i | \(-0.648416\pi\) |
0.893254 | + | 0.449552i | \(0.148416\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.17157 | − | 12.4853i | 0.241388 | − | 0.582763i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.3640 | + | 5.53553i | −0.622422 | + | 0.257816i | −0.671529 | − | 0.740978i | \(-0.734362\pi\) |
0.0491076 | + | 0.998793i | \(0.484362\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.9706i | − | 0.509845i | −0.966961 | − | 0.254923i | \(-0.917950\pi\) | ||
0.966961 | − | 0.254923i | \(-0.0820500\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.9706i | 1.15798i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 29.0919 | − | 12.0503i | 1.34621 | − | 0.557619i | 0.410977 | − | 0.911646i | \(-0.365188\pi\) |
0.935235 | + | 0.354027i | \(0.115188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.17157 | − | 5.24264i | 0.100274 | − | 0.242083i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.00000 | − | 1.00000i | 0.0460776 | − | 0.0460776i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.92893 | − | 1.92893i | −0.0886924 | − | 0.0886924i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −35.5061 | − | 14.7071i | −1.62913 | − | 0.674808i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.29289 | − | 3.12132i | −0.0591975 | − | 0.142915i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.97056 | 0.227111 | 0.113555 | − | 0.993532i | \(-0.463776\pi\) | ||||
0.113555 | + | 0.993532i | \(0.463776\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.41421 | 0.155675 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.242641 | + | 0.585786i | 0.0110405 | + | 0.0266542i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.72792 | − | 1.95837i | −0.214684 | − | 0.0889250i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0000 | + | 11.0000i | 0.498458 | + | 0.498458i | 0.910958 | − | 0.412500i | \(-0.135344\pi\) |
−0.412500 | + | 0.910958i | \(0.635344\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.7279 | + | 25.7279i | −1.16346 | + | 1.16346i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.33452 | + | 17.7071i | −0.331002 | + | 0.799111i | 0.667511 | + | 0.744600i | \(0.267360\pi\) |
−0.998513 | + | 0.0545104i | \(0.982640\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.65685 | + | 3.17157i | −0.344847 | + | 0.142840i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.443651i | 0.0199406i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.343146i | − | 0.0153922i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.94975 | − | 3.70711i | 0.400646 | − | 0.165953i | −0.173256 | − | 0.984877i | \(-0.555429\pi\) |
0.573902 | + | 0.818924i | \(0.305429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.34315 | − | 8.07107i | 0.149361 | − | 0.360589i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.1421 | + | 17.1421i | −0.764330 | + | 0.764330i | −0.977102 | − | 0.212772i | \(-0.931751\pi\) |
0.212772 | + | 0.977102i | \(0.431751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.3848 | − | 29.3848i | −1.30761 | − | 1.30761i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.3640 | − | 6.77817i | −0.726749 | − | 0.301029i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.0919 | − | 29.1924i | −0.535963 | − | 1.29393i | −0.927519 | − | 0.373776i | \(-0.878063\pi\) |
0.391556 | − | 0.920154i | \(-0.371937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | −0.619324 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.6274 | −1.26393 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.6863 | + | 33.0416i | 0.603090 | + | 1.45599i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.41421 | − | 1.41421i | −0.150157 | − | 0.0621970i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.58579 | + | 1.58579i | 0.0696083 | + | 0.0696083i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.6569 | − | 14.6569i | 0.642128 | − | 0.642128i | −0.308950 | − | 0.951078i | \(-0.599978\pi\) |
0.951078 | + | 0.308950i | \(0.0999775\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.807612 | − | 1.94975i | 0.0353144 | − | 0.0852565i | −0.905238 | − | 0.424904i | \(-0.860308\pi\) |
0.940553 | + | 0.339648i | \(0.110308\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.4853 | − | 6.41421i | 0.675833 | − | 0.279939i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.3137i | − | 0.492833i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9411i | 0.997440i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.53553 | − | 1.05025i | 0.110033 | − | 0.0455771i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.82843 | − | 14.0711i | 0.252457 | − | 0.609486i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.757359 | − | 0.757359i | 0.0327435 | − | 0.0327435i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.3137 | − | 20.3137i | −0.876601 | − | 0.876601i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.46447 | − | 0.606602i | −0.0630790 | − | 0.0261282i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.26346 | − | 12.7071i | −0.226294 | − | 0.546321i | 0.769427 | − | 0.638735i | \(-0.220542\pi\) |
−0.995721 | + | 0.0924135i | \(0.970542\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5858 | 0.454280 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.6985 | 0.672449 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4645 | − | 25.2635i | −0.447428 | − | 1.08019i | −0.973282 | − | 0.229612i | \(-0.926254\pi\) |
0.525854 | − | 0.850575i | \(-0.323746\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.292893 | + | 0.121320i | 0.0125004 | + | 0.00517783i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.4142 | + | 12.4142i | 0.528863 | + | 0.528863i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | − | 6.00000i | 0.255146 | − | 0.255146i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.41421 | − | 10.6569i | 0.187373 | − | 0.452358i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.8787 | + | 4.50610i | −0.460944 | + | 0.190929i | −0.601057 | − | 0.799206i | \(-0.705254\pi\) |
0.140113 | + | 0.990136i | \(0.455254\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8995i | 0.672477i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1.65685i | − | 0.0699524i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.1213 | − | 5.02082i | 0.510853 | − | 0.211602i | −0.112341 | − | 0.993670i | \(-0.535835\pi\) |
0.623194 | + | 0.782068i | \(0.285835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.8284 | + | 55.1127i | −0.960399 | + | 2.31861i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.0711 | − | 10.0711i | 0.422945 | − | 0.422945i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.34315 | + | 3.34315i | 0.140152 | + | 0.140152i | 0.773702 | − | 0.633550i | \(-0.218403\pi\) |
−0.633550 | + | 0.773702i | \(0.718403\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.29289 | − | 0.535534i | −0.0541059 | − | 0.0224114i | 0.355466 | − | 0.934689i | \(-0.384322\pi\) |
−0.409572 | + | 0.912278i | \(0.634322\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.48528 | + | 20.4853i | 0.354478 | + | 0.855785i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.55635 | −0.0649042 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.9706 | −0.623233 | −0.311616 | − | 0.950208i | \(-0.600870\pi\) | ||||
−0.311616 | + | 0.950208i | \(0.600870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.0711 | − | 31.5563i | −0.543215 | − | 1.31144i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.65685 | − | 3.58579i | −0.359147 | − | 0.148763i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.82843 | + | 1.82843i | 0.0757257 | + | 0.0757257i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.82843 | − | 1.82843i | 0.0755962 | − | 0.0755962i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.60660 | − | 20.7782i | 0.355232 | − | 0.857607i | −0.640724 | − | 0.767771i | \(-0.721366\pi\) |
0.995957 | − | 0.0898359i | \(-0.0286342\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.1421 | + | 9.17157i | −0.912351 | + | 0.377908i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 34.7279i | − | 1.42852i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 28.2843i | − | 1.16150i | −0.814083 | − | 0.580748i | \(-0.802760\pi\) | ||
0.814083 | − | 0.580748i | \(-0.197240\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4853 | + | 5.17157i | −0.511847 | + | 0.212014i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.9706 | − | 43.3848i | 0.735486 | − | 1.77562i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3431 | − | 15.3431i | 0.626904 | − | 0.626904i | −0.320384 | − | 0.947288i | \(-0.603812\pi\) |
0.947288 | + | 0.320384i | \(0.103812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.9706 | + | 11.9706i | 0.488289 | + | 0.488289i | 0.907766 | − | 0.419477i | \(-0.137786\pi\) |
−0.419477 | + | 0.907766i | \(0.637786\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.53553 | − | 0.636039i | −0.0625318 | − | 0.0259015i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 14.0919 | + | 34.0208i | 0.572917 | + | 1.38314i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.970563 | −0.0393939 | −0.0196970 | − | 0.999806i | \(-0.506270\pi\) | ||||
−0.0196970 | + | 0.999806i | \(0.506270\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.65685 | −0.310271 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.24264 | + | 19.8995i | 0.333462 | + | 0.805047i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −36.6777 | − | 15.1924i | −1.48140 | − | 0.613615i | −0.511972 | − | 0.859002i | \(-0.671085\pi\) |
−0.969425 | + | 0.245387i | \(0.921085\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.3848 | − | 36.3848i | −1.46718 | − | 1.46718i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.7990 | + | 16.7990i | −0.676302 | + | 0.676302i | −0.959161 | − | 0.282859i | \(-0.908717\pi\) |
0.282859 | + | 0.959161i | \(0.408717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.22183 | + | 15.0208i | −0.250076 | + | 0.603738i | −0.998210 | − | 0.0598107i | \(-0.980950\pi\) |
0.748133 | + | 0.663548i | \(0.230950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.07107 | + | 0.443651i | −0.0429805 | + | 0.0178031i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.31371i | 0.212889i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 15.9289i | − | 0.637157i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.24264 | + | 1.34315i | −0.129499 | + | 0.0536401i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.00000 | + | 4.82843i | −0.0797452 | + | 0.192522i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4558 | − | 18.4558i | 0.734716 | − | 0.734716i | −0.236834 | − | 0.971550i | \(-0.576110\pi\) |
0.971550 | + | 0.236834i | \(0.0761099\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.656854 | + | 0.656854i | 0.0261076 | + | 0.0261076i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 65.4558 | + | 27.1127i | 2.59754 | + | 1.07593i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.53553 | + | 8.53553i | 0.140083 | + | 0.338190i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.100505 | −0.00397592 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.4558 | −1.71640 | −0.858201 | − | 0.513313i | \(-0.828418\pi\) | ||||
−0.858201 | + | 0.513313i | \(0.828418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.4350 | − | 37.2635i | −0.608698 | − | 1.46953i | −0.864417 | − | 0.502776i | \(-0.832312\pi\) |
0.255719 | − | 0.966751i | \(-0.417688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.6274 | + | 20.5563i | 1.95408 | + | 0.809405i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.8284 | − | 11.8284i | −0.465023 | − | 0.465023i | 0.435274 | − | 0.900298i | \(-0.356651\pi\) |
−0.900298 | + | 0.435274i | \(0.856651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.48528 | + | 1.48528i | −0.0583024 | + | 0.0583024i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | − | 9.65685i | 0.156772 | − | 0.378482i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.0919 | − | 14.9497i | 1.41238 | − | 0.585029i | 0.459450 | − | 0.888204i | \(-0.348047\pi\) |
0.952935 | + | 0.303175i | \(0.0980467\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 32.1005i | − | 1.25427i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.10051i | 0.159976i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.87868 | + | 2.43503i | −0.229001 | + | 0.0948553i | −0.494234 | − | 0.869329i | \(-0.664551\pi\) |
0.265233 | + | 0.964184i | \(0.414551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.74874 | + | 18.7071i | −0.301391 | + | 0.727622i | 0.698536 | + | 0.715574i | \(0.253835\pi\) |
−0.999927 | + | 0.0120477i | \(0.996165\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.82843 | + | 6.82843i | −0.265194 | + | 0.265194i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.2426 | + | 20.2426i | 0.784976 | + | 0.784976i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.656854 | + | 0.272078i | 0.0254335 | + | 0.0105349i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.17157 | − | 22.1421i | −0.354593 | − | 0.856064i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.242641 | −0.00936704 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.51472 | 0.212577 | 0.106288 | − | 0.994335i | \(-0.466103\pi\) | ||||
0.106288 | + | 0.994335i | \(0.466103\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 11.7279 | + | 28.3137i | 0.451408 | + | 1.08980i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.60660 | + | 2.32233i | 0.215479 | + | 0.0892544i | 0.487812 | − | 0.872949i | \(-0.337795\pi\) |
−0.272333 | + | 0.962203i | \(0.587795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.51472 | + | 1.51472i | 0.0581296 | + | 0.0581296i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.89949 | − | 8.89949i | 0.341029 | − | 0.341029i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.87868 | + | 14.1924i | −0.224941 | + | 0.543057i | −0.995548 | − | 0.0942543i | \(-0.969953\pi\) |
0.770607 | + | 0.637311i | \(0.219953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.7279 | − | 4.85786i | 0.448101 | − | 0.185609i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.5563i | 1.89069i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15.0711i | − | 0.574162i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.5061 | + | 11.8076i | −1.08442 | + | 0.449183i | −0.852059 | − | 0.523446i | \(-0.824646\pi\) |
−0.232364 | + | 0.972629i | \(0.574646\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0710678 | − | 0.171573i | 0.00269964 | − | 0.00651751i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −32.4142 | + | 32.4142i | −1.22954 | + | 1.22954i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.4853 | + | 16.4853i | 0.624425 | + | 0.624425i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 20.8995 | + | 8.65685i | 0.790491 | + | 0.327432i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.12132 | − | 17.1924i | −0.268969 | − | 0.649348i | 0.730467 | − | 0.682948i | \(-0.239303\pi\) |
−0.999435 | + | 0.0336007i | \(0.989303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.0711 | 0.417553 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 72.7696 | 2.74066 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.65685 | + | 16.0711i | 0.250357 | + | 0.604415i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.77817 | + | 2.80761i | 0.254560 | + | 0.105442i | 0.506314 | − | 0.862349i | \(-0.331008\pi\) |
−0.251755 | + | 0.967791i | \(0.581008\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75736 | − | 1.75736i | −0.0659061 | − | 0.0659061i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.686292 | + | 0.686292i | −0.0257018 | + | 0.0257018i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.757359 | + | 1.82843i | −0.0283236 | + | 0.0683793i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −29.5563 | + | 12.2426i | −1.10380 | + | 0.457210i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.3431i | 0.907846i | 0.891041 | + | 0.453923i | \(0.149976\pi\) | ||||
−0.891041 | + | 0.453923i | \(0.850024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 14.9706i | − | 0.557533i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.4853 | − | 6.00000i | 0.538713 | − | 0.223142i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.19239 | − | 17.3640i | 0.267119 | − | 0.644881i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.9706 | + | 23.9706i | −0.889019 | + | 0.889019i | −0.994429 | − | 0.105410i | \(-0.966385\pi\) |
0.105410 | + | 0.994429i | \(0.466385\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7782 | + | 15.7782i | 0.584377 | + | 0.584377i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −22.4853 | − | 9.31371i | −0.831648 | − | 0.344480i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.736544 | + | 1.77817i | 0.0272049 | + | 0.0656784i | 0.936898 | − | 0.349602i | \(-0.113683\pi\) |
−0.909693 | + | 0.415281i | \(0.863683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.2132 | 1.15132 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.27208 | 0.0468576 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.53553 | + | 18.1924i | 0.277199 | + | 0.669218i | 0.999756 | − | 0.0220937i | \(-0.00703323\pi\) |
−0.722557 | + | 0.691312i | \(0.757033\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.8995 | + | 7.82843i | 0.694290 | + | 0.287584i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.6274 | + | 13.6274i | 0.499941 | + | 0.499941i | 0.911420 | − | 0.411478i | \(-0.134987\pi\) |
−0.411478 | + | 0.911420i | \(0.634987\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −35.0000 | + | 35.0000i | −1.28230 | + | 1.28230i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.05025 | + | 2.53553i | −0.0384267 | + | 0.0927703i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.414214 | + | 0.171573i | −0.0151350 | + | 0.00626914i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.9706i | 0.838208i | 0.907938 | + | 0.419104i | \(0.137656\pi\) | ||||
−0.907938 | + | 0.419104i | \(0.862344\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 29.2132i | − | 1.06459i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −68.3553 | + | 28.3137i | −2.48771 | + | 1.03044i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.736544 | − | 1.77817i | 0.0267701 | − | 0.0646289i | −0.909929 | − | 0.414764i | \(-0.863864\pi\) |
0.936699 | + | 0.350135i | \(0.113864\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.100505 | + | 0.100505i | −0.00364810 | + | 0.00364810i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1716 | − | 24.1716i | −0.876219 | − | 0.876219i | 0.116922 | − | 0.993141i | \(-0.462697\pi\) |
−0.993141 | + | 0.116922i | \(0.962697\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.07107 | − | 2.51472i | −0.219787 | − | 0.0910389i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.51472 | + | 3.65685i | 0.0547648 | + | 0.132214i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.2426 | 0.442056 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.4853 | 0.810840 | 0.405420 | − | 0.914131i | \(-0.367125\pi\) | ||||
0.405420 | + | 0.914131i | \(0.367125\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.24264 | + | 10.2426i | 0.152795 | + | 0.368880i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.0919 | + | 10.8076i | 0.938460 | + | 0.388723i | 0.798882 | − | 0.601488i | \(-0.205425\pi\) |
0.139578 | + | 0.990211i | \(0.455425\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.1421 | + | 18.1421i | 0.651685 | + | 0.651685i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.41421 | + | 3.41421i | −0.122484 | + | 0.122484i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.8995 | − | 45.6274i | 0.677145 | − | 1.63477i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0710678 | − | 0.0294373i | 0.00254301 | − | 0.00105335i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 14.0000i | − | 0.500319i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.58579i | − | 0.0922907i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.94975 | − | 3.70711i | 0.319024 | − | 0.132144i | −0.217424 | − | 0.976077i | \(-0.569766\pi\) |
0.536448 | + | 0.843933i | \(0.319766\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.171573 | + | 0.414214i | −0.00610816 | + | 0.0147464i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.6569 | − | 17.6569i | 0.627805 | − | 0.627805i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | + | 1.00000i | 0.0355110 | + | 0.0355110i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −47.0416 | − | 19.4853i | −1.66839 | − | 0.691072i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.0919 | − | 29.1924i | −0.428316 | − | 1.03405i | −0.979821 | − | 0.199876i | \(-0.935946\pi\) |
0.551505 | − | 0.834172i | \(-0.314054\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.9706 | −1.16641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.55635 | 0.0549909 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.20101 | − | 2.89949i | −0.0423827 | − | 0.102321i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.07107 | + | 0.443651i | 0.0377502 | + | 0.0156366i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.89949 | − | 6.89949i | −0.242874 | − | 0.242874i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.857864 | + | 0.857864i | −0.0301609 | + | 0.0301609i | −0.722026 | − | 0.691865i | \(-0.756789\pi\) |
0.691865 | + | 0.722026i | \(0.256789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.73654 | + | 23.5061i | −0.341896 | + | 0.825411i | 0.655628 | + | 0.755084i | \(0.272404\pi\) |
−0.997524 | + | 0.0703264i | \(0.977596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.7279 | + | 12.7279i | −1.07768 | + | 0.446388i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.5269i | 2.33034i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.5563i | 1.80373i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.00000 | + | 0.414214i | −0.0349428 | + | 0.0144738i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.393398 | − | 0.949747i | 0.0137297 | − | 0.0331464i | −0.916866 | − | 0.399195i | \(-0.869290\pi\) |
0.930596 | + | 0.366049i | \(0.119290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.02944 | + | 2.02944i | −0.0707417 | + | 0.0707417i | −0.741592 | − | 0.670851i | \(-0.765929\pi\) |
0.670851 | + | 0.741592i | \(0.265929\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.65685 | + | 2.65685i | 0.0924998 | + | 0.0924998i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.8787 | + | 4.92031i | 0.413062 | + | 0.171096i | 0.579530 | − | 0.814951i | \(-0.303236\pi\) |
−0.166468 | + | 0.986047i | \(0.553236\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.8076 | − | 38.1630i | −0.549021 | − | 1.32545i | −0.918208 | − | 0.396099i | \(-0.870364\pi\) |
0.369187 | − | 0.929355i | \(-0.379636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.41421 | −0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.1421 | −0.489996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.11270 | − | 14.7574i | −0.211539 | − | 0.510699i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.6569 | + | 7.31371i | 0.610310 | + | 0.252799i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.3137 | − | 32.3137i | −1.11559 | − | 1.11559i | −0.992380 | − | 0.123213i | \(-0.960680\pi\) |
−0.123213 | − | 0.992380i | \(-0.539320\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4350 | − | 14.4350i | 0.497760 | − | 0.497760i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.17157 | − | 14.8995i | 0.212560 | − | 0.513166i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −29.9203 | + | 12.3934i | −1.02929 | + | 0.426346i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.4142i | − | 0.529639i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 19.5563i | − | 0.671172i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.414214 | − | 0.171573i | 0.0141991 | − | 0.00588144i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.16295 | − | 2.80761i | 0.0398187 | − | 0.0961308i | −0.902719 | − | 0.430231i | \(-0.858432\pi\) |
0.942538 | + | 0.334100i | \(0.108432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.92893 | − | 5.92893i | 0.202765 | − | 0.202765i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.3137 | + | 32.3137i | 1.10382 | + | 1.10382i | 0.993946 | + | 0.109869i | \(0.0350432\pi\) |
0.109869 | + | 0.993946i | \(0.464957\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.6777 | + | 13.9497i | 1.14907 | + | 0.475959i | 0.874221 | − | 0.485529i | \(-0.161373\pi\) |
0.274847 | + | 0.961488i | \(0.411373\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.24264 | + | 19.8995i | 0.280908 | + | 0.678173i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 45.9411 | 1.56385 | 0.781927 | − | 0.623370i | \(-0.214237\pi\) | ||||
0.781927 | + | 0.623370i | \(0.214237\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.10051 | 0.139421 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.36396 | + | 15.3640i | 0.216131 | + | 0.521787i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.75736 | + | 0.727922i | 0.0596143 | + | 0.0246931i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.24264 | − | 5.24264i | −0.177640 | − | 0.177640i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.443651 | − | 0.443651i | 0.0150153 | − | 0.0150153i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.58579 | − | 6.24264i | 0.0874155 | − | 0.211040i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.2635 | − | 13.7782i | 1.12323 | − | 0.465256i | 0.257754 | − | 0.966211i | \(-0.417018\pi\) |
0.865473 | + | 0.500955i | \(0.167018\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 23.2132i | 0.782962i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.6274i | 0.762337i | 0.924506 | + | 0.381169i | \(0.124478\pi\) | ||||
−0.924506 | + | 0.381169i | \(0.875522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.4350 | − | 19.6482i | 1.59632 | − | 0.661216i | 0.605427 | − | 0.795901i | \(-0.293002\pi\) |
0.990888 | + | 0.134685i | \(0.0430022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.8284 | − | 38.2132i | 0.532067 | − | 1.28452i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.3137 | − | 20.3137i | 0.682068 | − | 0.682068i | −0.278398 | − | 0.960466i | \(-0.589803\pi\) |
0.960466 | + | 0.278398i | \(0.0898035\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.9706 | − | 20.9706i | −0.703330 | − | 0.703330i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.94975 | + | 1.22183i | 0.0988203 | + | 0.0409327i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.7279 | + | 64.5269i | 0.894416 | + | 2.15931i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −52.5269 | −1.75578 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.828427 | 0.0276604 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.48528 | − | 10.8284i | −0.149593 | − | 0.361148i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.3137 | + | 8.82843i | 0.710063 | + | 0.294118i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.8995 | − | 15.8995i | −0.529102 | − | 0.529102i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.6863 | − | 13.6863i | 0.454948 | − | 0.454948i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.221825 | + | 0.535534i | −0.00736559 | + | 0.0177821i | −0.927520 | − | 0.373775i | \(-0.878063\pi\) |
0.920154 | + | 0.391557i | \(0.128063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.70711 | − | 1.94975i | 0.156125 | − | 0.0646690i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.5980i | − | 1.51073i | −0.655305 | − | 0.755364i | \(-0.727460\pi\) | ||
0.655305 | − | 0.755364i | \(-0.272540\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.10051i | − | 0.0695166i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.41421 | − | 1.82843i | 0.145929 | − | 0.0604459i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.14214 | + | 12.4142i | −0.169808 | + | 0.409953i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4853 | − | 25.4853i | 0.840682 | − | 0.840682i | −0.148266 | − | 0.988948i | \(-0.547369\pi\) |
0.988948 | + | 0.148266i | \(0.0473691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.17157 | + | 4.17157i | 0.137458 | + | 0.137458i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.414214 | − | 0.171573i | −0.0136340 | − | 0.00564739i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.53553 | − | 10.9497i | −0.149127 | − | 0.360025i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.38478 | −0.144015 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.4853 | −0.868954 | −0.434477 | − | 0.900683i | \(-0.643067\pi\) | ||||
−0.434477 | + | 0.900683i | \(0.643067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4645 | + | 27.6777i | 0.375733 | + | 0.907099i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.8995 | − | 8.65685i | −0.684219 | − | 0.283413i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.14214 | − | 2.14214i | −0.0700553 | − | 0.0700553i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0000 | − | 19.0000i | 0.620703 | − | 0.620703i | −0.325008 | − | 0.945711i | \(-0.605367\pi\) |
0.945711 | + | 0.325008i | \(0.105367\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.48528 | + | 22.8995i | −0.309540 | + | 0.747297i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.3640 | + | 5.53553i | −0.435653 | + | 0.180453i | −0.589721 | − | 0.807607i | \(-0.700762\pi\) |
0.154068 | + | 0.988060i | \(0.450762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.00000i | − | 0.0651290i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 22.8284i | − | 0.742609i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.3345 | + | 15.4645i | −1.21321 | + | 0.502528i | −0.895245 | − | 0.445575i | \(-0.852999\pi\) |
−0.317964 | + | 0.948103i | \(0.602999\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.00000 | + | 16.8995i | −0.227230 | + | 0.548581i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.8284 | − | 15.8284i | 0.513272 | − | 0.513272i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.34315 | + | 3.34315i | 0.108295 | + | 0.108295i | 0.759178 | − | 0.650883i | \(-0.225601\pi\) |
−0.650883 | + | 0.759178i | \(0.725601\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.4558 | + | 15.5147i | 1.21204 | + | 0.502045i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.656854 | − | 1.58579i | −0.0212331 | − | 0.0512612i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.31371 | −0.171589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0502525 | + | 0.121320i | 0.00161937 | + | 0.00390949i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −57.6985 | − | 23.8995i | −1.85738 | − | 0.769352i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.9706 | + | 39.9706i | 1.28537 | + | 1.28537i | 0.937570 | + | 0.347797i | \(0.113070\pi\) |
0.347797 | + | 0.937570i | \(0.386930\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.1421 | + | 22.1421i | −0.711308 | + | 0.711308i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.63604 | − | 23.2635i | 0.309235 | − | 0.746560i | −0.690495 | − | 0.723337i | \(-0.742607\pi\) |
0.999730 | − | 0.0232228i | \(-0.00739270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.7279 | − | 7.34315i | 0.568331 | − | 0.235410i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 21.8995i | − | 0.701345i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.1421i | 0.452447i | 0.974075 | + | 0.226224i | \(0.0726380\pi\) | ||||
−0.974075 | + | 0.226224i | \(0.927362\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.10051 | + | 0.455844i | −0.0351723 | + | 0.0145688i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.736544 | + | 1.77817i | −0.0235160 | + | 0.0567727i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.6274 | + | 25.6274i | −0.817388 | + | 0.817388i | −0.985729 | − | 0.168341i | \(-0.946159\pi\) |
0.168341 | + | 0.985729i | \(0.446159\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −44.8995 | − | 44.8995i | −1.43062 | − | 1.43062i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.1421 | − | 11.6569i | −0.895774 | − | 0.371042i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.798990 | + | 1.92893i | 0.0254064 | + | 0.0613365i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.0711 | −0.414798 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.8579 | − | 79.3259i | −1.04166 | − | 2.51480i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.80761 | + | 0.748737i | 0.0572476 | + | 0.0237127i | 0.411124 | − | 0.911580i | \(-0.365136\pi\) |
−0.353876 | + | 0.935292i | \(0.615136\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.24264 | − | 6.24264i | −0.197508 | − | 0.197508i |
(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 | 256.2.g.a.225.1 | 4 | ||
4.3 | odd | 2 | 256.2.g.b.225.1 | 4 | |||
8.3 | odd | 2 | 32.2.g.a.5.1 | ✓ | 4 | ||
8.5 | even | 2 | 128.2.g.a.113.1 | 4 | |||
16.3 | odd | 4 | 512.2.g.d.193.1 | 4 | |||
16.5 | even | 4 | 512.2.g.c.193.1 | 4 | |||
16.11 | odd | 4 | 512.2.g.a.193.1 | 4 | |||
16.13 | even | 4 | 512.2.g.b.193.1 | 4 | |||
24.5 | odd | 2 | 1152.2.v.a.1009.1 | 4 | |||
24.11 | even | 2 | 288.2.v.a.37.1 | 4 | |||
32.3 | odd | 8 | 32.2.g.a.13.1 | yes | 4 | ||
32.5 | even | 8 | 512.2.g.b.321.1 | 4 | |||
32.11 | odd | 8 | 512.2.g.a.321.1 | 4 | |||
32.13 | even | 8 | inner | 256.2.g.a.33.1 | 4 | ||
32.19 | odd | 8 | 256.2.g.b.33.1 | 4 | |||
32.21 | even | 8 | 512.2.g.c.321.1 | 4 | |||
32.27 | odd | 8 | 512.2.g.d.321.1 | 4 | |||
32.29 | even | 8 | 128.2.g.a.17.1 | 4 | |||
40.3 | even | 4 | 800.2.ba.a.549.1 | 4 | |||
40.19 | odd | 2 | 800.2.y.a.101.1 | 4 | |||
40.27 | even | 4 | 800.2.ba.b.549.1 | 4 | |||
64.13 | even | 16 | 4096.2.a.f.1.4 | 4 | |||
64.19 | odd | 16 | 4096.2.a.e.1.4 | 4 | |||
64.45 | even | 16 | 4096.2.a.f.1.1 | 4 | |||
64.51 | odd | 16 | 4096.2.a.e.1.1 | 4 | |||
96.29 | odd | 8 | 1152.2.v.a.145.1 | 4 | |||
96.35 | even | 8 | 288.2.v.a.109.1 | 4 | |||
160.3 | even | 8 | 800.2.ba.b.749.1 | 4 | |||
160.67 | even | 8 | 800.2.ba.a.749.1 | 4 | |||
160.99 | odd | 8 | 800.2.y.a.301.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.2.g.a.5.1 | ✓ | 4 | 8.3 | odd | 2 | ||
32.2.g.a.13.1 | yes | 4 | 32.3 | odd | 8 | ||
128.2.g.a.17.1 | 4 | 32.29 | even | 8 | |||
128.2.g.a.113.1 | 4 | 8.5 | even | 2 | |||
256.2.g.a.33.1 | 4 | 32.13 | even | 8 | inner | ||
256.2.g.a.225.1 | 4 | 1.1 | even | 1 | trivial | ||
256.2.g.b.33.1 | 4 | 32.19 | odd | 8 | |||
256.2.g.b.225.1 | 4 | 4.3 | odd | 2 | |||
288.2.v.a.37.1 | 4 | 24.11 | even | 2 | |||
288.2.v.a.109.1 | 4 | 96.35 | even | 8 | |||
512.2.g.a.193.1 | 4 | 16.11 | odd | 4 | |||
512.2.g.a.321.1 | 4 | 32.11 | odd | 8 | |||
512.2.g.b.193.1 | 4 | 16.13 | even | 4 | |||
512.2.g.b.321.1 | 4 | 32.5 | even | 8 | |||
512.2.g.c.193.1 | 4 | 16.5 | even | 4 | |||
512.2.g.c.321.1 | 4 | 32.21 | even | 8 | |||
512.2.g.d.193.1 | 4 | 16.3 | odd | 4 | |||
512.2.g.d.321.1 | 4 | 32.27 | odd | 8 | |||
800.2.y.a.101.1 | 4 | 40.19 | odd | 2 | |||
800.2.y.a.301.1 | 4 | 160.99 | odd | 8 | |||
800.2.ba.a.549.1 | 4 | 40.3 | even | 4 | |||
800.2.ba.a.749.1 | 4 | 160.67 | even | 8 | |||
800.2.ba.b.549.1 | 4 | 40.27 | even | 4 | |||
800.2.ba.b.749.1 | 4 | 160.3 | even | 8 | |||
1152.2.v.a.145.1 | 4 | 96.29 | odd | 8 | |||
1152.2.v.a.1009.1 | 4 | 24.5 | odd | 2 | |||
4096.2.a.e.1.1 | 4 | 64.51 | odd | 16 | |||
4096.2.a.e.1.4 | 4 | 64.19 | odd | 16 | |||
4096.2.a.f.1.1 | 4 | 64.45 | even | 16 | |||
4096.2.a.f.1.4 | 4 | 64.13 | even | 16 |