Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(65,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, 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("512.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.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: | \(4.08834058349\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 512.193 |
Dual form | 512.2.g.c.321.1 |
$q$-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 \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.70711 | − | 0.707107i | 0.985599 | − | 0.408248i | 0.169102 | − | 0.985599i | \(-0.445913\pi\) |
0.816497 | + | 0.577350i | \(0.195913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.29289 | + | 3.12132i | −0.578199 | + | 1.39590i | 0.316228 | + | 0.948683i | \(0.397584\pi\) |
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.00000i | 0.377964 | + | 0.377964i | 0.870367 | − | 0.492403i | \(-0.163881\pi\) |
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.292893 | − | 0.292893i | 0.0976311 | − | 0.0976311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.292893 | + | 0.121320i | 0.0883106 | + | 0.0365795i | 0.426401 | − | 0.904534i | \(-0.359781\pi\) |
−0.338091 | + | 0.941113i | \(0.609781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.707107 | + | 1.70711i | 0.196116 | + | 0.473466i | 0.991093 | − | 0.133174i | \(-0.0425169\pi\) |
−0.794977 | + | 0.606640i | \(0.792517\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | 2.29289 | + | 5.53553i | 0.526026 | + | 1.26994i | 0.934107 | + | 0.356993i | \(0.116198\pi\) |
−0.408081 | + | 0.912946i | \(0.633802\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.41421 | + | 1.00000i | 0.526825 | + | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.171573 | − | 0.171573i | 0.0357754 | − | 0.0357754i | −0.688993 | − | 0.724768i | \(-0.741947\pi\) |
0.724768 | + | 0.688993i | \(0.241947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.53553 | − | 4.53553i | −0.907107 | − | 0.907107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.82843 | + | 4.41421i | −0.351881 | + | 0.849516i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.70711 | + | 1.12132i | −0.502697 | + | 0.208224i | −0.619598 | − | 0.784920i | \(-0.712704\pi\) |
0.116900 | + | 0.993144i | \(0.462704\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −4.41421 | + | 1.82843i | −0.746138 | + | 0.309061i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.707107 | − | 1.70711i | 0.116248 | − | 0.280647i | −0.855037 | − | 0.518567i | \(-0.826466\pi\) |
0.971285 | + | 0.237920i | \(0.0764657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.41421 | + | 2.41421i | 0.386584 | + | 0.386584i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.82843 | − | 5.82843i | 0.910247 | − | 0.910247i | −0.0860440 | − | 0.996291i | \(-0.527423\pi\) |
0.996291 | + | 0.0860440i | \(0.0274225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.94975 | + | 3.29289i | 1.21233 | + | 0.502162i | 0.894962 | − | 0.446143i | \(-0.147203\pi\) |
0.317363 | + | 0.948304i | \(0.397203\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.535534 | + | 1.29289i | 0.0798327 | + | 0.192733i | ||||
\(46\) | 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 | ||||||||
\(51\) | −2.00000 | − | 4.82843i | −0.280056 | − | 0.676115i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.53553 | − | 3.12132i | −1.03509 | − | 0.428746i | −0.200540 | − | 0.979686i | \(-0.564270\pi\) |
−0.834545 | + | 0.550939i | \(0.814270\pi\) | |||||||
\(54\) | 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 | ||||||||
\(59\) | 2.53553 | − | 6.12132i | 0.330098 | − | 0.796928i | −0.668485 | − | 0.743725i | \(-0.733057\pi\) |
0.998584 | − | 0.0532027i | \(-0.0169429\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.707107 | + | 0.292893i | −0.0905357 | + | 0.0375011i | −0.427492 | − | 0.904019i | \(-0.640603\pi\) |
0.336956 | + | 0.941520i | \(0.390603\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.585786 | 0.0738022 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.24264 | −0.774304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70711 | − | 1.53553i | 0.452895 | − | 0.187595i | −0.144563 | − | 0.989496i | \(-0.546178\pi\) |
0.597458 | + | 0.801900i | \(0.296178\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.171573 | − | 0.414214i | 0.0206549 | − | 0.0498655i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.171573 | − | 0.171573i | −0.0203620 | − | 0.0203620i | 0.696853 | − | 0.717214i | \(-0.254583\pi\) |
−0.717214 | + | 0.696853i | \(0.754583\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.00000 | + | 7.00000i | −0.819288 | + | 0.819288i | −0.986005 | − | 0.166717i | \(-0.946683\pi\) |
0.166717 | + | 0.986005i | \(0.446683\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.9497 | − | 4.53553i | −1.26437 | − | 0.523718i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.171573 | + | 0.414214i | 0.0195525 | + | 0.0472040i | ||||
\(78\) | 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 | ||||||||
\(83\) | −2.53553 | − | 6.12132i | −0.278311 | − | 0.671902i | 0.721478 | − | 0.692437i | \(-0.243463\pi\) |
−0.999789 | + | 0.0205350i | \(0.993463\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.82843 | + | 3.65685i | 0.957577 | + | 0.396642i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.82843 | + | 3.82843i | −0.410450 | + | 0.410450i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.65685 | + | 2.65685i | 0.281626 | + | 0.281626i | 0.833757 | − | 0.552131i | \(-0.186185\pi\) |
−0.552131 | + | 0.833757i | \(0.686185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | + | 2.41421i | −0.104828 | + | 0.253078i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.82843 | − | 2.82843i | 0.708075 | − | 0.293294i | ||||
\(94\) | 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 | ||||||||
\(99\) | 0.121320 | − | 0.0502525i | 0.0121932 | − | 0.00505057i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.70711 | − | 11.3640i | 0.468375 | − | 1.13076i | −0.496498 | − | 0.868038i | \(-0.665381\pi\) |
0.964873 | − | 0.262718i | \(-0.0846190\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.48528 | − | 7.48528i | −0.737547 | − | 0.737547i | 0.234556 | − | 0.972103i | \(-0.424636\pi\) |
−0.972103 | + | 0.234556i | \(0.924636\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.24264 | + | 6.24264i | −0.609219 | + | 0.609219i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.292893 | + | 0.121320i | 0.0283151 | + | 0.0117285i | 0.396796 | − | 0.917907i | \(-0.370122\pi\) |
−0.368481 | + | 0.929635i | \(0.620122\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.77817 | − | 4.29289i | −0.170318 | − | 0.411185i | 0.815555 | − | 0.578680i | \(-0.196432\pi\) |
−0.985873 | + | 0.167496i | \(0.946432\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 0.313708 | + | 0.757359i | 0.0292535 | + | 0.0706241i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.707107 | + | 0.292893i | 0.0653720 | + | 0.0270780i | ||||
\(118\) | 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 | ||||||||
\(123\) | 5.82843 | − | 14.0711i | 0.525532 | − | 1.26875i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.41421 | − | 1.82843i | 0.394819 | − | 0.163539i | ||||
\(126\) | 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 | ||||||||
\(131\) | −8.77817 | + | 3.63604i | −0.766953 | + | 0.317682i | −0.731637 | − | 0.681694i | \(-0.761244\pi\) |
−0.0353153 | + | 0.999376i | \(0.511244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.24264 | + | 7.82843i | −0.281173 | + | 0.678811i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.4142 | − | 11.4142i | −0.982379 | − | 0.982379i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.65685 | + | 2.65685i | −0.226990 | + | 0.226990i | −0.811434 | − | 0.584444i | \(-0.801313\pi\) |
0.584444 | + | 0.811434i | \(0.301313\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.5355 | − | 5.19239i | −1.06325 | − | 0.440413i | −0.218646 | − | 0.975804i | \(-0.570164\pi\) |
−0.844604 | + | 0.535392i | \(0.820164\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.24264 | − | 19.8995i | −0.694156 | − | 1.67584i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.585786i | 0.0489859i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 9.89949i | − | 0.822108i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.53553 | − | 8.53553i | −0.291606 | − | 0.703999i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5355 | − | 5.60660i | −1.10887 | − | 0.459311i | −0.248324 | − | 0.968677i | \(-0.579880\pi\) |
−0.860550 | + | 0.509366i | \(0.829880\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.4853 | − | 15.4853i | 1.26017 | − | 1.26017i | 0.309166 | − | 0.951008i | \(-0.399950\pi\) |
0.951008 | − | 0.309166i | \(-0.100050\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.828427 | − | 0.828427i | −0.0669744 | − | 0.0669744i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.17157 | + | 12.4853i | −0.415391 | + | 1.00284i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.707107 | + | 0.292893i | −0.0564333 | + | 0.0233754i | −0.410722 | − | 0.911761i | \(-0.634723\pi\) |
0.354288 | + | 0.935136i | \(0.384723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −15.0711 | −1.19521 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.343146 | 0.0270437 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.1924 | − | 7.53553i | 1.42494 | − | 0.590229i | 0.468842 | − | 0.883282i | \(-0.344671\pi\) |
0.956096 | + | 0.293054i | \(0.0946714\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.757359 | + | 1.82843i | −0.0589603 | + | 0.142343i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.34315 | + | 3.34315i | 0.258700 | + | 0.258700i | 0.824525 | − | 0.565825i | \(-0.191442\pi\) |
−0.565825 | + | 0.824525i | \(0.691442\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.77817 | − | 6.77817i | 0.521398 | − | 0.521398i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.29289 | + | 0.949747i | 0.175342 | + | 0.0726290i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.464466 | − | 1.12132i | −0.0353127 | − | 0.0852524i | 0.905239 | − | 0.424902i | \(-0.139691\pi\) |
−0.940552 | + | 0.339650i | \(0.889691\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 9.07107i | − | 0.685708i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.2426i | − | 0.920213i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.94975 | + | 14.3640i | 0.444705 | + | 1.07361i | 0.974278 | + | 0.225349i | \(0.0723521\pi\) |
−0.529573 | + | 0.848264i | \(0.677648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.29289 | + | 2.19239i | 0.393418 | + | 0.162959i | 0.570618 | − | 0.821216i | \(-0.306704\pi\) |
−0.177200 | + | 0.984175i | \(0.556704\pi\) | |||||||
\(182\) | 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 | ||||||||
\(187\) | 0.343146 | − | 0.828427i | 0.0250933 | − | 0.0605806i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.24264 | + | 2.58579i | −0.454085 | + | 0.188088i | ||||
\(190\) | 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 | ||||||||
\(195\) | −10.6569 | + | 4.41421i | −0.763153 | + | 0.316108i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.19239 | − | 17.3640i | 0.512436 | − | 1.23713i | −0.430025 | − | 0.902817i | \(-0.641495\pi\) |
0.942462 | − | 0.334314i | \(-0.108505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.9706 | + | 17.9706i | 1.27390 | + | 1.27390i | 0.944025 | + | 0.329875i | \(0.107006\pi\) |
0.329875 | + | 0.944025i | \(0.392994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.24264 | − | 5.24264i | 0.369787 | − | 0.369787i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.82843 | − | 1.58579i | −0.268703 | − | 0.111300i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.6569 | + | 25.7279i | 0.744307 | + | 1.79692i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.100505i | − | 0.00698558i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.89949i | 0.131391i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.192388 | − | 0.464466i | −0.0132445 | − | 0.0319752i | 0.917119 | − | 0.398614i | \(-0.130509\pi\) |
−0.930363 | + | 0.366639i | \(0.880509\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.414214 | − | 0.171573i | −0.0283814 | − | 0.0117560i | ||||
\(214\) | 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 | ||||||||
\(219\) | −7.00000 | + | 16.8995i | −0.473016 | + | 1.14196i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.82843 | − | 2.00000i | 0.324795 | − | 0.134535i | ||||
\(222\) | 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 | ||||||||
\(227\) | −6.29289 | + | 2.60660i | −0.417674 | + | 0.173006i | −0.581616 | − | 0.813464i | \(-0.697579\pi\) |
0.163942 | + | 0.986470i | \(0.447579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.2635 | + | 24.7782i | −0.678228 | + | 1.63739i | 0.0890139 | + | 0.996030i | \(0.471628\pi\) |
−0.767242 | + | 0.641357i | \(0.778372\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.585786 | + | 0.585786i | 0.0385419 | + | 0.0385419i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.65685 | + | 8.65685i | −0.567129 | + | 0.567129i | −0.931323 | − | 0.364194i | \(-0.881345\pi\) |
0.364194 | + | 0.931323i | \(0.381345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 36.3848 | + | 15.0711i | 2.37348 | + | 0.983128i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.24264 | + | 10.2426i | 0.275589 | + | 0.665331i | ||||
\(238\) | 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 | ||||||||
\(243\) | 1.63604 | + | 3.94975i | 0.104952 | + | 0.253376i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.6066 | + | 6.46447i | 0.997069 | + | 0.413000i | ||||
\(246\) | 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 | ||||||||
\(251\) | 6.05025 | − | 14.6066i | 0.381889 | − | 0.921961i | −0.609712 | − | 0.792623i | \(-0.708715\pi\) |
0.991601 | − | 0.129338i | \(-0.0412851\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0710678 | − | 0.0294373i | 0.00446800 | − | 0.00185070i | ||||
\(254\) | 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 | ||||||||
\(259\) | 2.41421 | − | 1.00000i | 0.150012 | − | 0.0621370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.464466 | + | 1.12132i | −0.0287497 | + | 0.0694080i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.171573 | − | 0.171573i | −0.0105796 | − | 0.0105796i | 0.701797 | − | 0.712377i | \(-0.252381\pi\) |
−0.712377 | + | 0.701797i | \(0.752381\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.4853 | − | 19.4853i | 1.19697 | − | 1.19697i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.41421 | + | 2.65685i | 0.392543 | + | 0.162597i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.02082 | + | 4.87868i | 0.123211 | + | 0.297458i | 0.973435 | − | 0.228963i | \(-0.0735335\pi\) |
−0.850224 | + | 0.526421i | \(0.823533\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −0.778175 | − | 1.87868i | −0.0469257 | − | 0.113289i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.707107 | − | 0.292893i | −0.0424859 | − | 0.0175982i | 0.361339 | − | 0.932434i | \(-0.382320\pi\) |
−0.403825 | + | 0.914836i | \(0.632320\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.17157 | − | 1.17157i | 0.0701402 | − | 0.0701402i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.17157 | + | 6.17157i | 0.368165 | + | 0.368165i | 0.866808 | − | 0.498643i | \(-0.166168\pi\) |
−0.498643 | + | 0.866808i | \(0.666168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.05025 | − | 9.77817i | 0.240763 | − | 0.581252i | −0.756596 | − | 0.653882i | \(-0.773139\pi\) |
0.997359 | + | 0.0726300i | \(0.0231392\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −34.5563 | + | 14.3137i | −2.04694 | + | 0.847871i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.6569 | 0.688082 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000 | 0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.58579 | + | 1.07107i | −0.151581 | + | 0.0627871i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.80761 | + | 11.6066i | −0.280864 | + | 0.678065i | −0.999856 | − | 0.0169528i | \(-0.994603\pi\) |
0.718993 | + | 0.695018i | \(0.244603\pi\) | |||||||
\(294\) | 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 | ||||||||
\(299\) | 0.414214 | + | 0.171573i | 0.0239546 | + | 0.00992232i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.65685 | + | 11.2426i | 0.268417 | + | 0.648015i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 22.7279i | − | 1.30569i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.58579i | − | 0.148062i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.22183 | − | 2.94975i | −0.0697333 | − | 0.168351i | 0.885170 | − | 0.465267i | \(-0.154042\pi\) |
−0.954904 | + | 0.296916i | \(0.904042\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.0711 | − | 7.48528i | −1.02803 | − | 0.425823i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.65685 | − | 8.65685i | 0.490885 | − | 0.490885i | −0.417700 | − | 0.908585i | \(-0.637164\pi\) |
0.908585 | + | 0.417700i | \(0.137164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.48528 | − | 9.48528i | −0.536140 | − | 0.536140i | 0.386253 | − | 0.922393i | \(-0.373769\pi\) |
−0.922393 | + | 0.386253i | \(0.873769\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.757359 | + | 1.82843i | −0.0426724 | + | 0.103020i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.1924 | + | 4.63604i | −0.628627 | + | 0.260386i | −0.674170 | − | 0.738577i | \(-0.735498\pi\) |
0.0455425 | + | 0.998962i | \(0.485498\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.928932 | −0.0520102 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.585786 | 0.0326954 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.6569 | − | 6.48528i | 0.871171 | − | 0.360851i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.53553 | − | 10.9497i | 0.251586 | − | 0.607383i | ||||
\(326\) | 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 | ||||||||
\(331\) | −6.53553 | − | 2.70711i | −0.359225 | − | 0.148796i | 0.195769 | − | 0.980650i | \(-0.437280\pi\) |
−0.554995 | + | 0.831854i | \(0.687280\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.292893 | − | 0.707107i | −0.0160504 | − | 0.0387492i | ||||
\(334\) | 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 | ||||||||
\(339\) | 12.4853 | + | 30.1421i | 0.678107 | + | 1.63710i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.17157 | + | 0.485281i | 0.0634442 | + | 0.0262795i | ||||
\(342\) | 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 | ||||||||
\(347\) | −5.94975 | + | 14.3640i | −0.319399 | + | 0.771098i | 0.679887 | + | 0.733317i | \(0.262029\pi\) |
−0.999286 | + | 0.0377808i | \(0.987971\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.7782 | − | 10.6777i | 1.37987 | − | 0.571563i | 0.435426 | − | 0.900224i | \(-0.356598\pi\) |
0.944448 | + | 0.328662i | \(0.106598\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 0.757359 | − | 0.313708i | 0.0401965 | − | 0.0166499i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.82843 | − | 6.82843i | 0.149696 | − | 0.361399i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.1716 | − | 12.1716i | −0.642391 | − | 0.642391i | 0.308752 | − | 0.951143i | \(-0.400089\pi\) |
−0.951143 | + | 0.308752i | \(0.900089\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.9497 | + | 11.9497i | −0.628934 | + | 0.628934i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.6066 | − | 7.70711i | −0.976593 | − | 0.404518i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7990 | − | 30.8995i | −0.669930 | − | 1.61735i | ||||
\(366\) | 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 | ||||||||
\(371\) | −4.41421 | − | 10.6569i | −0.229175 | − | 0.553276i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2635 | + | 11.7071i | 1.46343 | + | 0.606171i | 0.965349 | − | 0.260962i | \(-0.0840396\pi\) |
0.498077 | + | 0.867133i | \(0.334040\pi\) | |||||||
\(374\) | 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 | ||||||||
\(379\) | −8.97918 | + | 21.6777i | −0.461230 | + | 1.11351i | 0.506663 | + | 0.862144i | \(0.330879\pi\) |
−0.967893 | + | 0.251363i | \(0.919121\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.7990 | − | 14.8284i | 1.83404 | − | 0.759683i | ||||
\(382\) | 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 | ||||||||
\(387\) | 3.29289 | − | 1.36396i | 0.167387 | − | 0.0693340i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.2635 | + | 29.6066i | −0.621782 | + | 1.50111i | 0.227827 | + | 0.973702i | \(0.426838\pi\) |
−0.849609 | + | 0.527413i | \(0.823162\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | −18.7279 | − | 7.75736i | −0.942304 | − | 0.390315i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2635 | − | 24.7782i | −0.515108 | − | 1.24358i | −0.940877 | − | 0.338749i | \(-0.889996\pi\) |
0.425769 | − | 0.904832i | \(-0.360004\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | 2.82843 | + | 6.82843i | 0.140894 | + | 0.340148i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −31.4350 | − | 13.0208i | −1.56202 | − | 0.647010i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.414214 | − | 0.414214i | 0.0205318 | − | 0.0205318i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.51472 | − | 4.51472i | −0.223238 | − | 0.223238i | 0.586622 | − | 0.809861i | \(-0.300457\pi\) |
−0.809861 | + | 0.586622i | \(0.800457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.65685 | + | 6.41421i | −0.131053 | + | 0.316390i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.65685 | − | 3.58579i | 0.425976 | − | 0.176445i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.3848 | 1.09883 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.0711 | −1.22774 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.7782 | + | 8.60660i | −1.01508 | + | 0.420460i | −0.827306 | − | 0.561752i | \(-0.810127\pi\) |
−0.187775 | + | 0.982212i | \(0.560127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.19239 | − | 7.70711i | 0.155587 | − | 0.375621i | −0.826795 | − | 0.562504i | \(-0.809838\pi\) |
0.982382 | + | 0.186882i | \(0.0598383\pi\) | |||||||
\(422\) | 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 | ||||||||
\(427\) | −1.00000 | − | 0.414214i | −0.0483934 | − | 0.0200452i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.414214 | + | 1.00000i | 0.0199984 | + | 0.0482805i | ||||
\(430\) | 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 | ||||||||
\(435\) | −7.00000 | − | 16.8995i | −0.335624 | − | 0.810269i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.34315 | + | 0.556349i | 0.0642514 | + | 0.0266138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.0000 | + | 17.0000i | −0.811366 | + | 0.811366i | −0.984839 | − | 0.173473i | \(-0.944501\pi\) |
0.173473 | + | 0.984839i | \(0.444501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.46447 | − | 1.46447i | −0.0697365 | − | 0.0697365i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.53553 | − | 20.6066i | 0.405535 | − | 0.979049i | −0.580762 | − | 0.814073i | \(-0.697245\pi\) |
0.986298 | − | 0.164976i | \(-0.0527546\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.7279 | + | 4.85786i | −0.555957 | + | 0.230285i | ||||
\(446\) | 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 | ||||||||
\(451\) | 2.41421 | − | 1.00000i | 0.113681 | − | 0.0470882i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.4853 | − | 37.3848i | 0.727562 | − | 1.75649i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.24264 | − | 6.24264i | −0.292660 | − | 0.292660i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.48528 | + | 9.48528i | −0.443703 | + | 0.443703i | −0.893254 | − | 0.449552i | \(-0.851584\pi\) |
0.449552 | + | 0.893254i | \(0.351584\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.4853 | + | 5.17157i | 0.582763 | + | 0.241388i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.53553 | + | 13.3640i | 0.257816 | + | 0.622422i | 0.998793 | − | 0.0491076i | \(-0.0156377\pi\) |
−0.740978 | + | 0.671529i | \(0.765638\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | −12.0503 | − | 29.0919i | −0.557619 | − | 1.34621i | −0.911646 | − | 0.410977i | \(-0.865188\pi\) |
0.354027 | − | 0.935235i | \(-0.384812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.24264 | + | 2.17157i | 0.242083 | + | 0.100274i | ||||
\(470\) | 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 | ||||||||
\(475\) | 14.7071 | − | 35.5061i | 0.674808 | − | 1.62913i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.12132 | + | 1.29289i | −0.142915 | + | 0.0591975i | ||||
\(478\) | 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 | ||||||||
\(483\) | 0.585786 | − | 0.242641i | 0.0266542 | − | 0.0110405i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.95837 | − | 4.72792i | 0.0889250 | − | 0.214684i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | − | 11.0000i | −0.498458 | − | 0.498458i | 0.412500 | − | 0.910958i | \(-0.364656\pi\) |
−0.910958 | + | 0.412500i | \(0.864656\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.7279 | − | 25.7279i | 1.16346 | − | 1.16346i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.7071 | − | 7.33452i | −0.799111 | − | 0.331002i | −0.0545104 | − | 0.998513i | \(-0.517360\pi\) |
−0.744600 | + | 0.667511i | \(0.767360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.17157 | + | 7.65685i | 0.142840 | + | 0.344847i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.443651i | 0.0199406i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.343146i | − | 0.0153922i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.70711 | − | 8.94975i | −0.165953 | − | 0.400646i | 0.818924 | − | 0.573902i | \(-0.194571\pi\) |
−0.984877 | + | 0.173256i | \(0.944571\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.07107 | + | 3.34315i | 0.360589 | + | 0.149361i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.1421 | − | 17.1421i | 0.764330 | − | 0.764330i | −0.212772 | − | 0.977102i | \(-0.568249\pi\) |
0.977102 | + | 0.212772i | \(0.0682491\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.3848 | + | 29.3848i | 1.30761 | + | 1.30761i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.77817 | − | 16.3640i | 0.301029 | − | 0.726749i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.1924 | + | 12.0919i | −1.29393 | + | 0.535963i | −0.920154 | − | 0.391556i | \(-0.871937\pi\) |
−0.373776 | + | 0.927519i | \(0.621937\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.0000 | −0.619324 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.6274 | −1.26393 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 33.0416 | − | 13.6863i | 1.45599 | − | 0.603090i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.41421 | − | 3.41421i | 0.0621970 | − | 0.150157i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.58579 | − | 1.58579i | −0.0696083 | − | 0.0696083i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.6569 | + | 14.6569i | −0.642128 | + | 0.642128i | −0.951078 | − | 0.308950i | \(-0.900022\pi\) |
0.308950 | + | 0.951078i | \(0.400022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.94975 | + | 0.807612i | 0.0852565 | + | 0.0353144i | 0.424904 | − | 0.905238i | \(-0.360308\pi\) |
−0.339648 | + | 0.940553i | \(0.610308\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.41421 | − | 15.4853i | −0.279939 | − | 0.675833i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.3137i | − | 0.492833i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9411i | 0.997440i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.05025 | − | 2.53553i | −0.0455771 | − | 0.110033i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.0711 | + | 5.82843i | 0.609486 | + | 0.252457i | ||||
\(534\) | 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 | ||||||||
\(539\) | 0.606602 | − | 1.46447i | 0.0261282 | − | 0.0630790i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.7071 | + | 5.26346i | −0.546321 | + | 0.226294i | −0.638735 | − | 0.769427i | \(-0.720542\pi\) |
0.0924135 | + | 0.995721i | \(0.470542\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.5858 | 0.454280 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.6985 | 0.672449 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.2635 | + | 10.4645i | −1.08019 | + | 0.447428i | −0.850575 | − | 0.525854i | \(-0.823746\pi\) |
−0.229612 | + | 0.973282i | \(0.573746\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.121320 | + | 0.292893i | −0.00517783 | + | 0.0125004i | ||||
\(550\) | 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 | ||||||||
\(555\) | 10.6569 | + | 4.41421i | 0.452358 | + | 0.187373i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50610 | + | 10.8787i | 0.190929 | + | 0.460944i | 0.990136 | − | 0.140113i | \(-0.0447464\pi\) |
−0.799206 | + | 0.601057i | \(0.794746\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8995i | 0.672477i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 1.65685i | − | 0.0699524i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.02082 | − | 12.1213i | −0.211602 | − | 0.510853i | 0.782068 | − | 0.623194i | \(-0.214165\pi\) |
−0.993670 | + | 0.112341i | \(0.964165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −55.1127 | − | 22.8284i | −2.31861 | − | 0.960399i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.0711 | + | 10.0711i | −0.422945 | + | 0.422945i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.34315 | − | 3.34315i | −0.140152 | − | 0.140152i | 0.633550 | − | 0.773702i | \(-0.281597\pi\) |
−0.773702 | + | 0.633550i | \(0.781597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.535534 | − | 1.29289i | 0.0224114 | − | 0.0541059i | −0.912278 | − | 0.409572i | \(-0.865678\pi\) |
0.934689 | + | 0.355466i | \(0.115678\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.4853 | − | 8.48528i | 0.855785 | − | 0.354478i | ||||
\(574\) | 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 | ||||||||
\(579\) | −31.5563 | + | 13.0711i | −1.31144 | + | 0.543215i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.58579 | − | 8.65685i | 0.148763 | − | 0.359147i | ||||
\(582\) | 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 | ||||||||
\(587\) | 20.7782 | + | 8.60660i | 0.857607 | + | 0.355232i | 0.767771 | − | 0.640724i | \(-0.221366\pi\) |
0.0898359 | + | 0.995957i | \(0.471366\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.17157 | + | 22.1421i | 0.377908 | + | 0.912351i | ||||
\(590\) | 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 | ||||||||
\(595\) | 5.17157 | + | 12.4853i | 0.212014 | + | 0.511847i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 43.3848 | + | 17.9706i | 1.77562 | + | 0.735486i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.3431 | + | 15.3431i | −0.626904 | + | 0.626904i | −0.947288 | − | 0.320384i | \(-0.896188\pi\) |
0.320384 | + | 0.947288i | \(0.396188\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.9706 | − | 11.9706i | −0.488289 | − | 0.488289i | 0.419477 | − | 0.907766i | \(-0.362214\pi\) |
−0.907766 | + | 0.419477i | \(0.862214\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.636039 | − | 1.53553i | 0.0259015 | − | 0.0625318i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.0208 | − | 14.0919i | 1.38314 | − | 0.572917i | ||||
\(606\) | 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 | ||||||||
\(611\) | 19.8995 | − | 8.24264i | 0.805047 | − | 0.333462i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.1924 | − | 36.6777i | 0.613615 | − | 1.48140i | −0.245387 | − | 0.969425i | \(-0.578915\pi\) |
0.859002 | − | 0.511972i | \(-0.171085\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 36.3848 | + | 36.3848i | 1.46718 | + | 1.46718i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.7990 | − | 16.7990i | 0.676302 | − | 0.676302i | −0.282859 | − | 0.959161i | \(-0.591283\pi\) |
0.959161 | + | 0.282859i | \(0.0912830\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.0208 | − | 6.22183i | −0.603738 | − | 0.250076i | 0.0598107 | − | 0.998210i | \(-0.480950\pi\) |
−0.663548 | + | 0.748133i | \(0.730950\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.443651 | + | 1.07107i | 0.0178031 | + | 0.0429805i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.31371i | 0.212889i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 15.9289i | − | 0.637157i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.34315 | + | 3.24264i | 0.0536401 | + | 0.129499i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.82843 | − | 2.00000i | −0.192522 | − | 0.0797452i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.4558 | + | 18.4558i | −0.734716 | + | 0.734716i | −0.971550 | − | 0.236834i | \(-0.923890\pi\) |
0.236834 | + | 0.971550i | \(0.423890\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.656854 | − | 0.656854i | −0.0261076 | − | 0.0261076i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27.1127 | + | 65.4558i | −1.07593 | + | 2.59754i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.53553 | − | 3.53553i | 0.338190 | − | 0.140083i | ||||
\(638\) | 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 | ||||||||
\(643\) | −37.2635 | + | 15.4350i | −1.46953 | + | 0.608698i | −0.966751 | − | 0.255719i | \(-0.917688\pi\) |
−0.502776 | + | 0.864417i | \(0.667688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.5563 | + | 49.6274i | −0.809405 | + | 1.95408i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.8284 | + | 11.8284i | 0.465023 | + | 0.465023i | 0.900298 | − | 0.435274i | \(-0.143349\pi\) |
−0.435274 | + | 0.900298i | \(0.643349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.48528 | − | 1.48528i | 0.0583024 | − | 0.0583024i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.65685 | + | 4.00000i | 0.378482 | + | 0.156772i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.9497 | − | 36.0919i | −0.585029 | − | 1.41238i | −0.888204 | − | 0.459450i | \(-0.848047\pi\) |
0.303175 | − | 0.952935i | \(-0.401953\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 32.1005i | − | 1.25427i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.10051i | 0.159976i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.43503 | + | 5.87868i | 0.0948553 | + | 0.229001i | 0.964184 | − | 0.265233i | \(-0.0854488\pi\) |
−0.869329 | + | 0.494234i | \(0.835449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.7071 | − | 7.74874i | −0.727622 | − | 0.301391i | −0.0120477 | − | 0.999927i | \(-0.503835\pi\) |
−0.715574 | + | 0.698536i | \(0.753835\pi\) | |||||||
\(662\) | 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 | ||||||||
\(667\) | −0.272078 | + | 0.656854i | −0.0105349 | + | 0.0254335i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −22.1421 | + | 9.17157i | −0.856064 | + | 0.354593i | ||||
\(670\) | 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 | ||||||||
\(675\) | 28.3137 | − | 11.7279i | 1.08980 | − | 0.451408i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.32233 | + | 5.60660i | −0.0892544 | + | 0.215479i | −0.962203 | − | 0.272333i | \(-0.912205\pi\) |
0.872949 | + | 0.487812i | \(0.162205\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | −14.1924 | − | 5.87868i | −0.543057 | − | 0.224941i | 0.0942543 | − | 0.995548i | \(-0.469953\pi\) |
−0.637311 | + | 0.770607i | \(0.719953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85786 | − | 11.7279i | −0.185609 | − | 0.448101i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.5563i | 1.89069i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 15.0711i | − | 0.574162i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.8076 | + | 28.5061i | 0.449183 | + | 1.08442i | 0.972629 | + | 0.232364i | \(0.0746461\pi\) |
−0.523446 | + | 0.852059i | \(0.675354\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.171573 | + | 0.0710678i | 0.00651751 | + | 0.00269964i | ||||
\(694\) | 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 | ||||||||
\(699\) | −8.65685 | + | 20.8995i | −0.327432 | + | 0.790491i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.1924 | + | 7.12132i | −0.649348 | + | 0.268969i | −0.682948 | − | 0.730467i | \(-0.739303\pi\) |
0.0336007 | + | 0.999435i | \(0.489303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.0711 | 0.417553 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 72.7696 | 2.74066 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.0711 | − | 6.65685i | 0.604415 | − | 0.250357i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.80761 | + | 6.77817i | −0.105442 | + | 0.254560i | −0.967791 | − | 0.251755i | \(-0.918992\pi\) |
0.862349 | + | 0.506314i | \(0.168992\pi\) | |||||||
\(710\) | 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 | ||||||||
\(715\) | −1.82843 | − | 0.757359i | −0.0683793 | − | 0.0283236i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.2426 | + | 29.5563i | 0.457210 | + | 1.10380i | ||||
\(718\) | 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 | ||||||||
\(723\) | −6.00000 | − | 14.4853i | −0.223142 | − | 0.538713i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.3640 | + | 7.19239i | 0.644881 | + | 0.267119i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.9706 | − | 23.9706i | 0.889019 | − | 0.889019i | −0.105410 | − | 0.994429i | \(-0.533615\pi\) |
0.994429 | + | 0.105410i | \(0.0336155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.7782 | − | 15.7782i | −0.584377 | − | 0.584377i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.31371 | − | 22.4853i | 0.344480 | − | 0.831648i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.77817 | − | 0.736544i | 0.0656784 | − | 0.0272049i | −0.349602 | − | 0.936898i | \(-0.613683\pi\) |
0.415281 | + | 0.909693i | \(0.363683\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 31.2132 | 1.15132 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.27208 | 0.0468576 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.1924 | − | 7.53553i | 0.669218 | − | 0.277199i | −0.0220937 | − | 0.999756i | \(-0.507033\pi\) |
0.691312 | + | 0.722557i | \(0.257033\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.82843 | + | 18.8995i | −0.287584 | + | 0.694290i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.6274 | − | 13.6274i | −0.499941 | − | 0.499941i | 0.411478 | − | 0.911420i | \(-0.365013\pi\) |
−0.911420 | + | 0.411478i | \(0.865013\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.0000 | − | 35.0000i | 1.28230 | − | 1.28230i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.53553 | − | 1.05025i | −0.0927703 | − | 0.0384267i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.171573 | + | 0.414214i | 0.00626914 | + | 0.0151350i | ||||
\(750\) | 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 | ||||||||
\(755\) | 28.3137 | + | 68.3553i | 1.03044 | + | 2.48771i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.77817 | + | 0.736544i | 0.0646289 | + | 0.0267701i | 0.414764 | − | 0.909929i | \(-0.363864\pi\) |
−0.350135 | + | 0.936699i | \(0.613864\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.100505 | − | 0.100505i | 0.00364810 | − | 0.00364810i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.1716 | + | 24.1716i | 0.876219 | + | 0.876219i | 0.993141 | − | 0.116922i | \(-0.0373028\pi\) |
−0.116922 | + | 0.993141i | \(0.537303\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.51472 | − | 6.07107i | 0.0910389 | − | 0.219787i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.65685 | − | 1.51472i | 0.132214 | − | 0.0547648i | ||||
\(766\) | 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 | ||||||||
\(771\) | 10.2426 | − | 4.24264i | 0.368880 | − | 0.152795i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.8076 | + | 26.0919i | −0.388723 | + | 0.938460i | 0.601488 | + | 0.798882i | \(0.294575\pi\) |
−0.990211 | + | 0.139578i | \(0.955425\pi\) | |||||||
\(774\) | 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 | ||||||||
\(779\) | 45.6274 | + | 18.8995i | 1.63477 | + | 0.677145i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0294373 | − | 0.0710678i | −0.00105335 | − | 0.00254301i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 14.0000i | − | 0.500319i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.58579i | − | 0.0922907i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.70711 | − | 8.94975i | −0.132144 | − | 0.319024i | 0.843933 | − | 0.536448i | \(-0.180234\pi\) |
−0.976077 | + | 0.217424i | \(0.930234\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.414214 | − | 0.171573i | −0.0147464 | − | 0.00610816i | ||||
\(790\) | 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 | ||||||||
\(795\) | 19.4853 | − | 47.0416i | 0.691072 | − | 1.66839i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.1924 | + | 12.0919i | −1.03405 | + | 0.428316i | −0.834172 | − | 0.551505i | \(-0.814054\pi\) |
−0.199876 | + | 0.979821i | \(0.564054\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.9706 | −1.16641 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.55635 | 0.0549909 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.89949 | + | 1.20101i | −0.102321 | + | 0.0423827i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.443651 | + | 1.07107i | −0.0156366 | + | 0.0377502i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.89949 | + | 6.89949i | 0.242874 | + | 0.242874i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.857864 | − | 0.857864i | 0.0301609 | − | 0.0301609i | −0.691865 | − | 0.722026i | \(-0.743211\pi\) |
0.722026 | + | 0.691865i | \(0.243211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.5061 | − | 9.73654i | −0.825411 | − | 0.341896i | −0.0703264 | − | 0.997524i | \(-0.522404\pi\) |
−0.755084 | + | 0.655628i | \(0.772404\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.7279 | + | 30.7279i | 0.446388 | + | 1.07768i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.5269i | 2.33034i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 51.5563i | 1.80373i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.414214 | + | 1.00000i | 0.0144738 | + | 0.0349428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.949747 | + | 0.393398i | 0.0331464 | + | 0.0137297i | 0.399195 | − | 0.916866i | \(-0.369290\pi\) |
−0.366049 | + | 0.930596i | \(0.619290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.02944 | − | 2.02944i | 0.0707417 | − | 0.0707417i | −0.670851 | − | 0.741592i | \(-0.734071\pi\) |
0.741592 | + | 0.670851i | \(0.234071\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.65685 | − | 2.65685i | −0.0924998 | − | 0.0924998i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.92031 | + | 11.8787i | −0.171096 | + | 0.413062i | −0.986047 | − | 0.166468i | \(-0.946764\pi\) |
0.814951 | + | 0.579530i | \(0.196764\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.1630 | + | 15.8076i | −1.32545 | + | 0.549021i | −0.929355 | − | 0.369187i | \(-0.879636\pi\) |
−0.396099 | + | 0.918208i | \(0.629636\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.41421 | −0.0490585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.1421 | −0.489996 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.7574 | + | 6.11270i | −0.510699 | + | 0.211539i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.31371 | + | 17.6569i | −0.252799 | + | 0.610310i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32.3137 | + | 32.3137i | 1.11559 | + | 1.11559i | 0.992380 | + | 0.123213i | \(0.0393198\pi\) |
0.123213 | + | 0.992380i | \(0.460680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4350 | + | 14.4350i | −0.497760 | + | 0.497760i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14.8995 | + | 6.17157i | 0.513166 | + | 0.212560i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.3934 | + | 29.9203i | 0.426346 | + | 1.02929i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.4142i | − | 0.529639i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 19.5563i | − | 0.671172i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.171573 | − | 0.414214i | −0.00588144 | − | 0.0141991i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.80761 | + | 1.16295i | 0.0961308 | + | 0.0398187i | 0.430231 | − | 0.902719i | \(-0.358432\pi\) |
−0.334100 | + | 0.942538i | \(0.608432\pi\) | |||||||
\(854\) | 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 | \(-0.964957\pi\) |
−0.109869 | − | 0.993946i | \(-0.535043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.9497 | + | 33.6777i | −0.475959 | + | 1.14907i | 0.485529 | + | 0.874221i | \(0.338627\pi\) |
−0.961488 | + | 0.274847i | \(0.911373\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 19.8995 | − | 8.24264i | 0.678173 | − | 0.280908i | ||||
\(862\) | 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 | ||||||||
\(867\) | 15.3640 | − | 6.36396i | 0.521787 | − | 0.216131i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.727922 | + | 1.75736i | −0.0246931 | + | 0.0596143i | ||||
\(870\) | 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 | ||||||||
\(875\) | 6.24264 | + | 2.58579i | 0.211040 | + | 0.0874155i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.7782 | − | 33.2635i | −0.465256 | − | 1.12323i | −0.966211 | − | 0.257754i | \(-0.917018\pi\) |
0.500955 | − | 0.865473i | \(-0.332982\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | −19.6482 | − | 47.4350i | −0.661216 | − | 1.59632i | −0.795901 | − | 0.605427i | \(-0.793002\pi\) |
0.134685 | − | 0.990888i | \(-0.456998\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 38.2132 | + | 15.8284i | 1.28452 | + | 0.532067i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.3137 | + | 20.3137i | −0.682068 | + | 0.682068i | −0.960466 | − | 0.278398i | \(-0.910197\pi\) |
0.278398 | + | 0.960466i | \(0.410197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.9706 | + | 20.9706i | 0.703330 | + | 0.703330i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.22183 | + | 2.94975i | −0.0409327 | + | 0.0988203i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.5269 | − | 26.7279i | 2.15931 | − | 0.894416i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −52.5269 | −1.75578 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.828427 | 0.0276604 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −10.8284 | + | 4.48528i | −0.361148 | + | 0.149593i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.82843 | + | 21.3137i | −0.294118 | + | 0.710063i | ||||
\(902\) | 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 | ||||||||
\(907\) | −0.535534 | − | 0.221825i | −0.0177821 | − | 0.00736559i | 0.373775 | − | 0.927520i | \(-0.378063\pi\) |
−0.391557 | + | 0.920154i | \(0.628063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.94975 | − | 4.70711i | −0.0646690 | − | 0.156125i | ||||
\(910\) | 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 | ||||||||
\(915\) | −1.82843 | − | 4.41421i | −0.0604459 | − | 0.145929i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.4142 | − | 5.14214i | −0.409953 | − | 0.169808i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.4853 | + | 25.4853i | −0.840682 | + | 0.840682i | −0.988948 | − | 0.148266i | \(-0.952631\pi\) |
0.148266 | + | 0.988948i | \(0.452631\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.17157 | − | 4.17157i | −0.137458 | − | 0.137458i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.171573 | − | 0.414214i | 0.00564739 | − | 0.0136340i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.9497 | + | 4.53553i | −0.360025 | + | 0.149127i | ||||
\(926\) | 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 | ||||||||
\(931\) | 27.6777 | − | 11.4645i | 0.907099 | − | 0.375733i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.65685 | − | 20.8995i | 0.283413 | − | 0.684219i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.14214 | + | 2.14214i | 0.0700553 | + | 0.0700553i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.0000 | + | 19.0000i | −0.620703 | + | 0.620703i | −0.945711 | − | 0.325008i | \(-0.894633\pi\) |
0.325008 | + | 0.945711i | \(0.394633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.8995 | − | 9.48528i | −0.747297 | − | 0.309540i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.53553 | + | 13.3640i | 0.180453 | + | 0.435653i | 0.988060 | − | 0.154068i | \(-0.0492376\pi\) |
−0.807607 | + | 0.589721i | \(0.799238\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.00000i | − | 0.0651290i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 22.8284i | − | 0.742609i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.4645 | + | 37.3345i | 0.502528 | + | 1.21321i | 0.948103 | + | 0.317964i | \(0.102999\pi\) |
−0.445575 | + | 0.895245i | \(0.647001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.8995 | − | 7.00000i | −0.548581 | − | 0.227230i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.8284 | + | 15.8284i | −0.513272 | + | 0.513272i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.34315 | − | 3.34315i | −0.108295 | − | 0.108295i | 0.650883 | − | 0.759178i | \(-0.274399\pi\) |
−0.759178 | + | 0.650883i | \(0.774399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.5147 | + | 37.4558i | −0.502045 | + | 1.21204i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.58579 | + | 0.656854i | −0.0512612 | + | 0.0212331i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.31371 | −0.171589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.121320 | − | 0.0502525i | 0.00390949 | − | 0.00161937i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.8995 | − | 57.6985i | 0.769352 | − | 1.85738i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.9706 | − | 39.9706i | −1.28537 | − | 1.28537i | −0.937570 | − | 0.347797i | \(-0.886930\pi\) |
−0.347797 | − | 0.937570i | \(-0.613070\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.1421 | − | 22.1421i | 0.711308 | − | 0.711308i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.2635 | + | 9.63604i | 0.746560 | + | 0.309235i | 0.723337 | − | 0.690495i | \(-0.242607\pi\) |
0.0232228 | + | 0.999730i | \(0.492607\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.34315 | − | 17.7279i | −0.235410 | − | 0.568331i | ||||
\(974\) | 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 | ||||||||
\(979\) | 0.455844 | + | 1.10051i | 0.0145688 | + | 0.0351723i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.77817 | − | 0.736544i | −0.0567727 | − | 0.0235160i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.6274 | − | 25.6274i | 0.817388 | − | 0.817388i | −0.168341 | − | 0.985729i | \(-0.553841\pi\) |
0.985729 | + | 0.168341i | \(0.0538410\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 44.8995 | + | 44.8995i | 1.43062 | + | 1.43062i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.6569 | − | 28.1421i | 0.371042 | − | 0.895774i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.92893 | − | 0.798990i | 0.0613365 | − | 0.0254064i | ||||
\(990\) | 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 | ||||||||
\(995\) | −79.3259 | + | 32.8579i | −2.51480 | + | 1.04166i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.748737 | + | 1.80761i | −0.0237127 | + | 0.0572476i | −0.935292 | − | 0.353876i | \(-0.884864\pi\) |
0.911580 | + | 0.411124i | \(0.134864\pi\) | |||||||
\(998\) | 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 | 512.2.g.c.193.1 | 4 | ||
4.3 | odd | 2 | 512.2.g.a.193.1 | 4 | |||
8.3 | odd | 2 | 512.2.g.d.193.1 | 4 | |||
8.5 | even | 2 | 512.2.g.b.193.1 | 4 | |||
16.3 | odd | 4 | 256.2.g.b.225.1 | 4 | |||
16.5 | even | 4 | 128.2.g.a.113.1 | 4 | |||
16.11 | odd | 4 | 32.2.g.a.5.1 | ✓ | 4 | ||
16.13 | even | 4 | 256.2.g.a.225.1 | 4 | |||
32.3 | odd | 8 | 512.2.g.a.321.1 | 4 | |||
32.5 | even | 8 | 128.2.g.a.17.1 | 4 | |||
32.11 | odd | 8 | 256.2.g.b.33.1 | 4 | |||
32.13 | even | 8 | 512.2.g.b.321.1 | 4 | |||
32.19 | odd | 8 | 512.2.g.d.321.1 | 4 | |||
32.21 | even | 8 | 256.2.g.a.33.1 | 4 | |||
32.27 | odd | 8 | 32.2.g.a.13.1 | yes | 4 | ||
32.29 | even | 8 | inner | 512.2.g.c.321.1 | 4 | ||
48.5 | odd | 4 | 1152.2.v.a.1009.1 | 4 | |||
48.11 | even | 4 | 288.2.v.a.37.1 | 4 | |||
64.3 | odd | 16 | 4096.2.a.e.1.4 | 4 | |||
64.29 | even | 16 | 4096.2.a.f.1.4 | 4 | |||
64.35 | odd | 16 | 4096.2.a.e.1.1 | 4 | |||
64.61 | even | 16 | 4096.2.a.f.1.1 | 4 | |||
80.27 | even | 4 | 800.2.ba.b.549.1 | 4 | |||
80.43 | even | 4 | 800.2.ba.a.549.1 | 4 | |||
80.59 | odd | 4 | 800.2.y.a.101.1 | 4 | |||
96.5 | odd | 8 | 1152.2.v.a.145.1 | 4 | |||
96.59 | even | 8 | 288.2.v.a.109.1 | 4 | |||
160.27 | even | 8 | 800.2.ba.a.749.1 | 4 | |||
160.59 | odd | 8 | 800.2.y.a.301.1 | 4 | |||
160.123 | even | 8 | 800.2.ba.b.749.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.2.g.a.5.1 | ✓ | 4 | 16.11 | odd | 4 | ||
32.2.g.a.13.1 | yes | 4 | 32.27 | odd | 8 | ||
128.2.g.a.17.1 | 4 | 32.5 | even | 8 | |||
128.2.g.a.113.1 | 4 | 16.5 | even | 4 | |||
256.2.g.a.33.1 | 4 | 32.21 | even | 8 | |||
256.2.g.a.225.1 | 4 | 16.13 | even | 4 | |||
256.2.g.b.33.1 | 4 | 32.11 | odd | 8 | |||
256.2.g.b.225.1 | 4 | 16.3 | odd | 4 | |||
288.2.v.a.37.1 | 4 | 48.11 | even | 4 | |||
288.2.v.a.109.1 | 4 | 96.59 | even | 8 | |||
512.2.g.a.193.1 | 4 | 4.3 | odd | 2 | |||
512.2.g.a.321.1 | 4 | 32.3 | odd | 8 | |||
512.2.g.b.193.1 | 4 | 8.5 | even | 2 | |||
512.2.g.b.321.1 | 4 | 32.13 | even | 8 | |||
512.2.g.c.193.1 | 4 | 1.1 | even | 1 | trivial | ||
512.2.g.c.321.1 | 4 | 32.29 | even | 8 | inner | ||
512.2.g.d.193.1 | 4 | 8.3 | odd | 2 | |||
512.2.g.d.321.1 | 4 | 32.19 | odd | 8 | |||
800.2.y.a.101.1 | 4 | 80.59 | odd | 4 | |||
800.2.y.a.301.1 | 4 | 160.59 | odd | 8 | |||
800.2.ba.a.549.1 | 4 | 80.43 | even | 4 | |||
800.2.ba.a.749.1 | 4 | 160.27 | even | 8 | |||
800.2.ba.b.549.1 | 4 | 80.27 | even | 4 | |||
800.2.ba.b.749.1 | 4 | 160.123 | even | 8 | |||
1152.2.v.a.145.1 | 4 | 96.5 | odd | 8 | |||
1152.2.v.a.1009.1 | 4 | 48.5 | odd | 4 | |||
4096.2.a.e.1.1 | 4 | 64.35 | odd | 16 | |||
4096.2.a.e.1.4 | 4 | 64.3 | odd | 16 | |||
4096.2.a.f.1.1 | 4 | 64.61 | even | 16 | |||
4096.2.a.f.1.4 | 4 | 64.29 | even | 16 |