Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(160,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.160");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.342102016.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 160.2 | ||
Root | \(-1.17915 + 0.780776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.160 |
Dual form | 483.2.h.a.160.6 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | −0.353553 | − | 0.935414i | \(-0.615027\pi\) | ||||
−0.353553 | + | 0.935414i | \(0.615027\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.69614 | −0.758537 | −0.379269 | − | 0.925287i | \(-0.623824\pi\) | ||||
−0.379269 | + | 0.925287i | \(0.623824\pi\) | |||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.17238 | − | 1.51022i | 0.821081 | − | 0.570811i | ||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.69614 | 0.536367 | ||||||||
\(11\) | 1.32431i | 0.399294i | 0.979868 | + | 0.199647i | \(0.0639795\pi\) | ||||
−0.979868 | + | 0.199647i | \(0.936021\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | − | 5.12311i | − | 1.42089i | −0.703751 | − | 0.710447i | \(-0.748493\pi\) | ||
0.703751 | − | 0.710447i | \(-0.251507\pi\) | |||||||
\(14\) | −2.17238 | + | 1.51022i | −0.580592 | + | 0.403624i | ||||
\(15\) | 1.69614i | 0.437942i | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.69614 | 0.411375 | 0.205687 | − | 0.978618i | \(-0.434057\pi\) | ||||
0.205687 | + | 0.978618i | \(0.434057\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −7.73704 | −1.77500 | −0.887499 | − | 0.460810i | \(-0.847559\pi\) | ||||
−0.887499 | + | 0.460810i | \(0.847559\pi\) | |||||||
\(20\) | 1.69614 | 0.379269 | ||||||||
\(21\) | −1.51022 | − | 2.17238i | −0.329558 | − | 0.474052i | ||||
\(22\) | − | 1.32431i | − | 0.282343i | ||||||
\(23\) | −2.56155 | + | 4.05444i | −0.534121 | + | 0.845408i | ||||
\(24\) | − | 3.00000i | − | 0.612372i | ||||||
\(25\) | −2.12311 | −0.424621 | ||||||||
\(26\) | 5.12311i | 1.00472i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.17238 | + | 1.51022i | −0.410541 | + | 0.285406i | ||||
\(29\) | −8.24621 | −1.53128 | −0.765641 | − | 0.643268i | \(-0.777578\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | − | 1.69614i | − | 0.309672i | ||||||
\(31\) | − | 6.24621i | − | 1.12185i | −0.827866 | − | 0.560926i | \(-0.810445\pi\) | ||
0.827866 | − | 0.560926i | \(-0.189555\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 1.32431 | 0.230532 | ||||||||
\(34\) | −1.69614 | −0.290886 | ||||||||
\(35\) | −3.68466 | + | 2.56155i | −0.622821 | + | 0.432981i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.04090i | 0.993117i | 0.868003 | + | 0.496559i | \(0.165403\pi\) | ||||
−0.868003 | + | 0.496559i | \(0.834597\pi\) | |||||||
\(38\) | 7.73704 | 1.25511 | ||||||||
\(39\) | −5.12311 | −0.820353 | ||||||||
\(40\) | −5.08842 | −0.804550 | ||||||||
\(41\) | − | 2.87689i | − | 0.449295i | −0.974440 | − | 0.224648i | \(-0.927877\pi\) | ||
0.974440 | − | 0.224648i | \(-0.0721231\pi\) | |||||||
\(42\) | 1.51022 | + | 2.17238i | 0.233033 | + | 0.335205i | ||||
\(43\) | 3.02045i | 0.460614i | 0.973118 | + | 0.230307i | \(0.0739730\pi\) | ||||
−0.973118 | + | 0.230307i | \(0.926027\pi\) | |||||||
\(44\) | − | 1.32431i | − | 0.199647i | ||||||
\(45\) | 1.69614 | 0.252846 | ||||||||
\(46\) | 2.56155 | − | 4.05444i | 0.377680 | − | 0.597794i | ||||
\(47\) | 1.12311i | 0.163822i | 0.996640 | + | 0.0819109i | \(0.0261023\pi\) | ||||
−0.996640 | + | 0.0819109i | \(0.973898\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 2.43845 | − | 6.56155i | 0.348350 | − | 0.937365i | ||||
\(50\) | 2.12311 | 0.300252 | ||||||||
\(51\) | − | 1.69614i | − | 0.237507i | ||||||
\(52\) | 5.12311i | 0.710447i | ||||||||
\(53\) | 5.08842i | 0.698949i | 0.936946 | + | 0.349474i | \(0.113640\pi\) | ||||
−0.936946 | + | 0.349474i | \(0.886360\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | − | 2.24621i | − | 0.302879i | ||||||
\(56\) | 6.51713 | − | 4.53067i | 0.870888 | − | 0.605436i | ||||
\(57\) | 7.73704i | 1.02480i | ||||||||
\(58\) | 8.24621 | 1.08278 | ||||||||
\(59\) | − | 1.12311i | − | 0.146216i | −0.997324 | − | 0.0731079i | \(-0.976708\pi\) | ||
0.997324 | − | 0.0731079i | \(-0.0232918\pi\) | |||||||
\(60\) | − | 1.69614i | − | 0.218971i | ||||||
\(61\) | −6.04090 | −0.773457 | −0.386729 | − | 0.922194i | \(-0.626395\pi\) | ||||
−0.386729 | + | 0.922194i | \(0.626395\pi\) | |||||||
\(62\) | 6.24621i | 0.793270i | ||||||||
\(63\) | −2.17238 | + | 1.51022i | −0.273694 | + | 0.190270i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 8.68951i | 1.07780i | ||||||||
\(66\) | −1.32431 | −0.163011 | ||||||||
\(67\) | − | 15.1022i | − | 1.84503i | −0.385959 | − | 0.922516i | \(-0.626129\pi\) | ||
0.385959 | − | 0.922516i | \(-0.373871\pi\) | |||||||
\(68\) | −1.69614 | −0.205687 | ||||||||
\(69\) | 4.05444 | + | 2.56155i | 0.488097 | + | 0.308375i | ||||
\(70\) | 3.68466 | − | 2.56155i | 0.440401 | − | 0.306164i | ||||
\(71\) | −2.87689 | −0.341425 | −0.170712 | − | 0.985321i | \(-0.554607\pi\) | ||||
−0.170712 | + | 0.985321i | \(0.554607\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | − | 10.2462i | − | 1.19923i | −0.800289 | − | 0.599614i | \(-0.795321\pi\) | ||
0.800289 | − | 0.599614i | \(-0.204679\pi\) | |||||||
\(74\) | − | 6.04090i | − | 0.702240i | ||||||
\(75\) | 2.12311i | 0.245155i | ||||||||
\(76\) | 7.73704 | 0.887499 | ||||||||
\(77\) | 2.00000 | + | 2.87689i | 0.227921 | + | 0.327853i | ||||
\(78\) | 5.12311 | 0.580077 | ||||||||
\(79\) | − | 2.27678i | − | 0.256158i | −0.991764 | − | 0.128079i | \(-0.959119\pi\) | ||
0.991764 | − | 0.128079i | \(-0.0408811\pi\) | |||||||
\(80\) | 1.69614 | 0.189634 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.87689i | 0.317700i | ||||||||
\(83\) | −5.29723 | −0.581446 | −0.290723 | − | 0.956807i | \(-0.593896\pi\) | ||||
−0.290723 | + | 0.956807i | \(0.593896\pi\) | |||||||
\(84\) | 1.51022 | + | 2.17238i | 0.164779 | + | 0.237026i | ||||
\(85\) | −2.87689 | −0.312043 | ||||||||
\(86\) | − | 3.02045i | − | 0.325703i | ||||||
\(87\) | 8.24621i | 0.884087i | ||||||||
\(88\) | 3.97292i | 0.423515i | ||||||||
\(89\) | −5.08842 | −0.539372 | −0.269686 | − | 0.962948i | \(-0.586920\pi\) | ||||
−0.269686 | + | 0.962948i | \(0.586920\pi\) | |||||||
\(90\) | −1.69614 | −0.178789 | ||||||||
\(91\) | −7.73704 | − | 11.1293i | −0.811062 | − | 1.16667i | ||||
\(92\) | 2.56155 | − | 4.05444i | 0.267060 | − | 0.422704i | ||||
\(93\) | −6.24621 | −0.647702 | ||||||||
\(94\) | − | 1.12311i | − | 0.115840i | ||||||
\(95\) | 13.1231 | 1.34640 | ||||||||
\(96\) | 5.00000i | 0.510310i | ||||||||
\(97\) | 6.04090 | 0.613360 | 0.306680 | − | 0.951813i | \(-0.400782\pi\) | ||||
0.306680 | + | 0.951813i | \(0.400782\pi\) | |||||||
\(98\) | −2.43845 | + | 6.56155i | −0.246320 | + | 0.662817i | ||||
\(99\) | − | 1.32431i | − | 0.133098i | ||||||
\(100\) | 2.12311 | 0.212311 | ||||||||
\(101\) | 5.12311i | 0.509768i | 0.966972 | + | 0.254884i | \(0.0820373\pi\) | ||||
−0.966972 | + | 0.254884i | \(0.917963\pi\) | |||||||
\(102\) | 1.69614i | 0.167943i | ||||||||
\(103\) | −4.34475 | −0.428101 | −0.214051 | − | 0.976823i | \(-0.568666\pi\) | ||||
−0.214051 | + | 0.976823i | \(0.568666\pi\) | |||||||
\(104\) | − | 15.3693i | − | 1.50709i | ||||||
\(105\) | 2.56155 | + | 3.68466i | 0.249982 | + | 0.359586i | ||||
\(106\) | − | 5.08842i | − | 0.494231i | ||||||
\(107\) | − | 8.10887i | − | 0.783914i | −0.919984 | − | 0.391957i | \(-0.871798\pi\) | ||
0.919984 | − | 0.391957i | \(-0.128202\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | 14.7304i | 1.41092i | 0.708751 | + | 0.705458i | \(0.249259\pi\) | ||||
−0.708751 | + | 0.705458i | \(0.750741\pi\) | |||||||
\(110\) | 2.24621i | 0.214168i | ||||||||
\(111\) | 6.04090 | 0.573376 | ||||||||
\(112\) | −2.17238 | + | 1.51022i | −0.205270 | + | 0.142703i | ||||
\(113\) | − | 16.4265i | − | 1.54528i | −0.634845 | − | 0.772640i | \(-0.718936\pi\) | ||
0.634845 | − | 0.772640i | \(-0.281064\pi\) | |||||||
\(114\) | − | 7.73704i | − | 0.724640i | ||||||
\(115\) | 4.34475 | − | 6.87689i | 0.405150 | − | 0.641274i | ||||
\(116\) | 8.24621 | 0.765641 | ||||||||
\(117\) | 5.12311i | 0.473631i | ||||||||
\(118\) | 1.12311i | 0.103390i | ||||||||
\(119\) | 3.68466 | − | 2.56155i | 0.337772 | − | 0.234817i | ||||
\(120\) | 5.08842i | 0.464507i | ||||||||
\(121\) | 9.24621 | 0.840565 | ||||||||
\(122\) | 6.04090 | 0.546917 | ||||||||
\(123\) | −2.87689 | −0.259401 | ||||||||
\(124\) | 6.24621i | 0.560926i | ||||||||
\(125\) | 12.0818 | 1.08063 | ||||||||
\(126\) | 2.17238 | − | 1.51022i | 0.193531 | − | 0.134541i | ||||
\(127\) | 10.2462 | 0.909204 | 0.454602 | − | 0.890695i | \(-0.349781\pi\) | ||||
0.454602 | + | 0.890695i | \(0.349781\pi\) | |||||||
\(128\) | 3.00000 | 0.265165 | ||||||||
\(129\) | 3.02045 | 0.265936 | ||||||||
\(130\) | − | 8.68951i | − | 0.762120i | ||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | −1.32431 | −0.115266 | ||||||||
\(133\) | −16.8078 | + | 11.6847i | −1.45742 | + | 1.01319i | ||||
\(134\) | 15.1022i | 1.30463i | ||||||||
\(135\) | − | 1.69614i | − | 0.145981i | ||||||
\(136\) | 5.08842 | 0.436329 | ||||||||
\(137\) | 14.5216i | 1.24066i | 0.784339 | + | 0.620332i | \(0.213002\pi\) | ||||
−0.784339 | + | 0.620332i | \(0.786998\pi\) | |||||||
\(138\) | −4.05444 | − | 2.56155i | −0.345136 | − | 0.218054i | ||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | 3.68466 | − | 2.56155i | 0.311410 | − | 0.216491i | ||||
\(141\) | 1.12311 | 0.0945826 | ||||||||
\(142\) | 2.87689 | 0.241424 | ||||||||
\(143\) | 6.78456 | 0.567354 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 13.9867 | 1.16154 | ||||||||
\(146\) | 10.2462i | 0.847982i | ||||||||
\(147\) | −6.56155 | − | 2.43845i | −0.541188 | − | 0.201120i | ||||
\(148\) | − | 6.04090i | − | 0.496559i | ||||||
\(149\) | − | 13.7779i | − | 1.12873i | −0.825525 | − | 0.564366i | \(-0.809121\pi\) | ||
0.825525 | − | 0.564366i | \(-0.190879\pi\) | |||||||
\(150\) | − | 2.12311i | − | 0.173351i | ||||||
\(151\) | 12.4924 | 1.01662 | 0.508309 | − | 0.861174i | \(-0.330271\pi\) | ||||
0.508309 | + | 0.861174i | \(0.330271\pi\) | |||||||
\(152\) | −23.2111 | −1.88267 | ||||||||
\(153\) | −1.69614 | −0.137125 | ||||||||
\(154\) | −2.00000 | − | 2.87689i | −0.161165 | − | 0.231827i | ||||
\(155\) | 10.5945i | 0.850967i | ||||||||
\(156\) | 5.12311 | 0.410177 | ||||||||
\(157\) | 0.743668 | 0.0593512 | 0.0296756 | − | 0.999560i | \(-0.490553\pi\) | ||||
0.0296756 | + | 0.999560i | \(0.490553\pi\) | |||||||
\(158\) | 2.27678i | 0.181131i | ||||||||
\(159\) | 5.08842 | 0.403538 | ||||||||
\(160\) | 8.48071 | 0.670459 | ||||||||
\(161\) | 0.558446 | + | 12.6763i | 0.0440117 | + | 0.999031i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 12.0000 | 0.939913 | 0.469956 | − | 0.882690i | \(-0.344270\pi\) | ||||
0.469956 | + | 0.882690i | \(0.344270\pi\) | |||||||
\(164\) | 2.87689i | 0.224648i | ||||||||
\(165\) | −2.24621 | −0.174867 | ||||||||
\(166\) | 5.29723 | 0.411145 | ||||||||
\(167\) | − | 22.2462i | − | 1.72146i | −0.509059 | − | 0.860732i | \(-0.670006\pi\) | ||
0.509059 | − | 0.860732i | \(-0.329994\pi\) | |||||||
\(168\) | −4.53067 | − | 6.51713i | −0.349549 | − | 0.502808i | ||||
\(169\) | −13.2462 | −1.01894 | ||||||||
\(170\) | 2.87689 | 0.220648 | ||||||||
\(171\) | 7.73704 | 0.591666 | ||||||||
\(172\) | − | 3.02045i | − | 0.230307i | ||||||
\(173\) | − | 5.12311i | − | 0.389503i | −0.980853 | − | 0.194751i | \(-0.937610\pi\) | ||
0.980853 | − | 0.194751i | \(-0.0623900\pi\) | |||||||
\(174\) | − | 8.24621i | − | 0.625144i | ||||||
\(175\) | −4.61219 | + | 3.20636i | −0.348649 | + | 0.242378i | ||||
\(176\) | − | 1.32431i | − | 0.0998234i | ||||||
\(177\) | −1.12311 | −0.0844178 | ||||||||
\(178\) | 5.08842 | 0.381393 | ||||||||
\(179\) | −4.00000 | −0.298974 | −0.149487 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149487 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(180\) | −1.69614 | −0.126423 | ||||||||
\(181\) | −14.7304 | −1.09490 | −0.547451 | − | 0.836838i | \(-0.684402\pi\) | ||||
−0.547451 | + | 0.836838i | \(0.684402\pi\) | |||||||
\(182\) | 7.73704 | + | 11.1293i | 0.573507 | + | 0.824960i | ||||
\(183\) | 6.04090i | 0.446556i | ||||||||
\(184\) | −7.68466 | + | 12.1633i | −0.566521 | + | 0.896691i | ||||
\(185\) | − | 10.2462i | − | 0.753316i | ||||||
\(186\) | 6.24621 | 0.457994 | ||||||||
\(187\) | 2.24621i | 0.164259i | ||||||||
\(188\) | − | 1.12311i | − | 0.0819109i | ||||||
\(189\) | 1.51022 | + | 2.17238i | 0.109853 | + | 0.158017i | ||||
\(190\) | −13.1231 | −0.952050 | ||||||||
\(191\) | − | 26.2316i | − | 1.89805i | −0.315202 | − | 0.949024i | \(-0.602072\pi\) | ||
0.315202 | − | 0.949024i | \(-0.397928\pi\) | |||||||
\(192\) | − | 7.00000i | − | 0.505181i | ||||||
\(193\) | −15.6155 | −1.12403 | −0.562015 | − | 0.827127i | \(-0.689974\pi\) | ||||
−0.562015 | + | 0.827127i | \(0.689974\pi\) | |||||||
\(194\) | −6.04090 | −0.433711 | ||||||||
\(195\) | 8.68951 | 0.622269 | ||||||||
\(196\) | −2.43845 | + | 6.56155i | −0.174175 | + | 0.468682i | ||||
\(197\) | −14.4924 | −1.03254 | −0.516271 | − | 0.856425i | \(-0.672680\pi\) | ||||
−0.516271 | + | 0.856425i | \(0.672680\pi\) | |||||||
\(198\) | 1.32431i | 0.0941144i | ||||||||
\(199\) | −4.34475 | −0.307992 | −0.153996 | − | 0.988072i | \(-0.549214\pi\) | ||||
−0.153996 | + | 0.988072i | \(0.549214\pi\) | |||||||
\(200\) | −6.36932 | −0.450379 | ||||||||
\(201\) | −15.1022 | −1.06523 | ||||||||
\(202\) | − | 5.12311i | − | 0.360460i | ||||||
\(203\) | −17.9139 | + | 12.4536i | −1.25731 | + | 0.874073i | ||||
\(204\) | 1.69614i | 0.118754i | ||||||||
\(205\) | 4.87962i | 0.340807i | ||||||||
\(206\) | 4.34475 | 0.302713 | ||||||||
\(207\) | 2.56155 | − | 4.05444i | 0.178040 | − | 0.281803i | ||||
\(208\) | 5.12311i | 0.355223i | ||||||||
\(209\) | − | 10.2462i | − | 0.708745i | ||||||
\(210\) | −2.56155 | − | 3.68466i | −0.176764 | − | 0.254266i | ||||
\(211\) | 6.24621 | 0.430007 | 0.215003 | − | 0.976613i | \(-0.431024\pi\) | ||||
0.215003 | + | 0.976613i | \(0.431024\pi\) | |||||||
\(212\) | − | 5.08842i | − | 0.349474i | ||||||
\(213\) | 2.87689i | 0.197122i | ||||||||
\(214\) | 8.10887i | 0.554311i | ||||||||
\(215\) | − | 5.12311i | − | 0.349393i | ||||||
\(216\) | 3.00000i | 0.204124i | ||||||||
\(217\) | −9.43318 | − | 13.5691i | −0.640366 | − | 0.921132i | ||||
\(218\) | − | 14.7304i | − | 0.997669i | ||||||
\(219\) | −10.2462 | −0.692375 | ||||||||
\(220\) | 2.24621i | 0.151440i | ||||||||
\(221\) | − | 8.68951i | − | 0.584520i | ||||||
\(222\) | −6.04090 | −0.405438 | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | −10.8619 | + | 7.55112i | −0.725740 | + | 0.504530i | ||||
\(225\) | 2.12311 | 0.141540 | ||||||||
\(226\) | 16.4265i | 1.09268i | ||||||||
\(227\) | 3.39228 | 0.225154 | 0.112577 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112577 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(228\) | − | 7.73704i | − | 0.512398i | ||||||
\(229\) | −14.7304 | −0.973413 | −0.486706 | − | 0.873566i | \(-0.661802\pi\) | ||||
−0.486706 | + | 0.873566i | \(0.661802\pi\) | |||||||
\(230\) | −4.34475 | + | 6.87689i | −0.286485 | + | 0.453449i | ||||
\(231\) | 2.87689 | − | 2.00000i | 0.189286 | − | 0.131590i | ||||
\(232\) | −24.7386 | −1.62417 | ||||||||
\(233\) | −20.2462 | −1.32637 | −0.663187 | − | 0.748454i | \(-0.730796\pi\) | ||||
−0.663187 | + | 0.748454i | \(0.730796\pi\) | |||||||
\(234\) | − | 5.12311i | − | 0.334908i | ||||||
\(235\) | − | 1.90495i | − | 0.124265i | ||||||
\(236\) | 1.12311i | 0.0731079i | ||||||||
\(237\) | −2.27678 | −0.147893 | ||||||||
\(238\) | −3.68466 | + | 2.56155i | −0.238841 | + | 0.166041i | ||||
\(239\) | 23.3693 | 1.51164 | 0.755818 | − | 0.654782i | \(-0.227240\pi\) | ||||
0.755818 | + | 0.654782i | \(0.227240\pi\) | |||||||
\(240\) | − | 1.69614i | − | 0.109485i | ||||||
\(241\) | 12.8255 | 0.826161 | 0.413080 | − | 0.910695i | \(-0.364453\pi\) | ||||
0.413080 | + | 0.910695i | \(0.364453\pi\) | |||||||
\(242\) | −9.24621 | −0.594369 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 6.04090 | 0.386729 | ||||||||
\(245\) | −4.13595 | + | 11.1293i | −0.264236 | + | 0.711026i | ||||
\(246\) | 2.87689 | 0.183424 | ||||||||
\(247\) | 39.6377i | 2.52208i | ||||||||
\(248\) | − | 18.7386i | − | 1.18990i | ||||||
\(249\) | 5.29723i | 0.335698i | ||||||||
\(250\) | −12.0818 | −0.764120 | ||||||||
\(251\) | 27.5559 | 1.73931 | 0.869655 | − | 0.493659i | \(-0.164341\pi\) | ||||
0.869655 | + | 0.493659i | \(0.164341\pi\) | |||||||
\(252\) | 2.17238 | − | 1.51022i | 0.136847 | − | 0.0951352i | ||||
\(253\) | −5.36932 | − | 3.39228i | −0.337566 | − | 0.213271i | ||||
\(254\) | −10.2462 | −0.642904 | ||||||||
\(255\) | 2.87689i | 0.180158i | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | − | 7.36932i | − | 0.459685i | −0.973228 | − | 0.229843i | \(-0.926179\pi\) | ||
0.973228 | − | 0.229843i | \(-0.0738212\pi\) | |||||||
\(258\) | −3.02045 | −0.188045 | ||||||||
\(259\) | 9.12311 | + | 13.1231i | 0.566882 | + | 0.815430i | ||||
\(260\) | − | 8.68951i | − | 0.538901i | ||||||
\(261\) | 8.24621 | 0.510428 | ||||||||
\(262\) | − | 12.0000i | − | 0.741362i | ||||||
\(263\) | 20.9343i | 1.29087i | 0.763817 | + | 0.645433i | \(0.223323\pi\) | ||||
−0.763817 | + | 0.645433i | \(0.776677\pi\) | |||||||
\(264\) | 3.97292 | 0.244516 | ||||||||
\(265\) | − | 8.63068i | − | 0.530179i | ||||||
\(266\) | 16.8078 | − | 11.6847i | 1.03055 | − | 0.716432i | ||||
\(267\) | 5.08842i | 0.311406i | ||||||||
\(268\) | 15.1022i | 0.922516i | ||||||||
\(269\) | − | 31.3693i | − | 1.91262i | −0.292353 | − | 0.956311i | \(-0.594438\pi\) | ||
0.292353 | − | 0.956311i | \(-0.405562\pi\) | |||||||
\(270\) | 1.69614i | 0.103224i | ||||||||
\(271\) | − | 16.4924i | − | 1.00184i | −0.865493 | − | 0.500922i | \(-0.832994\pi\) | ||
0.865493 | − | 0.500922i | \(-0.167006\pi\) | |||||||
\(272\) | −1.69614 | −0.102844 | ||||||||
\(273\) | −11.1293 | + | 7.73704i | −0.673577 | + | 0.468267i | ||||
\(274\) | − | 14.5216i | − | 0.877282i | ||||||
\(275\) | − | 2.81164i | − | 0.169548i | ||||||
\(276\) | −4.05444 | − | 2.56155i | −0.244048 | − | 0.154187i | ||||
\(277\) | −0.246211 | −0.0147934 | −0.00739670 | − | 0.999973i | \(-0.502354\pi\) | ||||
−0.00739670 | + | 0.999973i | \(0.502354\pi\) | |||||||
\(278\) | − | 12.0000i | − | 0.719712i | ||||||
\(279\) | 6.24621i | 0.373951i | ||||||||
\(280\) | −11.0540 | + | 7.68466i | −0.660601 | + | 0.459246i | ||||
\(281\) | − | 9.64198i | − | 0.575192i | −0.957752 | − | 0.287596i | \(-0.907144\pi\) | ||
0.957752 | − | 0.287596i | \(-0.0928561\pi\) | |||||||
\(282\) | −1.12311 | −0.0668800 | ||||||||
\(283\) | 25.1161 | 1.49299 | 0.746497 | − | 0.665388i | \(-0.231734\pi\) | ||||
0.746497 | + | 0.665388i | \(0.231734\pi\) | |||||||
\(284\) | 2.87689 | 0.170712 | ||||||||
\(285\) | − | 13.1231i | − | 0.777346i | ||||||
\(286\) | −6.78456 | −0.401180 | ||||||||
\(287\) | −4.34475 | − | 6.24970i | −0.256463 | − | 0.368908i | ||||
\(288\) | 5.00000 | 0.294628 | ||||||||
\(289\) | −14.1231 | −0.830771 | ||||||||
\(290\) | −13.9867 | −0.821329 | ||||||||
\(291\) | − | 6.04090i | − | 0.354124i | ||||||
\(292\) | 10.2462i | 0.599614i | ||||||||
\(293\) | −32.6443 | −1.90710 | −0.953550 | − | 0.301235i | \(-0.902601\pi\) | ||||
−0.953550 | + | 0.301235i | \(0.902601\pi\) | |||||||
\(294\) | 6.56155 | + | 2.43845i | 0.382678 | + | 0.142213i | ||||
\(295\) | 1.90495i | 0.110910i | ||||||||
\(296\) | 18.1227i | 1.05336i | ||||||||
\(297\) | −1.32431 | −0.0768441 | ||||||||
\(298\) | 13.7779i | 0.798134i | ||||||||
\(299\) | 20.7713 | + | 13.1231i | 1.20124 | + | 0.758929i | ||||
\(300\) | − | 2.12311i | − | 0.122578i | ||||||
\(301\) | 4.56155 | + | 6.56155i | 0.262924 | + | 0.378202i | ||||
\(302\) | −12.4924 | −0.718858 | ||||||||
\(303\) | 5.12311 | 0.294315 | ||||||||
\(304\) | 7.73704 | 0.443749 | ||||||||
\(305\) | 10.2462 | 0.586696 | ||||||||
\(306\) | 1.69614 | 0.0969619 | ||||||||
\(307\) | − | 14.2462i | − | 0.813074i | −0.913634 | − | 0.406537i | \(-0.866736\pi\) | ||
0.913634 | − | 0.406537i | \(-0.133264\pi\) | |||||||
\(308\) | −2.00000 | − | 2.87689i | −0.113961 | − | 0.163926i | ||||
\(309\) | 4.34475i | 0.247164i | ||||||||
\(310\) | − | 10.5945i | − | 0.601725i | ||||||
\(311\) | 27.3693i | 1.55197i | 0.630750 | + | 0.775986i | \(0.282747\pi\) | ||||
−0.630750 | + | 0.775986i | \(0.717253\pi\) | |||||||
\(312\) | −15.3693 | −0.870116 | ||||||||
\(313\) | 28.2995 | 1.59958 | 0.799792 | − | 0.600277i | \(-0.204943\pi\) | ||||
0.799792 | + | 0.600277i | \(0.204943\pi\) | |||||||
\(314\) | −0.743668 | −0.0419676 | ||||||||
\(315\) | 3.68466 | − | 2.56155i | 0.207607 | − | 0.144327i | ||||
\(316\) | 2.27678i | 0.128079i | ||||||||
\(317\) | −14.0000 | −0.786318 | −0.393159 | − | 0.919470i | \(-0.628618\pi\) | ||||
−0.393159 | + | 0.919470i | \(0.628618\pi\) | |||||||
\(318\) | −5.08842 | −0.285345 | ||||||||
\(319\) | − | 10.9205i | − | 0.611431i | ||||||
\(320\) | −11.8730 | −0.663720 | ||||||||
\(321\) | −8.10887 | −0.452593 | ||||||||
\(322\) | −0.558446 | − | 12.6763i | −0.0311210 | − | 0.706422i | ||||
\(323\) | −13.1231 | −0.730189 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 10.8769i | 0.603342i | ||||||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | 14.7304 | 0.814593 | ||||||||
\(328\) | − | 8.63068i | − | 0.476550i | ||||||
\(329\) | 1.69614 | + | 2.43981i | 0.0935113 | + | 0.134511i | ||||
\(330\) | 2.24621 | 0.123650 | ||||||||
\(331\) | 16.4924 | 0.906506 | 0.453253 | − | 0.891382i | \(-0.350263\pi\) | ||||
0.453253 | + | 0.891382i | \(0.350263\pi\) | |||||||
\(332\) | 5.29723 | 0.290723 | ||||||||
\(333\) | − | 6.04090i | − | 0.331039i | ||||||
\(334\) | 22.2462i | 1.21726i | ||||||||
\(335\) | 25.6155i | 1.39953i | ||||||||
\(336\) | 1.51022 | + | 2.17238i | 0.0823895 | + | 0.118513i | ||||
\(337\) | − | 3.39228i | − | 0.184789i | −0.995722 | − | 0.0923947i | \(-0.970548\pi\) | ||
0.995722 | − | 0.0923947i | \(-0.0294521\pi\) | |||||||
\(338\) | 13.2462 | 0.720499 | ||||||||
\(339\) | −16.4265 | −0.892168 | ||||||||
\(340\) | 2.87689 | 0.156022 | ||||||||
\(341\) | 8.27190 | 0.447949 | ||||||||
\(342\) | −7.73704 | −0.418371 | ||||||||
\(343\) | −4.61219 | − | 17.9368i | −0.249035 | − | 0.968495i | ||||
\(344\) | 9.06134i | 0.488555i | ||||||||
\(345\) | −6.87689 | − | 4.34475i | −0.370240 | − | 0.233914i | ||||
\(346\) | 5.12311i | 0.275420i | ||||||||
\(347\) | 16.4924 | 0.885360 | 0.442680 | − | 0.896680i | \(-0.354028\pi\) | ||||
0.442680 | + | 0.896680i | \(0.354028\pi\) | |||||||
\(348\) | − | 8.24621i | − | 0.442043i | ||||||
\(349\) | 15.3693i | 0.822701i | 0.911477 | + | 0.411350i | \(0.134943\pi\) | ||||
−0.911477 | + | 0.411350i | \(0.865057\pi\) | |||||||
\(350\) | 4.61219 | − | 3.20636i | 0.246532 | − | 0.171387i | ||||
\(351\) | 5.12311 | 0.273451 | ||||||||
\(352\) | − | 6.62153i | − | 0.352929i | ||||||
\(353\) | 7.36932i | 0.392229i | 0.980581 | + | 0.196115i | \(0.0628325\pi\) | ||||
−0.980581 | + | 0.196115i | \(0.937168\pi\) | |||||||
\(354\) | 1.12311 | 0.0596924 | ||||||||
\(355\) | 4.87962 | 0.258983 | ||||||||
\(356\) | 5.08842 | 0.269686 | ||||||||
\(357\) | −2.56155 | − | 3.68466i | −0.135572 | − | 0.195013i | ||||
\(358\) | 4.00000 | 0.211407 | ||||||||
\(359\) | − | 30.3675i | − | 1.60274i | −0.598172 | − | 0.801368i | \(-0.704106\pi\) | ||
0.598172 | − | 0.801368i | \(-0.295894\pi\) | |||||||
\(360\) | 5.08842 | 0.268183 | ||||||||
\(361\) | 40.8617 | 2.15062 | ||||||||
\(362\) | 14.7304 | 0.774213 | ||||||||
\(363\) | − | 9.24621i | − | 0.485300i | ||||||
\(364\) | 7.73704 | + | 11.1293i | 0.405531 | + | 0.583335i | ||||
\(365\) | 17.3790i | 0.909659i | ||||||||
\(366\) | − | 6.04090i | − | 0.315763i | ||||||
\(367\) | −28.5083 | −1.48812 | −0.744062 | − | 0.668111i | \(-0.767103\pi\) | ||||
−0.744062 | + | 0.668111i | \(0.767103\pi\) | |||||||
\(368\) | 2.56155 | − | 4.05444i | 0.133530 | − | 0.211352i | ||||
\(369\) | 2.87689i | 0.149765i | ||||||||
\(370\) | 10.2462i | 0.532675i | ||||||||
\(371\) | 7.68466 | + | 11.0540i | 0.398968 | + | 0.573894i | ||||
\(372\) | 6.24621 | 0.323851 | ||||||||
\(373\) | − | 0.743668i | − | 0.0385057i | −0.999815 | − | 0.0192528i | \(-0.993871\pi\) | ||
0.999815 | − | 0.0192528i | \(-0.00612875\pi\) | |||||||
\(374\) | − | 2.24621i | − | 0.116149i | ||||||
\(375\) | − | 12.0818i | − | 0.623901i | ||||||
\(376\) | 3.36932i | 0.173759i | ||||||||
\(377\) | 42.2462i | 2.17579i | ||||||||
\(378\) | −1.51022 | − | 2.17238i | −0.0776775 | − | 0.111735i | ||||
\(379\) | − | 20.3995i | − | 1.04785i | −0.851764 | − | 0.523925i | \(-0.824467\pi\) | ||
0.851764 | − | 0.523925i | \(-0.175533\pi\) | |||||||
\(380\) | −13.1231 | −0.673201 | ||||||||
\(381\) | − | 10.2462i | − | 0.524929i | ||||||
\(382\) | 26.2316i | 1.34212i | ||||||||
\(383\) | 22.2586 | 1.13736 | 0.568682 | − | 0.822558i | \(-0.307454\pi\) | ||||
0.568682 | + | 0.822558i | \(0.307454\pi\) | |||||||
\(384\) | − | 3.00000i | − | 0.153093i | ||||||
\(385\) | −3.39228 | − | 4.87962i | −0.172887 | − | 0.248688i | ||||
\(386\) | 15.6155 | 0.794809 | ||||||||
\(387\) | − | 3.02045i | − | 0.153538i | ||||||
\(388\) | −6.04090 | −0.306680 | ||||||||
\(389\) | − | 34.5492i | − | 1.75172i | −0.482569 | − | 0.875858i | \(-0.660296\pi\) | ||
0.482569 | − | 0.875858i | \(-0.339704\pi\) | |||||||
\(390\) | −8.68951 | −0.440010 | ||||||||
\(391\) | −4.34475 | + | 6.87689i | −0.219724 | + | 0.347779i | ||||
\(392\) | 7.31534 | − | 19.6847i | 0.369481 | − | 0.994225i | ||||
\(393\) | 12.0000 | 0.605320 | ||||||||
\(394\) | 14.4924 | 0.730118 | ||||||||
\(395\) | 3.86174i | 0.194305i | ||||||||
\(396\) | 1.32431i | 0.0665489i | ||||||||
\(397\) | − | 12.4924i | − | 0.626977i | −0.949592 | − | 0.313488i | \(-0.898502\pi\) | ||
0.949592 | − | 0.313488i | \(-0.101498\pi\) | |||||||
\(398\) | 4.34475 | 0.217783 | ||||||||
\(399\) | 11.6847 | + | 16.8078i | 0.584965 | + | 0.841441i | ||||
\(400\) | 2.12311 | 0.106155 | ||||||||
\(401\) | 0.952473i | 0.0475642i | 0.999717 | + | 0.0237821i | \(0.00757079\pi\) | ||||
−0.999717 | + | 0.0237821i | \(0.992429\pi\) | |||||||
\(402\) | 15.1022 | 0.753231 | ||||||||
\(403\) | −32.0000 | −1.59403 | ||||||||
\(404\) | − | 5.12311i | − | 0.254884i | ||||||
\(405\) | −1.69614 | −0.0842819 | ||||||||
\(406\) | 17.9139 | − | 12.4536i | 0.889051 | − | 0.618063i | ||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | − | 5.08842i | − | 0.251914i | ||||||
\(409\) | 23.3693i | 1.15554i | 0.816200 | + | 0.577769i | \(0.196077\pi\) | ||||
−0.816200 | + | 0.577769i | \(0.803923\pi\) | |||||||
\(410\) | − | 4.87962i | − | 0.240987i | ||||||
\(411\) | 14.5216 | 0.716298 | ||||||||
\(412\) | 4.34475 | 0.214051 | ||||||||
\(413\) | −1.69614 | − | 2.43981i | −0.0834616 | − | 0.120055i | ||||
\(414\) | −2.56155 | + | 4.05444i | −0.125893 | + | 0.199265i | ||||
\(415\) | 8.98485 | 0.441049 | ||||||||
\(416\) | 25.6155i | 1.25590i | ||||||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 10.2462i | 0.501159i | ||||||||
\(419\) | −18.8664 | −0.921682 | −0.460841 | − | 0.887483i | \(-0.652452\pi\) | ||||
−0.460841 | + | 0.887483i | \(0.652452\pi\) | |||||||
\(420\) | −2.56155 | − | 3.68466i | −0.124991 | − | 0.179793i | ||||
\(421\) | − | 7.94584i | − | 0.387257i | −0.981075 | − | 0.193628i | \(-0.937974\pi\) | ||
0.981075 | − | 0.193628i | \(-0.0620256\pi\) | |||||||
\(422\) | −6.24621 | −0.304061 | ||||||||
\(423\) | − | 1.12311i | − | 0.0546073i | ||||||
\(424\) | 15.2653i | 0.741347i | ||||||||
\(425\) | −3.60109 | −0.174678 | ||||||||
\(426\) | − | 2.87689i | − | 0.139386i | ||||||
\(427\) | −13.1231 | + | 9.12311i | −0.635072 | + | 0.441498i | ||||
\(428\) | 8.10887i | 0.391957i | ||||||||
\(429\) | − | 6.78456i | − | 0.327562i | ||||||
\(430\) | 5.12311i | 0.247058i | ||||||||
\(431\) | 30.7851i | 1.48287i | 0.671026 | + | 0.741433i | \(0.265854\pi\) | ||||
−0.671026 | + | 0.741433i | \(0.734146\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | −16.2177 | −0.779375 | −0.389687 | − | 0.920947i | \(-0.627417\pi\) | ||||
−0.389687 | + | 0.920947i | \(0.627417\pi\) | |||||||
\(434\) | 9.43318 | + | 13.5691i | 0.452807 | + | 0.651339i | ||||
\(435\) | − | 13.9867i | − | 0.670613i | ||||||
\(436\) | − | 14.7304i | − | 0.705458i | ||||||
\(437\) | 19.8188 | − | 31.3693i | 0.948063 | − | 1.50060i | ||||
\(438\) | 10.2462 | 0.489583 | ||||||||
\(439\) | − | 38.2462i | − | 1.82539i | −0.408639 | − | 0.912696i | \(-0.633997\pi\) | ||
0.408639 | − | 0.912696i | \(-0.366003\pi\) | |||||||
\(440\) | − | 6.73863i | − | 0.321252i | ||||||
\(441\) | −2.43845 | + | 6.56155i | −0.116117 | + | 0.312455i | ||||
\(442\) | 8.68951i | 0.413318i | ||||||||
\(443\) | 4.63068 | 0.220010 | 0.110005 | − | 0.993931i | \(-0.464913\pi\) | ||||
0.110005 | + | 0.993931i | \(0.464913\pi\) | |||||||
\(444\) | −6.04090 | −0.286688 | ||||||||
\(445\) | 8.63068 | 0.409134 | ||||||||
\(446\) | − | 4.00000i | − | 0.189405i | ||||||
\(447\) | −13.7779 | −0.651674 | ||||||||
\(448\) | 15.2066 | − | 10.5716i | 0.718446 | − | 0.499460i | ||||
\(449\) | 34.4924 | 1.62780 | 0.813899 | − | 0.581006i | \(-0.197341\pi\) | ||||
0.813899 | + | 0.581006i | \(0.197341\pi\) | |||||||
\(450\) | −2.12311 | −0.100084 | ||||||||
\(451\) | 3.80989 | 0.179401 | ||||||||
\(452\) | 16.4265i | 0.772640i | ||||||||
\(453\) | − | 12.4924i | − | 0.586945i | ||||||
\(454\) | −3.39228 | −0.159208 | ||||||||
\(455\) | 13.1231 | + | 18.8769i | 0.615221 | + | 0.884962i | ||||
\(456\) | 23.2111i | 1.08696i | ||||||||
\(457\) | 29.0432i | 1.35858i | 0.733868 | + | 0.679292i | \(0.237713\pi\) | ||||
−0.733868 | + | 0.679292i | \(0.762287\pi\) | |||||||
\(458\) | 14.7304 | 0.688307 | ||||||||
\(459\) | 1.69614i | 0.0791691i | ||||||||
\(460\) | −4.34475 | + | 6.87689i | −0.202575 | + | 0.320637i | ||||
\(461\) | 15.3693i | 0.715820i | 0.933756 | + | 0.357910i | \(0.116511\pi\) | ||||
−0.933756 | + | 0.357910i | \(0.883489\pi\) | |||||||
\(462\) | −2.87689 | + | 2.00000i | −0.133845 | + | 0.0930484i | ||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 8.24621 | 0.382821 | ||||||||
\(465\) | 10.5945 | 0.491306 | ||||||||
\(466\) | 20.2462 | 0.937888 | ||||||||
\(467\) | 3.39228 | 0.156976 | 0.0784880 | − | 0.996915i | \(-0.474991\pi\) | ||||
0.0784880 | + | 0.996915i | \(0.474991\pi\) | |||||||
\(468\) | − | 5.12311i | − | 0.236816i | ||||||
\(469\) | −22.8078 | − | 32.8078i | −1.05316 | − | 1.51492i | ||||
\(470\) | 1.90495i | 0.0878686i | ||||||||
\(471\) | − | 0.743668i | − | 0.0342664i | ||||||
\(472\) | − | 3.36932i | − | 0.155085i | ||||||
\(473\) | −4.00000 | −0.183920 | ||||||||
\(474\) | 2.27678 | 0.104576 | ||||||||
\(475\) | 16.4265 | 0.753702 | ||||||||
\(476\) | −3.68466 | + | 2.56155i | −0.168886 | + | 0.117409i | ||||
\(477\) | − | 5.08842i | − | 0.232983i | ||||||
\(478\) | −23.3693 | −1.06889 | ||||||||
\(479\) | −30.9481 | −1.41406 | −0.707028 | − | 0.707185i | \(-0.749965\pi\) | ||||
−0.707028 | + | 0.707185i | \(0.749965\pi\) | |||||||
\(480\) | − | 8.48071i | − | 0.387089i | ||||||
\(481\) | 30.9481 | 1.41111 | ||||||||
\(482\) | −12.8255 | −0.584184 | ||||||||
\(483\) | 12.6763 | − | 0.558446i | 0.576791 | − | 0.0254102i | ||||
\(484\) | −9.24621 | −0.420282 | ||||||||
\(485\) | −10.2462 | −0.465256 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | 2.24621 | 0.101786 | 0.0508928 | − | 0.998704i | \(-0.483793\pi\) | ||||
0.0508928 | + | 0.998704i | \(0.483793\pi\) | |||||||
\(488\) | −18.1227 | −0.820376 | ||||||||
\(489\) | − | 12.0000i | − | 0.542659i | ||||||
\(490\) | 4.13595 | − | 11.1293i | 0.186843 | − | 0.502771i | ||||
\(491\) | 0.492423 | 0.0222227 | 0.0111114 | − | 0.999938i | \(-0.496463\pi\) | ||||
0.0111114 | + | 0.999938i | \(0.496463\pi\) | |||||||
\(492\) | 2.87689 | 0.129700 | ||||||||
\(493\) | −13.9867 | −0.629931 | ||||||||
\(494\) | − | 39.6377i | − | 1.78338i | ||||||
\(495\) | 2.24621i | 0.100960i | ||||||||
\(496\) | 6.24621i | 0.280463i | ||||||||
\(497\) | −6.24970 | + | 4.34475i | −0.280337 | + | 0.194889i | ||||
\(498\) | − | 5.29723i | − | 0.237374i | ||||||
\(499\) | 22.2462 | 0.995877 | 0.497939 | − | 0.867212i | \(-0.334090\pi\) | ||||
0.497939 | + | 0.867212i | \(0.334090\pi\) | |||||||
\(500\) | −12.0818 | −0.540314 | ||||||||
\(501\) | −22.2462 | −0.993887 | ||||||||
\(502\) | −27.5559 | −1.22988 | ||||||||
\(503\) | 10.5945 | 0.472383 | 0.236192 | − | 0.971706i | \(-0.424101\pi\) | ||||
0.236192 | + | 0.971706i | \(0.424101\pi\) | |||||||
\(504\) | −6.51713 | + | 4.53067i | −0.290296 | + | 0.201812i | ||||
\(505\) | − | 8.68951i | − | 0.386678i | ||||||
\(506\) | 5.36932 | + | 3.39228i | 0.238695 | + | 0.150805i | ||||
\(507\) | 13.2462i | 0.588285i | ||||||||
\(508\) | −10.2462 | −0.454602 | ||||||||
\(509\) | − | 25.6155i | − | 1.13539i | −0.823240 | − | 0.567694i | \(-0.807836\pi\) | ||
0.823240 | − | 0.567694i | \(-0.192164\pi\) | |||||||
\(510\) | − | 2.87689i | − | 0.127391i | ||||||
\(511\) | −15.4741 | − | 22.2586i | −0.684533 | − | 0.984664i | ||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | − | 7.73704i | − | 0.341599i | ||||||
\(514\) | 7.36932i | 0.325047i | ||||||||
\(515\) | 7.36932 | 0.324731 | ||||||||
\(516\) | −3.02045 | −0.132968 | ||||||||
\(517\) | −1.48734 | −0.0654130 | ||||||||
\(518\) | −9.12311 | − | 13.1231i | −0.400846 | − | 0.576596i | ||||
\(519\) | −5.12311 | −0.224879 | ||||||||
\(520\) | 26.0685i | 1.14318i | ||||||||
\(521\) | 1.69614 | 0.0743093 | 0.0371546 | − | 0.999310i | \(-0.488171\pi\) | ||||
0.0371546 | + | 0.999310i | \(0.488171\pi\) | |||||||
\(522\) | −8.24621 | −0.360927 | ||||||||
\(523\) | −0.952473 | −0.0416487 | −0.0208244 | − | 0.999783i | \(-0.506629\pi\) | ||||
−0.0208244 | + | 0.999783i | \(0.506629\pi\) | |||||||
\(524\) | − | 12.0000i | − | 0.524222i | ||||||
\(525\) | 3.20636 | + | 4.61219i | 0.139937 | + | 0.201292i | ||||
\(526\) | − | 20.9343i | − | 0.912780i | ||||||
\(527\) | − | 10.5945i | − | 0.461502i | ||||||
\(528\) | −1.32431 | −0.0576331 | ||||||||
\(529\) | −9.87689 | − | 20.7713i | −0.429430 | − | 0.903100i | ||||
\(530\) | 8.63068i | 0.374893i | ||||||||
\(531\) | 1.12311i | 0.0487386i | ||||||||
\(532\) | 16.8078 | − | 11.6847i | 0.728709 | − | 0.506594i | ||||
\(533\) | −14.7386 | −0.638401 | ||||||||
\(534\) | − | 5.08842i | − | 0.220198i | ||||||
\(535\) | 13.7538i | 0.594628i | ||||||||
\(536\) | − | 45.3067i | − | 1.95695i | ||||||
\(537\) | 4.00000i | 0.172613i | ||||||||
\(538\) | 31.3693i | 1.35243i | ||||||||
\(539\) | 8.68951 | + | 3.22925i | 0.374284 | + | 0.139094i | ||||
\(540\) | 1.69614i | 0.0729903i | ||||||||
\(541\) | 31.1231 | 1.33809 | 0.669043 | − | 0.743223i | \(-0.266704\pi\) | ||||
0.669043 | + | 0.743223i | \(0.266704\pi\) | |||||||
\(542\) | 16.4924i | 0.708410i | ||||||||
\(543\) | 14.7304i | 0.632142i | ||||||||
\(544\) | −8.48071 | −0.363607 | ||||||||
\(545\) | − | 24.9848i | − | 1.07023i | ||||||
\(546\) | 11.1293 | − | 7.73704i | 0.476291 | − | 0.331115i | ||||
\(547\) | 20.0000 | 0.855138 | 0.427569 | − | 0.903983i | \(-0.359370\pi\) | ||||
0.427569 | + | 0.903983i | \(0.359370\pi\) | |||||||
\(548\) | − | 14.5216i | − | 0.620332i | ||||||
\(549\) | 6.04090 | 0.257819 | ||||||||
\(550\) | 2.81164i | 0.119889i | ||||||||
\(551\) | 63.8012 | 2.71802 | ||||||||
\(552\) | 12.1633 | + | 7.68466i | 0.517705 | + | 0.327081i | ||||
\(553\) | −3.43845 | − | 4.94602i | −0.146218 | − | 0.210326i | ||||
\(554\) | 0.246211 | 0.0104605 | ||||||||
\(555\) | −10.2462 | −0.434927 | ||||||||
\(556\) | − | 12.0000i | − | 0.508913i | ||||||
\(557\) | 36.0366i | 1.52692i | 0.645856 | + | 0.763459i | \(0.276501\pi\) | ||||
−0.645856 | + | 0.763459i | \(0.723499\pi\) | |||||||
\(558\) | − | 6.24621i | − | 0.264423i | ||||||
\(559\) | 15.4741 | 0.654484 | ||||||||
\(560\) | 3.68466 | − | 2.56155i | 0.155705 | − | 0.108245i | ||||
\(561\) | 2.24621 | 0.0948351 | ||||||||
\(562\) | 9.64198i | 0.406722i | ||||||||
\(563\) | −27.5559 | −1.16134 | −0.580671 | − | 0.814139i | \(-0.697210\pi\) | ||||
−0.580671 | + | 0.814139i | \(0.697210\pi\) | |||||||
\(564\) | −1.12311 | −0.0472913 | ||||||||
\(565\) | 27.8617i | 1.17215i | ||||||||
\(566\) | −25.1161 | −1.05571 | ||||||||
\(567\) | 2.17238 | − | 1.51022i | 0.0912313 | − | 0.0634234i | ||||
\(568\) | −8.63068 | −0.362135 | ||||||||
\(569\) | 35.2929i | 1.47956i | 0.672851 | + | 0.739778i | \(0.265069\pi\) | ||||
−0.672851 | + | 0.739778i | \(0.734931\pi\) | |||||||
\(570\) | 13.1231i | 0.549666i | ||||||||
\(571\) | 4.92539i | 0.206121i | 0.994675 | + | 0.103061i | \(0.0328636\pi\) | ||||
−0.994675 | + | 0.103061i | \(0.967136\pi\) | |||||||
\(572\) | −6.78456 | −0.283677 | ||||||||
\(573\) | −26.2316 | −1.09584 | ||||||||
\(574\) | 4.34475 | + | 6.24970i | 0.181347 | + | 0.260857i | ||||
\(575\) | 5.43845 | − | 8.60799i | 0.226799 | − | 0.358978i | ||||
\(576\) | −7.00000 | −0.291667 | ||||||||
\(577\) | 18.8769i | 0.785855i | 0.919569 | + | 0.392928i | \(0.128538\pi\) | ||||
−0.919569 | + | 0.392928i | \(0.871462\pi\) | |||||||
\(578\) | 14.1231 | 0.587444 | ||||||||
\(579\) | 15.6155i | 0.648959i | ||||||||
\(580\) | −13.9867 | −0.580768 | ||||||||
\(581\) | −11.5076 | + | 8.00000i | −0.477415 | + | 0.331896i | ||||
\(582\) | 6.04090i | 0.250403i | ||||||||
\(583\) | −6.73863 | −0.279086 | ||||||||
\(584\) | − | 30.7386i | − | 1.27197i | ||||||
\(585\) | − | 8.68951i | − | 0.359267i | ||||||
\(586\) | 32.6443 | 1.34852 | ||||||||
\(587\) | 0.492423i | 0.0203245i | 0.999948 | + | 0.0101622i | \(0.00323479\pi\) | ||||
−0.999948 | + | 0.0101622i | \(0.996765\pi\) | |||||||
\(588\) | 6.56155 | + | 2.43845i | 0.270594 | + | 0.100560i | ||||
\(589\) | 48.3272i | 1.99129i | ||||||||
\(590\) | − | 1.90495i | − | 0.0784254i | ||||||
\(591\) | 14.4924i | 0.596139i | ||||||||
\(592\) | − | 6.04090i | − | 0.248279i | ||||||
\(593\) | 7.36932i | 0.302622i | 0.988486 | + | 0.151311i | \(0.0483494\pi\) | ||||
−0.988486 | + | 0.151311i | \(0.951651\pi\) | |||||||
\(594\) | 1.32431 | 0.0543370 | ||||||||
\(595\) | −6.24970 | + | 4.34475i | −0.256213 | + | 0.178118i | ||||
\(596\) | 13.7779i | 0.564366i | ||||||||
\(597\) | 4.34475i | 0.177819i | ||||||||
\(598\) | −20.7713 | − | 13.1231i | −0.849402 | − | 0.536644i | ||||
\(599\) | −39.3693 | −1.60859 | −0.804293 | − | 0.594232i | \(-0.797456\pi\) | ||||
−0.804293 | + | 0.594232i | \(0.797456\pi\) | |||||||
\(600\) | 6.36932i | 0.260026i | ||||||||
\(601\) | 8.63068i | 0.352053i | 0.984385 | + | 0.176026i | \(0.0563244\pi\) | ||||
−0.984385 | + | 0.176026i | \(0.943676\pi\) | |||||||
\(602\) | −4.56155 | − | 6.56155i | −0.185915 | − | 0.267429i | ||||
\(603\) | 15.1022i | 0.615011i | ||||||||
\(604\) | −12.4924 | −0.508309 | ||||||||
\(605\) | −15.6829 | −0.637600 | ||||||||
\(606\) | −5.12311 | −0.208112 | ||||||||
\(607\) | − | 26.7386i | − | 1.08529i | −0.839963 | − | 0.542644i | \(-0.817423\pi\) | ||
0.839963 | − | 0.542644i | \(-0.182577\pi\) | |||||||
\(608\) | 38.6852 | 1.56889 | ||||||||
\(609\) | 12.4536 | + | 17.9139i | 0.504646 | + | 0.725907i | ||||
\(610\) | −10.2462 | −0.414857 | ||||||||
\(611\) | 5.75379 | 0.232773 | ||||||||
\(612\) | 1.69614 | 0.0685624 | ||||||||
\(613\) | 14.3128i | 0.578088i | 0.957316 | + | 0.289044i | \(0.0933375\pi\) | ||||
−0.957316 | + | 0.289044i | \(0.906663\pi\) | |||||||
\(614\) | 14.2462i | 0.574930i | ||||||||
\(615\) | 4.87962 | 0.196765 | ||||||||
\(616\) | 6.00000 | + | 8.63068i | 0.241747 | + | 0.347740i | ||||
\(617\) | − | 26.6034i | − | 1.07101i | −0.844531 | − | 0.535506i | \(-0.820121\pi\) | ||
0.844531 | − | 0.535506i | \(-0.179879\pi\) | |||||||
\(618\) | − | 4.34475i | − | 0.174772i | ||||||
\(619\) | 33.8056 | 1.35876 | 0.679380 | − | 0.733786i | \(-0.262249\pi\) | ||||
0.679380 | + | 0.733786i | \(0.262249\pi\) | |||||||
\(620\) | − | 10.5945i | − | 0.425484i | ||||||
\(621\) | −4.05444 | − | 2.56155i | −0.162699 | − | 0.102792i | ||||
\(622\) | − | 27.3693i | − | 1.09741i | ||||||
\(623\) | −11.0540 | + | 7.68466i | −0.442868 | + | 0.307879i | ||||
\(624\) | 5.12311 | 0.205088 | ||||||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | −28.2995 | −1.13108 | ||||||||
\(627\) | −10.2462 | −0.409194 | ||||||||
\(628\) | −0.743668 | −0.0296756 | ||||||||
\(629\) | 10.2462i | 0.408543i | ||||||||
\(630\) | −3.68466 | + | 2.56155i | −0.146800 | + | 0.102055i | ||||
\(631\) | − | 5.66906i | − | 0.225682i | −0.993613 | − | 0.112841i | \(-0.964005\pi\) | ||
0.993613 | − | 0.112841i | \(-0.0359950\pi\) | |||||||
\(632\) | − | 6.83034i | − | 0.271696i | ||||||
\(633\) | − | 6.24621i | − | 0.248265i | ||||||
\(634\) | 14.0000 | 0.556011 | ||||||||
\(635\) | −17.3790 | −0.689665 | ||||||||
\(636\) | −5.08842 | −0.201769 | ||||||||
\(637\) | −33.6155 | − | 12.4924i | −1.33190 | − | 0.494968i | ||||
\(638\) | 10.9205i | 0.432347i | ||||||||
\(639\) | 2.87689 | 0.113808 | ||||||||
\(640\) | −5.08842 | −0.201138 | ||||||||
\(641\) | 11.5469i | 0.456076i | 0.973652 | + | 0.228038i | \(0.0732311\pi\) | ||||
−0.973652 | + | 0.228038i | \(0.926769\pi\) | |||||||
\(642\) | 8.10887 | 0.320032 | ||||||||
\(643\) | −2.85742 | −0.112686 | −0.0563428 | − | 0.998411i | \(-0.517944\pi\) | ||||
−0.0563428 | + | 0.998411i | \(0.517944\pi\) | |||||||
\(644\) | −0.558446 | − | 12.6763i | −0.0220059 | − | 0.499516i | ||||
\(645\) | −5.12311 | −0.201722 | ||||||||
\(646\) | 13.1231 | 0.516322 | ||||||||
\(647\) | 5.61553i | 0.220769i | 0.993889 | + | 0.110385i | \(0.0352083\pi\) | ||||
−0.993889 | + | 0.110385i | \(0.964792\pi\) | |||||||
\(648\) | 3.00000 | 0.117851 | ||||||||
\(649\) | 1.48734 | 0.0583831 | ||||||||
\(650\) | − | 10.8769i | − | 0.426627i | ||||||
\(651\) | −13.5691 | + | 9.43318i | −0.531816 | + | 0.369715i | ||||
\(652\) | −12.0000 | −0.469956 | ||||||||
\(653\) | 14.0000 | 0.547862 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(654\) | −14.7304 | −0.576004 | ||||||||
\(655\) | − | 20.3537i | − | 0.795285i | ||||||
\(656\) | 2.87689i | 0.112324i | ||||||||
\(657\) | 10.2462i | 0.399743i | ||||||||
\(658\) | −1.69614 | − | 2.43981i | −0.0661225 | − | 0.0951137i | ||||
\(659\) | 8.85254i | 0.344846i | 0.985023 | + | 0.172423i | \(0.0551596\pi\) | ||||
−0.985023 | + | 0.172423i | \(0.944840\pi\) | |||||||
\(660\) | 2.24621 | 0.0874337 | ||||||||
\(661\) | −26.3946 | −1.02663 | −0.513315 | − | 0.858200i | \(-0.671583\pi\) | ||||
−0.513315 | + | 0.858200i | \(0.671583\pi\) | |||||||
\(662\) | −16.4924 | −0.640996 | ||||||||
\(663\) | −8.68951 | −0.337473 | ||||||||
\(664\) | −15.8917 | −0.616717 | ||||||||
\(665\) | 28.5083 | − | 19.8188i | 1.10551 | − | 0.768541i | ||||
\(666\) | 6.04090i | 0.234080i | ||||||||
\(667\) | 21.1231 | − | 33.4337i | 0.817890 | − | 1.29456i | ||||
\(668\) | 22.2462i | 0.860732i | ||||||||
\(669\) | 4.00000 | 0.154649 | ||||||||
\(670\) | − | 25.6155i | − | 0.989614i | ||||||
\(671\) | − | 8.00000i | − | 0.308837i | ||||||
\(672\) | 7.55112 | + | 10.8619i | 0.291291 | + | 0.419006i | ||||
\(673\) | −4.87689 | −0.187990 | −0.0939952 | − | 0.995573i | \(-0.529964\pi\) | ||||
−0.0939952 | + | 0.995573i | \(0.529964\pi\) | |||||||
\(674\) | 3.39228i | 0.130666i | ||||||||
\(675\) | − | 2.12311i | − | 0.0817184i | ||||||
\(676\) | 13.2462 | 0.509470 | ||||||||
\(677\) | −32.6443 | −1.25462 | −0.627311 | − | 0.778769i | \(-0.715844\pi\) | ||||
−0.627311 | + | 0.778769i | \(0.715844\pi\) | |||||||
\(678\) | 16.4265 | 0.630858 | ||||||||
\(679\) | 13.1231 | − | 9.12311i | 0.503619 | − | 0.350113i | ||||
\(680\) | −8.63068 | −0.330972 | ||||||||
\(681\) | − | 3.39228i | − | 0.129993i | ||||||
\(682\) | −8.27190 | −0.316747 | ||||||||
\(683\) | −1.12311 | −0.0429744 | −0.0214872 | − | 0.999769i | \(-0.506840\pi\) | ||||
−0.0214872 | + | 0.999769i | \(0.506840\pi\) | |||||||
\(684\) | −7.73704 | −0.295833 | ||||||||
\(685\) | − | 24.6307i | − | 0.941090i | ||||||
\(686\) | 4.61219 | + | 17.9368i | 0.176094 | + | 0.684829i | ||||
\(687\) | 14.7304i | 0.562000i | ||||||||
\(688\) | − | 3.02045i | − | 0.115153i | ||||||
\(689\) | 26.0685 | 0.993132 | ||||||||
\(690\) | 6.87689 | + | 4.34475i | 0.261799 | + | 0.165402i | ||||
\(691\) | − | 14.2462i | − | 0.541951i | −0.962586 | − | 0.270976i | \(-0.912654\pi\) | ||
0.962586 | − | 0.270976i | \(-0.0873463\pi\) | |||||||
\(692\) | 5.12311i | 0.194751i | ||||||||
\(693\) | −2.00000 | − | 2.87689i | −0.0759737 | − | 0.109284i | ||||
\(694\) | −16.4924 | −0.626044 | ||||||||
\(695\) | − | 20.3537i | − | 0.772060i | ||||||
\(696\) | 24.7386i | 0.937715i | ||||||||
\(697\) | − | 4.87962i | − | 0.184829i | ||||||
\(698\) | − | 15.3693i | − | 0.581737i | ||||||
\(699\) | 20.2462i | 0.765782i | ||||||||
\(700\) | 4.61219 | − | 3.20636i | 0.174324 | − | 0.121189i | ||||
\(701\) | 6.99337i | 0.264136i | 0.991241 | + | 0.132068i | \(0.0421617\pi\) | ||||
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(702\) | −5.12311 | −0.193359 | ||||||||
\(703\) | − | 46.7386i | − | 1.76278i | ||||||
\(704\) | 9.27015i | 0.349382i | ||||||||
\(705\) | −1.90495 | −0.0717444 | ||||||||
\(706\) | − | 7.36932i | − | 0.277348i | ||||||
\(707\) | 7.73704 | + | 11.1293i | 0.290981 | + | 0.418561i | ||||
\(708\) | 1.12311 | 0.0422089 | ||||||||
\(709\) | 35.0841i | 1.31761i | 0.752313 | + | 0.658805i | \(0.228938\pi\) | ||||
−0.752313 | + | 0.658805i | \(0.771062\pi\) | |||||||
\(710\) | −4.87962 | −0.183129 | ||||||||
\(711\) | 2.27678i | 0.0853859i | ||||||||
\(712\) | −15.2653 | −0.572090 | ||||||||
\(713\) | 25.3249 | + | 16.0000i | 0.948423 | + | 0.599205i | ||||
\(714\) | 2.56155 | + | 3.68466i | 0.0958637 | + | 0.137895i | ||||
\(715\) | −11.5076 | −0.430359 | ||||||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | − | 23.3693i | − | 0.872743i | ||||||
\(718\) | 30.3675i | 1.13331i | ||||||||
\(719\) | 27.3693i | 1.02070i | 0.859966 | + | 0.510352i | \(0.170485\pi\) | ||||
−0.859966 | + | 0.510352i | \(0.829515\pi\) | |||||||
\(720\) | −1.69614 | −0.0632114 | ||||||||
\(721\) | −9.43845 | + | 6.56155i | −0.351506 | + | 0.244365i | ||||
\(722\) | −40.8617 | −1.52072 | ||||||||
\(723\) | − | 12.8255i | − | 0.476984i | ||||||
\(724\) | 14.7304 | 0.547451 | ||||||||
\(725\) | 17.5076 | 0.650215 | ||||||||
\(726\) | 9.24621i | 0.343159i | ||||||||
\(727\) | 8.15465 | 0.302439 | 0.151220 | − | 0.988500i | \(-0.451680\pi\) | ||||
0.151220 | + | 0.988500i | \(0.451680\pi\) | |||||||
\(728\) | −23.2111 | − | 33.3880i | −0.860261 | − | 1.23744i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | − | 17.3790i | − | 0.643226i | ||||||
\(731\) | 5.12311i | 0.189485i | ||||||||
\(732\) | − | 6.04090i | − | 0.223278i | ||||||
\(733\) | 2.64861 | 0.0978288 | 0.0489144 | − | 0.998803i | \(-0.484424\pi\) | ||||
0.0489144 | + | 0.998803i | \(0.484424\pi\) | |||||||
\(734\) | 28.5083 | 1.05226 | ||||||||
\(735\) | 11.1293 | + | 4.13595i | 0.410511 | + | 0.152557i | ||||
\(736\) | 12.8078 | − | 20.2722i | 0.472100 | − | 0.747242i | ||||
\(737\) | 20.0000 | 0.736709 | ||||||||
\(738\) | − | 2.87689i | − | 0.105900i | ||||||
\(739\) | −34.7386 | −1.27788 | −0.638941 | − | 0.769256i | \(-0.720627\pi\) | ||||
−0.638941 | + | 0.769256i | \(0.720627\pi\) | |||||||
\(740\) | 10.2462i | 0.376658i | ||||||||
\(741\) | 39.6377 | 1.45613 | ||||||||
\(742\) | −7.68466 | − | 11.0540i | −0.282113 | − | 0.405804i | ||||
\(743\) | 14.1498i | 0.519105i | 0.965729 | + | 0.259552i | \(0.0835750\pi\) | ||||
−0.965729 | + | 0.259552i | \(0.916425\pi\) | |||||||
\(744\) | −18.7386 | −0.686992 | ||||||||
\(745\) | 23.3693i | 0.856186i | ||||||||
\(746\) | 0.743668i | 0.0272276i | ||||||||
\(747\) | 5.29723 | 0.193815 | ||||||||
\(748\) | − | 2.24621i | − | 0.0821296i | ||||||
\(749\) | −12.2462 | − | 17.6155i | −0.447467 | − | 0.643657i | ||||
\(750\) | 12.0818i | 0.441165i | ||||||||
\(751\) | − | 40.0095i | − | 1.45997i | −0.683465 | − | 0.729984i | \(-0.739528\pi\) | ||
0.683465 | − | 0.729984i | \(-0.260472\pi\) | |||||||
\(752\) | − | 1.12311i | − | 0.0409554i | ||||||
\(753\) | − | 27.5559i | − | 1.00419i | ||||||
\(754\) | − | 42.2462i | − | 1.53852i | ||||||
\(755\) | −21.1889 | −0.771143 | ||||||||
\(756\) | −1.51022 | − | 2.17238i | −0.0549263 | − | 0.0790086i | ||||
\(757\) | − | 14.7304i | − | 0.535386i | −0.963504 | − | 0.267693i | \(-0.913739\pi\) | ||
0.963504 | − | 0.267693i | \(-0.0862612\pi\) | |||||||
\(758\) | 20.3995i | 0.740942i | ||||||||
\(759\) | −3.39228 | + | 5.36932i | −0.123132 | + | 0.194894i | ||||
\(760\) | 39.3693 | 1.42808 | ||||||||
\(761\) | − | 29.1231i | − | 1.05571i | −0.849334 | − | 0.527856i | \(-0.822996\pi\) | ||
0.849334 | − | 0.527856i | \(-0.177004\pi\) | |||||||
\(762\) | 10.2462i | 0.371181i | ||||||||
\(763\) | 22.2462 | + | 32.0000i | 0.805367 | + | 1.15848i | ||||
\(764\) | 26.2316i | 0.949024i | ||||||||
\(765\) | 2.87689 | 0.104014 | ||||||||
\(766\) | −22.2586 | −0.804237 | ||||||||
\(767\) | −5.75379 | −0.207757 | ||||||||
\(768\) | 17.0000i | 0.613435i | ||||||||
\(769\) | −53.9505 | −1.94550 | −0.972752 | − | 0.231850i | \(-0.925522\pi\) | ||||
−0.972752 | + | 0.231850i | \(0.925522\pi\) | |||||||
\(770\) | 3.39228 | + | 4.87962i | 0.122249 | + | 0.175849i | ||||
\(771\) | −7.36932 | −0.265399 | ||||||||
\(772\) | 15.6155 | 0.562015 | ||||||||
\(773\) | −34.5492 | −1.24265 | −0.621325 | − | 0.783553i | \(-0.713405\pi\) | ||||
−0.621325 | + | 0.783553i | \(0.713405\pi\) | |||||||
\(774\) | 3.02045i | 0.108568i | ||||||||
\(775\) | 13.2614i | 0.476362i | ||||||||
\(776\) | 18.1227 | 0.650567 | ||||||||
\(777\) | 13.1231 | − | 9.12311i | 0.470789 | − | 0.327290i | ||||
\(778\) | 34.5492i | 1.23865i | ||||||||
\(779\) | 22.2586i | 0.797498i | ||||||||
\(780\) | −8.68951 | −0.311134 | ||||||||
\(781\) | − | 3.80989i | − | 0.136329i | ||||||
\(782\) | 4.34475 | − | 6.87689i | 0.155368 | − | 0.245917i | ||||
\(783\) | − | 8.24621i | − | 0.294696i | ||||||
\(784\) | −2.43845 | + | 6.56155i | −0.0870874 | + | 0.234341i | ||||
\(785\) | −1.26137 | −0.0450201 | ||||||||
\(786\) | −12.0000 | −0.428026 | ||||||||
\(787\) | −33.8056 | −1.20504 | −0.602519 | − | 0.798104i | \(-0.705836\pi\) | ||||
−0.602519 | + | 0.798104i | \(0.705836\pi\) | |||||||
\(788\) | 14.4924 | 0.516271 | ||||||||
\(789\) | 20.9343 | 0.745282 | ||||||||
\(790\) | − | 3.86174i | − | 0.137395i | ||||||
\(791\) | −24.8078 | − | 35.6847i | −0.882063 | − | 1.26880i | ||||
\(792\) | − | 3.97292i | − | 0.141172i | ||||||
\(793\) | 30.9481i | 1.09900i | ||||||||
\(794\) | 12.4924i | 0.443339i | ||||||||
\(795\) | −8.63068 | −0.306099 | ||||||||
\(796\) | 4.34475 | 0.153996 | ||||||||
\(797\) | −19.0752 | −0.675677 | −0.337838 | − | 0.941204i | \(-0.609696\pi\) | ||||
−0.337838 | + | 0.941204i | \(0.609696\pi\) | |||||||
\(798\) | −11.6847 | − | 16.8078i | −0.413632 | − | 0.594988i | ||||
\(799\) | 1.90495i | 0.0673921i | ||||||||
\(800\) | 10.6155 | 0.375316 | ||||||||
\(801\) | 5.08842 | 0.179791 | ||||||||
\(802\) | − | 0.952473i | − | 0.0336330i | ||||||
\(803\) | 13.5691 | 0.478844 | ||||||||
\(804\) | 15.1022 | 0.532615 | ||||||||
\(805\) | −0.947203 | − | 21.5008i | −0.0333845 | − | 0.757802i | ||||
\(806\) | 32.0000 | 1.12715 | ||||||||
\(807\) | −31.3693 | −1.10425 | ||||||||
\(808\) | 15.3693i | 0.540691i | ||||||||
\(809\) | −0.246211 | −0.00865633 | −0.00432816 | − | 0.999991i | \(-0.501378\pi\) | ||||
−0.00432816 | + | 0.999991i | \(0.501378\pi\) | |||||||
\(810\) | 1.69614 | 0.0595963 | ||||||||
\(811\) | − | 30.2462i | − | 1.06209i | −0.847344 | − | 0.531044i | \(-0.821800\pi\) | ||
0.847344 | − | 0.531044i | \(-0.178200\pi\) | |||||||
\(812\) | 17.9139 | − | 12.4536i | 0.628654 | − | 0.437037i | ||||
\(813\) | −16.4924 | −0.578415 | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | −20.3537 | −0.712959 | ||||||||
\(816\) | 1.69614i | 0.0593768i | ||||||||
\(817\) | − | 23.3693i | − | 0.817589i | ||||||
\(818\) | − | 23.3693i | − | 0.817089i | ||||||
\(819\) | 7.73704 | + | 11.1293i | 0.270354 | + | 0.388890i | ||||
\(820\) | − | 4.87962i | − | 0.170404i | ||||||
\(821\) | −20.7386 | −0.723783 | −0.361892 | − | 0.932220i | \(-0.617869\pi\) | ||||
−0.361892 | + | 0.932220i | \(0.617869\pi\) | |||||||
\(822\) | −14.5216 | −0.506499 | ||||||||
\(823\) | 26.2462 | 0.914885 | 0.457443 | − | 0.889239i | \(-0.348765\pi\) | ||||
0.457443 | + | 0.889239i | \(0.348765\pi\) | |||||||
\(824\) | −13.0343 | −0.454070 | ||||||||
\(825\) | −2.81164 | −0.0978889 | ||||||||
\(826\) | 1.69614 | + | 2.43981i | 0.0590163 | + | 0.0848918i | ||||
\(827\) | 7.36520i | 0.256113i | 0.991767 | + | 0.128057i | \(0.0408739\pi\) | ||||
−0.991767 | + | 0.128057i | \(0.959126\pi\) | |||||||
\(828\) | −2.56155 | + | 4.05444i | −0.0890201 | + | 0.140901i | ||||
\(829\) | 21.1231i | 0.733636i | 0.930293 | + | 0.366818i | \(0.119553\pi\) | ||||
−0.930293 | + | 0.366818i | \(0.880447\pi\) | |||||||
\(830\) | −8.98485 | −0.311869 | ||||||||
\(831\) | 0.246211i | 0.00854097i | ||||||||
\(832\) | − | 35.8617i | − | 1.24328i | ||||||
\(833\) | 4.13595 | − | 11.1293i | 0.143302 | − | 0.385608i | ||||
\(834\) | −12.0000 | −0.415526 | ||||||||
\(835\) | 37.7327i | 1.30579i | ||||||||
\(836\) | 10.2462i | 0.354373i | ||||||||
\(837\) | 6.24621 | 0.215901 | ||||||||
\(838\) | 18.8664 | 0.651727 | ||||||||
\(839\) | −19.2840 | −0.665756 | −0.332878 | − | 0.942970i | \(-0.608020\pi\) | ||||
−0.332878 | + | 0.942970i | \(0.608020\pi\) | |||||||
\(840\) | 7.68466 | + | 11.0540i | 0.265146 | + | 0.381398i | ||||
\(841\) | 39.0000 | 1.34483 | ||||||||
\(842\) | 7.94584i | 0.273832i | ||||||||
\(843\) | −9.64198 | −0.332088 | ||||||||
\(844\) | −6.24621 | −0.215003 | ||||||||
\(845\) | 22.4674 | 0.772904 | ||||||||
\(846\) | 1.12311i | 0.0386132i | ||||||||
\(847\) | 20.0863 | − | 13.9638i | 0.690172 | − | 0.479804i | ||||
\(848\) | − | 5.08842i | − | 0.174737i | ||||||
\(849\) | − | 25.1161i | − | 0.861981i | ||||||
\(850\) | 3.60109 | 0.123516 | ||||||||
\(851\) | −24.4924 | − | 15.4741i | −0.839589 | − | 0.530444i | ||||
\(852\) | − | 2.87689i | − | 0.0985608i | ||||||
\(853\) | − | 8.00000i | − | 0.273915i | −0.990577 | − | 0.136957i | \(-0.956268\pi\) | ||
0.990577 | − | 0.136957i | \(-0.0437323\pi\) | |||||||
\(854\) | 13.1231 | − | 9.12311i | 0.449063 | − | 0.312186i | ||||
\(855\) | −13.1231 | −0.448801 | ||||||||
\(856\) | − | 24.3266i | − | 0.831467i | ||||||
\(857\) | 8.63068i | 0.294819i | 0.989076 | + | 0.147409i | \(0.0470934\pi\) | ||||
−0.989076 | + | 0.147409i | \(0.952907\pi\) | |||||||
\(858\) | 6.78456i | 0.231621i | ||||||||
\(859\) | 12.0000i | 0.409435i | 0.978821 | + | 0.204717i | \(0.0656275\pi\) | ||||
−0.978821 | + | 0.204717i | \(0.934372\pi\) | |||||||
\(860\) | 5.12311i | 0.174696i | ||||||||
\(861\) | −6.24970 | + | 4.34475i | −0.212989 | + | 0.148069i | ||||
\(862\) | − | 30.7851i | − | 1.04855i | ||||||
\(863\) | −56.0000 | −1.90626 | −0.953131 | − | 0.302558i | \(-0.902160\pi\) | ||||
−0.953131 | + | 0.302558i | \(0.902160\pi\) | |||||||
\(864\) | − | 5.00000i | − | 0.170103i | ||||||
\(865\) | 8.68951i | 0.295452i | ||||||||
\(866\) | 16.2177 | 0.551101 | ||||||||
\(867\) | 14.1231i | 0.479646i | ||||||||
\(868\) | 9.43318 | + | 13.5691i | 0.320183 | + | 0.460566i | ||||
\(869\) | 3.01515 | 0.102282 | ||||||||
\(870\) | 13.9867i | 0.474195i | ||||||||
\(871\) | −77.3704 | −2.62159 | ||||||||
\(872\) | 44.1912i | 1.49650i | ||||||||
\(873\) | −6.04090 | −0.204453 | ||||||||
\(874\) | −19.8188 | + | 31.3693i | −0.670382 | + | 1.06108i | ||||
\(875\) | 26.2462 | − | 18.2462i | 0.887284 | − | 0.616835i | ||||
\(876\) | 10.2462 | 0.346187 | ||||||||
\(877\) | −24.2462 | −0.818736 | −0.409368 | − | 0.912369i | \(-0.634251\pi\) | ||||
−0.409368 | + | 0.912369i | \(0.634251\pi\) | |||||||
\(878\) | 38.2462i | 1.29075i | ||||||||
\(879\) | 32.6443i | 1.10106i | ||||||||
\(880\) | 2.24621i | 0.0757198i | ||||||||
\(881\) | −29.2520 | −0.985525 | −0.492763 | − | 0.870164i | \(-0.664013\pi\) | ||||
−0.492763 | + | 0.870164i | \(0.664013\pi\) | |||||||
\(882\) | 2.43845 | − | 6.56155i | 0.0821068 | − | 0.220939i | ||||
\(883\) | −8.49242 | −0.285793 | −0.142896 | − | 0.989738i | \(-0.545642\pi\) | ||||
−0.142896 | + | 0.989738i | \(0.545642\pi\) | |||||||
\(884\) | 8.68951i | 0.292260i | ||||||||
\(885\) | 1.90495 | 0.0640340 | ||||||||
\(886\) | −4.63068 | −0.155571 | ||||||||
\(887\) | − | 7.86174i | − | 0.263971i | −0.991252 | − | 0.131986i | \(-0.957865\pi\) | ||
0.991252 | − | 0.131986i | \(-0.0421353\pi\) | |||||||
\(888\) | 18.1227 | 0.608158 | ||||||||
\(889\) | 22.2586 | − | 15.4741i | 0.746531 | − | 0.518984i | ||||
\(890\) | −8.63068 | −0.289301 | ||||||||
\(891\) | 1.32431i | 0.0443660i | ||||||||
\(892\) | − | 4.00000i | − | 0.133930i | ||||||
\(893\) | − | 8.68951i | − | 0.290783i | ||||||
\(894\) | 13.7779 | 0.460803 | ||||||||
\(895\) | 6.78456 | 0.226783 | ||||||||
\(896\) | 6.51713 | − | 4.53067i | 0.217722 | − | 0.151359i | ||||
\(897\) | 13.1231 | − | 20.7713i | 0.438168 | − | 0.693534i | ||||
\(898\) | −34.4924 | −1.15103 | ||||||||
\(899\) | 51.5076i | 1.71787i | ||||||||
\(900\) | −2.12311 | −0.0707702 | ||||||||
\(901\) | 8.63068i | 0.287530i | ||||||||
\(902\) | −3.80989 | −0.126855 | ||||||||
\(903\) | 6.56155 | − | 4.56155i | 0.218355 | − | 0.151799i | ||||
\(904\) | − | 49.2796i | − | 1.63902i | ||||||
\(905\) | 24.9848 | 0.830524 | ||||||||
\(906\) | 12.4924i | 0.415033i | ||||||||
\(907\) | − | 1.85917i | − | 0.0617327i | −0.999524 | − | 0.0308664i | \(-0.990173\pi\) | ||
0.999524 | − | 0.0308664i | \(-0.00982663\pi\) | |||||||
\(908\) | −3.39228 | −0.112577 | ||||||||
\(909\) | − | 5.12311i | − | 0.169923i | ||||||
\(910\) | −13.1231 | − | 18.8769i | −0.435027 | − | 0.625763i | ||||
\(911\) | − | 37.5697i | − | 1.24474i | −0.782724 | − | 0.622370i | \(-0.786170\pi\) | ||
0.782724 | − | 0.622370i | \(-0.213830\pi\) | |||||||
\(912\) | − | 7.73704i | − | 0.256199i | ||||||
\(913\) | − | 7.01515i | − | 0.232168i | ||||||
\(914\) | − | 29.0432i | − | 0.960664i | ||||||
\(915\) | − | 10.2462i | − | 0.338729i | ||||||
\(916\) | 14.7304 | 0.486706 | ||||||||
\(917\) | 18.1227 | + | 26.0685i | 0.598464 | + | 0.860859i | ||||
\(918\) | − | 1.69614i | − | 0.0559810i | ||||||
\(919\) | 3.02045i | 0.0996354i | 0.998758 | + | 0.0498177i | \(0.0158640\pi\) | ||||
−0.998758 | + | 0.0498177i | \(0.984136\pi\) | |||||||
\(920\) | 13.0343 | − | 20.6307i | 0.429727 | − | 0.680173i | ||||
\(921\) | −14.2462 | −0.469429 | ||||||||
\(922\) | − | 15.3693i | − | 0.506161i | ||||||
\(923\) | 14.7386i | 0.485128i | ||||||||
\(924\) | −2.87689 | + | 2.00000i | −0.0946429 | + | 0.0657952i | ||||
\(925\) | − | 12.8255i | − | 0.421699i | ||||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | 4.34475 | 0.142700 | ||||||||
\(928\) | 41.2311 | 1.35348 | ||||||||
\(929\) | − | 18.8769i | − | 0.619331i | −0.950846 | − | 0.309665i | \(-0.899783\pi\) | ||
0.950846 | − | 0.309665i | \(-0.100217\pi\) | |||||||
\(930\) | −10.5945 | −0.347406 | ||||||||
\(931\) | −18.8664 | + | 50.7670i | −0.618320 | + | 1.66382i | ||||
\(932\) | 20.2462 | 0.663187 | ||||||||
\(933\) | 27.3693 | 0.896031 | ||||||||
\(934\) | −3.39228 | −0.110999 | ||||||||
\(935\) | − | 3.80989i | − | 0.124597i | ||||||
\(936\) | 15.3693i | 0.502362i | ||||||||
\(937\) | 10.9205 | 0.356758 | 0.178379 | − | 0.983962i | \(-0.442915\pi\) | ||||
0.178379 | + | 0.983962i | \(0.442915\pi\) | |||||||
\(938\) | 22.8078 | + | 32.8078i | 0.744700 | + | 1.07121i | ||||
\(939\) | − | 28.2995i | − | 0.923520i | ||||||
\(940\) | 1.90495i | 0.0621325i | ||||||||
\(941\) | −6.57576 | −0.214364 | −0.107182 | − | 0.994239i | \(-0.534183\pi\) | ||||
−0.107182 | + | 0.994239i | \(0.534183\pi\) | |||||||
\(942\) | 0.743668i | 0.0242300i | ||||||||
\(943\) | 11.6642 | + | 7.36932i | 0.379838 | + | 0.239978i | ||||
\(944\) | 1.12311i | 0.0365540i | ||||||||
\(945\) | −2.56155 | − | 3.68466i | −0.0833273 | − | 0.119862i | ||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −0.492423 | −0.0160016 | −0.00800079 | − | 0.999968i | \(-0.502547\pi\) | ||||
−0.00800079 | + | 0.999968i | \(0.502547\pi\) | |||||||
\(948\) | 2.27678 | 0.0739464 | ||||||||
\(949\) | −52.4924 | −1.70398 | ||||||||
\(950\) | −16.4265 | −0.532948 | ||||||||
\(951\) | 14.0000i | 0.453981i | ||||||||
\(952\) | 11.0540 | − | 7.68466i | 0.358261 | − | 0.249061i | ||||
\(953\) | 54.1593i | 1.75439i | 0.480134 | + | 0.877195i | \(0.340588\pi\) | ||||
−0.480134 | + | 0.877195i | \(0.659412\pi\) | |||||||
\(954\) | 5.08842i | 0.164744i | ||||||||
\(955\) | 44.4924i | 1.43974i | ||||||||
\(956\) | −23.3693 | −0.755818 | ||||||||
\(957\) | −10.9205 | −0.353010 | ||||||||
\(958\) | 30.9481 | 0.999889 | ||||||||
\(959\) | 21.9309 | + | 31.5464i | 0.708185 | + | 1.01869i | ||||
\(960\) | 11.8730i | 0.383199i | ||||||||
\(961\) | −8.01515 | −0.258553 | ||||||||
\(962\) | −30.9481 | −0.997808 | ||||||||
\(963\) | 8.10887i | 0.261305i | ||||||||
\(964\) | −12.8255 | −0.413080 | ||||||||
\(965\) | 26.4861 | 0.852619 | ||||||||
\(966\) | −12.6763 | + | 0.558446i | −0.407853 | + | 0.0179677i | ||||
\(967\) | 24.0000 | 0.771788 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(968\) | 27.7386 | 0.891553 | ||||||||
\(969\) | 13.1231i | 0.421575i | ||||||||
\(970\) | 10.2462 | 0.328986 | ||||||||
\(971\) | −3.39228 | −0.108864 | −0.0544318 | − | 0.998517i | \(-0.517335\pi\) | ||||
−0.0544318 | + | 0.998517i | \(0.517335\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 18.1227 | + | 26.0685i | 0.580987 | + | 0.835719i | ||||
\(974\) | −2.24621 | −0.0719733 | ||||||||
\(975\) | 10.8769 | 0.348339 | ||||||||
\(976\) | 6.04090 | 0.193364 | ||||||||
\(977\) | − | 48.8620i | − | 1.56323i | −0.623758 | − | 0.781617i | \(-0.714395\pi\) | ||
0.623758 | − | 0.781617i | \(-0.285605\pi\) | |||||||
\(978\) | 12.0000i | 0.383718i | ||||||||
\(979\) | − | 6.73863i | − | 0.215368i | ||||||
\(980\) | 4.13595 | − | 11.1293i | 0.132118 | − | 0.355513i | ||||
\(981\) | − | 14.7304i | − | 0.470306i | ||||||
\(982\) | −0.492423 | −0.0157138 | ||||||||
\(983\) | 58.9216 | 1.87931 | 0.939654 | − | 0.342126i | \(-0.111147\pi\) | ||||
0.939654 | + | 0.342126i | \(0.111147\pi\) | |||||||
\(984\) | −8.63068 | −0.275136 | ||||||||
\(985\) | 24.5812 | 0.783222 | ||||||||
\(986\) | 13.9867 | 0.445428 | ||||||||
\(987\) | 2.43981 | − | 1.69614i | 0.0776600 | − | 0.0539888i | ||||
\(988\) | − | 39.6377i | − | 1.26104i | ||||||
\(989\) | −12.2462 | − | 7.73704i | −0.389407 | − | 0.246023i | ||||
\(990\) | − | 2.24621i | − | 0.0713893i | ||||||
\(991\) | −3.50758 | −0.111422 | −0.0557109 | − | 0.998447i | \(-0.517743\pi\) | ||||
−0.0557109 | + | 0.998447i | \(0.517743\pi\) | |||||||
\(992\) | 31.2311i | 0.991587i | ||||||||
\(993\) | − | 16.4924i | − | 0.523371i | ||||||
\(994\) | 6.24970 | − | 4.34475i | 0.198228 | − | 0.137807i | ||||
\(995\) | 7.36932 | 0.233623 | ||||||||
\(996\) | − | 5.29723i | − | 0.167849i | ||||||
\(997\) | − | 53.1231i | − | 1.68243i | −0.540704 | − | 0.841213i | \(-0.681842\pi\) | ||
0.540704 | − | 0.841213i | \(-0.318158\pi\) | |||||||
\(998\) | −22.2462 | −0.704192 | ||||||||
\(999\) | −6.04090 | −0.191125 |
(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 | 483.2.h.a.160.2 | ✓ | 8 | |
3.2 | odd | 2 | 1449.2.h.d.1126.5 | 8 | |||
7.6 | odd | 2 | inner | 483.2.h.a.160.7 | yes | 8 | |
21.20 | even | 2 | 1449.2.h.d.1126.3 | 8 | |||
23.22 | odd | 2 | inner | 483.2.h.a.160.3 | yes | 8 | |
69.68 | even | 2 | 1449.2.h.d.1126.4 | 8 | |||
161.160 | even | 2 | inner | 483.2.h.a.160.6 | yes | 8 | |
483.482 | odd | 2 | 1449.2.h.d.1126.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.h.a.160.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
483.2.h.a.160.3 | yes | 8 | 23.22 | odd | 2 | inner | |
483.2.h.a.160.6 | yes | 8 | 161.160 | even | 2 | inner | |
483.2.h.a.160.7 | yes | 8 | 7.6 | odd | 2 | inner | |
1449.2.h.d.1126.3 | 8 | 21.20 | even | 2 | |||
1449.2.h.d.1126.4 | 8 | 69.68 | even | 2 | |||
1449.2.h.d.1126.5 | 8 | 3.2 | odd | 2 | |||
1449.2.h.d.1126.6 | 8 | 483.482 | odd | 2 |