Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,3,Mod(319,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.6948632272\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 30 x^{13} + 76 x^{12} - 144 x^{11} + 424 x^{10} - 912 x^{9} + 1552 x^{8} - 3648 x^{7} + 6784 x^{6} - 9216 x^{5} + 19456 x^{4} - 30720 x^{3} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 511.3 | ||
Root | \(-0.710719 - 1.86946i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.511 |
Dual form | 576.3.o.g.319.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.32245 | − | 1.89900i | −0.774151 | − | 0.633001i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.35609 | − | 2.34881i | −0.271218 | − | 0.469763i | 0.697956 | − | 0.716140i | \(-0.254093\pi\) |
−0.969174 | + | 0.246378i | \(0.920760\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.0431 | − | 5.79837i | −1.43473 | − | 0.828339i | −0.437249 | − | 0.899340i | \(-0.644047\pi\) |
−0.997476 | + | 0.0710013i | \(0.977381\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.78756 | + | 8.82069i | 0.198618 | + | 0.980077i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.54822 | − | 4.93532i | −0.777111 | − | 0.448665i | 0.0582943 | − | 0.998299i | \(-0.481434\pi\) |
−0.835406 | + | 0.549634i | \(0.814767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.296185 | − | 0.513008i | −0.0227835 | − | 0.0394622i | 0.854409 | − | 0.519601i | \(-0.173920\pi\) |
−0.877192 | + | 0.480139i | \(0.840586\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.31096 | + | 8.03023i | −0.0873972 | + | 0.535348i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.87968 | −0.522334 | −0.261167 | − | 0.965294i | \(-0.584107\pi\) | ||||
−0.261167 | + | 0.965294i | \(0.584107\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.0989i | 0.742046i | 0.928624 | + | 0.371023i | \(0.120993\pi\) | ||||
−0.928624 | + | 0.371023i | \(0.879007\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.3134 | + | 32.5383i | 0.586354 | + | 1.54944i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.2754 | − | 10.5513i | 0.794583 | − | 0.458753i | −0.0469902 | − | 0.998895i | \(-0.514963\pi\) |
0.841574 | + | 0.540142i | \(0.181630\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.82205 | − | 15.2802i | 0.352882 | − | 0.611209i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.5990 | − | 23.8802i | 0.466630 | − | 0.884453i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −10.1764 | + | 17.6260i | −0.350910 | + | 0.607793i | −0.986409 | − | 0.164308i | \(-0.947461\pi\) |
0.635499 | + | 0.772101i | \(0.280794\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.3357 | + | 8.27670i | −0.462441 | + | 0.266990i | −0.713070 | − | 0.701093i | \(-0.752696\pi\) |
0.250629 | + | 0.968083i | \(0.419362\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.4806 | + | 27.6952i | 0.317595 | + | 0.839247i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 31.4524i | 0.898641i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 40.6557 | 1.09880 | 0.549401 | − | 0.835559i | \(-0.314856\pi\) | ||||
0.549401 | + | 0.835559i | \(0.314856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.286328 | + | 1.75389i | −0.00734176 | + | 0.0449716i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.2177 | + | 36.7502i | 0.517506 | + | 0.896346i | 0.999793 | + | 0.0203330i | \(0.00647263\pi\) |
−0.482288 | + | 0.876013i | \(0.660194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −32.2385 | − | 18.6129i | −0.749732 | − | 0.432858i | 0.0758649 | − | 0.997118i | \(-0.475828\pi\) |
−0.825597 | + | 0.564260i | \(0.809162\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 18.2941 | − | 16.1603i | 0.406535 | − | 0.359118i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.57134 | − | 0.907211i | −0.0334327 | − | 0.0193024i | 0.483191 | − | 0.875515i | \(-0.339478\pi\) |
−0.516623 | + | 0.856213i | \(0.672811\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 42.7423 | + | 74.0318i | 0.872291 | + | 1.51085i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.6226 | + | 16.8625i | 0.404365 | + | 0.330638i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 21.1005 | 0.398122 | 0.199061 | − | 0.979987i | \(-0.436211\pi\) | ||||
0.199061 | + | 0.979987i | \(0.436211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 26.7709i | 0.486744i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 26.7738 | − | 32.7440i | 0.469716 | − | 0.574456i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 76.6879 | − | 44.2758i | 1.29980 | − | 0.750437i | 0.319427 | − | 0.947611i | \(-0.396510\pi\) |
0.980369 | + | 0.197174i | \(0.0631764\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.4925 | + | 63.2069i | −0.598238 | + | 1.03618i | 0.394843 | + | 0.918749i | \(0.370799\pi\) |
−0.993081 | + | 0.117431i | \(0.962534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 33.1930 | − | 98.9519i | 0.526873 | − | 1.57066i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.803307 | + | 1.39137i | −0.0123586 | + | 0.0214057i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −38.3110 | + | 22.1189i | −0.571807 | + | 0.330133i | −0.757871 | − | 0.652405i | \(-0.773760\pi\) |
0.186064 | + | 0.982538i | \(0.440427\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −62.4808 | − | 10.2002i | −0.905519 | − | 0.147829i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 111.798i | 1.57462i | 0.616557 | + | 0.787310i | \(0.288527\pi\) | ||||
−0.616557 | + | 0.787310i | \(0.711473\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.2003 | −1.04384 | −0.521920 | − | 0.852995i | \(-0.674784\pi\) | ||||
−0.521920 | + | 0.852995i | \(0.674784\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −49.5060 | + | 18.7345i | −0.660080 | + | 0.249793i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 57.2337 | + | 99.1316i | 0.743294 | + | 1.28742i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.30434 | + | 4.79451i | 0.105118 | + | 0.0606901i | 0.551637 | − | 0.834084i | \(-0.314003\pi\) |
−0.446519 | + | 0.894774i | \(0.647337\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −74.6092 | + | 31.5351i | −0.921102 | + | 0.389322i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 73.6244 | + | 42.5070i | 0.887041 | + | 0.512133i | 0.872973 | − | 0.487768i | \(-0.162189\pi\) |
0.0140672 | + | 0.999901i | \(0.495522\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0416 | + | 20.8567i | 0.141666 | + | 0.245373i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 57.1060 | − | 21.6106i | 0.656391 | − | 0.248397i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 64.7845 | 0.727916 | 0.363958 | − | 0.931415i | \(-0.381425\pi\) | ||||
0.363958 | + | 0.931415i | \(0.381425\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.86958i | 0.0754898i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 49.0114 | + | 8.00125i | 0.527004 | + | 0.0860350i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 33.1157 | − | 19.1193i | 0.348586 | − | 0.201256i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.59139 | + | 6.22047i | −0.0370246 | + | 0.0641285i | −0.883944 | − | 0.467593i | \(-0.845121\pi\) |
0.846919 | + | 0.531721i | \(0.178455\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 28.2524 | − | 84.2235i | 0.285378 | − | 0.850742i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 55.5037 | − | 96.1353i | 0.549542 | − | 0.951834i | −0.448764 | − | 0.893650i | \(-0.648136\pi\) |
0.998306 | − | 0.0581840i | \(-0.0185310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −79.6133 | + | 45.9648i | −0.772945 | + | 0.446260i | −0.833924 | − | 0.551879i | \(-0.813911\pi\) |
0.0609793 | + | 0.998139i | \(0.480578\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 59.7283 | − | 73.0468i | 0.568841 | − | 0.695683i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 107.741i | 1.00693i | 0.864016 | + | 0.503465i | \(0.167942\pi\) | ||||
−0.864016 | + | 0.503465i | \(0.832058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −86.5562 | −0.794093 | −0.397047 | − | 0.917798i | \(-0.629965\pi\) | ||||
−0.397047 | + | 0.917798i | \(0.629965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −94.4209 | − | 77.2054i | −0.850639 | − | 0.695544i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.35198 | − | 4.07376i | −0.0208140 | − | 0.0360509i | 0.855431 | − | 0.517917i | \(-0.173292\pi\) |
−0.876245 | + | 0.481866i | \(0.839959\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −49.5662 | − | 28.6170i | −0.431010 | − | 0.248844i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.99564 | − | 3.52960i | 0.0341507 | − | 0.0301675i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 89.1793 | + | 51.4877i | 0.749406 | + | 0.432670i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.7852 | − | 20.4126i | −0.0973987 | − | 0.168700i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.5116 | − | 125.643i | 0.166761 | − | 1.02149i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −115.658 | −0.925267 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.37118i | − | 0.0659148i | −0.999457 | − | 0.0329574i | \(-0.989507\pi\) | ||
0.999457 | − | 0.0329574i | \(-0.0104926\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 39.5264 | + | 104.449i | 0.306406 | + | 0.809679i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −115.067 | + | 66.4338i | −0.878372 | + | 0.507129i | −0.870121 | − | 0.492837i | \(-0.835960\pi\) |
−0.00825098 | + | 0.999966i | \(0.502626\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 81.7506 | − | 141.596i | 0.614666 | − | 1.06463i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −73.1756 | + | 2.79099i | −0.542041 | + | 0.0206740i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.5579 | − | 39.0715i | 0.164656 | − | 0.285193i | −0.771877 | − | 0.635772i | \(-0.780682\pi\) |
0.936533 | + | 0.350579i | \(0.114015\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −130.744 | + | 75.4848i | −0.940601 | + | 0.543056i | −0.890149 | − | 0.455670i | \(-0.849400\pi\) |
−0.0504522 | + | 0.998726i | \(0.516066\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.92655 | + | 5.09093i | 0.0136635 | + | 0.0361059i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.84708i | 0.0408887i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 55.2003 | 0.380692 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 41.3198 | − | 253.103i | 0.281087 | − | 1.72179i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −71.3914 | − | 123.653i | −0.479137 | − | 0.829889i | 0.520577 | − | 0.853815i | \(-0.325717\pi\) |
−0.999714 | + | 0.0239255i | \(0.992384\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −220.027 | − | 127.033i | −1.45713 | − | 0.841276i | −0.458263 | − | 0.888817i | \(-0.651528\pi\) |
−0.998869 | + | 0.0475407i | \(0.984862\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.8730 | − | 78.3249i | −0.103745 | − | 0.511927i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 38.8808 | + | 22.4479i | 0.250844 | + | 0.144825i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.65361 | − | 4.59618i | −0.0169020 | − | 0.0292751i | 0.857451 | − | 0.514566i | \(-0.172047\pi\) |
−0.874353 | + | 0.485291i | \(0.838714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −49.0048 | − | 40.0698i | −0.308206 | − | 0.252012i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −244.722 | −1.52001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 59.5534i | 0.365359i | 0.983173 | + | 0.182679i | \(0.0584770\pi\) | ||||
−0.983173 | + | 0.182679i | \(0.941523\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 50.8381 | − | 62.1742i | 0.308110 | − | 0.376813i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 85.7434 | − | 49.5040i | 0.513434 | − | 0.296431i | −0.220810 | − | 0.975317i | \(-0.570870\pi\) |
0.734244 | + | 0.678886i | \(0.237537\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 84.3245 | − | 146.054i | 0.498962 | − | 0.864227i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −124.362 | + | 25.2027i | −0.727263 | + | 0.147384i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.2965 | + | 33.4225i | −0.111540 | + | 0.193193i | −0.916391 | − | 0.400283i | \(-0.868912\pi\) |
0.804851 | + | 0.593477i | \(0.202245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −177.201 | + | 102.307i | −1.01258 | + | 0.584612i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −262.184 | − | 42.8023i | −1.48126 | − | 0.241821i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 36.4264i | 0.203499i | 0.994810 | + | 0.101750i | \(0.0324441\pi\) | ||||
−0.994810 | + | 0.101750i | \(0.967556\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5921 | 0.102719 | 0.0513594 | − | 0.998680i | \(-0.483645\pi\) | ||||
0.0513594 | + | 0.998680i | \(0.483645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 204.782 | − | 77.4956i | 1.11903 | − | 0.423473i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −55.1327 | − | 95.4927i | −0.298015 | − | 0.516177i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 75.9055 | + | 43.8240i | 0.405912 | + | 0.234353i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −264.999 | + | 166.777i | −1.40211 | + | 0.882419i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 244.973 | + | 141.435i | 1.28258 | + | 0.740497i | 0.977319 | − | 0.211772i | \(-0.0679233\pi\) |
0.305260 | + | 0.952269i | \(0.401257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −151.542 | − | 262.479i | −0.785193 | − | 1.35999i | −0.928884 | − | 0.370372i | \(-0.879230\pi\) |
0.143691 | − | 0.989623i | \(-0.454103\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.50786 | − | 1.70590i | 0.0231172 | − | 0.00874822i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −139.184 | −0.706520 | −0.353260 | − | 0.935525i | \(-0.614927\pi\) | ||||
−0.353260 | + | 0.935525i | \(0.614927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 11.2337i | − | 0.0564505i | −0.999602 | − | 0.0282253i | \(-0.991014\pi\) | ||
0.999602 | − | 0.0282253i | \(-0.00898558\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 130.979 | + | 21.3828i | 0.651639 | + | 0.106382i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 204.404 | − | 118.013i | 1.00692 | − | 0.581344i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 57.5462 | − | 99.6730i | 0.280713 | − | 0.486210i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 125.738 | + | 142.341i | 0.607432 | + | 0.687636i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 69.5825 | − | 120.520i | 0.332931 | − | 0.576653i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −112.017 | + | 64.6728i | −0.530884 | + | 0.306506i | −0.741376 | − | 0.671090i | \(-0.765827\pi\) |
0.210492 | + | 0.977595i | \(0.432493\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 212.305 | − | 259.646i | 0.996737 | − | 1.21899i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 100.963i | 0.469595i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 191.966 | 0.884634 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 176.971 | + | 144.705i | 0.808089 | + | 0.660752i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.63003 | + | 4.55535i | 0.0119006 | + | 0.0206124i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 209.210 | + | 120.787i | 0.938159 | + | 0.541647i | 0.889383 | − | 0.457163i | \(-0.151134\pi\) |
0.0487765 | + | 0.998810i | \(0.484468\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 150.552 | + | 50.5022i | 0.669121 | + | 0.224454i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 330.710 | + | 190.936i | 1.45687 | + | 0.841126i | 0.998856 | − | 0.0478181i | \(-0.0152268\pi\) |
0.458016 | + | 0.888944i | \(0.348560\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −74.6642 | − | 129.322i | −0.326044 | − | 0.564725i | 0.655679 | − | 0.755040i | \(-0.272383\pi\) |
−0.981723 | + | 0.190315i | \(0.939049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 55.3289 | − | 338.915i | 0.239519 | − | 1.46717i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −218.934 | −0.939631 | −0.469816 | − | 0.882765i | \(-0.655680\pi\) | ||||
−0.469816 | + | 0.882765i | \(0.655680\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.92103i | 0.0209406i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.1816 | − | 26.9050i | −0.0429605 | − | 0.113523i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −218.254 | + | 126.009i | −0.913197 | + | 0.527235i | −0.881458 | − | 0.472262i | \(-0.843438\pi\) |
−0.0317388 | + | 0.999496i | \(0.510104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −226.014 | + | 391.467i | −0.937816 | + | 1.62435i | −0.168282 | + | 0.985739i | \(0.553822\pi\) |
−0.769534 | + | 0.638606i | \(0.779511\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 233.162 | + | 68.4445i | 0.959513 | + | 0.281664i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 115.925 | − | 200.787i | 0.473162 | − | 0.819540i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.23284 | − | 4.17588i | 0.0292828 | − | 0.0169064i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −90.2680 | − | 238.534i | −0.362522 | − | 0.957966i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 139.429i | − | 0.555492i | −0.960655 | − | 0.277746i | \(-0.910413\pi\) | ||
0.960655 | − | 0.277746i | \(-0.0895874\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −208.297 | −0.823306 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.6409 | − | 71.3058i | 0.0456505 | − | 0.279631i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 235.308 | + | 407.565i | 0.915594 | + | 1.58586i | 0.806029 | + | 0.591875i | \(0.201612\pi\) |
0.109564 | + | 0.993980i | \(0.465054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −408.308 | − | 235.737i | −1.57648 | − | 0.910181i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −173.665 | − | 58.2551i | −0.665381 | − | 0.223200i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.2028 | − | 12.8188i | −0.0844214 | − | 0.0487407i | 0.457195 | − | 0.889366i | \(-0.348854\pi\) |
−0.541616 | + | 0.840626i | \(0.682187\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.6141 | − | 49.5610i | −0.107978 | − | 0.187023i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −150.459 | − | 123.026i | −0.563517 | − | 0.460772i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.15075 | −0.0303002 | −0.0151501 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151501 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 401.979i | 1.48332i | 0.670777 | + | 0.741659i | \(0.265961\pi\) | ||||
−0.670777 | + | 0.741659i | \(0.734039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.0454 | − | 15.9543i | 0.0477852 | − | 0.0584405i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −150.826 | + | 87.0792i | −0.548457 | + | 0.316652i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −56.2021 | + | 97.3449i | −0.202896 | + | 0.351426i | −0.949460 | − | 0.313887i | \(-0.898369\pi\) |
0.746565 | + | 0.665313i | \(0.231702\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −98.6321 | − | 111.655i | −0.353520 | − | 0.400198i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 268.867 | − | 465.692i | 0.956823 | − | 1.65727i | 0.226681 | − | 0.973969i | \(-0.427212\pi\) |
0.730141 | − | 0.683296i | \(-0.239454\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −122.303 | + | 70.6114i | −0.432164 | + | 0.249510i | −0.700268 | − | 0.713880i | \(-0.746936\pi\) |
0.268104 | + | 0.963390i | \(0.413603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −113.217 | − | 18.4830i | −0.397253 | − | 0.0648528i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 492.113i | − | 1.71468i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −210.151 | −0.727167 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.1535 | − | 7.62667i | 0.0692561 | − | 0.0262085i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 230.291 | + | 398.875i | 0.785975 | + | 1.36135i | 0.928415 | + | 0.371545i | \(0.121172\pi\) |
−0.142440 | + | 0.989803i | \(0.545495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −207.991 | − | 120.084i | −0.705055 | − | 0.407064i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −225.556 | + | 141.953i | −0.759447 | + | 0.477958i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.8258 | − | 6.25029i | −0.0362068 | − | 0.0209040i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 215.849 | + | 373.862i | 0.717107 | + | 1.24206i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −311.466 | + | 117.868i | −1.02794 | + | 0.389002i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 197.948 | 0.649011 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 210.322i | − | 0.685089i | −0.939502 | − | 0.342545i | \(-0.888711\pi\) | ||
0.939502 | − | 0.342545i | \(-0.111289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 272.185 | + | 44.4351i | 0.880859 | + | 0.143803i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −110.993 | + | 64.0821i | −0.356892 | + | 0.206052i | −0.667717 | − | 0.744416i | \(-0.732728\pi\) |
0.310824 | + | 0.950467i | \(0.399395\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.62140 | + | 6.27245i | −0.0115700 | + | 0.0200398i | −0.871752 | − | 0.489947i | \(-0.837016\pi\) |
0.860182 | + | 0.509986i | \(0.170350\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −277.432 | + | 56.2233i | −0.880737 | + | 0.178487i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 120.145 | − | 208.098i | 0.379007 | − | 0.656460i | −0.611911 | − | 0.790927i | \(-0.709599\pi\) |
0.990918 | + | 0.134467i | \(0.0429322\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 173.980 | − | 100.447i | 0.545392 | − | 0.314882i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 204.602 | − | 250.224i | 0.637388 | − | 0.779515i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 125.194i | − | 0.387596i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.4518 | −0.0321595 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 201.023 | + | 164.371i | 0.614748 | + | 0.502662i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5207 | + | 18.2224i | 0.0319778 | + | 0.0553872i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 370.385 | + | 213.842i | 1.11899 | + | 0.646048i | 0.941142 | − | 0.338011i | \(-0.109754\pi\) |
0.177845 | + | 0.984058i | \(0.443087\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 72.6747 | + | 358.612i | 0.218242 | + | 1.07691i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 103.906 | + | 59.9904i | 0.310168 | + | 0.179076i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 152.442 | + | 264.037i | 0.452349 | + | 0.783492i | 0.998531 | − | 0.0541746i | \(-0.0172528\pi\) |
−0.546182 | + | 0.837666i | \(0.683919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.27371 | + | 13.9275i | −0.00670711 | + | 0.0410842i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 163.393 | 0.479157 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 423.102i | − | 1.23353i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 60.7712 | + | 160.588i | 0.176148 | + | 0.465473i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −146.406 | + | 84.5276i | −0.421919 | + | 0.243595i | −0.695898 | − | 0.718140i | \(-0.744994\pi\) |
0.273979 | + | 0.961736i | \(0.411660\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −107.298 | + | 185.846i | −0.307444 | + | 0.532509i | −0.977802 | − | 0.209529i | \(-0.932807\pi\) |
0.670358 | + | 0.742037i | \(0.266140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.9824 | + | 0.609584i | −0.0455339 | + | 0.00173671i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −275.895 | + | 477.865i | −0.781574 | + | 1.35373i | 0.149451 | + | 0.988769i | \(0.452249\pi\) |
−0.931025 | + | 0.364956i | \(0.881084\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 262.593 | − | 151.608i | 0.739698 | − | 0.427065i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −109.339 | − | 288.930i | −0.306272 | − | 0.809326i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 554.828i | 1.54548i | 0.634721 | + | 0.772741i | \(0.281115\pi\) | ||||
−0.634721 | + | 0.772741i | \(0.718885\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 162.222 | 0.449367 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.3930 | + | 69.7876i | −0.0313858 | + | 0.192252i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 103.334 | + | 178.980i | 0.283108 | + | 0.490357i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −145.642 | − | 84.0864i | −0.396845 | − | 0.229118i | 0.288277 | − | 0.957547i | \(-0.406918\pi\) |
−0.685122 | + | 0.728429i | \(0.740251\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −286.234 | + | 252.848i | −0.775702 | + | 0.685226i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −211.913 | − | 122.348i | −0.571195 | − | 0.329780i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −171.699 | − | 297.391i | −0.460318 | − | 0.797295i | 0.538658 | − | 0.842524i | \(-0.318931\pi\) |
−0.998977 | + | 0.0452296i | \(0.985598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 268.611 | + | 219.636i | 0.716296 | + | 0.585695i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0564 | 0.0319798 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 602.392i | 1.58943i | 0.606986 | + | 0.794713i | \(0.292379\pi\) | ||||
−0.606986 | + | 0.794713i | \(0.707621\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.8969 | + | 19.4417i | −0.0417242 | + | 0.0510280i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 315.762 | − | 182.305i | 0.824443 | − | 0.475992i | −0.0275035 | − | 0.999622i | \(-0.508756\pi\) |
0.851946 | + | 0.523630i | \(0.175422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 155.228 | − | 268.862i | 0.403189 | − | 0.698344i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 106.550 | − | 317.638i | 0.275324 | − | 0.820769i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −107.326 | + | 185.893i | −0.275901 | + | 0.477875i | −0.970362 | − | 0.241656i | \(-0.922310\pi\) |
0.694461 | + | 0.719530i | \(0.255643\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −162.280 | + | 93.6923i | −0.415038 | + | 0.239622i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 393.395 | + | 64.2229i | 1.00101 | + | 0.163417i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 26.0071i | − | 0.0658409i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 684.628 | 1.72450 | 0.862251 | − | 0.506480i | \(-0.169054\pi\) | ||||
0.862251 | + | 0.506480i | \(0.169054\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −458.754 | + | 173.606i | −1.14976 | + | 0.435102i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 95.1918 | + | 164.877i | 0.237386 | + | 0.411164i | 0.959963 | − | 0.280125i | \(-0.0903761\pi\) |
−0.722577 | + | 0.691290i | \(0.757043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.49203 | + | 4.90287i | 0.0210720 | + | 0.0121659i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 175.247 | + | 132.479i | 0.432708 | + | 0.327108i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −347.534 | − | 200.649i | −0.853892 | − | 0.492995i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 188.978 | + | 327.320i | 0.462049 | + | 0.800293i | 0.999063 | − | 0.0432806i | \(-0.0137809\pi\) |
−0.537014 | + | 0.843574i | \(0.680448\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −126.587 | + | 47.9040i | −0.307997 | + | 0.116555i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1026.91 | −2.48647 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 230.573i | − | 0.555598i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 446.991 | + | 72.9727i | 1.07192 | + | 0.174994i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −267.326 | + | 154.341i | −0.638009 | + | 0.368355i | −0.783847 | − | 0.620954i | \(-0.786745\pi\) |
0.145838 | + | 0.989308i | \(0.453412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −176.834 | + | 306.286i | −0.420034 | + | 0.727521i | −0.995942 | − | 0.0899938i | \(-0.971315\pi\) |
0.575908 | + | 0.817514i | \(0.304649\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.19337 | − | 15.4820i | 0.0122775 | − | 0.0366004i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −78.3369 | + | 135.684i | −0.184322 | + | 0.319255i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 732.995 | − | 423.195i | 1.71662 | − | 0.991088i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.1036 | − | 13.5796i | 0.0258826 | − | 0.0316540i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 472.777i | − | 1.09693i | −0.836174 | − | 0.548465i | \(-0.815213\pi\) | ||
0.836174 | − | 0.548465i | \(-0.184787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 61.4188 | 0.141845 | 0.0709224 | − | 0.997482i | \(-0.477406\pi\) | ||||
0.0709224 | + | 0.997482i | \(0.477406\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −128.200 | − | 104.826i | −0.294713 | − | 0.240978i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 148.762 | + | 257.663i | 0.340416 | + | 0.589618i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 354.347 | + | 204.582i | 0.807169 | + | 0.466019i | 0.845972 | − | 0.533228i | \(-0.179021\pi\) |
−0.0388030 | + | 0.999247i | \(0.512354\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −576.607 | + | 509.353i | −1.30750 | + | 1.15500i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −668.806 | − | 386.136i | −1.50972 | − | 0.871638i | −0.999936 | − | 0.0113360i | \(-0.996392\pi\) |
−0.509785 | − | 0.860302i | \(-0.670275\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −87.8536 | − | 152.167i | −0.197424 | − | 0.341948i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −69.0155 | + | 422.752i | −0.154397 | + | 0.945753i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −789.037 | −1.75732 | −0.878660 | − | 0.477448i | \(-0.841562\pi\) | ||||
−0.878660 | + | 0.477448i | \(0.841562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 418.865i | − | 0.928747i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 269.767 | + | 712.859i | 0.595511 | + | 1.57364i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.1354 | − | 9.31575i | 0.0354623 | − | 0.0204742i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 138.165 | − | 239.309i | 0.302331 | − | 0.523653i | −0.674332 | − | 0.738428i | \(-0.735568\pi\) |
0.976664 | + | 0.214775i | \(0.0689018\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −111.875 | + | 212.049i | −0.243737 | + | 0.461980i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 294.041 | − | 509.295i | 0.637834 | − | 1.10476i | −0.348073 | − | 0.937467i | \(-0.613164\pi\) |
0.985907 | − | 0.167293i | \(-0.0535027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 677.285 | − | 391.031i | 1.46282 | − | 0.844558i | 0.463677 | − | 0.886004i | \(-0.346530\pi\) |
0.999141 | + | 0.0414459i | \(0.0131964\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −47.6703 | − | 125.969i | −0.102517 | − | 0.270901i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 663.203i | 1.42014i | 0.704133 | + | 0.710068i | \(0.251336\pi\) | ||||
−0.704133 | + | 0.710068i | \(0.748664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 513.014 | 1.09385 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.56530 | + | 15.7136i | −0.00544649 | + | 0.0333623i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 183.721 | + | 318.214i | 0.388417 | + | 0.672758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 215.434 | + | 124.381i | 0.453546 | + | 0.261855i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 37.7184 | + | 186.121i | 0.0790743 | + | 0.390190i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −562.018 | − | 324.481i | −1.17331 | − | 0.677414i | −0.218856 | − | 0.975757i | \(-0.570233\pi\) |
−0.954459 | + | 0.298344i | \(0.903566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0416 | − | 20.8567i | −0.0250346 | − | 0.0433611i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 568.355 | + | 464.728i | 1.17672 | + | 0.962170i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 19.4810 | 0.0401669 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 282.104i | 0.579269i | 0.957137 | + | 0.289635i | \(0.0935338\pi\) | ||||
−0.957137 | + | 0.289635i | \(0.906466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 113.092 | − | 138.310i | 0.231272 | − | 0.282843i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 652.933 | − | 376.971i | 1.32980 | − | 0.767762i | 0.344534 | − | 0.938774i | \(-0.388037\pi\) |
0.985269 | + | 0.171012i | \(0.0547036\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 90.3630 | − | 156.513i | 0.183292 | − | 0.317471i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −236.138 | + | 47.8548i | −0.477047 | + | 0.0966763i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 648.247 | − | 1122.80i | 1.30432 | − | 2.25915i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −446.169 | + | 257.596i | −0.894126 | + | 0.516224i | −0.875290 | − | 0.483599i | \(-0.839329\pi\) |
−0.0188362 | + | 0.999823i | \(0.505996\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −293.143 | − | 47.8565i | −0.585116 | − | 0.0955220i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 523.660i | 1.04107i | 0.853839 | + | 0.520537i | \(0.174268\pi\) | ||||
−0.853839 | + | 0.520537i | \(0.825732\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −301.072 | −0.596182 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −473.198 | + | 179.072i | −0.933329 | + | 0.353198i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 267.685 | + | 463.645i | 0.525905 | + | 0.910893i | 0.999545 | + | 0.0301749i | \(0.00960643\pi\) |
−0.473640 | + | 0.880719i | \(0.657060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 765.285 | + | 441.838i | 1.49762 | + | 0.864653i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 336.684 | + | 177.632i | 0.656305 | + | 0.346261i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 215.925 | + | 124.665i | 0.419273 | + | 0.242067i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.95475 | + | 15.5101i | 0.0173206 | + | 0.0300002i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 108.285 | − | 40.9780i | 0.208641 | − | 0.0789557i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 177.268 | 0.340246 | 0.170123 | − | 0.985423i | \(-0.445584\pi\) | ||||
0.170123 | + | 0.985423i | \(0.445584\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 444.206i | − | 0.849343i | −0.905347 | − | 0.424672i | \(-0.860390\pi\) | ||
0.905347 | − | 0.424672i | \(-0.139610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 605.822 | + | 98.9023i | 1.15395 | + | 0.188385i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 127.296 | − | 73.4944i | 0.241548 | − | 0.139458i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.8394 | + | 72.4679i | −0.0790914 | + | 0.136990i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 527.628 | + | 597.295i | 0.993649 | + | 1.12485i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.5688 | − | 21.7697i | 0.0235812 | − | 0.0408438i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 253.065 | − | 146.107i | 0.473018 | − | 0.273097i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 69.1739 | − | 84.5986i | 0.128815 | − | 0.157539i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 843.787i | − | 1.56547i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −571.163 | −1.05575 | −0.527877 | − | 0.849321i | \(-0.677012\pi\) | ||||
−0.527877 | + | 0.849321i | \(0.677012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −43.1793 | − | 35.3065i | −0.0795198 | − | 0.0650211i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 117.378 | + | 203.304i | 0.215372 | + | 0.373036i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 139.875 | + | 80.7569i | 0.255713 | + | 0.147636i | 0.622377 | − | 0.782717i | \(-0.286167\pi\) |
−0.366664 | + | 0.930353i | \(0.619500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −622.762 | − | 208.903i | −1.13436 | − | 0.380515i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −248.507 | − | 143.476i | −0.451011 | − | 0.260391i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −55.6008 | − | 96.3034i | −0.100544 | − | 0.174147i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −53.2979 | + | 326.475i | −0.0960323 | + | 0.588242i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 568.917 | 1.02139 | 0.510697 | − | 0.859761i | \(-0.329387\pi\) | ||||
0.510697 | + | 0.859761i | \(0.329387\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.0515i | 0.0394481i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −93.0647 | − | 245.924i | −0.165891 | − | 0.438367i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 250.527 | − | 144.642i | 0.444985 | − | 0.256912i | −0.260725 | − | 0.965413i | \(-0.583962\pi\) |
0.705710 | + | 0.708501i | \(0.250628\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.37900 | + | 11.0487i | −0.0112903 | + | 0.0195553i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 932.159 | + | 115.903i | 1.64402 | + | 0.204414i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −223.117 | + | 386.450i | −0.392121 | + | 0.679174i | −0.992729 | − | 0.120370i | \(-0.961592\pi\) |
0.600608 | + | 0.799544i | \(0.294925\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 372.386 | − | 214.997i | 0.652164 | − | 0.376527i | −0.137121 | − | 0.990554i | \(-0.543785\pi\) |
0.789285 | + | 0.614027i | \(0.210451\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −300.351 | − | 793.680i | −0.524173 | − | 1.38513i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 372.337i | − | 0.647542i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 50.9694 | 0.0883353 | 0.0441676 | − | 0.999024i | \(-0.485936\pi\) | ||||
0.0441676 | + | 0.999024i | \(0.485936\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −146.499 | + | 897.374i | −0.253021 | + | 1.54987i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −492.943 | − | 853.803i | −0.848440 | − | 1.46954i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −180.371 | − | 104.137i | −0.309385 | − | 0.178623i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.7088 | − | 4.59856i | −0.0234339 | − | 0.00786079i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −643.771 | − | 371.681i | −1.09671 | − | 0.633188i | −0.161358 | − | 0.986896i | \(-0.551587\pi\) |
−0.935356 | + | 0.353708i | \(0.884921\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −116.692 | − | 202.117i | −0.198119 | − | 0.343152i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 323.249 | + | 264.312i | 0.546953 | + | 0.447228i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −382.547 | −0.645104 | −0.322552 | − | 0.946552i | \(-0.604541\pi\) | ||||
−0.322552 | + | 0.946552i | \(0.604541\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 279.287i | − | 0.469391i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −21.3328 | + | 26.0896i | −0.0357333 | + | 0.0437012i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −856.248 | + | 494.355i | −1.42946 | + | 0.825301i | −0.997078 | − | 0.0763888i | \(-0.975661\pi\) |
−0.432384 | + | 0.901689i | \(0.642328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −263.280 | + | 456.015i | −0.438070 | + | 0.758760i | −0.997541 | − | 0.0700905i | \(-0.977671\pi\) |
0.559470 | + | 0.828850i | \(0.311005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −263.587 | − | 298.391i | −0.437127 | − | 0.494844i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −31.9637 | + | 55.3627i | −0.0528325 | + | 0.0915086i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −447.631 | + | 258.440i | −0.737448 | + | 0.425766i | −0.821141 | − | 0.570726i | \(-0.806662\pi\) |
0.0836928 | + | 0.996492i | \(0.473329\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −698.826 | − | 114.085i | −1.14750 | − | 0.187332i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.07481i | 0.00175910i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −762.957 | −1.24463 | −0.622314 | − | 0.782768i | \(-0.713807\pi\) | ||||
−0.622314 | + | 0.782768i | \(0.713807\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −322.928 | + | 122.205i | −0.525086 | + | 0.198708i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 60.9168 | + | 105.511i | 0.0987307 | + | 0.171007i | 0.911160 | − | 0.412054i | \(-0.135188\pi\) |
−0.812429 | + | 0.583060i | \(0.801855\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 265.675 | + | 153.388i | 0.429200 | + | 0.247799i | 0.699006 | − | 0.715116i | \(-0.253626\pi\) |
−0.269806 | + | 0.962915i | \(0.586959\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.7158 | − | 569.357i | −0.0349692 | − | 0.916839i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −650.636 | − | 375.645i | −1.04436 | − | 0.602961i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −63.7082 | − | 110.346i | −0.101933 | − | 0.176553i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −390.471 | + | 147.765i | −0.622760 | + | 0.235670i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −361.010 | −0.573942 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1071.11i | − | 1.69749i | −0.528805 | − | 0.848744i | \(-0.677360\pi\) | ||
0.528805 | − | 0.848744i | \(-0.322640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 382.967 | + | 62.5205i | 0.605003 | + | 0.0987685i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.6623 | + | 11.3521i | −0.0309643 | + | 0.0178773i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 25.3193 | − | 43.8543i | 0.0397477 | − | 0.0688450i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −986.136 | + | 199.846i | −1.54325 | + | 0.312748i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 527.259 | − | 913.240i | 0.822557 | − | 1.42471i | −0.0812143 | − | 0.996697i | \(-0.525880\pi\) |
0.903772 | − | 0.428015i | \(-0.140787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.0680 | + | 24.2880i | −0.0654246 | + | 0.0377729i | −0.532355 | − | 0.846521i | \(-0.678693\pi\) |
0.466931 | + | 0.884294i | \(0.345360\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 191.729 | − | 234.482i | 0.297254 | − | 0.363537i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 539.373i | − | 0.833653i | −0.908986 | − | 0.416826i | \(-0.863142\pi\) | ||
0.908986 | − | 0.416826i | \(-0.136858\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −874.061 | −1.34678 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −445.831 | − | 364.543i | −0.684840 | − | 0.559974i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 276.457 | + | 478.838i | 0.423365 | + | 0.733290i | 0.996266 | − | 0.0863348i | \(-0.0275155\pi\) |
−0.572901 | + | 0.819624i | \(0.694182\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 312.081 | + | 180.180i | 0.476460 | + | 0.275084i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −136.213 | − | 672.139i | −0.207326 | − | 1.02304i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −734.162 | − | 423.869i | −1.11406 | − | 0.643200i | −0.174178 | − | 0.984714i | \(-0.555727\pi\) |
−0.939877 | + | 0.341514i | \(0.889060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 359.447 | + | 622.580i | 0.543792 | + | 0.941876i | 0.998682 | + | 0.0513280i | \(0.0163454\pi\) |
−0.454890 | + | 0.890548i | \(0.650321\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.54250 | − | 15.5740i | 0.00383485 | − | 0.0234902i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −443.444 | −0.666833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 429.497i | 0.643923i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −256.504 | − | 677.812i | −0.383414 | − | 1.01317i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 623.893 | − | 360.205i | 0.929796 | − | 0.536818i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 288.488 | − | 499.675i | 0.428659 | − | 0.742460i | −0.568095 | − | 0.822963i | \(-0.692319\pi\) |
0.996754 | + | 0.0805033i | \(0.0256528\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −253.746 | − | 403.188i | −0.375921 | − | 0.597316i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 101.021 | − | 174.974i | 0.149219 | − | 0.258454i | −0.781720 | − | 0.623629i | \(-0.785657\pi\) |
0.930939 | + | 0.365175i | \(0.118991\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.1372 | − | 41.6484i | 0.106240 | − | 0.0613379i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −405.471 | − | 1071.46i | −0.595405 | − | 1.57336i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 568.249i | − | 0.831990i | −0.909367 | − | 0.415995i | \(-0.863433\pi\) | ||
0.909367 | − | 0.415995i | \(-0.136567\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −122.362 | −0.178631 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −72.1793 | + | 442.132i | −0.105065 | + | 0.643569i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.24965 | − | 10.8247i | −0.00907060 | − | 0.0157107i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −351.376 | − | 202.867i | −0.508504 | − | 0.293585i | 0.223714 | − | 0.974655i | \(-0.428182\pi\) |
−0.732218 | + | 0.681070i | \(0.761515\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −772.100 | + | 682.045i | −1.11414 | + | 0.984191i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 354.600 | + | 204.728i | 0.510215 | + | 0.294573i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −188.407 | − | 326.330i | −0.270311 | − | 0.468192i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 508.464 | + | 415.757i | 0.727416 | + | 0.594788i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −83.5164 | −0.119139 | −0.0595695 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595695 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 573.200i | 0.815363i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.34506 | − | 11.4289i | 0.0132554 | − | 0.0162112i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1114.86 | + | 643.663i | −1.57688 | + | 0.910414i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 173.908 | − | 301.217i | 0.245286 | − | 0.424848i | −0.716926 | − | 0.697149i | \(-0.754452\pi\) |
0.962212 | + | 0.272302i | \(0.0877849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.4464 | + | 81.8205i | −0.0386025 | + | 0.115078i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −174.660 | + | 302.520i | −0.244965 | + | 0.424292i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.7337 | − | 7.92916i | 0.0192080 | − | 0.0110897i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 746.177 | + | 121.816i | 1.04069 | + | 0.169896i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 536.277i | − | 0.745865i | −0.927858 | − | 0.372933i | \(-0.878352\pi\) | ||
0.927858 | − | 0.372933i | \(-0.121648\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1066.08 | 1.47862 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1268.30 | − | 479.963i | 1.75422 | − | 0.663849i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 179.553 | + | 310.995i | 0.247659 | + | 0.428959i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −815.055 | − | 470.573i | −1.12112 | − | 0.647280i | −0.179435 | − | 0.983770i | \(-0.557427\pi\) |
−0.941687 | + | 0.336490i | \(0.890760\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −411.530 | − | 601.734i | −0.564514 | − | 0.825424i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 286.267 | + | 165.277i | 0.391611 | + | 0.226096i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −311.063 | − | 538.777i | −0.424370 | − | 0.735030i | 0.571991 | − | 0.820260i | \(-0.306171\pi\) |
−0.996361 | + | 0.0852294i | \(0.972838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −650.525 | + | 246.178i | −0.885068 | + | 0.334935i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 436.655 | 0.592477 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 444.439i | − | 0.601406i | −0.953718 | − | 0.300703i | \(-0.902779\pi\) | ||
0.953718 | − | 0.300703i | \(-0.0972213\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.7279 | − | 4.03691i | −0.0333710 | − | 0.00544792i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 66.2270 | − | 38.2362i | 0.0891346 | − | 0.0514619i | −0.454770 | − | 0.890609i | \(-0.650279\pi\) |
0.543905 | + | 0.839147i | \(0.316945\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −193.626 | + | 335.370i | −0.259901 | + | 0.450161i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −243.333 | + | 725.402i | −0.325747 | + | 0.971087i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 624.725 | − | 1082.06i | 0.834079 | − | 1.44467i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 949.025 | − | 547.920i | 1.26368 | − | 0.729587i | 0.289897 | − | 0.957058i | \(-0.406379\pi\) |
0.973785 | + | 0.227471i | \(0.0730457\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −264.775 | + | 323.816i | −0.351627 | + | 0.430034i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 689.070i | 0.912676i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 346.346 | 0.457525 | 0.228762 | − | 0.973482i | \(-0.426532\pi\) | ||||
0.228762 | + | 0.973482i | \(0.426532\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 483.759 | + | 395.556i | 0.637363 | + | 0.521154i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −106.565 | − | 184.576i | −0.140033 | − | 0.242544i | 0.787476 | − | 0.616345i | \(-0.211387\pi\) |
−0.927509 | + | 0.373802i | \(0.878054\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 869.291 | + | 501.885i | 1.13931 | + | 0.657779i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −162.445 | + | 143.498i | −0.212347 | + | 0.187579i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.4277 | − | 26.2277i | −0.0592277 | − | 0.0341952i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −270.786 | − | 469.015i | −0.352127 | − | 0.609902i | 0.634495 | − | 0.772927i | \(-0.281208\pi\) |
−0.986622 | + | 0.163025i | \(0.947875\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 227.477 | − | 1393.40i | 0.295041 | − | 1.80726i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1255.73 | −1.62449 | −0.812245 | − | 0.583317i | \(-0.801755\pi\) | ||||
−0.812245 | + | 0.583317i | \(0.801755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 292.070i | 0.376864i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 500.611 | + | 1322.87i | 0.644287 | + | 1.70253i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −518.136 | + | 299.146i | −0.665130 | + | 0.384013i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 551.759 | − | 955.675i | 0.706478 | − | 1.22366i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 292.701 | + | 465.084i | 0.373820 | + | 0.593977i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.19706 | + | 12.4657i | −0.00916822 | + | 0.0158798i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 859.448 | − | 496.202i | 1.09206 | − | 0.630499i | 0.157933 | − | 0.987450i | \(-0.449517\pi\) |
0.934123 | + | 0.356951i | \(0.116184\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.2220 | + | 71.9343i | 0.0345019 | + | 0.0911715i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 54.5507i | 0.0689643i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.2342 | 0.0545198 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −27.6618 | + | 169.441i | −0.0347947 | + | 0.213134i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −319.262 | − | 552.978i | −0.400580 | − | 0.693824i | 0.593216 | − | 0.805043i | \(-0.297858\pi\) |
−0.993796 | + | 0.111219i | \(0.964525\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.9530 | + | 8.05574i | 0.0174630 | + | 0.0100823i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 115.807 | + | 571.445i | 0.144577 | + | 0.713414i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 651.377 | + | 376.073i | 0.811179 | + | 0.468335i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 331.865 | + | 574.806i | 0.412254 | + | 0.714045i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.9297 | + | 15.4783i | 0.0234569 | + | 0.0191801i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −174.260 | −0.215401 | −0.107701 | − | 0.994183i | \(-0.534349\pi\) | ||||
−0.107701 | + | 0.994183i | \(0.534349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1182.19i | 1.45770i | 0.684675 | + | 0.728849i | \(0.259944\pi\) | ||||
−0.684675 | + | 0.728849i | \(0.740056\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 763.360 | − | 933.577i | 0.938942 | − | 1.14831i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 139.880 | − | 80.7597i | 0.171632 | − | 0.0990917i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 262.421 | − | 454.527i | 0.321201 | − | 0.556336i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −60.5944 | + | 12.2798i | −0.0739858 | + | 0.0149937i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −293.955 | + | 509.144i | −0.358045 | + | 0.620151i | −0.987634 | − | 0.156777i | \(-0.949890\pi\) |
0.629590 | + | 0.776928i | \(0.283223\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −98.0750 | + | 56.6236i | −0.119168 | + | 0.0688015i | −0.558399 | − | 0.829573i | \(-0.688584\pi\) |
0.439231 | + | 0.898374i | \(0.355251\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 515.649 | + | 84.1813i | 0.625029 | + | 0.102038i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 800.560i | − | 0.968030i | −0.875060 | − | 0.484015i | \(-0.839178\pi\) | ||
0.875060 | − | 0.484015i | \(-0.160822\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1162.87 | −1.40274 | −0.701369 | − | 0.712798i | \(-0.747427\pi\) | ||||
−0.701369 | + | 0.712798i | \(0.747427\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 315.385 | − | 119.351i | 0.379525 | − | 0.143623i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −379.538 | − | 657.378i | −0.455627 | − | 0.789170i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −232.551 | − | 134.264i | −0.278505 | − | 0.160795i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.0344 | + | 446.617i | 0.0203517 | + | 0.533592i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1355.92 | + | 782.842i | 1.61612 | + | 0.933065i | 0.987912 | + | 0.155017i | \(0.0495432\pi\) |
0.628205 | + | 0.778048i | \(0.283790\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 213.383 | + | 369.590i | 0.253725 | + | 0.439464i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1508.78 | + | 570.966i | −1.78978 | + | 0.677303i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −457.406 | −0.541309 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 273.341i | 0.322717i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 418.133 | + | 68.2615i | 0.492501 | + | 0.0804022i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 743.000 | − | 428.971i | 0.873091 | − | 0.504079i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 68.8088 | − | 119.180i | 0.0806668 | − | 0.139719i | −0.822870 | − | 0.568230i | \(-0.807628\pi\) |
0.903537 | + | 0.428511i | \(0.140962\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 227.842 | + | 257.926i | 0.266482 | + | 0.301668i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −384.489 | + | 665.955i | −0.448646 | + | 0.777077i | −0.998298 | − | 0.0583164i | \(-0.981427\pi\) |
0.549653 | + | 0.835393i | \(0.314760\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 178.353 | − | 102.972i | 0.207629 | − | 0.119875i | −0.392580 | − | 0.919718i | \(-0.628417\pi\) |
0.600209 | + | 0.799843i | \(0.295084\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −934.525 | + | 1142.91i | −1.08540 | + | 1.32742i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 772.757i | 0.895431i | 0.894176 | + | 0.447716i | \(0.147762\pi\) | ||||
−0.894176 | + | 0.447716i | \(0.852238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 104.671 | 0.121007 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 488.066 | + | 399.078i | 0.562937 | + | 0.460298i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −47.3249 | − | 81.9692i | −0.0544591 | − | 0.0943258i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.6943 | + | 13.1026i | 0.0260555 | + | 0.0150432i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −61.2887 | − | 20.5590i | −0.0702047 | − | 0.0235499i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1161.57 | + | 670.630i | 1.32750 | + | 0.766435i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 200.096 | + | 346.577i | 0.228160 | + | 0.395185i | 0.957263 | − | 0.289219i | \(-0.0933957\pi\) |
−0.729103 | + | 0.684404i | \(0.760062\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 222.627 | − | 1363.69i | 0.253273 | − | 1.55141i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −728.323 | −0.826700 | −0.413350 | − | 0.910572i | \(-0.635641\pi\) | ||||
−0.413350 | + | 0.910572i | \(0.635641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 383.413i | − | 0.434216i | −0.976148 | − | 0.217108i | \(-0.930338\pi\) | ||
0.976148 | − | 0.217108i | \(-0.0696625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 255.010 | + | 673.865i | 0.288147 | + | 0.761429i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1255.91 | + | 725.098i | −1.41590 | + | 0.817473i | −0.995936 | − | 0.0900662i | \(-0.971292\pi\) |
−0.419968 | + | 0.907539i | \(0.637959\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −48.5392 | + | 84.0724i | −0.0545998 | + | 0.0945696i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793.412 | + | 98.6511i | 0.890474 | + | 0.110720i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.7907 | − | 22.1541i | 0.0143232 | − | 0.0248086i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 85.5589 | − | 49.3974i | 0.0955965 | − | 0.0551927i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.2731 | + | 35.0743i | 0.0147972 | + | 0.0391018i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 336.907i | − | 0.374758i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −187.365 | −0.207952 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 208.666 | − | 1278.17i | 0.231080 | − | 1.41547i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.2125 | − | 43.6694i | −0.0278592 | − | 0.0482535i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −533.290 | − | 307.895i | −0.587971 | − | 0.339465i | 0.176324 | − | 0.984332i | \(-0.443580\pi\) |
−0.764295 | + | 0.644867i | \(0.776913\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 947.196 | + | 317.733i | 1.04202 | + | 0.349541i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −227.031 | − | 131.076i | −0.249211 | − | 0.143882i | 0.370192 | − | 0.928955i | \(-0.379292\pi\) |
−0.619403 | + | 0.785073i | \(0.712625\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −419.572 | − | 726.720i | −0.459553 | − | 0.795969i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −459.726 | − | 375.905i | −0.502433 | − | 0.410825i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1540.83 | 1.68030 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 566.458i | − | 0.616385i | −0.951324 | − | 0.308193i | \(-0.900276\pi\) | ||
0.951324 | − | 0.308193i | \(-0.0997241\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −399.403 | + | 488.464i | −0.433663 | + | 0.530362i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 57.3533 | − | 33.1130i | 0.0621379 | − | 0.0358754i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 358.667 | − | 621.229i | 0.387748 | − | 0.671599i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −547.755 | − | 620.080i | −0.590890 | − | 0.668910i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 298.745 | − | 517.442i | 0.321577 | − | 0.556988i | −0.659236 | − | 0.751936i | \(-0.729120\pi\) |
0.980814 | + | 0.194948i | \(0.0624537\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1043.77 | + | 602.618i | −1.12112 | + | 0.647281i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 379.469 | + | 61.9495i | 0.406719 | + | 0.0663982i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 237.717i | − | 0.254243i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 457.785 | 0.488564 | 0.244282 | − | 0.969704i | \(-0.421448\pi\) | ||||
0.244282 | + | 0.969704i | \(0.421448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.3220 | − | 7.69041i | 0.0216421 | − | 0.00819000i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 677.858 | + | 1174.09i | 0.720360 | + | 1.24770i | 0.960856 | + | 0.277049i | \(0.0893566\pi\) |
−0.240496 | + | 0.970650i | \(0.577310\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 775.526 | + | 447.750i | 0.822403 | + | 0.474814i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 751.091 | + | 396.269i | 0.794805 | + | 0.419332i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −567.925 | − | 327.891i | −0.599709 | − | 0.346242i | 0.169218 | − | 0.985579i | \(-0.445876\pi\) |
−0.768927 | + | 0.639336i | \(0.779209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.5694 | + | 39.0914i | 0.0237823 | + | 0.0411922i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −674.210 | + | 255.141i | −0.708949 | + | 0.268287i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 554.778 | 0.582139 | 0.291069 | − | 0.956702i | \(-0.405989\pi\) | ||||
0.291069 | + | 0.956702i | \(0.405989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 767.193i | − | 0.803344i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −594.810 | − | 97.1045i | −0.621536 | − | 0.101468i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −453.102 | + | 261.599i | −0.472474 | + | 0.272783i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −343.493 | + | 594.947i | −0.357432 | + | 0.619091i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −950.354 | + | 192.595i | −0.986869 | + | 0.199995i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −411.009 | + | 711.889i | −0.425917 | + | 0.737709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −502.000 | + | 289.830i | −0.519131 | + | 0.299720i | −0.736579 | − | 0.676351i | \(-0.763560\pi\) |
0.217448 | + | 0.976072i | \(0.430227\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −237.743 | + | 290.756i | −0.245349 | + | 0.300058i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 260.660i | 0.268445i | 0.990951 | + | 0.134223i | \(0.0428537\pi\) | ||||
−0.990951 | + | 0.134223i | \(0.957146\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1750.76 | 1.79934 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 24.2739 | + | 19.8481i | 0.0248963 | + | 0.0203570i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 638.953 | + | 1106.70i | 0.653995 | + | 1.13275i | 0.982145 | + | 0.188127i | \(0.0602417\pi\) |
−0.328149 | + | 0.944626i | \(0.606425\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −553.793 | − | 319.732i | −0.565672 | − | 0.326591i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −154.725 | − | 763.486i | −0.157721 | − | 0.778273i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −378.325 | − | 218.426i | −0.384868 | − | 0.222204i | 0.295066 | − | 0.955477i | \(-0.404658\pi\) |
−0.679934 | + | 0.733273i | \(0.737992\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 188.746 | + | 326.918i | 0.191621 | + | 0.331897i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1706 | − | 62.2994i | 0.0103045 | − | 0.0631200i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −785.562 | −0.794300 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1344.50i | 1.35671i | 0.734734 | + | 0.678356i | \(0.237307\pi\) | ||||
−0.734734 | + | 0.678356i | \(0.762693\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −454.114 | − | 1200.00i | −0.457316 | − | 1.20846i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.3858 | + | 15.2338i | −0.0265184 | + | 0.0153104i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −942.397 | + | 1632.28i | −0.945233 | + | 1.63719i | −0.189949 | + | 0.981794i | \(0.560832\pi\) |
−0.755284 | + | 0.655398i | \(0.772501\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 512.221 | − | 970.868i | 0.512734 | − | 0.971839i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 576.3.o.g.511.3 | 16 | ||
3.2 | odd | 2 | 1728.3.o.g.127.5 | 16 | |||
4.3 | odd | 2 | inner | 576.3.o.g.511.6 | 16 | ||
8.3 | odd | 2 | 36.3.f.c.7.7 | yes | 16 | ||
8.5 | even | 2 | 36.3.f.c.7.6 | ✓ | 16 | ||
9.4 | even | 3 | inner | 576.3.o.g.319.6 | 16 | ||
9.5 | odd | 6 | 1728.3.o.g.1279.6 | 16 | |||
12.11 | even | 2 | 1728.3.o.g.127.6 | 16 | |||
24.5 | odd | 2 | 108.3.f.c.19.3 | 16 | |||
24.11 | even | 2 | 108.3.f.c.19.2 | 16 | |||
36.23 | even | 6 | 1728.3.o.g.1279.5 | 16 | |||
36.31 | odd | 6 | inner | 576.3.o.g.319.3 | 16 | ||
72.5 | odd | 6 | 108.3.f.c.91.2 | 16 | |||
72.11 | even | 6 | 324.3.d.g.163.8 | 8 | |||
72.13 | even | 6 | 36.3.f.c.31.7 | yes | 16 | ||
72.29 | odd | 6 | 324.3.d.g.163.7 | 8 | |||
72.43 | odd | 6 | 324.3.d.i.163.1 | 8 | |||
72.59 | even | 6 | 108.3.f.c.91.3 | 16 | |||
72.61 | even | 6 | 324.3.d.i.163.2 | 8 | |||
72.67 | odd | 6 | 36.3.f.c.31.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
36.3.f.c.7.6 | ✓ | 16 | 8.5 | even | 2 | ||
36.3.f.c.7.7 | yes | 16 | 8.3 | odd | 2 | ||
36.3.f.c.31.6 | yes | 16 | 72.67 | odd | 6 | ||
36.3.f.c.31.7 | yes | 16 | 72.13 | even | 6 | ||
108.3.f.c.19.2 | 16 | 24.11 | even | 2 | |||
108.3.f.c.19.3 | 16 | 24.5 | odd | 2 | |||
108.3.f.c.91.2 | 16 | 72.5 | odd | 6 | |||
108.3.f.c.91.3 | 16 | 72.59 | even | 6 | |||
324.3.d.g.163.7 | 8 | 72.29 | odd | 6 | |||
324.3.d.g.163.8 | 8 | 72.11 | even | 6 | |||
324.3.d.i.163.1 | 8 | 72.43 | odd | 6 | |||
324.3.d.i.163.2 | 8 | 72.61 | even | 6 | |||
576.3.o.g.319.3 | 16 | 36.31 | odd | 6 | inner | ||
576.3.o.g.319.6 | 16 | 9.4 | even | 3 | inner | ||
576.3.o.g.511.3 | 16 | 1.1 | even | 1 | trivial | ||
576.3.o.g.511.6 | 16 | 4.3 | odd | 2 | inner | ||
1728.3.o.g.127.5 | 16 | 3.2 | odd | 2 | |||
1728.3.o.g.127.6 | 16 | 12.11 | even | 2 | |||
1728.3.o.g.1279.5 | 16 | 36.23 | even | 6 | |||
1728.3.o.g.1279.6 | 16 | 9.5 | odd | 6 |