Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [117,5,Mod(73,117)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(117, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("117.73");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 117 = 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 117.j (of order \(4\), degree \(2\), 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: | \(12.0942856808\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{10} \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 73.3 | ||
Root | \(-2.89776 - 2.89776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.73 |
Dual form | 117.5.j.b.109.3 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.89776 | − | 2.89776i | −0.724440 | − | 0.724440i | 0.245066 | − | 0.969506i | \(-0.421190\pi\) |
−0.969506 | + | 0.245066i | \(0.921190\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.794047i | 0.0496279i | ||||||||
\(5\) | −18.6373 | − | 18.6373i | −0.745491 | − | 0.745491i | 0.228138 | − | 0.973629i | \(-0.426736\pi\) |
−0.973629 | + | 0.228138i | \(0.926736\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.2549 | + | 15.2549i | −0.311324 | + | 0.311324i | −0.845422 | − | 0.534098i | \(-0.820651\pi\) |
0.534098 | + | 0.845422i | \(0.320651\pi\) | |||||||
\(8\) | −44.0632 | + | 44.0632i | −0.688488 | + | 0.688488i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 108.013i | 1.08013i | ||||||||
\(11\) | 59.2741 | − | 59.2741i | 0.489869 | − | 0.489869i | −0.418396 | − | 0.908265i | \(-0.637408\pi\) |
0.908265 | + | 0.418396i | \(0.137408\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −157.156 | − | 62.1541i | −0.929915 | − | 0.367776i | ||||
\(14\) | 88.4101 | 0.451072 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 268.074 | 1.04717 | ||||||||
\(17\) | 272.906i | 0.944312i | 0.881515 | + | 0.472156i | \(0.156524\pi\) | ||||
−0.881515 | + | 0.472156i | \(0.843476\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −54.5892 | − | 54.5892i | −0.151217 | − | 0.151217i | 0.627445 | − | 0.778661i | \(-0.284101\pi\) |
−0.778661 | + | 0.627445i | \(0.784101\pi\) | |||||||
\(20\) | 14.7989 | − | 14.7989i | 0.0369972 | − | 0.0369972i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −343.524 | −0.709761 | ||||||||
\(23\) | 596.223i | 1.12708i | 0.826090 | + | 0.563538i | \(0.190560\pi\) | ||||
−0.826090 | + | 0.563538i | \(0.809440\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 69.6962i | 0.111514i | ||||||||
\(26\) | 275.292 | + | 635.507i | 0.407236 | + | 0.940099i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −12.1131 | − | 12.1131i | −0.0154504 | − | 0.0154504i | ||||
\(29\) | 1314.18 | 1.56263 | 0.781317 | − | 0.624135i | \(-0.214548\pi\) | ||||
0.781317 | + | 0.624135i | \(0.214548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 874.924 | + | 874.924i | 0.910431 | + | 0.910431i | 0.996306 | − | 0.0858748i | \(-0.0273685\pi\) |
−0.0858748 | + | 0.996306i | \(0.527368\pi\) | |||||||
\(32\) | −71.8036 | − | 71.8036i | −0.0701207 | − | 0.0701207i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 790.817 | − | 790.817i | 0.684098 | − | 0.684098i | ||||
\(35\) | 568.619 | 0.464179 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −403.847 | + | 403.847i | −0.294994 | + | 0.294994i | −0.839049 | − | 0.544055i | \(-0.816888\pi\) |
0.544055 | + | 0.839049i | \(0.316888\pi\) | |||||||
\(38\) | 316.373i | 0.219095i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1642.44 | 1.02652 | ||||||||
\(41\) | −983.966 | − | 983.966i | −0.585346 | − | 0.585346i | 0.351022 | − | 0.936367i | \(-0.385834\pi\) |
−0.936367 | + | 0.351022i | \(0.885834\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2237.13i | 1.20991i | 0.796258 | + | 0.604957i | \(0.206810\pi\) | ||||
−0.796258 | + | 0.604957i | \(0.793190\pi\) | |||||||
\(44\) | 47.0664 | + | 47.0664i | 0.0243112 | + | 0.0243112i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1727.71 | − | 1727.71i | 0.816500 | − | 0.816500i | ||||
\(47\) | 369.867 | − | 369.867i | 0.167437 | − | 0.167437i | −0.618415 | − | 0.785852i | \(-0.712225\pi\) |
0.785852 | + | 0.618415i | \(0.212225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1935.58i | 0.806154i | ||||||||
\(50\) | 201.963 | − | 201.963i | 0.0807852 | − | 0.0807852i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 49.3532 | − | 124.789i | 0.0182519 | − | 0.0461497i | ||||
\(53\) | −4399.13 | −1.56608 | −0.783041 | − | 0.621970i | \(-0.786333\pi\) | ||||
−0.783041 | + | 0.621970i | \(0.786333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2209.42 | −0.730385 | ||||||||
\(56\) | − | 1344.36i | − | 0.428686i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3808.17 | − | 3808.17i | −1.13204 | − | 1.13204i | ||||
\(59\) | −976.401 | + | 976.401i | −0.280495 | + | 0.280495i | −0.833306 | − | 0.552812i | \(-0.813555\pi\) |
0.552812 | + | 0.833306i | \(0.313555\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6163.60 | −1.65644 | −0.828219 | − | 0.560405i | \(-0.810646\pi\) | ||||
−0.828219 | + | 0.560405i | \(0.810646\pi\) | |||||||
\(62\) | − | 5070.64i | − | 1.31911i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 3873.05i | − | 0.945568i | ||||||
\(65\) | 1770.57 | + | 4087.33i | 0.419070 | + | 0.967416i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1708.57 | − | 1708.57i | −0.380612 | − | 0.380612i | 0.490711 | − | 0.871322i | \(-0.336737\pi\) |
−0.871322 | + | 0.490711i | \(0.836737\pi\) | |||||||
\(68\) | −216.700 | −0.0468642 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1647.72 | − | 1647.72i | −0.336270 | − | 0.336270i | ||||
\(71\) | −672.586 | − | 672.586i | −0.133423 | − | 0.133423i | 0.637241 | − | 0.770664i | \(-0.280075\pi\) |
−0.770664 | + | 0.637241i | \(0.780075\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1169.63 | + | 1169.63i | −0.219485 | + | 0.219485i | −0.808281 | − | 0.588797i | \(-0.799602\pi\) |
0.588797 | + | 0.808281i | \(0.299602\pi\) | |||||||
\(74\) | 2340.51 | 0.427412 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 43.3464 | − | 43.3464i | 0.00750457 | − | 0.00750457i | ||||
\(77\) | 1808.44i | 0.305016i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8345.50 | 1.33720 | 0.668602 | − | 0.743620i | \(-0.266893\pi\) | ||||
0.668602 | + | 0.743620i | \(0.266893\pi\) | |||||||
\(80\) | −4996.17 | − | 4996.17i | −0.780652 | − | 0.780652i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5702.60i | 0.848096i | ||||||||
\(83\) | −6513.68 | − | 6513.68i | −0.945519 | − | 0.945519i | 0.0530714 | − | 0.998591i | \(-0.483099\pi\) |
−0.998591 | + | 0.0530714i | \(0.983099\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5086.23 | − | 5086.23i | 0.703976 | − | 0.703976i | ||||
\(86\) | 6482.67 | − | 6482.67i | 0.876510 | − | 0.876510i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5223.62i | 0.674537i | ||||||||
\(89\) | −8366.65 | + | 8366.65i | −1.05626 | + | 1.05626i | −0.0579425 | + | 0.998320i | \(0.518454\pi\) |
−0.998320 | + | 0.0579425i | \(0.981546\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3345.55 | − | 1449.24i | 0.404003 | − | 0.175008i | ||||
\(92\) | −473.429 | −0.0559345 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2143.57 | −0.242596 | ||||||||
\(95\) | 2034.79i | 0.225461i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2271.58 | + | 2271.58i | 0.241426 | + | 0.241426i | 0.817440 | − | 0.576014i | \(-0.195393\pi\) |
−0.576014 | + | 0.817440i | \(0.695393\pi\) | |||||||
\(98\) | 5608.84 | − | 5608.84i | 0.584011 | − | 0.584011i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −55.3421 | −0.00553421 | ||||||||
\(101\) | 6490.97i | 0.636308i | 0.948039 | + | 0.318154i | \(0.103063\pi\) | ||||
−0.948039 | + | 0.318154i | \(0.896937\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5614.96i | 0.529264i | 0.964350 | + | 0.264632i | \(0.0852504\pi\) | ||||
−0.964350 | + | 0.264632i | \(0.914750\pi\) | |||||||
\(104\) | 9663.49 | − | 4186.07i | 0.893444 | − | 0.387026i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12747.6 | + | 12747.6i | 1.13453 | + | 1.13453i | ||||
\(107\) | −9686.14 | −0.846025 | −0.423012 | − | 0.906124i | \(-0.639027\pi\) | ||||
−0.423012 | + | 0.906124i | \(0.639027\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16372.1 | − | 16372.1i | −1.37801 | − | 1.37801i | −0.847980 | − | 0.530029i | \(-0.822181\pi\) |
−0.530029 | − | 0.847980i | \(-0.677819\pi\) | |||||||
\(110\) | 6402.36 | + | 6402.36i | 0.529121 | + | 0.529121i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4089.44 | + | 4089.44i | −0.326008 | + | 0.326008i | ||||
\(113\) | 19245.1 | 1.50717 | 0.753585 | − | 0.657350i | \(-0.228323\pi\) | ||||
0.753585 | + | 0.657350i | \(0.228323\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11112.0 | − | 11112.0i | 0.840225 | − | 0.840225i | ||||
\(116\) | 1043.52i | 0.0775503i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5658.76 | 0.406403 | ||||||||
\(119\) | −4163.15 | − | 4163.15i | −0.293987 | − | 0.293987i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7614.16i | 0.520057i | ||||||||
\(122\) | 17860.7 | + | 17860.7i | 1.19999 | + | 1.19999i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −694.731 | + | 694.731i | −0.0451828 | + | 0.0451828i | ||||
\(125\) | −10349.4 | + | 10349.4i | −0.662358 | + | 0.662358i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 26337.0i | 1.63290i | 0.577417 | + | 0.816449i | \(0.304061\pi\) | ||||
−0.577417 | + | 0.816449i | \(0.695939\pi\) | |||||||
\(128\) | −12372.0 | + | 12372.0i | −0.755129 | + | 0.755129i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6713.43 | − | 16974.8i | 0.397245 | − | 1.00443i | ||||
\(131\) | 3094.41 | 0.180316 | 0.0901581 | − | 0.995927i | \(-0.471263\pi\) | ||||
0.0901581 | + | 0.995927i | \(0.471263\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1665.51 | 0.0941549 | ||||||||
\(134\) | 9902.03i | 0.551461i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12025.1 | − | 12025.1i | −0.650147 | − | 0.650147i | ||||
\(137\) | 10453.9 | − | 10453.9i | 0.556978 | − | 0.556978i | −0.371467 | − | 0.928446i | \(-0.621145\pi\) |
0.928446 | + | 0.371467i | \(0.121145\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5922.48 | 0.306531 | 0.153265 | − | 0.988185i | \(-0.451021\pi\) | ||||
0.153265 | + | 0.988185i | \(0.451021\pi\) | |||||||
\(140\) | 451.511i | 0.0230363i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3897.99i | 0.193314i | ||||||||
\(143\) | −12999.4 | + | 5631.13i | −0.635698 | + | 0.275374i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24492.6 | − | 24492.6i | −1.16493 | − | 1.16493i | ||||
\(146\) | 6778.64 | 0.318007 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −320.674 | − | 320.674i | −0.0146400 | − | 0.0146400i | ||||
\(149\) | 22740.7 | + | 22740.7i | 1.02431 | + | 1.02431i | 0.999697 | + | 0.0246105i | \(0.00783457\pi\) |
0.0246105 | + | 0.999697i | \(0.492165\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −30969.3 | + | 30969.3i | −1.35824 | + | 1.35824i | −0.482161 | + | 0.876082i | \(0.660148\pi\) |
−0.876082 | + | 0.482161i | \(0.839852\pi\) | |||||||
\(152\) | 4810.76 | 0.208222 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5240.43 | − | 5240.43i | 0.220966 | − | 0.220966i | ||||
\(155\) | − | 32612.4i | − | 1.35744i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16868.7 | −0.684358 | −0.342179 | − | 0.939635i | \(-0.611165\pi\) | ||||
−0.342179 | + | 0.939635i | \(0.611165\pi\) | |||||||
\(158\) | −24183.3 | − | 24183.3i | −0.968725 | − | 0.968725i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2676.45i | 0.104549i | ||||||||
\(161\) | −9095.32 | − | 9095.32i | −0.350886 | − | 0.350886i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23110.4 | − | 23110.4i | 0.869826 | − | 0.869826i | −0.122626 | − | 0.992453i | \(-0.539132\pi\) |
0.992453 | + | 0.122626i | \(0.0391317\pi\) | |||||||
\(164\) | 781.315 | − | 781.315i | 0.0290495 | − | 0.0290495i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 37750.2i | 1.36994i | ||||||||
\(167\) | −16613.8 | + | 16613.8i | −0.595710 | + | 0.595710i | −0.939168 | − | 0.343458i | \(-0.888402\pi\) |
0.343458 | + | 0.939168i | \(0.388402\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 20834.7 | + | 19535.7i | 0.729482 | + | 0.684000i | ||||
\(170\) | −29477.3 | −1.01998 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1776.39 | −0.0600455 | ||||||||
\(173\) | 9230.43i | 0.308411i | 0.988039 | + | 0.154206i | \(0.0492818\pi\) | ||||
−0.988039 | + | 0.154206i | \(0.950718\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1063.21 | − | 1063.21i | −0.0347170 | − | 0.0347170i | ||||
\(176\) | 15889.9 | − | 15889.9i | 0.512973 | − | 0.512973i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 48489.1 | 1.53040 | ||||||||
\(179\) | − | 28771.7i | − | 0.897965i | −0.893541 | − | 0.448982i | \(-0.851787\pi\) | ||
0.893541 | − | 0.448982i | \(-0.148213\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2334.88i | 0.0712700i | 0.999365 | + | 0.0356350i | \(0.0113454\pi\) | ||||
−0.999365 | + | 0.0356350i | \(0.988655\pi\) | |||||||
\(182\) | −13894.1 | − | 5495.05i | −0.419458 | − | 0.165893i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −26271.5 | − | 26271.5i | −0.775978 | − | 0.775978i | ||||
\(185\) | 15053.2 | 0.439831 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16176.3 | + | 16176.3i | 0.462589 | + | 0.462589i | ||||
\(188\) | 293.692 | + | 293.692i | 0.00830953 | + | 0.00830953i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5896.34 | − | 5896.34i | 0.163333 | − | 0.163333i | ||||
\(191\) | 11500.7 | 0.315251 | 0.157625 | − | 0.987499i | \(-0.449616\pi\) | ||||
0.157625 | + | 0.987499i | \(0.449616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 36690.3 | − | 36690.3i | 0.985002 | − | 0.985002i | −0.0148869 | − | 0.999889i | \(-0.504739\pi\) |
0.999889 | + | 0.0148869i | \(0.00473884\pi\) | |||||||
\(194\) | − | 13165.0i | − | 0.349797i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1536.94 | −0.0400078 | ||||||||
\(197\) | −3775.20 | − | 3775.20i | −0.0972763 | − | 0.0972763i | 0.656794 | − | 0.754070i | \(-0.271912\pi\) |
−0.754070 | + | 0.656794i | \(0.771912\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 47612.3i | − | 1.20230i | −0.799136 | − | 0.601151i | \(-0.794709\pi\) | ||
0.799136 | − | 0.601151i | \(-0.205291\pi\) | |||||||
\(200\) | −3071.04 | − | 3071.04i | −0.0767760 | − | 0.0767760i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 18809.3 | − | 18809.3i | 0.460967 | − | 0.460967i | ||||
\(203\) | −20047.6 | + | 20047.6i | −0.486486 | + | 0.486486i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 36676.9i | 0.872740i | ||||||||
\(206\) | 16270.8 | − | 16270.8i | 0.383420 | − | 0.383420i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −42129.4 | − | 16661.9i | −0.973774 | − | 0.385122i | ||||
\(209\) | −6471.46 | −0.148153 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −75668.4 | −1.69961 | −0.849806 | − | 0.527096i | \(-0.823281\pi\) | ||||
−0.849806 | + | 0.527096i | \(0.823281\pi\) | |||||||
\(212\) | − | 3493.11i | − | 0.0777215i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28068.1 | + | 28068.1i | 0.612894 | + | 0.612894i | ||||
\(215\) | 41694.0 | − | 41694.0i | 0.901980 | − | 0.901980i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26693.8 | −0.566879 | ||||||||
\(218\) | 94885.0i | 1.99657i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 1754.38i | − | 0.0362475i | ||||||
\(221\) | 16962.2 | − | 42888.7i | 0.347295 | − | 0.878129i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −953.201 | − | 953.201i | −0.0191679 | − | 0.0191679i | 0.697458 | − | 0.716626i | \(-0.254314\pi\) |
−0.716626 | + | 0.697458i | \(0.754314\pi\) | |||||||
\(224\) | 2190.71 | 0.0436606 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −55767.6 | − | 55767.6i | −1.09186 | − | 1.09186i | ||||
\(227\) | −6110.06 | − | 6110.06i | −0.118575 | − | 0.118575i | 0.645329 | − | 0.763905i | \(-0.276720\pi\) |
−0.763905 | + | 0.645329i | \(0.776720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9576.99 | − | 9576.99i | 0.182624 | − | 0.182624i | −0.609874 | − | 0.792498i | \(-0.708780\pi\) |
0.792498 | + | 0.609874i | \(0.208780\pi\) | |||||||
\(230\) | −64399.7 | −1.21739 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −57906.8 | + | 57906.8i | −1.07585 | + | 1.07585i | ||||
\(233\) | 72801.5i | 1.34100i | 0.741910 | + | 0.670500i | \(0.233920\pi\) | ||||
−0.741910 | + | 0.670500i | \(0.766080\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13786.6 | −0.249645 | ||||||||
\(236\) | −775.309 | − | 775.309i | −0.0139204 | − | 0.0139204i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 24127.7i | 0.425952i | ||||||||
\(239\) | −72643.5 | − | 72643.5i | −1.27175 | − | 1.27175i | −0.945170 | − | 0.326578i | \(-0.894105\pi\) |
−0.326578 | − | 0.945170i | \(-0.605895\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 64322.5 | − | 64322.5i | 1.10746 | − | 1.10746i | 0.113978 | − | 0.993483i | \(-0.463641\pi\) |
0.993483 | − | 0.113978i | \(-0.0363593\pi\) | |||||||
\(242\) | 22064.0 | − | 22064.0i | 0.376751 | − | 0.376751i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 4894.19i | − | 0.0822056i | ||||||
\(245\) | 36073.9 | − | 36073.9i | 0.600981 | − | 0.600981i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5186.06 | + | 11971.9i | 0.0850048 | + | 0.196232i | ||||
\(248\) | −77104.0 | −1.25364 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 59979.9 | 0.959678 | ||||||||
\(251\) | 49293.7i | 0.782427i | 0.920300 | + | 0.391213i | \(0.127945\pi\) | ||||
−0.920300 | + | 0.391213i | \(0.872055\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35340.6 | + | 35340.6i | 0.552119 | + | 0.552119i | ||||
\(254\) | 76318.4 | − | 76318.4i | 1.18294 | − | 1.18294i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9733.62 | 0.148523 | ||||||||
\(257\) | 82424.4i | 1.24793i | 0.781453 | + | 0.623964i | \(0.214479\pi\) | ||||
−0.781453 | + | 0.623964i | \(0.785521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12321.3i | − | 0.183678i | ||||||
\(260\) | −3245.54 | + | 1405.92i | −0.0480109 | + | 0.0207976i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8966.85 | − | 8966.85i | −0.130628 | − | 0.130628i | ||||
\(263\) | −41367.3 | −0.598062 | −0.299031 | − | 0.954243i | \(-0.596663\pi\) | ||||
−0.299031 | + | 0.954243i | \(0.596663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 81987.7 | + | 81987.7i | 1.16750 | + | 1.16750i | ||||
\(266\) | −4826.24 | − | 4826.24i | −0.0682096 | − | 0.0682096i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1356.68 | − | 1356.68i | 0.0188890 | − | 0.0188890i | ||||
\(269\) | 59626.2 | 0.824011 | 0.412005 | − | 0.911181i | \(-0.364828\pi\) | ||||
0.412005 | + | 0.911181i | \(0.364828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −75798.8 | + | 75798.8i | −1.03210 | + | 1.03210i | −0.0326374 | + | 0.999467i | \(0.510391\pi\) |
−0.999467 | + | 0.0326374i | \(0.989609\pi\) | |||||||
\(272\) | 73159.1i | 0.988850i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −60586.0 | −0.806996 | ||||||||
\(275\) | 4131.18 | + | 4131.18i | 0.0546272 | + | 0.0546272i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 134127.i | 1.74806i | 0.485876 | + | 0.874028i | \(0.338501\pi\) | ||||
−0.485876 | + | 0.874028i | \(0.661499\pi\) | |||||||
\(278\) | −17161.9 | − | 17161.9i | −0.222063 | − | 0.222063i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −25055.2 | + | 25055.2i | −0.319582 | + | 0.319582i | ||||
\(281\) | 19968.0 | − | 19968.0i | 0.252885 | − | 0.252885i | −0.569268 | − | 0.822152i | \(-0.692773\pi\) |
0.822152 | + | 0.569268i | \(0.192773\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 151960.i | − | 1.89739i | −0.316186 | − | 0.948697i | \(-0.602402\pi\) | ||
0.316186 | − | 0.948697i | \(-0.397598\pi\) | |||||||
\(284\) | 534.065 | − | 534.065i | 0.00662151 | − | 0.00662151i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 53986.8 | + | 21351.4i | 0.660017 | + | 0.261033i | ||||
\(287\) | 30020.6 | 0.364465 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9043.27 | 0.108275 | ||||||||
\(290\) | 141948.i | 1.68784i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −928.744 | − | 928.744i | −0.0108926 | − | 0.0108926i | ||||
\(293\) | −22398.8 | + | 22398.8i | −0.260909 | + | 0.260909i | −0.825423 | − | 0.564514i | \(-0.809063\pi\) |
0.564514 | + | 0.825423i | \(0.309063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36394.9 | 0.418212 | ||||||||
\(296\) | − | 35589.6i | − | 0.406200i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 131794.i | − | 1.48410i | ||||||
\(299\) | 37057.7 | − | 93699.8i | 0.414511 | − | 1.04808i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34127.2 | − | 34127.2i | −0.376676 | − | 0.376676i | ||||
\(302\) | 179483. | 1.96793 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −14634.0 | − | 14634.0i | −0.158349 | − | 0.158349i | ||||
\(305\) | 114873. | + | 114873.i | 1.23486 | + | 1.23486i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 36789.1 | − | 36789.1i | 0.390339 | − | 0.390339i | −0.484469 | − | 0.874808i | \(-0.660987\pi\) |
0.874808 | + | 0.484469i | \(0.160987\pi\) | |||||||
\(308\) | −1435.99 | −0.0151373 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −94503.0 | + | 94503.0i | −0.983382 | + | 0.983382i | ||||
\(311\) | 78846.4i | 0.815194i | 0.913162 | + | 0.407597i | \(0.133633\pi\) | ||||
−0.913162 | + | 0.407597i | \(0.866367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20618.6 | 0.210460 | 0.105230 | − | 0.994448i | \(-0.466442\pi\) | ||||
0.105230 | + | 0.994448i | \(0.466442\pi\) | |||||||
\(314\) | 48881.6 | + | 48881.6i | 0.495777 | + | 0.495777i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6626.72i | 0.0663627i | ||||||||
\(317\) | −42129.4 | − | 42129.4i | −0.419244 | − | 0.419244i | 0.465699 | − | 0.884943i | \(-0.345803\pi\) |
−0.884943 | + | 0.465699i | \(0.845803\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 77896.6 | − | 77896.6i | 0.765485 | − | 0.765485i | ||||
\(320\) | −72183.1 | + | 72183.1i | −0.704913 | + | 0.704913i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 52712.2i | 0.508392i | ||||||||
\(323\) | 14897.7 | − | 14897.7i | 0.142796 | − | 0.142796i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4331.90 | − | 10953.2i | 0.0410121 | − | 0.103698i | ||||
\(326\) | −133937. | −1.26027 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 86713.5 | 0.806007 | ||||||||
\(329\) | 11284.6i | 0.104254i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 68308.6 | + | 68308.6i | 0.623476 | + | 0.623476i | 0.946418 | − | 0.322943i | \(-0.104672\pi\) |
−0.322943 | + | 0.946418i | \(0.604672\pi\) | |||||||
\(332\) | 5172.17 | − | 5172.17i | 0.0469242 | − | 0.0469242i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 96285.5 | 0.863113 | ||||||||
\(335\) | 63686.0i | 0.567485i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 87835.7i | 0.773412i | 0.922203 | + | 0.386706i | \(0.126387\pi\) | ||||
−0.922203 | + | 0.386706i | \(0.873613\pi\) | |||||||
\(338\) | −3764.29 | − | 116984.i | −0.0329495 | − | 1.02398i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4038.70 | + | 4038.70i | 0.0349369 | + | 0.0349369i | ||||
\(341\) | 103721. | 0.891983 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −66154.0 | − | 66154.0i | −0.562300 | − | 0.562300i | ||||
\(344\) | −98575.2 | − | 98575.2i | −0.833011 | − | 0.833011i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 26747.6 | − | 26747.6i | 0.223425 | − | 0.223425i | ||||
\(347\) | −98270.4 | −0.816138 | −0.408069 | − | 0.912951i | \(-0.633798\pi\) | ||||
−0.408069 | + | 0.912951i | \(0.633798\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17440.9 | + | 17440.9i | −0.143192 | + | 0.143192i | −0.775069 | − | 0.631877i | \(-0.782285\pi\) |
0.631877 | + | 0.775069i | \(0.282285\pi\) | |||||||
\(350\) | 6161.85i | 0.0503008i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8512.19 | −0.0686999 | ||||||||
\(353\) | −63740.5 | − | 63740.5i | −0.511524 | − | 0.511524i | 0.403469 | − | 0.914993i | \(-0.367804\pi\) |
−0.914993 | + | 0.403469i | \(0.867804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25070.3i | 0.198931i | ||||||||
\(356\) | −6643.52 | − | 6643.52i | −0.0524201 | − | 0.0524201i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −83373.5 | + | 83373.5i | −0.650522 | + | 0.650522i | ||||
\(359\) | 168217. | − | 168217.i | 1.30521 | − | 1.30521i | 0.380377 | − | 0.924831i | \(-0.375794\pi\) |
0.924831 | − | 0.380377i | \(-0.124206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 124361.i | − | 0.954267i | ||||||
\(362\) | 6765.91 | − | 6765.91i | 0.0516308 | − | 0.0516308i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1150.76 | + | 2656.52i | 0.00868527 | + | 0.0200498i | ||||
\(365\) | 43597.6 | 0.327248 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4967.29 | 0.0368797 | 0.0184399 | − | 0.999830i | \(-0.494130\pi\) | ||||
0.0184399 | + | 0.999830i | \(0.494130\pi\) | |||||||
\(368\) | 159832.i | 1.18023i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −43620.7 | − | 43620.7i | −0.318632 | − | 0.318632i | ||||
\(371\) | 67108.2 | − | 67108.2i | 0.487560 | − | 0.487560i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −115465. | −0.829914 | −0.414957 | − | 0.909841i | \(-0.636203\pi\) | ||||
−0.414957 | + | 0.909841i | \(0.636203\pi\) | |||||||
\(374\) | − | 93749.9i | − | 0.670236i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32595.1i | 0.230556i | ||||||||
\(377\) | −206530. | − | 81681.3i | −1.45312 | − | 0.574698i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −79418.8 | − | 79418.8i | −0.552898 | − | 0.552898i | 0.374378 | − | 0.927276i | \(-0.377856\pi\) |
−0.927276 | + | 0.374378i | \(0.877856\pi\) | |||||||
\(380\) | −1615.72 | −0.0111892 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −33326.2 | − | 33326.2i | −0.228380 | − | 0.228380i | ||||
\(383\) | −30297.2 | − | 30297.2i | −0.206540 | − | 0.206540i | 0.596255 | − | 0.802795i | \(-0.296655\pi\) |
−0.802795 | + | 0.596255i | \(0.796655\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33704.4 | − | 33704.4i | 0.227387 | − | 0.227387i | ||||
\(386\) | −212640. | −1.42715 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1803.74 | + | 1803.74i | −0.0119815 | + | 0.0119815i | ||||
\(389\) | − | 135764.i | − | 0.897193i | −0.893734 | − | 0.448597i | \(-0.851924\pi\) | ||
0.893734 | − | 0.448597i | \(-0.148076\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −162713. | −1.06431 | ||||||||
\(392\) | −85287.7 | − | 85287.7i | −0.555028 | − | 0.555028i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21879.2i | 0.140942i | ||||||||
\(395\) | −155537. | − | 155537.i | −0.996874 | − | 0.996874i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −122596. | + | 122596.i | −0.777851 | + | 0.777851i | −0.979465 | − | 0.201614i | \(-0.935381\pi\) |
0.201614 | + | 0.979465i | \(0.435381\pi\) | |||||||
\(398\) | −137969. | + | 137969.i | −0.870996 | + | 0.870996i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18683.8i | 0.116774i | ||||||||
\(401\) | −132123. | + | 132123.i | −0.821653 | + | 0.821653i | −0.986345 | − | 0.164692i | \(-0.947337\pi\) |
0.164692 | + | 0.986345i | \(0.447337\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −83119.1 | − | 191879.i | −0.511789 | − | 1.18146i | ||||
\(404\) | −5154.14 | −0.0315786 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 116186. | 0.704860 | ||||||||
\(407\) | 47875.4i | 0.289017i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2700.68 | + | 2700.68i | 0.0161445 | + | 0.0161445i | 0.715133 | − | 0.698988i | \(-0.246366\pi\) |
−0.698988 | + | 0.715133i | \(0.746366\pi\) | |||||||
\(410\) | 106281. | − | 106281.i | 0.632248 | − | 0.632248i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4458.54 | −0.0262663 | ||||||||
\(413\) | − | 29789.8i | − | 0.174650i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 242795.i | 1.40975i | ||||||||
\(416\) | 6821.45 | + | 15747.2i | 0.0394176 | + | 0.0909950i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18752.7 | + | 18752.7i | 0.107328 | + | 0.107328i | ||||
\(419\) | 94447.5 | 0.537975 | 0.268988 | − | 0.963144i | \(-0.413311\pi\) | ||||
0.268988 | + | 0.963144i | \(0.413311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15371.4 | + | 15371.4i | 0.0867262 | + | 0.0867262i | 0.749139 | − | 0.662413i | \(-0.230468\pi\) |
−0.662413 | + | 0.749139i | \(0.730468\pi\) | |||||||
\(422\) | 219269. | + | 219269.i | 1.23127 | + | 1.23127i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 193840. | − | 193840.i | 1.07823 | − | 1.07823i | ||||
\(425\) | −19020.5 | −0.105304 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 94025.1 | − | 94025.1i | 0.515689 | − | 0.515689i | ||||
\(428\) | − | 7691.25i | − | 0.0419865i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −241639. | −1.30686 | ||||||||
\(431\) | 42041.0 | + | 42041.0i | 0.226317 | + | 0.226317i | 0.811152 | − | 0.584835i | \(-0.198841\pi\) |
−0.584835 | + | 0.811152i | \(0.698841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 29381.2i | − | 0.156709i | −0.996926 | − | 0.0783545i | \(-0.975033\pi\) | ||
0.996926 | − | 0.0783545i | \(-0.0249666\pi\) | |||||||
\(434\) | 77352.1 | + | 77352.1i | 0.410670 | + | 0.410670i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13000.2 | − | 13000.2i | 0.0683877 | − | 0.0683877i | ||||
\(437\) | 32547.4 | − | 32547.4i | 0.170433 | − | 0.170433i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 354668.i | − | 1.84032i | −0.391542 | − | 0.920160i | \(-0.628058\pi\) | ||
0.391542 | − | 0.920160i | \(-0.371942\pi\) | |||||||
\(440\) | 97354.0 | − | 97354.0i | 0.502862 | − | 0.502862i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −173434. | + | 75128.8i | −0.887747 | + | 0.384558i | ||||
\(443\) | 22527.8 | 0.114792 | 0.0573960 | − | 0.998351i | \(-0.481720\pi\) | ||||
0.0573960 | + | 0.998351i | \(0.481720\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 311863. | 1.57487 | ||||||||
\(446\) | 5524.30i | 0.0277720i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 59082.9 | + | 59082.9i | 0.294378 | + | 0.294378i | ||||
\(449\) | 53263.7 | − | 53263.7i | 0.264204 | − | 0.264204i | −0.562556 | − | 0.826759i | \(-0.690182\pi\) |
0.826759 | + | 0.562556i | \(0.190182\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −116647. | −0.573485 | ||||||||
\(452\) | 15281.5i | 0.0747978i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 35411.0i | 0.171801i | ||||||||
\(455\) | −89361.7 | − | 35342.0i | −0.431647 | − | 0.170714i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 94033.6 | + | 94033.6i | 0.450247 | + | 0.450247i | 0.895436 | − | 0.445189i | \(-0.146864\pi\) |
−0.445189 | + | 0.895436i | \(0.646864\pi\) | |||||||
\(458\) | −55503.7 | −0.264601 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8823.43 | + | 8823.43i | 0.0416986 | + | 0.0416986i | ||||
\(461\) | 220771. | + | 220771.i | 1.03882 | + | 1.03882i | 0.999215 | + | 0.0396051i | \(0.0126100\pi\) |
0.0396051 | + | 0.999215i | \(0.487390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −148393. | + | 148393.i | −0.692231 | + | 0.692231i | −0.962722 | − | 0.270491i | \(-0.912814\pi\) |
0.270491 | + | 0.962722i | \(0.412814\pi\) | |||||||
\(464\) | 352296. | 1.63634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 210962. | − | 210962.i | 0.971474 | − | 0.971474i | ||||
\(467\) | 89596.5i | 0.410826i | 0.978675 | + | 0.205413i | \(0.0658537\pi\) | ||||
−0.978675 | + | 0.205413i | \(0.934146\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 52128.0 | 0.236987 | ||||||||
\(470\) | 39950.4 | + | 39950.4i | 0.180853 | + | 0.180853i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 86046.8i | − | 0.386234i | ||||||
\(473\) | 132604. | + | 132604.i | 0.592699 | + | 0.592699i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3804.66 | − | 3804.66i | 0.0168628 | − | 0.0168628i | ||||
\(476\) | 3305.74 | − | 3305.74i | 0.0145900 | − | 0.0145900i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 421007.i | 1.84261i | ||||||||
\(479\) | −290497. | + | 290497.i | −1.26611 | + | 1.26611i | −0.318023 | + | 0.948083i | \(0.603019\pi\) |
−0.948083 | + | 0.318023i | \(0.896981\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 88567.6 | − | 38366.1i | 0.382811 | − | 0.165828i | ||||
\(482\) | −372782. | −1.60458 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6046.00 | −0.0258094 | ||||||||
\(485\) | − | 84672.0i | − | 0.359962i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 186744. | + | 186744.i | 0.787388 | + | 0.787388i | 0.981065 | − | 0.193677i | \(-0.0620414\pi\) |
−0.193677 | + | 0.981065i | \(0.562041\pi\) | |||||||
\(488\) | 271588. | − | 271588.i | 1.14044 | − | 1.14044i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −209067. | −0.870750 | ||||||||
\(491\) | 26475.0i | 0.109818i | 0.998491 | + | 0.0549088i | \(0.0174868\pi\) | ||||
−0.998491 | + | 0.0549088i | \(0.982513\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 358646.i | 1.47561i | ||||||||
\(494\) | 19663.9 | − | 49719.8i | 0.0805778 | − | 0.203740i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 234545. | + | 234545.i | 0.953372 | + | 0.953372i | ||||
\(497\) | 20520.4 | 0.0830757 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 72703.0 | + | 72703.0i | 0.291979 | + | 0.291979i | 0.837862 | − | 0.545883i | \(-0.183806\pi\) |
−0.545883 | + | 0.837862i | \(0.683806\pi\) | |||||||
\(500\) | −8217.87 | − | 8217.87i | −0.0328715 | − | 0.0328715i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 142841. | − | 142841.i | 0.566822 | − | 0.566822i | ||||
\(503\) | −245797. | −0.971496 | −0.485748 | − | 0.874099i | \(-0.661453\pi\) | ||||
−0.485748 | + | 0.874099i | \(0.661453\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 120974. | − | 120974.i | 0.474362 | − | 0.474362i | ||||
\(506\) | − | 204817.i | − | 0.799955i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −20912.8 | −0.0810374 | ||||||||
\(509\) | 105992. | + | 105992.i | 0.409109 | + | 0.409109i | 0.881428 | − | 0.472319i | \(-0.156583\pi\) |
−0.472319 | + | 0.881428i | \(0.656583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 35685.3i | − | 0.136662i | ||||||
\(512\) | 169747. | + | 169747.i | 0.647533 | + | 0.647533i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 238846. | − | 238846.i | 0.904049 | − | 0.904049i | ||||
\(515\) | 104648. | − | 104648.i | 0.394561 | − | 0.394561i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 43847.1i | − | 0.164044i | ||||||
\(518\) | −35704.2 | + | 35704.2i | −0.133064 | + | 0.133064i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −258118. | − | 102084.i | −0.954579 | − | 0.377530i | ||||
\(521\) | −408225. | −1.50392 | −0.751959 | − | 0.659209i | \(-0.770891\pi\) | ||||
−0.751959 | + | 0.659209i | \(0.770891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −145126. | −0.530567 | −0.265284 | − | 0.964170i | \(-0.585466\pi\) | ||||
−0.265284 | + | 0.964170i | \(0.585466\pi\) | |||||||
\(524\) | 2457.10i | 0.00894872i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 119873. | + | 119873.i | 0.433260 | + | 0.433260i | ||||
\(527\) | −238772. | + | 238772.i | −0.859731 | + | 0.859731i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −75641.2 | −0.270300 | ||||||||
\(530\) | − | 475162.i | − | 1.69157i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1322.49i | 0.00467271i | ||||||||
\(533\) | 93478.3 | + | 215793.i | 0.329046 | + | 0.759597i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 180523. | + | 180523.i | 0.630704 | + | 0.630704i | ||||
\(536\) | 150570. | 0.524093 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −172783. | − | 172783.i | −0.596947 | − | 0.596947i | ||||
\(539\) | 114730. | + | 114730.i | 0.394910 | + | 0.394910i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −376207. | + | 376207.i | −1.28538 | + | 1.28538i | −0.347823 | + | 0.937560i | \(0.613079\pi\) |
−0.937560 | + | 0.347823i | \(0.886921\pi\) | |||||||
\(542\) | 439294. | 1.49540 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 19595.6 | − | 19595.6i | 0.0662158 | − | 0.0662158i | ||||
\(545\) | 610263.i | 2.05459i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −110782. | −0.370249 | −0.185124 | − | 0.982715i | \(-0.559269\pi\) | ||||
−0.185124 | + | 0.982715i | \(0.559269\pi\) | |||||||
\(548\) | 8300.91 | + | 8300.91i | 0.0276417 | + | 0.0276417i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | − | 23942.4i | − | 0.0791483i | ||||||
\(551\) | −71739.8 | − | 71739.8i | −0.236296 | − | 0.236296i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −127310. | + | 127310.i | −0.416304 | + | 0.416304i | ||||
\(554\) | 388667. | − | 388667.i | 1.26636 | − | 1.26636i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4702.73i | 0.0152125i | ||||||||
\(557\) | −141690. | + | 141690.i | −0.456696 | + | 0.456696i | −0.897569 | − | 0.440873i | \(-0.854669\pi\) |
0.440873 | + | 0.897569i | \(0.354669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 139047. | − | 351577.i | 0.444977 | − | 1.12512i | ||||
\(560\) | 152432. | 0.486072 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −115725. | −0.366400 | ||||||||
\(563\) | − | 301845.i | − | 0.952287i | −0.879368 | − | 0.476143i | \(-0.842034\pi\) | ||
0.879368 | − | 0.476143i | \(-0.157966\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −358675. | − | 358675.i | −1.12358 | − | 1.12358i | ||||
\(566\) | −440345. | + | 440345.i | −1.37455 | + | 1.37455i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 59272.6 | 0.183720 | ||||||||
\(569\) | 149750.i | 0.462532i | 0.972891 | + | 0.231266i | \(0.0742867\pi\) | ||||
−0.972891 | + | 0.231266i | \(0.925713\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 477531.i | − | 1.46463i | −0.680964 | − | 0.732317i | \(-0.738439\pi\) | ||
0.680964 | − | 0.732317i | \(-0.261561\pi\) | |||||||
\(572\) | −4471.38 | − | 10322.1i | −0.0136663 | − | 0.0315484i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −86992.5 | − | 86992.5i | −0.264033 | − | 0.264033i | ||||
\(575\) | −41554.5 | −0.125685 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 108891. | + | 108891.i | 0.327069 | + | 0.327069i | 0.851471 | − | 0.524402i | \(-0.175711\pi\) |
−0.524402 | + | 0.851471i | \(0.675711\pi\) | |||||||
\(578\) | −26205.2 | − | 26205.2i | −0.0784391 | − | 0.0784391i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19448.3 | − | 19448.3i | 0.0578131 | − | 0.0578131i | ||||
\(581\) | 198731. | 0.588726 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −260754. | + | 260754.i | −0.767175 | + | 0.767175i | ||||
\(584\) | − | 103076.i | − | 0.302225i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 129813. | 0.378026 | ||||||||
\(587\) | −379654. | − | 379654.i | −1.10182 | − | 1.10182i | −0.994191 | − | 0.107632i | \(-0.965673\pi\) |
−0.107632 | − | 0.994191i | \(-0.534327\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 95522.9i | − | 0.275345i | ||||||
\(590\) | −105464. | − | 105464.i | −0.302970 | − | 0.302970i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −108261. | + | 108261.i | −0.308908 | + | 0.308908i | ||||
\(593\) | −20445.7 | + | 20445.7i | −0.0581423 | + | 0.0581423i | −0.735580 | − | 0.677438i | \(-0.763090\pi\) |
0.677438 | + | 0.735580i | \(0.263090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 155180.i | 0.438330i | ||||||||
\(596\) | −18057.1 | + | 18057.1i | −0.0508343 | + | 0.0508343i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −378904. | + | 164135.i | −1.05956 | + | 0.458986i | ||||
\(599\) | −45314.1 | −0.126293 | −0.0631466 | − | 0.998004i | \(-0.520114\pi\) | ||||
−0.0631466 | + | 0.998004i | \(0.520114\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −71319.6 | −0.197451 | −0.0987256 | − | 0.995115i | \(-0.531477\pi\) | ||||
−0.0987256 | + | 0.995115i | \(0.531477\pi\) | |||||||
\(602\) | 197785.i | 0.545758i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24591.1 | − | 24591.1i | −0.0674068 | − | 0.0674068i | ||||
\(605\) | 141907. | − | 141907.i | 0.387698 | − | 0.387698i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37835.4 | 0.102688 | 0.0513441 | − | 0.998681i | \(-0.483649\pi\) | ||||
0.0513441 | + | 0.998681i | \(0.483649\pi\) | |||||||
\(608\) | 7839.41i | 0.0212069i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 665748.i | − | 1.78916i | ||||||
\(611\) | −81115.5 | + | 35138.0i | −0.217281 | + | 0.0941226i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 269915. | + | 269915.i | 0.718301 | + | 0.718301i | 0.968257 | − | 0.249956i | \(-0.0804162\pi\) |
−0.249956 | + | 0.968257i | \(0.580416\pi\) | |||||||
\(614\) | −213212. | −0.565555 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −79685.7 | − | 79685.7i | −0.210000 | − | 0.210000i | ||||
\(617\) | −128460. | − | 128460.i | −0.337440 | − | 0.337440i | 0.517963 | − | 0.855403i | \(-0.326690\pi\) |
−0.855403 | + | 0.517963i | \(0.826690\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −78942.1 | + | 78942.1i | −0.206029 | + | 0.206029i | −0.802577 | − | 0.596548i | \(-0.796538\pi\) |
0.596548 | + | 0.802577i | \(0.296538\pi\) | |||||||
\(620\) | 25895.8 | 0.0673668 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 228478. | − | 228478.i | 0.590560 | − | 0.590560i | ||||
\(623\) | − | 255265.i | − | 0.657680i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 429328. | 1.09908 | ||||||||
\(626\) | −59747.7 | − | 59747.7i | −0.152466 | − | 0.152466i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 13394.6i | − | 0.0339633i | ||||||
\(629\) | −110212. | − | 110212.i | −0.278567 | − | 0.278567i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −138220. | + | 138220.i | −0.347146 | + | 0.347146i | −0.859045 | − | 0.511899i | \(-0.828942\pi\) |
0.511899 | + | 0.859045i | \(0.328942\pi\) | |||||||
\(632\) | −367729. | + | 367729.i | −0.920649 | + | 0.920649i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 244162.i | 0.607435i | ||||||||
\(635\) | 490850. | − | 490850.i | 1.21731 | − | 1.21731i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 120304. | − | 304187.i | 0.296484 | − | 0.749655i | ||||
\(638\) | −451451. | −1.10910 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 461162. | 1.12588 | ||||||||
\(641\) | − | 369011.i | − | 0.898098i | −0.893507 | − | 0.449049i | \(-0.851763\pi\) | ||
0.893507 | − | 0.449049i | \(-0.148237\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 111450. | + | 111450.i | 0.269561 | + | 0.269561i | 0.828923 | − | 0.559362i | \(-0.188954\pi\) |
−0.559362 | + | 0.828923i | \(0.688954\pi\) | |||||||
\(644\) | 7222.11 | − | 7222.11i | 0.0174138 | − | 0.0174138i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −86340.2 | −0.206894 | ||||||||
\(647\) | − | 401104.i | − | 0.958184i | −0.877765 | − | 0.479092i | \(-0.840966\pi\) | ||
0.877765 | − | 0.479092i | \(-0.159034\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 115751.i | 0.274811i | ||||||||
\(650\) | −44292.5 | + | 19186.8i | −0.104834 | + | 0.0454125i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18350.8 | + | 18350.8i | 0.0431677 | + | 0.0431677i | ||||
\(653\) | 341135. | 0.800018 | 0.400009 | − | 0.916511i | \(-0.369007\pi\) | ||||
0.400009 | + | 0.916511i | \(0.369007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57671.3 | − | 57671.3i | −0.134424 | − | 0.134424i | ||||
\(656\) | −263776. | − | 263776.i | −0.612954 | − | 0.612954i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 32700.0 | − | 32700.0i | 0.0755259 | − | 0.0755259i | ||||
\(659\) | −32739.6 | −0.0753881 | −0.0376941 | − | 0.999289i | \(-0.512001\pi\) | ||||
−0.0376941 | + | 0.999289i | \(0.512001\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20237.5 | − | 20237.5i | 0.0463184 | − | 0.0463184i | −0.683568 | − | 0.729887i | \(-0.739573\pi\) |
0.729887 | + | 0.683568i | \(0.239573\pi\) | |||||||
\(662\) | − | 395884.i | − | 0.903342i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 574028. | 1.30196 | ||||||||
\(665\) | −31040.5 | − | 31040.5i | −0.0701916 | − | 0.0701916i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 783542.i | 1.76121i | ||||||||
\(668\) | −13192.1 | − | 13192.1i | −0.0295639 | − | 0.0295639i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 184547. | − | 184547.i | 0.411109 | − | 0.411109i | ||||
\(671\) | −365342. | + | 365342.i | −0.811437 | + | 0.811437i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 151692.i | − | 0.334914i | −0.985879 | − | 0.167457i | \(-0.946444\pi\) | ||
0.985879 | − | 0.167457i | \(-0.0535556\pi\) | |||||||
\(674\) | 254527. | − | 254527.i | 0.560291 | − | 0.560291i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15512.3 | + | 16543.8i | −0.0339455 | + | 0.0362027i | ||||
\(677\) | 753102. | 1.64315 | 0.821574 | − | 0.570102i | \(-0.193096\pi\) | ||||
0.821574 | + | 0.570102i | \(0.193096\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −69305.3 | −0.150323 | ||||||||
\(680\) | 448231.i | 0.969358i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −300558. | − | 300558.i | −0.646189 | − | 0.646189i | ||||
\(683\) | −50909.1 | + | 50909.1i | −0.109132 | + | 0.109132i | −0.759564 | − | 0.650432i | \(-0.774588\pi\) |
0.650432 | + | 0.759564i | \(0.274588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −389666. | −0.830445 | ||||||||
\(686\) | 383397.i | 0.814705i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 599717.i | 1.26698i | ||||||||
\(689\) | 691347. | + | 273424.i | 1.45632 | + | 0.575967i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −281346. | − | 281346.i | −0.589230 | − | 0.589230i | 0.348193 | − | 0.937423i | \(-0.386795\pi\) |
−0.937423 | + | 0.348193i | \(0.886795\pi\) | |||||||
\(692\) | −7329.40 | −0.0153058 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 284764. | + | 284764.i | 0.591243 | + | 0.591243i | ||||
\(695\) | −110379. | − | 110379.i | −0.228516 | − | 0.228516i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 268530. | − | 268530.i | 0.552749 | − | 0.552749i | ||||
\(698\) | 101079. | 0.207468 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 844.238 | − | 844.238i | 0.00172293 | − | 0.00172293i | ||||
\(701\) | 212436.i | 0.432307i | 0.976359 | + | 0.216154i | \(0.0693512\pi\) | ||||
−0.976359 | + | 0.216154i | \(0.930649\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44091.4 | 0.0892161 | ||||||||
\(704\) | −229571. | − | 229571.i | −0.463204 | − | 0.463204i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 369410.i | 0.741138i | ||||||||
\(707\) | −99019.1 | − | 99019.1i | −0.198098 | − | 0.198098i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27433.3 | − | 27433.3i | 0.0545741 | − | 0.0545741i | −0.679293 | − | 0.733867i | \(-0.737713\pi\) |
0.733867 | + | 0.679293i | \(0.237713\pi\) | |||||||
\(710\) | 72647.8 | − | 72647.8i | 0.144114 | − | 0.144114i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 737324.i | − | 1.45445i | ||||||
\(713\) | −521650. | + | 521650.i | −1.02613 | + | 1.02613i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 347222. | + | 137324.i | 0.679196 | + | 0.268618i | ||||
\(716\) | 22846.1 | 0.0445641 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −974903. | −1.89109 | ||||||||
\(719\) | − | 537471.i | − | 1.03967i | −0.854265 | − | 0.519837i | \(-0.825993\pi\) | ||
0.854265 | − | 0.519837i | \(-0.174007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −85655.6 | − | 85655.6i | −0.164773 | − | 0.164773i | ||||
\(722\) | −360369. | + | 360369.i | −0.691310 | + | 0.691310i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1854.00 | −0.00353698 | ||||||||
\(725\) | 91593.1i | 0.174256i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 330967.i | − | 0.626204i | −0.949720 | − | 0.313102i | \(-0.898632\pi\) | ||
0.949720 | − | 0.313102i | \(-0.101368\pi\) | |||||||
\(728\) | −83557.4 | + | 211274.i | −0.157660 | + | 0.398642i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −126335. | − | 126335.i | −0.237071 | − | 0.237071i | ||||
\(731\) | −610526. | −1.14254 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −164154. | − | 164154.i | −0.305522 | − | 0.305522i | 0.537648 | − | 0.843170i | \(-0.319313\pi\) |
−0.843170 | + | 0.537648i | \(0.819313\pi\) | |||||||
\(734\) | −14394.0 | − | 14394.0i | −0.0267171 | − | 0.0267171i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 42811.0 | − | 42811.0i | 0.0790314 | − | 0.0790314i | ||||
\(737\) | −202547. | −0.372899 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −268903. | + | 268903.i | −0.492387 | + | 0.492387i | −0.909058 | − | 0.416670i | \(-0.863197\pi\) |
0.416670 | + | 0.909058i | \(0.363197\pi\) | |||||||
\(740\) | 11953.0i | 0.0218279i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −388927. | −0.706416 | ||||||||
\(743\) | 397022. | + | 397022.i | 0.719180 | + | 0.719180i | 0.968437 | − | 0.249258i | \(-0.0801866\pi\) |
−0.249258 | + | 0.968437i | \(0.580187\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 847648.i | − | 1.52722i | ||||||
\(746\) | 334590. | + | 334590.i | 0.601223 | + | 0.601223i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12844.7 | + | 12844.7i | −0.0229573 | + | 0.0229573i | ||||
\(749\) | 147761. | − | 147761.i | 0.263388 | − | 0.263388i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 100943.i | 0.178976i | 0.995988 | + | 0.0894882i | \(0.0285231\pi\) | ||||
−0.995988 | + | 0.0894882i | \(0.971477\pi\) | |||||||
\(752\) | 99151.9 | − | 99151.9i | 0.175334 | − | 0.175334i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 361782. | + | 835168.i | 0.636361 | + | 1.46903i | ||||
\(755\) | 1.15437e6 | 2.02512 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −418346. | −0.730035 | −0.365018 | − | 0.931001i | \(-0.618937\pi\) | ||||
−0.365018 | + | 0.931001i | \(0.618937\pi\) | |||||||
\(758\) | 460273.i | 0.801083i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −89659.4 | − | 89659.4i | −0.155227 | − | 0.155227i | ||||
\(761\) | 70616.1 | − | 70616.1i | 0.121937 | − | 0.121937i | −0.643505 | − | 0.765442i | \(-0.722520\pi\) |
0.765442 | + | 0.643505i | \(0.222520\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 499510. | 0.858015 | ||||||||
\(764\) | 9132.06i | 0.0156452i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 175588.i | 0.299253i | ||||||||
\(767\) | 214134. | − | 92759.6i | 0.363995 | − | 0.157677i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −642589. | − | 642589.i | −1.08663 | − | 1.08663i | −0.995873 | − | 0.0907545i | \(-0.971072\pi\) |
−0.0907545 | − | 0.995873i | \(-0.528928\pi\) | |||||||
\(770\) | −195335. | −0.329456 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29133.9 | + | 29133.9i | 0.0488836 | + | 0.0488836i | ||||
\(773\) | −152962. | − | 152962.i | −0.255990 | − | 0.255990i | 0.567431 | − | 0.823421i | \(-0.307937\pi\) |
−0.823421 | + | 0.567431i | \(0.807937\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −60978.9 | + | 60978.9i | −0.101526 | + | 0.101526i | ||||
\(776\) | −200186. | −0.332438 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −393412. | + | 393412.i | −0.649963 | + | 0.649963i | ||||
\(779\) | 107428.i | 0.177028i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −79733.8 | −0.130720 | ||||||||
\(782\) | 471503. | + | 471503.i | 0.771030 | + | 0.771030i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 518878.i | 0.844177i | ||||||||
\(785\) | 314387. | + | 314387.i | 0.510183 | + | 0.510183i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 210034. | − | 210034.i | 0.339110 | − | 0.339110i | −0.516922 | − | 0.856032i | \(-0.672922\pi\) |
0.856032 | + | 0.516922i | \(0.172922\pi\) | |||||||
\(788\) | 2997.68 | − | 2997.68i | 0.00482762 | − | 0.00482762i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 901420.i | 1.44435i | ||||||||
\(791\) | −293581. | + | 293581.i | −0.469219 | + | 0.469219i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 968645. | + | 383093.i | 1.54035 | + | 0.609197i | ||||
\(794\) | 710510. | 1.12701 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 37806.4 | 0.0596677 | ||||||||
\(797\) | − | 508211.i | − | 0.800069i | −0.916500 | − | 0.400035i | \(-0.868998\pi\) | ||
0.916500 | − | 0.400035i | \(-0.131002\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 100939. | + | 100939.i | 0.158112 | + | 0.158112i | ||||
\(800\) | 5004.44 | − | 5004.44i | 0.00781944 | − | 0.00781944i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 765719. | 1.19048 | ||||||||
\(803\) | 138658.i | 0.215037i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 339024.i | 0.523165i | ||||||||
\(806\) | −315161. | + | 796880.i | −0.485135 | + | 1.22666i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −286013. | − | 286013.i | −0.438090 | − | 0.438090i | ||||
\(809\) | 302513. | 0.462218 | 0.231109 | − | 0.972928i | \(-0.425765\pi\) | ||||
0.231109 | + | 0.972928i | \(0.425765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 261828. | + | 261828.i | 0.398083 | + | 0.398083i | 0.877557 | − | 0.479473i | \(-0.159172\pi\) |
−0.479473 | + | 0.877557i | \(0.659172\pi\) | |||||||
\(812\) | −15918.7 | − | 15918.7i | −0.0241433 | − | 0.0241433i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 138731. | − | 138731.i | 0.209376 | − | 0.209376i | ||||
\(815\) | −861431. | −1.29690 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 122123. | − | 122123.i | 0.182959 | − | 0.182959i | ||||
\(818\) | − | 15651.8i | − | 0.0233915i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −29123.2 | −0.0433123 | ||||||||
\(821\) | 141594. | + | 141594.i | 0.210068 | + | 0.210068i | 0.804296 | − | 0.594228i | \(-0.202542\pi\) |
−0.594228 | + | 0.804296i | \(0.702542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.05798e6i | − | 1.56199i | −0.624540 | − | 0.780993i | \(-0.714713\pi\) | ||
0.624540 | − | 0.780993i | \(-0.285287\pi\) | |||||||
\(824\) | −247413. | − | 247413.i | −0.364392 | − | 0.364392i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −86323.7 | + | 86323.7i | −0.126523 | + | 0.126523i | ||||
\(827\) | −95483.6 | + | 95483.6i | −0.139610 | + | 0.139610i | −0.773458 | − | 0.633848i | \(-0.781475\pi\) |
0.633848 | + | 0.773458i | \(0.281475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 623513.i | 0.907270i | 0.891188 | + | 0.453635i | \(0.149873\pi\) | ||||
−0.891188 | + | 0.453635i | \(0.850127\pi\) | |||||||
\(830\) | 703561. | − | 703561.i | 1.02128 | − | 1.02128i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −240726. | + | 608671.i | −0.347757 | + | 0.879298i | ||||
\(833\) | −528231. | −0.761261 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 619271. | 0.888193 | ||||||||
\(836\) | − | 5138.64i | − | 0.00735251i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −273686. | − | 273686.i | −0.389731 | − | 0.389731i | ||||
\(839\) | 666830. | − | 666830.i | 0.947308 | − | 0.947308i | −0.0513717 | − | 0.998680i | \(-0.516359\pi\) |
0.998680 | + | 0.0513717i | \(0.0163593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.01978e6 | 1.44182 | ||||||||
\(842\) | − | 89085.5i | − | 0.125656i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 60084.3i | − | 0.0843482i | ||||||
\(845\) | −24210.4 | − | 752395.i | −0.0339070 | − | 1.05374i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −116153. | − | 116153.i | −0.161907 | − | 0.161907i | ||||
\(848\) | −1.17929e6 | −1.63995 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 55117.0 | + | 55117.0i | 0.0762864 | + | 0.0762864i | ||||
\(851\) | −240783. | − | 240783.i | −0.332481 | − | 0.332481i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −515777. | + | 515777.i | −0.708866 | + | 0.708866i | −0.966297 | − | 0.257431i | \(-0.917124\pi\) |
0.257431 | + | 0.966297i | \(0.417124\pi\) | |||||||
\(854\) | −544925. | −0.747172 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 426802. | − | 426802.i | 0.582478 | − | 0.582478i | ||||
\(857\) | − | 489846.i | − | 0.666957i | −0.942758 | − | 0.333479i | \(-0.891778\pi\) | ||
0.942758 | − | 0.333479i | \(-0.108222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.37694e6 | 1.86607 | 0.933037 | − | 0.359780i | \(-0.117148\pi\) | ||||
0.933037 | + | 0.359780i | \(0.117148\pi\) | |||||||
\(860\) | 33107.0 | + | 33107.0i | 0.0447634 | + | 0.0447634i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 243649.i | − | 0.327907i | ||||||
\(863\) | 715898. | + | 715898.i | 0.961235 | + | 0.961235i | 0.999276 | − | 0.0380415i | \(-0.0121119\pi\) |
−0.0380415 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 172030. | − | 172030.i | 0.229918 | − | 0.229918i | ||||
\(866\) | −85139.8 | + | 85139.8i | −0.113526 | + | 0.113526i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 21196.1i | − | 0.0281330i | ||||||
\(869\) | 494672. | − | 494672.i | 0.655055 | − | 0.655055i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 162316. | + | 374705.i | 0.213957 | + | 0.493916i | ||||
\(872\) | 1.44282e6 | 1.89748 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −188629. | −0.246937 | ||||||||
\(875\) | − | 315756.i | − | 0.412417i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −123217. | − | 123217.i | −0.160203 | − | 0.160203i | 0.622454 | − | 0.782657i | \(-0.286136\pi\) |
−0.782657 | + | 0.622454i | \(0.786136\pi\) | |||||||
\(878\) | −1.02774e6 | + | 1.02774e6i | −1.33320 | + | 1.33320i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −592288. | −0.764834 | ||||||||
\(881\) | 863892.i | 1.11303i | 0.830837 | + | 0.556516i | \(0.187862\pi\) | ||||
−0.830837 | + | 0.556516i | \(0.812138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 268829.i | − | 0.344790i | −0.985028 | − | 0.172395i | \(-0.944850\pi\) | ||
0.985028 | − | 0.172395i | \(-0.0551505\pi\) | |||||||
\(884\) | 34055.7 | + | 13468.8i | 0.0435797 | + | 0.0172355i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −65280.2 | − | 65280.2i | −0.0831599 | − | 0.0831599i | ||||
\(887\) | −1.04691e6 | −1.33065 | −0.665323 | − | 0.746556i | \(-0.731706\pi\) | ||||
−0.665323 | + | 0.746556i | \(0.731706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −401768. | − | 401768.i | −0.508361 | − | 0.508361i | ||||
\(890\) | −903706. | − | 903706.i | −1.14090 | − | 1.14090i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 756.886 | − | 756.886i | 0.000951263 | − | 0.000951263i | ||||
\(893\) | −40381.5 | −0.0506384 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −536226. | + | 536226.i | −0.669425 | + | 0.669425i | ||||
\(896\) | − | 377468.i | − | 0.470180i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −308691. | −0.382800 | ||||||||
\(899\) | 1.14980e6 | + | 1.14980e6i | 1.42267 | + | 1.42267i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.20055e6i | − | 1.47887i | ||||||
\(902\) | 338016. | + | 338016.i | 0.415456 | + | 0.415456i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −847999. | + | 847999.i | −1.03767 | + | 1.03767i | ||||
\(905\) | 43515.7 | − | 43515.7i | 0.0531311 | − | 0.0531311i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 293077.i | − | 0.356260i | −0.984007 | − | 0.178130i | \(-0.942995\pi\) | ||
0.984007 | − | 0.178130i | \(-0.0570047\pi\) | |||||||
\(908\) | 4851.68 | − | 4851.68i | 0.00588464 | − | 0.00588464i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 156536. | + | 361362.i | 0.189031 | + | 0.436374i | ||||
\(911\) | 1.22775e6 | 1.47936 | 0.739681 | − | 0.672958i | \(-0.234976\pi\) | ||||
0.739681 | + | 0.672958i | \(0.234976\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −772185. | −0.926361 | ||||||||
\(914\) | − | 544974.i | − | 0.652354i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7604.58 | + | 7604.58i | 0.00906326 | + | 0.00906326i | ||||
\(917\) | −47204.8 | + | 47204.8i | −0.0561368 | + | 0.0561368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −952406. | −1.12769 | −0.563847 | − | 0.825879i | \(-0.690679\pi\) | ||||
−0.563847 | + | 0.825879i | \(0.690679\pi\) | |||||||
\(920\) | 979259.i | 1.15697i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.27948e6i | − | 1.50513i | ||||||
\(923\) | 63896.6 | + | 147504.i | 0.0750023 | + | 0.173142i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28146.6 | − | 28146.6i | −0.0328960 | − | 0.0328960i | ||||
\(926\) | 860015. | 1.00296 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −94362.5 | − | 94362.5i | −0.109573 | − | 0.109573i | ||||
\(929\) | −865268. | − | 865268.i | −1.00258 | − | 1.00258i | −0.999997 | − | 0.00258353i | \(-0.999178\pi\) |
−0.00258353 | − | 0.999997i | \(-0.500822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 105662. | − | 105662.i | 0.121904 | − | 0.121904i | ||||
\(932\) | −57807.8 | −0.0665511 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 259629. | − | 259629.i | 0.297619 | − | 0.297619i | ||||
\(935\) | − | 602963.i | − | 0.689712i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −829106. | −0.944345 | −0.472173 | − | 0.881506i | \(-0.656530\pi\) | ||||
−0.472173 | + | 0.881506i | \(0.656530\pi\) | |||||||
\(938\) | −151054. | − | 151054.i | −0.171683 | − | 0.171683i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 10947.2i | − | 0.0123894i | ||||||
\(941\) | −1.18512e6 | − | 1.18512e6i | −1.33839 | − | 1.33839i | −0.897618 | − | 0.440774i | \(-0.854704\pi\) |
−0.440774 | − | 0.897618i | \(-0.645296\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 586664. | − | 586664.i | 0.659729 | − | 0.659729i | ||||
\(944\) | −261748. | + | 261748.i | −0.293724 | + | 0.293724i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 768509.i | − | 0.858750i | ||||||
\(947\) | −94860.4 | + | 94860.4i | −0.105775 | + | 0.105775i | −0.758014 | − | 0.652238i | \(-0.773830\pi\) |
0.652238 | + | 0.758014i | \(0.273830\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 256512. | − | 111117.i | 0.284823 | − | 0.123381i | ||||
\(950\) | −22050.0 | −0.0244322 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 366884. | 0.404813 | ||||||||
\(953\) | − | 313080.i | − | 0.344723i | −0.985034 | − | 0.172361i | \(-0.944860\pi\) | ||
0.985034 | − | 0.172361i | \(-0.0551397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −214341. | − | 214341.i | −0.235016 | − | 0.235016i | ||||
\(956\) | 57682.4 | − | 57682.4i | 0.0631142 | − | 0.0631142i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.68358e6 | 1.83444 | ||||||||
\(959\) | 318947.i | 0.346802i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 607464.i | 0.657770i | ||||||||
\(962\) | −367824. | − | 145472.i | −0.397456 | − | 0.157192i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 51075.1 | + | 51075.1i | 0.0549610 | + | 0.0549610i | ||||
\(965\) | −1.36762e6 | −1.46862 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 359201. | + | 359201.i | 0.384136 | + | 0.384136i | 0.872590 | − | 0.488454i | \(-0.162439\pi\) |
−0.488454 | + | 0.872590i | \(0.662439\pi\) | |||||||
\(968\) | −335504. | − | 335504.i | −0.358053 | − | 0.358053i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −245359. | + | 245359.i | −0.260771 | + | 0.260771i | ||||
\(971\) | 1.68455e6 | 1.78668 | 0.893338 | − | 0.449385i | \(-0.148357\pi\) | ||||
0.893338 | + | 0.449385i | \(0.148357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −90346.8 | + | 90346.8i | −0.0954305 | + | 0.0954305i | ||||
\(974\) | − | 1.08228e6i | − | 1.14083i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.65230e6 | −1.73456 | ||||||||
\(977\) | −857213. | − | 857213.i | −0.898048 | − | 0.898048i | 0.0972150 | − | 0.995263i | \(-0.469007\pi\) |
−0.995263 | + | 0.0972150i | \(0.969007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 991852.i | 1.03486i | ||||||||
\(980\) | 28644.4 | + | 28644.4i | 0.0298254 | + | 0.0298254i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 76718.1 | − | 76718.1i | 0.0795564 | − | 0.0795564i | ||||
\(983\) | −821373. | + | 821373.i | −0.850029 | + | 0.850029i | −0.990136 | − | 0.140107i | \(-0.955255\pi\) |
0.140107 | + | 0.990136i | \(0.455255\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 140719.i | 0.145037i | ||||||||
\(986\) | 1.03927e6 | − | 1.03927e6i | 1.06899 | − | 1.06899i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9506.29 | + | 4117.98i | −0.00973861 | + | 0.00421861i | ||||
\(989\) | −1.33383e6 | −1.36366 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.01521e6 | −1.03374 | −0.516868 | − | 0.856065i | \(-0.672902\pi\) | ||||
−0.516868 | + | 0.856065i | \(0.672902\pi\) | |||||||
\(992\) | − | 125645.i | − | 0.127680i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −59463.3 | − | 59463.3i | −0.0601834 | − | 0.0601834i | ||||
\(995\) | −887364. | + | 887364.i | −0.896305 | + | 0.896305i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 590999. | 0.594561 | 0.297280 | − | 0.954790i | \(-0.403920\pi\) | ||||
0.297280 | + | 0.954790i | \(0.403920\pi\) | |||||||
\(998\) | − | 421352.i | − | 0.423043i | ||||||
\(999\) | 0 | 0 |
(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 | 117.5.j.b.73.3 | 20 | ||
3.2 | odd | 2 | 39.5.g.a.34.8 | yes | 20 | ||
13.5 | odd | 4 | inner | 117.5.j.b.109.3 | 20 | ||
39.5 | even | 4 | 39.5.g.a.31.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.8 | ✓ | 20 | 39.5 | even | 4 | ||
39.5.g.a.34.8 | yes | 20 | 3.2 | odd | 2 | ||
117.5.j.b.73.3 | 20 | 1.1 | even | 1 | trivial | ||
117.5.j.b.109.3 | 20 | 13.5 | odd | 4 | inner |