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 | 109.3 | ||
Root | \(-2.89776 + 2.89776i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 117.109 |
Dual form | 117.5.j.b.73.3 |
$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(92\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | −0.969506 | − | 0.245066i | \(-0.921190\pi\) |
0.245066 | + | 0.969506i | \(0.421190\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 0.794047i | − | 0.0496279i | ||||||
\(5\) | −18.6373 | + | 18.6373i | −0.745491 | + | 0.745491i | −0.973629 | − | 0.228138i | \(-0.926736\pi\) |
0.228138 | + | 0.973629i | \(0.426736\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.2549 | − | 15.2549i | −0.311324 | − | 0.311324i | 0.534098 | − | 0.845422i | \(-0.320651\pi\) |
−0.845422 | + | 0.534098i | \(0.820651\pi\) | |||||||
\(8\) | −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 | 0.908265 | − | 0.418396i | \(-0.137408\pi\) |
−0.418396 | + | 0.908265i | \(0.637408\pi\) | |||||||
\(12\) | 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 | \(-0.843476\pi\) | ||
0.881515 | − | 0.472156i | \(-0.156524\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −54.5892 | + | 54.5892i | −0.151217 | + | 0.151217i | −0.778661 | − | 0.627445i | \(-0.784101\pi\) |
0.627445 | + | 0.778661i | \(0.284101\pi\) | |||||||
\(20\) | 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 | \(-0.809440\pi\) | ||
0.826090 | − | 0.563538i | \(-0.190560\pi\) | |||||||
\(24\) | 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 | −0.0858748 | − | 0.996306i | \(-0.527368\pi\) |
0.996306 | + | 0.0858748i | \(0.0273685\pi\) | |||||||
\(32\) | −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 | 0.544055 | − | 0.839049i | \(-0.316888\pi\) |
−0.839049 | + | 0.544055i | \(0.816888\pi\) | |||||||
\(38\) | − | 316.373i | − | 0.219095i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1642.44 | 1.02652 | ||||||||
\(41\) | −983.966 | + | 983.966i | −0.585346 | + | 0.585346i | −0.936367 | − | 0.351022i | \(-0.885834\pi\) |
0.351022 | + | 0.936367i | \(0.385834\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2237.13i | − | 1.20991i | −0.796258 | − | 0.604957i | \(-0.793190\pi\) | ||
0.796258 | − | 0.604957i | \(-0.206810\pi\) | |||||||
\(44\) | 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 | 0.785852 | − | 0.618415i | \(-0.212225\pi\) |
−0.618415 | + | 0.785852i | \(0.712225\pi\) | |||||||
\(48\) | 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 | 0.552812 | − | 0.833306i | \(-0.313555\pi\) |
−0.833306 | + | 0.552812i | \(0.813555\pi\) | |||||||
\(60\) | 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 | −0.871322 | − | 0.490711i | \(-0.836737\pi\) |
0.490711 | + | 0.871322i | \(0.336737\pi\) | |||||||
\(68\) | −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 | −0.770664 | − | 0.637241i | \(-0.780075\pi\) |
0.637241 | + | 0.770664i | \(0.280075\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1169.63 | − | 1169.63i | −0.219485 | − | 0.219485i | 0.588797 | − | 0.808281i | \(-0.299602\pi\) |
−0.808281 | + | 0.588797i | \(0.799602\pi\) | |||||||
\(74\) | 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 | −0.998591 | − | 0.0530714i | \(-0.983099\pi\) |
0.0530714 | + | 0.998591i | \(0.483099\pi\) | |||||||
\(84\) | 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 | −0.998320 | − | 0.0579425i | \(-0.981546\pi\) |
−0.0579425 | − | 0.998320i | \(-0.518454\pi\) | |||||||
\(90\) | 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 | −0.576014 | − | 0.817440i | \(-0.695393\pi\) |
0.817440 | + | 0.576014i | \(0.195393\pi\) | |||||||
\(98\) | 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 | \(-0.896937\pi\) | ||
0.948039 | − | 0.318154i | \(-0.103063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5614.96i | − | 0.529264i | −0.964350 | − | 0.264632i | \(-0.914750\pi\) | ||
0.964350 | − | 0.264632i | \(-0.0852504\pi\) | |||||||
\(104\) | 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 | −0.530029 | + | 0.847980i | \(0.677819\pi\) |
−0.847980 | + | 0.530029i | \(0.822181\pi\) | |||||||
\(110\) | 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 | \(-0.695939\pi\) | ||
0.577417 | − | 0.816449i | \(-0.304061\pi\) | |||||||
\(128\) | −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 | 0.928446 | − | 0.371467i | \(-0.121145\pi\) |
−0.371467 | + | 0.928446i | \(0.621145\pi\) | |||||||
\(138\) | 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 | 0.0246105 | − | 0.999697i | \(-0.492165\pi\) |
0.999697 | − | 0.0246105i | \(-0.00783457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −30969.3 | − | 30969.3i | −1.35824 | − | 1.35824i | −0.876082 | − | 0.482161i | \(-0.839852\pi\) |
−0.482161 | − | 0.876082i | \(-0.660148\pi\) | |||||||
\(152\) | 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 | 0.992453 | − | 0.122626i | \(-0.0391317\pi\) |
−0.122626 | + | 0.992453i | \(0.539132\pi\) | |||||||
\(164\) | 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 | 0.343458 | − | 0.939168i | \(-0.388402\pi\) |
−0.939168 | + | 0.343458i | \(0.888402\pi\) | |||||||
\(168\) | 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 | \(-0.950718\pi\) | ||
0.988039 | − | 0.154206i | \(-0.0492818\pi\) | |||||||
\(174\) | 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 | \(0.148213\pi\) | ||||
−0.893541 | + | 0.448982i | \(0.851787\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2334.88i | − | 0.0712700i | −0.999365 | − | 0.0356350i | \(-0.988655\pi\) | ||
0.999365 | − | 0.0356350i | \(-0.0113454\pi\) | |||||||
\(182\) | −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 | 0.999889 | − | 0.0148869i | \(-0.00473884\pi\) |
−0.0148869 | + | 0.999889i | \(0.504739\pi\) | |||||||
\(194\) | 13165.0i | 0.349797i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1536.94 | −0.0400078 | ||||||||
\(197\) | −3775.20 | + | 3775.20i | −0.0972763 | + | 0.0972763i | −0.754070 | − | 0.656794i | \(-0.771912\pi\) |
0.656794 | + | 0.754070i | \(0.271912\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 47612.3i | 1.20230i | 0.799136 | + | 0.601151i | \(0.205291\pi\) | ||||
−0.799136 | + | 0.601151i | \(0.794709\pi\) | |||||||
\(200\) | −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 | −0.716626 | − | 0.697458i | \(-0.754314\pi\) |
0.697458 | + | 0.716626i | \(0.254314\pi\) | |||||||
\(224\) | 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 | −0.763905 | − | 0.645329i | \(-0.776720\pi\) |
0.645329 | + | 0.763905i | \(0.276720\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9576.99 | + | 9576.99i | 0.182624 | + | 0.182624i | 0.792498 | − | 0.609874i | \(-0.208780\pi\) |
−0.609874 | + | 0.792498i | \(0.708780\pi\) | |||||||
\(230\) | −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 | \(-0.766080\pi\) | ||
0.741910 | − | 0.670500i | \(-0.233920\pi\) | |||||||
\(234\) | 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 | −0.326578 | + | 0.945170i | \(0.605895\pi\) |
−0.945170 | + | 0.326578i | \(0.894105\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 64322.5 | + | 64322.5i | 1.10746 | + | 1.10746i | 0.993483 | + | 0.113978i | \(0.0363593\pi\) |
0.113978 | + | 0.993483i | \(0.463641\pi\) | |||||||
\(242\) | 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 | \(-0.872055\pi\) | ||
0.920300 | − | 0.391213i | \(-0.127945\pi\) | |||||||
\(252\) | 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 | \(-0.785521\pi\) | ||
0.781453 | − | 0.623964i | \(-0.214479\pi\) | |||||||
\(258\) | 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 | −0.999467 | − | 0.0326374i | \(-0.989609\pi\) |
−0.0326374 | − | 0.999467i | \(-0.510391\pi\) | |||||||
\(272\) | − | 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 | \(-0.661499\pi\) | ||
0.485876 | − | 0.874028i | \(-0.338501\pi\) | |||||||
\(278\) | −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 | 0.822152 | − | 0.569268i | \(-0.192773\pi\) |
−0.569268 | + | 0.822152i | \(0.692773\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 151960.i | 1.89739i | 0.316186 | + | 0.948697i | \(0.397598\pi\) | ||||
−0.316186 | + | 0.948697i | \(0.602402\pi\) | |||||||
\(284\) | 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 | 0.564514 | − | 0.825423i | \(-0.309063\pi\) |
−0.825423 | + | 0.564514i | \(0.809063\pi\) | |||||||
\(294\) | 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 | 0.874808 | − | 0.484469i | \(-0.160987\pi\) |
−0.484469 | + | 0.874808i | \(0.660987\pi\) | |||||||
\(308\) | −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 | \(-0.866367\pi\) | ||
0.913162 | − | 0.407597i | \(-0.133633\pi\) | |||||||
\(312\) | 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 | −0.884943 | − | 0.465699i | \(-0.845803\pi\) |
0.465699 | + | 0.884943i | \(0.345803\pi\) | |||||||
\(318\) | 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 | −0.322943 | − | 0.946418i | \(-0.604672\pi\) |
0.946418 | + | 0.322943i | \(0.104672\pi\) | |||||||
\(332\) | 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 | \(-0.873613\pi\) | ||
0.922203 | − | 0.386706i | \(-0.126387\pi\) | |||||||
\(338\) | −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 | 0.631877 | − | 0.775069i | \(-0.282285\pi\) |
−0.775069 | + | 0.631877i | \(0.782285\pi\) | |||||||
\(350\) | − | 6161.85i | − | 0.0503008i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8512.19 | −0.0686999 | ||||||||
\(353\) | −63740.5 | + | 63740.5i | −0.511524 | + | 0.511524i | −0.914993 | − | 0.403469i | \(-0.867804\pi\) |
0.403469 | + | 0.914993i | \(0.367804\pi\) | |||||||
\(354\) | 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 | 0.924831 | + | 0.380377i | \(0.124206\pi\) |
0.380377 | + | 0.924831i | \(0.375794\pi\) | |||||||
\(360\) | 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 | −0.927276 | − | 0.374378i | \(-0.877856\pi\) |
0.374378 | + | 0.927276i | \(0.377856\pi\) | |||||||
\(380\) | −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 | −0.802795 | − | 0.596255i | \(-0.796655\pi\) |
0.596255 | + | 0.802795i | \(0.296655\pi\) | |||||||
\(384\) | 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 | \(0.148076\pi\) | ||||
−0.893734 | + | 0.448597i | \(0.851924\pi\) | |||||||
\(390\) | 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 | 0.201614 | − | 0.979465i | \(-0.435381\pi\) |
−0.979465 | + | 0.201614i | \(0.935381\pi\) | |||||||
\(398\) | −137969. | − | 137969.i | −0.870996 | − | 0.870996i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 18683.8i | − | 0.116774i | ||||||
\(401\) | −132123. | − | 132123.i | −0.821653 | − | 0.821653i | 0.164692 | − | 0.986345i | \(-0.447337\pi\) |
−0.986345 | + | 0.164692i | \(0.947337\pi\) | |||||||
\(402\) | 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 | −0.698988 | − | 0.715133i | \(-0.746366\pi\) |
0.715133 | + | 0.698988i | \(0.246366\pi\) | |||||||
\(410\) | 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 | −0.662413 | − | 0.749139i | \(-0.730468\pi\) |
0.749139 | + | 0.662413i | \(0.230468\pi\) | |||||||
\(422\) | 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 | −0.584835 | − | 0.811152i | \(-0.698841\pi\) |
0.811152 | + | 0.584835i | \(0.198841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29381.2i | 0.156709i | 0.996926 | + | 0.0783545i | \(0.0249666\pi\) | ||||
−0.996926 | + | 0.0783545i | \(0.975033\pi\) | |||||||
\(434\) | 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 | \(0.371942\pi\) | ||||
−0.391542 | + | 0.920160i | \(0.628058\pi\) | |||||||
\(440\) | 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 | 0.826759 | − | 0.562556i | \(-0.190182\pi\) |
−0.562556 | + | 0.826759i | \(0.690182\pi\) | |||||||
\(450\) | 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 | −0.445189 | − | 0.895436i | \(-0.646864\pi\) |
0.895436 | + | 0.445189i | \(0.146864\pi\) | |||||||
\(458\) | −55503.7 | −0.264601 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8823.43 | − | 8823.43i | 0.0416986 | − | 0.0416986i | ||||
\(461\) | 220771. | − | 220771.i | 1.03882 | − | 1.03882i | 0.0396051 | − | 0.999215i | \(-0.487390\pi\) |
0.999215 | − | 0.0396051i | \(-0.0126100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −148393. | − | 148393.i | −0.692231 | − | 0.692231i | 0.270491 | − | 0.962722i | \(-0.412814\pi\) |
−0.962722 | + | 0.270491i | \(0.912814\pi\) | |||||||
\(464\) | 352296. | 1.63634 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 210962. | + | 210962.i | 0.971474 | + | 0.971474i | ||||
\(467\) | − | 89596.5i | − | 0.410826i | −0.978675 | − | 0.205413i | \(-0.934146\pi\) | ||
0.978675 | − | 0.205413i | \(-0.0658537\pi\) | |||||||
\(468\) | 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 | −0.948083 | − | 0.318023i | \(-0.896981\pi\) |
−0.318023 | − | 0.948083i | \(-0.603019\pi\) | |||||||
\(480\) | 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 | −0.193677 | − | 0.981065i | \(-0.562041\pi\) |
0.981065 | + | 0.193677i | \(0.0620414\pi\) | |||||||
\(488\) | 271588. | + | 271588.i | 1.14044 | + | 1.14044i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −209067. | −0.870750 | ||||||||
\(491\) | − | 26475.0i | − | 0.109818i | −0.998491 | − | 0.0549088i | \(-0.982513\pi\) | ||
0.998491 | − | 0.0549088i | \(-0.0174868\pi\) | |||||||
\(492\) | 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 | −0.545883 | − | 0.837862i | \(-0.683806\pi\) |
0.837862 | + | 0.545883i | \(0.183806\pi\) | |||||||
\(500\) | −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 | −0.472319 | − | 0.881428i | \(-0.656583\pi\) |
0.881428 | + | 0.472319i | \(0.156583\pi\) | |||||||
\(510\) | 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 | −0.937560 | − | 0.347823i | \(-0.886921\pi\) |
−0.347823 | − | 0.937560i | \(-0.613079\pi\) | |||||||
\(542\) | 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 | 0.440873 | − | 0.897569i | \(-0.354669\pi\) |
−0.897569 | + | 0.440873i | \(0.854669\pi\) | |||||||
\(558\) | 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 | \(0.157966\pi\) | ||||
−0.879368 | + | 0.476143i | \(0.842034\pi\) | |||||||
\(564\) | 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 | \(-0.925713\pi\) | ||
0.972891 | − | 0.231266i | \(-0.0742867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 477531.i | 1.46463i | 0.680964 | + | 0.732317i | \(0.261561\pi\) | ||||
−0.680964 | + | 0.732317i | \(0.738439\pi\) | |||||||
\(572\) | −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 | −0.524402 | − | 0.851471i | \(-0.675711\pi\) |
0.851471 | + | 0.524402i | \(0.175711\pi\) | |||||||
\(578\) | −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 | −0.107632 | + | 0.994191i | \(0.534327\pi\) |
−0.994191 | + | 0.107632i | \(0.965673\pi\) | |||||||
\(588\) | 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 | 0.677438 | − | 0.735580i | \(-0.263090\pi\) |
−0.735580 | + | 0.677438i | \(0.763090\pi\) | |||||||
\(594\) | 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 | −0.249956 | − | 0.968257i | \(-0.580416\pi\) |
0.968257 | + | 0.249956i | \(0.0804162\pi\) | |||||||
\(614\) | −213212. | −0.565555 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −79685.7 | + | 79685.7i | −0.210000 | + | 0.210000i | ||||
\(617\) | −128460. | + | 128460.i | −0.337440 | + | 0.337440i | −0.855403 | − | 0.517963i | \(-0.826690\pi\) |
0.517963 | + | 0.855403i | \(0.326690\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −78942.1 | − | 78942.1i | −0.206029 | − | 0.206029i | 0.596548 | − | 0.802577i | \(-0.296538\pi\) |
−0.802577 | + | 0.596548i | \(0.796538\pi\) | |||||||
\(620\) | 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 | 0.511899 | − | 0.859045i | \(-0.328942\pi\) |
−0.859045 | + | 0.511899i | \(0.828942\pi\) | |||||||
\(632\) | −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 | \(0.148237\pi\) | ||||
−0.893507 | + | 0.449049i | \(0.851763\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 111450. | − | 111450.i | 0.269561 | − | 0.269561i | −0.559362 | − | 0.828923i | \(-0.688954\pi\) |
0.828923 | + | 0.559362i | \(0.188954\pi\) | |||||||
\(644\) | 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 | \(0.159034\pi\) | ||||
−0.877765 | + | 0.479092i | \(0.840966\pi\) | |||||||
\(648\) | 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 | 0.729887 | − | 0.683568i | \(-0.239573\pi\) |
−0.683568 | + | 0.729887i | \(0.739573\pi\) | |||||||
\(662\) | 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 | \(0.0535556\pi\) | ||||
−0.985879 | + | 0.167457i | \(0.946444\pi\) | |||||||
\(674\) | 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 | 0.650432 | − | 0.759564i | \(-0.274588\pi\) |
−0.759564 | + | 0.650432i | \(0.774588\pi\) | |||||||
\(684\) | 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 | −0.937423 | − | 0.348193i | \(-0.886795\pi\) |
0.348193 | + | 0.937423i | \(0.386795\pi\) | |||||||
\(692\) | −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 | \(-0.930649\pi\) | ||
0.976359 | − | 0.216154i | \(-0.0693512\pi\) | |||||||
\(702\) | 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 | 0.733867 | − | 0.679293i | \(-0.237713\pi\) |
−0.679293 | + | 0.733867i | \(0.737713\pi\) | |||||||
\(710\) | 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 | \(0.174007\pi\) | ||||
−0.854265 | + | 0.519837i | \(0.825993\pi\) | |||||||
\(720\) | 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 | \(0.101368\pi\) | ||||
−0.949720 | + | 0.313102i | \(0.898632\pi\) | |||||||
\(728\) | −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 | −0.843170 | − | 0.537648i | \(-0.819313\pi\) |
0.537648 | + | 0.843170i | \(0.319313\pi\) | |||||||
\(734\) | −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 | 0.416670 | − | 0.909058i | \(-0.363197\pi\) |
−0.909058 | + | 0.416670i | \(0.863197\pi\) | |||||||
\(740\) | − | 11953.0i | − | 0.0218279i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −388927. | −0.706416 | ||||||||
\(743\) | 397022. | − | 397022.i | 0.719180 | − | 0.719180i | −0.249258 | − | 0.968437i | \(-0.580187\pi\) |
0.968437 | + | 0.249258i | \(0.0801866\pi\) | |||||||
\(744\) | 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 | \(-0.971477\pi\) | ||
0.995988 | − | 0.0894882i | \(-0.0285231\pi\) | |||||||
\(752\) | 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 | 0.765442 | − | 0.643505i | \(-0.222520\pi\) |
−0.643505 | + | 0.765442i | \(0.722520\pi\) | |||||||
\(762\) | 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 | −0.0907545 | + | 0.995873i | \(0.528928\pi\) |
−0.995873 | + | 0.0907545i | \(0.971072\pi\) | |||||||
\(770\) | −195335. | −0.329456 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 29133.9 | − | 29133.9i | 0.0488836 | − | 0.0488836i | ||||
\(773\) | −152962. | + | 152962.i | −0.255990 | + | 0.255990i | −0.823421 | − | 0.567431i | \(-0.807937\pi\) |
0.567431 | + | 0.823421i | \(0.307937\pi\) | |||||||
\(774\) | 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 | 0.856032 | − | 0.516922i | \(-0.172922\pi\) |
−0.516922 | + | 0.856032i | \(0.672922\pi\) | |||||||
\(788\) | 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 | \(0.131002\pi\) | ||||
−0.916500 | + | 0.400035i | \(0.868998\pi\) | |||||||
\(798\) | 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 | −0.479473 | − | 0.877557i | \(-0.659172\pi\) |
0.877557 | + | 0.479473i | \(0.159172\pi\) | |||||||
\(812\) | −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 | −0.594228 | − | 0.804296i | \(-0.702542\pi\) |
0.804296 | + | 0.594228i | \(0.202542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.05798e6i | 1.56199i | 0.624540 | + | 0.780993i | \(0.285287\pi\) | ||||
−0.624540 | + | 0.780993i | \(0.714713\pi\) | |||||||
\(824\) | −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 | 0.633848 | − | 0.773458i | \(-0.281475\pi\) |
−0.773458 | + | 0.633848i | \(0.781475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 623513.i | − | 0.907270i | −0.891188 | − | 0.453635i | \(-0.850127\pi\) | ||
0.891188 | − | 0.453635i | \(-0.149873\pi\) | |||||||
\(830\) | 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 | 0.998680 | − | 0.0513717i | \(-0.0163593\pi\) |
−0.0513717 | + | 0.998680i | \(0.516359\pi\) | |||||||
\(840\) | 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 | 0.257431 | − | 0.966297i | \(-0.417124\pi\) |
−0.966297 | + | 0.257431i | \(0.917124\pi\) | |||||||
\(854\) | −544925. | −0.747172 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 426802. | + | 426802.i | 0.582478 | + | 0.582478i | ||||
\(857\) | 489846.i | 0.666957i | 0.942758 | + | 0.333479i | \(0.108222\pi\) | ||||
−0.942758 | + | 0.333479i | \(0.891778\pi\) | |||||||
\(858\) | 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 | −0.0380415 | − | 0.999276i | \(-0.512112\pi\) |
0.999276 | + | 0.0380415i | \(0.0121119\pi\) | |||||||
\(864\) | 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 | −0.782657 | − | 0.622454i | \(-0.786136\pi\) |
0.622454 | + | 0.782657i | \(0.286136\pi\) | |||||||
\(878\) | −1.02774e6 | − | 1.02774e6i | −1.33320 | − | 1.33320i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −592288. | −0.764834 | ||||||||
\(881\) | − | 863892.i | − | 1.11303i | −0.830837 | − | 0.556516i | \(-0.812138\pi\) | ||
0.830837 | − | 0.556516i | \(-0.187862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 268829.i | 0.344790i | 0.985028 | + | 0.172395i | \(0.0551505\pi\) | ||||
−0.985028 | + | 0.172395i | \(0.944850\pi\) | |||||||
\(884\) | 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 | \(0.0570047\pi\) | ||||
−0.984007 | + | 0.178130i | \(0.942995\pi\) | |||||||
\(908\) | 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 | −0.00258353 | + | 0.999997i | \(0.500822\pi\) |
−0.999997 | + | 0.00258353i | \(0.999178\pi\) | |||||||
\(930\) | 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 | −0.440774 | + | 0.897618i | \(0.645296\pi\) |
−0.897618 | + | 0.440774i | \(0.854704\pi\) | |||||||
\(942\) | 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 | 0.652238 | − | 0.758014i | \(-0.273830\pi\) |
−0.758014 | + | 0.652238i | \(0.773830\pi\) | |||||||
\(948\) | 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 | \(0.0551397\pi\) | ||||
−0.985034 | + | 0.172361i | \(0.944860\pi\) | |||||||
\(954\) | 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 | −0.488454 | − | 0.872590i | \(-0.662439\pi\) |
0.872590 | + | 0.488454i | \(0.162439\pi\) | |||||||
\(968\) | −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 | −0.995263 | − | 0.0972150i | \(-0.969007\pi\) |
0.0972150 | + | 0.995263i | \(0.469007\pi\) | |||||||
\(978\) | 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 | 0.140107 | − | 0.990136i | \(-0.455255\pi\) |
−0.990136 | + | 0.140107i | \(0.955255\pi\) | |||||||
\(984\) | 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.109.3 | 20 | ||
3.2 | odd | 2 | 39.5.g.a.31.8 | ✓ | 20 | ||
13.8 | odd | 4 | inner | 117.5.j.b.73.3 | 20 | ||
39.8 | even | 4 | 39.5.g.a.34.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.8 | ✓ | 20 | 3.2 | odd | 2 | ||
39.5.g.a.34.8 | yes | 20 | 39.8 | even | 4 | ||
117.5.j.b.73.3 | 20 | 13.8 | odd | 4 | inner | ||
117.5.j.b.109.3 | 20 | 1.1 | even | 1 | trivial |