Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(17,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.bi (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.23 | ||
Character | \(\chi\) | \(=\) | 672.17 |
Dual form | 672.2.bi.c.593.23 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.70617 | + | 0.298296i | 0.985058 | + | 0.172221i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.337879 | + | 0.195075i | −0.151104 | + | 0.0872401i | −0.573646 | − | 0.819103i | \(-0.694471\pi\) |
0.422542 | + | 0.906344i | \(0.361138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.39526 | + | 2.24795i | −0.527357 | + | 0.849644i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82204 | + | 1.01789i | 0.940680 | + | 0.339296i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.748582 | + | 1.29658i | −0.225706 | + | 0.390934i | −0.956531 | − | 0.291631i | \(-0.905802\pi\) |
0.730825 | + | 0.682565i | \(0.239136\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.28768 | 0.911838 | 0.455919 | − | 0.890021i | \(-0.349311\pi\) | ||||
0.455919 | + | 0.890021i | \(0.349311\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.634670 | + | 0.232043i | −0.163871 | + | 0.0599132i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.68169 | − | 2.91278i | 0.407871 | − | 0.706453i | −0.586780 | − | 0.809746i | \(-0.699605\pi\) |
0.994651 | + | 0.103293i | \(0.0329381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.56203 | + | 4.43756i | 0.587769 | + | 1.01805i | 0.994524 | + | 0.104509i | \(0.0333270\pi\) |
−0.406755 | + | 0.913537i | \(0.633340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.05110 | + | 3.41918i | −0.665805 | + | 0.746126i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.72764 | + | 2.72950i | −0.985780 | + | 0.569141i | −0.904010 | − | 0.427511i | \(-0.859391\pi\) |
−0.0817700 | + | 0.996651i | \(0.526057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.42389 | + | 4.19830i | −0.484778 | + | 0.839661i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.51125 | + | 2.57850i | 0.868190 | + | 0.496232i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.13801 | 0.768410 | 0.384205 | − | 0.923248i | \(-0.374476\pi\) | ||||
0.384205 | + | 0.923248i | \(0.374476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.60237 | + | 2.07983i | 0.647005 | + | 0.373549i | 0.787308 | − | 0.616560i | \(-0.211474\pi\) |
−0.140303 | + | 0.990109i | \(0.544808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.66397 | + | 1.98889i | −0.289661 | + | 0.346222i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0329110 | − | 1.03171i | 0.00556298 | − | 0.174391i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.46581 | − | 4.31038i | 1.22737 | − | 0.708623i | 0.260892 | − | 0.965368i | \(-0.415983\pi\) |
0.966479 | + | 0.256745i | \(0.0826501\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.60934 | + | 0.980702i | 0.898214 | + | 0.157038i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.1607 | −1.74301 | −0.871505 | − | 0.490387i | \(-0.836855\pi\) | ||||
−0.871505 | + | 0.490387i | \(0.836855\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.79323i | − | 0.730961i | −0.930819 | − | 0.365480i | \(-0.880905\pi\) | ||
0.930819 | − | 0.365480i | \(-0.119095\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.15207 | + | 0.206585i | −0.171741 | + | 0.0307959i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.51067 | − | 4.34861i | −0.366219 | − | 0.634310i | 0.622752 | − | 0.782419i | \(-0.286015\pi\) |
−0.988971 | + | 0.148109i | \(0.952681\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.10652 | − | 6.27292i | −0.443788 | − | 0.896132i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.73813 | − | 4.46806i | 0.523443 | − | 0.625653i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.499243 | − | 0.864715i | 0.0685763 | − | 0.118778i | −0.829699 | − | 0.558212i | \(-0.811488\pi\) |
0.898275 | + | 0.439434i | \(0.144821\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.584118i | − | 0.0787624i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.04755 | + | 8.33548i | 0.403657 | + | 1.10406i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.36034 | + | 0.785391i | 0.177101 | + | 0.102249i | 0.585930 | − | 0.810362i | \(-0.300729\pi\) |
−0.408829 | + | 0.912611i | \(0.634063\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.40889 | + | 5.90437i | 0.436464 | + | 0.755977i | 0.997414 | − | 0.0718723i | \(-0.0228974\pi\) |
−0.560950 | + | 0.827850i | \(0.689564\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.22563 | + | 4.92357i | −0.784355 | + | 0.620312i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.11084 | + | 0.641343i | −0.137783 | + | 0.0795488i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.05467 | − | 1.76361i | −0.373187 | − | 0.215460i | 0.301663 | − | 0.953415i | \(-0.402458\pi\) |
−0.674850 | + | 0.737955i | \(0.735792\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −8.88036 | + | 3.24676i | −1.06907 | + | 0.390864i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.3360i | − | 1.70137i | −0.525677 | − | 0.850684i | \(-0.676188\pi\) | ||
0.525677 | − | 0.850684i | \(-0.323812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.76107 | + | 1.59410i | 0.323159 | + | 0.186576i | 0.652800 | − | 0.757531i | \(-0.273594\pi\) |
−0.329641 | + | 0.944106i | \(0.606928\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.38791 | + | 6.43999i | −0.622142 | + | 0.743626i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.87018 | − | 3.49184i | −0.213127 | − | 0.397932i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.239413 | + | 0.414676i | 0.0269361 | + | 0.0466547i | 0.879179 | − | 0.476491i | \(-0.158092\pi\) |
−0.852243 | + | 0.523146i | \(0.824758\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.92781 | + | 5.74504i | 0.769756 | + | 0.638338i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.4548i | − | 1.91591i | −0.286911 | − | 0.957957i | \(-0.592628\pi\) | ||
0.286911 | − | 0.957957i | \(-0.407372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.31222i | 0.142331i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.06016 | + | 1.23435i | 0.756928 | + | 0.132337i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.54840 | − | 4.41396i | −0.270130 | − | 0.467879i | 0.698765 | − | 0.715351i | \(-0.253733\pi\) |
−0.968895 | + | 0.247473i | \(0.920400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.58716 | + | 7.39053i | −0.480865 | + | 0.774738i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.52586 | + | 4.62312i | 0.573005 | + | 0.479395i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.73131 | − | 0.999573i | −0.177629 | − | 0.102554i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.00074i | − | 0.913887i | −0.889496 | − | 0.456943i | \(-0.848944\pi\) | ||
0.889496 | − | 0.456943i | \(-0.151056\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.43230 | + | 2.89703i | −0.344959 | + | 0.291163i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.63907 | + | 2.67837i | 0.461605 | + | 0.266508i | 0.712719 | − | 0.701450i | \(-0.247464\pi\) |
−0.251114 | + | 0.967958i | \(0.580797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.70831 | + | 4.45039i | −0.759522 | + | 0.438510i | −0.829124 | − | 0.559065i | \(-0.811160\pi\) |
0.0696021 | + | 0.997575i | \(0.477827\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.363908 | − | 1.75046i | 0.0355138 | − | 0.170828i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.85256 | + | 13.6010i | 0.759135 | + | 1.31486i | 0.943292 | + | 0.331964i | \(0.107711\pi\) |
−0.184157 | + | 0.982897i | \(0.558955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.1582 | − | 8.75159i | −1.45189 | − | 0.838250i | −0.453303 | − | 0.891357i | \(-0.649754\pi\) |
−0.998589 | + | 0.0531069i | \(0.983088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0237 | − | 5.12723i | 1.33107 | − | 0.486655i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.0726142i | 0.00683097i | 0.999994 | + | 0.00341549i | \(0.00108718\pi\) | ||||
−0.999994 | + | 0.00341549i | \(0.998913\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.06491 | − | 1.84448i | 0.0993037 | − | 0.171999i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.27796 | + | 3.34649i | 0.857748 | + | 0.309383i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.20138 | + | 7.84443i | 0.385139 | + | 0.719098i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.37925 | + | 7.58508i | 0.398114 | + | 0.689553i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.0421 | − | 3.32920i | −1.71697 | − | 0.300183i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3.84211i | − | 0.343649i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.81577 | 0.782273 | 0.391137 | − | 0.920333i | \(-0.372082\pi\) | ||||
0.391137 | + | 0.920333i | \(0.372082\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.42980 | − | 8.17807i | 0.125887 | − | 0.720039i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.36183 | − | 2.51830i | 0.381095 | − | 0.220025i | −0.297200 | − | 0.954815i | \(-0.596053\pi\) |
0.678294 | + | 0.734790i | \(0.262719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5501 | − | 0.432239i | −1.17494 | − | 0.0374799i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.02726 | + | 0.00881014i | −0.174478 | + | 0.000758256i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.34787 | + | 3.66494i | 0.542335 | + | 0.313117i | 0.746025 | − | 0.665918i | \(-0.231960\pi\) |
−0.203690 | + | 0.979035i | \(0.565293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7497 | −1.33587 | −0.667935 | − | 0.744220i | \(-0.732822\pi\) | ||||
−0.667935 | + | 0.744220i | \(0.732822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.98646 | − | 8.16840i | −0.251505 | − | 0.687903i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.46110 | + | 4.26275i | −0.205807 | + | 0.356469i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.39815 | + | 0.807222i | −0.116110 | + | 0.0670361i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.42906 | − | 11.6293i | −0.282824 | − | 0.959172i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.98969 | − | 15.5706i | −0.736464 | − | 1.27559i | −0.954078 | − | 0.299559i | \(-0.903161\pi\) |
0.217613 | − | 0.976035i | \(-0.430173\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.89149 | − | 13.6685i | 0.642201 | − | 1.11232i | −0.342740 | − | 0.939430i | \(-0.611355\pi\) |
0.984940 | − | 0.172894i | \(-0.0553117\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.71069 | − | 6.50820i | 0.623373 | − | 0.526157i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.62289 | −0.130354 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53274 | + | 4.38683i | −0.202134 | + | 0.350107i | −0.949216 | − | 0.314625i | \(-0.898121\pi\) |
0.747082 | + | 0.664732i | \(0.231454\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.10974 | − | 1.32643i | 0.0880077 | − | 0.105193i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.460494 | − | 14.4358i | 0.0362920 | − | 1.13770i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.8745 | − | 6.27840i | 0.851757 | − | 0.491762i | −0.00948597 | − | 0.999955i | \(-0.503020\pi\) |
0.861243 | + | 0.508193i | \(0.169686\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.174240 | − | 0.996605i | 0.0135646 | − | 0.0775856i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.43145 | −0.575063 | −0.287531 | − | 0.957771i | \(-0.592835\pi\) | ||||
−0.287531 | + | 0.957771i | \(0.592835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.19116 | −0.168551 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.71320 | + | 15.1308i | 0.207483 | + | 1.15708i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.2445 | + | 8.80144i | −1.15902 | + | 0.669161i | −0.951069 | − | 0.308978i | \(-0.900013\pi\) |
−0.207952 | + | 0.978139i | \(0.566680\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.05561 | − | 11.3065i | −0.457761 | − | 0.854690i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.08669 | + | 1.74579i | 0.156845 | + | 0.131222i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.11784 | − | 14.0605i | 0.606756 | − | 1.05093i | −0.385016 | − | 0.922910i | \(-0.625804\pi\) |
0.991771 | − | 0.128022i | \(-0.0408627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.19340 | −0.460351 | −0.230176 | − | 0.973149i | \(-0.573930\pi\) | ||||
−0.230176 | + | 0.973149i | \(0.573930\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.05490 | + | 11.0907i | 0.299747 | + | 0.819850i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.68169 | + | 2.91278i | −0.123641 | + | 0.214152i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.51777 | + | 4.36091i | 0.184118 | + | 0.318901i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.0907 | + | 6.54338i | −0.879467 | + | 0.475961i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.28788 | + | 4.20766i | −0.527333 | + | 0.304456i | −0.739930 | − | 0.672684i | \(-0.765141\pi\) |
0.212597 | + | 0.977140i | \(0.431808\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.57333 | − | 11.3853i | 0.473158 | − | 0.819534i | −0.526370 | − | 0.850256i | \(-0.676447\pi\) |
0.999528 | + | 0.0307215i | \(0.00978048\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.08659 | + | 0.762882i | −0.149424 | + | 0.0546311i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.6119 | 1.25480 | 0.627398 | − | 0.778699i | \(-0.284120\pi\) | ||||
0.627398 | + | 0.778699i | \(0.284120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.2688 | − | 9.97017i | −1.22416 | − | 0.706767i | −0.258354 | − | 0.966050i | \(-0.583180\pi\) |
−0.965801 | + | 0.259284i | \(0.916514\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.68570 | − | 3.92022i | −0.330504 | − | 0.276511i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.77359 | + | 9.30203i | −0.405227 | + | 0.652874i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.77097 | − | 2.17717i | 0.263376 | − | 0.152060i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.1199 | + | 2.89055i | −1.12041 | + | 0.200907i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.67154 | −0.530652 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.5159i | − | 0.999314i | −0.866223 | − | 0.499657i | \(-0.833459\pi\) | ||
0.866223 | − | 0.499657i | \(-0.166541\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.27637 | − | 24.4596i | 0.293012 | − | 1.67595i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.935038 | + | 1.61953i | 0.0637691 | + | 0.110451i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.70158 | + | 5.19604i | −0.658586 | + | 0.352730i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.23534 | + | 3.54343i | 0.286198 | + | 0.239443i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.52887 | − | 9.57629i | 0.371912 | − | 0.644171i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.77897i | 0.186093i | 0.995662 | + | 0.0930467i | \(0.0296606\pi\) | ||||
−0.995662 | + | 0.0930467i | \(0.970339\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.1137 | + | 9.38052i | −0.740915 | + | 0.625368i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.0438 | − | 8.10819i | −0.932119 | − | 0.538159i | −0.0446379 | − | 0.999003i | \(-0.514213\pi\) |
−0.887481 | + | 0.460844i | \(0.847547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.3150 | + | 17.8661i | 0.681633 | + | 1.18062i | 0.974482 | + | 0.224464i | \(0.0720633\pi\) |
−0.292849 | + | 0.956159i | \(0.594603\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.14925 | − | 6.51554i | −0.141410 | − | 0.428691i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.80462 | − | 1.04190i | 0.118225 | − | 0.0682572i | −0.439721 | − | 0.898134i | \(-0.644923\pi\) |
0.557946 | + | 0.829877i | \(0.311589\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.69661 | + | 0.979538i | 0.110675 | + | 0.0638980i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.284784 | + | 0.778925i | 0.0184987 | + | 0.0505966i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.851762i | 0.0550959i | 0.999620 | + | 0.0275480i | \(0.00876990\pi\) | ||||
−0.999620 | + | 0.0275480i | \(0.991230\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.0417 | + | 7.52961i | 0.840087 | + | 0.485025i | 0.857294 | − | 0.514827i | \(-0.172144\pi\) |
−0.0172066 | + | 0.999852i | \(0.505477\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.1063 | + | 11.8686i | 0.648319 | + | 0.761369i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.27332 | + | 1.51349i | 0.145237 | + | 0.0966932i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.42312 | + | 14.5893i | 0.535950 | + | 0.928293i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.20670 | − | 29.7809i | 0.329961 | − | 1.88729i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8022i | 0.744948i | 0.928043 | + | 0.372474i | \(0.121490\pi\) | ||||
−0.928043 | + | 0.372474i | \(0.878510\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.17302i | − | 0.513834i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.391432 | + | 2.23888i | −0.0245124 | + | 0.140204i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.86901 | + | 15.3616i | 0.553233 | + | 0.958228i | 0.998039 | + | 0.0626011i | \(0.0199396\pi\) |
−0.444805 | + | 0.895627i | \(0.646727\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.727204 | + | 22.7968i | −0.0451863 | + | 1.41653i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.6776 | + | 4.21204i | 0.722827 | + | 0.260719i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.27815 | + | 3.62469i | 0.387128 | + | 0.223508i | 0.680915 | − | 0.732363i | \(-0.261582\pi\) |
−0.293787 | + | 0.955871i | \(0.594916\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.389559i | 0.0239304i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.03134 | − | 8.29114i | −0.185515 | − | 0.507410i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.95817 | + | 1.70790i | 0.180363 | + | 0.104132i | 0.587463 | − | 0.809251i | \(-0.300127\pi\) |
−0.407100 | + | 0.913383i | \(0.633460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.96989 | + | 2.29201i | −0.241153 | + | 0.139230i | −0.615707 | − | 0.787975i | \(-0.711129\pi\) |
0.374553 | + | 0.927205i | \(0.377796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.0310 | + | 11.2412i | −0.607106 | + | 0.680346i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.62896 | − | 6.28555i | −0.218835 | − | 0.379033i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6940 | − | 6.17421i | −0.642543 | − | 0.370972i | 0.143050 | − | 0.989715i | \(-0.454309\pi\) |
−0.785593 | + | 0.618743i | \(0.787642\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.04900 | + | 9.53617i | 0.481881 | + | 0.570916i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.91565i | − | 0.472208i | −0.971728 | − | 0.236104i | \(-0.924129\pi\) | ||
0.971728 | − | 0.236104i | \(-0.0758706\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3552 | − | 19.6678i | 0.674999 | − | 1.16913i | −0.301471 | − | 0.953475i | \(-0.597478\pi\) |
0.976469 | − | 0.215656i | \(-0.0691891\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.65574 | − | 2.22189i | −0.157313 | − | 0.131613i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5720 | − | 25.0887i | 0.919189 | − | 1.48094i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.84381 | + | 4.92562i | 0.167283 | + | 0.289742i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.68489 | − | 15.3568i | 0.157391 | − | 0.900232i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.8246i | 0.749220i | 0.927183 | + | 0.374610i | \(0.122223\pi\) | ||||
−0.927183 | + | 0.374610i | \(0.877777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.612840 | −0.0356809 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.72027 | + | 3.91899i | −0.389950 | + | 0.227403i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.5430 | + | 8.97373i | −0.898872 | + | 0.518964i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.7749 | + | 6.68778i | 0.621056 | + | 0.385477i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.11610 | + | 5.95357i | 0.408809 | + | 0.342024i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.30359 | − | 1.32998i | −0.131903 | − | 0.0761542i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3622 | 0.705549 | 0.352774 | − | 0.935708i | \(-0.385238\pi\) | ||||
0.352774 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.4792 | + | 5.29377i | −0.823694 | + | 0.301152i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.720819 | − | 1.24850i | 0.0408739 | − | 0.0707957i | −0.844865 | − | 0.534980i | \(-0.820319\pi\) |
0.885739 | + | 0.464184i | \(0.153652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.8822 | + | 12.0564i | −1.18033 | + | 0.681466i | −0.956092 | − | 0.293067i | \(-0.905324\pi\) |
−0.224242 | + | 0.974533i | \(0.571991\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.14305 | − | 2.87804i | 0.0644033 | − | 0.162159i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.4686 | + | 23.3283i | 0.756472 | + | 1.31025i | 0.944639 | + | 0.328111i | \(0.106412\pi\) |
−0.188167 | + | 0.982137i | \(0.560255\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.09764 | + | 5.36527i | −0.173435 | + | 0.300398i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.34067 | + | 25.5481i | 0.521345 | + | 1.42595i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.2342 | 0.958935 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.96898 | + | 13.8027i | −0.442039 | + | 0.765635i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −23.2519 | − | 19.4533i | −1.28583 | − | 1.07577i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.2785 | + | 0.423575i | 0.732066 | + | 0.0233524i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.2782 | − | 8.82087i | 0.839766 | − | 0.484839i | −0.0174189 | − | 0.999848i | \(-0.505545\pi\) |
0.857185 | + | 0.515009i | \(0.172212\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 25.4563 | − | 4.56471i | 1.39500 | − | 0.250145i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.37615 | 0.0751868 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0396 | 0.601365 | 0.300682 | − | 0.953724i | \(-0.402786\pi\) | ||||
0.300682 | + | 0.953724i | \(0.402786\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0216605 | + | 0.123892i | −0.00117644 | + | 0.00672890i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.39334 | + | 3.11385i | −0.292066 | + | 0.168624i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4356 | + | 1.76905i | 0.995428 | + | 0.0955198i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.36713 | − | 2.82935i | 0.127442 | − | 0.152327i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.8299 | + | 18.7579i | −0.581377 | + | 1.00697i | 0.413940 | + | 0.910304i | \(0.364152\pi\) |
−0.995316 | + | 0.0966701i | \(0.969181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.46130 | 0.345865 | 0.172933 | − | 0.984934i | \(-0.444676\pi\) | ||||
0.172933 | + | 0.984934i | \(0.444676\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.8315 | + | 8.47727i | 0.791649 | + | 0.452483i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.9846 | + | 25.9541i | −0.797549 | + | 1.38140i | 0.123659 | + | 0.992325i | \(0.460537\pi\) |
−0.921208 | + | 0.389071i | \(0.872796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.79659 | + | 4.84383i | 0.148428 | + | 0.257084i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.82830 | + | 14.6372i | 0.255541 | + | 0.774683i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.44412 | − | 5.45257i | 0.498442 | − | 0.287775i | −0.229628 | − | 0.973278i | \(-0.573751\pi\) |
0.728070 | + | 0.685503i | \(0.240418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.62795 | + | 6.28380i | −0.190945 | + | 0.330726i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.20915 | + | 14.2478i | 0.273409 | + | 0.747814i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.24388 | −0.0651075 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.43552 | + | 1.40615i | 0.127133 | + | 0.0734002i | 0.562218 | − | 0.826989i | \(-0.309948\pi\) |
−0.435085 | + | 0.900389i | \(0.643282\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.4959 | − | 11.3604i | −1.63961 | − | 0.591396i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.24726 | + | 2.32877i | 0.0647545 | + | 0.120904i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.9266 | − | 15.5461i | 1.39421 | − | 0.804947i | 0.400431 | − | 0.916327i | \(-0.368860\pi\) |
0.993778 | + | 0.111380i | \(0.0355271\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.14609 | − | 6.55529i | 0.0591836 | − | 0.338514i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.6045 | 0.700665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6950i | 0.908931i | 0.890764 | + | 0.454465i | \(0.150170\pi\) | ||||
−0.890764 | + | 0.454465i | \(0.849830\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.0412 | + | 2.62971i | 0.770585 | + | 0.134724i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.4953 | + | 30.3028i | 0.893968 | + | 1.54840i | 0.835076 | + | 0.550134i | \(0.185423\pi\) |
0.0588917 | + | 0.998264i | \(0.481243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.31306 | + | 0.814994i | 0.0669200 | + | 0.0415359i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.87897 | − | 13.5267i | 0.248012 | − | 0.687600i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.4422 | + | 18.0864i | −0.529439 | + | 0.917015i | 0.469971 | + | 0.882682i | \(0.344264\pi\) |
−0.999410 | + | 0.0343338i | \(0.989069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.3608i | 0.928543i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.19322 | − | 2.99554i | 0.413293 | − | 0.151105i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.161786 | − | 0.0934070i | −0.00814032 | − | 0.00469982i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.44443 | + | 4.23387i | 0.122682 | + | 0.212492i | 0.920825 | − | 0.389977i | \(-0.127517\pi\) |
−0.798142 | + | 0.602469i | \(0.794184\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.9898 | − | 4.77941i | −1.15093 | − | 0.239270i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.62355 | + | 3.82411i | −0.330764 | + | 0.190967i | −0.656180 | − | 0.754604i | \(-0.727829\pi\) |
0.325416 | + | 0.945571i | \(0.394496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8434 | + | 6.83782i | 0.589964 | + | 0.340616i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.46148 | − | 0.589691i | −0.172002 | − | 0.0293020i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.9067i | 0.639762i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.66584 | − | 3.84852i | −0.329604 | − | 0.190297i | 0.326061 | − | 0.945349i | \(-0.394279\pi\) |
−0.655666 | + | 0.755051i | \(0.727612\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.73731 | + | 8.14656i | 0.480306 | + | 0.401840i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.66354 | + | 1.96214i | −0.180271 | + | 0.0965507i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.40499 | + | 5.89762i | 0.167145 | + | 0.289503i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.8716 | − | 4.69807i | −1.31591 | − | 0.230065i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 4.38235i | − | 0.214092i | −0.994254 | − | 0.107046i | \(-0.965861\pi\) | ||
0.994254 | − | 0.107046i | \(-0.0341392\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.9400i | − | 0.581921i | −0.956735 | − | 0.290961i | \(-0.906025\pi\) | ||
0.956735 | − | 0.290961i | \(-0.0939749\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.65881 | − | 14.8275i | −0.129276 | − | 0.720940i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.15249 | + | 14.1205i | 0.395454 | + | 0.684946i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.0290 | − | 0.575113i | −0.872484 | − | 0.0278317i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.47061 | + | 6.53884i | −0.264124 | + | 0.315698i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.588922 | − | 0.340014i | −0.0283674 | − | 0.0163779i | 0.485749 | − | 0.874098i | \(-0.338547\pi\) |
−0.514117 | + | 0.857720i | \(0.671880\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.238499i | − | 0.0114615i | −0.999984 | − | 0.00573077i | \(-0.998176\pi\) | ||
0.999984 | − | 0.00573077i | \(-0.00182417\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.62627 | + | 0.960196i | −0.125920 | + | 0.0460379i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.2247 | − | 13.9861i | −1.15882 | − | 0.669046i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.29894 | + | 1.90465i | −0.157450 | + | 0.0909038i | −0.576655 | − | 0.816988i | \(-0.695642\pi\) |
0.419205 | + | 0.907892i | \(0.362309\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.38158 | − | 20.8645i | −0.113409 | − | 0.993548i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.02001 | + | 5.23080i | 0.143485 | + | 0.248523i | 0.928807 | − | 0.370565i | \(-0.120836\pi\) |
−0.785322 | + | 0.619088i | \(0.787503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.72210 | + | 0.994257i | 0.0816355 | + | 0.0471323i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.6933 | − | 29.2477i | −0.505776 | − | 1.38337i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 28.1482i | − | 1.32839i | −0.747558 | − | 0.664197i | \(-0.768774\pi\) | ||
0.747558 | − | 0.664197i | \(-0.231226\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.35470 | − | 14.4708i | 0.393408 | − | 0.681402i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.5415 | − | 20.9667i | 0.824171 | − | 0.985103i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.108201 | − | 3.39194i | 0.00507254 | − | 0.159017i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.23304 | − | 10.7959i | −0.291569 | − | 0.505013i | 0.682612 | − | 0.730781i | \(-0.260844\pi\) |
−0.974181 | + | 0.225768i | \(0.927511\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 15.0971 | − | 8.80403i | 0.704674 | − | 0.410937i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 31.6209i | − | 1.47273i | −0.676583 | − | 0.736367i | \(-0.736540\pi\) | ||
0.676583 | − | 0.736367i | \(-0.263460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.5095 | −1.09258 | −0.546290 | − | 0.837596i | \(-0.683960\pi\) | ||||
−0.546290 | + | 0.837596i | \(0.683960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.76893 | − | 0.484102i | −0.128406 | − | 0.0224497i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.7642 | + | 7.36942i | −0.590657 | + | 0.341016i | −0.765357 | − | 0.643606i | \(-0.777438\pi\) |
0.174700 | + | 0.984622i | \(0.444104\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.22655 | − | 4.40603i | 0.379867 | − | 0.203452i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.62985 | + | 6.72917i | −0.259410 | + | 0.310064i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.21481 | + | 3.58812i | 0.285757 | + | 0.164982i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.8403 | −1.13975 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.28907 | − | 1.93208i | 0.104809 | − | 0.0884641i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.3034 | + | 29.9703i | −0.790611 | + | 1.36938i | 0.134979 | + | 0.990848i | \(0.456903\pi\) |
−0.925589 | + | 0.378529i | \(0.876430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5452 | − | 14.1712i | 1.11916 | − | 0.646150i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.09183 | − | 24.4926i | 0.231686 | − | 1.11445i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.75582 | + | 3.04117i | 0.0797276 | + | 0.138092i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.0284 | − | 20.8338i | 0.545058 | − | 0.944068i | −0.453545 | − | 0.891233i | \(-0.649841\pi\) |
0.998603 | − | 0.0528351i | \(-0.0168258\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.4266 | − | 7.46820i | 0.923723 | − | 0.337724i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3708 | 0.693675 | 0.346837 | − | 0.937925i | \(-0.387256\pi\) | ||||
0.346837 | + | 0.937925i | \(0.387256\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.95887 | − | 12.0531i | 0.313412 | − | 0.542845i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.594567 | − | 1.64840i | 0.0267238 | − | 0.0740902i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 32.2265 | + | 20.0024i | 1.44556 | + | 0.897229i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.8684 | + | 13.2031i | −1.02373 | + | 0.591051i | −0.915182 | − | 0.403040i | \(-0.867953\pi\) |
−0.108548 | + | 0.994091i | \(0.534620\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.6793 | − | 2.21677i | −0.566470 | − | 0.0990381i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.3616 | −1.26458 | −0.632291 | − | 0.774731i | \(-0.717885\pi\) | ||||
−0.632291 | + | 0.774731i | \(0.717885\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.08993 | −0.0930006 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.73850 | − | 0.653615i | −0.166032 | − | 0.0290281i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.3731 | + | 10.6077i | −0.814373 | + | 0.470179i | −0.848472 | − | 0.529240i | \(-0.822477\pi\) |
0.0340991 | + | 0.999418i | \(0.489144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.43586 | + | 3.98255i | −0.328943 | + | 0.176178i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.115709 | + | 26.6251i | 0.00510866 | + | 1.17553i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.73632 | − | 3.00739i | 0.0765113 | − | 0.132522i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.51778 | 0.330631 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.6352 | + | 10.4694i | −1.25695 | + | 0.459554i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.91179 | − | 10.2395i | 0.259000 | − | 0.448601i | −0.706974 | − | 0.707239i | \(-0.749940\pi\) |
0.965974 | + | 0.258638i | \(0.0832737\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.37960 | − | 5.85364i | −0.147780 | − | 0.255962i | 0.782627 | − | 0.622491i | \(-0.213879\pi\) |
−0.930407 | + | 0.366529i | \(0.880546\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.95922 | − | 21.0972i | −0.303725 | − | 0.920756i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.1162 | − | 6.99528i | 0.527789 | − | 0.304719i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.40036 | − | 5.88960i | 0.147842 | − | 0.256070i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.03948 | + | 3.60108i | 0.131902 | + | 0.156273i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.6928 | −1.58934 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.30643 | − | 3.06367i | −0.229417 | − | 0.132454i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.0446 | − | 21.5681i | 0.778683 | − | 0.930733i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.4588 | + | 0.667940i | 0.450494 | + | 0.0287702i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.3128 | + | 8.84087i | −0.658351 | + | 0.380099i | −0.791648 | − | 0.610977i | \(-0.790777\pi\) |
0.133298 | + | 0.991076i | \(0.457443\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.5670 | − | 1.84747i | −0.453473 | − | 0.0792824i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.82885 | 0.292516 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.49834i | 0.0640644i | 0.999487 | + | 0.0320322i | \(0.0101979\pi\) | ||||
−0.999487 | + | 0.0320322i | \(0.989802\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.61003 | + | 20.1322i | 0.154072 | + | 0.859223i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.6017 | + | 18.3627i | 0.451647 | + | 0.782276i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.26621 | − | 0.0403914i | −0.0538448 | − | 0.00171762i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.73813 | + | 4.46806i | −0.158675 | + | 0.189658i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.46808 | − | 2.54278i | 0.0622044 | − | 0.107741i | −0.833246 | − | 0.552902i | \(-0.813520\pi\) |
0.895450 | + | 0.445161i | \(0.146854\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.7586i | − | 0.666518i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.99491 | + | 8.19150i | 0.126445 | + | 0.345845i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.3950 | + | 8.31096i | 0.606677 | + | 0.350265i | 0.771664 | − | 0.636031i | \(-0.219425\pi\) |
−0.164987 | + | 0.986296i | \(0.552758\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.0141652 | − | 0.0245348i | −0.000595934 | − | 0.00103219i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.5806 | + | 7.55752i | −0.948296 | + | 0.317386i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.2204 | + | 11.0969i | −0.805763 | + | 0.465207i | −0.845482 | − | 0.534003i | \(-0.820687\pi\) |
0.0397194 | + | 0.999211i | \(0.487354\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.22532 | − | 3.01684i | −0.218673 | − | 0.126251i | 0.386663 | − | 0.922221i | \(-0.373628\pi\) |
−0.605336 | + | 0.795970i | \(0.706961\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.6895 | + | 5.00504i | −0.571887 | + | 0.209089i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 26.4641i | − | 1.10363i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.4549 | − | 10.0776i | −0.726659 | − | 0.419537i | 0.0905396 | − | 0.995893i | \(-0.471141\pi\) |
−0.817199 | + | 0.576356i | \(0.804474\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.6114 | − | 17.4645i | 0.607230 | − | 0.725801i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.2375 | + | 24.3539i | 1.62784 | + | 1.01037i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.747449 | + | 1.29462i | 0.0309562 | + | 0.0536177i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.78765 | + | 0.679185i | −0.156600 | + | 0.0280808i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 0.369829i | − | 0.0152645i | −0.999971 | − | 0.00763224i | \(-0.997571\pi\) | ||
0.999971 | − | 0.00763224i | \(-0.00242944\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.3143i | 0.878241i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.0489 | + | 5.25356i | 1.23605 | + | 0.216103i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.89233 | − | 8.47376i | −0.200904 | − | 0.347976i | 0.747916 | − | 0.663793i | \(-0.231055\pi\) |
−0.948820 | + | 0.315818i | \(0.897721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.94981 | − | 1.83089i | −0.120930 | − | 0.0750592i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −26.4895 | − | 22.1620i | −1.08414 | − | 0.907032i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.2524 | + | 18.0436i | 1.27694 | + | 0.737240i | 0.976284 | − | 0.216494i | \(-0.0694621\pi\) |
0.300653 | + | 0.953734i | \(0.402795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.75944i | 0.398096i | 0.979990 | + | 0.199048i | \(0.0637849\pi\) | ||||
−0.979990 | + | 0.199048i | \(0.936215\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.82523 | − | 8.08629i | −0.277945 | − | 0.329299i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.95932 | − | 1.70856i | −0.120313 | − | 0.0694629i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.33740 | − | 4.23625i | 0.297816 | − | 0.171944i | −0.343645 | − | 0.939099i | \(-0.611662\pi\) |
0.641461 | + | 0.767155i | \(0.278328\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.6255 | + | 14.1486i | −0.511611 | + | 0.573331i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.25429 | − | 14.2968i | −0.333933 | − | 0.578388i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.1968 | − | 5.88712i | −0.411844 | − | 0.237779i | 0.279737 | − | 0.960077i | \(-0.409753\pi\) |
−0.691582 | + | 0.722298i | \(0.743086\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.08336 | − | 2.58976i | 0.285629 | − | 0.104429i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 17.5244i | − | 0.705506i | −0.935717 | − | 0.352753i | \(-0.885246\pi\) | ||
0.935717 | − | 0.352753i | \(-0.114754\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.8081 | + | 22.1843i | −0.514801 | + | 0.891661i | 0.485052 | + | 0.874485i | \(0.338801\pi\) |
−0.999852 | + | 0.0171755i | \(0.994533\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.3655 | + | 0.123272i | −1.13827 | + | 0.00494674i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.4780 | + | 0.429940i | 0.539985 | + | 0.0172252i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.3700 | − | 19.6933i | −0.454798 | − | 0.787734i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.0890 | − | 2.28839i | −0.522723 | − | 0.0913896i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 28.9950i | − | 1.15611i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.24555 | 0.288441 | 0.144220 | − | 0.989546i | \(-0.453933\pi\) | ||||
0.144220 | + | 0.989546i | \(0.453933\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.33003 | − | 24.7666i | 0.172103 | − | 0.984383i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.97867 | + | 1.71973i | −0.118205 | + | 0.0682456i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.2132 | − | 20.6234i | −0.404663 | − | 0.817127i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.5924 | − | 40.4567i | 0.577268 | − | 1.60044i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.9401 | + | 6.89362i | 0.471606 | + | 0.272282i | 0.716912 | − | 0.697164i | \(-0.245555\pi\) |
−0.245306 | + | 0.969446i | \(0.578888\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.7470 | −0.818184 | −0.409092 | − | 0.912493i | \(-0.634154\pi\) | ||||
−0.409092 | + | 0.912493i | \(0.634154\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.11223 | + | 3.04212i | 0.0437942 | + | 0.119783i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.1242 | − | 27.9279i | 0.633907 | − | 1.09796i | −0.352838 | − | 0.935684i | \(-0.614783\pi\) |
0.986746 | − | 0.162275i | \(-0.0518832\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.03665 | + | 1.17586i | −0.0799454 | + | 0.0461565i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.1025 | + | 5.97139i | −0.709493 | + | 0.234037i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.95455 | + | 17.2418i | 0.389552 | + | 0.674723i | 0.992389 | − | 0.123141i | \(-0.0392966\pi\) |
−0.602838 | + | 0.797864i | \(0.705963\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.982514 | + | 1.70176i | −0.0383900 | + | 0.0664934i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.16923 | + | 7.30909i | 0.240684 | + | 0.285155i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.4275 | −0.445153 | −0.222576 | − | 0.974915i | \(-0.571447\pi\) | ||||
−0.222576 | + | 0.974915i | \(0.571447\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.31268 | + | 4.00568i | −0.0899529 | + | 0.155803i | −0.907491 | − | 0.420071i | \(-0.862005\pi\) |
0.817538 | + | 0.575875i | \(0.195338\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.2898 | − | 14.6895i | 0.477295 | − | 0.570495i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.66261 | − | 2.49723i | 0.180808 | − | 0.0968385i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.5630 | + | 11.2947i | −0.757483 | + | 0.437333i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.828955 | + | 4.74139i | −0.0320493 | + | 0.183313i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.2073 | −0.394050 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.2606 | 0.742441 | 0.371220 | − | 0.928545i | \(-0.378939\pi\) | ||||
0.371220 | + | 0.928545i | \(0.378939\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.7601 | + | 12.6896i | −0.837546 | + | 0.488423i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 36.2236 | − | 20.9137i | 1.39219 | − | 0.803780i | 0.398630 | − | 0.917112i | \(-0.369486\pi\) |
0.993557 | + | 0.113332i | \(0.0361524\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2332 | + | 12.5583i | 0.776478 | + | 0.481945i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.5425 | − | 18.0232i | −0.825509 | − | 0.690649i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.73357 | − | 11.6629i | 0.257653 | − | 0.446268i | −0.707960 | − | 0.706253i | \(-0.750384\pi\) |
0.965613 | + | 0.259985i | \(0.0837176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.85975 | −0.109265 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.2697 | + | 33.5595i | 0.468120 | + | 1.28037i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.64135 | − | 2.84291i | 0.0625305 | − | 0.108306i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2232 | − | 26.3674i | −0.579118 | − | 1.00306i | −0.995581 | − | 0.0939090i | \(-0.970064\pi\) |
0.416463 | − | 0.909153i | \(-0.363270\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.72342 | − | 11.7577i | −0.0654675 | − | 0.446639i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.32149 | − | 3.07236i | 0.201856 | − | 0.116541i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.7689 | + | 32.5087i | −0.710923 | + | 1.23135i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.38979 | − | 1.23935i | 0.128214 | − | 0.0468764i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.2839 | 1.40819 | 0.704096 | − | 0.710105i | \(-0.251353\pi\) | ||||
0.704096 | + | 0.710105i | \(0.251353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38.2552 | + | 22.0866i | 1.44282 | + | 0.833013i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.60251 | + | 2.17735i | 0.0980163 | + | 0.0820038i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.4935 | + | 6.69137i | −0.469867 | + | 0.251655i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −39.5076 | + | 22.8097i | −1.48374 | + | 0.856637i | −0.999829 | − | 0.0184810i | \(-0.994117\pi\) |
−0.483910 | + | 0.875118i | \(0.660784\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.253540 | + | 1.41393i | 0.00950848 | + | 0.0530265i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.7076 | −0.850406 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.92039i | − | 0.0718186i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.254077 | + | 1.45325i | −0.00948869 | + | 0.0542727i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.37315 | − | 14.5027i | −0.312266 | − | 0.540860i | 0.666587 | − | 0.745428i | \(-0.267755\pi\) |
−0.978853 | + | 0.204567i | \(0.934421\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.750825 | − | 23.5373i | 0.0279622 | − | 0.876575i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.0053 | + | 16.7371i | 0.744003 | + | 0.622458i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.0301 | + | 17.3726i | −0.372508 | + | 0.645204i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 14.7144i | − | 0.545726i | −0.962053 | − | 0.272863i | \(-0.912029\pi\) | ||
0.962053 | − | 0.272863i | \(-0.0879705\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.7027 | + | 23.2645i | 0.507508 | + | 0.861647i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.9616 | − | 8.06075i | −0.516389 | − | 0.298137i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.1186 | − | 29.6503i | −0.632290 | − | 1.09516i | −0.987082 | − | 0.160213i | \(-0.948782\pi\) |
0.354793 | − | 0.934945i | \(-0.384551\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.42720 | + | 3.26039i | 0.126414 | + | 0.120261i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.57334 | − | 2.64042i | 0.168461 | − | 0.0972610i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.92964 | − | 1.11408i | −0.0709829 | − | 0.0409820i | 0.464089 | − | 0.885789i | \(-0.346382\pi\) |
−0.535071 | + | 0.844807i | \(0.679715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.0194 | + | 27.4044i | 0.368070 | + | 1.00673i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14.7964i | − | 0.542829i | −0.962463 | − | 0.271414i | \(-0.912509\pi\) | ||
0.962463 | − | 0.271414i | \(-0.0874914\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.07486 | + | 3.50732i | 0.222566 | + | 0.128498i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.7671 | − | 49.2582i | 0.650063 | − | 1.80226i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −41.5307 | − | 1.32480i | −1.51750 | − | 0.0484073i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.2439 | − | 31.5994i | −0.665729 | − | 1.15308i | −0.979087 | − | 0.203442i | \(-0.934787\pi\) |
0.313358 | − | 0.949635i | \(-0.398546\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.52055 | + | 20.1366i | −0.128296 | + | 0.733817i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.15772i | 0.224103i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 19.9557i | − | 0.725302i | −0.931925 | − | 0.362651i | \(-0.881872\pi\) | ||
0.931925 | − | 0.362651i | \(-0.118128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.43798 | − | 13.9446i | 0.0884931 | − | 0.506156i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.2013 | + | 31.5257i | 0.659798 | + | 1.14280i | 0.980668 | + | 0.195681i | \(0.0626917\pi\) |
−0.320869 | + | 0.947124i | \(0.603975\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.8227 | − | 21.8641i | 1.47788 | − | 0.791533i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.33570 | + | 3.70315i | −0.0482923 | + | 0.133888i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.47235 | + | 2.58211i | 0.161487 | + | 0.0932347i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 33.7570i | − | 1.21731i | −0.793436 | − | 0.608654i | \(-0.791710\pi\) | ||
0.793436 | − | 0.608654i | \(-0.208290\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.5497 | + | 28.8551i | 0.379940 | + | 1.03919i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3297 | + | 20.3976i | 1.27072 | + | 0.733651i | 0.975124 | − | 0.221662i | \(-0.0711481\pi\) |
0.295597 | + | 0.955313i | \(0.404481\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.4635 | + | 10.0826i | −0.627308 | + | 0.362176i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.04094 | + | 38.6783i | −0.288467 | + | 1.38758i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.5940 | − | 49.5263i | −1.02449 | − | 1.77446i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.5878 | + | 10.7317i | 0.665123 | + | 0.384009i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.6676 | + | 10.6698i | 0.667126 | + | 0.381309i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.97629i | − | 0.0705368i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.80545 | + | 10.0553i | −0.206942 | + | 0.358434i | −0.950750 | − | 0.309960i | \(-0.899684\pi\) |
0.743808 | + | 0.668394i | \(0.233018\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.63037 | + | 8.05710i | 0.342850 | + | 0.286840i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.163233 | − | 0.101315i | −0.00580389 | − | 0.00360236i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.2073 | + | 19.4117i | 0.397984 | + | 0.689329i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.116204 | + | 0.664654i | −0.00412133 | + | 0.0235729i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.90792i | 0.350956i | 0.984483 | + | 0.175478i | \(0.0561472\pi\) | ||||
−0.984483 | + | 0.175478i | \(0.943853\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.8887 | −0.597481 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.69877 | − | 15.0503i | −0.0953562 | − | 0.531778i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.13377 | + | 2.38664i | −0.145878 | + | 0.0842225i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.66047 | + | 4.96740i | 0.0937694 | + | 0.175078i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.53768 | + | 3.79638i | 0.159734 | + | 0.133639i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3590 | − | 8.29016i | −0.504835 | − | 0.291466i | 0.225873 | − | 0.974157i | \(-0.427477\pi\) |
−0.730708 | + | 0.682690i | \(0.760810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.5706 | 1.74066 | 0.870330 | − | 0.492470i | \(-0.163906\pi\) | ||||
0.870330 | + | 0.492470i | \(0.163906\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.45700 | + | 2.72637i | −0.261528 | + | 0.0956179i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.44952 | + | 4.24268i | −0.0858028 | + | 0.148615i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.2702 | − | 12.2804i | 0.744151 | − | 0.429636i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −20.4679 | + | 16.1871i | −0.715205 | + | 0.565624i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.4055 | − | 45.7357i | −0.921559 | − | 1.59619i | −0.797004 | − | 0.603973i | \(-0.793583\pi\) |
−0.124554 | − | 0.992213i | \(-0.539750\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.3351 | + | 21.3650i | −0.429975 | + | 0.744739i | −0.996871 | − | 0.0790510i | \(-0.974811\pi\) |
0.566896 | + | 0.823790i | \(0.308144\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.31668 | − | 11.8067i | −0.150287 | − | 0.411057i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.0662 | 0.802091 | 0.401045 | − | 0.916058i | \(-0.368647\pi\) | ||||
0.401045 | + | 0.916058i | \(0.368647\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.2068 | + | 21.1429i | −0.423961 | + | 0.734322i | −0.996323 | − | 0.0856795i | \(-0.972694\pi\) |
0.572362 | + | 0.820001i | \(0.306027\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.4041 | − | 13.7243i | −0.569053 | − | 0.476089i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.4959 | − | 1.50053i | −0.814083 | − | 0.0519904i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.51093 | − | 1.44969i | 0.0868944 | − | 0.0501685i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.8884 | + | 18.6713i | 0.376357 | + | 0.645376i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −48.3464 | −1.66910 | −0.834551 | − | 0.550931i | \(-0.814273\pi\) | ||||
−0.834551 | + | 0.550931i | \(0.814273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.8768 | −0.409546 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.36121 | − | 13.5055i | 0.0813244 | − | 0.465153i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.740348 | − | 0.427440i | 0.0254688 | − | 0.0147044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.1610 | − | 0.738822i | −0.795823 | − | 0.0253862i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.2408 | − | 30.1695i | 0.866262 | − | 1.03541i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −23.5304 | + | 40.7559i | −0.806612 | + | 1.39709i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.6867 | 1.18765 | 0.593825 | − | 0.804595i | \(-0.297617\pi\) | ||||
0.593825 | + | 0.804595i | \(0.297617\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.86837 | − | 4.58312i | −0.132296 | − | 0.156739i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.7545 | + | 18.6273i | −0.367366 | + | 0.636297i | −0.989153 | − | 0.146889i | \(-0.953074\pi\) |
0.621786 | + | 0.783187i | \(0.286407\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.332259 | + | 0.575490i | 0.0113365 | + | 0.0196355i | 0.871638 | − | 0.490150i | \(-0.163058\pi\) |
−0.860301 | + | 0.509786i | \(0.829725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 34.0524 | − | 38.1605i | 1.16050 | − | 1.30050i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −14.2150 | + | 8.20702i | −0.483883 | + | 0.279370i | −0.722033 | − | 0.691858i | \(-0.756792\pi\) |
0.238150 | + | 0.971228i | \(0.423459\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.43388 | − | 5.94765i | 0.116755 | − | 0.202226i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.38273 | + | 9.25225i | 0.114884 | + | 0.314223i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.716882 | −0.0243186 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0428 | − | 5.79819i | −0.340286 | − | 0.196464i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.16175 | − | 25.4004i | 0.310078 | − | 0.859675i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.63685 | + | 5.36073i | 0.291979 | + | 0.181226i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.1473 | + | 6.43591i | −0.376419 | + | 0.217325i | −0.676259 | − | 0.736664i | \(-0.736400\pi\) |
0.299840 | + | 0.953989i | \(0.403067\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.82552 | + | 21.8809i | −0.129032 | + | 0.738025i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.1373 | −1.41964 | −0.709821 | − | 0.704382i | \(-0.751224\pi\) | ||||
−0.709821 | + | 0.704382i | \(0.751224\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3108i | 0.481596i | 0.970575 | + | 0.240798i | \(0.0774091\pi\) | ||||
−0.970575 | + | 0.240798i | \(0.922591\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.04561 | − | 0.182808i | −0.0351478 | − | 0.00614502i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.93855 | − | 6.82176i | −0.132243 | − | 0.229052i | 0.792298 | − | 0.610135i | \(-0.208885\pi\) |
−0.924541 | + | 0.381082i | \(0.875551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.3003 | + | 19.8174i | −0.412538 | + | 0.664653i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.6349 | + | 4.68183i | −0.423287 | + | 0.156847i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.8648 | − | 22.2825i | 0.430505 | − | 0.745656i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.33434i | 0.211734i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.1958 | + | 10.6743i | −0.974818 | + | 0.356405i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.9067 | + | 8.60636i | 0.497165 | + | 0.287038i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.67915 | − | 2.90837i | −0.0559406 | − | 0.0968919i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.3889 | + | 14.6246i | 0.545389 | + | 0.486677i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.09262 | − | 1.20818i | 0.0695611 | − | 0.0401611i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.8886 | + | 14.3694i | 0.826413 | + | 0.477130i | 0.852623 | − | 0.522527i | \(-0.175011\pi\) |
−0.0262101 | + | 0.999656i | \(0.508344\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3654 | + | 12.2805i | 0.343797 | + | 0.407319i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.32207i | 0.143197i | 0.997434 | + | 0.0715983i | \(0.0228100\pi\) | ||||
−0.997434 | + | 0.0715983i | \(0.977190\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.6316 | + | 13.0664i | 0.748996 | + | 0.432433i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.53359 | − | 2.95632i | −0.116817 | − | 0.0977329i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.424862 | + | 13.3188i | −0.0140302 | + | 0.439826i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.1008 | − | 31.3515i | −0.597089 | − | 1.03419i | −0.993248 | − | 0.116007i | \(-0.962990\pi\) |
0.396159 | − | 0.918182i | \(-0.370343\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.0921 | + | 3.68760i | 0.695007 | + | 0.121511i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 47.1321i | − | 1.55137i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.7916i | 1.37410i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.2831 | + | 4.71298i | −0.863252 | + | 0.154795i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.370626 | + | 0.641943i | 0.0121598 | + | 0.0210615i | 0.872041 | − | 0.489432i | \(-0.162796\pi\) |
−0.859881 | + | 0.510494i | \(0.829463\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.8775 | − | 29.8567i | 0.651458 | − | 0.978515i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.60226 | − | 1.91513i | 0.0524557 | − | 0.0626985i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.70141 | − | 0.982307i | −0.0556419 | − | 0.0321249i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 49.0746i | 1.60320i | 0.597863 | + | 0.801598i | \(0.296017\pi\) | ||||
−0.597863 | + | 0.801598i | \(0.703983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −39.2250 | + | 14.3411i | −1.28006 | + | 0.468005i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.9660 | − | 15.5688i | −0.879065 | − | 0.507529i | −0.00871528 | − | 0.999962i | \(-0.502774\pi\) |
−0.870350 | + | 0.492433i | \(0.836108\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.7638 | − | 30.4632i | 1.71822 | − | 0.992017i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.80874 | − | 4.56946i | 0.0913683 | − | 0.148644i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.6780 | + | 20.2270i | 0.379485 | + | 0.657288i | 0.990987 | − | 0.133955i | \(-0.0427678\pi\) |
−0.611502 | + | 0.791243i | \(0.709434\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.07751 | + | 5.24090i | 0.294669 | + | 0.170127i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.0210 | + | 43.8197i | 0.519517 | + | 1.42095i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 37.3593i | − | 1.21019i | −0.796155 | − | 0.605093i | \(-0.793136\pi\) | ||
0.796155 | − | 0.605093i | \(-0.206864\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.64162 | − | 2.84336i | 0.0531215 | − | 0.0920091i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.88555 | + | 8.23006i | −0.222578 | + | 0.266040i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.0955 | + | 9.15612i | −0.552042 | + | 0.295667i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.84861 | − | 11.8621i | −0.220923 | − | 0.382650i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.31589 | + | 46.3757i | 0.267976 | + | 1.49443i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.12916i | 0.165114i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.9761 | 1.06044 | 0.530220 | − | 0.847860i | \(-0.322109\pi\) | ||||
0.530220 | + | 0.847860i | \(0.322109\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29.4045 | + | 5.14089i | 0.944607 | + | 0.165149i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3859 | − | 8.30570i | 0.461665 | − | 0.266543i | −0.251079 | − | 0.967967i | \(-0.580785\pi\) |
0.712744 | + | 0.701424i | \(0.247452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.9748 | − | 35.4044i | 0.704481 | − | 1.13501i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −17.7137 | + | 21.1726i | −0.567293 | + | 0.678066i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.641595 | + | 0.370425i | 0.0205264 | + | 0.0118509i | 0.510228 | − | 0.860039i | \(-0.329561\pi\) |
−0.489702 | + | 0.871890i | \(0.662894\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.63074 | 0.243880 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.8689 | − | 40.1267i | −1.08135 | − | 1.28115i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.11340 | + | 8.85666i | −0.163092 | + | 0.282484i | −0.935976 | − | 0.352064i | \(-0.885480\pi\) |
0.772884 | + | 0.634547i | \(0.218813\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.95069 | + | 3.43563i | −0.189605 | + | 0.109468i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.5290 | + | 4.68361i | 0.717106 | + | 0.149081i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.0831 | + | 22.6606i | 0.416019 | + | 0.720567i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.7297 | + | 39.3690i | −0.722032 | + | 1.25060i | 0.238152 | + | 0.971228i | \(0.423459\pi\) |
−0.960184 | + | 0.279369i | \(0.909875\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.6984 | − | 10.4925i | 0.910718 | − | 0.332969i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.77971 | 0.246633 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.6051 | − | 23.5647i | 0.430877 | − | 0.746300i | −0.566072 | − | 0.824356i | \(-0.691538\pi\) |
0.996949 | + | 0.0780552i | \(0.0248710\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.7944 | − | 0.194670i | 1.41723 | − | 0.00615907i |
(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 | 672.2.bi.c.17.23 | 48 | ||
3.2 | odd | 2 | inner | 672.2.bi.c.17.6 | 48 | ||
4.3 | odd | 2 | 168.2.ba.c.101.9 | yes | 48 | ||
7.5 | odd | 6 | inner | 672.2.bi.c.593.19 | 48 | ||
8.3 | odd | 2 | 168.2.ba.c.101.1 | yes | 48 | ||
8.5 | even | 2 | inner | 672.2.bi.c.17.2 | 48 | ||
12.11 | even | 2 | 168.2.ba.c.101.16 | yes | 48 | ||
21.5 | even | 6 | inner | 672.2.bi.c.593.2 | 48 | ||
24.5 | odd | 2 | inner | 672.2.bi.c.17.19 | 48 | ||
24.11 | even | 2 | 168.2.ba.c.101.24 | yes | 48 | ||
28.19 | even | 6 | 168.2.ba.c.5.24 | yes | 48 | ||
56.5 | odd | 6 | inner | 672.2.bi.c.593.6 | 48 | ||
56.19 | even | 6 | 168.2.ba.c.5.16 | yes | 48 | ||
84.47 | odd | 6 | 168.2.ba.c.5.1 | ✓ | 48 | ||
168.5 | even | 6 | inner | 672.2.bi.c.593.23 | 48 | ||
168.131 | odd | 6 | 168.2.ba.c.5.9 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.ba.c.5.1 | ✓ | 48 | 84.47 | odd | 6 | ||
168.2.ba.c.5.9 | yes | 48 | 168.131 | odd | 6 | ||
168.2.ba.c.5.16 | yes | 48 | 56.19 | even | 6 | ||
168.2.ba.c.5.24 | yes | 48 | 28.19 | even | 6 | ||
168.2.ba.c.101.1 | yes | 48 | 8.3 | odd | 2 | ||
168.2.ba.c.101.9 | yes | 48 | 4.3 | odd | 2 | ||
168.2.ba.c.101.16 | yes | 48 | 12.11 | even | 2 | ||
168.2.ba.c.101.24 | yes | 48 | 24.11 | even | 2 | ||
672.2.bi.c.17.2 | 48 | 8.5 | even | 2 | inner | ||
672.2.bi.c.17.6 | 48 | 3.2 | odd | 2 | inner | ||
672.2.bi.c.17.19 | 48 | 24.5 | odd | 2 | inner | ||
672.2.bi.c.17.23 | 48 | 1.1 | even | 1 | trivial | ||
672.2.bi.c.593.2 | 48 | 21.5 | even | 6 | inner | ||
672.2.bi.c.593.6 | 48 | 56.5 | odd | 6 | inner | ||
672.2.bi.c.593.19 | 48 | 7.5 | odd | 6 | inner | ||
672.2.bi.c.593.23 | 48 | 168.5 | even | 6 | inner |