Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.9 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.f.757.10 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.671239 | − | 1.24476i | −0.474638 | − | 0.880181i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.09888 | + | 1.67107i | −0.549438 | + | 0.835534i | ||||
\(5\) | 3.66698i | 1.63993i | 0.572417 | + | 0.819963i | \(0.306006\pi\) | ||||
−0.572417 | + | 0.819963i | \(0.693994\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 2.81770 | + | 0.246156i | 0.996206 | + | 0.0870294i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.56453 | − | 2.46142i | 1.44343 | − | 0.778370i | ||||
\(11\) | 4.45794i | 1.34412i | 0.740498 | + | 0.672059i | \(0.234590\pi\) | ||||
−0.740498 | + | 0.672059i | \(0.765410\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.51546i | 0.420314i | 0.977668 | + | 0.210157i | \(0.0673975\pi\) | ||||
−0.977668 | + | 0.210157i | \(0.932602\pi\) | |||||||
\(14\) | −0.671239 | − | 1.24476i | −0.179396 | − | 0.332677i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.58494 | − | 3.67260i | −0.396235 | − | 0.918149i | ||||
\(17\) | 3.45516 | 0.838000 | 0.419000 | − | 0.907986i | \(-0.362381\pi\) | ||||
0.419000 | + | 0.907986i | \(0.362381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.29933i | 0.527503i | 0.964591 | + | 0.263752i | \(0.0849600\pi\) | ||||
−0.964591 | + | 0.263752i | \(0.915040\pi\) | |||||||
\(20\) | −6.12778 | − | 4.02956i | −1.37021 | − | 0.901038i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.54908 | − | 2.99234i | 1.18307 | − | 0.637969i | ||||
\(23\) | 8.76326 | 1.82727 | 0.913633 | − | 0.406539i | \(-0.133265\pi\) | ||||
0.913633 | + | 0.406539i | \(0.133265\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.44677 | −1.68935 | ||||||||
\(26\) | 1.88640 | − | 1.01724i | 0.369953 | − | 0.199497i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.09888 | + | 1.67107i | −0.207668 | + | 0.315802i | ||||
\(29\) | − | 1.62037i | − | 0.300895i | −0.988618 | − | 0.150448i | \(-0.951928\pi\) | ||
0.988618 | − | 0.150448i | \(-0.0480715\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.26498 | −1.66404 | −0.832020 | − | 0.554746i | \(-0.812816\pi\) | ||||
−0.832020 | + | 0.554746i | \(0.812816\pi\) | |||||||
\(32\) | −3.50764 | + | 4.43807i | −0.620070 | + | 0.784547i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.31924 | − | 4.30086i | −0.397746 | − | 0.737592i | ||||
\(35\) | 3.66698i | 0.619833i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.69381i | − | 0.936056i | −0.883714 | − | 0.468028i | \(-0.844965\pi\) | ||
0.883714 | − | 0.468028i | \(-0.155035\pi\) | |||||||
\(38\) | 2.86213 | − | 1.54340i | 0.464299 | − | 0.250373i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.902651 | + | 10.3324i | −0.142722 | + | 1.63370i | ||||
\(41\) | 6.86926 | 1.07280 | 0.536399 | − | 0.843965i | \(-0.319784\pi\) | ||||
0.536399 | + | 0.843965i | \(0.319784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.880042i | 0.134205i | 0.997746 | + | 0.0671026i | \(0.0213755\pi\) | ||||
−0.997746 | + | 0.0671026i | \(0.978625\pi\) | |||||||
\(44\) | −7.44952 | − | 4.89872i | −1.12306 | − | 0.738510i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.88224 | − | 10.9082i | −0.867289 | − | 1.60833i | ||||
\(47\) | −10.5955 | −1.54551 | −0.772753 | − | 0.634707i | \(-0.781121\pi\) | ||||
−0.772753 | + | 0.634707i | \(0.781121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 5.66980 | + | 10.5142i | 0.801831 | + | 1.48694i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.53244 | − | 1.66531i | −0.351187 | − | 0.230937i | ||||
\(53\) | 11.5036i | 1.58014i | 0.613014 | + | 0.790072i | \(0.289957\pi\) | ||||
−0.613014 | + | 0.790072i | \(0.710043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −16.3472 | −2.20425 | ||||||||
\(56\) | 2.81770 | + | 0.246156i | 0.376530 | + | 0.0328940i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.01698 | + | 1.08766i | −0.264843 | + | 0.142816i | ||||
\(59\) | − | 2.99426i | − | 0.389819i | −0.980821 | − | 0.194909i | \(-0.937559\pi\) | ||
0.980821 | − | 0.194909i | \(-0.0624413\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.51202i | − | 1.08985i | −0.838484 | − | 0.544926i | \(-0.816558\pi\) | ||
0.838484 | − | 0.544926i | \(-0.183442\pi\) | |||||||
\(62\) | 6.21902 | + | 11.5327i | 0.789816 | + | 1.46466i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.87881 | + | 1.38719i | 0.984852 | + | 0.173398i | ||||
\(65\) | −5.55718 | −0.689284 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6629i | 1.30268i | 0.758786 | + | 0.651341i | \(0.225793\pi\) | ||||
−0.758786 | + | 0.651341i | \(0.774207\pi\) | |||||||
\(68\) | −3.79680 | + | 5.77381i | −0.460429 | + | 0.700178i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.56453 | − | 2.46142i | 0.545566 | − | 0.294196i | ||||
\(71\) | −10.6172 | −1.26003 | −0.630015 | − | 0.776583i | \(-0.716951\pi\) | ||||
−0.630015 | + | 0.776583i | \(0.716951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.85523 | 0.919385 | 0.459692 | − | 0.888078i | \(-0.347960\pi\) | ||||
0.459692 | + | 0.888078i | \(0.347960\pi\) | |||||||
\(74\) | −7.08745 | + | 3.82191i | −0.823899 | + | 0.444288i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.84235 | − | 2.52668i | −0.440747 | − | 0.289831i | ||||
\(77\) | 4.45794i | 0.508029i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.57730 | 0.514986 | 0.257493 | − | 0.966280i | \(-0.417104\pi\) | ||||
0.257493 | + | 0.966280i | \(0.417104\pi\) | |||||||
\(80\) | 13.4674 | − | 5.81195i | 1.50570 | − | 0.649796i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.61091 | − | 8.55061i | −0.509190 | − | 0.944257i | ||||
\(83\) | 2.60500i | 0.285936i | 0.989727 | + | 0.142968i | \(0.0456645\pi\) | ||||
−0.989727 | + | 0.142968i | \(0.954335\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.6700i | 1.37426i | ||||||||
\(86\) | 1.09545 | − | 0.590719i | 0.118125 | − | 0.0636988i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.09735 | + | 12.5611i | −0.116978 | + | 1.33902i | ||||
\(89\) | 2.14381 | 0.227244 | 0.113622 | − | 0.993524i | \(-0.463755\pi\) | ||||
0.113622 | + | 0.993524i | \(0.463755\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.51546i | 0.158864i | ||||||||
\(92\) | −9.62974 | + | 14.6440i | −1.00397 | + | 1.52674i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.11208 | + | 13.1888i | 0.733555 | + | 1.36033i | ||||
\(95\) | −8.43162 | −0.865066 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.8317 | −1.40440 | −0.702199 | − | 0.711981i | \(-0.747798\pi\) | ||||
−0.702199 | + | 0.711981i | \(0.747798\pi\) | |||||||
\(98\) | −0.671239 | − | 1.24476i | −0.0678054 | − | 0.125740i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.28196 | − | 14.1151i | 0.928196 | − | 1.41151i | ||||
\(101\) | 10.2333i | 1.01826i | 0.860691 | + | 0.509128i | \(0.170032\pi\) | ||||
−0.860691 | + | 0.509128i | \(0.829968\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.7223 | −1.25357 | −0.626784 | − | 0.779193i | \(-0.715629\pi\) | ||||
−0.626784 | + | 0.779193i | \(0.715629\pi\) | |||||||
\(104\) | −0.373041 | + | 4.27012i | −0.0365797 | + | 0.418719i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.3193 | − | 7.72168i | 1.39081 | − | 0.749996i | ||||
\(107\) | 6.40575i | 0.619268i | 0.950856 | + | 0.309634i | \(0.100206\pi\) | ||||
−0.950856 | + | 0.309634i | \(0.899794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.38839i | − | 0.324549i | −0.986746 | − | 0.162274i | \(-0.948117\pi\) | ||
0.986746 | − | 0.162274i | \(-0.0518829\pi\) | |||||||
\(110\) | 10.9729 | + | 20.3484i | 1.04622 | + | 1.94014i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.58494 | − | 3.67260i | −0.149763 | − | 0.347028i | ||||
\(113\) | 1.40668 | 0.132329 | 0.0661644 | − | 0.997809i | \(-0.478924\pi\) | ||||
0.0661644 | + | 0.997809i | \(0.478924\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 32.1347i | 2.99658i | ||||||||
\(116\) | 2.70775 | + | 1.78059i | 0.251408 | + | 0.165323i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.72714 | + | 2.00986i | −0.343111 | + | 0.185023i | ||||
\(119\) | 3.45516 | 0.316734 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.87319 | −0.806653 | ||||||||
\(122\) | −10.5955 | + | 5.71360i | −0.959268 | + | 0.517285i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.1811 | − | 15.4824i | 0.914287 | − | 1.39036i | ||||
\(125\) | − | 12.6393i | − | 1.13049i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4597 | 0.928152 | 0.464076 | − | 0.885795i | \(-0.346386\pi\) | ||||
0.464076 | + | 0.885795i | \(0.346386\pi\) | |||||||
\(128\) | −3.56185 | − | 10.7384i | −0.314826 | − | 0.949150i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.73020 | + | 6.91738i | 0.327160 | + | 0.606695i | ||||
\(131\) | − | 12.6638i | − | 1.10644i | −0.833034 | − | 0.553221i | \(-0.813398\pi\) | ||
0.833034 | − | 0.553221i | \(-0.186602\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.29933i | 0.199378i | ||||||||
\(134\) | 13.2728 | − | 7.15736i | 1.14660 | − | 0.618301i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.73559 | + | 0.850510i | 0.834820 | + | 0.0729306i | ||||
\(137\) | 6.87026 | 0.586966 | 0.293483 | − | 0.955964i | \(-0.405186\pi\) | ||||
0.293483 | + | 0.955964i | \(0.405186\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 13.4362i | − | 1.13964i | −0.821768 | − | 0.569822i | \(-0.807012\pi\) | ||
0.821768 | − | 0.569822i | \(-0.192988\pi\) | |||||||
\(140\) | −6.12778 | − | 4.02956i | −0.517892 | − | 0.340560i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.12668 | + | 13.2159i | 0.598058 | + | 1.10905i | ||||
\(143\) | −6.75584 | −0.564952 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.94188 | 0.493446 | ||||||||
\(146\) | −5.27273 | − | 9.77790i | −0.436374 | − | 0.809225i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.51475 | + | 6.25679i | 0.782107 | + | 0.514305i | ||||
\(149\) | 6.35294i | 0.520453i | 0.965548 | + | 0.260227i | \(0.0837973\pi\) | ||||
−0.965548 | + | 0.260227i | \(0.916203\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5918 | 1.59436 | 0.797179 | − | 0.603743i | \(-0.206325\pi\) | ||||
0.797179 | + | 0.603743i | \(0.206325\pi\) | |||||||
\(152\) | −0.565996 | + | 6.47882i | −0.0459083 | + | 0.525502i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.54908 | − | 2.99234i | 0.447158 | − | 0.241130i | ||||
\(155\) | − | 33.9745i | − | 2.72890i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 22.6978i | − | 1.81148i | −0.423834 | − | 0.905740i | \(-0.639316\pi\) | ||
0.423834 | − | 0.905740i | \(-0.360684\pi\) | |||||||
\(158\) | −3.07246 | − | 5.69766i | −0.244432 | − | 0.453281i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.2743 | − | 12.8625i | −1.28660 | − | 1.01687i | ||||
\(161\) | 8.76326 | 0.690642 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 3.60107i | − | 0.282058i | −0.990005 | − | 0.141029i | \(-0.954959\pi\) | ||
0.990005 | − | 0.141029i | \(-0.0450410\pi\) | |||||||
\(164\) | −7.54847 | + | 11.4790i | −0.589436 | + | 0.896359i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.24261 | − | 1.74857i | 0.251675 | − | 0.135716i | ||||
\(167\) | 5.46351 | 0.422779 | 0.211390 | − | 0.977402i | \(-0.432201\pi\) | ||||
0.211390 | + | 0.977402i | \(0.432201\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7034 | 0.823336 | ||||||||
\(170\) | 15.7712 | − | 8.50461i | 1.20960 | − | 0.652274i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.47061 | − | 0.967058i | −0.112133 | − | 0.0737375i | ||||
\(173\) | 1.71944i | 0.130727i | 0.997862 | + | 0.0653634i | \(0.0208207\pi\) | ||||
−0.997862 | + | 0.0653634i | \(0.979179\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.44677 | −0.638516 | ||||||||
\(176\) | 16.3722 | − | 7.06556i | 1.23410 | − | 0.532587i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.43901 | − | 2.66854i | −0.107858 | − | 0.200016i | ||||
\(179\) | 10.9956i | 0.821846i | 0.911670 | + | 0.410923i | \(0.134794\pi\) | ||||
−0.911670 | + | 0.410923i | \(0.865206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.6227i | 1.97885i | 0.145040 | + | 0.989426i | \(0.453669\pi\) | ||||
−0.145040 | + | 0.989426i | \(0.546331\pi\) | |||||||
\(182\) | 1.88640 | − | 1.01724i | 0.139829 | − | 0.0754027i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.6922 | + | 2.15713i | 1.82033 | + | 0.159026i | ||||
\(185\) | 20.8791 | 1.53506 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.4029i | 1.12637i | ||||||||
\(188\) | 11.6431 | − | 17.7057i | 0.849160 | − | 1.29132i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.65963 | + | 10.4954i | 0.410593 | + | 0.761415i | ||||
\(191\) | −22.1581 | −1.60330 | −0.801652 | − | 0.597791i | \(-0.796045\pi\) | ||||
−0.801652 | + | 0.597791i | \(0.796045\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.5599 | 0.832098 | 0.416049 | − | 0.909342i | \(-0.363414\pi\) | ||||
0.416049 | + | 0.909342i | \(0.363414\pi\) | |||||||
\(194\) | 9.28438 | + | 17.2172i | 0.666580 | + | 1.23612i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.09888 | + | 1.67107i | −0.0784912 | + | 0.119362i | ||||
\(197\) | − | 13.1740i | − | 0.938611i | −0.883036 | − | 0.469305i | \(-0.844504\pi\) | ||
0.883036 | − | 0.469305i | \(-0.155496\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1012 | −0.857828 | −0.428914 | − | 0.903345i | \(-0.641104\pi\) | ||||
−0.428914 | + | 0.903345i | \(0.641104\pi\) | |||||||
\(200\) | −23.8004 | − | 2.07923i | −1.68294 | − | 0.147024i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.7381 | − | 6.86902i | 0.896250 | − | 0.483302i | ||||
\(203\) | − | 1.62037i | − | 0.113728i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.1895i | 1.75931i | ||||||||
\(206\) | 8.53972 | + | 15.8363i | 0.594990 | + | 1.10337i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.56569 | − | 2.40192i | 0.385911 | − | 0.166543i | ||||
\(209\) | −10.2503 | −0.709027 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 21.7501i | − | 1.49734i | −0.662944 | − | 0.748669i | \(-0.730693\pi\) | ||
0.662944 | − | 0.748669i | \(-0.269307\pi\) | |||||||
\(212\) | −19.2233 | − | 12.6411i | −1.32027 | − | 0.868192i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.97365 | − | 4.29979i | 0.545068 | − | 0.293928i | ||||
\(215\) | −3.22710 | −0.220086 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.26498 | −0.628948 | ||||||||
\(218\) | −4.21774 | + | 2.27442i | −0.285662 | + | 0.154043i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.9635 | − | 27.3173i | 1.21110 | − | 1.84173i | ||||
\(221\) | 5.23617i | 0.352223i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.00739 | −0.201390 | −0.100695 | − | 0.994917i | \(-0.532107\pi\) | ||||
−0.100695 | + | 0.994917i | \(0.532107\pi\) | |||||||
\(224\) | −3.50764 | + | 4.43807i | −0.234364 | + | 0.296531i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.944215 | − | 1.75098i | −0.0628083 | − | 0.116473i | ||||
\(227\) | 11.1508i | 0.740102i | 0.929011 | + | 0.370051i | \(0.120660\pi\) | ||||
−0.929011 | + | 0.370051i | \(0.879340\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.46317i | 0.162771i | 0.996683 | + | 0.0813853i | \(0.0259344\pi\) | ||||
−0.996683 | + | 0.0813853i | \(0.974066\pi\) | |||||||
\(230\) | 40.0002 | − | 21.5701i | 2.63753 | − | 1.42229i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.398865 | − | 4.56571i | 0.0261867 | − | 0.299754i | ||||
\(233\) | 26.1143 | 1.71080 | 0.855401 | − | 0.517966i | \(-0.173311\pi\) | ||||
0.855401 | + | 0.517966i | \(0.173311\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 38.8534i | − | 2.53451i | ||||||
\(236\) | 5.00361 | + | 3.29032i | 0.325707 | + | 0.214181i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.31924 | − | 4.30086i | −0.150334 | − | 0.278783i | ||||
\(239\) | −24.4496 | −1.58151 | −0.790757 | − | 0.612130i | \(-0.790313\pi\) | ||||
−0.790757 | + | 0.612130i | \(0.790313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.01348 | −0.580609 | −0.290305 | − | 0.956934i | \(-0.593757\pi\) | ||||
−0.290305 | + | 0.956934i | \(0.593757\pi\) | |||||||
\(242\) | 5.95603 | + | 11.0450i | 0.382868 | + | 0.710001i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.2242 | + | 9.35366i | 0.910609 | + | 0.598807i | ||||
\(245\) | 3.66698i | 0.234275i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.48456 | −0.221717 | ||||||||
\(248\) | −26.1059 | − | 2.28063i | −1.65773 | − | 0.144820i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −15.7329 | + | 8.48397i | −0.995036 | + | 0.536573i | ||||
\(251\) | − | 24.7649i | − | 1.56315i | −0.623814 | − | 0.781573i | \(-0.714418\pi\) | ||
0.623814 | − | 0.781573i | \(-0.285582\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 39.0661i | 2.45606i | ||||||||
\(254\) | −7.02099 | − | 13.0199i | −0.440536 | − | 0.816942i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.9759 | + | 11.6417i | −0.685996 | + | 0.727606i | ||||
\(257\) | −17.1618 | −1.07052 | −0.535262 | − | 0.844686i | \(-0.679787\pi\) | ||||
−0.535262 | + | 0.844686i | \(0.679787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.69381i | − | 0.353796i | ||||||
\(260\) | 6.10666 | − | 9.28644i | 0.378719 | − | 0.575920i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.7635 | + | 8.50045i | −0.973870 | + | 0.525159i | ||||
\(263\) | −4.02861 | −0.248415 | −0.124207 | − | 0.992256i | \(-0.539639\pi\) | ||||
−0.124207 | + | 0.992256i | \(0.539639\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −42.1836 | −2.59132 | ||||||||
\(266\) | 2.86213 | − | 1.54340i | 0.175488 | − | 0.0946321i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −17.8184 | − | 11.7172i | −1.08843 | − | 0.715743i | ||||
\(269\) | 24.4193i | 1.48887i | 0.667693 | + | 0.744436i | \(0.267282\pi\) | ||||
−0.667693 | + | 0.744436i | \(0.732718\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.21510 | −0.0738120 | −0.0369060 | − | 0.999319i | \(-0.511750\pi\) | ||||
−0.0369060 | + | 0.999319i | \(0.511750\pi\) | |||||||
\(272\) | −5.47622 | − | 12.6894i | −0.332045 | − | 0.769409i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.61159 | − | 8.55185i | −0.278596 | − | 0.516636i | ||||
\(275\) | − | 37.6552i | − | 2.27069i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.1239i | 0.668371i | 0.942507 | + | 0.334185i | \(0.108461\pi\) | ||||
−0.942507 | + | 0.334185i | \(0.891539\pi\) | |||||||
\(278\) | −16.7249 | + | 9.01890i | −1.00309 | + | 0.540918i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.902651 | + | 10.3324i | −0.0539437 | + | 0.617482i | ||||
\(281\) | 29.4678 | 1.75790 | 0.878952 | − | 0.476910i | \(-0.158243\pi\) | ||||
0.878952 | + | 0.476910i | \(0.158243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0312i | 0.774624i | 0.921949 | + | 0.387312i | \(0.126596\pi\) | ||||
−0.921949 | + | 0.387312i | \(0.873404\pi\) | |||||||
\(284\) | 11.6670 | − | 17.7421i | 0.692309 | − | 1.05280i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.53478 | + | 8.40943i | 0.268147 | + | 0.497260i | ||||
\(287\) | 6.86926 | 0.405479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.06186 | −0.297756 | ||||||||
\(290\) | −3.98842 | − | 7.39624i | −0.234208 | − | 0.434322i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.63192 | + | 13.1266i | −0.505145 | + | 0.768177i | ||||
\(293\) | − | 4.86503i | − | 0.284218i | −0.989851 | − | 0.142109i | \(-0.954612\pi\) | ||
0.989851 | − | 0.142109i | \(-0.0453883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.9799 | 0.639274 | ||||||||
\(296\) | 1.40157 | − | 16.0434i | 0.0814644 | − | 0.932505i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.90792 | − | 4.26434i | 0.458093 | − | 0.247027i | ||||
\(299\) | 13.2804i | 0.768026i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.880042i | 0.0507248i | ||||||||
\(302\) | −13.1508 | − | 24.3872i | −0.756742 | − | 1.40332i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.44453 | − | 3.64431i | 0.484327 | − | 0.209015i | ||||
\(305\) | 31.2134 | 1.78728 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.07611i | 0.518001i | 0.965877 | + | 0.259000i | \(0.0833931\pi\) | ||||
−0.965877 | + | 0.259000i | \(0.916607\pi\) | |||||||
\(308\) | −7.44952 | − | 4.89872i | −0.424476 | − | 0.279131i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −42.2903 | + | 22.8050i | −2.40193 | + | 1.29524i | ||||
\(311\) | −1.21020 | −0.0686240 | −0.0343120 | − | 0.999411i | \(-0.510924\pi\) | ||||
−0.0343120 | + | 0.999411i | \(0.510924\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.15697 | −0.178443 | −0.0892214 | − | 0.996012i | \(-0.528438\pi\) | ||||
−0.0892214 | + | 0.996012i | \(0.528438\pi\) | |||||||
\(314\) | −28.2534 | + | 15.2356i | −1.59443 | + | 0.859796i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.02989 | + | 7.64898i | −0.282953 | + | 0.430289i | ||||
\(317\) | − | 7.08197i | − | 0.397763i | −0.980024 | − | 0.198882i | \(-0.936269\pi\) | ||
0.980024 | − | 0.198882i | \(-0.0637309\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.22351 | 0.404439 | ||||||||
\(320\) | −5.08679 | + | 28.8915i | −0.284360 | + | 1.61508i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.88224 | − | 10.9082i | −0.327805 | − | 0.607890i | ||||
\(323\) | 7.94457i | 0.442048i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.8008i | − | 0.710060i | ||||||
\(326\) | −4.48248 | + | 2.41718i | −0.248262 | + | 0.133875i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 19.3555 | + | 1.69091i | 1.06873 | + | 0.0933649i | ||||
\(329\) | −10.5955 | −0.584146 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.34765i | − | 0.403863i | −0.979400 | − | 0.201932i | \(-0.935278\pi\) | ||
0.979400 | − | 0.201932i | \(-0.0647219\pi\) | |||||||
\(332\) | −4.35313 | − | 2.86257i | −0.238909 | − | 0.157104i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.66732 | − | 6.80078i | −0.200667 | − | 0.372122i | ||||
\(335\) | −39.1007 | −2.13630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.9873 | −1.47009 | −0.735046 | − | 0.678017i | \(-0.762840\pi\) | ||||
−0.735046 | + | 0.678017i | \(0.762840\pi\) | |||||||
\(338\) | −7.18452 | − | 13.3232i | −0.390786 | − | 0.724685i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21.1725 | − | 13.9228i | −1.14824 | − | 0.755069i | ||||
\(341\) | − | 41.3027i | − | 2.23667i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.216628 | + | 2.47969i | −0.0116798 | + | 0.133696i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.14030 | − | 1.15416i | 0.115063 | − | 0.0620479i | ||||
\(347\) | 9.06776i | 0.486783i | 0.969928 | + | 0.243391i | \(0.0782599\pi\) | ||||
−0.969928 | + | 0.243391i | \(0.921740\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6784i | 0.732191i | 0.930577 | + | 0.366095i | \(0.119306\pi\) | ||||
−0.930577 | + | 0.366095i | \(0.880694\pi\) | |||||||
\(350\) | 5.66980 | + | 10.5142i | 0.303064 | + | 0.562010i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −19.7846 | − | 15.6368i | −1.05452 | − | 0.833447i | ||||
\(353\) | 0.949067 | 0.0505138 | 0.0252569 | − | 0.999681i | \(-0.491960\pi\) | ||||
0.0252569 | + | 0.999681i | \(0.491960\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 38.9331i | − | 2.06636i | ||||||
\(356\) | −2.35578 | + | 3.58246i | −0.124856 | + | 0.189870i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.6869 | − | 7.38064i | 0.723374 | − | 0.390079i | ||||
\(359\) | 15.0508 | 0.794351 | 0.397175 | − | 0.917743i | \(-0.369991\pi\) | ||||
0.397175 | + | 0.917743i | \(0.369991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.7131 | 0.721740 | ||||||||
\(362\) | 33.1390 | − | 17.8702i | 1.74175 | − | 0.939237i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.53244 | − | 1.66531i | −0.132736 | − | 0.0872859i | ||||
\(365\) | 28.8050i | 1.50772i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.70674 | −0.193490 | −0.0967451 | − | 0.995309i | \(-0.530843\pi\) | ||||
−0.0967451 | + | 0.995309i | \(0.530843\pi\) | |||||||
\(368\) | −13.8892 | − | 32.1839i | −0.724027 | − | 1.67770i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.0149 | − | 25.9896i | −0.728598 | − | 1.35113i | ||||
\(371\) | 11.5036i | 0.597239i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 31.3688i | − | 1.62421i | −0.583508 | − | 0.812107i | \(-0.698320\pi\) | ||
0.583508 | − | 0.812107i | \(-0.301680\pi\) | |||||||
\(374\) | 19.1730 | − | 10.3390i | 0.991410 | − | 0.534618i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −29.8548 | − | 2.60814i | −1.53964 | − | 0.134504i | ||||
\(377\) | 2.45562 | 0.126471 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6560i | 0.906930i | 0.891274 | + | 0.453465i | \(0.149812\pi\) | ||||
−0.891274 | + | 0.453465i | \(0.850188\pi\) | |||||||
\(380\) | 9.26531 | − | 14.0898i | 0.475301 | − | 0.722792i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.8734 | + | 27.5816i | 0.760989 | + | 1.41120i | ||||
\(383\) | 17.7974 | 0.909402 | 0.454701 | − | 0.890644i | \(-0.349746\pi\) | ||||
0.454701 | + | 0.890644i | \(0.349746\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3472 | −0.833129 | ||||||||
\(386\) | −7.75944 | − | 14.3893i | −0.394945 | − | 0.732397i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15.1993 | − | 23.1137i | 0.771630 | − | 1.17342i | ||||
\(389\) | 25.1886i | 1.27711i | 0.769574 | + | 0.638557i | \(0.220468\pi\) | ||||
−0.769574 | + | 0.638557i | \(0.779532\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.2785 | 1.53125 | ||||||||
\(392\) | 2.81770 | + | 0.246156i | 0.142315 | + | 0.0124328i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.3986 | + | 8.84292i | −0.826148 | + | 0.445500i | ||||
\(395\) | 16.7849i | 0.844539i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 34.3710i | − | 1.72503i | −0.506032 | − | 0.862515i | \(-0.668888\pi\) | ||
0.506032 | − | 0.862515i | \(-0.331112\pi\) | |||||||
\(398\) | 8.12276 | + | 15.0631i | 0.407157 | + | 0.755044i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.3876 | + | 31.0216i | 0.669382 | + | 1.55108i | ||||
\(401\) | −9.65560 | −0.482178 | −0.241089 | − | 0.970503i | \(-0.577505\pi\) | ||||
−0.241089 | + | 0.970503i | \(0.577505\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 14.0408i | − | 0.699420i | ||||||
\(404\) | −17.1006 | − | 11.2452i | −0.850788 | − | 0.559469i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.01698 | + | 1.08766i | −0.100101 | + | 0.0539795i | ||||
\(407\) | 25.3826 | 1.25817 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.4161 | 1.40509 | 0.702543 | − | 0.711642i | \(-0.252048\pi\) | ||||
0.702543 | + | 0.711642i | \(0.252048\pi\) | |||||||
\(410\) | 31.3549 | − | 16.9081i | 1.54851 | − | 0.835034i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.9803 | − | 21.2599i | 0.688758 | − | 1.04740i | ||||
\(413\) | − | 2.99426i | − | 0.147338i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.55248 | −0.468913 | ||||||||
\(416\) | −6.72573 | − | 5.31571i | −0.329756 | − | 0.260624i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.88039 | + | 12.7592i | 0.336531 | + | 0.624072i | ||||
\(419\) | − | 11.5381i | − | 0.563673i | −0.959462 | − | 0.281837i | \(-0.909056\pi\) | ||
0.959462 | − | 0.281837i | \(-0.0909436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 6.84814i | − | 0.333758i | −0.985977 | − | 0.166879i | \(-0.946631\pi\) | ||
0.985977 | − | 0.166879i | \(-0.0533689\pi\) | |||||||
\(422\) | −27.0737 | + | 14.5995i | −1.31793 | + | 0.710692i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.83169 | + | 32.4137i | −0.137519 | + | 1.57415i | ||||
\(425\) | −29.1850 | −1.41568 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.51202i | − | 0.411925i | ||||||
\(428\) | −10.7045 | − | 7.03913i | −0.517419 | − | 0.340249i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.16616 | + | 4.01698i | 0.104461 | + | 0.193716i | ||||
\(431\) | −10.4500 | −0.503357 | −0.251679 | − | 0.967811i | \(-0.580983\pi\) | ||||
−0.251679 | + | 0.967811i | \(0.580983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1818 | 0.873763 | 0.436882 | − | 0.899519i | \(-0.356083\pi\) | ||||
0.436882 | + | 0.899519i | \(0.356083\pi\) | |||||||
\(434\) | 6.21902 | + | 11.5327i | 0.298522 | + | 0.553588i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.66223 | + | 3.72342i | 0.271171 | + | 0.178319i | ||||
\(437\) | 20.1497i | 0.963889i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.91836 | 0.377923 | 0.188961 | − | 0.981985i | \(-0.439488\pi\) | ||||
0.188961 | + | 0.981985i | \(0.439488\pi\) | |||||||
\(440\) | −46.0614 | − | 4.02396i | −2.19589 | − | 0.191835i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.51780 | − | 3.51472i | 0.310020 | − | 0.167178i | ||||
\(443\) | − | 18.2916i | − | 0.869062i | −0.900657 | − | 0.434531i | \(-0.856914\pi\) | ||
0.900657 | − | 0.434531i | \(-0.143086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.86132i | 0.372662i | ||||||||
\(446\) | 2.01868 | + | 3.74350i | 0.0955873 | + | 0.177260i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.87881 | + | 1.38719i | 0.372239 | + | 0.0655384i | ||||
\(449\) | 15.2172 | 0.718144 | 0.359072 | − | 0.933310i | \(-0.383093\pi\) | ||||
0.359072 | + | 0.933310i | \(0.383093\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.6227i | 1.44197i | ||||||||
\(452\) | −1.54576 | + | 2.35065i | −0.0727066 | + | 0.110565i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.8801 | − | 7.48482i | 0.651424 | − | 0.351280i | ||||
\(455\) | −5.55718 | −0.260525 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.6658 | 1.80871 | 0.904354 | − | 0.426783i | \(-0.140353\pi\) | ||||
0.904354 | + | 0.426783i | \(0.140353\pi\) | |||||||
\(458\) | 3.06606 | − | 1.65337i | 0.143268 | − | 0.0772570i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −53.6994 | − | 35.3121i | −2.50375 | − | 1.64644i | ||||
\(461\) | − | 5.18888i | − | 0.241670i | −0.992673 | − | 0.120835i | \(-0.961443\pi\) | ||
0.992673 | − | 0.120835i | \(-0.0385572\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.81583 | −0.177337 | −0.0886683 | − | 0.996061i | \(-0.528261\pi\) | ||||
−0.0886683 | + | 0.996061i | \(0.528261\pi\) | |||||||
\(464\) | −5.95097 | + | 2.56819i | −0.276267 | + | 0.119225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.5289 | − | 32.5061i | −0.812011 | − | 1.50582i | ||||
\(467\) | − | 7.29246i | − | 0.337455i | −0.985663 | − | 0.168727i | \(-0.946034\pi\) | ||
0.985663 | − | 0.168727i | \(-0.0539657\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.6629i | 0.492367i | ||||||||
\(470\) | −48.3633 | + | 26.0799i | −2.23083 | + | 1.20298i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.737055 | − | 8.43690i | 0.0339257 | − | 0.388340i | ||||
\(473\) | −3.92317 | −0.180388 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 19.4220i | − | 0.891140i | ||||||
\(476\) | −3.79680 | + | 5.77381i | −0.174026 | + | 0.264642i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.4115 | + | 30.4340i | 0.750646 | + | 1.39202i | ||||
\(479\) | −16.2695 | −0.743371 | −0.371686 | − | 0.928359i | \(-0.621220\pi\) | ||||
−0.371686 | + | 0.928359i | \(0.621220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.62876 | 0.393438 | ||||||||
\(482\) | 6.05020 | + | 11.2197i | 0.275579 | + | 0.511042i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.75054 | − | 14.8277i | 0.443206 | − | 0.673986i | ||||
\(485\) | − | 50.7207i | − | 2.30311i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.16667 | 0.324753 | 0.162376 | − | 0.986729i | \(-0.448084\pi\) | ||||
0.162376 | + | 0.986729i | \(0.448084\pi\) | |||||||
\(488\) | 2.09529 | − | 23.9843i | 0.0948492 | − | 1.08572i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.56453 | − | 2.46142i | 0.206205 | − | 0.111196i | ||||
\(491\) | − | 17.8247i | − | 0.804418i | −0.915548 | − | 0.402209i | \(-0.868243\pi\) | ||
0.915548 | − | 0.402209i | \(-0.131757\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 5.59864i | − | 0.252150i | ||||||
\(494\) | 2.33897 | + | 4.33746i | 0.105235 | + | 0.195151i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 14.6844 | + | 34.0265i | 0.659351 | + | 1.52784i | ||||
\(497\) | −10.6172 | −0.476247 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 37.6121i | 1.68375i | 0.539673 | + | 0.841875i | \(0.318548\pi\) | ||||
−0.539673 | + | 0.841875i | \(0.681452\pi\) | |||||||
\(500\) | 21.1211 | + | 13.8890i | 0.944563 | + | 0.621135i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.8265 | + | 16.6232i | −1.37585 | + | 0.741928i | ||||
\(503\) | 20.3707 | 0.908286 | 0.454143 | − | 0.890929i | \(-0.349945\pi\) | ||||
0.454143 | + | 0.890929i | \(0.349945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −37.5255 | −1.66986 | ||||||||
\(506\) | 48.6280 | − | 26.2227i | 2.16178 | − | 1.16574i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.4940 | + | 17.4789i | −0.509962 | + | 0.775503i | ||||
\(509\) | 26.6481i | 1.18116i | 0.806980 | + | 0.590578i | \(0.201100\pi\) | ||||
−0.806980 | + | 0.590578i | \(0.798900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.85523 | 0.347495 | ||||||||
\(512\) | 21.8586 | + | 5.84809i | 0.966024 | + | 0.258451i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.5197 | + | 21.3624i | 0.508111 | + | 0.942256i | ||||
\(515\) | − | 46.6526i | − | 2.05576i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 47.2339i | − | 2.07734i | ||||||
\(518\) | −7.08745 | + | 3.82191i | −0.311405 | + | 0.167925i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15.6585 | − | 1.36794i | −0.686669 | − | 0.0599880i | ||||
\(521\) | 13.2614 | 0.580992 | 0.290496 | − | 0.956876i | \(-0.406180\pi\) | ||||
0.290496 | + | 0.956876i | \(0.406180\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.3786i | 0.934821i | 0.884040 | + | 0.467411i | \(0.154813\pi\) | ||||
−0.884040 | + | 0.467411i | \(0.845187\pi\) | |||||||
\(524\) | 21.1621 | + | 13.9160i | 0.924471 | + | 0.607922i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.70416 | + | 5.01467i | 0.117907 | + | 0.218650i | ||||
\(527\) | −32.0120 | −1.39447 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.7948 | 2.33890 | ||||||||
\(530\) | 28.3153 | + | 52.5087i | 1.22994 | + | 2.28083i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.84235 | − | 2.52668i | −0.166587 | − | 0.109546i | ||||
\(533\) | 10.4101i | 0.450912i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.4898 | −1.01555 | ||||||||
\(536\) | −2.62474 | + | 30.0448i | −0.113372 | + | 1.29774i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.3963 | − | 16.3912i | 1.31048 | − | 0.706675i | ||||
\(539\) | 4.45794i | 0.192017i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 31.4969i | − | 1.35416i | −0.735910 | − | 0.677080i | \(-0.763245\pi\) | ||
0.735910 | − | 0.677080i | \(-0.236755\pi\) | |||||||
\(542\) | 0.815621 | + | 1.51251i | 0.0350339 | + | 0.0649679i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −12.1195 | + | 15.3342i | −0.519618 | + | 0.657450i | ||||
\(545\) | 12.4252 | 0.532235 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.38840i | 0.0593637i | 0.999559 | + | 0.0296819i | \(0.00944942\pi\) | ||||
−0.999559 | + | 0.0296819i | \(0.990551\pi\) | |||||||
\(548\) | −7.54957 | + | 11.4807i | −0.322502 | + | 0.490430i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −46.8718 | + | 25.2756i | −1.99862 | + | 1.07776i | ||||
\(551\) | 3.72578 | 0.158723 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.57730 | 0.194647 | ||||||||
\(554\) | 13.8466 | − | 7.46680i | 0.588287 | − | 0.317234i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.4528 | + | 14.7647i | 0.952212 | + | 0.626164i | ||||
\(557\) | − | 10.8246i | − | 0.458654i | −0.973349 | − | 0.229327i | \(-0.926347\pi\) | ||
0.973349 | − | 0.229327i | \(-0.0736525\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.33367 | −0.0564083 | ||||||||
\(560\) | 13.4674 | − | 5.81195i | 0.569100 | − | 0.245600i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.7800 | − | 36.6805i | −0.834367 | − | 1.54727i | ||||
\(563\) | − | 7.56473i | − | 0.318816i | −0.987213 | − | 0.159408i | \(-0.949042\pi\) | ||
0.987213 | − | 0.159408i | \(-0.0509585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.15826i | 0.217009i | ||||||||
\(566\) | 16.2208 | − | 8.74704i | 0.681810 | − | 0.367666i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.9160 | − | 2.61349i | −1.25525 | − | 0.109660i | ||||
\(569\) | 21.9063 | 0.918360 | 0.459180 | − | 0.888343i | \(-0.348143\pi\) | ||||
0.459180 | + | 0.888343i | \(0.348143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 43.6061i | − | 1.82486i | −0.409235 | − | 0.912429i | \(-0.634204\pi\) | ||
0.409235 | − | 0.912429i | \(-0.365796\pi\) | |||||||
\(572\) | 7.42384 | − | 11.2895i | 0.310406 | − | 0.472037i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.61091 | − | 8.55061i | −0.192456 | − | 0.356895i | ||||
\(575\) | −74.0213 | −3.08690 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.6116 | 0.525028 | 0.262514 | − | 0.964928i | \(-0.415448\pi\) | ||||
0.262514 | + | 0.964928i | \(0.415448\pi\) | |||||||
\(578\) | 3.39772 | + | 6.30082i | 0.141326 | + | 0.262080i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.52939 | + | 9.92928i | −0.271118 | + | 0.412291i | ||||
\(581\) | 2.60500i | 0.108073i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.2824 | −2.12390 | ||||||||
\(584\) | 22.1336 | + | 1.93361i | 0.915896 | + | 0.0800135i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.05581 | + | 3.26560i | −0.250163 | + | 0.134901i | ||||
\(587\) | − | 10.5118i | − | 0.433866i | −0.976186 | − | 0.216933i | \(-0.930395\pi\) | ||
0.976186 | − | 0.216933i | \(-0.0696054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21.3033i | − | 0.877787i | ||||||
\(590\) | −7.37013 | − | 13.6674i | −0.303423 | − | 0.562677i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.9111 | + | 9.02435i | −0.859439 | + | 0.370898i | ||||
\(593\) | 23.9765 | 0.984598 | 0.492299 | − | 0.870426i | \(-0.336157\pi\) | ||||
0.492299 | + | 0.870426i | \(0.336157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.6700i | 0.519420i | ||||||||
\(596\) | −10.6162 | − | 6.98110i | −0.434857 | − | 0.285957i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.5310 | − | 8.91433i | 0.676002 | − | 0.364534i | ||||
\(599\) | 32.2302 | 1.31689 | 0.658446 | − | 0.752628i | \(-0.271214\pi\) | ||||
0.658446 | + | 0.752628i | \(0.271214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.3405 | 1.76790 | 0.883949 | − | 0.467584i | \(-0.154875\pi\) | ||||
0.883949 | + | 0.467584i | \(0.154875\pi\) | |||||||
\(602\) | 1.09545 | − | 0.590719i | 0.0446470 | − | 0.0240759i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.5290 | + | 32.7392i | −0.876001 | + | 1.33214i | ||||
\(605\) | − | 32.5378i | − | 1.32285i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.2372 | −0.537283 | −0.268642 | − | 0.963240i | \(-0.586575\pi\) | ||||
−0.268642 | + | 0.963240i | \(0.586575\pi\) | |||||||
\(608\) | −10.2046 | − | 8.06525i | −0.413851 | − | 0.327089i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.9517 | − | 38.8534i | −0.848308 | − | 1.57313i | ||||
\(611\) | − | 16.0570i | − | 0.649598i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 6.23612i | − | 0.251874i | −0.992038 | − | 0.125937i | \(-0.959806\pi\) | ||
0.992038 | − | 0.125937i | \(-0.0401938\pi\) | |||||||
\(614\) | 11.2976 | − | 6.09224i | 0.455935 | − | 0.245863i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.09735 | + | 12.5611i | −0.0442134 | + | 0.506101i | ||||
\(617\) | −7.66713 | −0.308667 | −0.154334 | − | 0.988019i | \(-0.549323\pi\) | ||||
−0.154334 | + | 0.988019i | \(0.549323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.9974i | 1.12531i | 0.826692 | + | 0.562655i | \(0.190220\pi\) | ||||
−0.826692 | + | 0.562655i | \(0.809780\pi\) | |||||||
\(620\) | 56.7738 | + | 37.3338i | 2.28009 | + | 1.49936i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.812332 | + | 1.50641i | 0.0325715 | + | 0.0604016i | ||||
\(623\) | 2.14381 | 0.0858900 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.11412 | 0.164565 | ||||||||
\(626\) | 2.11908 | + | 3.92969i | 0.0846956 | + | 0.157062i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 37.9295 | + | 24.9421i | 1.51355 | + | 0.995297i | ||||
\(629\) | − | 19.6730i | − | 0.784415i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.2806 | 0.727739 | 0.363869 | − | 0.931450i | \(-0.381455\pi\) | ||||
0.363869 | + | 0.931450i | \(0.381455\pi\) | |||||||
\(632\) | 12.8974 | + | 1.12673i | 0.513032 | + | 0.0448189i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.81539 | + | 4.75370i | −0.350104 | + | 0.188793i | ||||
\(635\) | 38.3557i | 1.52210i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.51546i | 0.0600449i | ||||||||
\(638\) | −4.84870 | − | 8.99157i | −0.191962 | − | 0.355980i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.3775 | − | 13.0612i | 1.55653 | − | 0.516291i | ||||
\(641\) | −5.99361 | −0.236733 | −0.118367 | − | 0.992970i | \(-0.537766\pi\) | ||||
−0.118367 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.0547i | 1.14581i | 0.819623 | + | 0.572903i | \(0.194183\pi\) | ||||
−0.819623 | + | 0.572903i | \(0.805817\pi\) | |||||||
\(644\) | −9.62974 | + | 14.6440i | −0.379465 | + | 0.577055i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.88912 | − | 5.33271i | 0.389082 | − | 0.209812i | ||||
\(647\) | −26.7288 | −1.05082 | −0.525408 | − | 0.850850i | \(-0.676087\pi\) | ||||
−0.525408 | + | 0.850850i | \(0.676087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.3482 | 0.523963 | ||||||||
\(650\) | −15.9340 | + | 8.59238i | −0.624981 | + | 0.337021i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.01763 | + | 3.95713i | 0.235669 | + | 0.154973i | ||||
\(653\) | − | 41.0011i | − | 1.60450i | −0.596991 | − | 0.802248i | \(-0.703637\pi\) | ||
0.596991 | − | 0.802248i | \(-0.296363\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.4380 | 1.81448 | ||||||||
\(656\) | −10.8874 | − | 25.2280i | −0.425080 | − | 0.984988i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.11208 | + | 13.1888i | 0.277258 | + | 0.514155i | ||||
\(659\) | 1.91818i | 0.0747219i | 0.999302 | + | 0.0373609i | \(0.0118951\pi\) | ||||
−0.999302 | + | 0.0373609i | \(0.988105\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.9347i | 0.425312i | 0.977127 | + | 0.212656i | \(0.0682114\pi\) | ||||
−0.977127 | + | 0.212656i | \(0.931789\pi\) | |||||||
\(662\) | −9.14609 | + | 4.93203i | −0.355473 | + | 0.191689i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.641236 | + | 7.34009i | −0.0248848 | + | 0.284851i | ||||
\(665\) | −8.43162 | −0.326964 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 14.1997i | − | 0.549816i | ||||||
\(668\) | −6.00373 | + | 9.12990i | −0.232291 | + | 0.353247i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 26.2459 | + | 48.6712i | 1.01397 | + | 1.88033i | ||||
\(671\) | 37.9460 | 1.46489 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0071 | 0.385745 | 0.192872 | − | 0.981224i | \(-0.438220\pi\) | ||||
0.192872 | + | 0.981224i | \(0.438220\pi\) | |||||||
\(674\) | 18.1149 | + | 33.5928i | 0.697761 | + | 1.29395i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.7617 | + | 17.8861i | −0.452372 | + | 0.687925i | ||||
\(677\) | 35.4441i | 1.36223i | 0.732178 | + | 0.681113i | \(0.238504\pi\) | ||||
−0.732178 | + | 0.681113i | \(0.761496\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8317 | −0.530812 | ||||||||
\(680\) | −3.11881 | + | 35.7003i | −0.119601 | + | 1.36904i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −51.4121 | + | 27.7240i | −1.96867 | + | 1.06161i | ||||
\(683\) | 34.8397i | 1.33310i | 0.745459 | + | 0.666551i | \(0.232230\pi\) | ||||
−0.745459 | + | 0.666551i | \(0.767770\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25.1931i | 0.962580i | ||||||||
\(686\) | −0.671239 | − | 1.24476i | −0.0256280 | − | 0.0475253i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.23204 | − | 1.39481i | 0.123220 | − | 0.0531768i | ||||
\(689\) | −17.4333 | −0.664157 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2381i | 0.617727i | 0.951106 | + | 0.308864i | \(0.0999486\pi\) | ||||
−0.951106 | + | 0.308864i | \(0.900051\pi\) | |||||||
\(692\) | −2.87331 | − | 1.88946i | −0.109227 | − | 0.0718263i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11.2872 | − | 6.08663i | 0.428457 | − | 0.231045i | ||||
\(695\) | 49.2704 | 1.86893 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.7344 | 0.899004 | ||||||||
\(698\) | 17.0264 | − | 9.18151i | 0.644461 | − | 0.347525i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.28196 | − | 14.1151i | 0.350825 | − | 0.533502i | ||||
\(701\) | 28.8081i | 1.08807i | 0.839064 | + | 0.544033i | \(0.183103\pi\) | ||||
−0.839064 | + | 0.544033i | \(0.816897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.0920 | 0.493773 | ||||||||
\(704\) | −6.18399 | + | 35.1232i | −0.233068 | + | 1.32376i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.637051 | − | 1.18137i | −0.0239757 | − | 0.0444613i | ||||
\(707\) | 10.2333i | 0.384864i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.1039i | − | 0.679906i | −0.940442 | − | 0.339953i | \(-0.889589\pi\) | ||
0.940442 | − | 0.339953i | \(-0.110411\pi\) | |||||||
\(710\) | −48.4626 | + | 26.1334i | −1.81877 | + | 0.980770i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.04061 | + | 0.527713i | 0.226381 | + | 0.0197769i | ||||
\(713\) | −81.1915 | −3.04064 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.7736i | − | 0.926479i | ||||||
\(716\) | −18.3743 | − | 12.0828i | −0.686681 | − | 0.451554i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.1027 | − | 18.7347i | −0.377029 | − | 0.699173i | ||||
\(719\) | 12.7731 | 0.476357 | 0.238179 | − | 0.971221i | \(-0.423450\pi\) | ||||
0.238179 | + | 0.971221i | \(0.423450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.7223 | −0.473804 | ||||||||
\(722\) | −9.20474 | − | 17.0695i | −0.342565 | − | 0.635262i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −44.4884 | − | 29.2551i | −1.65340 | − | 1.08726i | ||||
\(725\) | 13.6869i | 0.508319i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1654 | −0.377012 | −0.188506 | − | 0.982072i | \(-0.560365\pi\) | ||||
−0.188506 | + | 0.982072i | \(0.560365\pi\) | |||||||
\(728\) | −0.373041 | + | 4.27012i | −0.0138258 | + | 0.158261i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 35.8554 | − | 19.3350i | 1.32707 | − | 0.715621i | ||||
\(731\) | 3.04069i | 0.112464i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 26.1041i | − | 0.964178i | −0.876122 | − | 0.482089i | \(-0.839878\pi\) | ||
0.876122 | − | 0.482089i | \(-0.160122\pi\) | |||||||
\(734\) | 2.48811 | + | 4.61402i | 0.0918377 | + | 0.170307i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.7384 | + | 38.8919i | −1.13303 | + | 1.43358i | ||||
\(737\) | −47.5345 | −1.75096 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.90517i | 0.364368i | 0.983264 | + | 0.182184i | \(0.0583166\pi\) | ||||
−0.983264 | + | 0.182184i | \(0.941683\pi\) | |||||||
\(740\) | −22.9436 | + | 34.8904i | −0.843422 | + | 1.28260i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.3193 | − | 7.72168i | 0.525678 | − | 0.283472i | ||||
\(743\) | −33.5353 | −1.23029 | −0.615146 | − | 0.788413i | \(-0.710903\pi\) | ||||
−0.615146 | + | 0.788413i | \(0.710903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.2961 | −0.853504 | ||||||||
\(746\) | −39.0468 | + | 21.0560i | −1.42960 | + | 0.770913i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −25.7393 | − | 16.9259i | −0.941121 | − | 0.618871i | ||||
\(749\) | 6.40575i | 0.234061i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.8436 | 1.96478 | 0.982391 | − | 0.186839i | \(-0.0598243\pi\) | ||||
0.982391 | + | 0.186839i | \(0.0598243\pi\) | |||||||
\(752\) | 16.7932 | + | 38.9128i | 0.612384 | + | 1.41901i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.64830 | − | 3.05666i | −0.0600277 | − | 0.111317i | ||||
\(755\) | 71.8428i | 2.61463i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.18921i | 0.0432225i | 0.999766 | + | 0.0216113i | \(0.00687962\pi\) | ||||
−0.999766 | + | 0.0216113i | \(0.993120\pi\) | |||||||
\(758\) | 21.9776 | − | 11.8514i | 0.798262 | − | 0.430463i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −23.7577 | − | 2.07550i | −0.861784 | − | 0.0752862i | ||||
\(761\) | 38.0810 | 1.38043 | 0.690217 | − | 0.723602i | \(-0.257515\pi\) | ||||
0.690217 | + | 0.723602i | \(0.257515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.38839i | − | 0.122668i | ||||||
\(764\) | 24.3490 | − | 37.0277i | 0.880917 | − | 1.33962i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11.9463 | − | 22.1535i | −0.431637 | − | 0.800439i | ||||
\(767\) | 4.53769 | 0.163846 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.6053 | −1.39214 | −0.696071 | − | 0.717973i | \(-0.745070\pi\) | ||||
−0.696071 | + | 0.717973i | \(0.745070\pi\) | |||||||
\(770\) | 10.9729 | + | 20.3484i | 0.395434 | + | 0.733305i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.7029 | + | 19.3173i | −0.457187 | + | 0.695246i | ||||
\(773\) | 18.5902i | 0.668642i | 0.942459 | + | 0.334321i | \(0.108507\pi\) | ||||
−0.942459 | + | 0.334321i | \(0.891493\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 78.2592 | 2.81115 | ||||||||
\(776\) | −38.9736 | − | 3.40476i | −1.39907 | − | 0.122224i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.3539 | − | 16.9076i | 1.12409 | − | 0.606166i | ||||
\(779\) | 15.7947i | 0.565905i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 47.3308i | − | 1.69363i | ||||||
\(782\) | −20.3241 | − | 37.6896i | −0.726788 | − | 1.34778i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.58494 | − | 3.67260i | −0.0566050 | − | 0.131164i | ||||
\(785\) | 83.2324 | 2.97069 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 17.3947i | − | 0.620056i | −0.950727 | − | 0.310028i | \(-0.899662\pi\) | ||
0.950727 | − | 0.310028i | \(-0.100338\pi\) | |||||||
\(788\) | 22.0147 | + | 14.4766i | 0.784241 | + | 0.515709i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.8932 | − | 11.2667i | 0.743347 | − | 0.400850i | ||||
\(791\) | 1.40668 | 0.0500156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8997 | 0.458080 | ||||||||
\(794\) | −42.7838 | + | 23.0711i | −1.51834 | + | 0.818764i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.2977 | − | 20.2219i | 0.471324 | − | 0.716745i | ||||
\(797\) | 15.3683i | 0.544374i | 0.962244 | + | 0.272187i | \(0.0877470\pi\) | ||||
−0.962244 | + | 0.272187i | \(0.912253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.6090 | −1.29513 | ||||||||
\(800\) | 29.6283 | − | 37.4873i | 1.04752 | − | 1.32538i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.48122 | + | 12.0190i | 0.228860 | + | 0.424404i | ||||
\(803\) | 35.0181i | 1.23576i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.1347i | 1.13260i | ||||||||
\(806\) | −17.4774 | + | 9.42470i | −0.615616 | + | 0.331971i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.51900 | + | 28.8344i | −0.0886182 | + | 1.01439i | ||||
\(809\) | −29.7888 | −1.04732 | −0.523659 | − | 0.851928i | \(-0.675433\pi\) | ||||
−0.523659 | + | 0.851928i | \(0.675433\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.50515i | 0.228427i | 0.993456 | + | 0.114213i | \(0.0364347\pi\) | ||||
−0.993456 | + | 0.114213i | \(0.963565\pi\) | |||||||
\(812\) | 2.70775 | + | 1.78059i | 0.0950235 | + | 0.0624864i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.0378 | − | 31.5954i | −0.597175 | − | 1.10742i | ||||
\(815\) | 13.2051 | 0.462553 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.02351 | −0.0707937 | ||||||||
\(818\) | −19.0740 | − | 35.3713i | −0.666906 | − | 1.23673i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −42.0933 | − | 27.6801i | −1.46996 | − | 0.966631i | ||||
\(821\) | 3.89581i | 0.135965i | 0.997687 | + | 0.0679823i | \(0.0216562\pi\) | ||||
−0.997687 | + | 0.0679823i | \(0.978344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.1577 | 1.64381 | 0.821907 | − | 0.569621i | \(-0.192910\pi\) | ||||
0.821907 | + | 0.569621i | \(0.192910\pi\) | |||||||
\(824\) | −35.8476 | − | 3.13168i | −1.24881 | − | 0.109097i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.72714 | + | 2.00986i | −0.129684 | + | 0.0699320i | ||||
\(827\) | 30.9915i | 1.07768i | 0.842408 | + | 0.538841i | \(0.181138\pi\) | ||||
−0.842408 | + | 0.538841i | \(0.818862\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.2090i | − | 1.18813i | −0.804417 | − | 0.594065i | \(-0.797522\pi\) | ||
0.804417 | − | 0.594065i | \(-0.202478\pi\) | |||||||
\(830\) | 6.41200 | + | 11.8906i | 0.222564 | + | 0.412728i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.10223 | + | 11.9401i | −0.0728818 | + | 0.413947i | ||||
\(833\) | 3.45516 | 0.119714 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.0346i | 0.693326i | ||||||||
\(836\) | 11.2638 | − | 17.1289i | 0.389567 | − | 0.592416i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.3622 | + | 7.74483i | −0.496135 | + | 0.267541i | ||||
\(839\) | 40.9980 | 1.41541 | 0.707704 | − | 0.706509i | \(-0.249731\pi\) | ||||
0.707704 | + | 0.706509i | \(0.249731\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.3744 | 0.909462 | ||||||||
\(842\) | −8.52432 | + | 4.59674i | −0.293768 | + | 0.158414i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 36.3459 | + | 23.9007i | 1.25108 | + | 0.822694i | ||||
\(845\) | 39.2491i | 1.35021i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.87319 | −0.304886 | ||||||||
\(848\) | 42.2482 | − | 18.2326i | 1.45081 | − | 0.626109i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19.5901 | + | 36.3284i | 0.671934 | + | 1.24605i | ||||
\(851\) | − | 49.8963i | − | 1.71042i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.3408i | 0.901891i | 0.892551 | + | 0.450946i | \(0.148913\pi\) | ||||
−0.892551 | + | 0.450946i | \(0.851087\pi\) | |||||||
\(854\) | −10.5955 | + | 5.71360i | −0.362569 | + | 0.195515i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.57682 | + | 18.0495i | −0.0538945 | + | 0.616918i | ||||
\(857\) | 56.4187 | 1.92723 | 0.963613 | − | 0.267300i | \(-0.0861316\pi\) | ||||
0.963613 | + | 0.267300i | \(0.0861316\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 34.5693i | − | 1.17949i | −0.807589 | − | 0.589745i | \(-0.799228\pi\) | ||
0.807589 | − | 0.589745i | \(-0.200772\pi\) | |||||||
\(860\) | 3.54619 | − | 5.39271i | 0.120924 | − | 0.183890i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.01443 | + | 13.0078i | 0.238912 | + | 0.443046i | ||||
\(863\) | −1.52709 | −0.0519826 | −0.0259913 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259913 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.30517 | −0.214382 | ||||||||
\(866\) | −12.2044 | − | 22.6321i | −0.414721 | − | 0.769070i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.1811 | − | 15.4824i | 0.345568 | − | 0.525508i | ||||
\(869\) | 20.4053i | 0.692202i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.1593 | −0.547535 | ||||||||
\(872\) | 0.834073 | − | 9.54744i | 0.0282453 | − | 0.323317i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.0816 | − | 13.5252i | 0.848397 | − | 0.457498i | ||||
\(875\) | − | 12.6393i | − | 0.427285i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 20.5638i | − | 0.694389i | −0.937793 | − | 0.347195i | \(-0.887134\pi\) | ||
0.937793 | − | 0.347195i | \(-0.112866\pi\) | |||||||
\(878\) | −5.31511 | − | 9.85650i | −0.179376 | − | 0.332641i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 25.9093 | + | 60.0366i | 0.873402 | + | 2.02383i | ||||
\(881\) | 16.8073 | 0.566252 | 0.283126 | − | 0.959083i | \(-0.408629\pi\) | ||||
0.283126 | + | 0.959083i | \(0.408629\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.7849i | 0.463900i | 0.972728 | + | 0.231950i | \(0.0745105\pi\) | ||||
−0.972728 | + | 0.231950i | \(0.925489\pi\) | |||||||
\(884\) | −8.75001 | − | 5.75391i | −0.294295 | − | 0.193525i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.7688 | + | 12.2781i | −0.764932 | + | 0.412490i | ||||
\(887\) | 25.0037 | 0.839541 | 0.419771 | − | 0.907630i | \(-0.362111\pi\) | ||||
0.419771 | + | 0.907630i | \(0.362111\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.4597 | 0.350808 | ||||||||
\(890\) | 9.78550 | − | 5.27683i | 0.328011 | − | 0.176880i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.30475 | − | 5.02556i | 0.110651 | − | 0.168268i | ||||
\(893\) | − | 24.3625i | − | 0.815260i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −40.3205 | −1.34777 | ||||||||
\(896\) | −3.56185 | − | 10.7384i | −0.118993 | − | 0.358745i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.2144 | − | 18.9418i | −0.340858 | − | 0.632097i | ||||
\(899\) | 15.0127i | 0.500702i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.7469i | 1.32416i | ||||||||
\(902\) | 38.1181 | − | 20.5551i | 1.26919 | − | 0.684412i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.96358 | + | 0.346262i | 0.131827 | + | 0.0115165i | ||||
\(905\) | −97.6251 | −3.24517 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.5827i | − | 0.783052i | −0.920167 | − | 0.391526i | \(-0.871947\pi\) | ||
0.920167 | − | 0.391526i | \(-0.128053\pi\) | |||||||
\(908\) | −18.6337 | − | 12.2533i | −0.618380 | − | 0.406640i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.73020 | + | 6.91738i | 0.123655 | + | 0.229309i | ||||
\(911\) | 29.1770 | 0.966677 | 0.483338 | − | 0.875434i | \(-0.339424\pi\) | ||||
0.483338 | + | 0.875434i | \(0.339424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.6129 | −0.384331 | ||||||||
\(914\) | −25.9540 | − | 48.1298i | −0.858481 | − | 1.59199i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.11612 | − | 2.70671i | −0.136000 | − | 0.0894324i | ||||
\(917\) | − | 12.6638i | − | 0.418196i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.6854 | 1.70494 | 0.852472 | − | 0.522772i | \(-0.175102\pi\) | ||||
0.852472 | + | 0.522772i | \(0.175102\pi\) | |||||||
\(920\) | −7.91017 | + | 90.5459i | −0.260791 | + | 2.98521i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.45893 | + | 3.48298i | −0.212713 | + | 0.114706i | ||||
\(923\) | − | 16.0900i | − | 0.529609i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.0943i | 1.58133i | ||||||||
\(926\) | 2.56133 | + | 4.74981i | 0.0841707 | + | 0.156088i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.19132 | + | 5.68369i | 0.236067 | + | 0.186576i | ||||
\(929\) | 20.0819 | 0.658865 | 0.329432 | − | 0.944179i | \(-0.393143\pi\) | ||||
0.329432 | + | 0.944179i | \(0.393143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.29933i | 0.0753576i | ||||||||
\(932\) | −28.6964 | + | 43.6387i | −0.939980 | + | 1.42943i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.07739 | + | 4.89498i | −0.297021 | + | 0.160169i | ||||
\(935\) | −56.4821 | −1.84716 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19.1583 | −0.625875 | −0.312937 | − | 0.949774i | \(-0.601313\pi\) | ||||
−0.312937 | + | 0.949774i | \(0.601313\pi\) | |||||||
\(938\) | 13.2728 | − | 7.15736i | 0.433372 | − | 0.233696i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 64.9266 | + | 42.6951i | 2.11767 | + | 1.39256i | ||||
\(941\) | 54.2409i | 1.76820i | 0.467296 | + | 0.884101i | \(0.345228\pi\) | ||||
−0.467296 | + | 0.884101i | \(0.654772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60.1971 | 1.96029 | ||||||||
\(944\) | −10.9967 | + | 4.74572i | −0.357912 | + | 0.154460i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.63339 | + | 4.88342i | 0.0856187 | + | 0.158774i | ||||
\(947\) | 47.7355i | 1.55120i | 0.631228 | + | 0.775598i | \(0.282551\pi\) | ||||
−0.631228 | + | 0.775598i | \(0.717449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.9043i | 0.386430i | ||||||||
\(950\) | −24.1758 | + | 13.0368i | −0.784365 | + | 0.422969i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.73559 | + | 0.850510i | 0.315532 | + | 0.0275652i | ||||
\(953\) | −11.2075 | −0.363046 | −0.181523 | − | 0.983387i | \(-0.558103\pi\) | ||||
−0.181523 | + | 0.983387i | \(0.558103\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 81.2534i | − | 2.62930i | ||||||
\(956\) | 26.8671 | − | 40.8570i | 0.868945 | − | 1.32141i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.9207 | + | 20.2517i | 0.352832 | + | 0.654301i | ||||
\(959\) | 6.87026 | 0.221852 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54.8399 | 1.76903 | ||||||||
\(962\) | −5.79196 | − | 10.7408i | −0.186740 | − | 0.346297i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.90470 | − | 15.0621i | 0.319009 | − | 0.485119i | ||||
\(965\) | 42.3899i | 1.36458i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.5979 | −0.726701 | −0.363350 | − | 0.931653i | \(-0.618367\pi\) | ||||
−0.363350 | + | 0.931653i | \(0.618367\pi\) | |||||||
\(968\) | −25.0019 | − | 2.18419i | −0.803593 | − | 0.0702025i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −63.1353 | + | 34.0457i | −2.02715 | + | 1.09314i | ||||
\(971\) | 46.5586i | 1.49414i | 0.664747 | + | 0.747068i | \(0.268539\pi\) | ||||
−0.664747 | + | 0.747068i | \(0.731461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13.4362i | − | 0.430745i | ||||||
\(974\) | −4.81055 | − | 8.92081i | −0.154140 | − | 0.285841i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.2612 | + | 13.4910i | −1.00065 | + | 0.431838i | ||||
\(977\) | 43.5968 | 1.39479 | 0.697393 | − | 0.716689i | \(-0.254343\pi\) | ||||
0.697393 | + | 0.716689i | \(0.254343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.55697i | 0.305442i | ||||||||
\(980\) | −6.12778 | − | 4.02956i | −0.195745 | − | 0.128720i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.1876 | + | 11.9646i | −0.708034 | + | 0.381807i | ||||
\(983\) | −22.5407 | −0.718937 | −0.359469 | − | 0.933157i | \(-0.617042\pi\) | ||||
−0.359469 | + | 0.933157i | \(0.617042\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.3090 | 1.53925 | ||||||||
\(986\) | −6.96899 | + | 3.75803i | −0.221938 | + | 0.119680i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.82910 | − | 5.82294i | 0.121820 | − | 0.185252i | ||||
\(989\) | 7.71204i | 0.245229i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2444 | 0.770148 | 0.385074 | − | 0.922886i | \(-0.374176\pi\) | ||||
0.385074 | + | 0.922886i | \(0.374176\pi\) | |||||||
\(992\) | 32.4983 | − | 41.1186i | 1.03182 | − | 1.30552i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.12668 | + | 13.2159i | 0.226045 | + | 0.419183i | ||||
\(995\) | − | 44.3747i | − | 1.40677i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 49.3412i | 1.56265i | 0.624124 | + | 0.781325i | \(0.285456\pi\) | ||||
−0.624124 | + | 0.781325i | \(0.714544\pi\) | |||||||
\(998\) | 46.8182 | − | 25.2467i | 1.48201 | − | 0.799171i | ||||
\(999\) | 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 | 1512.2.c.f.757.9 | ✓ | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.f.757.16 | yes | 24 | |
4.3 | odd | 2 | 6048.2.c.g.3025.24 | 24 | |||
8.3 | odd | 2 | 6048.2.c.g.3025.1 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.f.757.10 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.g.3025.2 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.f.757.15 | yes | 24 | |
24.11 | even | 2 | 6048.2.c.g.3025.23 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.f.757.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1512.2.c.f.757.10 | yes | 24 | 8.5 | even | 2 | inner | |
1512.2.c.f.757.15 | yes | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.f.757.16 | yes | 24 | 3.2 | odd | 2 | inner | |
6048.2.c.g.3025.1 | 24 | 8.3 | odd | 2 | |||
6048.2.c.g.3025.2 | 24 | 12.11 | even | 2 | |||
6048.2.c.g.3025.23 | 24 | 24.11 | even | 2 | |||
6048.2.c.g.3025.24 | 24 | 4.3 | odd | 2 |