Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,2,Mod(911,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.911");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.cc (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: | \(11.4984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 911.10 | ||
Character | \(\chi\) | \(=\) | 1440.911 |
Dual form | 1440.2.cc.a.1391.10 |
$q$-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 \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.424591 | − | 1.67920i | −0.245138 | − | 0.969488i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.88456 | + | 2.24275i | 1.46822 | + | 0.847680i | 0.999366 | − | 0.0355937i | \(-0.0113322\pi\) |
0.468858 | + | 0.883273i | \(0.344666\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.63944 | + | 1.42595i | −0.879815 | + | 0.475317i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.05081 | − | 0.606687i | −0.316832 | − | 0.182923i | 0.333148 | − | 0.942875i | \(-0.391889\pi\) |
−0.649980 | + | 0.759952i | \(0.725223\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.71090 | + | 0.987790i | −0.474519 | + | 0.273964i | −0.718130 | − | 0.695909i | \(-0.755001\pi\) |
0.243611 | + | 0.969873i | \(0.421668\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.24194 | + | 1.20731i | −0.320667 | + | 0.311726i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 5.28743i | − | 1.28239i | −0.767378 | − | 0.641195i | \(-0.778439\pi\) | ||
0.767378 | − | 0.641195i | \(-0.221561\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.86627 | 1.11640 | 0.558200 | − | 0.829707i | \(-0.311492\pi\) | ||||
0.558200 | + | 0.829707i | \(0.311492\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.11668 | − | 7.47521i | 0.461898 | − | 1.63122i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.40767 | + | 2.43816i | 0.293520 | + | 0.508392i | 0.974640 | − | 0.223781i | \(-0.0718399\pi\) |
−0.681119 | + | 0.732172i | \(0.738507\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.51514 | + | 3.82672i | 0.676490 | + | 0.736452i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.20865 | − | 7.28960i | 0.781527 | − | 1.35364i | −0.149525 | − | 0.988758i | \(-0.547775\pi\) |
0.931052 | − | 0.364886i | \(-0.118892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.04943 | − | 3.49264i | 1.08651 | − | 0.627296i | 0.153864 | − | 0.988092i | \(-0.450828\pi\) |
0.932645 | + | 0.360796i | \(0.117495\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.572584 | + | 2.02212i | −0.0996742 | + | 0.352006i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.48550i | − | 0.758188i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.71412i | − | 0.774997i | −0.921870 | − | 0.387499i | \(-0.873339\pi\) | ||
0.921870 | − | 0.387499i | \(-0.126661\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.38513 | + | 2.45355i | 0.381927 | + | 0.392882i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.30898 | + | 3.06514i | −0.829123 | + | 0.478695i | −0.853552 | − | 0.521007i | \(-0.825557\pi\) |
0.0244291 | + | 0.999702i | \(0.492223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.17866 | + | 2.04150i | −0.179744 | + | 0.311326i | −0.941793 | − | 0.336194i | \(-0.890860\pi\) |
0.762049 | + | 0.647520i | \(0.224194\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.55463 | + | 1.57285i | 0.380822 | + | 0.234467i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.97373 | − | 10.3468i | 0.871358 | − | 1.50924i | 0.0107652 | − | 0.999942i | \(-0.496573\pi\) |
0.860593 | − | 0.509294i | \(-0.170093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.55985 | + | 11.3620i | 0.937122 | + | 1.62314i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.87867 | + | 2.24500i | −1.24326 | + | 0.314362i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.739256 | −0.101545 | −0.0507723 | − | 0.998710i | \(-0.516168\pi\) | ||||
−0.0507723 | + | 0.998710i | \(0.516168\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.21337i | 0.163611i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.06618 | − | 8.17146i | −0.273672 | − | 1.08234i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.70932 | + | 0.986877i | −0.222535 | + | 0.128480i | −0.607123 | − | 0.794608i | \(-0.707677\pi\) |
0.384589 | + | 0.923088i | \(0.374343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.81044 | + | 2.77731i | 0.615914 | + | 0.355598i | 0.775277 | − | 0.631622i | \(-0.217611\pi\) |
−0.159362 | + | 0.987220i | \(0.550944\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.4511 | − | 0.380430i | −1.69468 | − | 0.0479296i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.71090 | + | 0.987790i | 0.212211 | + | 0.122520i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.58725 | − | 2.74920i | −0.193913 | − | 0.335868i | 0.752630 | − | 0.658443i | \(-0.228785\pi\) |
−0.946544 | + | 0.322576i | \(0.895451\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.49648 | − | 3.39899i | 0.420927 | − | 0.409190i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.40951 | 0.404635 | 0.202317 | − | 0.979320i | \(-0.435153\pi\) | ||||
0.202317 | + | 0.979320i | \(0.435153\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.69774 | −0.783911 | −0.391956 | − | 0.919984i | \(-0.628201\pi\) | ||||
−0.391956 | + | 0.919984i | \(0.628201\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.66653 | + | 0.471895i | 0.192434 | + | 0.0544897i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.72129 | − | 4.71342i | −0.310120 | − | 0.537144i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.2535 | − | 6.49720i | −1.26612 | − | 0.730992i | −0.291865 | − | 0.956459i | \(-0.594276\pi\) |
−0.974251 | + | 0.225467i | \(0.927609\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.93333 | − | 7.52743i | 0.548148 | − | 0.836381i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.00954 | + | 2.89226i | 0.549868 | + | 0.317467i | 0.749069 | − | 0.662492i | \(-0.230501\pi\) |
−0.199201 | + | 0.979959i | \(0.563835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.57905 | + | 2.64371i | −0.496667 | + | 0.286751i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.0277 | − | 3.97208i | −1.50392 | − | 0.425851i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.71936i | − | 0.288252i | −0.989559 | − | 0.144126i | \(-0.953963\pi\) | ||
0.989559 | − | 0.144126i | \(-0.0460370\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.86146 | −0.928934 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.43338 | − | 8.67527i | −0.874501 | − | 0.899584i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.43314 | − | 4.21431i | −0.249634 | − | 0.432380i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.61075 | − | 14.9143i | 0.874289 | − | 1.51431i | 0.0167712 | − | 0.999859i | \(-0.494661\pi\) |
0.857518 | − | 0.514454i | \(-0.172005\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.63867 | + | 0.102910i | 0.365700 | + | 0.0103429i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.65852 | − | 4.60469i | 0.264532 | − | 0.458183i | −0.702909 | − | 0.711280i | \(-0.748116\pi\) |
0.967441 | + | 0.253097i | \(0.0814491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.2519 | − | 7.65097i | 1.30575 | − | 0.753873i | 0.324363 | − | 0.945933i | \(-0.394850\pi\) |
0.981383 | + | 0.192060i | \(0.0615169\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.53206 | + | 1.90450i | −0.735054 | + | 0.185861i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.25445i | − | 0.701314i | −0.936504 | − | 0.350657i | \(-0.885958\pi\) | ||
0.936504 | − | 0.350657i | \(-0.114042\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.6200i | 1.78347i | 0.452558 | + | 0.891735i | \(0.350512\pi\) | ||||
−0.452558 | + | 0.891735i | \(0.649488\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.91597 | + | 2.00158i | −0.751351 | + | 0.189981i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.19909 | + | 3.00170i | −0.489090 | + | 0.282376i | −0.724197 | − | 0.689593i | \(-0.757789\pi\) |
0.235107 | + | 0.971969i | \(0.424456\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.40767 | − | 2.43816i | 0.131266 | − | 0.227360i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.10729 | − | 5.04688i | 0.287269 | − | 0.466584i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.8584 | − | 20.5393i | 1.08706 | − | 1.88284i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.76386 | − | 8.25125i | −0.433078 | − | 0.750114i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.40114 | + | 7.61342i | 0.667338 | + | 0.686479i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.151104i | 0.0134083i | 0.999978 | + | 0.00670414i | \(0.00213401\pi\) | ||||
−0.999978 | + | 0.00670414i | \(0.997866\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.92854 | + | 1.11241i | 0.345889 | + | 0.0979420i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8788 | + | 8.59027i | −1.29997 | + | 0.750536i | −0.980398 | − | 0.197028i | \(-0.936871\pi\) |
−0.319568 | + | 0.947563i | \(0.603538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.9033 | + | 10.9138i | 1.63912 | + | 0.946349i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.55646 | − | 4.95756i | 0.133959 | − | 0.426679i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.1817 | + | 8.18778i | 1.21162 | + | 0.699529i | 0.963112 | − | 0.269100i | \(-0.0867264\pi\) |
0.248508 | + | 0.968630i | \(0.420060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.13746 | − | 10.6304i | −0.520573 | − | 0.901658i | −0.999714 | − | 0.0239203i | \(-0.992385\pi\) |
0.479141 | − | 0.877738i | \(-0.340948\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.9108 | − | 5.63794i | −1.67679 | − | 0.474800i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.39712 | 0.200457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.41730 | −0.699019 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.2938 | − | 15.8395i | 1.34389 | − | 1.30642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.4468 | − | 18.0944i | −0.855836 | − | 1.48235i | −0.875868 | − | 0.482552i | \(-0.839710\pi\) |
0.0200319 | − | 0.999799i | \(-0.493623\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.72496 | + | 1.57326i | 0.221754 | + | 0.128030i | 0.606762 | − | 0.794883i | \(-0.292468\pi\) |
−0.385008 | + | 0.922913i | \(0.625801\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.53961 | + | 13.9559i | 0.609541 | + | 1.12827i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.04943 | − | 3.49264i | −0.485902 | − | 0.280535i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.64516 | + | 5.56863i | −0.769767 | + | 0.444425i | −0.832792 | − | 0.553587i | \(-0.813259\pi\) |
0.0630243 | + | 0.998012i | \(0.479925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.313882 | + | 1.24136i | 0.0248924 | + | 0.0984463i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.6282i | 0.995244i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.567815 | 0.0444747 | 0.0222373 | − | 0.999753i | \(-0.492921\pi\) | ||||
0.0222373 | + | 0.999753i | \(0.492921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.03750 | − | 0.515188i | 0.158619 | − | 0.0401073i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.59132 | + | 16.6127i | 0.742199 | + | 1.28553i | 0.951492 | + | 0.307673i | \(0.0995503\pi\) |
−0.209293 | + | 0.977853i | \(0.567116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.54854 | + | 7.87831i | −0.349888 | + | 0.606023i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.8443 | + | 6.93906i | −0.982224 | + | 0.530643i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.727868 | − | 1.26070i | 0.0553388 | − | 0.0958496i | −0.837029 | − | 0.547159i | \(-0.815709\pi\) |
0.892368 | + | 0.451309i | \(0.149043\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.88456 | + | 2.24275i | −0.293645 | + | 0.169536i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.38293 | + | 2.45128i | 0.179112 | + | 0.184249i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.1074i | 1.57764i | 0.614623 | + | 0.788821i | \(0.289308\pi\) | ||||
−0.614623 | + | 0.788821i | \(0.710692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.53010i | 0.634037i | 0.948419 | + | 0.317019i | \(0.102682\pi\) | ||||
−0.948419 | + | 0.317019i | \(0.897318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.62120 | − | 9.25693i | 0.193764 | − | 0.684292i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.08255 | + | 2.35706i | −0.300155 | + | 0.173295i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.20781 | + | 5.55610i | −0.234579 | + | 0.406302i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.07241 | + | 22.7487i | 0.368964 | + | 1.65472i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.214023 | − | 0.370698i | 0.0154861 | − | 0.0268228i | −0.858178 | − | 0.513351i | \(-0.828404\pi\) |
0.873665 | + | 0.486529i | \(0.161737\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.74084 | − | 8.21138i | −0.341253 | − | 0.591068i | 0.643412 | − | 0.765520i | \(-0.277518\pi\) |
−0.984666 | + | 0.174452i | \(0.944185\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.932265 | − | 3.29236i | 0.0667609 | − | 0.235771i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.16402 | 0.296674 | 0.148337 | − | 0.988937i | \(-0.452608\pi\) | ||||
0.148337 | + | 0.988937i | \(0.452608\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.4857i | 1.45219i | 0.687594 | + | 0.726095i | \(0.258667\pi\) | ||||
−0.687594 | + | 0.726095i | \(0.741333\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.94252 | + | 3.83260i | −0.278084 | + | 0.270331i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 32.6975 | − | 18.8779i | 2.29491 | − | 1.32497i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.30898 | + | 3.06514i | 0.370795 | + | 0.214079i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.19217 | − | 4.42812i | −0.499890 | − | 0.307776i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.11354 | − | 2.95230i | −0.353711 | − | 0.204215i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8150 | + | 22.1963i | 0.882222 | + | 1.52805i | 0.848865 | + | 0.528610i | \(0.177287\pi\) |
0.0333576 | + | 0.999443i | \(0.489380\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.44765 | − | 5.72527i | −0.0991914 | − | 0.392289i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.35732 | 0.160768 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31.3325 | 2.12699 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.84380 | + | 11.2469i | 0.192166 | + | 0.759993i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.22287 | + | 9.04628i | 0.351328 | + | 0.608518i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.577728 | + | 0.333551i | 0.0386875 | + | 0.0223363i | 0.519219 | − | 0.854641i | \(-0.326223\pi\) |
−0.480531 | + | 0.876977i | \(0.659556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0848132 | − | 2.99880i | 0.00565421 | − | 0.199920i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.21685 | − | 1.85725i | −0.213510 | − | 0.123270i | 0.389432 | − | 0.921055i | \(-0.372671\pi\) |
−0.602941 | + | 0.797785i | \(0.706005\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.27024 | − | 3.04277i | 0.348267 | − | 0.201072i | −0.315655 | − | 0.948874i | \(-0.602224\pi\) |
0.663922 | + | 0.747802i | \(0.268891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.75935 | + | 6.57088i | −0.444733 | + | 0.432332i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 11.4524i | − | 0.750269i | −0.926970 | − | 0.375134i | \(-0.877597\pi\) | ||
0.926970 | − | 0.375134i | \(-0.122403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.9475 | −0.779366 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.13199 | + | 21.6555i | −0.398315 | + | 1.40668i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5.82006 | + | 10.0806i | 0.376468 | + | 0.652062i | 0.990546 | − | 0.137184i | \(-0.0438050\pi\) |
−0.614077 | + | 0.789246i | \(0.710472\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.24695 | − | 5.62388i | 0.209154 | − | 0.362266i | −0.742294 | − | 0.670074i | \(-0.766262\pi\) |
0.951448 | + | 0.307808i | \(0.0995955\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7347 | − | 5.08798i | −0.945234 | − | 0.326394i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.55985 | − | 11.3620i | 0.419094 | − | 0.725892i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.32572 | + | 4.80685i | −0.529753 | + | 0.305853i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.72968 | − | 9.64006i | 0.172987 | − | 0.610914i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.49601i | 0.220666i | 0.993895 | + | 0.110333i | \(0.0351917\pi\) | ||||
−0.993895 | + | 0.110333i | \(0.964808\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3.41607i | − | 0.214766i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.38356 | + | 6.56665i | 0.399754 | + | 0.411220i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.88796 | + | 1.66737i | −0.180146 | + | 0.104007i | −0.587361 | − | 0.809325i | \(-0.699833\pi\) |
0.407215 | + | 0.913332i | \(0.366500\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5726 | − | 18.3123i | 0.656949 | − | 1.13787i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.713898 | + | 25.2418i | −0.0441892 | + | 1.56243i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.66510 | − | 11.5443i | 0.410988 | − | 0.711852i | −0.584010 | − | 0.811746i | \(-0.698517\pi\) |
0.994998 | + | 0.0998946i | \(0.0318505\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.369628 | + | 0.640214i | 0.0227061 | + | 0.0393280i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.56636 | + | 1.15462i | −0.279457 | + | 0.0706615i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.95866 | 0.119421 | 0.0597107 | − | 0.998216i | \(-0.480982\pi\) | ||||
0.0597107 | + | 0.998216i | \(0.480982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.5736i | 1.37125i | 0.727955 | + | 0.685625i | \(0.240471\pi\) | ||||
−0.727955 | + | 0.685625i | \(0.759529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.76250 | + | 14.8802i | 0.227717 | + | 0.900590i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.05081 | − | 0.606687i | 0.0633664 | − | 0.0365846i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.8634 | + | 12.0455i | 1.25356 | + | 0.723744i | 0.971815 | − | 0.235745i | \(-0.0757530\pi\) |
0.281746 | + | 0.959489i | \(0.409086\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.9868 | + | 17.8448i | −0.657762 | + | 1.06834i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.4445 | − | 15.2677i | −1.57755 | − | 0.910796i | −0.995201 | − | 0.0978540i | \(-0.968802\pi\) |
−0.582344 | − | 0.812942i | \(-0.697864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.84951 | − | 6.66756i | −0.228830 | − | 0.396345i | 0.728632 | − | 0.684906i | \(-0.240157\pi\) |
−0.957462 | + | 0.288561i | \(0.906823\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.04360 | + | 5.87509i | −0.357992 | + | 0.348010i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −27.4974 | −1.62312 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.9569 | −0.644524 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.7001 | − | 8.12673i | −1.68243 | − | 0.476397i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.03781 | + | 15.6539i | 0.527994 | + | 0.914513i | 0.999467 | + | 0.0326326i | \(0.0103891\pi\) |
−0.471473 | + | 0.881880i | \(0.656278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.70932 | + | 0.986877i | 0.0995206 | + | 0.0574582i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.37214 | − | 6.15375i | −0.0796196 | − | 0.357077i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.81678 | − | 2.78097i | −0.278562 | − | 0.160828i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.15715 | + | 5.28688i | −0.527809 | + | 0.304731i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.86099 | − | 2.50908i | −0.509050 | − | 0.144143i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.55462i | − | 0.318057i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7235 | 1.35397 | 0.676986 | − | 0.735996i | \(-0.263286\pi\) | ||||
0.676986 | + | 0.735996i | \(0.263286\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4742 | − | 19.0040i | −1.05096 | − | 1.08110i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.24004 | + | 10.8081i | 0.353840 | + | 0.612869i | 0.986919 | − | 0.161219i | \(-0.0515424\pi\) |
−0.633079 | + | 0.774087i | \(0.718209\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.40717 | + | 12.8296i | −0.418678 | + | 0.725171i | −0.995807 | − | 0.0914817i | \(-0.970840\pi\) |
0.577129 | + | 0.816653i | \(0.304173\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.39610 | + | 11.8392i | 0.360379 | + | 0.667065i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5991 | − | 20.0903i | 0.651473 | − | 1.12838i | −0.331292 | − | 0.943528i | \(-0.607485\pi\) |
0.982766 | − | 0.184856i | \(-0.0591820\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.84500 | + | 5.10667i | −0.495225 | + | 0.285918i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.1817 | + | 3.08018i | −0.679916 | + | 0.171919i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 25.7301i | − | 1.43166i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 1.97558i | − | 0.109585i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 31.2667 | − | 7.90588i | 1.72905 | − | 0.437196i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 46.4106 | − | 26.7952i | 2.55870 | − | 1.47726i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.40861 | + | 5.90389i | −0.187354 | + | 0.324507i | −0.944367 | − | 0.328893i | \(-0.893325\pi\) |
0.757013 | + | 0.653400i | \(0.226658\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.72210 | + | 12.4427i | 0.368369 | + | 0.681854i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.58725 | + | 2.74920i | −0.0867207 | + | 0.150205i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.18185 | + | 7.24318i | 0.227800 | + | 0.394561i | 0.957156 | − | 0.289573i | \(-0.0935134\pi\) |
−0.729356 | + | 0.684135i | \(0.760180\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.24795 | + | 7.45584i | 0.393655 | + | 0.404945i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.47575 | −0.458988 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 27.4500i | 1.48216i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.69185 | − | 1.32855i | −0.252601 | − | 0.0715265i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.4465 | − | 7.18596i | 0.668161 | − | 0.385763i | −0.127219 | − | 0.991875i | \(-0.540605\pi\) |
0.795379 | + | 0.606112i | \(0.207272\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.20288 | − | 3.00388i | −0.278504 | − | 0.160794i | 0.354242 | − | 0.935154i | \(-0.384739\pi\) |
−0.632746 | + | 0.774360i | \(0.718072\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.79406 | − | 3.07491i | −0.522768 | − | 0.164127i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6839 | − | 7.32305i | −0.675096 | − | 0.389767i | 0.122909 | − | 0.992418i | \(-0.460778\pi\) |
−0.798005 | + | 0.602651i | \(0.794111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.70476 | − | 2.95273i | −0.0904791 | − | 0.156714i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −39.5246 | − | 11.1918i | −2.09187 | − | 0.592333i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.983893 | −0.0519279 | −0.0259639 | − | 0.999663i | \(-0.508266\pi\) | ||||
−0.0259639 | + | 0.999663i | \(0.508266\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.68059 | 0.246347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.8328 | + | 11.5029i | −0.621062 | + | 0.603746i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.34887 | + | 5.80041i | 0.175288 | + | 0.303608i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.8347 | + | 13.1836i | 1.19196 | + | 0.688180i | 0.958751 | − | 0.284246i | \(-0.0917433\pi\) |
0.233211 | + | 0.972426i | \(0.425077\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.64202 | − | 15.6606i | 0.501943 | − | 0.815259i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.87168 | − | 1.65797i | −0.149090 | − | 0.0860773i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.428139 | − | 0.247186i | 0.0221682 | − | 0.0127988i | −0.488875 | − | 0.872354i | \(-0.662593\pi\) |
0.511043 | + | 0.859555i | \(0.329259\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.424591 | − | 1.67920i | −0.0219258 | − | 0.0867137i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.6291i | 0.856440i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0342 | 1.02909 | 0.514544 | − | 0.857464i | \(-0.327961\pi\) | ||||
0.514544 | + | 0.857464i | \(0.327961\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.253734 | − | 0.0641573i | 0.0129992 | − | 0.00328688i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.16431 | − | 12.4089i | −0.366079 | − | 0.634068i | 0.622870 | − | 0.782326i | \(-0.285967\pi\) |
−0.988949 | + | 0.148258i | \(0.952633\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.72129 | + | 4.71342i | −0.138690 | + | 0.240218i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.199932 | − | 7.06914i | 0.0101631 | − | 0.359345i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.19727 | + | 12.4660i | −0.364916 | + | 0.632053i | −0.988763 | − | 0.149494i | \(-0.952236\pi\) |
0.623847 | + | 0.781547i | \(0.285569\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.8916 | − | 7.44297i | 0.651957 | − | 0.376407i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.7422 | + | 21.3371i | 1.04631 | + | 1.07632i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.9944i | 0.653820i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.1034i | − | 0.607454i | −0.952759 | − | 0.303727i | \(-0.901769\pi\) | ||
0.952759 | − | 0.303727i | \(-0.0982311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.3004 | − | 36.3764i | 0.515663 | − | 1.82110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.6874 | + | 8.47977i | −0.733454 | + | 0.423460i | −0.819684 | − | 0.572816i | \(-0.805851\pi\) |
0.0862307 | + | 0.996275i | \(0.472518\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.89999 | + | 11.9511i | −0.343713 | + | 0.595328i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.98561 | − | 0.508676i | −0.446499 | − | 0.0252763i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.86000 | + | 4.95366i | −0.141765 | + | 0.245544i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.3239 | + | 21.3456i | 0.609376 | + | 1.05547i | 0.991343 | + | 0.131294i | \(0.0419132\pi\) |
−0.381968 | + | 0.924176i | \(0.624753\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.72754 | − | 27.2903i | 0.381171 | − | 1.34613i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.85328 | −0.435641 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.78452i | − | 0.283951i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.2447 | + | 14.8196i | −0.746535 | + | 0.725720i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −22.0686 | + | 12.7413i | −1.07812 | + | 0.622455i | −0.930390 | − | 0.366572i | \(-0.880531\pi\) |
−0.147734 | + | 0.989027i | \(0.547198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.84113 | + | 1.64033i | 0.138468 | + | 0.0799446i | 0.567634 | − | 0.823281i | \(-0.307859\pi\) |
−0.429166 | + | 0.903226i | \(0.641192\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.01330 | + | 35.8280i | −0.0492684 | + | 1.74202i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.57905 | + | 2.64371i | 0.222116 | + | 0.128239i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.4576 | + | 21.5772i | 0.602867 | + | 1.04420i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.01780 | − | 4.02525i | −0.0491396 | − | 0.194341i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.5731 | −0.509290 | −0.254645 | − | 0.967035i | \(-0.581959\pi\) | ||||
−0.254645 | + | 0.967035i | \(0.581959\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.9701 | −0.527191 | −0.263596 | − | 0.964633i | \(-0.584908\pi\) | ||||
−0.263596 | + | 0.964633i | \(0.584908\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.57391 | + | 14.1344i | 0.171356 | + | 0.677690i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.85012 | + | 11.8648i | 0.327686 | + | 0.567568i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.06638 | + | 4.65712i | 0.384987 | + | 0.222272i | 0.679986 | − | 0.733225i | \(-0.261986\pi\) |
−0.294999 | + | 0.955498i | \(0.595319\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −33.5160 | − | 20.6353i | −1.59600 | − | 0.982636i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.06647 | + | 0.615728i | 0.0506696 | + | 0.0292541i | 0.525121 | − | 0.851028i | \(-0.324020\pi\) |
−0.474451 | + | 0.880282i | \(0.657353\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.35504 | + | 1.35968i | −0.111639 | + | 0.0644551i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.9485 | + | 25.2250i | −1.22732 | + | 1.19310i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.49670i | 0.306598i | 0.988180 | + | 0.153299i | \(0.0489898\pi\) | ||||
−0.988180 | + | 0.153299i | \(0.951010\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.43832 | 0.350257 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.48482 | − | 5.24375i | 0.0697630 | − | 0.246373i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.43073 | + | 7.67425i | 0.207716 | + | 0.359775i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.9191 | − | 20.6444i | 0.557550 | − | 0.965706i | −0.440150 | − | 0.897924i | \(-0.645075\pi\) |
0.997700 | − | 0.0677813i | \(-0.0215920\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.2335 | − | 18.5861i | 0.944418 | − | 0.867524i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.00659 | − | 13.8678i | 0.372904 | − | 0.645889i | −0.617107 | − | 0.786879i | \(-0.711695\pi\) |
0.990011 | + | 0.140991i | \(0.0450287\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.9383 | + | 14.3982i | −1.15898 | + | 0.669139i | −0.951060 | − | 0.309006i | \(-0.900004\pi\) |
−0.207923 | + | 0.978145i | \(0.566670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.29631 | + | 11.6412i | −0.152863 | + | 0.539846i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.0588i | 1.25213i | 0.779769 | + | 0.626067i | \(0.215336\pi\) | ||||
−0.779769 | + | 0.626067i | \(0.784664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 14.2392i | − | 0.657505i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.4461 | + | 13.8318i | 0.619564 | + | 0.637335i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.47710 | − | 1.43016i | 0.113897 | − | 0.0657587i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.43314 | + | 4.21431i | −0.111640 | + | 0.193366i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.95122 | − | 1.05414i | 0.0893404 | − | 0.0482658i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.93681 | + | 10.2829i | −0.271260 | + | 0.469836i | −0.969185 | − | 0.246335i | \(-0.920774\pi\) |
0.697925 | + | 0.716171i | \(0.254107\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.65656 | + | 8.06541i | 0.212321 | + | 0.367751i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 21.2054 | − | 5.36184i | 0.964878 | − | 0.243972i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.2215 | −0.781988 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.2361i | − | 0.509158i | −0.967052 | − | 0.254579i | \(-0.918063\pi\) | ||
0.967052 | − | 0.254579i | \(-0.0819369\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.241089 | − | 0.953476i | −0.0109024 | − | 0.0431177i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.2016 | + | 15.1275i | −1.18246 | + | 0.682694i | −0.956582 | − | 0.291462i | \(-0.905858\pi\) |
−0.225877 | + | 0.974156i | \(0.572525\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.5432 | − | 22.2529i | −1.73590 | − | 1.00222i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.73021 | − | 3.20263i | −0.0777672 | − | 0.143948i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.2445 | + | 7.64669i | 0.594095 | + | 0.343001i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.81293 | − | 8.33624i | −0.215456 | − | 0.373182i | 0.737957 | − | 0.674847i | \(-0.235791\pi\) |
−0.953414 | + | 0.301666i | \(0.902457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.8236 | − | 23.1594i | 1.06436 | − | 1.03468i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.3463 | −1.26390 | −0.631950 | − | 0.775009i | \(-0.717745\pi\) | ||||
−0.631950 | + | 0.775009i | \(0.717745\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.31703 | −0.236605 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.1605 | + | 4.29286i | 0.673303 | + | 0.190653i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.7957 | + | 34.2872i | 0.877431 | + | 1.51976i | 0.854150 | + | 0.520026i | \(0.174078\pi\) |
0.0232807 | + | 0.999729i | \(0.492589\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.0178 | − | 15.0214i | −1.15096 | − | 0.664506i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17.1056 | + | 18.6218i | 0.755233 | + | 0.822174i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.2519 | − | 7.65097i | −0.583947 | − | 0.337142i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.5545 | + | 7.24837i | −0.552148 | + | 0.318783i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.42603 | − | 0.686954i | −0.106491 | − | 0.0301539i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 35.6218i | 1.56062i | 0.625393 | + | 0.780310i | \(0.284939\pi\) | ||||
−0.625393 | + | 0.780310i | \(0.715061\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0675 | −0.571404 | −0.285702 | − | 0.958319i | \(-0.592227\pi\) | ||||
−0.285702 | + | 0.958319i | \(0.592227\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.41538 | + | 5.57071i | 0.236347 | + | 0.243126i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.4671 | − | 31.9859i | −0.804438 | − | 1.39333i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.53691 | − | 13.0543i | 0.327692 | − | 0.567579i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.10442 | − | 5.04222i | 0.134720 | − | 0.218814i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.05543 | − | 10.4883i | 0.262290 | − | 0.454299i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.28254 | + | 3.62723i | −0.271618 | + | 0.156819i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 35.4436 | − | 8.96203i | 1.52951 | − | 0.386740i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 15.9191i | − | 0.685685i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 41.8805i | − | 1.80059i | −0.435285 | − | 0.900293i | \(-0.643353\pi\) | ||
0.435285 | − | 0.900293i | \(-0.356647\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.3238 | − | 3.62181i | 0.614692 | − | 0.155427i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.1254 | − | 9.30999i | 0.690735 | − | 0.398796i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.32180 | + | 14.4138i | −0.355814 | + | 0.616288i | −0.987257 | − | 0.159134i | \(-0.949130\pi\) |
0.631443 | + | 0.775423i | \(0.282463\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.6572 | − | 0.471105i | −0.710912 | − | 0.0201063i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.4804 | − | 35.4732i | 0.872496 | − | 1.51121i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −29.1432 | − | 50.4775i | −1.23930 | − | 2.14652i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.69140 | + | 5.85464i | 0.241587 | + | 0.248516i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.8296 | 0.458863 | 0.229431 | − | 0.973325i | \(-0.426313\pi\) | ||||
0.229431 | + | 0.973325i | \(0.426313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.65708i | − | 0.196973i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.6918 | + | 3.02750i | 0.451409 | + | 0.127821i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 16.4450 | − | 9.49453i | 0.693074 | − | 0.400147i | −0.111688 | − | 0.993743i | \(-0.535626\pi\) |
0.804763 | + | 0.593597i | \(0.202293\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.19909 | + | 3.00170i | 0.218727 | + | 0.126282i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 36.0460 | − | 18.1765i | 1.51379 | − | 0.763341i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.51839 | − | 4.34075i | −0.315187 | − | 0.181974i | 0.334058 | − | 0.942553i | \(-0.391582\pi\) |
−0.649245 | + | 0.760579i | \(0.724915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18.8435 | − | 32.6378i | −0.788574 | − | 1.36585i | −0.926840 | − | 0.375456i | \(-0.877486\pi\) |
0.138266 | − | 0.990395i | \(-0.455847\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.713349 | − | 0.201992i | −0.0298006 | − | 0.00843834i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.81535 | −0.117408 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −45.5995 | −1.89833 | −0.949166 | − | 0.314776i | \(-0.898071\pi\) | ||||
−0.949166 | + | 0.314776i | \(0.898071\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.7757 | + | 11.4473i | −0.489379 | + | 0.475734i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.9732 | + | 22.4703i | 0.538220 | + | 0.932225i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.776819 | + | 0.448497i | 0.0321726 | + | 0.0185748i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.92437 | − | 0.167555i | −0.244943 | − | 0.00692756i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.14708 | − | 4.70372i | −0.336266 | − | 0.194143i | 0.322354 | − | 0.946619i | \(-0.395526\pi\) |
−0.658620 | + | 0.752476i | \(0.728859\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.4381 | − | 16.9961i | 1.21298 | − | 0.700313i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.76801 | − | 6.99224i | −0.0727261 | − | 0.287622i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14.4808i | − | 0.594657i | −0.954775 | − | 0.297328i | \(-0.903904\pi\) | ||
0.954775 | − | 0.297328i | \(-0.0960956\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −23.7168 | −0.972292 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 34.3996 | − | 8.69804i | 1.40788 | − | 0.355987i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.00132 | + | 3.46639i | 0.0817718 | + | 0.141633i | 0.904011 | − | 0.427509i | \(-0.140609\pi\) |
−0.822239 | + | 0.569142i | \(0.807275\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21.9214 | + | 37.9690i | −0.894193 | + | 1.54879i | −0.0593924 | + | 0.998235i | \(0.518916\pi\) |
−0.834800 | + | 0.550553i | \(0.814417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.10967 | + | 4.99301i | 0.330251 | + | 0.203331i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.76386 | + | 8.25125i | −0.193679 | + | 0.335461i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.60723 | − | 3.23734i | 0.227591 | − | 0.131399i | −0.381869 | − | 0.924216i | \(-0.624720\pi\) |
0.609460 | + | 0.792817i | \(0.291386\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −45.5829 | − | 46.8903i | −1.84711 | − | 1.90009i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.6032i | 0.954882i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.2895i | 1.62728i | 0.581370 | + | 0.813639i | \(0.302517\pi\) | ||||
−0.581370 | + | 0.813639i | \(0.697483\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.89285 | − | 10.2163i | 0.116651 | − | 0.411960i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.7460 | + | 7.93629i | −0.553395 | + | 0.319503i | −0.750490 | − | 0.660882i | \(-0.770183\pi\) |
0.197095 | + | 0.980384i | \(0.436849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.1549 | − | 34.9094i | 0.810095 | − | 1.40313i | −0.102702 | − | 0.994712i | \(-0.532749\pi\) |
0.912797 | − | 0.408413i | \(-0.133918\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.38198 | + | 13.9573i | −0.175843 | + | 0.560085i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.09885 | − | 10.5635i | 0.244345 | − | 0.423218i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.78635 | + | 9.84019i | −0.111276 | + | 0.392979i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.9256 | −0.993849 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.05567i | 0.360500i | 0.983621 | + | 0.180250i | \(0.0576908\pi\) | ||||
−0.983621 | + | 0.180250i | \(0.942309\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.8309 | − | 30.9434i | 1.26516 | − | 1.22989i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.130860 | − | 0.0755518i | 0.00519300 | − | 0.00299818i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.4465 | − | 12.9595i | −0.889365 | − | 0.513475i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.99922 | + | 4.86180i | −0.356004 | + | 0.192330i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.53980 | − | 4.35311i | −0.297804 | − | 0.171937i | 0.343652 | − | 0.939097i | \(-0.388336\pi\) |
−0.641456 | + | 0.767160i | \(0.721669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5478 | − | 18.2693i | −0.415963 | − | 0.720469i | 0.579566 | − | 0.814925i | \(-0.303222\pi\) |
−0.995529 | + | 0.0944562i | \(0.969889\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.00090 | − | 3.95842i | −0.0394103 | − | 0.155863i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.6479 | 1.44078 | 0.720388 | − | 0.693571i | \(-0.243964\pi\) | ||||
0.720388 | + | 0.693571i | \(0.243964\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.39490 | 0.0940081 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.3035 | − | 52.6135i | −0.521405 | − | 2.06209i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.680992 | − | 1.17951i | −0.0266493 | − | 0.0461579i | 0.852393 | − | 0.522901i | \(-0.175150\pi\) |
−0.879042 | + | 0.476743i | \(0.841817\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8788 | + | 8.59027i | 0.581362 | + | 0.335650i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.6783 | − | 9.55065i | 0.689697 | − | 0.372606i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.5744 | + | 10.1466i | 0.684600 | + | 0.395254i | 0.801586 | − | 0.597879i | \(-0.203990\pi\) |
−0.116986 | + | 0.993134i | \(0.537323\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.63502 | − | 3.83073i | 0.258073 | − | 0.148998i | −0.365382 | − | 0.930857i | \(-0.619062\pi\) |
0.623455 | + | 0.781859i | \(0.285728\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9729 | − | 12.6112i | 0.503828 | − | 0.489780i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 21.8277i | − | 0.846440i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.6976 | 0.917575 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.314802 | − | 1.11175i | 0.0121710 | − | 0.0429826i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.36992 | − | 5.83686i | −0.130094 | − | 0.225330i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.53849 | − | 16.5212i | 0.367682 | − | 0.636844i | −0.621521 | − | 0.783398i | \(-0.713485\pi\) |
0.989203 | + | 0.146554i | \(0.0468182\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.07161 | + | 1.13085i | −0.195206 | + | 0.0435263i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.09868 | + | 15.7594i | −0.349690 | + | 0.605682i | −0.986194 | − | 0.165592i | \(-0.947047\pi\) |
0.636504 | + | 0.771273i | \(0.280380\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 66.8979 | − | 38.6235i | 2.56731 | − | 1.48223i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.75285 | + | 6.19031i | −0.0671694 | + | 0.237213i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.17953i | 0.159925i | 0.996798 | + | 0.0799626i | \(0.0254801\pi\) | ||||
−0.996798 | + | 0.0799626i | \(0.974520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 16.3756i | − | 0.625678i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.34713 | − | 7.55786i | −0.280311 | − | 0.288351i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.26479 | − | 0.730229i | 0.0481848 | − | 0.0278195i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.99450 | − | 5.18663i | 0.113916 | − | 0.197309i | −0.803430 | − | 0.595400i | \(-0.796994\pi\) |
0.917346 | + | 0.398091i | \(0.130327\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 13.9038 | + | 8.56038i | 0.528162 | + | 0.325182i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.13746 | + | 10.6304i | −0.232807 | + | 0.403234i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.2067 | + | 28.0709i | 0.613873 | + | 1.06326i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.2308 | + | 4.86257i | −0.727377 | + | 0.183919i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.5227 | 0.699592 | 0.349796 | − | 0.936826i | \(-0.386251\pi\) | ||||
0.349796 | + | 0.936826i | \(0.386251\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 22.9402i | − | 0.865206i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.07279 | + | 20.0622i | 0.191052 | + | 0.755586i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.6543 | − | 11.9248i | 0.776786 | − | 0.448477i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.4280 | + | 10.0621i | 0.654522 | + | 0.377888i | 0.790187 | − | 0.612866i | \(-0.209984\pi\) |
−0.135665 | + | 0.990755i | \(0.543317\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 38.9676 | + | 1.10210i | 1.46140 | + | 0.0413319i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.0312 | + | 9.83299i | 0.637825 | + | 0.368248i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.19856 | − | 2.07596i | −0.0448235 | − | 0.0776367i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.4563 | − | 14.0532i | 0.539880 | − | 0.524827i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.2181 | −0.977768 | −0.488884 | − | 0.872349i | \(-0.662596\pi\) | ||||
−0.488884 | + | 0.872349i | \(0.662596\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 68.6369 | 2.55617 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.8223 | − | 3.06444i | −0.402484 | − | 0.113968i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.20865 | + | 7.28960i | 0.156305 | + | 0.270729i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.5836 | − | 11.8839i | −0.763402 | − | 0.440750i | 0.0671138 | − | 0.997745i | \(-0.478621\pi\) |
−0.830516 | + | 0.556995i | \(0.811954\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.28752 | + | 26.9029i | −0.0847228 | + | 0.996405i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.7943 | + | 6.23209i | 0.399241 | + | 0.230502i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.5140 | + | 10.1117i | −0.646894 | + | 0.373485i | −0.787265 | − | 0.616614i | \(-0.788504\pi\) |
0.140371 | + | 0.990099i | \(0.455170\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.8644 | − | 6.19112i | −0.806479 | − | 0.228363i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.85185i | 0.141885i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.0224 | −0.920463 | −0.460232 | − | 0.887799i | \(-0.652234\pi\) | ||||
−0.460232 | + | 0.887799i | \(0.652234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6067 | + | 11.9396i | 0.426383 | + | 0.438613i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.871379 | − | 1.50927i | −0.0319678 | − | 0.0553699i | 0.849599 | − | 0.527429i | \(-0.176844\pi\) |
−0.881567 | + | 0.472060i | \(0.843511\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.4468 | + | 18.0944i | −0.382741 | + | 0.662927i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.3466 | − | 0.490603i | −0.634680 | − | 0.0179502i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.2699 | − | 28.1803i | 0.594490 | − | 1.02969i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.6053 | + | 8.43240i | −0.532957 | + | 0.307703i | −0.742220 | − | 0.670157i | \(-0.766227\pi\) |
0.209263 | + | 0.977859i | \(0.432894\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.87050 | − | 1.48437i | 0.213933 | − | 0.0540936i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.14651i | − | 0.114513i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 25.4545i | − | 0.925160i | −0.886577 | − | 0.462580i | \(-0.846924\pi\) | ||
0.886577 | − | 0.462580i | \(-0.153076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.73627 | + | 1.45043i | −0.208213 | + | 0.0526474i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.3748 | + | 22.7331i | −1.42734 | + | 0.824073i | −0.996910 | − | 0.0785520i | \(-0.974970\pi\) |
−0.430427 | + | 0.902625i | \(0.641637\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.7600 | + | 72.3304i | −1.51181 | + | 2.61853i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.31634 | − | 13.5074i | 0.300678 | − | 0.488362i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.94966 | − | 3.37690i | 0.0703980 | − | 0.121933i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.11507 | + | 10.5916i | 0.220515 | + | 0.381943i | 0.954965 | − | 0.296720i | \(-0.0958928\pi\) |
−0.734449 | + | 0.678663i | \(0.762559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.02605 | + | 4.14153i | 0.144995 | + | 0.149153i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.0762 | −0.829992 | −0.414996 | − | 0.909823i | \(-0.636217\pi\) | ||||
−0.414996 | + | 0.909823i | \(0.636217\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.98528i | 0.250919i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −35.2391 | − | 9.97830i | −1.26419 | − | 0.357970i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.8349 | + | 14.9158i | −0.925633 | + | 0.534414i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.58276 | − | 2.06851i | −0.128201 | − | 0.0740170i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 42.6892 | − | 9.51867i | 1.52559 | − | 0.340170i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.64516 | + | 5.56863i | 0.344250 | + | 0.198753i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.21382 | − | 14.2268i | −0.292791 | − | 0.507129i | 0.681678 | − | 0.731653i | \(-0.261251\pi\) |
−0.974469 | + | 0.224524i | \(0.927917\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.2152 | − | 6.29045i | −0.790881 | − | 0.223946i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.9282 | −0.957458 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.9736 | −0.389684 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.918109 | − | 0.892510i | 0.0325620 | − | 0.0316541i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.7569 | + | 32.4878i | 0.664402 | + | 1.15078i | 0.979447 | + | 0.201701i | \(0.0646470\pi\) |
−0.315045 | + | 0.949077i | \(0.602020\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −54.7080 | − | 31.5857i | −1.93543 | − | 1.11742i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.87768 | + | 7.17761i | 0.137011 | + | 0.253608i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.03807 | + | 4.06343i | 0.248368 | + | 0.143395i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.9364 | − | 6.31412i | 0.385457 | − | 0.222543i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.831628 | − | 3.28898i | −0.0292747 | − | 0.115778i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 13.7094i | − | 0.481998i | −0.970525 | − | 0.240999i | \(-0.922525\pi\) | ||
0.970525 | − | 0.240999i | \(-0.0774751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.6781 | 1.67420 | 0.837102 | − | 0.547047i | \(-0.184248\pi\) | ||||
0.837102 | + | 0.547047i | \(0.184248\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37.9057 | − | 9.58457i | 1.32941 | − | 0.336146i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.283907 | − | 0.491742i | −0.00994484 | − | 0.0172250i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.73568 | + | 9.93450i | −0.200666 | + | 0.347564i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.3893 | − | 12.6360i | 0.817290 | − | 0.441538i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.6238 | + | 25.3292i | −0.510376 | + | 0.883997i | 0.489552 | + | 0.871974i | \(0.337160\pi\) |
−0.999928 | + | 0.0120227i | \(0.996173\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.6471 | − | 17.1168i | 1.03343 | − | 0.596653i | 0.115466 | − | 0.993311i | \(-0.463164\pi\) |
0.917966 | + | 0.396659i | \(0.129830\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.46492 | − | 1.50693i | −0.0510018 | − | 0.0524647i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2917i | 0.636065i | 0.948080 | + | 0.318032i | \(0.103022\pi\) | ||||
−0.948080 | + | 0.318032i | \(0.896978\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 11.0727i | − | 0.384572i | −0.981339 | − | 0.192286i | \(-0.938410\pi\) | ||
0.981339 | − | 0.192286i | \(-0.0615902\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3684 | − | 40.1483i | 0.394366 | − | 1.39273i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 60.0758 | − | 34.6848i | 2.08150 | − | 1.20176i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.59132 | − | 16.6127i | 0.331921 | − | 0.574905i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.6299 | + | 10.8723i | 1.19699 | + | 0.375802i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.6805 | + | 37.5517i | −0.748494 | + | 1.29643i | 0.200051 | + | 0.979785i | \(0.435889\pi\) |
−0.948545 | + | 0.316643i | \(0.897444\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.9255 | − | 36.2440i | −0.721568 | − | 1.24979i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.4095 | + | 50.8882i | −0.496290 | + | 1.75268i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.09708 | 0.312949 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 42.7366i | − | 1.46845i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.56171 | + | 9.29510i | −0.328157 | + | 0.319007i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4938 | − | 6.63595i | 0.394002 | − | 0.227477i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.7351 | − | 10.8167i | −0.641479 | − | 0.370358i | 0.143705 | − | 0.989621i | \(-0.454098\pi\) |
−0.785184 | + | 0.619263i | \(0.787432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.4315 | + | 7.65392i | 0.425149 | + | 0.261758i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.5218 | − | 6.07474i | −0.359417 | − | 0.207509i | 0.309408 | − | 0.950929i | \(-0.399869\pi\) |
−0.668825 | + | 0.743420i | \(0.733202\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.1108 | + | 27.9048i | 0.549694 | + | 0.952098i | 0.998295 | + | 0.0583659i | \(0.0185890\pi\) |
−0.448601 | + | 0.893732i | \(0.648078\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6751 | + | 46.1737i | 0.397888 | + | 1.57359i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.86707 | −0.267798 | −0.133899 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133899 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.45574 | −0.0494965 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.65221 | + | 18.3989i | 0.157997 | + | 0.624858i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.88354 | + | 13.6547i | 0.267431 | + | 0.463203i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.43126 | + | 3.13574i | 0.184031 | + | 0.106250i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.46061 | + | 51.6438i | −0.0494342 | + | 1.74788i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.88456 | + | 2.24275i | 0.131322 | + | 0.0758188i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.62451 | − | 5.55672i | 0.324997 | − | 0.187637i | −0.328621 | − | 0.944462i | \(-0.606584\pi\) |
0.653618 | + | 0.756825i | \(0.273250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.4488 | − | 21.8228i | 0.757178 | − | 0.736066i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.03742i | − | 0.0349514i | −0.999847 | − | 0.0174757i | \(-0.994437\pi\) | ||
0.999847 | − | 0.0174757i | \(-0.00556298\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.3991 | −1.59511 | −0.797554 | − | 0.603248i | \(-0.793873\pi\) | ||||
−0.797554 | + | 0.603248i | \(0.793873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.931404 | − | 3.28932i | 0.0313088 | − | 0.110569i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.80889 | + | 13.5254i | 0.262197 | + | 0.454139i | 0.966825 | − | 0.255438i | \(-0.0822196\pi\) |
−0.704628 | + | 0.709576i | \(0.748886\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.338887 | + | 0.586970i | −0.0113659 | + | 0.0196864i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.75080 | + | 4.91693i | −0.326664 | + | 0.164723i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.0698 | − | 50.3503i | 0.972783 | − | 1.68491i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.2796 | − | 10.5537i | 0.611018 | − | 0.352772i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.62465 | + | 9.26913i | −0.0876345 | + | 0.309487i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 58.7972i | − | 1.96100i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.90876i | 0.130220i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.7658 | + | 13.1319i | 0.424819 | + | 0.437004i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.38728 | − | 4.26505i | 0.245562 | − | 0.141775i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0385 | − | 43.3680i | 0.831390 | − | 1.44001i | −0.0655459 | − | 0.997850i | \(-0.520879\pi\) |
0.896936 | − | 0.442160i | \(-0.145788\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.450955 | + | 15.9447i | −0.0149572 | + | 0.528853i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.7564 | + | 18.6307i | −0.356376 | + | 0.617262i | −0.987353 | − | 0.158540i | \(-0.949321\pi\) |
0.630976 | + | 0.775802i | \(0.282655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.50939 | − | 6.07844i | −0.116144 | − | 0.201167i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.32733 | + | 2.35844i | −0.308352 | + | 0.0779678i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −77.0633 | −2.54486 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28.7522i | − | 0.948448i | −0.880404 | − | 0.474224i | \(-0.842729\pi\) | ||
0.880404 | − | 0.474224i | \(-0.157271\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0728 | − | 39.8366i | −0.331910 | − | 1.31266i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.83335 | + | 3.36788i | −0.192007 | + | 0.110855i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.08255 | + | 2.35706i | 0.134233 | + | 0.0774997i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −24.0677 | + | 39.0908i | −0.790486 | + | 1.28391i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.7995 | + | 17.2047i | 0.977689 | + | 0.564469i | 0.901572 | − | 0.432630i | \(-0.142414\pi\) |
0.0761173 | + | 0.997099i | \(0.475748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.9220 | + | 55.2906i | 1.04620 | + | 1.81208i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.4995 | − | 15.0673i | 0.507430 | − | 0.493281i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.41563 | 0.209813 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.52071 | 0.311028 | 0.155514 | − | 0.987834i | \(-0.450297\pi\) | ||||
0.155514 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.6885 | + | 6.99080i | 0.805679 | + | 0.228136i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.3517 | − | 38.7143i | −0.728646 | − | 1.26205i | −0.957456 | − | 0.288580i | \(-0.906817\pi\) |
0.228810 | − | 0.973471i | \(-0.426517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.9466 | − | 8.62943i | −0.486729 | − | 0.281013i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 17.1647 | − | 15.7672i | 0.558369 | − | 0.512906i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.64574 | − | 4.41427i | −0.248453 | − | 0.143444i | 0.370603 | − | 0.928792i | \(-0.379151\pi\) |
−0.619056 | + | 0.785347i | \(0.712485\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.4592 | − | 6.61596i | 0.371981 | − | 0.214763i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −38.6606 | − | 10.9471i | −1.25366 | − | 0.354986i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25.0780i | − | 0.812356i | −0.913794 | − | 0.406178i | \(-0.866861\pi\) | ||
0.913794 | − | 0.406178i | \(-0.133139\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.428045 | −0.0138512 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.3306 | + | 12.6843i | 0.398593 | + | 0.410026i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.7263 | + | 63.6118i | 1.18595 | + | 2.05413i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.89704 | − | 15.4101i | 0.287001 | − | 0.497101i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.3445 | + | 19.1477i | 0.333346 | + | 0.617027i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.74084 | + | 8.21138i | −0.152613 | + | 0.264334i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.2843 | + | 26.7222i | −1.48840 | + | 0.859329i | −0.999912 | − | 0.0132411i | \(-0.995785\pi\) |
−0.488489 | + | 0.872570i | \(0.662452\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −43.2060 | + | 10.9248i | −1.38798 | + | 0.350954i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.47479i | − | 0.0473284i | −0.999720 | − | 0.0236642i | \(-0.992467\pi\) | ||
0.999720 | − | 0.0236642i | \(-0.00753325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 55.0592i | − | 1.76512i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.31740 | + | 0.838814i | −0.106242 | + | 0.0268636i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.3937 | + | 21.5892i | −1.19633 | + | 0.690701i | −0.959735 | − | 0.280908i | \(-0.909365\pi\) |
−0.236594 | + | 0.971609i | \(0.576031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.64980 | + | 2.85754i | −0.0527279 | + | 0.0913274i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.5512 | − | 49.1464i | −0.847713 | − | 1.56912i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.00102 | − | 5.19791i | 0.0957175 | − | 0.165788i | −0.814190 | − | 0.580598i | \(-0.802819\pi\) |
0.909908 | + | 0.414810i | \(0.136152\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.08201 | − | 3.60615i | −0.0663384 | − | 0.114901i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −64.7000 | − | 66.5558i | −2.05942 | − | 2.11849i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.63668 | −0.211034 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 60.8130i | − | 1.93179i | −0.258939 | − | 0.965894i | \(-0.583373\pi\) | ||
0.258939 | − | 0.965894i | \(-0.416627\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.3611 | + | 3.21701i | 0.360533 | + | 0.102089i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.7411 | − | 10.2428i | 0.562431 | − | 0.324720i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.61374 | + | 0.931694i | 0.0511077 | + | 0.0295070i | 0.525336 | − | 0.850895i | \(-0.323940\pi\) |
−0.474228 | + | 0.880402i | \(0.657273\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.0396 | − | 16.5708i | 0.570748 | − | 0.524278i |
(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 | 1440.2.cc.a.911.10 | 48 | ||
3.2 | odd | 2 | 4320.2.cc.b.1871.22 | 48 | |||
4.3 | odd | 2 | 360.2.bm.a.11.6 | ✓ | 48 | ||
8.3 | odd | 2 | 1440.2.cc.b.911.10 | 48 | |||
8.5 | even | 2 | 360.2.bm.b.11.3 | yes | 48 | ||
9.4 | even | 3 | 4320.2.cc.a.3311.3 | 48 | |||
9.5 | odd | 6 | 1440.2.cc.b.1391.10 | 48 | |||
12.11 | even | 2 | 1080.2.bm.b.251.19 | 48 | |||
24.5 | odd | 2 | 1080.2.bm.a.251.22 | 48 | |||
24.11 | even | 2 | 4320.2.cc.a.1871.3 | 48 | |||
36.23 | even | 6 | 360.2.bm.b.131.3 | yes | 48 | ||
36.31 | odd | 6 | 1080.2.bm.a.611.22 | 48 | |||
72.5 | odd | 6 | 360.2.bm.a.131.6 | yes | 48 | ||
72.13 | even | 6 | 1080.2.bm.b.611.19 | 48 | |||
72.59 | even | 6 | inner | 1440.2.cc.a.1391.10 | 48 | ||
72.67 | odd | 6 | 4320.2.cc.b.3311.22 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.bm.a.11.6 | ✓ | 48 | 4.3 | odd | 2 | ||
360.2.bm.a.131.6 | yes | 48 | 72.5 | odd | 6 | ||
360.2.bm.b.11.3 | yes | 48 | 8.5 | even | 2 | ||
360.2.bm.b.131.3 | yes | 48 | 36.23 | even | 6 | ||
1080.2.bm.a.251.22 | 48 | 24.5 | odd | 2 | |||
1080.2.bm.a.611.22 | 48 | 36.31 | odd | 6 | |||
1080.2.bm.b.251.19 | 48 | 12.11 | even | 2 | |||
1080.2.bm.b.611.19 | 48 | 72.13 | even | 6 | |||
1440.2.cc.a.911.10 | 48 | 1.1 | even | 1 | trivial | ||
1440.2.cc.a.1391.10 | 48 | 72.59 | even | 6 | inner | ||
1440.2.cc.b.911.10 | 48 | 8.3 | odd | 2 | |||
1440.2.cc.b.1391.10 | 48 | 9.5 | odd | 6 | |||
4320.2.cc.a.1871.3 | 48 | 24.11 | even | 2 | |||
4320.2.cc.a.3311.3 | 48 | 9.4 | even | 3 | |||
4320.2.cc.b.1871.22 | 48 | 3.2 | odd | 2 | |||
4320.2.cc.b.3311.22 | 48 | 72.67 | odd | 6 |