Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1120,2,Mod(719,1120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1120.719");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1120 = 2^{5} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1120.bq (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: | \(8.94324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 280) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 719.18 | ||
Character | \(\chi\) | \(=\) | 1120.719 |
Dual form | 1120.2.bq.b.1039.18 |
$q$-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 \(\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(421\) | \(801\) | \(897\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.360276 | − | 0.624015i | −0.208005 | − | 0.360276i | 0.743081 | − | 0.669202i | \(-0.233364\pi\) |
−0.951086 | + | 0.308926i | \(0.900030\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.56432 | − | 1.59778i | 0.699587 | − | 0.714548i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.35637 | − | 2.27162i | 0.512658 | − | 0.858593i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.24040 | − | 2.14844i | 0.413468 | − | 0.716147i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.95654 | − | 3.38883i | −0.589920 | − | 1.02177i | −0.994242 | − | 0.107155i | \(-0.965826\pi\) |
0.404322 | − | 0.914616i | \(-0.367507\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.55354i | − | 0.708224i | −0.935203 | − | 0.354112i | \(-0.884783\pi\) | ||
0.935203 | − | 0.354112i | \(-0.115217\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.56063 | − | 0.400522i | −0.402952 | − | 0.103414i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.55984 | + | 4.43377i | 0.620852 | + | 1.07535i | 0.989327 | + | 0.145709i | \(0.0465464\pi\) |
−0.368476 | + | 0.929637i | \(0.620120\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.25858 | − | 1.88134i | −0.747569 | − | 0.431609i | 0.0772457 | − | 0.997012i | \(-0.475387\pi\) |
−0.824815 | + | 0.565403i | \(0.808721\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.90619 | − | 0.0279831i | −0.415966 | − | 0.00610642i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.50209 | + | 6.06580i | −0.730237 | + | 1.26481i | 0.226545 | + | 0.974001i | \(0.427257\pi\) |
−0.956782 | + | 0.290807i | \(0.906076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.105783 | − | 4.99888i | −0.0211566 | − | 0.999776i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.94920 | −0.760024 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.39188i | 0.629856i | 0.949116 | + | 0.314928i | \(0.101980\pi\) | ||||
−0.949116 | + | 0.314928i | \(0.898020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.59267 | + | 2.75858i | 0.286052 | + | 0.495456i | 0.972864 | − | 0.231379i | \(-0.0743237\pi\) |
−0.686812 | + | 0.726835i | \(0.740990\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.40979 | + | 2.44183i | −0.245413 | + | 0.425067i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.50775 | − | 5.72072i | −0.254857 | − | 0.966979i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.850773 | + | 1.47358i | −0.139866 | + | 0.242256i | −0.927446 | − | 0.373957i | \(-0.878001\pi\) |
0.787580 | + | 0.616213i | \(0.211334\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.59345 | + | 0.919977i | −0.255156 | + | 0.147314i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.97345i | − | 0.620548i | −0.950647 | − | 0.310274i | \(-0.899579\pi\) | ||
0.950647 | − | 0.310274i | \(-0.100421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.898763i | 0.137060i | 0.997649 | + | 0.0685300i | \(0.0218309\pi\) | ||||
−0.997649 | + | 0.0685300i | \(0.978169\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.49234 | − | 5.34275i | −0.222465 | − | 0.796449i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.64460 | + | 3.25891i | 0.823350 | + | 0.475361i | 0.851570 | − | 0.524240i | \(-0.175651\pi\) |
−0.0282202 | + | 0.999602i | \(0.508984\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.32054 | − | 6.16230i | −0.474363 | − | 0.880329i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.84449 | − | 3.19476i | 0.258281 | − | 0.447355i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.92487 | + | 5.06602i | 0.401761 | + | 0.695871i | 0.993939 | − | 0.109937i | \(-0.0350648\pi\) |
−0.592177 | + | 0.805808i | \(0.701731\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.47526 | − | 2.17511i | −1.14280 | − | 0.293292i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.71120i | 0.359108i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2528 | − | 5.91946i | 1.33480 | − | 0.770648i | 0.348771 | − | 0.937208i | \(-0.386599\pi\) |
0.986031 | + | 0.166560i | \(0.0532659\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.94508 | + | 10.2972i | −0.761190 | + | 1.31842i | 0.181048 | + | 0.983474i | \(0.442051\pi\) |
−0.942238 | + | 0.334945i | \(0.891282\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.19801 | − | 5.73180i | −0.402911 | − | 0.722139i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.07998 | − | 3.99456i | −0.506060 | − | 0.495464i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.68095 | − | 1.54785i | 0.327530 | − | 0.189100i | −0.327214 | − | 0.944950i | \(-0.606110\pi\) |
0.654744 | + | 0.755851i | \(0.272776\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.04687 | 0.607572 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.3374i | − | 1.46418i | −0.681207 | − | 0.732091i | \(-0.738544\pi\) | ||
0.681207 | − | 0.732091i | \(-0.261456\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.59351 | − | 4.49209i | −0.303547 | − | 0.525759i | 0.673390 | − | 0.739288i | \(-0.264838\pi\) |
−0.976937 | + | 0.213529i | \(0.931504\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.08127 | + | 1.86698i | −0.355794 | + | 0.215581i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.3519 | − | 0.151968i | −1.17971 | − | 0.0173183i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.84693 | + | 5.10778i | 0.995358 | + | 0.574670i | 0.906871 | − | 0.421407i | \(-0.138464\pi\) |
0.0884863 | + | 0.996077i | \(0.471797\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.29841 | − | 3.98096i | −0.255379 | − | 0.442329i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.786461 | −0.0863253 | −0.0431626 | − | 0.999068i | \(-0.513743\pi\) | ||||
−0.0431626 | + | 0.999068i | \(0.513743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.0886 | + | 2.84580i | 1.20273 | + | 0.308670i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.11658 | − | 1.22201i | 0.226922 | − | 0.131013i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.679974 | − | 0.392583i | −0.0720771 | − | 0.0416137i | 0.463528 | − | 0.886082i | \(-0.346583\pi\) |
−0.535605 | + | 0.844468i | \(0.679917\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.80068 | − | 3.46353i | −0.608076 | − | 0.363077i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.14760 | − | 1.98770i | 0.119000 | − | 0.206115i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.10344 | + | 2.26346i | −0.831395 | + | 0.232226i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.5331 | −1.67868 | −0.839340 | − | 0.543607i | \(-0.817058\pi\) | ||||
−0.839340 | + | 0.543607i | \(0.817058\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.70761 | −0.975651 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.01482 | − | 10.4180i | −0.598497 | − | 1.03663i | −0.993043 | − | 0.117751i | \(-0.962432\pi\) |
0.394547 | − | 0.918876i | \(-0.370902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.132170 | + | 0.0763082i | 0.0130231 | + | 0.00751887i | 0.506497 | − | 0.862241i | \(-0.330940\pi\) |
−0.493474 | + | 0.869760i | \(0.664273\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.02661 | + | 3.00190i | −0.295367 | + | 0.292955i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.38413 | + | 0.799129i | 0.133809 | + | 0.0772548i | 0.565410 | − | 0.824810i | \(-0.308718\pi\) |
−0.431601 | + | 0.902065i | \(0.642051\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.5710 | − | 7.83523i | 1.29987 | − | 0.750479i | 0.319486 | − | 0.947591i | \(-0.396490\pi\) |
0.980381 | + | 0.197112i | \(0.0631563\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.22605 | 0.116372 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 8.17675i | − | 0.769204i | −0.923082 | − | 0.384602i | \(-0.874339\pi\) | ||
0.923082 | − | 0.384602i | \(-0.125661\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.21339 | + | 15.0844i | 0.392901 | + | 1.40663i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.48613 | − | 3.16742i | −0.507193 | − | 0.292828i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.5439 | + | 0.198826i | 1.24157 | + | 0.0182264i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.15612 | + | 3.73451i | −0.196011 | + | 0.339501i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.47949 | + | 1.43154i | −0.223568 | + | 0.129077i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.15258 | − | 7.65085i | −0.729189 | − | 0.684313i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.7657 | 1.22151 | 0.610756 | − | 0.791819i | \(-0.290866\pi\) | ||||
0.610756 | + | 0.791819i | \(0.290866\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.560842 | − | 0.323802i | 0.0493794 | − | 0.0285092i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.10845 | + | 4.68141i | 0.708438 | + | 0.409017i | 0.810483 | − | 0.585763i | \(-0.199205\pi\) |
−0.102044 | + | 0.994780i | \(0.532538\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.69352 | + | 4.85048i | −0.753824 | + | 0.420590i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.17783 | + | 6.30994i | −0.531703 | + | 0.543073i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.1440 | − | 9.32074i | 1.37927 | − | 0.796325i | 0.387202 | − | 0.921995i | \(-0.373441\pi\) |
0.992072 | + | 0.125670i | \(0.0401081\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.50951i | − | 0.382491i | −0.981542 | − | 0.191246i | \(-0.938747\pi\) | ||
0.981542 | − | 0.191246i | \(-0.0612527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.69643i | − | 0.395511i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.65351 | + | 4.99611i | −0.723643 | + | 0.417795i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.41946 | + | 5.30599i | 0.450062 | + | 0.440639i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.64906 | + | 4.29220i | −0.218491 | + | 0.354015i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.1713 | + | 11.6459i | 1.65249 | + | 0.954067i | 0.976043 | + | 0.217579i | \(0.0698161\pi\) |
0.676451 | + | 0.736488i | \(0.263517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.61940 | + | 4.97642i | −0.701437 | + | 0.404975i | −0.807882 | − | 0.589344i | \(-0.799386\pi\) |
0.106445 | + | 0.994319i | \(0.466053\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12.7009 | 1.02681 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.89905 | + | 1.77059i | 0.554145 | + | 0.142217i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.97707 | + | 5.76026i | −0.796257 | + | 0.459719i | −0.842161 | − | 0.539227i | \(-0.818717\pi\) |
0.0459037 | + | 0.998946i | \(0.485383\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.10752 | − | 3.65033i | 0.167137 | − | 0.289490i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.02910 | + | 16.1829i | 0.711593 | + | 1.27539i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.80019 | + | 3.92609i | 0.532632 | + | 0.307515i | 0.742087 | − | 0.670303i | \(-0.233836\pi\) |
−0.209456 | + | 0.977818i | \(0.567169\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.69613 | + | 6.07233i | 0.132043 | + | 0.472731i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 17.7066i | − | 1.37018i | −0.728459 | − | 0.685090i | \(-0.759763\pi\) | ||
0.728459 | − | 0.685090i | \(-0.240237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.47944 | 0.498419 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.08390 | + | 4.66724i | −0.618191 | + | 0.356913i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.71071 | + | 2.14238i | 0.282120 | + | 0.162882i | 0.634383 | − | 0.773019i | \(-0.281254\pi\) |
−0.352263 | + | 0.935901i | \(0.614588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.4991 | − | 6.54001i | −0.869247 | − | 0.494378i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.38767 | − | 4.26527i | −0.555291 | − | 0.320598i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.86299 | + | 11.8870i | 0.512964 | + | 0.888479i | 0.999887 | + | 0.0150343i | \(0.00478576\pi\) |
−0.486923 | + | 0.873445i | \(0.661881\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.40055 | −0.698738 | −0.349369 | − | 0.936985i | \(-0.613604\pi\) | ||||
−0.349369 | + | 0.936985i | \(0.613604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.56747 | 0.633326 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.02357 | + | 3.66451i | 0.0752545 | + | 0.269420i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0169 | − | 17.3497i | 0.732505 | − | 1.26874i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.35656 | + | 8.97110i | −0.389632 | + | 0.652551i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.4640 | − | 8.92815i | −1.11894 | − | 0.646019i | −0.177808 | − | 0.984065i | \(-0.556900\pi\) |
−0.941129 | + | 0.338047i | \(0.890234\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.8035 | + | 11.4335i | −1.42548 | + | 0.823004i | −0.996760 | − | 0.0804313i | \(-0.974370\pi\) |
−0.428725 | + | 0.903435i | \(0.641037\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.02275 | + | 3.98512i | −0.0732406 | + | 0.285380i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.6688 | 0.973859 | 0.486929 | − | 0.873441i | \(-0.338117\pi\) | ||||
0.486929 | + | 0.873441i | \(0.338117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4509 | + | 19.8335i | 0.811732 | + | 1.40596i | 0.911651 | + | 0.410966i | \(0.134809\pi\) |
−0.0999183 | + | 0.994996i | \(0.531858\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.93176 | − | 1.11530i | −0.136256 | − | 0.0786675i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.70507 | + | 4.60063i | 0.540790 | + | 0.322901i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.34868 | − | 6.21576i | −0.443411 | − | 0.434127i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.68801 | + | 15.0481i | 0.603859 | + | 1.04591i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.7237i | 1.01846i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.80653 | 0.262052 | 0.131026 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131026 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.69874 | + | 4.44487i | −0.527509 | + | 0.304558i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.43602 | + | 1.40596i | 0.0979359 | + | 0.0958854i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.42670 | + | 0.123705i | 0.572042 | + | 0.00839763i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.86876 | + | 3.23678i | −0.126279 | + | 0.218721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 11.3218 | − | 6.53664i | 0.761586 | − | 0.439702i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.1551i | − | 1.01486i | −0.861693 | − | 0.507430i | \(-0.830595\pi\) | ||
0.861693 | − | 0.507430i | \(-0.169405\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.8710 | − | 5.97336i | −0.724734 | − | 0.398224i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.92282 | − | 10.2586i | −0.393111 | − | 0.680888i | 0.599747 | − | 0.800190i | \(-0.295268\pi\) |
−0.992858 | + | 0.119301i | \(0.961935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.242540 | − | 0.420091i | 0.0160275 | − | 0.0277604i | −0.857900 | − | 0.513816i | \(-0.828231\pi\) |
0.873928 | + | 0.486056i | \(0.161565\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.63472 | + | 6.51452i | 0.239147 | + | 0.428624i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.8163 | + | 13.1730i | 1.49475 | + | 0.862992i | 0.999982 | − | 0.00603553i | \(-0.00192118\pi\) |
0.494764 | + | 0.869027i | \(0.335255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.0370 | − | 3.92082i | 0.915673 | − | 0.255766i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 7.36083i | − | 0.478137i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.78403i | 0.115399i | 0.998334 | + | 0.0576997i | \(0.0183766\pi\) | ||||
−0.998334 | + | 0.0576997i | \(0.981623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.29829 | + | 4.21367i | −0.470124 | + | 0.271426i | −0.716292 | − | 0.697801i | \(-0.754162\pi\) |
0.246167 | + | 0.969227i | \(0.420829\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.57992 | + | 13.1288i | −0.486252 | + | 0.842214i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.0404 | − | 4.33435i | −0.960895 | − | 0.276911i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.80408 | + | 8.32091i | −0.305676 | + | 0.529447i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.283342 | + | 0.490764i | 0.0179561 | + | 0.0311009i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.9871i | 1.26157i | 0.775956 | + | 0.630787i | \(0.217268\pi\) | ||||
−0.775956 | + | 0.630787i | \(0.782732\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.4080 | 1.72312 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.21912 | − | 7.94472i | −0.138967 | − | 0.497518i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.516455 | + | 0.894526i | −0.0322156 | + | 0.0557990i | −0.881684 | − | 0.471841i | \(-0.843590\pi\) |
0.849468 | + | 0.527640i | \(0.176923\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.19346 | + | 3.93135i | 0.136295 | + | 0.244282i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.28725 | + | 4.20729i | 0.451069 | + | 0.260425i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.33070 | + | 5.76894i | 0.205380 | + | 0.355728i | 0.950254 | − | 0.311477i | \(-0.100824\pi\) |
−0.744874 | + | 0.667205i | \(0.767490\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.6698 | + | 3.25161i | 0.778300 | + | 0.199745i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.565752i | 0.0346235i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.75055 | + | 6.49615i | 0.228675 | + | 0.396077i | 0.957416 | − | 0.288713i | \(-0.0932273\pi\) |
−0.728740 | + | 0.684790i | \(0.759894\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.07782 | − | 1.86684i | 0.0654730 | − | 0.113402i | −0.831431 | − | 0.555628i | \(-0.812478\pi\) |
0.896904 | + | 0.442226i | \(0.145811\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.0714560 | + | 4.86754i | −0.00432471 | + | 0.294597i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −16.7334 | + | 10.1390i | −1.00906 | + | 0.611405i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.98545 | − | 10.3671i | −0.359631 | − | 0.622899i | 0.628268 | − | 0.777997i | \(-0.283764\pi\) |
−0.987899 | + | 0.155098i | \(0.950431\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.90220 | 0.473093 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.06151 | 0.182634 | 0.0913171 | − | 0.995822i | \(-0.470892\pi\) | ||||
0.0913171 | + | 0.995822i | \(0.470892\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.3523 | − | 17.9308i | −0.615383 | − | 1.06587i | −0.990317 | − | 0.138823i | \(-0.955668\pi\) |
0.374934 | − | 0.927051i | \(-0.377665\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.33190 | + | 4.24120i | 0.256600 | + | 0.251227i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.02617 | − | 5.38945i | −0.532798 | − | 0.318129i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.60553 | + | 7.97701i | −0.270913 | + | 0.469236i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.95647 | + | 10.3169i | 0.349174 | + | 0.604787i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.5374i | − | 1.78402i | −0.452020 | − | 0.892008i | \(-0.649296\pi\) | ||
0.452020 | − | 0.892008i | \(-0.350704\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.58073 | − | 25.6417i | 0.383145 | − | 1.49291i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.72678 | + | 13.3832i | 0.448353 | + | 0.776571i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.4893 | + | 8.94273i | 0.895767 | + | 0.517171i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.04165 | + | 1.21905i | 0.117679 | + | 0.0702649i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.33398 | + | 7.50668i | −0.248981 | + | 0.431247i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.15257 | + | 25.6070i | 0.409555 | + | 1.46625i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.15470 | 0.408340 | 0.204170 | − | 0.978935i | \(-0.434550\pi\) | ||||
0.204170 | + | 0.978935i | \(0.434550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 0.109968i | − | 0.00625586i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.60675 | + | 7.97912i | 0.261225 | + | 0.452454i | 0.966568 | − | 0.256412i | \(-0.0825403\pi\) |
−0.705343 | + | 0.708866i | \(0.749207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.15408 | − | 8.92713i | 0.291326 | − | 0.504591i | −0.682798 | − | 0.730608i | \(-0.739237\pi\) |
0.974124 | + | 0.226016i | \(0.0725702\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.1609 | − | 3.85669i | −0.797874 | − | 0.217300i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7268 | + | 28.9716i | −0.939469 | + | 1.62721i | −0.173004 | + | 0.984921i | \(0.555347\pi\) |
−0.766464 | + | 0.642287i | \(0.777986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.4945 | − | 6.63635i | 0.643568 | − | 0.371564i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 1.15163i | − | 0.0642776i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 19.2637i | − | 1.07186i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.7648 | + | 0.270121i | −0.708066 | + | 0.0149836i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.77861 | − | 5.64568i | −0.540758 | − | 0.312207i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0592 | − | 8.40213i | 0.830239 | − | 0.463225i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.130885 | + | 0.226700i | −0.00719411 | + | 0.0124606i | −0.869600 | − | 0.493757i | \(-0.835623\pi\) |
0.862406 | + | 0.506217i | \(0.168957\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.11060 | + | 3.65567i | 0.115660 | + | 0.200330i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.72076 | − | 6.70490i | 0.0940152 | − | 0.366328i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7546i | 0.749262i | 0.927174 | + | 0.374631i | \(0.122231\pi\) | ||||
−0.927174 | + | 0.374631i | \(0.877769\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.10242 | + | 2.94588i | −0.277125 | + | 0.159998i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.23225 | − | 10.7946i | 0.337495 | − | 0.584559i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.5023 | − | 0.815316i | −0.999031 | − | 0.0440229i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.89494 | − | 8.06378i | 0.425049 | − | 0.434139i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.9110 | + | 14.3824i | −1.33729 | + | 0.772086i | −0.986405 | − | 0.164332i | \(-0.947453\pi\) |
−0.350887 | + | 0.936418i | \(0.614120\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9493 | 1.28197 | 0.640987 | − | 0.767551i | \(-0.278525\pi\) | ||||
0.640987 | + | 0.767551i | \(0.278525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.0844i | 0.538267i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.9932 | − | 20.7729i | −0.638336 | − | 1.10563i | −0.985798 | − | 0.167937i | \(-0.946290\pi\) |
0.347462 | − | 0.937694i | \(-0.387044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.7124 | − | 19.2997i | −1.04623 | − | 1.02432i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.75547 | − | 8.52325i | −0.251686 | − | 0.451098i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.3298 | + | 8.85066i | 0.809075 | + | 0.467120i | 0.846635 | − | 0.532175i | \(-0.178625\pi\) |
−0.0375594 | + | 0.999294i | \(0.511958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.42111 | − | 4.19349i | −0.127427 | − | 0.220710i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.10719 | 0.163085 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.2344 | − | 2.88323i | −0.588038 | − | 0.150915i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3340 | + | 6.54368i | −0.591629 | + | 0.341577i | −0.765742 | − | 0.643148i | \(-0.777628\pi\) |
0.174112 | + | 0.984726i | \(0.444294\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.53672 | − | 4.92868i | −0.444404 | − | 0.256577i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.4753 | + | 0.227179i | 0.803436 | + | 0.0117945i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.0243 | + | 19.0947i | −0.570817 | + | 0.988684i | 0.425665 | + | 0.904881i | \(0.360040\pi\) |
−0.996482 | + | 0.0838033i | \(0.973293\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.83708 | + | 7.84375i | −0.0948662 | + | 0.405049i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.66129 | 0.446079 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18.8729 | −0.969437 | −0.484719 | − | 0.874670i | \(-0.661078\pi\) | ||||
−0.484719 | + | 0.874670i | \(0.661078\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.95946 | − | 8.59004i | −0.254081 | − | 0.440081i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.2851 | + | 8.24751i | 0.729935 | + | 0.421428i | 0.818398 | − | 0.574651i | \(-0.194862\pi\) |
−0.0884637 | + | 0.996079i | \(0.528196\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.4366 | + | 16.3024i | −0.837686 | + | 0.830845i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.93094 | + | 1.11483i | 0.0981551 | + | 0.0566699i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.28484 | + | 0.741804i | −0.0651441 | + | 0.0376110i | −0.532218 | − | 0.846607i | \(-0.678641\pi\) |
0.467074 | + | 0.884218i | \(0.345308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.8591 | −1.81347 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.74639i | − | 0.340311i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.0006 | − | 6.14521i | 1.10697 | − | 0.309199i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.3671 | + | 13.4910i | 1.17276 | + | 0.677093i | 0.954329 | − | 0.298759i | \(-0.0965727\pi\) |
0.218431 | + | 0.975852i | \(0.429906\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.15884 | + | 3.67739i | 0.308327 | + | 0.184100i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.72660 | − | 8.18671i | 0.236035 | − | 0.408825i | −0.723538 | − | 0.690285i | \(-0.757485\pi\) |
0.959573 | + | 0.281460i | \(0.0908186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.04415 | − | 4.06694i | 0.350894 | − | 0.202589i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.95614 | − | 2.55517i | −0.494725 | − | 0.126967i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.65830 | 0.330040 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.4734 | + | 10.6656i | −0.913451 | + | 0.527381i | −0.881540 | − | 0.472110i | \(-0.843493\pi\) |
−0.0319110 | + | 0.999491i | \(0.510159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.6326 | − | 6.71607i | −0.573792 | − | 0.331279i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.459773 | − | 31.3195i | 0.0226240 | − | 1.54113i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.23028 | + | 1.25659i | −0.0603920 | + | 0.0616835i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.81400 | + | 1.62466i | −0.137802 | + | 0.0795602i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 27.0871i | − | 1.32329i | −0.749816 | − | 0.661646i | \(-0.769858\pi\) | ||
0.749816 | − | 0.661646i | \(-0.230142\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.8575i | 0.529163i | 0.964363 | + | 0.264581i | \(0.0852338\pi\) | ||||
−0.964363 | + | 0.264581i | \(0.914766\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.0032 | − | 8.08473i | 0.680857 | − | 0.393093i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 21.8931 | − | 13.2653i | 1.06197 | − | 0.643463i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.3276 | + | 27.4717i | 0.741755 | + | 1.32945i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.23530 | + | 3.59995i | 0.301043 | + | 0.173807i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.43863 | − | 0.830592i | 0.0692963 | − | 0.0400082i | −0.464952 | − | 0.885336i | \(-0.653928\pi\) |
0.534248 | + | 0.845328i | \(0.320595\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.7666 | −1.47855 | −0.739274 | − | 0.673405i | \(-0.764831\pi\) | ||||
−0.739274 | + | 0.673405i | \(0.764831\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.35852 | − | 5.29345i | 0.0651361 | − | 0.253801i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.8237 | − | 13.1773i | 1.09181 | − | 0.630354i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.33622 | − | 9.24260i | 0.254684 | − | 0.441125i | −0.710126 | − | 0.704075i | \(-0.751362\pi\) |
0.964810 | + | 0.262950i | \(0.0846953\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.3582 | − | 0.509749i | −0.826579 | − | 0.0242738i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.4954 | + | 6.05950i | 0.498650 | + | 0.287896i | 0.728156 | − | 0.685412i | \(-0.240378\pi\) |
−0.229506 | + | 0.973307i | \(0.573711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.69096 | + | 0.472319i | −0.0801591 | + | 0.0223901i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 16.7829i | − | 0.793804i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.0498 | 1.51252 | 0.756261 | − | 0.654270i | \(-0.227024\pi\) | ||||
0.756261 | + | 0.654270i | \(0.227024\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.4653 | + | 7.77422i | −0.634058 | + | 0.366074i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.21072 | + | 3.58576i | 0.291805 | + | 0.168474i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.6081 | + | 3.85010i | −0.684838 | + | 0.180496i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.80174 | − | 3.34963i | −0.271394 | − | 0.156689i | 0.358127 | − | 0.933673i | \(-0.383415\pi\) |
−0.629521 | + | 0.776984i | \(0.716749\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.1093 | − | 17.5098i | −0.471862 | − | 0.817289i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.4768 | −0.720828 | −0.360414 | − | 0.932792i | \(-0.617365\pi\) | ||||
−0.360414 | + | 0.932792i | \(0.617365\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.8717 | 0.691145 | 0.345572 | − | 0.938392i | \(-0.387685\pi\) | ||||
0.345572 | + | 0.938392i | \(0.387685\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.38068 | − | 4.94301i | −0.0640277 | − | 0.229227i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.0443182 | + | 0.0767615i | −0.00205080 | + | 0.00355210i | −0.867049 | − | 0.498223i | \(-0.833986\pi\) |
0.864998 | + | 0.501775i | \(0.167319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.120224 | − | 8.18956i | 0.00555141 | − | 0.378159i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.18899 | + | 4.15056i | 0.331251 | + | 0.191248i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.04576 | − | 1.75847i | 0.140044 | − | 0.0808544i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.05990 | + | 16.4883i | −0.415697 | + | 0.756533i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.5121 | 0.664462 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.36928 | − | 7.56782i | −0.199638 | − | 0.345783i | 0.748773 | − | 0.662826i | \(-0.230643\pi\) |
−0.948411 | + | 0.317044i | \(0.897310\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.76285 | + | 2.17248i | 0.171571 | + | 0.0990567i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.84541 | − | 11.4646i | 0.311477 | − | 0.521657i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −25.8631 | + | 26.4162i | −1.17438 | + | 1.19950i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.60661 | + | 14.9071i | 0.390003 | + | 0.675504i | 0.992449 | − | 0.122655i | \(-0.0391408\pi\) |
−0.602447 | + | 0.798159i | \(0.705807\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5.65789i | − | 0.255859i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0849 | 0.680770 | 0.340385 | − | 0.940286i | \(-0.389443\pi\) | ||||
0.340385 | + | 0.940286i | \(0.389443\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −15.0388 | + | 8.68265i | −0.677313 | + | 0.391047i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.1858 | + | 15.5106i | −0.682553 | + | 0.697149i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −28.0260 | − | 16.7341i | −1.25714 | − | 0.750625i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9769 | − | 22.4766i | 0.580925 | − | 1.00619i | −0.414445 | − | 0.910074i | \(-0.636024\pi\) |
0.995370 | − | 0.0961171i | \(-0.0306423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0492 | + | 6.37926i | −0.493642 | + | 0.285004i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 6.00776i | − | 0.267873i | −0.990990 | − | 0.133936i | \(-0.957238\pi\) | ||
0.990990 | − | 0.133936i | \(-0.0427618\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.0547 | − | 6.68674i | −1.15942 | − | 0.297556i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.33438 | − | 4.04327i | −0.103674 | − | 0.179568i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.28454 | + | 7.42104i | −0.189909 | + | 0.328932i | −0.945220 | − | 0.326435i | \(-0.894153\pi\) |
0.755311 | + | 0.655367i | \(0.227486\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.7221 | − | 0.201442i | −0.607029 | − | 0.00891125i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.8688 | + | 7.42979i | 0.568171 | + | 0.328033i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.328680 | − | 0.0918070i | 0.0144834 | − | 0.00404550i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 25.5048i | − | 1.12170i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.08739i | − | 0.135521i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.4208 | − | 9.48055i | 0.719408 | − | 0.415350i | −0.0951267 | − | 0.995465i | \(-0.530326\pi\) |
0.814535 | + | 0.580115i | \(0.196992\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.0605 | + | 31.2816i | −0.789729 | + | 1.36785i | 0.136404 | + | 0.990653i | \(0.456445\pi\) |
−0.926133 | + | 0.377197i | \(0.876888\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.0617588 | + | 9.53179i | 0.00269538 | + | 0.416002i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.15394 | + | 14.1230i | −0.355191 | + | 0.615209i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0293 | − | 22.5674i | −0.566492 | − | 0.981192i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 29.3701i | − | 1.27455i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.1463 | −0.439487 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.44206 | − | 0.961439i | 0.148813 | − | 0.0415666i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.94513 | − | 8.56522i | 0.213398 | − | 0.369616i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.3862 | + | 23.3096i | −0.619659 | + | 1.00401i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3425 | − | 7.12594i | −0.530645 | − | 0.306368i | 0.210634 | − | 0.977565i | \(-0.432447\pi\) |
−0.741279 | + | 0.671197i | \(0.765781\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.38679 | + | 5.86609i | 0.145341 | + | 0.251738i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.71051 | − | 33.9403i | 0.373117 | − | 1.45384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.3957i | 0.957570i | 0.877932 | + | 0.478785i | \(0.158923\pi\) | ||||
−0.877932 | + | 0.478785i | \(0.841077\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.7486 | + | 25.5453i | 0.629455 | + | 1.09025i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.38128 | − | 11.0527i | 0.271852 | − | 0.470861i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.6026 | − | 13.1689i | 1.00369 | − | 0.559998i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.91794 | − | 1.95896i | 0.0814121 | − | 0.0831531i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.3454 | + | 17.9188i | 0.438350 | + | 0.759244i | 0.997562 | − | 0.0697803i | \(-0.0222298\pi\) |
−0.559213 | + | 0.829024i | \(0.688897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.29502 | 0.0970692 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4353 | −0.609460 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8.03504 | + | 13.9171i | 0.338636 | + | 0.586536i | 0.984177 | − | 0.177191i | \(-0.0567010\pi\) |
−0.645540 | + | 0.763726i | \(0.723368\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.0646 | − | 12.7911i | −0.549633 | − | 0.538125i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.1607 | − | 0.178521i | −0.510703 | − | 0.00749717i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.09523 | − | 14.0213i | 0.339370 | − | 0.587805i | −0.644945 | − | 0.764229i | \(-0.723120\pi\) |
0.984314 | + | 0.176424i | \(0.0564530\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.6257 | − | 27.0645i | −0.653914 | − | 1.13261i | −0.982165 | − | 0.188022i | \(-0.939792\pi\) |
0.328251 | − | 0.944591i | \(-0.393541\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8664i | 0.537501i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.6927 | + | 16.8649i | 1.27997 | + | 0.703314i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.08399 | + | 1.87753i | 0.0451271 | + | 0.0781625i | 0.887707 | − | 0.460409i | \(-0.152297\pi\) |
−0.842580 | + | 0.538572i | \(0.818964\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.2694 | + | 8.23845i | 0.593016 | + | 0.342378i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.06673 | + | 1.78654i | −0.0442553 | + | 0.0741183i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.4453 | − | 19.8238i | 0.474014 | − | 0.821017i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.6429 | + | 3.81074i | −0.564065 | + | 0.157555i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.3449 | 1.25247 | 0.626235 | − | 0.779634i | \(-0.284595\pi\) | ||||
0.626235 | + | 0.779634i | \(0.284595\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.9854i | − | 0.493850i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.92452 | − | 8.52952i | −0.202568 | − | 0.350857i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.6695 | + | 32.3365i | −0.766664 | + | 1.32790i | 0.172699 | + | 0.984975i | \(0.444751\pi\) |
−0.939363 | + | 0.342926i | \(0.888582\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.5048 | − | 21.3291i | 0.881609 | − | 0.874410i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.25095 | − | 14.2911i | 0.337689 | − | 0.584895i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.2174 | − | 7.05370i | 0.499188 | − | 0.288206i | −0.229190 | − | 0.973382i | \(-0.573608\pi\) |
0.728378 | + | 0.685175i | \(0.240274\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.7058i | − | 0.803815i | −0.915680 | − | 0.401907i | \(-0.868347\pi\) | ||
0.915680 | − | 0.401907i | \(-0.131653\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.67982i | − | 0.312747i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.59404 | + | 9.28698i | 0.105463 | + | 0.377569i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.1585 | − | 16.2573i | −1.14292 | − | 0.659865i | −0.195768 | − | 0.980650i | \(-0.562720\pi\) |
−0.947152 | + | 0.320785i | \(0.896053\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.0949153 | − | 6.46557i | 0.00384616 | − | 0.261998i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.32176 | − | 14.4137i | 0.336662 | − | 0.583116i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.14971 | + | 10.6516i | 0.248384 | + | 0.430214i | 0.963078 | − | 0.269224i | \(-0.0867671\pi\) |
−0.714693 | + | 0.699438i | \(0.753434\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.59145 | + | 6.20106i | −0.0641736 | + | 0.250051i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 16.0440i | − | 0.645909i | −0.946415 | − | 0.322954i | \(-0.895324\pi\) | ||
0.946415 | − | 0.322954i | \(-0.104676\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.5927 | − | 11.8892i | 0.827691 | − | 0.477868i | −0.0253703 | − | 0.999678i | \(-0.508076\pi\) |
0.853061 | + | 0.521810i | \(0.174743\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.8305 | − | 23.9551i | 0.554997 | − | 0.961284i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.81409 | + | 1.01216i | −0.0726801 | + | 0.0405512i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.9776 | + | 1.05759i | −0.999105 | + | 0.0423038i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.18782 | − | 5.30459i | 0.366926 | − | 0.211845i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.71136 | −0.347345 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.0177i | − | 0.796893i | −0.917192 | − | 0.398447i | \(-0.869549\pi\) | ||
0.917192 | − | 0.398447i | \(-0.130451\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.37140 | − | 2.37533i | −0.0545082 | − | 0.0944109i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.5341 | − | 21.9946i | 0.854554 | − | 0.872829i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7357 | + | 8.47913i | −0.623470 | + | 0.335956i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.5062 | − | 15.3034i | −1.04857 | − | 0.605392i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.346690 | − | 0.600484i | −0.0136934 | − | 0.0237177i | 0.859097 | − | 0.511812i | \(-0.171026\pi\) |
−0.872791 | + | 0.488094i | \(0.837692\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −42.2717 | −1.66703 | −0.833516 | − | 0.552495i | \(-0.813676\pi\) | ||||
−0.833516 | + | 0.552495i | \(0.813676\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.359974 | − | 1.40263i | 0.0141740 | − | 0.0552286i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.8701 | + | 17.8229i | −1.21363 | + | 0.700690i | −0.963548 | − | 0.267535i | \(-0.913791\pi\) |
−0.250082 | + | 0.968225i | \(0.580458\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −40.1201 | − | 23.1634i | −1.57485 | − | 0.909242i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.95874 | − | 5.30296i | −0.115962 | − | 0.207839i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.40762 | − | 2.43807i | 0.0550845 | − | 0.0954091i | −0.837168 | − | 0.546945i | \(-0.815791\pi\) |
0.892253 | + | 0.451536i | \(0.149124\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.1641 | − | 5.63224i | 0.787876 | − | 0.220070i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.8680 | −0.502028 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.69907 | −0.338868 | −0.169434 | − | 0.985542i | \(-0.554194\pi\) | ||||
−0.169434 | + | 0.985542i | \(0.554194\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.7443 | + | 23.8058i | 0.534591 | + | 0.925939i | 0.999183 | + | 0.0404142i | \(0.0128677\pi\) |
−0.464592 | + | 0.885525i | \(0.653799\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.15793 | − | 4.70998i | −0.316828 | − | 0.182921i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.84951 | + | 21.4780i | −0.226834 | + | 0.832882i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.5745 | − | 11.8787i | −0.796646 | − | 0.459944i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.45702 | + | 5.46001i | −0.365630 | + | 0.211096i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 46.5272 | 1.79616 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.1015i | 0.466480i | 0.972419 | + | 0.233240i | \(0.0749328\pi\) | ||||
−0.972419 | + | 0.233240i | \(0.925067\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.417759 | + | 19.7416i | 0.0160795 | + | 0.759854i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.13926 | + | 2.96715i | 0.197518 | + | 0.114037i | 0.595497 | − | 0.803357i | \(-0.296955\pi\) |
−0.397979 | + | 0.917394i | \(0.630288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4249 | + | 37.5569i | −0.860589 | + | 1.44130i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.26769 | + | 7.39186i | −0.163538 | + | 0.283257i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.2951 | − | 8.83063i | 0.585250 | − | 0.337894i | −0.177967 | − | 0.984036i | \(-0.556952\pi\) |
0.763217 | + | 0.646142i | \(0.223619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.3620 | − | 40.3752i | 0.395910 | − | 1.54266i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.349524 | −0.0133352 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9363 | − | 7.46876i | 0.492833 | − | 0.284537i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.4396 | − | 6.60468i | −0.435184 | − | 0.251254i | 0.266368 | − | 0.963871i | \(-0.414176\pi\) |
−0.701553 | + | 0.712617i | \(0.747510\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.1671 | + | 22.0520i | −0.500176 | + | 0.837687i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.20519 | − | 7.05433i | −0.273308 | − | 0.267586i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.6173 | − | 10.1714i | 0.667304 | − | 0.385268i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 18.9836i | − | 0.718027i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.75429i | − | 0.255106i | −0.991832 | − | 0.127553i | \(-0.959288\pi\) | ||
0.991832 | − | 0.127553i | \(-0.0407123\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.54462 | − | 3.20119i | 0.209119 | − | 0.120735i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.50384 | − | 7.34673i | −0.282611 | − | 0.276694i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.8240 | − | 0.467180i | −1.19686 | − | 0.0175701i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.2027 | − | 19.7470i | −1.28451 | − | 0.741612i | −0.306841 | − | 0.951761i | \(-0.599272\pi\) |
−0.977669 | + | 0.210148i | \(0.932605\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.9475 | − | 12.6714i | 0.823097 | − | 0.475215i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.3107 | −0.835542 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.55423 | + | 21.6419i | −0.207716 | + | 0.809362i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.11326 | − | 0.642743i | 0.0415756 | − | 0.0240037i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.16021 | + | 7.20569i | −0.155150 | + | 0.268727i | −0.933113 | − | 0.359582i | \(-0.882919\pi\) |
0.777964 | + | 0.628309i | \(0.216253\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.352614 | − | 0.196738i | 0.0131320 | − | 0.00732690i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.25879 | + | 3.03616i | 0.195577 | + | 0.112916i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.9556 | − | 0.358803i | 0.629715 | − | 0.0133256i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.2319i | 0.453654i | 0.973935 | + | 0.226827i | \(0.0728353\pi\) | ||||
−0.973935 | + | 0.226827i | \(0.927165\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.86701 | −0.106186 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.98490 | + | 2.30069i | −0.147387 | + | 0.0850939i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.7710 | − | 10.8375i | −0.693324 | − | 0.400291i | 0.111532 | − | 0.993761i | \(-0.464424\pi\) |
−0.804856 | + | 0.593470i | \(0.797758\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.71398 | + | 10.9470i | 0.100107 | + | 0.403786i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.4908 | − | 6.05686i | −0.386433 | − | 0.223107i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.41640 | + | 7.64942i | 0.162460 | + | 0.281389i | 0.935750 | − | 0.352663i | \(-0.114724\pi\) |
−0.773291 | + | 0.634052i | \(0.781391\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.92316 | 0.254329 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8875 | 0.399425 | 0.199712 | − | 0.979855i | \(-0.435999\pi\) | ||||
0.199712 | + | 0.979855i | \(0.435999\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 50.1619 | − | 14.0112i | 1.83779 | − | 0.513332i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.975528 | + | 1.68966i | −0.0356927 | + | 0.0618216i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.69271 | − | 2.06032i | 0.134929 | − | 0.0752823i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.9728 | + | 9.79926i | 0.619347 | + | 0.357580i | 0.776615 | − | 0.629976i | \(-0.216935\pi\) |
−0.157268 | + | 0.987556i | \(0.550269\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.4723 | − | 7.20086i | 0.454514 | − | 0.262414i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.53234 | + | 21.5566i | −0.201342 | + | 0.784525i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5411 | 1.07369 | 0.536845 | − | 0.843681i | \(-0.319616\pi\) | ||||
0.536845 | + | 0.843681i | \(0.319616\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.87442 | − | 17.1030i | −0.358419 | − | 0.620800i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.6992 | + | 11.3734i | 0.714097 | + | 0.412284i | 0.812576 | − | 0.582855i | \(-0.198064\pi\) |
−0.0984792 | + | 0.995139i | \(0.531398\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.608573 | − | 41.4557i | 0.0220318 | − | 1.50080i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.8683 | − | 20.2932i | 0.718342 | − | 0.733703i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.1156 | − | 26.1809i | −0.545792 | − | 0.945339i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.3053i | 1.77799i | 0.457913 | + | 0.888997i | \(0.348597\pi\) | ||||
−0.457913 | + | 0.888997i | \(0.651403\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.744264 | 0.0268040 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 17.7806 | − | 10.2656i | 0.639522 | − | 0.369228i | −0.144908 | − | 0.989445i | \(-0.546289\pi\) |
0.784430 | + | 0.620217i | \(0.212955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.6213 | − | 8.25337i | 0.489293 | − | 0.296470i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.66297 | − | 2.78513i | 0.0596589 | − | 0.0999159i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.47541 | + | 12.9478i | −0.267834 | + | 0.463903i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −41.8094 | + | 24.1387i | −1.49606 | + | 0.863750i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 13.3952i | − | 0.478705i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.40375 | + | 24.9521i | −0.228560 | + | 0.890577i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.52258 | − | 2.63719i | −0.0542741 | − | 0.0940056i | 0.837612 | − | 0.546266i | \(-0.183951\pi\) |
−0.891886 | + | 0.452260i | \(0.850618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.39994 | − | 4.15682i | 0.0854401 | − | 0.147987i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.5745 | − | 11.0907i | −0.660433 | − | 0.394339i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.2942 | + | 15.1810i | 0.933736 | + | 0.539093i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.53557 | − | 9.07763i | −0.0899273 | − | 0.321950i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.2059i | 0.857418i | 0.903443 | + | 0.428709i | \(0.141031\pi\) | ||||
−0.903443 | + | 0.428709i | \(0.858969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.3692i | 1.18052i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.68688 | + | 0.973922i | −0.0596031 | + | 0.0344118i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.1486 | + | 17.5779i | −0.358137 | + | 0.620312i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 39.9811 | + | 10.8888i | 1.40915 | + | 0.383779i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.70246 | − | 4.68081i | 0.0951313 | − | 0.164772i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.22922 | + | 12.5214i | 0.254166 | + | 0.440228i | 0.964669 | − | 0.263466i | \(-0.0848657\pi\) |
−0.710503 | + | 0.703694i | \(0.751532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.5466i | 1.07264i | 0.844016 | + | 0.536318i | \(0.180185\pi\) | ||||
−0.844016 | + | 0.536318i | \(0.819815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.55325 | −0.0544749 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.9107 | − | 4.72351i | 0.592356 | − | 0.165457i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.69088 | − | 2.92869i | 0.0591564 | − | 0.102462i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.6364 | + | 8.16624i | −0.511436 | + | 0.285351i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.87448 | + | 2.81428i | 0.170120 | + | 0.0982191i | 0.582643 | − | 0.812728i | \(-0.302019\pi\) |
−0.412522 | + | 0.910948i | \(0.635352\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.359886 | − | 0.623340i | −0.0125448 | − | 0.0217283i | 0.859685 | − | 0.510825i | \(-0.170660\pi\) |
−0.872230 | + | 0.489097i | \(0.837327\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.3555 | + | 6.78906i | 0.430164 | + | 0.236365i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 54.5578i | − | 1.89716i | −0.316536 | − | 0.948580i | \(-0.602520\pi\) | ||
0.316536 | − | 0.948580i | \(-0.397480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.08127 | − | 12.2651i | −0.245943 | − | 0.425985i | 0.716454 | − | 0.697635i | \(-0.245764\pi\) |
−0.962396 | + | 0.271650i | \(0.912431\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.31283 | + | 7.47003i | −0.149610 | + | 0.259133i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.8222 | − | 30.4970i | 0.652150 | − | 1.05666i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.2912 | − | 27.6989i | −0.979059 | − | 0.958560i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.28977 | − | 10.8942i | −0.217406 | − | 0.376559i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −56.3376 | −1.94499 | −0.972495 | − | 0.232923i | \(-0.925171\pi\) | ||||
−0.972495 | + | 0.232923i | \(0.925171\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.4952 | 0.603282 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.10299 | − | 1.91043i | −0.0379888 | − | 0.0657986i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.1359 | − | 10.3527i | 0.348687 | − | 0.356144i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.55891 | + | 9.96325i | 0.191006 | + | 0.342341i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.45939 | + | 12.9200i | −0.256006 | + | 0.443415i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.95897 | − | 10.3212i | −0.204271 | − | 0.353808i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.4627i | 0.597912i | 0.954267 | + | 0.298956i | \(0.0966384\pi\) | ||||
−0.954267 | + | 0.298956i | \(0.903362\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.18863 | + | 20.2174i | −0.177447 | + | 0.691419i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.2887 | + | 26.4809i | 0.522253 | + | 0.904569i | 0.999665 | + | 0.0258890i | \(0.00824165\pi\) |
−0.477412 | + | 0.878680i | \(0.658425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.81716 | + | 5.66794i | 0.334957 | + | 0.193388i | 0.658040 | − | 0.752983i | \(-0.271386\pi\) |
−0.323083 | + | 0.946371i | \(0.604719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.111189 | + | 7.57416i | −0.00378933 | + | 0.258127i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.1411 | + | 40.0815i | −0.787731 | + | 1.36439i | 0.139623 | + | 0.990205i | \(0.455411\pi\) |
−0.927354 | + | 0.374186i | \(0.877922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.22780 | − | 2.57751i | 0.313755 | − | 0.0876381i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.63704 | 0.225406 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 39.9744i | − | 1.35604i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.95249 | − | 6.84591i | −0.133925 | − | 0.231965i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.5077 | + | 35.5204i | −0.694080 | + | 1.20218i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.4377 | + | 8.14223i | −0.961371 | + | 0.275258i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.36155 | − | 11.0185i | 0.214814 | − | 0.372069i | −0.738401 | − | 0.674362i | \(-0.764419\pi\) |
0.953215 | + | 0.302293i | \(0.0977521\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −19.0558 | + | 11.0019i | −0.642737 | + | 0.371084i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0552i | 0.406152i | 0.979163 | + | 0.203076i | \(0.0650938\pi\) | ||||
−0.979163 | + | 0.203076i | \(0.934906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.49917i | 0.117757i | 0.998265 | + | 0.0588783i | \(0.0187524\pi\) | ||||
−0.998265 | + | 0.0588783i | \(0.981248\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.3717 | + | 5.13158i | −0.617557 | + | 0.172496i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.9355 | + | 24.2115i | 1.40806 | + | 0.812941i | 0.995201 | − | 0.0978559i | \(-0.0311984\pi\) |
0.412855 | + | 0.910797i | \(0.364532\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.6714 | − | 31.2706i | 0.626218 | − | 1.04878i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.99387 | + | 15.5778i | −0.301306 | + | 0.521877i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.2623 | − | 21.2389i | −0.410341 | − | 0.710731i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.7288 | + | 7.62966i | 0.993723 | + | 0.255031i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 12.8874i | − | 0.430297i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.35677 | + | 5.40214i | −0.312066 | + | 0.180171i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.9744 | + | 25.9364i | −0.498868 | + | 0.864066i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.0251502 | − | 1.71322i | 0.000836946 | − | 0.0570122i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.7055 | + | 15.0200i | −0.488828 | + | 0.499281i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.7875 | + | 13.1563i | −0.756645 | + | 0.436849i | −0.828090 | − | 0.560595i | \(-0.810572\pi\) |
0.0714447 | + | 0.997445i | \(0.477239\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −29.8432 | −0.989836 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1244i | 1.09746i | 0.836000 | + | 0.548730i | \(0.184889\pi\) | ||||
−0.836000 | + | 0.548730i | \(0.815111\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.53874 | + | 2.66518i | 0.0509250 | + | 0.0882047i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.4023 | − | 13.6889i | 0.443066 | − | 0.452541i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.6324 | − | 12.0696i | 0.714366 | − | 0.398574i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.7579 | + | 7.94310i | 0.453830 | + | 0.262019i | 0.709446 | − | 0.704759i | \(-0.248945\pi\) |
−0.255616 | + | 0.966778i | \(0.582278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.57766 | − | 4.46464i | −0.0849368 | − | 0.147115i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −31.5041 | −1.03697 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.45626 | + | 4.09703i | 0.245160 | + | 0.134710i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.327887 | − | 0.189306i | 0.0107692 | − | 0.00621762i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.4594 | + | 6.61609i | 0.375971 | + | 0.217067i | 0.676064 | − | 0.736843i | \(-0.263684\pi\) |
−0.300093 | + | 0.953910i | \(0.597018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.773145 | + | 26.3274i | −0.0253388 | + | 0.862847i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.31940 | − | 5.74936i | 0.108672 | − | 0.188226i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0514 | − | 43.1453i | −0.394122 | − | 1.41100i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.6731 | 0.381345 | 0.190672 | − | 0.981654i | \(-0.438933\pi\) | ||||
0.190672 | + | 0.981654i | \(0.438933\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.42756 | −0.242389 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.6649 | + | 44.4529i | 0.836652 | + | 1.44912i | 0.892679 | + | 0.450694i | \(0.148823\pi\) |
−0.0560269 | + | 0.998429i | \(0.517843\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.1021 | + | 13.9154i | 0.784874 | + | 0.453147i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.95442 | + | 22.5923i | 0.193697 | + | 0.734927i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0314 | + | 9.25574i | 0.520951 | + | 0.300771i | 0.737324 | − | 0.675540i | \(-0.236089\pi\) |
−0.216373 | + | 0.976311i | \(0.569423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.4707 | + | 6.62262i | −0.372355 | + | 0.214979i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.1050 | 0.781657 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.91838i | 0.126929i | 0.997984 | + | 0.0634643i | \(0.0202149\pi\) | ||||
−0.997984 | + | 0.0634643i | \(0.979785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −38.4559 | + | 10.7415i | −1.24440 | + | 0.347588i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.28237 | − | 4.78183i | −0.267731 | − | 0.154575i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.723955 | − | 49.3154i | 0.0233777 | − | 1.59248i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.4268 | − | 18.0598i | 0.336349 | − | 0.582573i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.43377 | − | 1.98249i | 0.110652 | − | 0.0638847i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.7108 | + | 49.5273i | −0.409175 | + | 1.59434i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.1423 | −0.808522 | −0.404261 | − | 0.914644i | \(-0.632471\pi\) | ||||
−0.404261 | + | 0.914644i | \(0.632471\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0209 | + | 6.94024i | −0.386165 | + | 0.222953i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.10368 | + | 2.36926i | 0.131693 | + | 0.0760332i | 0.564399 | − | 0.825502i | \(-0.309108\pi\) |
−0.432706 | + | 0.901535i | \(0.642441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.2439 | − | 6.11654i | −0.328404 | − | 0.196087i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.76742 | + | 7.86814i | 0.152680 | + | 0.251982i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.73355 | − | 2.15557i | 0.119447 | − | 0.0689628i | −0.439086 | − | 0.898445i | \(-0.644698\pi\) |
0.558533 | + | 0.829482i | \(0.311364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.07242i | 0.0981950i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 38.8754i | − | 1.24119i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −44.5474 | + | 25.7195i | −1.42084 | + | 0.820324i | −0.996371 | − | 0.0851174i | \(-0.972873\pi\) |
−0.424472 | + | 0.905441i | \(0.639540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.3824 | − | 21.8396i | 0.681299 | − | 0.695868i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.6685 | − | 6.37007i | −0.339583 | − | 0.202762i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5.45172 | − | 3.14755i | −0.173355 | − | 0.100086i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.3827 | + | 8.88120i | −0.488647 | + | 0.282120i | −0.724013 | − | 0.689786i | \(-0.757704\pi\) |
0.235366 | + | 0.971907i | \(0.424371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.188619 | 0.00598565 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49.6025 | + | 12.7301i | 1.57250 | + | 0.403571i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1923 | − | 13.9674i | 0.766177 | − | 0.442353i | −0.0653318 | − | 0.997864i | \(-0.520811\pi\) |
0.831509 | + | 0.555511i | \(0.187477\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.35987 | − | 5.81947i | 0.106302 | − | 0.184120i |
(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 | 1120.2.bq.b.719.18 | 80 | ||
4.3 | odd | 2 | 280.2.ba.b.19.10 | yes | 80 | ||
5.4 | even | 2 | inner | 1120.2.bq.b.719.24 | 80 | ||
7.3 | odd | 6 | inner | 1120.2.bq.b.1039.23 | 80 | ||
8.3 | odd | 2 | inner | 1120.2.bq.b.719.17 | 80 | ||
8.5 | even | 2 | 280.2.ba.b.19.5 | ✓ | 80 | ||
20.19 | odd | 2 | 280.2.ba.b.19.31 | yes | 80 | ||
28.3 | even | 6 | 280.2.ba.b.59.36 | yes | 80 | ||
35.24 | odd | 6 | inner | 1120.2.bq.b.1039.17 | 80 | ||
40.19 | odd | 2 | inner | 1120.2.bq.b.719.23 | 80 | ||
40.29 | even | 2 | 280.2.ba.b.19.36 | yes | 80 | ||
56.3 | even | 6 | inner | 1120.2.bq.b.1039.24 | 80 | ||
56.45 | odd | 6 | 280.2.ba.b.59.31 | yes | 80 | ||
140.59 | even | 6 | 280.2.ba.b.59.5 | yes | 80 | ||
280.59 | even | 6 | inner | 1120.2.bq.b.1039.18 | 80 | ||
280.269 | odd | 6 | 280.2.ba.b.59.10 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.ba.b.19.5 | ✓ | 80 | 8.5 | even | 2 | ||
280.2.ba.b.19.10 | yes | 80 | 4.3 | odd | 2 | ||
280.2.ba.b.19.31 | yes | 80 | 20.19 | odd | 2 | ||
280.2.ba.b.19.36 | yes | 80 | 40.29 | even | 2 | ||
280.2.ba.b.59.5 | yes | 80 | 140.59 | even | 6 | ||
280.2.ba.b.59.10 | yes | 80 | 280.269 | odd | 6 | ||
280.2.ba.b.59.31 | yes | 80 | 56.45 | odd | 6 | ||
280.2.ba.b.59.36 | yes | 80 | 28.3 | even | 6 | ||
1120.2.bq.b.719.17 | 80 | 8.3 | odd | 2 | inner | ||
1120.2.bq.b.719.18 | 80 | 1.1 | even | 1 | trivial | ||
1120.2.bq.b.719.23 | 80 | 40.19 | odd | 2 | inner | ||
1120.2.bq.b.719.24 | 80 | 5.4 | even | 2 | inner | ||
1120.2.bq.b.1039.17 | 80 | 35.24 | odd | 6 | inner | ||
1120.2.bq.b.1039.18 | 80 | 280.59 | even | 6 | inner | ||
1120.2.bq.b.1039.23 | 80 | 7.3 | odd | 6 | inner | ||
1120.2.bq.b.1039.24 | 80 | 56.3 | even | 6 | inner |