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 | 719.7 | ||
Character | \(\chi\) | \(=\) | 1120.719 |
Dual form | 1120.2.bq.b.1039.7 |
$q$-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 | ||||||||
\(3\) | −1.13535 | − | 1.96648i | −0.655495 | − | 1.13535i | −0.981769 | − | 0.190075i | \(-0.939127\pi\) |
0.326275 | − | 0.945275i | \(-0.394207\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.406539 | − | 2.19880i | 0.181810 | − | 0.983334i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.551936 | + | 2.58754i | −0.208612 | + | 0.977998i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.07804 | + | 1.86722i | −0.359347 | + | 0.622407i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.454564 | + | 0.787328i | 0.137056 | + | 0.237388i | 0.926381 | − | 0.376587i | \(-0.122903\pi\) |
−0.789325 | + | 0.613976i | \(0.789569\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.66349i | 1.57077i | 0.619007 | + | 0.785385i | \(0.287535\pi\) | ||||
−0.619007 | + | 0.785385i | \(0.712465\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.78547 | + | 1.69696i | −1.23560 | + | 0.438153i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.14931 | + | 5.45476i | 0.763819 | + | 1.32297i | 0.940869 | + | 0.338771i | \(0.110011\pi\) |
−0.177050 | + | 0.984202i | \(0.556655\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.966292 | + | 0.557889i | 0.221683 | + | 0.127989i | 0.606729 | − | 0.794909i | \(-0.292481\pi\) |
−0.385047 | + | 0.922897i | \(0.625815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.71500 | − | 1.85239i | 1.24712 | − | 0.404225i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.14508 | + | 1.98334i | −0.238766 | + | 0.413555i | −0.960360 | − | 0.278761i | \(-0.910076\pi\) |
0.721594 | + | 0.692316i | \(0.243410\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.66945 | − | 1.78780i | −0.933891 | − | 0.357559i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.91628 | −0.368789 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.21463i | 1.15403i | 0.816734 | + | 0.577014i | \(0.195782\pi\) | ||||
−0.816734 | + | 0.577014i | \(0.804218\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.41914 | + | 2.45801i | 0.254884 | + | 0.441472i | 0.964864 | − | 0.262750i | \(-0.0846293\pi\) |
−0.709980 | + | 0.704222i | \(0.751296\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.03218 | − | 1.78779i | 0.179679 | − | 0.311214i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.46510 | + | 2.26553i | 0.923771 | + | 0.382945i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.789609 | + | 1.36764i | −0.129811 | + | 0.224839i | −0.923603 | − | 0.383350i | \(-0.874770\pi\) |
0.793792 | + | 0.608189i | \(0.208104\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.1372 | − | 6.43005i | 1.78337 | − | 1.02963i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.163067i | 0.0254668i | 0.999919 | + | 0.0127334i | \(0.00405327\pi\) | ||||
−0.999919 | + | 0.0127334i | \(0.995947\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.29346i | − | 1.26474i | −0.774666 | − | 0.632370i | \(-0.782082\pi\) | ||
0.774666 | − | 0.632370i | \(-0.217918\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.66738 | + | 3.12950i | 0.546701 | + | 0.466518i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.56191 | + | 4.94322i | 1.24888 | + | 0.721043i | 0.970887 | − | 0.239540i | \(-0.0769965\pi\) |
0.277996 | + | 0.960582i | \(0.410330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.39073 | − | 2.85631i | −0.912962 | − | 0.408045i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.15113 | − | 12.3861i | 1.00136 | − | 1.73440i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.56505 | − | 4.44280i | −0.352337 | − | 0.610266i | 0.634321 | − | 0.773070i | \(-0.281280\pi\) |
−0.986659 | + | 0.162803i | \(0.947946\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.91598 | − | 0.679417i | 0.258350 | − | 0.0916125i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.53360i | − | 0.335583i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.97768 | + | 5.76061i | −1.29898 | + | 0.749968i | −0.980228 | − | 0.197869i | \(-0.936598\pi\) |
−0.318754 | + | 0.947837i | \(0.603264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.977217 | − | 1.69259i | 0.125120 | − | 0.216714i | −0.796660 | − | 0.604428i | \(-0.793402\pi\) |
0.921780 | + | 0.387714i | \(0.126735\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.23650 | − | 3.82006i | −0.533749 | − | 0.481283i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.4529 | + | 2.30243i | 1.54459 | + | 0.285581i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.09472 | − | 3.51879i | 0.744589 | − | 0.429889i | −0.0791464 | − | 0.996863i | \(-0.525219\pi\) |
0.823735 | + | 0.566974i | \(0.191886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.20028 | 0.626040 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.811490i | 0.0963061i | 0.998840 | + | 0.0481531i | \(0.0153335\pi\) | ||||
−0.998840 | + | 0.0481531i | \(0.984666\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.54031 | − | 7.86404i | −0.531403 | − | 0.920417i | −0.999328 | − | 0.0366487i | \(-0.988332\pi\) |
0.467925 | − | 0.883768i | \(-0.345002\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.78579 | + | 11.2122i | 0.206206 | + | 1.29467i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.28813 | + | 0.741649i | −0.260757 | + | 0.0845187i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.82237 | + | 5.67095i | 1.10510 | + | 0.638031i | 0.937557 | − | 0.347833i | \(-0.113082\pi\) |
0.167546 | + | 0.985864i | \(0.446416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.40978 | + | 9.37001i | 0.601086 | + | 1.04111i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.80839 | −0.857082 | −0.428541 | − | 0.903522i | \(-0.640972\pi\) | ||||
−0.428541 | + | 0.903522i | \(0.640972\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.2742 | − | 4.70713i | 1.43979 | − | 0.510560i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.2210 | − | 7.05578i | 1.31023 | − | 0.756459i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.4104 | + | 7.16517i | 1.31550 | + | 0.759506i | 0.983002 | − | 0.183597i | \(-0.0587740\pi\) |
0.332502 | + | 0.943103i | \(0.392107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.6545 | − | 3.12589i | −1.53621 | − | 0.327682i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.22243 | − | 5.58142i | 0.334151 | − | 0.578766i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.61952 | − | 1.89788i | 0.166159 | − | 0.194718i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.99774 | −1.01512 | −0.507558 | − | 0.861618i | \(-0.669452\pi\) | ||||
−0.507558 | + | 0.861618i | \(0.669452\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.96016 | −0.197003 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.69267 | + | 15.0562i | 0.864953 | + | 1.49814i | 0.867093 | + | 0.498146i | \(0.165985\pi\) |
−0.00214005 | + | 0.999998i | \(0.500681\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.56602 | − | 0.904144i | −0.154305 | − | 0.0890880i | 0.420859 | − | 0.907126i | \(-0.361729\pi\) |
−0.575164 | + | 0.818038i | \(0.695062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.74967 | − | 13.3192i | −0.170751 | − | 1.29982i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.08558 | + | 1.78146i | 0.298294 | + | 0.172220i | 0.641676 | − | 0.766976i | \(-0.278239\pi\) |
−0.343382 | + | 0.939196i | \(0.611573\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.72947 | − | 0.998508i | 0.165653 | − | 0.0956398i | −0.414882 | − | 0.909875i | \(-0.636177\pi\) |
0.580534 | + | 0.814236i | \(0.302844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.58593 | 0.340361 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 13.5251i | − | 1.27234i | −0.771551 | − | 0.636168i | \(-0.780519\pi\) | ||
0.771551 | − | 0.636168i | \(-0.219481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.89545 | + | 3.32411i | 0.363253 | + | 0.309975i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.5750 | − | 6.10548i | −0.977659 | − | 0.564452i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.8526 | + | 5.13828i | −1.45321 | + | 0.471025i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.08674 | − | 8.81050i | 0.462431 | − | 0.800954i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.320669 | − | 0.185138i | 0.0289137 | − | 0.0166933i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.82932 | + | 9.54039i | −0.521390 | + | 0.853318i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.34956 | −0.119754 | −0.0598772 | − | 0.998206i | \(-0.519071\pi\) | ||||
−0.0598772 | + | 0.998206i | \(0.519071\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.3090 | + | 9.41598i | −1.43592 | + | 0.829031i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.08950 | + | 4.09312i | 0.619412 | + | 0.357618i | 0.776640 | − | 0.629944i | \(-0.216922\pi\) |
−0.157228 | + | 0.987562i | \(0.550256\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.97689 | + | 2.19240i | −0.171418 | + | 0.190105i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.779044 | + | 4.21353i | −0.0670494 | + | 0.362643i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.43159 | + | 2.55858i | −0.378616 | + | 0.218594i | −0.677216 | − | 0.735784i | \(-0.736814\pi\) |
0.298600 | + | 0.954378i | \(0.403480\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.9166i | 1.51967i | 0.650117 | + | 0.759834i | \(0.274720\pi\) | ||||
−0.650117 | + | 0.759834i | \(0.725280\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 22.4491i | − | 1.89056i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.45903 | + | 2.57442i | −0.372883 | + | 0.215284i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.6647 | + | 2.52649i | 1.13479 | + | 0.209813i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.63883 | + | 15.8102i | 0.135168 | + | 1.30400i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.16993 | − | 3.56221i | −0.505460 | − | 0.291827i | 0.225505 | − | 0.974242i | \(-0.427597\pi\) |
−0.730965 | + | 0.682414i | \(0.760930\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.46560 | + | 1.42352i | −0.200648 | + | 0.115844i | −0.596958 | − | 0.802273i | \(-0.703624\pi\) |
0.396310 | + | 0.918117i | \(0.370291\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.5803 | −1.09790 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.98162 | − | 2.12112i | 0.480455 | − | 0.170372i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4030 | + | 6.58353i | −0.910059 | + | 0.525423i | −0.880450 | − | 0.474139i | \(-0.842760\pi\) |
−0.0296091 | + | 0.999562i | \(0.509426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.82447 | + | 10.0883i | −0.461911 | + | 0.800053i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.49996 | − | 4.05762i | −0.354647 | − | 0.319785i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.9075 | + | 8.60684i | 1.16764 | + | 0.674139i | 0.953124 | − | 0.302580i | \(-0.0978480\pi\) |
0.214520 | + | 0.976720i | \(0.431181\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.51137 | − | 2.99636i | −0.273360 | − | 0.233266i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.285811i | 0.0221167i | 0.999939 | + | 0.0110584i | \(0.00352006\pi\) | ||||
−0.999939 | + | 0.0110584i | \(0.996480\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.0752 | −1.46732 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.08341 | + | 1.20285i | −0.159322 | + | 0.0919846i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.6842 | + | 9.63264i | 1.26848 | + | 0.732356i | 0.974700 | − | 0.223518i | \(-0.0717541\pi\) |
0.293778 | + | 0.955874i | \(0.405087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.20323 | − | 11.0956i | 0.544513 | − | 0.838752i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.6563 | + | 13.0806i | 1.70295 | + | 0.983200i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.701703 | − | 1.21539i | −0.0524478 | − | 0.0908422i | 0.838610 | − | 0.544733i | \(-0.183369\pi\) |
−0.891057 | + | 0.453891i | \(0.850036\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3818 | −1.14332 | −0.571660 | − | 0.820491i | \(-0.693700\pi\) | ||||
−0.571660 | + | 0.820491i | \(0.693700\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.43794 | −0.328062 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.68617 | + | 2.29219i | 0.197491 | + | 0.168525i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.86312 | + | 4.95908i | −0.209372 | + | 0.362644i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.05767 | − | 4.95847i | 0.0769339 | − | 0.360675i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.4587 | − | 11.2345i | −1.40798 | − | 0.812898i | −0.412787 | − | 0.910828i | \(-0.635444\pi\) |
−0.995193 | + | 0.0979302i | \(0.968778\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3435 | − | 8.28125i | 1.03247 | − | 0.596097i | 0.114779 | − | 0.993391i | \(-0.463384\pi\) |
0.917691 | + | 0.397294i | \(0.130051\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.61071 | − | 27.1025i | −0.688237 | − | 1.94085i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.1344 | −1.14953 | −0.574765 | − | 0.818318i | \(-0.694907\pi\) | ||||
−0.574765 | + | 0.818318i | \(0.694907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9134 | − | 18.9025i | −0.773629 | − | 1.33996i | −0.935562 | − | 0.353163i | \(-0.885106\pi\) |
0.161933 | − | 0.986802i | \(-0.448227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.8393 | − | 7.99012i | −0.976149 | − | 0.563580i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0806 | − | 3.43008i | −1.12864 | − | 0.240744i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.358552 | + | 0.0662930i | 0.0250423 | + | 0.00463011i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.46889 | − | 4.27624i | −0.171600 | − | 0.297219i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.01439i | 0.0701665i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.76612 | 0.672328 | 0.336164 | − | 0.941804i | \(-0.390870\pi\) | ||||
0.336164 | + | 0.941804i | \(0.390870\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.59578 | − | 0.921325i | 0.109341 | − | 0.0631282i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.2357 | − | 3.37161i | −1.24366 | − | 0.229942i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.14348 | + | 2.31540i | −0.484931 | + | 0.157180i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.3097 | + | 17.8569i | −0.696664 | + | 1.20666i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −30.8930 | + | 17.8361i | −2.07809 | + | 1.19978i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.6951i | 1.18495i | 0.805589 | + | 0.592474i | \(0.201849\pi\) | ||||
−0.805589 | + | 0.592474i | \(0.798151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.37207 | − | 6.79159i | 0.558138 | − | 0.452772i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.76537 | − | 15.1821i | −0.581778 | − | 1.00767i | −0.995269 | − | 0.0971611i | \(-0.969024\pi\) |
0.413490 | − | 0.910509i | \(-0.364310\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.45967 | − | 5.99232i | 0.228621 | − | 0.395984i | −0.728778 | − | 0.684750i | \(-0.759912\pi\) |
0.957400 | + | 0.288766i | \(0.0932449\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.05627 | + | 3.65755i | 0.266883 | + | 0.240649i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.78953 | − | 2.18788i | −0.248260 | − | 0.143333i | 0.370707 | − | 0.928750i | \(-0.379115\pi\) |
−0.618967 | + | 0.785417i | \(0.712449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.3499 | − | 16.8163i | 0.936084 | − | 1.09698i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 25.7540i | − | 1.67291i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.1535i | 0.915511i | 0.889078 | + | 0.457756i | \(0.151347\pi\) | ||||
−0.889078 | + | 0.457756i | \(0.848653\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.4126 | − | 7.74379i | 0.863984 | − | 0.498821i | −0.00136057 | − | 0.999999i | \(-0.500433\pi\) |
0.865344 | + | 0.501178i | \(0.167100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.40956 | − | 16.2978i | 0.603624 | − | 1.04551i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.87855 | + | 12.8907i | −0.567229 | + | 0.823560i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.15960 | + | 5.47259i | −0.201041 | + | 0.348213i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.86526 | + | 15.3551i | 0.561813 | + | 0.973088i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 6.13020i | − | 0.386935i | −0.981107 | − | 0.193467i | \(-0.938027\pi\) | ||
0.981107 | − | 0.193467i | \(-0.0619734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.08205 | −0.130898 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −24.3274 | − | 20.7594i | −1.52344 | − | 1.30000i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.21050 | − | 5.56075i | 0.200266 | − | 0.346870i | −0.748348 | − | 0.663306i | \(-0.769153\pi\) |
0.948614 | + | 0.316436i | \(0.102486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.10302 | − | 2.79800i | −0.192812 | − | 0.173859i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −11.6041 | − | 6.69962i | −0.718275 | − | 0.414696i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.23009 | + | 5.59468i | 0.199176 | + | 0.344983i | 0.948261 | − | 0.317491i | \(-0.102840\pi\) |
−0.749086 | + | 0.662473i | \(0.769507\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.8116 | + | 3.83387i | −0.664154 | + | 0.235513i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 32.5399i | − | 1.99141i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.755340 | − | 1.30829i | −0.0460539 | − | 0.0797677i | 0.842080 | − | 0.539353i | \(-0.181331\pi\) |
−0.888133 | + | 0.459586i | \(0.847998\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.66274 | − | 15.0043i | 0.526224 | − | 0.911447i | −0.473309 | − | 0.880896i | \(-0.656941\pi\) |
0.999533 | − | 0.0305504i | \(-0.00972602\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.4910 | + | 32.3669i | 0.634945 | + | 1.95893i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.714984 | − | 4.48906i | −0.0431152 | − | 0.270701i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.77685 | + | 10.0058i | 0.347097 | + | 0.601190i | 0.985733 | − | 0.168319i | \(-0.0538340\pi\) |
−0.638635 | + | 0.769510i | \(0.720501\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.11954 | −0.366368 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.6526 | 0.993408 | 0.496704 | − | 0.867920i | \(-0.334543\pi\) | ||||
0.496704 | + | 0.867920i | \(0.334543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3769 | + | 19.7053i | 0.676285 | + | 1.17136i | 0.976091 | + | 0.217360i | \(0.0697447\pi\) |
−0.299806 | + | 0.954000i | \(0.596922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.57088 | − | 1.03001i | −0.329990 | − | 0.0610123i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.421942 | − | 0.0900025i | −0.0249065 | − | 0.00531268i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.3363 | + | 19.6350i | −0.666839 | + | 1.15500i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.3509 | + | 19.6604i | 0.665404 | + | 1.15251i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.66311i | − | 0.506104i | −0.967453 | − | 0.253052i | \(-0.918566\pi\) | ||
0.967453 | − | 0.253052i | \(-0.0814344\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.61013 | + | 24.2808i | 0.501301 | + | 1.41368i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.871075 | − | 1.50875i | −0.0505449 | − | 0.0875463i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.2326 | − | 6.48516i | −0.649600 | − | 0.375047i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.4597 | + | 4.57746i | 1.23691 | + | 0.263840i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.7385 | − | 34.1880i | 1.13395 | − | 1.96405i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.32439 | − | 2.83681i | −0.190354 | − | 0.162435i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.6862 | −0.666967 | −0.333484 | − | 0.942756i | \(-0.608224\pi\) | ||||
−0.333484 | + | 0.942756i | \(0.608224\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.10608i | 0.233587i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.66670 | + | 9.81500i | 0.321329 | + | 0.556558i | 0.980762 | − | 0.195205i | \(-0.0625372\pi\) |
−0.659434 | + | 0.751763i | \(0.729204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7012 | + | 21.9992i | −0.717916 | + | 1.24347i | 0.243908 | + | 0.969798i | \(0.421570\pi\) |
−0.961824 | + | 0.273668i | \(0.911763\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.1219 | + | 7.76222i | −0.570302 | + | 0.437352i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9131 | − | 20.6342i | 0.669109 | − | 1.15893i | −0.309045 | − | 0.951048i | \(-0.600009\pi\) |
0.978154 | − | 0.207883i | \(-0.0666574\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.89295 | + | 2.82495i | −0.273953 | + | 0.158167i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 8.09033i | − | 0.451558i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.02785i | 0.391040i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1252 | − | 26.4454i | 0.561643 | − | 1.46693i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.92710 | − | 2.26731i | −0.217169 | − | 0.125383i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −17.5164 | + | 19.4259i | −0.965711 | + | 1.07099i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.35173 | − | 4.07331i | 0.129263 | − | 0.223889i | −0.794129 | − | 0.607750i | \(-0.792072\pi\) |
0.923391 | + | 0.383861i | \(0.125406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.70246 | − | 2.94875i | −0.0932943 | − | 0.161590i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.25938 | − | 14.8316i | −0.287351 | − | 0.810337i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.0355i | − | 0.546669i | −0.961919 | − | 0.273335i | \(-0.911873\pi\) | ||
0.961919 | − | 0.273335i | \(-0.0881267\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −26.5969 | + | 15.3557i | −1.44455 | + | 0.834009i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.29018 | + | 2.23465i | −0.0698670 | + | 0.121013i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.9181 | − | 14.9598i | 0.589522 | − | 0.807752i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.11411 | − | 11.4344i | 0.113820 | − | 0.615606i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.86288 | + | 3.96228i | −0.368418 | + | 0.212706i | −0.672767 | − | 0.739854i | \(-0.734894\pi\) |
0.304349 | + | 0.952561i | \(0.401561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.06729 | −0.324775 | −0.162387 | − | 0.986727i | \(-0.551919\pi\) | ||||
−0.162387 | + | 0.986727i | \(0.551919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 10.8529i | − | 0.579283i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3298 | + | 30.0161i | 0.922371 | + | 1.59759i | 0.795735 | + | 0.605644i | \(0.207085\pi\) |
0.126636 | + | 0.991949i | \(0.459582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.78430 | + | 0.329902i | 0.0947010 | + | 0.0175094i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 28.1026 | + | 25.3402i | 1.48735 | + | 1.34115i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.46664 | + | 2.57881i | 0.235740 | + | 0.136105i | 0.613217 | − | 0.789914i | \(-0.289875\pi\) |
−0.377477 | + | 0.926019i | \(0.623208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.87752 | − | 15.3763i | −0.467238 | − | 0.809280i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −23.1009 | −1.21248 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.1373 | + | 6.78619i | −1.00169 | + | 0.355206i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5217 | − | 7.22938i | 0.653625 | − | 0.377371i | −0.136218 | − | 0.990679i | \(-0.543495\pi\) |
0.789844 | + | 0.613308i | \(0.210162\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.304482 | − | 0.175793i | −0.0158507 | − | 0.00915141i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.9117 | − | 4.18504i | 0.670341 | − | 0.217276i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.13591 | + | 5.43156i | −0.162372 | + | 0.281236i | −0.935719 | − | 0.352747i | \(-0.885248\pi\) |
0.773347 | + | 0.633983i | \(0.218581\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.3793 | + | 0.631584i | 1.31058 | + | 0.0326148i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −35.1965 | −1.81271 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.4959 | 1.25827 | 0.629135 | − | 0.777296i | \(-0.283409\pi\) | ||||
0.629135 | + | 0.777296i | \(0.283409\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.53223 | + | 2.65390i | 0.0784984 | + | 0.135963i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.48398 | − | 4.32088i | −0.382413 | − | 0.220786i | 0.296454 | − | 0.955047i | \(-0.404196\pi\) |
−0.678868 | + | 0.734261i | \(0.737529\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.700523 | + | 5.33266i | 0.0357019 | + | 0.271778i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.4857 | + | 8.94069i | 0.787184 | + | 0.454481i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.34342 | + | 4.81708i | −0.423028 | + | 0.244235i | −0.696372 | − | 0.717681i | \(-0.745204\pi\) |
0.273344 | + | 0.961916i | \(0.411870\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.4249 | −0.729496 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 18.5885i | − | 0.937667i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.4625 | − | 19.2920i | 0.828316 | − | 0.970685i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5336 | + | 7.81361i | 0.679230 | + | 0.392154i | 0.799565 | − | 0.600580i | \(-0.205063\pi\) |
−0.120335 | + | 0.992733i | \(0.538397\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.55579 | + | 1.39838i | 0.328200 | + | 0.0700068i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4230 | + | 23.2493i | −0.670311 | + | 1.16101i | 0.307505 | + | 0.951546i | \(0.400506\pi\) |
−0.977816 | + | 0.209466i | \(0.932827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.9209 | + | 8.03726i | −0.693452 | + | 0.400365i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.8021 | − | 8.08575i | 1.13304 | − | 0.401784i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.43571 | −0.0711656 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.54259 | − | 5.50941i | 0.471850 | − | 0.272423i | −0.245164 | − | 0.969482i | \(-0.578842\pi\) |
0.717014 | + | 0.697059i | \(0.245508\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0628 | + | 5.80976i | 0.496362 | + | 0.286574i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.39878 | − | 28.9971i | −0.462484 | − | 1.42686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.17441 | + | 17.1691i | −0.155826 | + | 0.842797i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.2327 | − | 20.3416i | 1.72536 | − | 0.996134i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.97226i | 0.291764i | 0.989302 | + | 0.145882i | \(0.0466020\pi\) | ||||
−0.989302 | + | 0.145882i | \(0.953398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 20.0534i | − | 0.977344i | −0.872468 | − | 0.488672i | \(-0.837482\pi\) | ||
0.872468 | − | 0.488672i | \(-0.162518\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −18.4602 | + | 10.6580i | −0.897564 | + | 0.518209i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.95354 | − | 31.1010i | −0.240282 | − | 1.50862i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.84028 | + | 3.46279i | 0.185844 | + | 0.167576i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.1251 | + | 5.84574i | 0.488845 | + | 0.282235i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.7452 | + | 12.5546i | −1.04743 | + | 0.604734i | −0.921929 | − | 0.387359i | \(-0.873387\pi\) |
−0.125501 | + | 0.992093i | \(0.540054\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.4250 | 0.741276 | 0.370638 | − | 0.928777i | \(-0.379139\pi\) | ||||
0.370638 | + | 0.928777i | \(0.379139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.5460 | − | 29.7399i | −0.505640 | − | 1.42592i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.21297 | + | 1.27766i | −0.105861 | + | 0.0611186i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.54597 | − | 14.8021i | 0.407877 | − | 0.706464i | −0.586775 | − | 0.809750i | \(-0.699603\pi\) |
0.994652 | + | 0.103287i | \(0.0329359\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.2228 | − | 8.85369i | 0.582040 | − | 0.421605i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.3644 | + | 19.8403i | 1.63270 | + | 0.942640i | 0.983256 | + | 0.182231i | \(0.0583320\pi\) |
0.649445 | + | 0.760409i | \(0.275001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.8001 | − | 24.3752i | 0.986019 | − | 1.15549i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.1774i | 0.765166i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.32288 | −0.345588 | −0.172794 | − | 0.984958i | \(-0.555279\pi\) | ||||
−0.172794 | + | 0.984958i | \(0.555279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.128387 | + | 0.0741244i | −0.00604552 | + | 0.00349038i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.59865 | + | 3.23238i | 0.263048 | + | 0.151871i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.8308 | + | 30.9516i | −0.601519 | + | 1.45103i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.0598 | − | 12.1589i | −0.985137 | − | 0.568769i | −0.0813202 | − | 0.996688i | \(-0.525914\pi\) |
−0.903817 | + | 0.427919i | \(0.859247\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.03497 | − | 10.4529i | −0.281688 | − | 0.487898i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.3772 | 0.762764 | 0.381382 | − | 0.924417i | \(-0.375448\pi\) | ||||
0.381382 | + | 0.924417i | \(0.375448\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.64446 | −0.0764246 | −0.0382123 | − | 0.999270i | \(-0.512166\pi\) | ||||
−0.0382123 | + | 0.999270i | \(0.512166\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.9624 | − | 9.35455i | −0.508368 | − | 0.433807i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.96501 | − | 13.7958i | 0.368577 | − | 0.638393i | −0.620767 | − | 0.783995i | \(-0.713179\pi\) |
0.989343 | + | 0.145602i | \(0.0465119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.74112 | + | 17.7125i | 0.265100 | + | 0.817887i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.8928 | + | 14.9492i | 1.19308 | + | 0.688824i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.52967 | − | 3.76991i | 0.300235 | − | 0.173341i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.51466 | − | 4.33257i | −0.161264 | − | 0.198792i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.0609 | 0.506445 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.4844 | + | 23.3556i | 0.616116 | + | 1.06714i | 0.990188 | + | 0.139745i | \(0.0446282\pi\) |
−0.374071 | + | 0.927400i | \(0.622038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.74563 | − | 4.47194i | −0.353170 | − | 0.203903i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.87022 | + | 13.4559i | −0.130599 | + | 0.612266i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.06447 | + | 21.9830i | −0.184558 | + | 0.998198i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.04240 | − | 10.4658i | −0.273808 | − | 0.474249i | 0.696026 | − | 0.718017i | \(-0.254950\pi\) |
−0.969834 | + | 0.243768i | \(0.921616\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 39.0871i | − | 1.76758i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.7339 | −0.845450 | −0.422725 | − | 0.906258i | \(-0.638926\pi\) | ||||
−0.422725 | + | 0.906258i | \(0.638926\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −33.8993 | + | 19.5718i | −1.52675 | + | 0.881468i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.796879 | + | 4.30999i | −0.0358171 | + | 0.193720i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.09976 | − | 0.447890i | −0.0941872 | − | 0.0200906i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.4806 | + | 21.6171i | −0.558710 | + | 0.967714i | 0.438895 | + | 0.898539i | \(0.355370\pi\) |
−0.997605 | + | 0.0691754i | \(0.977963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.562043 | − | 0.324496i | 0.0251102 | − | 0.0144974i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 13.3328i | − | 0.594481i | −0.954803 | − | 0.297241i | \(-0.903934\pi\) | ||
0.954803 | − | 0.297241i | \(-0.0960663\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.6394 | − | 12.9926i | 1.63043 | − | 0.578161i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.6570 | + | 37.5110i | 0.961821 | + | 1.66592i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.32935 | + | 5.76661i | −0.147571 | + | 0.255600i | −0.930329 | − | 0.366726i | \(-0.880479\pi\) |
0.782758 | + | 0.622326i | \(0.213812\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.8545 | − | 7.40778i | 1.01102 | − | 0.327701i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.85169 | − | 1.06907i | −0.0817542 | − | 0.0472008i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.62468 | + | 3.07580i | −0.115657 | + | 0.135536i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.98804i | 0.395294i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 43.7457i | − | 1.92022i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.14654 | − | 3.54871i | 0.269285 | − | 0.155472i | −0.359278 | − | 0.933231i | \(-0.616977\pi\) |
0.628563 | + | 0.777759i | \(0.283644\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.40071 | − | 14.5505i | 0.367337 | − | 0.636247i | −0.621811 | − | 0.783167i | \(-0.713603\pi\) |
0.989148 | + | 0.146920i | \(0.0469361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −29.9976 | − | 1.56759i | −1.30920 | − | 0.0684155i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.93858 | + | 15.4821i | −0.389371 | + | 0.674410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.87758 | + | 15.3764i | 0.385982 | + | 0.668540i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 24.8407i | − | 1.07800i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.923529 | −0.0400025 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.17148 | − | 6.06034i | 0.223583 | − | 0.262012i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.59336 | + | 2.75978i | −0.0687585 | + | 0.119093i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.656142 | − | 6.32998i | −0.0282621 | − | 0.272652i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2808 | + | 8.24501i | 0.613979 | + | 0.354481i | 0.774521 | − | 0.632548i | \(-0.217991\pi\) |
−0.160542 | + | 0.987029i | \(0.551324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.4637 | + | 30.2481i | 0.749441 | + | 1.29807i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.49243 | − | 4.20869i | −0.0639285 | − | 0.180280i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.86184i | 0.207877i | 0.994584 | + | 0.103939i | \(0.0331446\pi\) | ||||
−0.994584 | + | 0.103939i | \(0.966855\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.10696 | + | 3.64936i | 0.0899229 | + | 0.155751i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.46707 | + | 6.00515i | −0.147702 | + | 0.255828i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0951 | + | 22.2858i | −0.854532 | + | 0.947688i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.45782 | − | 7.88475i | 0.0618810 | − | 0.334689i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.4750 | + | 19.8753i | 0.486211 | + | 0.842142i | 0.999874 | − | 0.0158495i | \(-0.00504525\pi\) |
−0.513663 | + | 0.857992i | \(0.671712\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.9699 | 1.98662 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.0026 | 0.548970 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.57987 | + | 13.1287i | 0.319453 | + | 0.553309i | 0.980374 | − | 0.197146i | \(-0.0631674\pi\) |
−0.660921 | + | 0.750456i | \(0.729834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −29.7390 | − | 5.49848i | −1.25113 | − | 0.231323i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −27.2311 | + | 8.82638i | −1.14360 | + | 0.370673i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.815340 | − | 1.41221i | 0.0341808 | − | 0.0592030i | −0.848429 | − | 0.529309i | \(-0.822451\pi\) |
0.882610 | + | 0.470106i | \(0.155784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5826 | − | 30.4540i | −0.735811 | − | 1.27446i | −0.954367 | − | 0.298637i | \(-0.903468\pi\) |
0.218556 | − | 0.975824i | \(-0.429865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 51.0202i | 2.13140i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.89271 | − | 7.21394i | 0.370852 | − | 0.300842i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.78749 | + | 13.4883i | 0.324198 | + | 0.561527i | 0.981350 | − | 0.192231i | \(-0.0615724\pi\) |
−0.657152 | + | 0.753758i | \(0.728239\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.5699 | − | 18.8042i | −1.35356 | − | 0.781477i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.30973 | − | 20.2045i | 0.178798 | − | 0.838225i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.33196 | − | 4.03908i | 0.0965801 | − | 0.167282i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.7239 | + | 20.7702i | −0.732792 | + | 0.858742i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.6761 | −0.729572 | −0.364786 | − | 0.931091i | \(-0.618858\pi\) | ||||
−0.364786 | + | 0.931091i | \(0.618858\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.16688i | 0.130489i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.3182 | + | 31.7281i | 0.753511 | + | 1.30512i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.15344 | − | 7.19397i | 0.170561 | − | 0.295421i | −0.768055 | − | 0.640384i | \(-0.778775\pi\) |
0.938616 | + | 0.344963i | \(0.112109\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.85335 | + | 36.9457i | 0.198968 | + | 1.51463i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.7810 | + | 42.9220i | −1.01422 | + | 1.75668i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.64713 | − | 0.950974i | 0.0673001 | − | 0.0388557i | −0.465972 | − | 0.884799i | \(-0.654295\pi\) |
0.533272 | + | 0.845944i | \(0.320962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.61199i | − | 0.147336i | −0.997283 | − | 0.0736680i | \(-0.976529\pi\) | ||
0.997283 | − | 0.0736680i | \(-0.0234705\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.1736i | 0.617917i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.3046 | − | 14.7665i | −0.703531 | − | 0.600345i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1622 | − | 13.3727i | −0.940124 | − | 0.542781i | −0.0501251 | − | 0.998743i | \(-0.515962\pi\) |
−0.889999 | + | 0.455962i | \(0.849295\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.5119 | + | 35.5166i | 0.466487 | + | 1.43921i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −27.9959 | + | 48.4903i | −1.13259 | + | 1.96171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.16951 | − | 7.22180i | −0.168405 | − | 0.291686i | 0.769454 | − | 0.638702i | \(-0.220528\pi\) |
−0.937859 | + | 0.347016i | \(0.887195\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.276718 | − | 0.780352i | −0.0111583 | − | 0.0314668i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 24.3929i | − | 0.982021i | −0.871154 | − | 0.491011i | \(-0.836628\pi\) | ||
0.871154 | − | 0.491011i | \(-0.163372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.5991 | − | 20.5532i | 1.43085 | − | 0.826102i | 0.433664 | − | 0.901075i | \(-0.357220\pi\) |
0.997186 | + | 0.0749730i | \(0.0238870\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.19430 | − | 3.80064i | 0.0880543 | − | 0.152515i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.3899 | + | 28.1578i | −1.01723 | + | 1.12812i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.6076 | + | 16.6961i | 0.744303 | + | 0.667842i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.99477 | − | 1.15168i | 0.0796636 | − | 0.0459938i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.94688 | −0.396608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.0578i | − | 1.39563i | −0.716279 | − | 0.697814i | \(-0.754156\pi\) | ||
0.716279 | − | 0.697814i | \(-0.245844\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −11.0880 | − | 19.2049i | −0.440707 | − | 0.763327i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.548650 | + | 2.96742i | −0.0217725 | + | 0.117759i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.1767 | − | 36.1939i | 0.640945 | − | 1.43405i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.51523 | − | 0.874819i | −0.0599416 | − | 0.0346073i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.51329 | − | 6.08519i | −0.138766 | − | 0.240351i | 0.788264 | − | 0.615338i | \(-0.210980\pi\) |
−0.927030 | + | 0.374987i | \(0.877647\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.42331 | −0.174438 | −0.0872191 | − | 0.996189i | \(-0.527798\pi\) | ||||
−0.0872191 | + | 0.996189i | \(0.527798\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.0736 | + | 39.6881i | 0.554149 | + | 1.56272i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.327418 | − | 0.189035i | 0.0128721 | − | 0.00743172i | −0.493550 | − | 0.869717i | \(-0.664301\pi\) |
0.506422 | + | 0.862286i | \(0.330968\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.07099 | − | 5.23714i | −0.356067 | − | 0.205576i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.6636 | + | 11.4188i | 0.496324 | + | 0.447536i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.4109 | − | 38.8168i | 0.877005 | − | 1.51902i | 0.0223938 | − | 0.999749i | \(-0.492871\pi\) |
0.854611 | − | 0.519268i | \(-0.173795\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8821 | − | 13.9244i | 0.464273 | − | 0.544071i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.5786 | 0.763832 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.4018 | 0.950557 | 0.475279 | − | 0.879835i | \(-0.342347\pi\) | ||||
0.475279 | + | 0.879835i | \(0.342347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.4940 | + | 25.1043i | 0.563751 | + | 0.976445i | 0.997165 | + | 0.0752499i | \(0.0239754\pi\) |
−0.433414 | + | 0.901195i | \(0.642691\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 70.1487 | + | 40.5004i | 2.72435 | + | 1.57290i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.01697 | + | 5.23809i | 0.155771 | + | 0.203124i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.3257 | − | 7.11626i | −0.477254 | − | 0.275543i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 34.7971 | − | 20.0901i | 1.34533 | − | 0.776728i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.77683 | 0.0685938 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.93910i | − | 0.0747467i | −0.999301 | − | 0.0373733i | \(-0.988101\pi\) | ||
0.999301 | − | 0.0373733i | \(-0.0118991\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.94800 | + | 3.42593i | 0.344409 | + | 0.131864i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.9976 | − | 21.3606i | −1.42193 | − | 0.820954i | −0.425470 | − | 0.904972i | \(-0.639891\pi\) |
−0.996464 | + | 0.0840182i | \(0.973225\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.51811 | − | 25.8695i | 0.211766 | − | 0.992782i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.9035 | + | 34.4739i | −0.762705 | + | 1.32104i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.6952 | − | 18.8766i | 1.25105 | − | 0.722293i | 0.279730 | − | 0.960079i | \(-0.409755\pi\) |
0.971318 | + | 0.237786i | \(0.0764217\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.82419 | + | 10.7843i | 0.146115 | + | 0.412048i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −15.7117 | −0.599440 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.1618 | − | 14.5272i | 0.958588 | − | 0.553441i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.4603 | − | 10.0807i | −0.664220 | − | 0.383487i | 0.129663 | − | 0.991558i | \(-0.458610\pi\) |
−0.793883 | + | 0.608071i | \(0.791944\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.08188 | − | 5.07198i | 0.0410972 | − | 0.192669i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39.3951 | + | 7.28380i | 1.49434 | + | 0.276290i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.889491 | + | 0.513548i | −0.0336919 | + | 0.0194520i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.93606i | 0.375816i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.2036i | 0.763080i | 0.924352 | + | 0.381540i | \(0.124606\pi\) | ||||
−0.924352 | + | 0.381540i | \(0.875394\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.52599 | + | 0.881028i | −0.0575536 | + | 0.0332286i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −49.3612 | − | 9.12645i | −1.85905 | − | 0.343722i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.7562 | + | 14.1826i | −1.64562 | + | 0.533392i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.7495 | + | 6.78358i | 0.441262 | + | 0.254763i | 0.704133 | − | 0.710068i | \(-0.251336\pi\) |
−0.262871 | + | 0.964831i | \(0.584669\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.1778 | + | 12.2270i | −0.794231 | + | 0.458549i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.50010 | −0.243431 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.84787 | + | 10.8511i | 0.143902 | + | 0.405809i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.8326 | − | 16.0691i | 1.03943 | − | 0.600113i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.1941 | + | 34.9772i | −0.753113 | + | 1.30443i | 0.193194 | + | 0.981161i | \(0.438115\pi\) |
−0.946307 | + | 0.323270i | \(0.895218\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.20385 | − | 3.55312i | 0.119318 | − | 0.132325i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −30.4561 | − | 17.5838i | −1.13267 | − | 0.653950i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.1105 | − | 29.0189i | 0.412633 | − | 1.07774i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.15590i | 0.265397i | 0.991156 | + | 0.132699i | \(0.0423643\pi\) | ||||
−0.991156 | + | 0.132699i | \(0.957636\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.2739 | −0.380516 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.2388 | − | 26.1186i | 1.67322 | − | 0.966033i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.8024 | + | 14.3197i | 0.916097 | + | 0.528909i | 0.882388 | − | 0.470523i | \(-0.155935\pi\) |
0.0337089 | + | 0.999432i | \(0.489268\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 35.4297 | + | 2.82400i | 1.30684 | + | 0.104165i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.54089 | + | 3.19903i | 0.204101 | + | 0.117838i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.4535 | + | 28.4983i | 0.605252 | + | 1.04833i | 0.992012 | + | 0.126147i | \(0.0402610\pi\) |
−0.386760 | + | 0.922181i | \(0.626406\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.3490 | 0.527124 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.3184 | −0.818782 | −0.409391 | − | 0.912359i | \(-0.634259\pi\) | ||||
−0.409391 | + | 0.912359i | \(0.634259\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3409 | + | 12.1183i | −0.378861 | + | 0.443979i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.41776 | − | 14.5800i | 0.307990 | − | 0.533454i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.31264 | + | 7.00081i | −0.230659 | + | 0.255804i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39.6036 | − | 22.8651i | −1.44516 | − | 0.834361i | −0.446968 | − | 0.894550i | \(-0.647496\pi\) |
−0.998187 | + | 0.0601891i | \(0.980830\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0549 | + | 6.95993i | −0.439307 | + | 0.253634i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.12767 | + | 6.00009i | 0.0774338 | + | 0.218366i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.8916 | 1.05008 | 0.525042 | − | 0.851076i | \(-0.324050\pi\) | ||||
0.525042 | + | 0.851076i | \(0.324050\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.36386 | + | 4.09432i | 0.0858027 | + | 0.148615i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.9186 | + | 16.1188i | 1.01205 | + | 0.584306i | 0.911791 | − | 0.410655i | \(-0.134700\pi\) |
0.100258 | + | 0.994962i | \(0.468033\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.62913 | + | 5.02618i | 0.0589783 | + | 0.181960i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.52093 | + | 29.8604i | −0.199610 | + | 1.07961i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32.6252 | − | 56.5085i | −1.17803 | − | 2.04040i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.89606i | − | 0.320800i | −0.987052 | − | 0.160400i | \(-0.948722\pi\) | ||
0.987052 | − | 0.160400i | \(-0.0512784\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.5802 | −0.525092 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.6869 | − | 14.2530i | 0.887925 | − | 0.512644i | 0.0146619 | − | 0.999893i | \(-0.495333\pi\) |
0.873263 | + | 0.487249i | \(0.161999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.23216 | − | 14.0147i | −0.0801815 | − | 0.503423i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.97920 | + | 9.27874i | −0.0710035 | + | 0.332873i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0909733 | + | 0.157570i | −0.00325946 | + | 0.00564554i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.638909 | + | 0.368874i | −0.0228620 | + | 0.0131994i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 11.9090i | − | 0.425593i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.84011 | + | 27.7494i | 0.351209 | + | 0.990419i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.7112 | − | 37.6050i | −0.773922 | − | 1.34047i | −0.935398 | − | 0.353595i | \(-0.884959\pi\) |
0.161477 | − | 0.986877i | \(-0.448374\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.33456 | − | 12.7038i | 0.261117 | − | 0.452269i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.9968 | + | 7.46500i | 1.24434 | + | 0.265425i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.58597 | + | 5.53446i | 0.340408 | + | 0.196535i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.8142 | + | 16.9081i | 0.702739 | + | 0.599670i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 11.3329i | 0.401432i | 0.979649 | + | 0.200716i | \(0.0643268\pi\) | ||||
−0.979649 | + | 0.200716i | \(0.935673\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.2708i | 2.20298i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −26.7579 | + | 15.4487i | −0.945444 | + | 0.545853i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.12772 | − | 7.14942i | 0.145664 | − | 0.252298i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.7513 | + | 8.24494i | −0.378934 | + | 0.290596i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.71515 | + | 2.97073i | −0.0603762 | + | 0.104575i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.3202 | − | 47.3199i | −0.960526 | − | 1.66368i | −0.721183 | − | 0.692745i | \(-0.756401\pi\) |
−0.239343 | − | 0.970935i | \(-0.576932\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 34.1338i | − | 1.19860i | −0.800525 | − | 0.599300i | \(-0.795446\pi\) | ||
0.800525 | − | 0.599300i | \(-0.204554\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −39.3410 | −1.37975 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.9852 | − | 29.2796i | 0.875193 | − | 1.02562i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.62683 | − | 8.01390i | 0.161872 | − | 0.280371i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 21.6349 | − | 23.9934i | 0.755984 | − | 0.838398i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4373 | − | 12.3768i | −0.748168 | − | 0.431955i | 0.0768637 | − | 0.997042i | \(-0.475509\pi\) |
−0.825032 | + | 0.565087i | \(0.808843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2123 | − | 21.1523i | −0.425694 | − | 0.737324i | 0.570791 | − | 0.821096i | \(-0.306637\pi\) |
−0.996485 | + | 0.0837714i | \(0.973303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −8.01591 | + | 6.50266i | −0.279078 | + | 0.226394i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7945i | 0.723096i | 0.932353 | + | 0.361548i | \(0.117752\pi\) | ||||
−0.932353 | + | 0.361548i | \(0.882248\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8195 | − | 37.7924i | −0.757822 | − | 1.31259i | −0.943959 | − | 0.330062i | \(-0.892930\pi\) |
0.186137 | − | 0.982524i | \(-0.440403\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.1175 | − | 22.7202i | 0.455041 | − | 0.788154i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.54588 | − | 43.8553i | −0.157505 | − | 1.51950i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.628441 | + | 0.116193i | 0.0217481 | + | 0.00402103i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.71947 | − | 4.71026i | −0.0939986 | − | 0.162810i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.4129 | −0.877351 | −0.438675 | − | 0.898646i | \(-0.644552\pi\) | ||||
−0.438675 | + | 0.898646i | \(0.644552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.62161 | −0.331779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.9065 | − | 32.7470i | −0.651174 | − | 1.12787i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.75479 | + | 41.9425i | −0.266773 | + | 1.44287i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.9900 | + | 18.0250i | 0.686863 | + | 0.619346i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.8335 | − | 44.7449i | 0.886603 | − | 1.53564i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.80833 | − | 3.13212i | −0.0619888 | − | 0.107368i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 3.10531i | − | 0.106324i | −0.998586 | − | 0.0531619i | \(-0.983070\pi\) | ||
0.998586 | − | 0.0531619i | \(-0.0169299\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.79785 | + | 5.07000i | 0.0614853 | + | 0.173390i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.1563 | + | 19.3233i | 0.381093 | + | 0.660072i | 0.991219 | − | 0.132233i | \(-0.0422146\pi\) |
−0.610126 | + | 0.792304i | \(0.708881\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.2253 | − | 10.5224i | −0.621838 | − | 0.359018i | 0.155746 | − | 0.987797i | \(-0.450222\pi\) |
−0.777584 | + | 0.628779i | \(0.783555\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.302064 | + | 0.931928i | 0.0102943 | + | 0.0317600i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.4205 | − | 30.1732i | 0.593001 | − | 1.02711i | −0.400825 | − | 0.916155i | \(-0.631277\pi\) |
0.993826 | − | 0.110953i | \(-0.0353902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.9630 | − | 32.7692i | 0.950772 | − | 1.11419i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 51.4825 | 1.74844 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.3112i | 0.349785i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.9286 | + | 34.5174i | 0.675256 | + | 1.16958i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.7780 | − | 18.6680i | 0.364779 | − | 0.631816i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.4687 | − | 20.3493i | −0.725776 | − | 0.687931i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.9212 | − | 34.5045i | 0.672691 | − | 1.16513i | −0.304448 | − | 0.952529i | \(-0.598472\pi\) |
0.977138 | − | 0.212605i | \(-0.0681948\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.0359 | + | 9.83567i | −0.574606 | + | 0.331749i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.2170i | 1.08542i | 0.839921 | + | 0.542709i | \(0.182601\pi\) | ||||
−0.839921 | + | 0.542709i | \(0.817399\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 57.8919i | − | 1.94822i | −0.226080 | − | 0.974109i | \(-0.572591\pi\) | ||
0.226080 | − | 0.974109i | \(-0.427409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 37.9724 | − | 44.4989i | 1.27643 | − | 1.49582i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.94580 | − | 4.58751i | −0.266794 | − | 0.154033i | 0.360636 | − | 0.932707i | \(-0.382560\pi\) |
−0.627430 | + | 0.778673i | \(0.715893\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.744873 | − | 3.49205i | 0.0249822 | − | 0.117120i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.91818 | + | 8.51854i | −0.164765 | + | 0.285382i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.51553 | + | 9.55319i | 0.184570 | + | 0.319685i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.95766 | + | 1.04880i | −0.0988637 | + | 0.0350577i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.4517i | 0.983365i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.2756 | + | 8.81940i | −0.509471 | + | 0.294143i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.1563 | − | 27.9835i | 0.538244 | − | 0.932266i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.3627 | − | 47.3971i | −0.511240 | − | 1.57728i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.25330 | + | 33.8215i | −0.207867 | + | 1.12427i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.48163 | + | 5.47422i | −0.314832 | + | 0.181769i | −0.649087 | − | 0.760714i | \(-0.724849\pi\) |
0.334254 | + | 0.942483i | \(0.391516\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.4842 | −1.24327 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.3120i | − | 0.341653i | −0.985301 | − | 0.170827i | \(-0.945356\pi\) | ||
0.985301 | − | 0.170827i | \(-0.0546438\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.54941 | − | 6.14776i | −0.117468 | − | 0.203461i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.80419 | + | 9.75814i | −0.0596448 | + | 0.322594i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.5041 | + | 16.0852i | −0.478967 | + | 0.531181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −42.1983 | − | 24.3632i | −1.39199 | − | 0.803669i | −0.398459 | − | 0.917186i | \(-0.630455\pi\) |
−0.993536 | + | 0.113518i | \(0.963788\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.2679 | + | 22.9808i | 0.437194 | + | 0.757242i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.59587 | −0.151275 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.13210 | − | 4.97448i | 0.201622 | − | 0.163560i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.37647 | − | 1.94941i | 0.110898 | − | 0.0640270i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.8399 | + | 17.8054i | 1.01182 | + | 0.584177i | 0.911725 | − | 0.410801i | \(-0.134751\pi\) |
0.100099 | + | 0.994977i | \(0.468084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.58181 | − | 6.32535i | −0.150163 | − | 0.207305i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.8674 | − | 22.2869i | 0.421259 | − | 0.729642i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.74005 | + | 8.31150i | 0.318534 | + | 0.271815i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.16006 | 0.0378974 | 0.0189487 | − | 0.999820i | \(-0.493968\pi\) | ||||
0.0189487 | + | 0.999820i | \(0.493968\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 57.6814 | 1.88236 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.49867 | + | 7.79192i | 0.146652 | + | 0.254009i | 0.929988 | − | 0.367589i | \(-0.119817\pi\) |
−0.783336 | + | 0.621599i | \(0.786483\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.323417 | − | 0.186725i | −0.0105319 | − | 0.00608060i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −10.4727 | − | 4.34141i | −0.340677 | − | 0.141226i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.2076 | + | 11.0895i | 0.624165 | + | 0.360362i | 0.778489 | − | 0.627659i | \(-0.215987\pi\) |
−0.154324 | + | 0.988020i | \(0.549320\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.5380 | − | 25.7140i | 1.44576 | − | 0.834712i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −54.1024 | −1.75439 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.9975i | 1.03650i | 0.855229 | + | 0.518250i | \(0.173416\pi\) | ||||
−0.855229 | + | 0.518250i | \(0.826584\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.6131 | + | 38.2185i | −1.05533 | + | 1.23672i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.1104 | + | 6.41461i | 0.359149 | + | 0.207355i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.17447 | − | 12.8791i | −0.134801 | − | 0.415887i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.4721 | − | 19.8703i | 0.370068 | − | 0.640977i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.65276 | + | 3.84097i | −0.214382 | + | 0.123774i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.3776 | − | 34.9052i | −0.398449 | − | 1.12364i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.0936 | 1.28932 | 0.644662 | − | 0.764468i | \(-0.276998\pi\) | ||||
0.644662 | + | 0.764468i | \(0.276998\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.8202 | − | 7.97908i | 0.443968 | − | 0.256325i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.9006 | + | 15.5311i | 0.863282 | + | 0.498416i | 0.865110 | − | 0.501582i | \(-0.167249\pi\) |
−0.00182815 | + | 0.999998i | \(0.500582\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46.3600 | − | 9.88882i | −1.48623 | − | 0.317021i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −63.5001 | + | 10.1138i | −2.03363 | + | 0.323902i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.2743 | + | 27.8712i | −1.54443 | + | 0.891678i | −0.545881 | + | 0.837863i | \(0.683805\pi\) |
−0.998551 | + | 0.0538151i | \(0.982862\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.0281i | 0.416380i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.30573i | 0.137471i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.4861 | + | 22.7973i | −1.25941 | + | 0.727122i | −0.972960 | − | 0.230973i | \(-0.925809\pi\) |
−0.286452 | + | 0.958095i | \(0.592476\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.55927 | + | 35.4764i | −0.208996 | + | 1.13037i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 58.0881 | + | 12.3905i | 1.84896 | + | 0.394394i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.4487 | + | 9.49669i | 0.523040 | + | 0.301977i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.9667 | + | 17.8786i | −0.983689 | + | 0.567933i | −0.903382 | − | 0.428837i | \(-0.858923\pi\) |
−0.0803071 | + | 0.996770i | \(0.525590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.6801 | −0.338924 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.9996 | + | 16.3117i | −1.45829 | + | 0.517117i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.48099 | + | 5.47385i | −0.300266 | + | 0.173359i | −0.642562 | − | 0.766233i | \(-0.722129\pi\) |
0.342296 | + | 0.939592i | \(0.388795\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.51312 | − | 2.62079i | 0.0478728 | − | 0.0829182i |
(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.719.7 | 80 | ||
4.3 | odd | 2 | 280.2.ba.b.19.28 | yes | 80 | ||
5.4 | even | 2 | inner | 1120.2.bq.b.719.33 | 80 | ||
7.3 | odd | 6 | inner | 1120.2.bq.b.1039.34 | 80 | ||
8.3 | odd | 2 | inner | 1120.2.bq.b.719.8 | 80 | ||
8.5 | even | 2 | 280.2.ba.b.19.15 | yes | 80 | ||
20.19 | odd | 2 | 280.2.ba.b.19.13 | ✓ | 80 | ||
28.3 | even | 6 | 280.2.ba.b.59.26 | yes | 80 | ||
35.24 | odd | 6 | inner | 1120.2.bq.b.1039.8 | 80 | ||
40.19 | odd | 2 | inner | 1120.2.bq.b.719.34 | 80 | ||
40.29 | even | 2 | 280.2.ba.b.19.26 | yes | 80 | ||
56.3 | even | 6 | inner | 1120.2.bq.b.1039.33 | 80 | ||
56.45 | odd | 6 | 280.2.ba.b.59.13 | yes | 80 | ||
140.59 | even | 6 | 280.2.ba.b.59.15 | yes | 80 | ||
280.59 | even | 6 | inner | 1120.2.bq.b.1039.7 | 80 | ||
280.269 | odd | 6 | 280.2.ba.b.59.28 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.ba.b.19.13 | ✓ | 80 | 20.19 | odd | 2 | ||
280.2.ba.b.19.15 | yes | 80 | 8.5 | even | 2 | ||
280.2.ba.b.19.26 | yes | 80 | 40.29 | even | 2 | ||
280.2.ba.b.19.28 | yes | 80 | 4.3 | odd | 2 | ||
280.2.ba.b.59.13 | yes | 80 | 56.45 | odd | 6 | ||
280.2.ba.b.59.15 | yes | 80 | 140.59 | even | 6 | ||
280.2.ba.b.59.26 | yes | 80 | 28.3 | even | 6 | ||
280.2.ba.b.59.28 | yes | 80 | 280.269 | odd | 6 | ||
1120.2.bq.b.719.7 | 80 | 1.1 | even | 1 | trivial | ||
1120.2.bq.b.719.8 | 80 | 8.3 | odd | 2 | inner | ||
1120.2.bq.b.719.33 | 80 | 5.4 | even | 2 | inner | ||
1120.2.bq.b.719.34 | 80 | 40.19 | odd | 2 | inner | ||
1120.2.bq.b.1039.7 | 80 | 280.59 | even | 6 | inner | ||
1120.2.bq.b.1039.8 | 80 | 35.24 | odd | 6 | inner | ||
1120.2.bq.b.1039.33 | 80 | 56.3 | even | 6 | inner | ||
1120.2.bq.b.1039.34 | 80 | 7.3 | odd | 6 | inner |