Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(41,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bu (of order \(6\), degree \(2\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.13 | ||
Character | \(\chi\) | \(=\) | 504.41 |
Dual form | 504.2.bu.a.209.13 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.0936255 | + | 1.72952i | 0.0540547 | + | 0.998538i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.26858 | − | 2.19724i | 0.567326 | − | 0.982637i | −0.429503 | − | 0.903065i | \(-0.641311\pi\) |
0.996829 | − | 0.0795717i | \(-0.0253553\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.521158 | + | 2.59391i | 0.196979 | + | 0.980408i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.98247 | + | 0.323854i | −0.994156 | + | 0.107951i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.68321 | + | 3.28120i | −1.71355 | + | 0.989320i | −0.783898 | + | 0.620889i | \(0.786772\pi\) |
−0.929655 | + | 0.368431i | \(0.879895\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.13890 | + | 2.96694i | 1.42527 | + | 0.822882i | 0.996743 | − | 0.0806450i | \(-0.0256980\pi\) |
0.428531 | + | 0.903527i | \(0.359031\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.91894 | + | 1.98831i | 1.01187 | + | 0.513380i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.52698 | 0.855419 | 0.427709 | − | 0.903916i | \(-0.359321\pi\) | ||||
0.427709 | + | 0.903916i | \(0.359321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.261355i | 0.0599590i | 0.999551 | + | 0.0299795i | \(0.00954420\pi\) | ||||
−0.999551 | + | 0.0299795i | \(0.990456\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.43743 | + | 1.14421i | −0.968327 | + | 0.249687i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.89967 | + | 1.67412i | 0.604622 | + | 0.349079i | 0.770858 | − | 0.637007i | \(-0.219828\pi\) |
−0.166236 | + | 0.986086i | \(0.553161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.718584 | − | 1.24462i | −0.143717 | − | 0.248925i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.839346 | − | 5.12791i | −0.161532 | − | 0.986867i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00813 | + | 0.582041i | −0.187204 | + | 0.108082i | −0.590673 | − | 0.806911i | \(-0.701138\pi\) |
0.403469 | + | 0.914993i | \(0.367804\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.69360 | + | 0.977800i | 0.304179 | + | 0.175618i | 0.644319 | − | 0.764757i | \(-0.277141\pi\) |
−0.340139 | + | 0.940375i | \(0.610474\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.20700 | − | 9.52202i | −1.08050 | − | 1.65757i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.36059 | + | 2.14547i | 1.07514 | + | 0.362651i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.16528 | −0.191570 | −0.0957851 | − | 0.995402i | \(-0.530536\pi\) | ||||
−0.0957851 | + | 0.995402i | \(0.530536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.65025 | + | 9.16560i | −0.744636 | + | 1.46767i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.85769 | + | 4.94966i | −0.446296 | + | 0.773007i | −0.998141 | − | 0.0609391i | \(-0.980590\pi\) |
0.551846 | + | 0.833946i | \(0.313924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.67364 | + | 4.63088i | 0.407726 | + | 0.706203i | 0.994635 | − | 0.103451i | \(-0.0329884\pi\) |
−0.586908 | + | 0.809654i | \(0.699655\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.07191 | + | 6.96404i | −0.457933 | + | 1.03814i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.79767 | − | 6.57775i | −0.553947 | − | 0.959464i | −0.997985 | − | 0.0634560i | \(-0.979788\pi\) |
0.444038 | − | 0.896008i | \(-0.353546\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.45679 | + | 2.70368i | −0.922398 | + | 0.386240i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.330215 | + | 6.09998i | 0.0462394 | + | 0.854168i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.54792i | − | 0.487344i | −0.969858 | − | 0.243672i | \(-0.921648\pi\) | ||
0.969858 | − | 0.243672i | \(-0.0783521\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.6499i | 2.24507i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.452019 | + | 0.0244695i | −0.0598714 | + | 0.00324107i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.47899 | − | 9.48989i | 0.713304 | − | 1.23548i | −0.250306 | − | 0.968167i | \(-0.580531\pi\) |
0.963610 | − | 0.267312i | \(-0.0861353\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.53699 | + | 3.19678i | −0.708939 | + | 0.409306i | −0.810668 | − | 0.585506i | \(-0.800896\pi\) |
0.101729 | + | 0.994812i | \(0.467562\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.39439 | − | 7.56749i | −0.301664 | − | 0.953414i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 13.0382 | − | 7.52760i | 1.61719 | − | 0.933684i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.54164 | − | 7.86635i | 0.554850 | − | 0.961028i | −0.443066 | − | 0.896489i | \(-0.646109\pi\) |
0.997915 | − | 0.0645384i | \(-0.0205575\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.62394 | + | 5.17177i | −0.315886 | + | 0.622608i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.5889i | − | 1.25667i | −0.777944 | − | 0.628334i | \(-0.783737\pi\) | ||
0.777944 | − | 0.628334i | \(-0.216263\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.72923i | − | 0.319433i | −0.987163 | − | 0.159716i | \(-0.948942\pi\) | ||
0.987163 | − | 0.159716i | \(-0.0510579\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.08532 | − | 1.35933i | 0.240792 | − | 0.156962i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.4730 | − | 13.0317i | −1.30747 | − | 1.48511i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.652687 | − | 1.13049i | −0.0734330 | − | 0.127190i | 0.826971 | − | 0.562245i | \(-0.190062\pi\) |
−0.900404 | + | 0.435055i | \(0.856729\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.79024 | − | 1.93177i | 0.976693 | − | 0.214641i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.53241 | − | 7.85037i | −0.497497 | − | 0.861690i | 0.502499 | − | 0.864578i | \(-0.332414\pi\) |
−0.999996 | + | 0.00288802i | \(0.999081\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.47426 | − | 7.74964i | 0.485301 | − | 0.840566i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.10104 | − | 1.68908i | −0.118044 | − | 0.181088i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.2599 | 1.51155 | 0.755776 | − | 0.654830i | \(-0.227260\pi\) | ||||
0.755776 | + | 0.654830i | \(0.227260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.01782 | + | 14.8761i | −0.526011 | + | 1.55944i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.53256 | + | 3.02066i | −0.158919 | + | 0.313228i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.574261 | + | 0.331550i | 0.0589180 | + | 0.0340163i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.95686 | − | 5.74859i | 1.01097 | − | 0.583681i | 0.0994914 | − | 0.995038i | \(-0.468278\pi\) |
0.911474 | + | 0.411357i | \(0.134945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.8874 | − | 11.6266i | 1.59674 | − | 1.16852i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.09191 | − | 1.89124i | −0.108649 | − | 0.188186i | 0.806574 | − | 0.591133i | \(-0.201319\pi\) |
−0.915223 | + | 0.402947i | \(0.867986\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.75576 | + | 5.63249i | 0.961264 | + | 0.554986i | 0.896562 | − | 0.442919i | \(-0.146057\pi\) |
0.0647021 | + | 0.997905i | \(0.479390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.11512 | + | 11.2016i | −0.304005 | + | 1.09317i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.82576i | 0.756545i | 0.925694 | + | 0.378272i | \(0.123482\pi\) | ||||
−0.925694 | + | 0.378272i | \(0.876518\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.5453 | −1.68053 | −0.840266 | − | 0.542174i | \(-0.817601\pi\) | ||||
−0.840266 | + | 0.542174i | \(0.817601\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.109100 | − | 2.01537i | −0.0103553 | − | 0.191290i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.81112 | + | 2.20035i | 0.358520 | + | 0.206992i | 0.668431 | − | 0.743774i | \(-0.266966\pi\) |
−0.309911 | + | 0.950765i | \(0.600299\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.35691 | − | 4.24751i | 0.686035 | − | 0.396083i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.2875 | − | 7.18456i | −1.50578 | − | 0.664213i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.83812 | + | 9.14869i | 0.168500 | + | 0.838659i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0326 | − | 27.7693i | 1.45751 | − | 2.52448i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.82808 | − | 4.47901i | −0.796001 | − | 0.403859i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.03946 | 0.808514 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.5689 | 1.73646 | 0.868228 | − | 0.496165i | \(-0.165259\pi\) | ||||
0.868228 | + | 0.496165i | \(0.165259\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.75888 | + | 5.05768i | −0.683131 | + | 0.445304i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.00967786 | − | 0.0167625i | 0.000845559 | − | 0.00146455i | −0.865602 | − | 0.500732i | \(-0.833064\pi\) |
0.866448 | + | 0.499268i | \(0.166398\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.677933 | + | 0.136207i | −0.0587843 | + | 0.0118107i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.3320 | − | 4.66091i | −1.06137 | − | 0.401148i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.67032 | + | 2.11906i | −0.313577 | + | 0.181044i | −0.648526 | − | 0.761193i | \(-0.724614\pi\) |
0.334949 | + | 0.942236i | \(0.391281\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.6403 | − | 10.1847i | −1.49623 | − | 0.863851i | −0.496244 | − | 0.868183i | \(-0.665288\pi\) |
−0.999991 | + | 0.00433182i | \(0.998621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.0208 | − | 7.18398i | 0.928118 | − | 0.605000i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −38.9406 | −3.25638 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.95346i | 0.245272i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.28058 | − | 10.9140i | −0.435535 | − | 0.900172i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.40370 | − | 3.69718i | −0.524611 | − | 0.302885i | 0.214208 | − | 0.976788i | \(-0.431283\pi\) |
−0.738819 | + | 0.673904i | \(0.764616\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.94189 | + | 12.0237i | 0.564923 | + | 0.978475i | 0.997057 | + | 0.0766658i | \(0.0244275\pi\) |
−0.432134 | + | 0.901809i | \(0.642239\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.5191 | + | 1.14223i | −0.850420 | + | 0.0923436i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.29693 | − | 2.48083i | 0.345138 | − | 0.199265i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.86713 | + | 1.07799i | 0.149013 | + | 0.0860329i | 0.572653 | − | 0.819798i | \(-0.305914\pi\) |
−0.423639 | + | 0.905831i | \(0.639248\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.13619 | − | 0.332176i | 0.486632 | − | 0.0263432i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.83135 | + | 8.39397i | −0.223142 | + | 0.661538i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.1866 | −1.34616 | −0.673079 | − | 0.739571i | \(-0.735029\pi\) | ||||
−0.673079 | + | 0.739571i | \(0.735029\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −28.7963 | + | 1.55885i | −2.24179 | + | 0.121356i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.40101 | − | 9.35482i | 0.417943 | − | 0.723898i | −0.577790 | − | 0.816186i | \(-0.696085\pi\) |
0.995732 | + | 0.0922879i | \(0.0294180\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1055 | + | 19.2353i | 0.854270 | + | 1.47964i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0846409 | − | 0.779484i | −0.00647265 | − | 0.0596086i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.55489 | + | 16.5495i | 0.726444 | + | 1.25824i | 0.958377 | + | 0.285507i | \(0.0921619\pi\) |
−0.231932 | + | 0.972732i | \(0.574505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.85395 | − | 2.51259i | 0.215739 | − | 0.189934i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9259 | + | 8.58752i | 1.27223 | + | 0.645477i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.9224i | − | 1.11536i | −0.830057 | − | 0.557678i | \(-0.811692\pi\) | ||
0.830057 | − | 0.557678i | \(-0.188308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 18.5179i | − | 1.37642i | −0.725511 | − | 0.688211i | \(-0.758396\pi\) | ||
0.725511 | − | 0.688211i | \(-0.241604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.04730 | − | 9.27703i | −0.447029 | − | 0.685777i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.47824 | + | 2.56039i | −0.108683 | + | 0.188244i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.0446 | + | 11.5728i | −1.46581 | + | 0.846283i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.8639 | − | 4.84965i | 0.935714 | − | 0.352760i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.08192 | + | 2.93405i | −0.367715 | + | 0.212300i | −0.672460 | − | 0.740134i | \(-0.734762\pi\) |
0.304745 | + | 0.952434i | \(0.401429\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.19577 | + | 14.1955i | −0.589945 | + | 1.02181i | 0.404294 | + | 0.914629i | \(0.367517\pi\) |
−0.994239 | + | 0.107185i | \(0.965816\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.2398 | + | 21.8450i | 1.01974 | + | 1.56435i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.90103i | 0.491678i | 0.969311 | + | 0.245839i | \(0.0790635\pi\) | ||||
−0.969311 | + | 0.245839i | \(0.920936\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 10.3555i | − | 0.734078i | −0.930205 | − | 0.367039i | \(-0.880371\pi\) | ||
0.930205 | − | 0.367039i | \(-0.119629\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.0302 | + | 7.11836i | 0.989615 | + | 0.502090i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.03516 | − | 2.31166i | −0.142840 | − | 0.162246i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.25041 | + | 12.5581i | 0.506390 | + | 0.877094i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.19034 | − | 4.05395i | −0.638772 | − | 0.281769i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.857560 | − | 1.48534i | −0.0593187 | − | 0.102743i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.43331 | − | 5.94667i | 0.236359 | − | 0.409385i | −0.723308 | − | 0.690526i | \(-0.757379\pi\) |
0.959667 | + | 0.281140i | \(0.0907126\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.3136 | − | 0.991387i | 1.25483 | − | 0.0679287i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.5669 | 0.925255 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.65370 | + | 4.90264i | −0.112260 | + | 0.332813i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.72026 | − | 0.255526i | 0.318966 | − | 0.0172668i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.1248 | + | 10.4644i | 1.21921 | + | 0.703909i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.467052 | − | 0.269653i | 0.0312761 | − | 0.0180573i | −0.484280 | − | 0.874913i | \(-0.660919\pi\) |
0.515557 | + | 0.856856i | \(0.327585\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.54623 | + | 3.47934i | 0.169749 | + | 0.231956i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.610518 | − | 1.05745i | −0.0405215 | − | 0.0701852i | 0.845053 | − | 0.534682i | \(-0.179569\pi\) |
−0.885575 | + | 0.464497i | \(0.846235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.4049 | − | 6.00725i | −0.687573 | − | 0.396970i | 0.115129 | − | 0.993351i | \(-0.463272\pi\) |
−0.802702 | + | 0.596380i | \(0.796605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 21.4645 | − | 21.0629i | 1.41226 | − | 1.38584i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.13142i | 0.336171i | 0.985772 | + | 0.168085i | \(0.0537584\pi\) | ||||
−0.985772 | + | 0.168085i | \(0.946242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.2706 | −1.25707 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.89409 | − | 1.23468i | 0.123034 | − | 0.0802008i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.5981 | + | 6.11881i | 0.685533 | + | 0.395793i | 0.801937 | − | 0.597409i | \(-0.203803\pi\) |
−0.116403 | + | 0.993202i | \(0.537137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9320 | − | 14.3945i | 1.60601 | − | 0.927231i | 0.615761 | − | 0.787933i | \(-0.288849\pi\) |
0.990251 | − | 0.139298i | \(-0.0444846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.16402 | + | 15.0220i | 0.267122 | + | 0.963663i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.25030 | + | 17.6170i | −0.143767 | + | 1.12551i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.775427 | + | 1.34308i | −0.0493392 | + | 0.0854580i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.1530 | − | 8.57388i | 0.833538 | − | 0.543348i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.82335 | 0.304447 | 0.152223 | − | 0.988346i | \(-0.451357\pi\) | ||||
0.152223 | + | 0.988346i | \(0.451357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21.9726 | −1.38140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.8220 | + | 7.01274i | 0.865570 | + | 0.439155i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.15022 | + | 3.72430i | −0.134127 | + | 0.232315i | −0.925264 | − | 0.379324i | \(-0.876156\pi\) |
0.791136 | + | 0.611640i | \(0.209490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.607293 | − | 3.02263i | −0.0377354 | − | 0.187817i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.81821 | − | 2.06241i | 0.174443 | − | 0.127660i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.2444 | + | 11.1107i | −1.18666 | + | 0.685118i | −0.957546 | − | 0.288282i | \(-0.906916\pi\) |
−0.229113 | + | 0.973400i | \(0.573583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.79564 | − | 4.50082i | −0.478883 | − | 0.276483i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.33509 | + | 24.6628i | 0.0817064 | + | 1.50934i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.6564 | −1.32042 | −0.660208 | − | 0.751083i | \(-0.729532\pi\) | ||||
−0.660208 | + | 0.751083i | \(0.729532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0808i | 1.03758i | 0.854901 | + | 0.518792i | \(0.173618\pi\) | ||||
−0.854901 | + | 0.518792i | \(0.826382\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.1983 | − | 7.28563i | −1.58559 | − | 0.440947i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.16774 | + | 4.71565i | 0.492533 | + | 0.284364i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.60480 | − | 2.77959i | −0.0964230 | − | 0.167009i | 0.813779 | − | 0.581175i | \(-0.197407\pi\) |
−0.910202 | + | 0.414165i | \(0.864073\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.36777 | − | 2.36778i | −0.321360 | − | 0.141755i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0599 | − | 10.4269i | 1.07736 | − | 0.622016i | 0.147179 | − | 0.989110i | \(-0.452981\pi\) |
0.930184 | + | 0.367094i | \(0.119647\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.99941 | + | 5.77316i | 0.594403 | + | 0.343179i | 0.766837 | − | 0.641842i | \(-0.221830\pi\) |
−0.172433 | + | 0.985021i | \(0.555163\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.519656 | + | 1.02424i | −0.0307818 | + | 0.0606706i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.3283 | − | 4.83304i | −0.845773 | − | 0.285286i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.56040 | −0.268259 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.8745 | + | 16.6824i | 0.637475 | + | 0.977937i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.1600 | + | 24.5259i | −0.827238 | + | 1.43282i | 0.0729596 | + | 0.997335i | \(0.476756\pi\) |
−0.900197 | + | 0.435483i | \(0.856578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.9011 | − | 24.0773i | −0.809351 | − | 1.40184i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.5959 | + | 26.3890i | 1.25312 | + | 1.53124i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.93406 | + | 17.2063i | 0.574501 | + | 0.995066i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6187 | + | 9.34862i | −0.612053 | + | 0.538845i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.16871 | − | 2.06554i | 0.182037 | − | 0.118662i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.2215i | 0.928839i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 24.2818i | − | 1.38584i | −0.721016 | − | 0.692918i | \(-0.756325\pi\) | ||
0.721016 | − | 0.692918i | \(-0.243675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.82811 | + | 17.4001i | −0.502214 | + | 0.989858i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3119 | + | 28.2531i | −0.924964 | + | 1.60209i | −0.133346 | + | 0.991070i | \(0.542572\pi\) |
−0.791619 | + | 0.611016i | \(0.790761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.5650 | − | 7.25443i | 0.710218 | − | 0.410045i | −0.100924 | − | 0.994894i | \(-0.532180\pi\) |
0.811142 | + | 0.584850i | \(0.198846\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −19.6651 | − | 4.33891i | −1.10800 | − | 0.244470i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0182 | − | 8.09338i | 0.787338 | − | 0.454570i | −0.0516867 | − | 0.998663i | \(-0.516460\pi\) |
0.839024 | + | 0.544094i | \(0.183126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.81959 | − | 6.61573i | 0.213856 | − | 0.370410i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5348 | + | 0.732691i | −0.755439 | + | 0.0408948i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.921796i | 0.0512901i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 8.52800i | − | 0.473048i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.64268 | − | 30.3449i | −0.0908407 | − | 1.67808i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 15.0829 | − | 13.2789i | 0.831550 | − | 0.732088i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6054 | + | 25.2973i | 0.802787 | + | 1.39047i | 0.917775 | + | 0.397100i | \(0.129984\pi\) |
−0.114989 | + | 0.993367i | \(0.536683\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.47540 | − | 0.377379i | 0.190451 | − | 0.0206803i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.5229 | − | 19.9582i | −0.629561 | − | 1.09043i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.46812 | + | 14.6672i | −0.461288 | + | 0.798974i | −0.999025 | − | 0.0441385i | \(-0.985946\pi\) |
0.537738 | + | 0.843112i | \(0.319279\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.44873 | + | 6.79741i | −0.187309 | + | 0.369185i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.8334 | −0.694970 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.3781 | − | 15.3393i | −0.560366 | − | 0.828245i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.03495 | + | 12.3262i | 0.432587 | + | 0.663622i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.7384 | − | 10.2413i | −0.952247 | − | 0.549780i | −0.0584689 | − | 0.998289i | \(-0.518622\pi\) |
−0.893778 | + | 0.448509i | \(0.851955\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.98087 | − | 3.45306i | 0.320149 | − | 0.184838i | −0.331310 | − | 0.943522i | \(-0.607491\pi\) |
0.651459 | + | 0.758684i | \(0.274157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.9009 | − | 28.8421i | 0.581848 | − | 1.53948i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.5025 | − | 18.1908i | −0.558990 | − | 0.968198i | −0.997581 | − | 0.0695118i | \(-0.977856\pi\) |
0.438592 | − | 0.898686i | \(-0.355477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.2663 | − | 13.4328i | −1.23485 | − | 0.712939i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.6507 | + | 4.03560i | −0.828325 | + | 0.213587i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.61864i | 0.138206i | 0.997610 | + | 0.0691032i | \(0.0220138\pi\) | ||||
−0.997610 | + | 0.0691032i | \(0.977986\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9317 | 0.996405 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 49.5286 | + | 25.1288i | 2.59958 | + | 1.31892i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.99679 | − | 3.46225i | −0.313886 | − | 0.181222i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8455 | − | 13.7672i | 1.24472 | − | 0.718641i | 0.274671 | − | 0.961538i | \(-0.411431\pi\) |
0.970052 | + | 0.242897i | \(0.0780977\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.92000 | − | 15.6877i | 0.360241 | − | 0.816668i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.20300 | − | 1.84903i | 0.477796 | − | 0.0959967i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.67768 | + | 4.63788i | −0.138645 | + | 0.240140i | −0.926984 | − | 0.375101i | \(-0.877608\pi\) |
0.788339 | + | 0.615241i | \(0.210941\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.846324 | + | 15.6339i | 0.0437040 | + | 0.807332i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.90754 | −0.355756 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.5330 | 1.10608 | 0.553038 | − | 0.833156i | \(-0.313468\pi\) | ||||
0.553038 | + | 0.833156i | \(0.313468\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.83214 | + | 33.8447i | 0.0938636 | + | 1.73392i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.85948 | + | 3.22071i | −0.0950149 | + | 0.164571i | −0.909615 | − | 0.415453i | \(-0.863623\pi\) |
0.814600 | + | 0.580023i | \(0.196957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −43.1883 | + | 8.67721i | −2.20108 | + | 0.442232i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.47378 | − | 12.9456i | −0.481579 | − | 0.658061i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.72516 | − | 4.46012i | 0.391681 | − | 0.226137i | −0.291207 | − | 0.956660i | \(-0.594057\pi\) |
0.682888 | + | 0.730523i | \(0.260724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2271 | + | 5.90460i | 0.517205 | + | 0.298609i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.0298972 | + | 0.0151686i | 0.00150812 | + | 0.000765157i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.31194 | −0.166642 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3591i | 0.670476i | 0.942134 | + | 0.335238i | \(0.108817\pi\) | ||||
−0.942134 | + | 0.335238i | \(0.891183\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.299045 | − | 1.15975i | −0.0149710 | − | 0.0580599i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6966 | − | 10.7945i | −0.933663 | − | 0.539051i | −0.0456950 | − | 0.998955i | \(-0.514550\pi\) |
−0.887968 | + | 0.459905i | \(0.847884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.80216 | + | 10.0496i | 0.289026 | + | 0.500608i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.90654 | − | 21.7649i | 0.343189 | − | 1.08151i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.62251 | − | 3.82351i | 0.328266 | − | 0.189524i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.8784 | − | 14.9409i | −1.27960 | − | 0.738779i | −0.302827 | − | 0.953045i | \(-0.597931\pi\) |
−0.976775 | + | 0.214266i | \(0.931264\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.00859 | − | 6.14950i | −0.197729 | − | 0.303332i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 27.4714 | + | 9.26630i | 1.35178 | + | 0.455965i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.9989 | −1.12897 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.9630 | − | 31.4628i | 0.781710 | − | 1.54074i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.30438 | + | 16.1157i | −0.454549 | + | 0.787302i | −0.998662 | − | 0.0517100i | \(-0.983533\pi\) |
0.544113 | + | 0.839012i | \(0.316866\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.79010 | − | 16.9570i | −0.477140 | − | 0.826431i | 0.522516 | − | 0.852629i | \(-0.324993\pi\) |
−0.999657 | + | 0.0261979i | \(0.991660\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.4567 | + | 18.3881i | 0.654285 | + | 0.894058i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.53443 | − | 4.38977i | −0.122938 | − | 0.212935i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.1778 | − | 12.6965i | −0.540933 | − | 0.614424i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.64583 | − | 67.3485i | −0.176022 | − | 3.25162i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.3632i | 0.643683i | 0.946794 | + | 0.321842i | \(0.104302\pi\) | ||||
−0.946794 | + | 0.321842i | \(0.895698\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.05246i | − | 0.146692i | −0.997307 | − | 0.0733458i | \(-0.976632\pi\) | ||
0.997307 | − | 0.0733458i | \(-0.0233677\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.10807 | + | 0.276519i | −0.244913 | + | 0.0132581i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.437541 | + | 0.757843i | −0.0209304 | + | 0.0362526i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.8139 | + | 9.70754i | −0.802486 | + | 0.463316i | −0.844340 | − | 0.535808i | \(-0.820007\pi\) |
0.0418537 | + | 0.999124i | \(0.486674\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.3816 | − | 10.1547i | 0.875313 | − | 0.483557i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −28.5753 | + | 16.4979i | −1.35765 | + | 0.783841i | −0.989307 | − | 0.145848i | \(-0.953409\pi\) |
−0.368345 | + | 0.929689i | \(0.620076\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0899 | − | 31.3326i | 0.857542 | − | 1.48531i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.79479 | − | 11.4215i | 0.274084 | − | 0.540217i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.72985i | 0.459180i | 0.973287 | + | 0.229590i | \(0.0737385\pi\) | ||||
−0.973287 | + | 0.229590i | \(0.926262\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 37.5066i | − | 1.76612i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.1453 | + | 13.1319i | −0.946508 | + | 0.616988i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.3209 | + | 29.8969i | 1.23394 | + | 1.40159i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.14815 | + | 12.3810i | 0.334376 | + | 0.579157i | 0.983365 | − | 0.181641i | \(-0.0581410\pi\) |
−0.648989 | + | 0.760798i | \(0.724808\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.96036 | − | 18.0861i | −0.138178 | − | 0.844185i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.95893 | − | 6.85706i | −0.184386 | − | 0.319365i | 0.758984 | − | 0.651110i | \(-0.225696\pi\) |
−0.943369 | + | 0.331744i | \(0.892363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.81566 | − | 15.2692i | 0.409698 | − | 0.709618i | −0.585157 | − | 0.810920i | \(-0.698967\pi\) |
0.994856 | + | 0.101301i | \(0.0323006\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.69295 | + | 7.19935i | 0.217630 | + | 0.333862i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.1745 | 1.16494 | 0.582469 | − | 0.812853i | \(-0.302087\pi\) | ||||
0.582469 | + | 0.812853i | \(0.302087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.7716 | + | 7.68101i | 1.05149 | + | 0.354676i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.68959 | + | 3.33017i | −0.0778523 | + | 0.153446i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −30.3897 | − | 17.5455i | −1.39732 | − | 0.806744i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.325289 | − | 0.187806i | 0.0149253 | − | 0.00861712i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.14901 | + | 10.5816i | 0.0526095 | + | 0.484496i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 11.3258 | + | 19.6168i | 0.517488 | + | 0.896316i | 0.999794 | + | 0.0203125i | \(0.00646613\pi\) |
−0.482306 | + | 0.876003i | \(0.660201\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.98823 | − | 3.45731i | −0.273040 | − | 0.157640i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.7826 | − | 4.11098i | −0.672632 | − | 0.187056i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 29.1702i | − | 1.32455i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.17391 | −0.279767 | −0.139883 | − | 0.990168i | \(-0.544673\pi\) | ||||
−0.139883 | + | 0.990168i | \(0.544673\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.60910 | − | 29.7245i | −0.0727661 | − | 1.34419i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8632 | + | 12.0454i | 0.941544 | + | 0.543601i | 0.890444 | − | 0.455093i | \(-0.150394\pi\) |
0.0511002 | + | 0.998694i | \(0.483727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.55564 | + | 2.05285i | −0.160138 | + | 0.0924557i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.39212 | − | 49.6577i | −0.242358 | − | 2.23195i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.4666 | − | 5.51847i | 1.23205 | − | 0.247537i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.18584 | + | 12.4462i | −0.321682 | + | 0.557170i | −0.980835 | − | 0.194839i | \(-0.937582\pi\) |
0.659153 | + | 0.752009i | \(0.270915\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.6850 | + | 8.46529i | 0.745431 | + | 0.378201i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.4937 | −0.824593 | −0.412296 | − | 0.911050i | \(-0.635273\pi\) | ||||
−0.412296 | + | 0.911050i | \(0.635273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.54069 | −0.246557 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.2281 | + | 21.0081i | −1.43130 | + | 0.933003i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.48887 | + | 12.9711i | −0.331938 | + | 0.574934i | −0.982892 | − | 0.184184i | \(-0.941036\pi\) |
0.650954 | + | 0.759118i | \(0.274369\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.07940 | − | 1.42236i | 0.313174 | − | 0.0629216i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.34021 | − | 0.219368i | 0.0591716 | − | 0.00968532i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.7519 | − | 14.2905i | 1.09070 | − | 0.629716i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.1659 | + | 24.9219i | 1.89843 | + | 1.09606i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.7282 | + | 18.0748i | −1.21713 | + | 0.793396i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.4043 | −0.674873 | −0.337436 | − | 0.941348i | \(-0.609560\pi\) | ||||
−0.337436 | + | 0.941348i | \(0.609560\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.9319i | − | 0.740381i | −0.928956 | − | 0.370191i | \(-0.879292\pi\) | ||
0.928956 | − | 0.370191i | \(-0.120708\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.61278 | + | 4.70072i | 0.201318 | + | 0.205156i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.97329 | + | 3.44868i | 0.260201 | + | 0.150227i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.89462 | − | 10.2098i | −0.256288 | − | 0.443904i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.2676 | + | 30.0777i | −0.575764 | + | 1.30526i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.3707 | + | 16.9572i | −1.27219 | + | 0.734498i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.1951 | + | 9.92760i | 0.743409 | + | 0.429207i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.8087 | − | 1.39712i | 1.11373 | − | 0.0602902i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 27.8240 | − | 36.5516i | 1.19846 | − | 1.57439i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.44265 | 0.276991 | 0.138496 | − | 0.990363i | \(-0.455773\pi\) | ||||
0.138496 | + | 0.990363i | \(0.455773\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.0270 | − | 1.73374i | 1.37441 | − | 0.0744021i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −22.2576 | + | 38.5512i | −0.953409 | + | 1.65135i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.89191 | − | 5.00893i | −0.123649 | − | 0.214166i | 0.797555 | − | 0.603246i | \(-0.206126\pi\) |
−0.921204 | + | 0.389080i | \(0.872793\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.4786 | − | 11.3275i | 0.660611 | − | 0.483445i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.152120 | − | 0.263479i | −0.00648051 | − | 0.0112246i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.59223 | − | 2.28218i | 0.110233 | − | 0.0970480i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.56665 | − | 2.31693i | −0.193844 | − | 0.0983483i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.86933i | − | 0.163949i | −0.996634 | − | 0.0819745i | \(-0.973877\pi\) | ||
0.996634 | − | 0.0819745i | \(-0.0261226\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 31.7302i | 1.34204i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.8920 | − | 33.5840i | −0.924280 | − | 1.41792i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.2712 | − | 21.2544i | 0.517171 | − | 0.895766i | −0.482630 | − | 0.875824i | \(-0.660319\pi\) |
0.999801 | − | 0.0199420i | \(-0.00634815\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.66941 | − | 5.58264i | 0.406795 | − | 0.234863i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.59195 | + | 21.7944i | 0.402824 | + | 0.915278i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.0119 | + | 6.93510i | −0.503567 | + | 0.290735i | −0.730185 | − | 0.683249i | \(-0.760566\pi\) |
0.226618 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.32890 | + | 5.76582i | −0.139310 | + | 0.241292i | −0.927236 | − | 0.374478i | \(-0.877822\pi\) |
0.787926 | + | 0.615770i | \(0.211155\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.55028 | − | 8.51457i | −0.231866 | − | 0.355701i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 4.81200i | − | 0.200674i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 20.4063i | − | 0.849525i | −0.905305 | − | 0.424763i | \(-0.860358\pi\) | ||
0.905305 | − | 0.424763i | \(-0.139642\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.3187 | − | 12.8457i | −1.05221 | − | 0.533848i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.0011 | − | 15.8480i | 0.746811 | − | 0.657485i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.6415 | + | 20.1636i | 0.482140 | + | 0.835090i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −36.4482 | + | 26.6733i | −1.50695 | + | 1.10281i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.43838 | − | 5.95544i | −0.141917 | − | 0.245807i | 0.786302 | − | 0.617843i | \(-0.211993\pi\) |
−0.928218 | + | 0.372036i | \(0.878660\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.255553 | + | 0.442631i | −0.0105299 | + | 0.0182383i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.9355 | + | 0.646113i | −0.490960 | + | 0.0265775i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.7068 | 0.562871 | 0.281435 | − | 0.959580i | \(-0.409189\pi\) | ||||
0.281435 | + | 0.959580i | \(0.409189\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.4337 | + | 7.56705i | 0.919692 | + | 0.310219i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.9099 | − | 0.969534i | 0.733005 | − | 0.0396804i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.3640 | + | 8.87044i | 0.627758 | + | 0.362436i | 0.779883 | − | 0.625925i | \(-0.215278\pi\) |
−0.152125 | + | 0.988361i | \(0.548612\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.31369 | + | 3.64521i | −0.257541 | + | 0.148691i | −0.623212 | − | 0.782053i | \(-0.714173\pi\) |
0.365671 | + | 0.930744i | \(0.380839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.9977 | + | 24.9320i | −0.447863 | + | 1.01531i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −40.6773 | − | 70.4551i | −1.65377 | − | 2.86441i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00042 | + | 3.46434i | 0.243550 | + | 0.140613i | 0.616807 | − | 0.787114i | \(-0.288426\pi\) |
−0.373258 | + | 0.927728i | \(0.621759\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.80751 | − | 3.73627i | 0.154288 | − | 0.151401i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 45.0699i | − | 1.82333i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.60656 | −0.186057 | −0.0930287 | − | 0.995663i | \(-0.529655\pi\) | ||||
−0.0930287 | + | 0.995663i | \(0.529655\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.0406 | + | 13.7155i | −0.848439 | + | 0.553061i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.4618 | − | 14.7004i | −1.02505 | − | 0.591816i | −0.109491 | − | 0.993988i | \(-0.534922\pi\) |
−0.915564 | + | 0.402172i | \(0.868255\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.9537 | − | 16.7165i | 1.16375 | − | 0.671891i | 0.211550 | − | 0.977367i | \(-0.432149\pi\) |
0.952200 | + | 0.305476i | \(0.0988157\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.15093 | − | 16.2744i | 0.246829 | − | 0.653070i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.43169 | + | 36.9891i | 0.297744 | + | 1.48194i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.0602 | − | 26.0850i | 0.602408 | − | 1.04340i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.48863 | − | 1.62223i | 0.0993863 | − | 0.0647857i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.10991 | −0.163873 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.3381 | −1.04850 | −0.524251 | − | 0.851564i | \(-0.675655\pi\) | ||||
−0.524251 | + | 0.851564i | \(0.675655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.6063 | + | 5.38121i | 0.421563 | + | 0.213884i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.8247 | − | 42.9976i | 0.985136 | − | 1.70631i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −41.2024 | − | 5.26300i | −1.63250 | − | 0.208528i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.42925 | + | 31.5810i | 0.135659 | + | 1.24932i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.6878 | − | 6.74797i | 0.461641 | − | 0.266529i | −0.251093 | − | 0.967963i | \(-0.580790\pi\) |
0.712734 | + | 0.701434i | \(0.247457\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.2270 | − | 11.1007i | −0.758239 | − | 0.437769i | 0.0704244 | − | 0.997517i | \(-0.477565\pi\) |
−0.828663 | + | 0.559748i | \(0.810898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.27021 | + | 23.4642i | 0.0500144 | + | 0.923902i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.6716 | −0.458856 | −0.229428 | − | 0.973326i | \(-0.573686\pi\) | ||||
−0.229428 | + | 0.973326i | \(0.573686\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 71.9107i | 2.82274i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.63404 | − | 2.40109i | −0.338395 | − | 0.0941060i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.3964 | + | 11.7759i | 0.798174 | + | 0.460826i | 0.842832 | − | 0.538177i | \(-0.180887\pi\) |
−0.0446586 | + | 0.999002i | \(0.514220\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.0245543 | − | 0.0425292i | −0.000959414 | − | 0.00166175i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.883873 | + | 8.13985i | 0.0344832 | + | 0.317566i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.47020 | + | 5.46763i | −0.368907 | + | 0.212988i | −0.672981 | − | 0.739660i | \(-0.734986\pi\) |
0.304074 | + | 0.952648i | \(0.401653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.96651 | − | 5.75417i | −0.387652 | − | 0.223811i | 0.293490 | − | 0.955962i | \(-0.405183\pi\) |
−0.681142 | + | 0.732151i | \(0.738517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16.4014 | + | 32.3269i | −0.636976 | + | 1.25547i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.560731 | + | 1.66237i | −0.0217442 | + | 0.0644641i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.89764 | −0.150917 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.510098 | + | 0.782529i | 0.0197215 | + | 0.0302543i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 20.9786 | − | 36.3360i | 0.809870 | − | 1.40274i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.5621 | − | 25.2224i | −0.561329 | − | 0.972251i | −0.997381 | − | 0.0723293i | \(-0.976957\pi\) |
0.436051 | − | 0.899922i | \(-0.356377\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.77919 | + | 4.72951i | −0.222441 | + | 0.182039i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.60972 | − | 7.98426i | −0.177166 | − | 0.306860i | 0.763743 | − | 0.645521i | \(-0.223360\pi\) |
−0.940909 | + | 0.338660i | \(0.890026\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.1005 | + | 22.8313i | 0.771385 | + | 0.876185i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.77171 | − | 1.15491i | 0.0678923 | − | 0.0442561i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.2370i | 0.659554i | 0.944059 | + | 0.329777i | \(0.106974\pi\) | ||||
−0.944059 | + | 0.329777i | \(0.893026\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.7528i | 0.410843i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.41549 | − | 18.5578i | 0.359223 | − | 0.708026i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.5265 | − | 18.2324i | 0.401027 | − | 0.694599i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.2875 | + | 7.67157i | −0.505482 | + | 0.291840i | −0.730975 | − | 0.682405i | \(-0.760934\pi\) |
0.225492 | + | 0.974245i | \(0.427601\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 38.4383 | + | 35.1512i | 1.46015 | + | 1.33528i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −44.7563 | + | 25.8401i | −1.69770 | + | 0.980170i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.0790 | + | 17.4574i | −0.381770 | + | 0.661245i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.87489 | + | 0.480432i | −0.335679 | + | 0.0181716i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.1791i | 0.497767i | 0.968533 | + | 0.248883i | \(0.0800636\pi\) | ||||
−0.968533 | + | 0.248883i | \(0.919936\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.304551i | − | 0.0114864i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.80422 | − | 33.3288i | −0.0679507 | − | 1.25524i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.33666 | − | 3.81795i | 0.163097 | − | 0.143589i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.23396 | + | 14.2616i | 0.309233 | + | 0.535607i | 0.978195 | − | 0.207690i | \(-0.0665944\pi\) |
−0.668962 | + | 0.743297i | \(0.733261\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.31273 | + | 3.16027i | 0.0867341 | + | 0.118519i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.27392 | + | 5.67059i | 0.122609 | + | 0.212365i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −49.3992 | + | 85.5620i | −1.84743 | + | 3.19984i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.59034 | + | 18.9025i | −0.358158 | + | 0.705925i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.3816 | 0.499048 | 0.249524 | − | 0.968369i | \(-0.419726\pi\) | ||||
0.249524 | + | 0.968369i | \(0.419726\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.52591 | + | 28.2410i | −0.354763 | + | 1.05175i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.2298 | + | 41.7727i | 1.01269 | + | 1.55354i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.44885 | + | 0.836492i | 0.0538088 | + | 0.0310665i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.16036 | + | 4.13403i | −0.265563 | + | 0.153323i | −0.626870 | − | 0.779124i | \(-0.715664\pi\) |
0.361307 | + | 0.932447i | \(0.382331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.5910 | + | 8.60819i | −0.947815 | + | 0.318822i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.42988 | + | 16.3330i | 0.348777 | + | 0.604099i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.1773 | − | 7.03056i | −0.449778 | − | 0.259679i | 0.257958 | − | 0.966156i | \(-0.416950\pi\) |
−0.707736 | + | 0.706477i | \(0.750284\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30.6796 | − | 2.24255i | −1.13163 | − | 0.0827176i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 59.6082i | 2.19570i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.8860 | 0.952231 | 0.476115 | − | 0.879383i | \(-0.342044\pi\) | ||||
0.476115 | + | 0.879383i | \(0.342044\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.39548 | − | 1.21537i | −0.0880001 | − | 0.0446477i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.5554 | − | 21.1053i | −1.34109 | − | 0.774277i | −0.354120 | − | 0.935200i | \(-0.615220\pi\) |
−0.986967 | + | 0.160923i | \(0.948553\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.2472 | + | 9.38032i | −0.595251 | + | 0.343668i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.0601 | + | 21.9456i | 0.587610 | + | 0.802949i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.2994 | + | 4.07846i | −0.741723 | + | 0.149024i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3157 | − | 36.9198i | 0.777820 | − | 1.34722i | −0.155375 | − | 0.987856i | \(-0.549659\pi\) |
0.933196 | − | 0.359369i | \(-0.117008\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.451588 | + | 8.34207i | 0.0164568 | + | 0.304002i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.2253 | 1.28198 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 51.5092 | 1.87213 | 0.936067 | − | 0.351823i | \(-0.114438\pi\) | ||||
0.936067 | + | 0.351823i | \(0.114438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.05719 | − | 38.0020i | −0.0746713 | − | 1.37938i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4845 | − | 26.8199i | 0.561313 | − | 0.972222i | −0.436070 | − | 0.899913i | \(-0.643630\pi\) |
0.997382 | − | 0.0723091i | \(-0.0230368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.14386 | − | 45.5110i | −0.331030 | − | 1.64761i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.8346 | + | 24.5621i | −0.391725 | + | 0.888043i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56.3119 | − | 32.5117i | 2.03331 | − | 1.17393i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.2004 | + | 23.7871i | 1.48572 | + | 0.857783i | 0.999868 | − | 0.0162553i | \(-0.00517444\pi\) |
0.485856 | + | 0.874039i | \(0.338508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.64256 | − | 3.37016i | −0.239226 | − | 0.121374i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.9971 | −1.00699 | −0.503493 | − | 0.864000i | \(-0.667952\pi\) | ||||
−0.503493 | + | 0.864000i | \(0.667952\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.81053i | − | 0.100957i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.17083 | − | 1.33332i | 0.185503 | − | 0.0478326i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.29362 | − | 0.746872i | −0.0463488 | − | 0.0267595i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.7442 | + | 60.1788i | 1.24325 | + | 2.15337i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.83082 | + | 4.68105i | 0.136902 | + | 0.167287i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.73721 | − | 2.73503i | 0.169078 | − | 0.0976174i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.86189 | + | 5.11642i | 0.315892 | + | 0.182381i | 0.649560 | − | 0.760310i | \(-0.274953\pi\) |
−0.333668 | + | 0.942691i | \(0.608286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.0180 | − | 32.2432i | −0.748260 | − | 1.14789i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.72133 | + | 11.0324i | −0.132315 | + | 0.392269i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −37.9387 | −1.34724 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.05437 | − | 13.9041i | 0.250193 | − | 0.493128i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.7557 | − | 30.7538i | 0.628940 | − | 1.08936i | −0.358825 | − | 0.933405i | \(-0.616823\pi\) |
0.987765 | − | 0.155951i | \(-0.0498441\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.3943 | − | 23.1996i | −0.473857 | − | 0.820744i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −42.5299 | + | 4.61814i | −1.50272 | + | 0.163174i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 8.95517 | + | 15.5108i | 0.316021 | + | 0.547365i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.8518 | + | 16.8696i | 0.523457 | + | 0.594574i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.02759 | − | 37.4552i | −0.0713747 | − | 1.31849i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 18.4932i | − | 0.650188i | −0.945682 | − | 0.325094i | \(-0.894604\pi\) | ||
0.945682 | − | 0.325094i | \(-0.105396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 35.6320i | − | 1.25121i | −0.780140 | − | 0.625605i | \(-0.784852\pi\) | ||
0.780140 | − | 0.625605i | \(-0.215148\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.5415 | + | 1.59920i | −1.03607 | + | 0.0560862i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.8026 | + | 37.7631i | −0.763710 | + | 1.32278i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.21031 | + | 0.698770i | −0.0423432 | + | 0.0244469i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.1478 | − | 45.9926i | 0.354593 | − | 1.60711i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.1389 | − | 9.89514i | 0.598151 | − | 0.345343i | −0.170163 | − | 0.985416i | \(-0.554429\pi\) |
0.768314 | + | 0.640073i | \(0.221096\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.47939 | + | 6.02647i | −0.121284 | + | 0.210070i | −0.920274 | − | 0.391274i | \(-0.872034\pi\) |
0.798990 | + | 0.601344i | \(0.205368\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.39109 | + | 14.5678i | −0.257325 | + | 0.507184i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.92505i | 0.171261i | 0.996327 | + | 0.0856304i | \(0.0272904\pi\) | ||||
−0.996327 | + | 0.0856304i | \(0.972710\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.9274i | 1.49093i | 0.666544 | + | 0.745466i | \(0.267773\pi\) | ||||
−0.666544 | + | 0.745466i | \(0.732227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.65710 | − | 3.03577i | 0.161553 | − | 0.105310i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.7730 | + | 9.53583i | −0.789037 | + | 0.330397i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.7032 | − | 23.7347i | −0.474219 | − | 0.821372i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.59256 | − | 9.50534i | 0.124177 | − | 0.328553i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.84639 | + | 15.3224i | 0.305411 | + | 0.528988i | 0.977353 | − | 0.211616i | \(-0.0678727\pi\) |
−0.671941 | + | 0.740604i | \(0.734539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.8225 | + | 23.9412i | −0.476636 | + | 0.825558i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.7244 | + | 30.2587i | 0.679343 | + | 1.04217i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 56.3529 | 1.93860 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 80.3867 | + | 27.1150i | 2.76212 | + | 0.931683i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.04859 | + | 17.8347i | −0.310547 | + | 0.612085i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.37891 | − | 1.95082i | −0.115828 | − | 0.0668731i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.5730 | − | 13.6099i | 0.807123 | − | 0.465993i | −0.0388328 | − | 0.999246i | \(-0.512364\pi\) |
0.845956 | + | 0.533253i | \(0.179031\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.82009 | − | 0.802860i | −0.0622457 | − | 0.0274572i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.8303 | + | 22.2227i | 0.438274 | + | 0.759113i | 0.997557 | − | 0.0698641i | \(-0.0222566\pi\) |
−0.559282 | + | 0.828977i | \(0.688923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.8087 | + | 9.70452i | 0.573506 | + | 0.331114i | 0.758549 | − | 0.651617i | \(-0.225909\pi\) |
−0.185042 | + | 0.982731i | \(0.559242\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.01734 | − | 25.2336i | 0.239150 | − | 0.859958i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 22.6418i | − | 0.770737i | −0.922763 | − | 0.385368i | \(-0.874074\pi\) | ||
0.922763 | − | 0.385368i | \(-0.125926\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.4845 | 1.64852 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.426969 | − | 7.88729i | −0.0145006 | − | 0.267866i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.41871 | + | 4.28320i | 0.251663 | + | 0.145298i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.6780 | − | 26.9496i | 1.58162 | − | 0.913152i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −27.8343 | + | 20.3696i | −0.942049 | + | 0.689405i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.71099 | + | 23.4476i | 0.159261 | + | 0.792674i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.6395 | + | 30.5525i | −0.595644 | + | 1.03169i | 0.397812 | + | 0.917467i | \(0.369770\pi\) |
−0.993456 | + | 0.114219i | \(0.963564\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −43.7437 | − | 22.1938i | −1.47544 | − | 0.748578i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.975907 | −0.0328791 | −0.0164396 | − | 0.999865i | \(-0.505233\pi\) | ||||
−0.0164396 | + | 0.999865i | \(0.505233\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.26917 | 0.110016 | 0.0550082 | − | 0.998486i | \(-0.482481\pi\) | ||||
0.0550082 | + | 0.998486i | \(0.482481\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 40.3407 | − | 26.2964i | 1.35604 | − | 0.883944i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.1653 | + | 21.0709i | −0.408470 | + | 0.707490i | −0.994718 | − | 0.102641i | \(-0.967271\pi\) |
0.586249 | + | 0.810131i | \(0.300604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.1985 | + | 50.7600i | 0.342046 | + | 1.70244i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −43.6183 | + | 39.8212i | −1.46127 | + | 1.33406i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.71913 | − | 0.992541i | 0.0575285 | − | 0.0332141i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.7882 | − | 18.9303i | −1.09599 | − | 0.632770i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −28.8285 | + | 18.7921i | −0.962556 | + | 0.627449i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.27648 | −0.0759249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 12.5135i | − | 0.416884i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.1628 | − | 17.4900i | −0.571142 | − | 0.582031i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −40.6882 | − | 23.4914i | −1.35252 | − | 0.780880i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.0508 | − | 38.1932i | −0.732186 | − | 1.26818i | −0.955947 | − | 0.293539i | \(-0.905167\pi\) |
0.223761 | − | 0.974644i | \(-0.428166\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.86907 | + | 5.28695i | 0.128329 | + | 0.175357i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1215 | + | 11.6171i | −0.666654 | + | 0.384893i | −0.794807 | − | 0.606862i | \(-0.792428\pi\) |
0.128154 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.5173 | + | 29.7435i | 1.70497 | + | 0.984368i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −28.0554 | + | 1.51874i | −0.927481 | + | 0.0502081i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0485243 | + | 0.0163676i | 0.00160241 | + | 0.000540506i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.91416 | 0.0961291 | 0.0480646 | − | 0.998844i | \(-0.484695\pi\) | ||||
0.0480646 | + | 0.998844i | \(0.484695\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.9959 | − | 2.27340i | 1.38381 | − | 0.0749110i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 31.4166 | − | 54.4151i | 1.03409 | − | 1.79109i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.837349 | + | 1.45033i | 0.0275319 | + | 0.0476866i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.9204 | − | 13.6393i | −1.01556 | − | 0.447973i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.34767 | + | 14.4586i | 0.273878 | + | 0.474371i | 0.969852 | − | 0.243697i | \(-0.0783601\pi\) |
−0.695973 | + | 0.718068i | \(0.745027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.706621 | − | 1.68752i | −0.0231586 | − | 0.0553061i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −50.3914 | − | 25.5666i | −1.64974 | − | 0.837012i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 58.7238i | 1.92047i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 40.4272i | − | 1.32070i | −0.750959 | − | 0.660349i | \(-0.770408\pi\) | ||
0.750959 | − | 0.660349i | \(-0.229592\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.7231 | + | 21.0523i | 0.447836 | + | 0.687015i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.9889 | − | 48.4782i | 0.912411 | − | 1.58034i | 0.101764 | − | 0.994809i | \(-0.467551\pi\) |
0.810648 | − | 0.585534i | \(-0.199115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.5727 | + | 9.56824i | −0.539681 | + | 0.311585i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.66307 | − | 34.4174i | 0.184220 | − | 1.11960i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.8498 | − | 10.3056i | 0.580041 | − | 0.334887i | −0.181109 | − | 0.983463i | \(-0.557969\pi\) |
0.761150 | + | 0.648576i | \(0.224635\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.09748 | − | 14.0253i | 0.262855 | − | 0.455279i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.3101 | + | 23.4869i | 0.496464 | + | 0.761615i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3803i | 0.563005i | 0.959561 | + | 0.281502i | \(0.0908327\pi\) | ||||
−0.959561 | + | 0.281502i | \(0.909167\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.8883i | 0.481773i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.7996 | + | 5.98666i | 0.381428 | + | 0.193521i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.40949 | − | 8.41614i | −0.239265 | − | 0.271771i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.5878 | − | 23.5348i | −0.438317 | − | 0.759187i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.53440 | − | 23.3401i | −0.0816700 | − | 0.752124i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 20.7940 | + | 36.0162i | 0.669381 | + | 1.15940i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.32992 | − | 2.30349i | 0.0427674 | − | 0.0740753i | −0.843849 | − | 0.536580i | \(-0.819716\pi\) |
0.886617 | + | 0.462505i | \(0.153049\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.59426 | + | 0.0863035i | −0.0512151 | + | 0.00277247i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.9474 | −1.12151 | −0.560757 | − | 0.827980i | \(-0.689490\pi\) | ||||
−0.560757 | + | 0.827980i | \(0.689490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.2247 | − | 51.0654i | 0.552199 | − | 1.63708i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.7493 | − | 0.798438i | 0.472357 | − | 0.0255705i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.6938 | + | 7.90614i | 0.438105 | + | 0.252940i | 0.702793 | − | 0.711394i | \(-0.251936\pi\) |
−0.264689 | + | 0.964334i | \(0.585269\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −81.0423 | + | 46.7898i | −2.59012 | + | 1.49541i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 52.3282 | − | 5.68211i | 1.67071 | − | 0.181416i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.2832 | − | 52.4521i | −0.965885 | − | 1.67296i | −0.707219 | − | 0.706994i | \(-0.750051\pi\) |
−0.258666 | − | 0.965967i | \(-0.583283\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.1632 | + | 8.75451i | 0.483141 | + | 0.278942i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.3782 | + | 24.8430i | 0.775967 | + | 0.790761i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17.9040i | 0.569315i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.00131 | 0.254170 | 0.127085 | − | 0.991892i | \(-0.459438\pi\) | ||||
0.127085 | + | 0.991892i | \(0.459438\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.3848 | + | 27.6288i | −1.34504 | + | 0.876774i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.7534 | − | 13.1367i | −0.721333 | − | 0.416462i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.8349 | + | 21.8440i | −1.19824 | + | 0.691805i | −0.960163 | − | 0.279440i | \(-0.909851\pi\) |
−0.238079 | + | 0.971246i | \(0.576518\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.978070 | + | 5.97544i | 0.0309448 | + | 0.189054i |
(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 | 504.2.bu.a.41.13 | yes | 48 | |
3.2 | odd | 2 | 1512.2.bu.a.881.5 | 48 | |||
4.3 | odd | 2 | 1008.2.cc.d.545.12 | 48 | |||
7.6 | odd | 2 | inner | 504.2.bu.a.41.12 | ✓ | 48 | |
9.2 | odd | 6 | inner | 504.2.bu.a.209.12 | yes | 48 | |
9.4 | even | 3 | 4536.2.k.a.3401.10 | 48 | |||
9.5 | odd | 6 | 4536.2.k.a.3401.39 | 48 | |||
9.7 | even | 3 | 1512.2.bu.a.1385.20 | 48 | |||
12.11 | even | 2 | 3024.2.cc.d.881.5 | 48 | |||
21.20 | even | 2 | 1512.2.bu.a.881.20 | 48 | |||
28.27 | even | 2 | 1008.2.cc.d.545.13 | 48 | |||
36.7 | odd | 6 | 3024.2.cc.d.2897.20 | 48 | |||
36.11 | even | 6 | 1008.2.cc.d.209.13 | 48 | |||
63.13 | odd | 6 | 4536.2.k.a.3401.40 | 48 | |||
63.20 | even | 6 | inner | 504.2.bu.a.209.13 | yes | 48 | |
63.34 | odd | 6 | 1512.2.bu.a.1385.5 | 48 | |||
63.41 | even | 6 | 4536.2.k.a.3401.9 | 48 | |||
84.83 | odd | 2 | 3024.2.cc.d.881.20 | 48 | |||
252.83 | odd | 6 | 1008.2.cc.d.209.12 | 48 | |||
252.223 | even | 6 | 3024.2.cc.d.2897.5 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bu.a.41.12 | ✓ | 48 | 7.6 | odd | 2 | inner | |
504.2.bu.a.41.13 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.bu.a.209.12 | yes | 48 | 9.2 | odd | 6 | inner | |
504.2.bu.a.209.13 | yes | 48 | 63.20 | even | 6 | inner | |
1008.2.cc.d.209.12 | 48 | 252.83 | odd | 6 | |||
1008.2.cc.d.209.13 | 48 | 36.11 | even | 6 | |||
1008.2.cc.d.545.12 | 48 | 4.3 | odd | 2 | |||
1008.2.cc.d.545.13 | 48 | 28.27 | even | 2 | |||
1512.2.bu.a.881.5 | 48 | 3.2 | odd | 2 | |||
1512.2.bu.a.881.20 | 48 | 21.20 | even | 2 | |||
1512.2.bu.a.1385.5 | 48 | 63.34 | odd | 6 | |||
1512.2.bu.a.1385.20 | 48 | 9.7 | even | 3 | |||
3024.2.cc.d.881.5 | 48 | 12.11 | even | 2 | |||
3024.2.cc.d.881.20 | 48 | 84.83 | odd | 2 | |||
3024.2.cc.d.2897.5 | 48 | 252.223 | even | 6 | |||
3024.2.cc.d.2897.20 | 48 | 36.7 | odd | 6 | |||
4536.2.k.a.3401.9 | 48 | 63.41 | even | 6 | |||
4536.2.k.a.3401.10 | 48 | 9.4 | even | 3 | |||
4536.2.k.a.3401.39 | 48 | 9.5 | odd | 6 | |||
4536.2.k.a.3401.40 | 48 | 63.13 | odd | 6 |