Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(757,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.757");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 757.22 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.g.757.21 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35918 | + | 0.390688i | 0.961084 | + | 0.276258i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.69473 | + | 1.06203i | 0.847363 | + | 0.531014i | ||||
\(5\) | − | 1.82986i | − | 0.818340i | −0.912458 | − | 0.409170i | \(-0.865818\pi\) | ||
0.912458 | − | 0.409170i | \(-0.134182\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.88851 | + | 2.10559i | 0.667690 | + | 0.744440i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.714906 | − | 2.48711i | 0.226073 | − | 0.786493i | ||||
\(11\) | 3.75866i | 1.13328i | 0.823966 | + | 0.566639i | \(0.191757\pi\) | ||||
−0.823966 | + | 0.566639i | \(0.808243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.09942i | 0.859623i | 0.902919 | + | 0.429812i | \(0.141420\pi\) | ||||
−0.902919 | + | 0.429812i | \(0.858580\pi\) | |||||||
\(14\) | 1.35918 | + | 0.390688i | 0.363255 | + | 0.104416i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.74419 | + | 3.59969i | 0.436048 | + | 0.899923i | ||||
\(17\) | 3.61074 | 0.875734 | 0.437867 | − | 0.899040i | \(-0.355734\pi\) | ||||
0.437867 | + | 0.899040i | \(0.355734\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.65297i | 0.379217i | 0.981860 | + | 0.189608i | \(0.0607218\pi\) | ||||
−0.981860 | + | 0.189608i | \(0.939278\pi\) | |||||||
\(20\) | 1.94337 | − | 3.10112i | 0.434550 | − | 0.693431i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.46846 | + | 5.10869i | −0.313077 | + | 1.08918i | ||||
\(23\) | −7.47934 | −1.55955 | −0.779775 | − | 0.626060i | \(-0.784666\pi\) | ||||
−0.779775 | + | 0.626060i | \(0.784666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.65160 | 0.330320 | ||||||||
\(26\) | −1.21090 | + | 4.21266i | −0.237478 | + | 0.826170i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.69473 | + | 1.06203i | 0.320273 | + | 0.200704i | ||||
\(29\) | − | 2.38629i | − | 0.443123i | −0.975146 | − | 0.221561i | \(-0.928885\pi\) | ||
0.975146 | − | 0.221561i | \(-0.0711153\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.97301 | 1.61160 | 0.805800 | − | 0.592188i | \(-0.201736\pi\) | ||||
0.805800 | + | 0.592188i | \(0.201736\pi\) | |||||||
\(32\) | 0.964311 | + | 5.57406i | 0.170468 | + | 0.985363i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.90764 | + | 1.41067i | 0.841653 | + | 0.241928i | ||||
\(35\) | − | 1.82986i | − | 0.309303i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.94392i | − | 1.47037i | −0.677865 | − | 0.735186i | \(-0.737095\pi\) | ||
0.677865 | − | 0.735186i | \(-0.262905\pi\) | |||||||
\(38\) | −0.645794 | + | 2.24668i | −0.104762 | + | 0.364459i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.85295 | − | 3.45572i | 0.609205 | − | 0.546397i | ||||
\(41\) | 3.04284 | 0.475212 | 0.237606 | − | 0.971362i | \(-0.423637\pi\) | ||||
0.237606 | + | 0.971362i | \(0.423637\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.82597i | 0.278457i | 0.990260 | + | 0.139229i | \(0.0444623\pi\) | ||||
−0.990260 | + | 0.139229i | \(0.955538\pi\) | |||||||
\(44\) | −3.99180 | + | 6.36990i | −0.601787 | + | 0.960299i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.1657 | − | 2.92209i | −1.49886 | − | 0.430838i | ||||
\(47\) | 6.21697 | 0.906838 | 0.453419 | − | 0.891297i | \(-0.350204\pi\) | ||||
0.453419 | + | 0.891297i | \(0.350204\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.24482 | + | 0.645259i | 0.317465 | + | 0.0912535i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.29167 | + | 5.25266i | −0.456472 | + | 0.728413i | ||||
\(53\) | − | 3.21435i | − | 0.441525i | −0.975328 | − | 0.220762i | \(-0.929145\pi\) | ||
0.975328 | − | 0.220762i | \(-0.0708546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.87784 | 0.927407 | ||||||||
\(56\) | 1.88851 | + | 2.10559i | 0.252363 | + | 0.281372i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.932294 | − | 3.24339i | 0.122416 | − | 0.425878i | ||||
\(59\) | − | 12.4366i | − | 1.61911i | −0.587046 | − | 0.809554i | \(-0.699709\pi\) | ||
0.587046 | − | 0.809554i | \(-0.300291\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.91962i | 1.27008i | 0.772480 | + | 0.635039i | \(0.219016\pi\) | ||||
−0.772480 | + | 0.635039i | \(0.780984\pi\) | |||||||
\(62\) | 12.1959 | + | 3.50565i | 1.54888 | + | 0.445218i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.867047 | + | 7.95288i | −0.108381 | + | 0.994109i | ||||
\(65\) | 5.67151 | 0.703464 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.73156i | 1.06673i | 0.845885 | + | 0.533365i | \(0.179073\pi\) | ||||
−0.845885 | + | 0.533365i | \(0.820927\pi\) | |||||||
\(68\) | 6.11922 | + | 3.83471i | 0.742064 | + | 0.465027i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.714906 | − | 2.48711i | 0.0854476 | − | 0.297266i | ||||
\(71\) | −12.4229 | −1.47432 | −0.737161 | − | 0.675717i | \(-0.763834\pi\) | ||||
−0.737161 | + | 0.675717i | \(0.763834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.79655 | 1.14660 | 0.573300 | − | 0.819346i | \(-0.305663\pi\) | ||||
0.573300 | + | 0.819346i | \(0.305663\pi\) | |||||||
\(74\) | 3.49428 | − | 12.1564i | 0.406202 | − | 1.41315i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.75550 | + | 2.80133i | −0.201369 | + | 0.321334i | ||||
\(77\) | 3.75866i | 0.428339i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.24388 | −0.815001 | −0.407500 | − | 0.913205i | \(-0.633599\pi\) | ||||
−0.407500 | + | 0.913205i | \(0.633599\pi\) | |||||||
\(80\) | 6.58695 | − | 3.19163i | 0.736443 | − | 0.356836i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.13577 | + | 1.18880i | 0.456719 | + | 0.131281i | ||||
\(83\) | − | 8.99325i | − | 0.987138i | −0.869707 | − | 0.493569i | \(-0.835692\pi\) | ||
0.869707 | − | 0.493569i | \(-0.164308\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 6.60717i | − | 0.716648i | ||||||
\(86\) | −0.713383 | + | 2.48181i | −0.0769261 | + | 0.267621i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.91421 | + | 7.09827i | −0.843658 | + | 0.756679i | ||||
\(89\) | −1.54944 | −0.164240 | −0.0821202 | − | 0.996622i | \(-0.526169\pi\) | ||||
−0.0821202 | + | 0.996622i | \(0.526169\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.09942i | 0.324907i | ||||||||
\(92\) | −12.6754 | − | 7.94327i | −1.32150 | − | 0.828143i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.44997 | + | 2.42890i | 0.871547 | + | 0.250521i | ||||
\(95\) | 3.02470 | 0.310328 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.2583 | −1.04158 | −0.520788 | − | 0.853686i | \(-0.674362\pi\) | ||||
−0.520788 | + | 0.853686i | \(0.674362\pi\) | |||||||
\(98\) | 1.35918 | + | 0.390688i | 0.137298 | + | 0.0394654i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.79901 | + | 1.75404i | 0.279901 | + | 0.175404i | ||||
\(101\) | − | 5.97880i | − | 0.594913i | −0.954735 | − | 0.297456i | \(-0.903862\pi\) | ||
0.954735 | − | 0.297456i | \(-0.0961383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9060 | −1.66579 | −0.832896 | − | 0.553429i | \(-0.813319\pi\) | ||||
−0.832896 | + | 0.553429i | \(0.813319\pi\) | |||||||
\(104\) | −6.52611 | + | 5.85328i | −0.639938 | + | 0.573962i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.25581 | − | 4.36887i | 0.121975 | − | 0.424342i | ||||
\(107\) | 2.14315i | 0.207186i | 0.994620 | + | 0.103593i | \(0.0330339\pi\) | ||||
−0.994620 | + | 0.103593i | \(0.966966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.34775i | − | 0.799569i | −0.916609 | − | 0.399785i | \(-0.869085\pi\) | ||
0.916609 | − | 0.399785i | \(-0.130915\pi\) | |||||||
\(110\) | 9.34820 | + | 2.68709i | 0.891316 | + | 0.256204i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.74419 | + | 3.59969i | 0.164811 | + | 0.340139i | ||||
\(113\) | −17.5901 | −1.65474 | −0.827369 | − | 0.561659i | \(-0.810163\pi\) | ||||
−0.827369 | + | 0.561659i | \(0.810163\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.6862i | 1.27624i | ||||||||
\(116\) | 2.53431 | − | 4.04411i | 0.235304 | − | 0.375486i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.85883 | − | 16.9035i | 0.447292 | − | 1.55610i | ||||
\(119\) | 3.61074 | 0.330996 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.12753 | −0.284321 | ||||||||
\(122\) | −3.87548 | + | 13.4825i | −0.350869 | + | 1.22065i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.2068 | + | 9.52959i | 1.36561 | + | 0.855782i | ||||
\(125\) | − | 12.1715i | − | 1.08865i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.73427 | 0.863777 | 0.431888 | − | 0.901927i | \(-0.357847\pi\) | ||||
0.431888 | + | 0.901927i | \(0.357847\pi\) | |||||||
\(128\) | −4.28556 | + | 10.4706i | −0.378794 | + | 0.925481i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.70859 | + | 2.21579i | 0.676088 | + | 0.194338i | ||||
\(131\) | 16.7317i | 1.46185i | 0.682456 | + | 0.730926i | \(0.260912\pi\) | ||||
−0.682456 | + | 0.730926i | \(0.739088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.65297i | 0.143330i | ||||||||
\(134\) | −3.41131 | + | 11.8677i | −0.294693 | + | 1.02522i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.81893 | + | 7.60275i | 0.584718 | + | 0.651931i | ||||
\(137\) | −15.1897 | −1.29774 | −0.648872 | − | 0.760897i | \(-0.724759\pi\) | ||||
−0.648872 | + | 0.760897i | \(0.724759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.32344i | 0.790804i | 0.918508 | + | 0.395402i | \(0.129395\pi\) | ||||
−0.918508 | + | 0.395402i | \(0.870605\pi\) | |||||||
\(140\) | 1.94337 | − | 3.10112i | 0.164244 | − | 0.262092i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.8849 | − | 4.85346i | −1.41695 | − | 0.407293i | ||||
\(143\) | −11.6497 | −0.974193 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.36658 | −0.362625 | ||||||||
\(146\) | 13.3152 | + | 3.82739i | 1.10198 | + | 0.316757i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.49870 | − | 15.1575i | 0.780788 | − | 1.24594i | ||||
\(149\) | − | 3.32322i | − | 0.272248i | −0.990692 | − | 0.136124i | \(-0.956535\pi\) | ||
0.990692 | − | 0.136124i | \(-0.0434646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3757 | 1.00712 | 0.503561 | − | 0.863960i | \(-0.332023\pi\) | ||||
0.503561 | + | 0.863960i | \(0.332023\pi\) | |||||||
\(152\) | −3.48048 | + | 3.12165i | −0.282304 | + | 0.253199i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.46846 | + | 5.10869i | −0.118332 | + | 0.411670i | ||||
\(155\) | − | 16.4194i | − | 1.31884i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.9811i | − | 1.03601i | −0.855378 | − | 0.518004i | \(-0.826675\pi\) | ||
0.855378 | − | 0.518004i | \(-0.173325\pi\) | |||||||
\(158\) | −9.84572 | − | 2.83010i | −0.783284 | − | 0.225150i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.1998 | − | 1.76456i | 0.806362 | − | 0.139500i | ||||
\(161\) | −7.47934 | −0.589454 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.17108i | 0.483356i | 0.970356 | + | 0.241678i | \(0.0776978\pi\) | ||||
−0.970356 | + | 0.241678i | \(0.922302\pi\) | |||||||
\(164\) | 5.15679 | + | 3.23159i | 0.402677 | + | 0.252345i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.51355 | − | 12.2234i | 0.272705 | − | 0.948722i | ||||
\(167\) | −5.75113 | −0.445036 | −0.222518 | − | 0.974929i | \(-0.571428\pi\) | ||||
−0.222518 | + | 0.974929i | \(0.571428\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.39362 | 0.261048 | ||||||||
\(170\) | 2.58134 | − | 8.98031i | 0.197980 | − | 0.688758i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.93923 | + | 3.09451i | −0.147865 | + | 0.235954i | ||||
\(173\) | − | 8.09698i | − | 0.615602i | −0.951451 | − | 0.307801i | \(-0.900407\pi\) | ||
0.951451 | − | 0.307801i | \(-0.0995931\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.65160 | 0.124849 | ||||||||
\(176\) | −13.5300 | + | 6.55583i | −1.01986 | + | 0.494164i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.10596 | − | 0.605347i | −0.157849 | − | 0.0453727i | ||||
\(179\) | − | 15.4128i | − | 1.15201i | −0.817447 | − | 0.576003i | \(-0.804611\pi\) | ||
0.817447 | − | 0.576003i | \(-0.195389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.06823i | − | 0.451048i | −0.974238 | − | 0.225524i | \(-0.927591\pi\) | ||
0.974238 | − | 0.225524i | \(-0.0724095\pi\) | |||||||
\(182\) | −1.21090 | + | 4.21266i | −0.0897582 | + | 0.312263i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.1248 | − | 15.7484i | −1.04130 | − | 1.16099i | ||||
\(185\) | −16.3662 | −1.20326 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5716i | 0.992450i | ||||||||
\(188\) | 10.5361 | + | 6.60260i | 0.768421 | + | 0.481544i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.11111 | + | 1.18172i | 0.298251 | + | 0.0857306i | ||||
\(191\) | −2.76632 | −0.200164 | −0.100082 | − | 0.994979i | \(-0.531910\pi\) | ||||
−0.100082 | + | 0.994979i | \(0.531910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.9782 | −1.29410 | −0.647048 | − | 0.762449i | \(-0.723997\pi\) | ||||
−0.647048 | + | 0.762449i | \(0.723997\pi\) | |||||||
\(194\) | −13.9429 | − | 4.00781i | −1.00104 | − | 0.287744i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.69473 | + | 1.06203i | 0.121052 | + | 0.0758592i | ||||
\(197\) | − | 10.5179i | − | 0.749369i | −0.927152 | − | 0.374684i | \(-0.877751\pi\) | ||
0.927152 | − | 0.374684i | \(-0.122249\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.09973 | 0.290622 | 0.145311 | − | 0.989386i | \(-0.453582\pi\) | ||||
0.145311 | + | 0.989386i | \(0.453582\pi\) | |||||||
\(200\) | 3.11906 | + | 3.47759i | 0.220551 | + | 0.245903i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.33584 | − | 8.12625i | 0.164349 | − | 0.571761i | ||||
\(203\) | − | 2.38629i | − | 0.167485i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 5.56799i | − | 0.388885i | ||||||
\(206\) | −22.9782 | − | 6.60495i | −1.60097 | − | 0.460189i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.1569 | + | 5.40598i | −0.773595 | + | 0.374837i | ||||
\(209\) | −6.21294 | −0.429758 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.1789i | 1.45802i | 0.684504 | + | 0.729009i | \(0.260019\pi\) | ||||
−0.684504 | + | 0.729009i | \(0.739981\pi\) | |||||||
\(212\) | 3.41373 | − | 5.44744i | 0.234456 | − | 0.374132i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.837301 | + | 2.91292i | −0.0572367 | + | 0.199123i | ||||
\(215\) | 3.34127 | 0.227873 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.97301 | 0.609128 | ||||||||
\(218\) | 3.26136 | − | 11.3461i | 0.220887 | − | 0.768453i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.6560 | + | 7.30446i | 0.785851 | + | 0.492466i | ||||
\(221\) | 11.1912i | 0.752801i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.30718 | −0.154500 | −0.0772502 | − | 0.997012i | \(-0.524614\pi\) | ||||
−0.0772502 | + | 0.997012i | \(0.524614\pi\) | |||||||
\(224\) | 0.964311 | + | 5.57406i | 0.0644307 | + | 0.372432i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −23.9081 | − | 6.87224i | −1.59034 | − | 0.457134i | ||||
\(227\) | − | 2.69006i | − | 0.178545i | −0.996007 | − | 0.0892727i | \(-0.971546\pi\) | ||
0.996007 | − | 0.0892727i | \(-0.0284543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.3215i | − | 1.01247i | −0.862394 | − | 0.506237i | \(-0.831036\pi\) | ||
0.862394 | − | 0.506237i | \(-0.168964\pi\) | |||||||
\(230\) | −5.34702 | + | 18.6019i | −0.352572 | + | 1.22657i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.02455 | − | 4.50653i | 0.329878 | − | 0.295868i | ||||
\(233\) | 21.3885 | 1.40121 | 0.700605 | − | 0.713549i | \(-0.252914\pi\) | ||||
0.700605 | + | 0.713549i | \(0.252914\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 11.3762i | − | 0.742102i | ||||||
\(236\) | 13.2080 | − | 21.0766i | 0.859769 | − | 1.37197i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.90764 | + | 1.41067i | 0.318115 | + | 0.0914404i | ||||
\(239\) | −7.04548 | −0.455734 | −0.227867 | − | 0.973692i | \(-0.573175\pi\) | ||||
−0.227867 | + | 0.973692i | \(0.573175\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.343612 | −0.0221340 | −0.0110670 | − | 0.999939i | \(-0.503523\pi\) | ||||
−0.0110670 | + | 0.999939i | \(0.503523\pi\) | |||||||
\(242\) | −4.25087 | − | 1.22189i | −0.273256 | − | 0.0785460i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.5349 | + | 16.8110i | −0.674429 | + | 1.07622i | ||||
\(245\) | − | 1.82986i | − | 0.116906i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.12323 | −0.325983 | ||||||||
\(248\) | 16.9456 | + | 18.8935i | 1.07605 | + | 1.19974i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.75526 | − | 16.5433i | 0.300749 | − | 1.04629i | ||||
\(251\) | − | 7.65363i | − | 0.483093i | −0.970389 | − | 0.241546i | \(-0.922345\pi\) | ||
0.970389 | − | 0.241546i | \(-0.0776546\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 28.1123i | − | 1.76740i | ||||||
\(254\) | 13.2306 | + | 3.80306i | 0.830162 | + | 0.238625i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.91558 | + | 12.5571i | −0.619724 | + | 0.784820i | ||||
\(257\) | 7.01134 | 0.437356 | 0.218678 | − | 0.975797i | \(-0.429826\pi\) | ||||
0.218678 | + | 0.975797i | \(0.429826\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.94392i | − | 0.555748i | ||||||
\(260\) | 9.61165 | + | 6.02330i | 0.596089 | + | 0.373549i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.53686 | + | 22.7413i | −0.403849 | + | 1.40496i | ||||
\(263\) | 24.0879 | 1.48532 | 0.742661 | − | 0.669667i | \(-0.233563\pi\) | ||||
0.742661 | + | 0.669667i | \(0.233563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.88182 | −0.361317 | ||||||||
\(266\) | −0.645794 | + | 2.24668i | −0.0395962 | + | 0.137753i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.27316 | + | 14.7976i | −0.566449 | + | 0.903907i | ||||
\(269\) | − | 14.4906i | − | 0.883507i | −0.897136 | − | 0.441753i | \(-0.854357\pi\) | ||
0.897136 | − | 0.441753i | \(-0.145643\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.3057 | 1.71945 | 0.859726 | − | 0.510756i | \(-0.170635\pi\) | ||||
0.859726 | + | 0.510756i | \(0.170635\pi\) | |||||||
\(272\) | 6.29783 | + | 12.9976i | 0.381862 | + | 0.788093i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.6455 | − | 5.93444i | −1.24724 | − | 0.358512i | ||||
\(275\) | 6.20780i | 0.374344i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.70296i | − | 0.582994i | −0.956572 | − | 0.291497i | \(-0.905847\pi\) | ||
0.956572 | − | 0.291497i | \(-0.0941534\pi\) | |||||||
\(278\) | −3.64256 | + | 12.6722i | −0.218466 | + | 0.760029i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.85295 | − | 3.45572i | 0.230258 | − | 0.206519i | ||||
\(281\) | −16.0412 | −0.956937 | −0.478469 | − | 0.878105i | \(-0.658808\pi\) | ||||
−0.478469 | + | 0.878105i | \(0.658808\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0326i | 0.655818i | 0.944709 | + | 0.327909i | \(0.106344\pi\) | ||||
−0.944709 | + | 0.327909i | \(0.893656\pi\) | |||||||
\(284\) | −21.0533 | − | 13.1934i | −1.24929 | − | 0.782886i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.8339 | − | 4.55138i | −0.936281 | − | 0.269129i | ||||
\(287\) | 3.04284 | 0.179613 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.96254 | −0.233091 | ||||||||
\(290\) | −5.93496 | − | 1.70597i | −0.348513 | − | 0.100178i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.6025 | + | 10.4042i | 0.971586 | + | 0.608860i | ||||
\(293\) | 10.9744i | 0.641131i | 0.947226 | + | 0.320566i | \(0.103873\pi\) | ||||
−0.947226 | + | 0.320566i | \(0.896127\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.7573 | −1.32498 | ||||||||
\(296\) | 18.8323 | − | 16.8907i | 1.09460 | − | 0.981752i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.29834 | − | 4.51684i | 0.0752108 | − | 0.261653i | ||||
\(299\) | − | 23.1816i | − | 1.34062i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.82597i | 0.105247i | ||||||||
\(302\) | 16.8208 | + | 4.83504i | 0.967928 | + | 0.278225i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.95018 | + | 2.88309i | −0.341266 | + | 0.165357i | ||||
\(305\) | 18.1516 | 1.03936 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 28.2184i | − | 1.61051i | −0.592931 | − | 0.805254i | \(-0.702029\pi\) | ||
0.592931 | − | 0.805254i | \(-0.297971\pi\) | |||||||
\(308\) | −3.99180 | + | 6.36990i | −0.227454 | + | 0.362959i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.41485 | − | 22.3169i | 0.364339 | − | 1.26751i | ||||
\(311\) | −24.3156 | −1.37881 | −0.689407 | − | 0.724375i | \(-0.742129\pi\) | ||||
−0.689407 | + | 0.724375i | \(0.742129\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.29548 | −0.468889 | −0.234444 | − | 0.972130i | \(-0.575327\pi\) | ||||
−0.234444 | + | 0.972130i | \(0.575327\pi\) | |||||||
\(314\) | 5.07157 | − | 17.6437i | 0.286205 | − | 0.995690i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.2764 | − | 7.69321i | −0.690601 | − | 0.432777i | ||||
\(317\) | − | 0.906822i | − | 0.0509322i | −0.999676 | − | 0.0254661i | \(-0.991893\pi\) | ||
0.999676 | − | 0.0254661i | \(-0.00810699\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.96925 | 0.502182 | ||||||||
\(320\) | 14.5527 | + | 1.58658i | 0.813519 | + | 0.0886924i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.1657 | − | 2.92209i | −0.566515 | − | 0.162841i | ||||
\(323\) | 5.96844i | 0.332093i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.11899i | 0.283950i | ||||||||
\(326\) | −2.41096 | + | 8.38759i | −0.133531 | + | 0.464546i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.74645 | + | 6.40699i | 0.317295 | + | 0.353767i | ||||
\(329\) | 6.21697 | 0.342753 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 31.7662i | − | 1.74603i | −0.487697 | − | 0.873013i | \(-0.662163\pi\) | ||
0.487697 | − | 0.873013i | \(-0.337837\pi\) | |||||||
\(332\) | 9.55109 | − | 15.2411i | 0.524184 | − | 0.836464i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.81681 | − | 2.24690i | −0.427717 | − | 0.122945i | ||||
\(335\) | 15.9776 | 0.872948 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.4231 | −1.87515 | −0.937573 | − | 0.347788i | \(-0.886933\pi\) | ||||
−0.937573 | + | 0.347788i | \(0.886933\pi\) | |||||||
\(338\) | 4.61253 | + | 1.32585i | 0.250889 | + | 0.0721166i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 7.01700 | − | 11.1973i | 0.380550 | − | 0.607261i | ||||
\(341\) | 33.7265i | 1.82639i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −3.84474 | + | 3.44836i | −0.207295 | + | 0.185923i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.16339 | − | 11.0052i | 0.170065 | − | 0.591645i | ||||
\(347\) | 23.5611i | 1.26483i | 0.774630 | + | 0.632414i | \(0.217936\pi\) | ||||
−0.774630 | + | 0.632414i | \(0.782064\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 28.6095i | − | 1.53143i | −0.643179 | − | 0.765716i | \(-0.722385\pi\) | ||
0.643179 | − | 0.765716i | \(-0.277615\pi\) | |||||||
\(350\) | 2.24482 | + | 0.645259i | 0.119990 | + | 0.0344906i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −20.9510 | + | 3.62452i | −1.11669 | + | 0.193187i | ||||
\(353\) | −7.03843 | −0.374618 | −0.187309 | − | 0.982301i | \(-0.559976\pi\) | ||||
−0.187309 | + | 0.982301i | \(0.559976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.7321i | 1.20650i | ||||||||
\(356\) | −2.62588 | − | 1.64555i | −0.139171 | − | 0.0872139i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.02159 | − | 20.9487i | 0.318251 | − | 1.10717i | ||||
\(359\) | −13.2261 | −0.698046 | −0.349023 | − | 0.937114i | \(-0.613487\pi\) | ||||
−0.349023 | + | 0.937114i | \(0.613487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.2677 | 0.856195 | ||||||||
\(362\) | 2.37079 | − | 8.24781i | 0.124606 | − | 0.433495i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.29167 | + | 5.25266i | −0.172530 | + | 0.275314i | ||||
\(365\) | − | 17.9263i | − | 0.938308i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.6530 | 0.608281 | 0.304140 | − | 0.952627i | \(-0.401631\pi\) | ||||
0.304140 | + | 0.952627i | \(0.401631\pi\) | |||||||
\(368\) | −13.0454 | − | 26.9233i | −0.680039 | − | 1.40347i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −22.2445 | − | 6.39406i | −1.15644 | − | 0.332411i | ||||
\(371\) | − | 3.21435i | − | 0.166881i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 9.85547i | − | 0.510297i | −0.966902 | − | 0.255148i | \(-0.917876\pi\) | ||
0.966902 | − | 0.255148i | \(-0.0821243\pi\) | |||||||
\(374\) | −5.30224 | + | 18.4462i | −0.274172 | + | 0.953828i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.7408 | + | 13.0904i | 0.605487 | + | 0.675087i | ||||
\(377\) | 7.39610 | 0.380919 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.5581i | 1.77513i | 0.460684 | + | 0.887564i | \(0.347604\pi\) | ||||
−0.460684 | + | 0.887564i | \(0.652396\pi\) | |||||||
\(380\) | 5.12605 | + | 3.21232i | 0.262961 | + | 0.164789i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.75992 | − | 1.08077i | −0.192374 | − | 0.0552968i | ||||
\(383\) | 11.4073 | 0.582884 | 0.291442 | − | 0.956589i | \(-0.405865\pi\) | ||||
0.291442 | + | 0.956589i | \(0.405865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.87784 | 0.350527 | ||||||||
\(386\) | −24.4355 | − | 7.02385i | −1.24373 | − | 0.357504i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −17.3851 | − | 10.8946i | −0.882593 | − | 0.553092i | ||||
\(389\) | 37.3093i | 1.89166i | 0.324667 | + | 0.945828i | \(0.394748\pi\) | ||||
−0.324667 | + | 0.945828i | \(0.605252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0060 | −1.36575 | ||||||||
\(392\) | 1.88851 | + | 2.10559i | 0.0953842 | + | 0.106349i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.10921 | − | 14.2957i | 0.207019 | − | 0.720206i | ||||
\(395\) | 13.2553i | 0.666947i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8903i | 0.546567i | 0.961934 | + | 0.273283i | \(0.0881097\pi\) | ||||
−0.961934 | + | 0.273283i | \(0.911890\pi\) | |||||||
\(398\) | 5.57226 | + | 1.60171i | 0.279312 | + | 0.0802867i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.88071 | + | 5.94525i | 0.144035 | + | 0.297262i | ||||
\(401\) | 20.6784 | 1.03263 | 0.516316 | − | 0.856398i | \(-0.327303\pi\) | ||||
0.516316 | + | 0.856398i | \(0.327303\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.8111i | 1.38537i | ||||||||
\(404\) | 6.34965 | − | 10.1324i | 0.315907 | − | 0.504107i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.932294 | − | 3.24339i | 0.0462690 | − | 0.160967i | ||||
\(407\) | 33.6172 | 1.66634 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.1209 | −0.797129 | −0.398565 | − | 0.917140i | \(-0.630492\pi\) | ||||
−0.398565 | + | 0.917140i | \(0.630492\pi\) | |||||||
\(410\) | 2.17535 | − | 7.56789i | 0.107433 | − | 0.373751i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.6510 | − | 17.9546i | −1.41153 | − | 0.884559i | ||||
\(413\) | − | 12.4366i | − | 0.611965i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4564 | −0.807814 | ||||||||
\(416\) | −17.2763 | + | 2.98880i | −0.847041 | + | 0.146538i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.44449 | − | 2.42732i | −0.413034 | − | 0.118724i | ||||
\(419\) | 26.5958i | 1.29929i | 0.760237 | + | 0.649645i | \(0.225083\pi\) | ||||
−0.760237 | + | 0.649645i | \(0.774917\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 27.2198i | − | 1.32661i | −0.748348 | − | 0.663307i | \(-0.769153\pi\) | ||
0.748348 | − | 0.663307i | \(-0.230847\pi\) | |||||||
\(422\) | −8.27435 | + | 28.7859i | −0.402789 | + | 1.40128i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.76811 | − | 6.07034i | 0.328689 | − | 0.294802i | ||||
\(425\) | 5.96350 | 0.289272 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.91962i | 0.480044i | ||||||||
\(428\) | −2.27608 | + | 3.63205i | −0.110019 | + | 0.175562i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.54138 | + | 1.30539i | 0.219005 | + | 0.0629517i | ||||
\(431\) | 4.58135 | 0.220676 | 0.110338 | − | 0.993894i | \(-0.464807\pi\) | ||||
0.110338 | + | 0.993894i | \(0.464807\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.43085 | 0.212933 | 0.106466 | − | 0.994316i | \(-0.466046\pi\) | ||||
0.106466 | + | 0.994316i | \(0.466046\pi\) | |||||||
\(434\) | 12.1959 | + | 3.50565i | 0.585423 | + | 0.168276i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.86554 | − | 14.1471i | 0.424582 | − | 0.677525i | ||||
\(437\) | − | 12.3631i | − | 0.591407i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2867 | −0.538685 | −0.269343 | − | 0.963044i | \(-0.586806\pi\) | ||||
−0.269343 | + | 0.963044i | \(0.586806\pi\) | |||||||
\(440\) | 12.9889 | + | 14.4819i | 0.619220 | + | 0.690399i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.37226 | + | 15.2108i | −0.207967 | + | 0.723505i | ||||
\(443\) | 3.69129i | 0.175378i | 0.996148 | + | 0.0876892i | \(0.0279482\pi\) | ||||
−0.996148 | + | 0.0876892i | \(0.972052\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.83526i | 0.134404i | ||||||||
\(446\) | −3.13587 | − | 0.901388i | −0.148488 | − | 0.0426820i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.867047 | + | 7.95288i | −0.0409641 | + | 0.375738i | ||||
\(449\) | −18.0692 | −0.852737 | −0.426368 | − | 0.904550i | \(-0.640207\pi\) | ||||
−0.426368 | + | 0.904550i | \(0.640207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.4370i | 0.538548i | ||||||||
\(452\) | −29.8104 | − | 18.6812i | −1.40216 | − | 0.878689i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.05097 | − | 3.65626i | 0.0493246 | − | 0.171597i | ||||
\(455\) | 5.67151 | 0.265884 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.4880 | −1.00517 | −0.502583 | − | 0.864529i | \(-0.667617\pi\) | ||||
−0.502583 | + | 0.864529i | \(0.667617\pi\) | |||||||
\(458\) | 5.98593 | − | 20.8247i | 0.279704 | − | 0.973073i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.5351 | + | 23.1943i | −0.677702 | + | 1.08144i | ||||
\(461\) | − | 16.7622i | − | 0.780695i | −0.920668 | − | 0.390348i | \(-0.872355\pi\) | ||
0.920668 | − | 0.390348i | \(-0.127645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.74065 | −0.452686 | −0.226343 | − | 0.974048i | \(-0.572677\pi\) | ||||
−0.226343 | + | 0.974048i | \(0.572677\pi\) | |||||||
\(464\) | 8.58991 | − | 4.16215i | 0.398776 | − | 0.193223i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 29.0708 | + | 8.35624i | 1.34668 | + | 0.387096i | ||||
\(467\) | 33.8683i | 1.56724i | 0.621241 | + | 0.783620i | \(0.286629\pi\) | ||||
−0.621241 | + | 0.783620i | \(0.713371\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.73156i | 0.403186i | ||||||||
\(470\) | 4.44455 | − | 15.4623i | 0.205012 | − | 0.713222i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 26.1864 | − | 23.4867i | 1.20533 | − | 1.08106i | ||||
\(473\) | −6.86319 | −0.315570 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.73004i | 0.125263i | ||||||||
\(476\) | 6.11922 | + | 3.83471i | 0.280474 | + | 0.175764i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.57606 | − | 2.75258i | −0.437999 | − | 0.125900i | ||||
\(479\) | −12.0611 | −0.551084 | −0.275542 | − | 0.961289i | \(-0.588857\pi\) | ||||
−0.275542 | + | 0.961289i | \(0.588857\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 27.7209 | 1.26397 | ||||||||
\(482\) | −0.467030 | − | 0.134245i | −0.0212726 | − | 0.00611470i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.30031 | − | 3.32153i | −0.240923 | − | 0.150978i | ||||
\(485\) | 18.7714i | 0.852364i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.5752 | −0.524522 | −0.262261 | − | 0.964997i | \(-0.584468\pi\) | ||||
−0.262261 | + | 0.964997i | \(0.584468\pi\) | |||||||
\(488\) | −20.8867 | + | 18.7333i | −0.945496 | + | 0.848018i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.714906 | − | 2.48711i | 0.0322961 | − | 0.112356i | ||||
\(491\) | − | 40.0965i | − | 1.80953i | −0.425911 | − | 0.904765i | \(-0.640046\pi\) | ||
0.425911 | − | 0.904765i | \(-0.359954\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.61627i | − | 0.388057i | ||||||
\(494\) | −6.96338 | − | 2.00158i | −0.313297 | − | 0.0900556i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.6507 | + | 32.3001i | 0.702735 | + | 1.45032i | ||||
\(497\) | −12.4229 | −0.557241 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 33.2035i | − | 1.48639i | −0.669073 | − | 0.743197i | \(-0.733309\pi\) | ||
0.669073 | − | 0.743197i | \(-0.266691\pi\) | |||||||
\(500\) | 12.9265 | − | 20.6274i | 0.578090 | − | 0.922485i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.99018 | − | 10.4026i | 0.133458 | − | 0.464292i | ||||
\(503\) | 4.46295 | 0.198993 | 0.0994967 | − | 0.995038i | \(-0.468277\pi\) | ||||
0.0994967 | + | 0.995038i | \(0.468277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9404 | −0.486841 | ||||||||
\(506\) | 10.9831 | − | 38.2096i | 0.488260 | − | 1.69862i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.4969 | + | 10.3381i | 0.731933 | + | 0.458678i | ||||
\(509\) | 28.2457i | 1.25197i | 0.779837 | + | 0.625983i | \(0.215302\pi\) | ||||
−0.779837 | + | 0.625983i | \(0.784698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.79655 | 0.433374 | ||||||||
\(512\) | −18.3830 | + | 13.1935i | −0.812419 | + | 0.583074i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.52966 | + | 2.73925i | 0.420335 | + | 0.120823i | ||||
\(515\) | 30.9356i | 1.36318i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.3675i | 1.02770i | ||||||||
\(518\) | 3.49428 | − | 12.1564i | 0.153530 | − | 0.534121i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.7107 | + | 11.9419i | 0.469696 | + | 0.523687i | ||||
\(521\) | 30.4655 | 1.33472 | 0.667359 | − | 0.744737i | \(-0.267425\pi\) | ||||
0.667359 | + | 0.744737i | \(0.267425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 36.5909i | − | 1.60001i | −0.599994 | − | 0.800004i | \(-0.704831\pi\) | ||
0.599994 | − | 0.800004i | \(-0.295169\pi\) | |||||||
\(524\) | −17.7695 | + | 28.3556i | −0.776264 | + | 1.23872i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32.7397 | + | 9.41085i | 1.42752 | + | 0.410332i | ||||
\(527\) | 32.3992 | 1.41133 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.9405 | 1.43219 | ||||||||
\(530\) | −7.99444 | − | 2.29796i | −0.347256 | − | 0.0998169i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.75550 | + | 2.80133i | −0.0761105 | + | 0.121453i | ||||
\(533\) | 9.43104i | 0.408504i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.92167 | 0.169548 | ||||||||
\(536\) | −18.3851 | + | 16.4897i | −0.794116 | + | 0.712245i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.66130 | − | 19.6953i | 0.244076 | − | 0.849124i | ||||
\(539\) | 3.75866i | 0.161897i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 42.8045i | − | 1.84031i | −0.391556 | − | 0.920154i | \(-0.628063\pi\) | ||
0.391556 | − | 0.920154i | \(-0.371937\pi\) | |||||||
\(542\) | 38.4725 | + | 11.0587i | 1.65254 | + | 0.475012i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.48188 | + | 20.1265i | 0.149284 | + | 0.862916i | ||||
\(545\) | −15.2752 | −0.654319 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.57128i | − | 0.280968i | −0.990083 | − | 0.140484i | \(-0.955134\pi\) | ||
0.990083 | − | 0.140484i | \(-0.0448658\pi\) | |||||||
\(548\) | −25.7424 | − | 16.1319i | −1.09966 | − | 0.689121i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.42531 | + | 8.43750i | −0.103416 | + | 0.359776i | ||||
\(551\) | 3.94446 | 0.168040 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.24388 | −0.308041 | ||||||||
\(554\) | 3.79083 | − | 13.1880i | 0.161057 | − | 0.560306i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.90176 | + | 15.8007i | −0.419928 | + | 0.670098i | ||||
\(557\) | 31.2762i | 1.32521i | 0.748967 | + | 0.662607i | \(0.230550\pi\) | ||||
−0.748967 | + | 0.662607i | \(0.769450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.65943 | −0.239368 | ||||||||
\(560\) | 6.58695 | − | 3.19163i | 0.278349 | − | 0.134871i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.8028 | − | 6.26710i | −0.919697 | − | 0.264362i | ||||
\(563\) | − | 3.69436i | − | 0.155699i | −0.996965 | − | 0.0778493i | \(-0.975195\pi\) | ||
0.996965 | − | 0.0778493i | \(-0.0248053\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.1875i | 1.35414i | ||||||||
\(566\) | −4.31029 | + | 14.9952i | −0.181175 | + | 0.630296i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23.4607 | − | 26.1575i | −0.984390 | − | 1.09754i | ||||
\(569\) | −11.6082 | −0.486641 | −0.243320 | − | 0.969946i | \(-0.578237\pi\) | ||||
−0.243320 | + | 0.969946i | \(0.578237\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8739i | 1.12464i | 0.826920 | + | 0.562319i | \(0.190091\pi\) | ||||
−0.826920 | + | 0.562319i | \(0.809909\pi\) | |||||||
\(572\) | −19.7430 | − | 12.3723i | −0.825495 | − | 0.517310i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.13577 | + | 1.18880i | 0.172624 | + | 0.0496197i | ||||
\(575\) | −12.3529 | −0.515150 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.2051 | 0.424843 | 0.212421 | − | 0.977178i | \(-0.431865\pi\) | ||||
0.212421 | + | 0.977178i | \(0.431865\pi\) | |||||||
\(578\) | −5.38580 | − | 1.54812i | −0.224020 | − | 0.0643932i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.40016 | − | 4.63743i | −0.307275 | − | 0.192559i | ||||
\(581\) | − | 8.99325i | − | 0.373103i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0817 | 0.500371 | ||||||||
\(584\) | 18.5009 | + | 20.6275i | 0.765573 | + | 0.853574i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.28756 | + | 14.9162i | −0.177118 | + | 0.616181i | ||||
\(587\) | − | 25.0075i | − | 1.03217i | −0.856538 | − | 0.516085i | \(-0.827389\pi\) | ||
0.856538 | − | 0.516085i | \(-0.172611\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8321i | 0.611146i | ||||||||
\(590\) | −30.9312 | − | 8.89100i | −1.27342 | − | 0.366037i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 32.1954 | − | 15.5999i | 1.32322 | − | 0.641153i | ||||
\(593\) | 43.4040 | 1.78239 | 0.891195 | − | 0.453620i | \(-0.149868\pi\) | ||||
0.891195 | + | 0.453620i | \(0.149868\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.60717i | − | 0.270867i | ||||||
\(596\) | 3.52935 | − | 5.63194i | 0.144568 | − | 0.230693i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.05676 | − | 31.5079i | 0.370358 | − | 1.28845i | ||||
\(599\) | −2.47057 | −0.100945 | −0.0504724 | − | 0.998725i | \(-0.516073\pi\) | ||||
−0.0504724 | + | 0.998725i | \(0.516073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.2142 | −0.539018 | −0.269509 | − | 0.962998i | \(-0.586861\pi\) | ||||
−0.269509 | + | 0.962998i | \(0.586861\pi\) | |||||||
\(602\) | −0.713383 | + | 2.48181i | −0.0290753 | + | 0.101151i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.9734 | + | 13.1434i | 0.853397 | + | 0.534795i | ||||
\(605\) | 5.72296i | 0.232671i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.4562 | 1.19559 | 0.597796 | − | 0.801649i | \(-0.296043\pi\) | ||||
0.597796 | + | 0.801649i | \(0.296043\pi\) | |||||||
\(608\) | −9.21373 | + | 1.59397i | −0.373666 | + | 0.0646442i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.6712 | + | 7.09159i | 0.998907 | + | 0.287130i | ||||
\(611\) | 19.2690i | 0.779539i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.9457i | 0.684429i | 0.939622 | + | 0.342215i | \(0.111177\pi\) | ||||
−0.939622 | + | 0.342215i | \(0.888823\pi\) | |||||||
\(614\) | 11.0246 | − | 38.3538i | 0.444916 | − | 1.54783i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.91421 | + | 7.09827i | −0.318873 | + | 0.285998i | ||||
\(617\) | 42.1917 | 1.69858 | 0.849288 | − | 0.527930i | \(-0.177032\pi\) | ||||
0.849288 | + | 0.527930i | \(0.177032\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.7508i | 1.91927i | 0.281256 | + | 0.959633i | \(0.409249\pi\) | ||||
−0.281256 | + | 0.959633i | \(0.590751\pi\) | |||||||
\(620\) | 17.4379 | − | 27.8264i | 0.700321 | − | 1.11753i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −33.0493 | − | 9.49982i | −1.32515 | − | 0.380908i | ||||
\(623\) | −1.54944 | −0.0620770 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.0142 | −0.560569 | ||||||||
\(626\) | −11.2750 | − | 3.24095i | −0.450641 | − | 0.129534i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.7863 | − | 21.9995i | 0.550135 | − | 0.877875i | ||||
\(629\) | − | 32.2942i | − | 1.28765i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3539 | 1.16856 | 0.584279 | − | 0.811553i | \(-0.301377\pi\) | ||||
0.584279 | + | 0.811553i | \(0.301377\pi\) | |||||||
\(632\) | −13.6802 | − | 15.2527i | −0.544167 | − | 0.606719i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.354284 | − | 1.23253i | 0.0140704 | − | 0.0489501i | ||||
\(635\) | − | 17.8124i | − | 0.706863i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.09942i | 0.122803i | ||||||||
\(638\) | 12.1908 | + | 3.50418i | 0.482638 | + | 0.138732i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 19.1598 | + | 7.84200i | 0.757358 | + | 0.309982i | ||||
\(641\) | 15.2796 | 0.603509 | 0.301754 | − | 0.953386i | \(-0.402428\pi\) | ||||
0.301754 | + | 0.953386i | \(0.402428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.8547i | − | 1.05905i | −0.848295 | − | 0.529524i | \(-0.822371\pi\) | ||
0.848295 | − | 0.529524i | \(-0.177629\pi\) | |||||||
\(644\) | −12.6754 | − | 7.94327i | −0.499482 | − | 0.313008i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.33180 | + | 8.11217i | −0.0917433 | + | 0.319169i | ||||
\(647\) | −13.6808 | −0.537850 | −0.268925 | − | 0.963161i | \(-0.586668\pi\) | ||||
−0.268925 | + | 0.963161i | \(0.586668\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 46.7450 | 1.83490 | ||||||||
\(650\) | −1.99993 | + | 6.95762i | −0.0784436 | + | 0.272900i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.55386 | + | 10.4583i | −0.256669 | + | 0.409578i | ||||
\(653\) | − | 5.65064i | − | 0.221127i | −0.993869 | − | 0.110563i | \(-0.964734\pi\) | ||
0.993869 | − | 0.110563i | \(-0.0352655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 30.6167 | 1.19629 | ||||||||
\(656\) | 5.30731 | + | 10.9533i | 0.207216 | + | 0.427655i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.44997 | + | 2.42890i | 0.329414 | + | 0.0946882i | ||||
\(659\) | 24.7127i | 0.962669i | 0.876537 | + | 0.481334i | \(0.159848\pi\) | ||||
−0.876537 | + | 0.481334i | \(0.840152\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 20.1467i | − | 0.783615i | −0.920047 | − | 0.391807i | \(-0.871850\pi\) | ||
0.920047 | − | 0.391807i | \(-0.128150\pi\) | |||||||
\(662\) | 12.4106 | − | 43.1758i | 0.482354 | − | 1.67808i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.9361 | − | 16.9839i | 0.734865 | − | 0.659102i | ||||
\(665\) | 3.02470 | 0.117293 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.8479i | 0.691072i | ||||||||
\(668\) | −9.74659 | − | 6.10786i | −0.377107 | − | 0.236320i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21.7163 | + | 6.24224i | 0.838976 | + | 0.241159i | ||||
\(671\) | −37.2845 | −1.43935 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.0926 | −0.890155 | −0.445077 | − | 0.895492i | \(-0.646824\pi\) | ||||
−0.445077 | + | 0.895492i | \(0.646824\pi\) | |||||||
\(674\) | −46.7871 | − | 13.4487i | −1.80217 | − | 0.518024i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.75126 | + | 3.60412i | 0.221202 | + | 0.138620i | ||||
\(677\) | − | 5.41515i | − | 0.208121i | −0.994571 | − | 0.104061i | \(-0.966816\pi\) | ||
0.994571 | − | 0.104061i | \(-0.0331836\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2583 | −0.393679 | ||||||||
\(680\) | 13.9120 | − | 12.4777i | 0.533501 | − | 0.478498i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.1765 | + | 45.8403i | −0.504556 | + | 1.75532i | ||||
\(683\) | 16.5403i | 0.632898i | 0.948609 | + | 0.316449i | \(0.102491\pi\) | ||||
−0.948609 | + | 0.316449i | \(0.897509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27.7951i | 1.06200i | ||||||||
\(686\) | 1.35918 | + | 0.390688i | 0.0518936 | + | 0.0149165i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.57292 | + | 3.18484i | −0.250590 | + | 0.121421i | ||||
\(689\) | 9.96261 | 0.379545 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 17.8893i | − | 0.680542i | −0.940327 | − | 0.340271i | \(-0.889481\pi\) | ||
0.940327 | − | 0.340271i | \(-0.110519\pi\) | |||||||
\(692\) | 8.59922 | − | 13.7222i | 0.326893 | − | 0.521638i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.20505 | + | 32.0238i | −0.349419 | + | 1.21561i | ||||
\(695\) | 17.0606 | 0.647147 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.9869 | 0.416160 | ||||||||
\(698\) | 11.1774 | − | 38.8854i | 0.423070 | − | 1.47183i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.79901 | + | 1.75404i | 0.105793 | + | 0.0662966i | ||||
\(701\) | 28.6956i | 1.08382i | 0.840437 | + | 0.541909i | \(0.182298\pi\) | ||||
−0.840437 | + | 0.541909i | \(0.817702\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.7840 | 0.557590 | ||||||||
\(704\) | −29.8922 | − | 3.25894i | −1.12660 | − | 0.122826i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.56647 | − | 2.74983i | −0.360039 | − | 0.103491i | ||||
\(707\) | − | 5.97880i | − | 0.224856i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.2083i | 1.62272i | 0.584546 | + | 0.811360i | \(0.301272\pi\) | ||||
−0.584546 | + | 0.811360i | \(0.698728\pi\) | |||||||
\(710\) | −8.88117 | + | 30.8970i | −0.333304 | + | 1.15954i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.92614 | − | 3.26249i | −0.109662 | − | 0.122267i | ||||
\(713\) | −67.1122 | −2.51337 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.3173i | 0.797221i | ||||||||
\(716\) | 16.3688 | − | 26.1205i | 0.611732 | − | 0.976168i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −17.9766 | − | 5.16727i | −0.670881 | − | 0.192841i | ||||
\(719\) | −40.7179 | −1.51852 | −0.759261 | − | 0.650786i | \(-0.774440\pi\) | ||||
−0.759261 | + | 0.650786i | \(0.774440\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.9060 | −0.629611 | ||||||||
\(722\) | 22.1107 | + | 6.35559i | 0.822875 | + | 0.236531i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.44463 | − | 10.2840i | 0.239513 | − | 0.382202i | ||||
\(725\) | − | 3.94119i | − | 0.146372i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.96551 | −0.0728967 | −0.0364483 | − | 0.999336i | \(-0.511604\pi\) | ||||
−0.0364483 | + | 0.999336i | \(0.511604\pi\) | |||||||
\(728\) | −6.52611 | + | 5.85328i | −0.241874 | + | 0.216937i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.00361 | − | 24.3651i | 0.259215 | − | 0.901792i | ||||
\(731\) | 6.59310i | 0.243854i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.1211i | 1.44497i | 0.691386 | + | 0.722486i | \(0.257001\pi\) | ||||
−0.691386 | + | 0.722486i | \(0.742999\pi\) | |||||||
\(734\) | 15.8385 | + | 4.55268i | 0.584609 | + | 0.168042i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.21240 | − | 41.6902i | −0.265853 | − | 1.53672i | ||||
\(737\) | −32.8190 | −1.20890 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1851i | 1.33109i | 0.746357 | + | 0.665546i | \(0.231801\pi\) | ||||
−0.746357 | + | 0.665546i | \(0.768199\pi\) | |||||||
\(740\) | −27.7362 | − | 17.3813i | −1.01960 | − | 0.638950i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.25581 | − | 4.36887i | 0.0461021 | − | 0.160386i | ||||
\(743\) | −20.1222 | −0.738210 | −0.369105 | − | 0.929388i | \(-0.620336\pi\) | ||||
−0.369105 | + | 0.929388i | \(0.620336\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.08103 | −0.222792 | ||||||||
\(746\) | 3.85041 | − | 13.3953i | 0.140974 | − | 0.490438i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.4134 | + | 23.0001i | −0.527005 | + | 0.840966i | ||||
\(749\) | 2.14315i | 0.0783089i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2627 | −1.32324 | −0.661622 | − | 0.749838i | \(-0.730131\pi\) | ||||
−0.661622 | + | 0.749838i | \(0.730131\pi\) | |||||||
\(752\) | 10.8436 | + | 22.3792i | 0.395425 | + | 0.816085i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.0526 | + | 2.88957i | 0.366095 | + | 0.105232i | ||||
\(755\) | − | 22.6459i | − | 0.824167i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 53.6865i | − | 1.95127i | −0.219401 | − | 0.975635i | \(-0.570410\pi\) | ||
0.219401 | − | 0.975635i | \(-0.429590\pi\) | |||||||
\(758\) | −13.5014 | + | 46.9705i | −0.490393 | + | 1.70605i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.71219 | + | 6.36880i | 0.207203 | + | 0.231021i | ||||
\(761\) | 37.3332 | 1.35333 | 0.676664 | − | 0.736292i | \(-0.263425\pi\) | ||||
0.676664 | + | 0.736292i | \(0.263425\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 8.34775i | − | 0.302209i | ||||||
\(764\) | −4.68815 | − | 2.93791i | −0.169611 | − | 0.106290i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.5045 | + | 4.45668i | 0.560200 | + | 0.161026i | ||||
\(767\) | 38.5462 | 1.39182 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5423 | 0.560469 | 0.280235 | − | 0.959932i | \(-0.409588\pi\) | ||||
0.280235 | + | 0.959932i | \(0.409588\pi\) | |||||||
\(770\) | 9.34820 | + | 2.68709i | 0.336886 | + | 0.0968359i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −30.4680 | − | 19.0933i | −1.09657 | − | 0.687183i | ||||
\(773\) | − | 39.0073i | − | 1.40299i | −0.712672 | − | 0.701497i | \(-0.752515\pi\) | ||
0.712672 | − | 0.701497i | \(-0.247485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.8198 | 0.532343 | ||||||||
\(776\) | −19.3730 | − | 21.5999i | −0.695450 | − | 0.775391i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.5763 | + | 50.7100i | −0.522585 | + | 1.81804i | ||||
\(779\) | 5.02972i | 0.180209i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 46.6933i | − | 1.67082i | ||||||
\(782\) | −36.7059 | − | 10.5509i | −1.31260 | − | 0.377299i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.74419 | + | 3.59969i | 0.0622926 | + | 0.128560i | ||||
\(785\) | −23.7537 | −0.847807 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.50805i | − | 0.338925i | −0.985537 | − | 0.169463i | \(-0.945797\pi\) | ||
0.985537 | − | 0.169463i | \(-0.0542032\pi\) | |||||||
\(788\) | 11.1703 | − | 17.8249i | 0.397925 | − | 0.634987i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.17869 | + | 18.0163i | −0.184250 | + | 0.640992i | ||||
\(791\) | −17.5901 | −0.625432 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.7450 | −1.09179 | ||||||||
\(794\) | −4.25469 | + | 14.8018i | −0.150993 | + | 0.525296i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.94792 | + | 4.35403i | 0.246262 | + | 0.154324i | ||||
\(797\) | 40.4120i | 1.43147i | 0.698374 | + | 0.715733i | \(0.253907\pi\) | ||||
−0.698374 | + | 0.715733i | \(0.746093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.4479 | 0.794149 | ||||||||
\(800\) | 1.59265 | + | 9.20610i | 0.0563088 | + | 0.325485i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.1057 | + | 8.07881i | 0.992445 | + | 0.285273i | ||||
\(803\) | 36.8219i | 1.29942i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.6862i | 0.482374i | ||||||||
\(806\) | −10.8655 | + | 37.8002i | −0.382719 | + | 1.33146i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.5889 | − | 11.2910i | 0.442877 | − | 0.397217i | ||||
\(809\) | 32.4907 | 1.14231 | 0.571157 | − | 0.820841i | \(-0.306495\pi\) | ||||
0.571157 | + | 0.820841i | \(0.306495\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.34275i | 0.292954i | 0.989214 | + | 0.146477i | \(0.0467934\pi\) | ||||
−0.989214 | + | 0.146477i | \(0.953207\pi\) | |||||||
\(812\) | 2.53431 | − | 4.04411i | 0.0889367 | − | 0.141920i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 45.6917 | + | 13.1338i | 1.60149 | + | 0.460340i | ||||
\(815\) | 11.2922 | 0.395550 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.01826 | −0.105596 | ||||||||
\(818\) | −21.9112 | − | 6.29826i | −0.766108 | − | 0.220213i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.91336 | − | 9.43622i | 0.206504 | − | 0.329527i | ||||
\(821\) | 30.6627i | 1.07014i | 0.844809 | + | 0.535068i | \(0.179714\pi\) | ||||
−0.844809 | + | 0.535068i | \(0.820286\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.5627 | −0.891059 | −0.445530 | − | 0.895267i | \(-0.646985\pi\) | ||||
−0.445530 | + | 0.895267i | \(0.646985\pi\) | |||||||
\(824\) | −31.9271 | − | 35.5971i | −1.11223 | − | 1.24008i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.85883 | − | 16.9035i | 0.169060 | − | 0.588150i | ||||
\(827\) | 12.4138i | 0.431670i | 0.976430 | + | 0.215835i | \(0.0692474\pi\) | ||||
−0.976430 | + | 0.215835i | \(0.930753\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.6360i | 0.751449i | 0.926731 | + | 0.375724i | \(0.122606\pi\) | ||||
−0.926731 | + | 0.375724i | \(0.877394\pi\) | |||||||
\(830\) | −22.3672 | − | 6.42933i | −0.776377 | − | 0.223165i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.6493 | − | 2.68734i | −0.854560 | − | 0.0931667i | ||||
\(833\) | 3.61074 | 0.125105 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.5238i | 0.364191i | ||||||||
\(836\) | −10.5292 | − | 6.59832i | −0.364161 | − | 0.228208i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.3907 | + | 36.1484i | −0.358939 | + | 1.24873i | ||||
\(839\) | 1.76288 | 0.0608612 | 0.0304306 | − | 0.999537i | \(-0.490312\pi\) | ||||
0.0304306 | + | 0.999537i | \(0.490312\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.3056 | 0.803642 | ||||||||
\(842\) | 10.6345 | − | 36.9966i | 0.366488 | − | 1.27499i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.4926 | + | 35.8925i | −0.774228 | + | 1.23547i | ||||
\(845\) | − | 6.20987i | − | 0.213626i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.12753 | −0.107463 | ||||||||
\(848\) | 11.5707 | − | 5.60645i | 0.397339 | − | 0.192526i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.10545 | + | 2.32987i | 0.278015 | + | 0.0799137i | ||||
\(851\) | 66.8946i | 2.29312i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.627765i | 0.0214943i | 0.999942 | + | 0.0107471i | \(0.00342098\pi\) | ||||
−0.999942 | + | 0.0107471i | \(0.996579\pi\) | |||||||
\(854\) | −3.87548 | + | 13.4825i | −0.132616 | + | 0.461362i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.51260 | + | 4.04736i | −0.154237 | + | 0.138336i | ||||
\(857\) | 35.3406 | 1.20721 | 0.603605 | − | 0.797283i | \(-0.293730\pi\) | ||||
0.603605 | + | 0.797283i | \(0.293730\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 50.5205i | − | 1.72374i | −0.507133 | − | 0.861868i | \(-0.669295\pi\) | ||
0.507133 | − | 0.861868i | \(-0.330705\pi\) | |||||||
\(860\) | 5.66254 | + | 3.54852i | 0.193091 | + | 0.121004i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.22687 | + | 1.78988i | 0.212088 | + | 0.0609635i | ||||
\(863\) | −35.7081 | −1.21552 | −0.607758 | − | 0.794122i | \(-0.707931\pi\) | ||||
−0.607758 | + | 0.794122i | \(0.707931\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.8164 | −0.503771 | ||||||||
\(866\) | 6.02231 | + | 1.73108i | 0.204646 | + | 0.0588244i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.2068 | + | 9.52959i | 0.516152 | + | 0.323455i | ||||
\(869\) | − | 27.2273i | − | 0.923623i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.0627 | −0.916986 | ||||||||
\(872\) | 17.5770 | − | 15.7648i | 0.595231 | − | 0.533864i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.83011 | − | 16.8036i | 0.163381 | − | 0.568392i | ||||
\(875\) | − | 12.1715i | − | 0.411472i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.7066i | 1.47587i | 0.674873 | + | 0.737934i | \(0.264198\pi\) | ||||
−0.674873 | + | 0.737934i | \(0.735802\pi\) | |||||||
\(878\) | −15.3406 | − | 4.40958i | −0.517722 | − | 0.148816i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 11.9963 | + | 24.7581i | 0.404394 | + | 0.834596i | ||||
\(881\) | 39.3404 | 1.32541 | 0.662705 | − | 0.748880i | \(-0.269408\pi\) | ||||
0.662705 | + | 0.748880i | \(0.269408\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 14.5600i | − | 0.489981i | −0.969525 | − | 0.244991i | \(-0.921215\pi\) | ||
0.969525 | − | 0.244991i | \(-0.0787849\pi\) | |||||||
\(884\) | −11.8854 | + | 18.9660i | −0.399748 | + | 0.637896i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.44214 | + | 5.01712i | −0.0484497 | + | 0.168553i | ||||
\(887\) | 24.2186 | 0.813182 | 0.406591 | − | 0.913610i | \(-0.366717\pi\) | ||||
0.406591 | + | 0.913610i | \(0.366717\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.73427 | 0.326477 | ||||||||
\(890\) | −1.10770 | + | 3.85363i | −0.0371303 | + | 0.129174i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.91004 | − | 2.45029i | −0.130918 | − | 0.0820419i | ||||
\(893\) | 10.2764i | 0.343888i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −28.2033 | −0.942733 | ||||||||
\(896\) | −4.28556 | + | 10.4706i | −0.143171 | + | 0.349799i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.5592 | − | 7.05941i | −0.819551 | − | 0.235575i | ||||
\(899\) | − | 21.4122i | − | 0.714137i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 11.6062i | − | 0.386658i | ||||||
\(902\) | −4.46830 | + | 15.5449i | −0.148778 | + | 0.517590i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.2191 | − | 37.0376i | −1.10485 | − | 1.23185i | ||||
\(905\) | −11.1040 | −0.369111 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 32.8766i | − | 1.09165i | −0.837899 | − | 0.545825i | \(-0.816216\pi\) | ||
0.837899 | − | 0.545825i | \(-0.183784\pi\) | |||||||
\(908\) | 2.85692 | − | 4.55891i | 0.0948101 | − | 0.151293i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.70859 | + | 2.21579i | 0.255537 | + | 0.0734527i | ||||
\(911\) | 17.8694 | 0.592039 | 0.296020 | − | 0.955182i | \(-0.404341\pi\) | ||||
0.296020 | + | 0.955182i | \(0.404341\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.8026 | 1.11870 | ||||||||
\(914\) | −29.2060 | − | 8.39510i | −0.966048 | − | 0.277685i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.2719 | − | 25.9658i | 0.537638 | − | 0.857933i | ||||
\(917\) | 16.7317i | 0.552528i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.3511 | 0.836257 | 0.418128 | − | 0.908388i | \(-0.362686\pi\) | ||||
0.418128 | + | 0.908388i | \(0.362686\pi\) | |||||||
\(920\) | −28.8175 | + | 25.8465i | −0.950085 | + | 0.852133i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.54880 | − | 22.7828i | 0.215673 | − | 0.750313i | ||||
\(923\) | − | 38.5036i | − | 1.26736i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 14.7718i | − | 0.485693i | ||||||
\(926\) | −13.2393 | − | 3.80555i | −0.435069 | − | 0.125058i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.3013 | − | 2.30112i | 0.436637 | − | 0.0755381i | ||||
\(929\) | −39.3410 | −1.29074 | −0.645368 | − | 0.763872i | \(-0.723296\pi\) | ||||
−0.645368 | + | 0.763872i | \(0.723296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65297i | 0.0541738i | ||||||||
\(932\) | 36.2477 | + | 22.7152i | 1.18733 | + | 0.744062i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −13.2319 | + | 46.0331i | −0.432962 | + | 1.50625i | ||||
\(935\) | 24.8341 | 0.812162 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.9769 | 1.46933 | 0.734665 | − | 0.678430i | \(-0.237339\pi\) | ||||
0.734665 | + | 0.678430i | \(0.237339\pi\) | |||||||
\(938\) | −3.41131 | + | 11.8677i | −0.111383 | + | 0.387495i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.0819 | − | 19.2796i | 0.394067 | − | 0.628830i | ||||
\(941\) | 0.488014i | 0.0159088i | 0.999968 | + | 0.00795440i | \(0.00253199\pi\) | ||||
−0.999968 | + | 0.00795440i | \(0.997468\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.7585 | −0.741117 | ||||||||
\(944\) | 44.7680 | − | 21.6918i | 1.45707 | − | 0.706009i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.32829 | − | 2.68137i | −0.303289 | − | 0.0871787i | ||||
\(947\) | 1.70377i | 0.0553652i | 0.999617 | + | 0.0276826i | \(0.00881278\pi\) | ||||
−0.999617 | + | 0.0276826i | \(0.991187\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30.3636i | 0.985643i | ||||||||
\(950\) | −1.06659 | + | 3.71061i | −0.0346048 | + | 0.120388i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.81893 | + | 7.60275i | 0.221003 | + | 0.246407i | ||||
\(953\) | −9.15979 | −0.296715 | −0.148357 | − | 0.988934i | \(-0.547399\pi\) | ||||
−0.148357 | + | 0.988934i | \(0.547399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.06198i | 0.163802i | ||||||||
\(956\) | −11.9402 | − | 7.48250i | −0.386172 | − | 0.242001i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.3931 | − | 4.71211i | −0.529638 | − | 0.152242i | ||||
\(959\) | −15.1897 | −0.490501 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.5149 | 1.59726 | ||||||||
\(962\) | 37.6777 | + | 10.8302i | 1.21478 | + | 0.349181i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.582329 | − | 0.364926i | −0.0187555 | − | 0.0117535i | ||||
\(965\) | 32.8976i | 1.05901i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.1742 | 1.16328 | 0.581642 | − | 0.813445i | \(-0.302411\pi\) | ||||
0.581642 | + | 0.813445i | \(0.302411\pi\) | |||||||
\(968\) | −5.90638 | − | 6.58531i | −0.189838 | − | 0.211660i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.33374 | + | 25.5136i | −0.235472 | + | 0.819193i | ||||
\(971\) | 7.10607i | 0.228045i | 0.993478 | + | 0.114022i | \(0.0363735\pi\) | ||||
−0.993478 | + | 0.114022i | \(0.963626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.32344i | 0.298896i | ||||||||
\(974\) | −15.7327 | − | 4.52229i | −0.504110 | − | 0.144903i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −35.7076 | + | 17.3017i | −1.14297 | + | 0.553815i | ||||
\(977\) | 56.6938 | 1.81380 | 0.906898 | − | 0.421349i | \(-0.138443\pi\) | ||||
0.906898 | + | 0.421349i | \(0.138443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5.82382i | − | 0.186130i | ||||||
\(980\) | 1.94337 | − | 3.10112i | 0.0620786 | − | 0.0990616i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.6652 | − | 54.4983i | 0.499897 | − | 1.73911i | ||||
\(983\) | −21.6213 | −0.689614 | −0.344807 | − | 0.938674i | \(-0.612056\pi\) | ||||
−0.344807 | + | 0.938674i | \(0.612056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19.2463 | −0.613238 | ||||||||
\(986\) | 3.36627 | − | 11.7110i | 0.107204 | − | 0.372956i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.68248 | − | 5.44102i | −0.276226 | − | 0.173102i | ||||
\(989\) | − | 13.6570i | − | 0.434268i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3945 | 0.711384 | 0.355692 | − | 0.934603i | \(-0.384245\pi\) | ||||
0.355692 | + | 0.934603i | \(0.384245\pi\) | |||||||
\(992\) | 8.65277 | + | 50.0161i | 0.274726 | + | 1.58801i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.8849 | − | 4.85346i | −0.535555 | − | 0.153942i | ||||
\(995\) | − | 7.50195i | − | 0.237828i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.3181i | 0.358448i | 0.983808 | + | 0.179224i | \(0.0573587\pi\) | ||||
−0.983808 | + | 0.179224i | \(0.942641\pi\) | |||||||
\(998\) | 12.9722 | − | 45.1295i | 0.410628 | − | 1.42855i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.c.g.757.22 | yes | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.g.757.3 | ✓ | 24 | |
4.3 | odd | 2 | 6048.2.c.f.3025.8 | 24 | |||
8.3 | odd | 2 | 6048.2.c.f.3025.17 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.g.757.21 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.f.3025.18 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.g.757.4 | yes | 24 | |
24.11 | even | 2 | 6048.2.c.f.3025.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.3 | ✓ | 24 | 3.2 | odd | 2 | inner | |
1512.2.c.g.757.4 | yes | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.g.757.21 | yes | 24 | 8.5 | even | 2 | inner | |
1512.2.c.g.757.22 | yes | 24 | 1.1 | even | 1 | trivial | |
6048.2.c.f.3025.7 | 24 | 24.11 | even | 2 | |||
6048.2.c.f.3025.8 | 24 | 4.3 | odd | 2 | |||
6048.2.c.f.3025.17 | 24 | 8.3 | odd | 2 | |||
6048.2.c.f.3025.18 | 24 | 12.11 | even | 2 |