Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(323,1512)]
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([1, 1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.j (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: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 323.30 | ||
Character | \(\chi\) | \(=\) | 1512.323 |
Dual form | 1512.2.j.d.323.29 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.508876 | + | 1.31949i | 0.359830 | + | 0.933018i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.48209 | + | 1.34291i | −0.741045 | + | 0.671455i | ||||
\(5\) | 2.29653 | 1.02704 | 0.513519 | − | 0.858078i | \(-0.328342\pi\) | ||||
0.513519 | + | 0.858078i | \(0.328342\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −2.52615 | − | 1.27222i | −0.893130 | − | 0.449799i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.16865 | + | 3.03024i | 0.369558 | + | 0.958245i | ||||
\(11\) | 4.02419i | 1.21334i | 0.794954 | + | 0.606670i | \(0.207495\pi\) | ||||
−0.794954 | + | 0.606670i | \(0.792505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.82461i | 0.506055i | 0.967459 | + | 0.253027i | \(0.0814263\pi\) | ||||
−0.967459 | + | 0.253027i | \(0.918574\pi\) | |||||||
\(14\) | −1.31949 | + | 0.508876i | −0.352648 | + | 0.136003i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.393186 | − | 3.98063i | 0.0982966 | − | 0.995157i | ||||
\(17\) | 0.430472i | 0.104405i | 0.998637 | + | 0.0522024i | \(0.0166241\pi\) | ||||
−0.998637 | + | 0.0522024i | \(0.983376\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.01046 | 1.14948 | 0.574739 | − | 0.818336i | \(-0.305103\pi\) | ||||
0.574739 | + | 0.818336i | \(0.305103\pi\) | |||||||
\(20\) | −3.40366 | + | 3.08403i | −0.761081 | + | 0.689609i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.30987 | + | 2.04781i | −1.13207 | + | 0.436595i | ||||
\(23\) | −3.49479 | −0.728715 | −0.364357 | − | 0.931259i | \(-0.618711\pi\) | ||||
−0.364357 | + | 0.931259i | \(0.618711\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.274031 | 0.0548062 | ||||||||
\(26\) | −2.40754 | + | 0.928498i | −0.472158 | + | 0.182093i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.34291 | − | 1.48209i | −0.253786 | − | 0.280089i | ||||
\(29\) | 2.16016 | 0.401131 | 0.200565 | − | 0.979680i | \(-0.435722\pi\) | ||||
0.200565 | + | 0.979680i | \(0.435722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.10635i | 0.378311i | 0.981947 | + | 0.189156i | \(0.0605750\pi\) | ||||
−0.981947 | + | 0.189156i | \(0.939425\pi\) | |||||||
\(32\) | 5.45247 | − | 1.50684i | 0.963870 | − | 0.266374i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.568002 | + | 0.219057i | −0.0974115 | + | 0.0375679i | ||||
\(35\) | 2.29653i | 0.388184i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.19775i | 0.361309i | 0.983547 | + | 0.180654i | \(0.0578215\pi\) | ||||
−0.983547 | + | 0.180654i | \(0.942178\pi\) | |||||||
\(38\) | 2.54970 | + | 6.61124i | 0.413616 | + | 1.07248i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.80137 | − | 2.92170i | −0.917278 | − | 0.461961i | ||||
\(41\) | 4.35032i | 0.679405i | 0.940533 | + | 0.339703i | \(0.110326\pi\) | ||||
−0.940533 | + | 0.339703i | \(0.889674\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.0354 | −1.83538 | −0.917690 | − | 0.397298i | \(-0.869948\pi\) | ||||
−0.917690 | + | 0.397298i | \(0.869948\pi\) | |||||||
\(44\) | −5.40413 | − | 5.96422i | −0.814703 | − | 0.899140i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.77842 | − | 4.61133i | −0.262213 | − | 0.679904i | ||||
\(47\) | 1.72531 | 0.251663 | 0.125831 | − | 0.992052i | \(-0.459840\pi\) | ||||
0.125831 | + | 0.992052i | \(0.459840\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0.139448 | + | 0.361580i | 0.0197209 | + | 0.0511351i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.45028 | − | 2.70423i | −0.339793 | − | 0.375010i | ||||
\(53\) | 10.0938 | 1.38649 | 0.693246 | − | 0.720701i | \(-0.256180\pi\) | ||||
0.693246 | + | 0.720701i | \(0.256180\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.24166i | 1.24615i | ||||||||
\(56\) | 1.27222 | − | 2.52615i | 0.170008 | − | 0.337571i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.09925 | + | 2.85030i | 0.144339 | + | 0.374262i | ||||
\(59\) | 10.6175i | 1.38228i | 0.722721 | + | 0.691140i | \(0.242891\pi\) | ||||
−0.722721 | + | 0.691140i | \(0.757109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.44575i | − | 1.08137i | −0.841226 | − | 0.540684i | \(-0.818166\pi\) | ||
0.841226 | − | 0.540684i | \(-0.181834\pi\) | |||||||
\(62\) | −2.77930 | + | 1.07187i | −0.352971 | + | 0.136127i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.76289 | + | 6.42767i | 0.595361 | + | 0.803458i | ||||
\(65\) | 4.19026i | 0.519737i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6358 | −1.54370 | −0.771852 | − | 0.635802i | \(-0.780669\pi\) | ||||
−0.771852 | + | 0.635802i | \(0.780669\pi\) | |||||||
\(68\) | −0.578085 | − | 0.637998i | −0.0701031 | − | 0.0773686i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.03024 | + | 1.16865i | −0.362182 | + | 0.139680i | ||||
\(71\) | 8.95532 | 1.06280 | 0.531401 | − | 0.847121i | \(-0.321666\pi\) | ||||
0.531401 | + | 0.847121i | \(0.321666\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.16051 | −0.838075 | −0.419037 | − | 0.907969i | \(-0.637632\pi\) | ||||
−0.419037 | + | 0.907969i | \(0.637632\pi\) | |||||||
\(74\) | −2.89991 | + | 1.11838i | −0.337108 | + | 0.130010i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.42596 | + | 6.72860i | −0.851816 | + | 0.771823i | ||||
\(77\) | −4.02419 | −0.458599 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.2405i | 1.71468i | 0.514747 | + | 0.857342i | \(0.327886\pi\) | ||||
−0.514747 | + | 0.857342i | \(0.672114\pi\) | |||||||
\(80\) | 0.902963 | − | 9.14162i | 0.100954 | − | 1.02206i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.74018 | + | 2.21377i | −0.633897 | + | 0.244470i | ||||
\(83\) | 13.4507i | 1.47640i | 0.674581 | + | 0.738201i | \(0.264324\pi\) | ||||
−0.674581 | + | 0.738201i | \(0.735676\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.988589i | 0.107228i | ||||||||
\(86\) | −6.12452 | − | 15.8805i | −0.660424 | − | 1.71244i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.11968 | − | 10.1657i | 0.545760 | − | 1.08367i | ||||
\(89\) | − | 7.44987i | − | 0.789684i | −0.918749 | − | 0.394842i | \(-0.870799\pi\) | ||
0.918749 | − | 0.394842i | \(-0.129201\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.82461 | −0.191271 | ||||||||
\(92\) | 5.17960 | − | 4.69319i | 0.540011 | − | 0.489299i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.877970 | + | 2.27653i | 0.0905556 | + | 0.234806i | ||||
\(95\) | 11.5067 | 1.18056 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.68878 | 0.171469 | 0.0857347 | − | 0.996318i | \(-0.472676\pi\) | ||||
0.0857347 | + | 0.996318i | \(0.472676\pi\) | |||||||
\(98\) | −0.508876 | − | 1.31949i | −0.0514042 | − | 0.133288i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.406139 | + | 0.367999i | −0.0406139 | + | 0.0367999i | ||||
\(101\) | 13.3668 | 1.33005 | 0.665024 | − | 0.746822i | \(-0.268421\pi\) | ||||
0.665024 | + | 0.746822i | \(0.268421\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.59723i | − | 0.452978i | −0.974014 | − | 0.226489i | \(-0.927275\pi\) | ||
0.974014 | − | 0.226489i | \(-0.0727248\pi\) | |||||||
\(104\) | 2.32131 | − | 4.60923i | 0.227623 | − | 0.451973i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.13650 | + | 13.3186i | 0.498901 | + | 1.29362i | ||||
\(107\) | − | 15.7048i | − | 1.51824i | −0.650951 | − | 0.759120i | \(-0.725630\pi\) | ||
0.650951 | − | 0.759120i | \(-0.274370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 16.0140i | − | 1.53386i | −0.641728 | − | 0.766932i | \(-0.721782\pi\) | ||
0.641728 | − | 0.766932i | \(-0.278218\pi\) | |||||||
\(110\) | −12.1943 | + | 4.70286i | −1.16268 | + | 0.448400i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.98063 | + | 0.393186i | 0.376134 | + | 0.0371526i | ||||
\(113\) | 1.46858i | 0.138152i | 0.997611 | + | 0.0690760i | \(0.0220051\pi\) | ||||
−0.997611 | + | 0.0690760i | \(0.977995\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.02588 | −0.748417 | ||||||||
\(116\) | −3.20155 | + | 2.90089i | −0.297256 | + | 0.269341i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.0096 | + | 5.40298i | −1.28969 | + | 0.497385i | ||||
\(119\) | −0.430472 | −0.0394613 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.19413 | −0.472193 | ||||||||
\(122\) | 11.1441 | − | 4.29784i | 1.00893 | − | 0.389108i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.82863 | − | 3.12180i | −0.254019 | − | 0.280346i | ||||
\(125\) | −10.8533 | −0.970750 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.35551i | − | 0.563960i | −0.959420 | − | 0.281980i | \(-0.909009\pi\) | ||
0.959420 | − | 0.281980i | \(-0.0909913\pi\) | |||||||
\(128\) | −6.05750 | + | 9.55545i | −0.535413 | + | 0.844591i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.52899 | + | 2.13232i | −0.484924 | + | 0.187017i | ||||
\(131\) | 7.75532i | 0.677585i | 0.940861 | + | 0.338793i | \(0.110018\pi\) | ||||
−0.940861 | + | 0.338793i | \(0.889982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.01046i | 0.434462i | ||||||||
\(134\) | −6.43003 | − | 16.6727i | −0.555470 | − | 1.44030i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.547657 | − | 1.08744i | 0.0469612 | − | 0.0932469i | ||||
\(137\) | − | 3.09831i | − | 0.264706i | −0.991203 | − | 0.132353i | \(-0.957747\pi\) | ||
0.991203 | − | 0.132353i | \(-0.0422533\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.76422 | −0.319277 | −0.159638 | − | 0.987176i | \(-0.551033\pi\) | ||||
−0.159638 | + | 0.987176i | \(0.551033\pi\) | |||||||
\(140\) | −3.08403 | − | 3.40366i | −0.260648 | − | 0.287662i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.55715 | + | 11.8164i | 0.382427 | + | 0.991613i | ||||
\(143\) | −7.34257 | −0.614016 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.96085 | 0.411976 | ||||||||
\(146\) | −3.64381 | − | 9.44820i | −0.301564 | − | 0.781939i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.95139 | − | 3.25727i | −0.242602 | − | 0.267746i | ||||
\(149\) | −6.57894 | −0.538968 | −0.269484 | − | 0.963005i | \(-0.586853\pi\) | ||||
−0.269484 | + | 0.963005i | \(0.586853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.08336i | 0.0881627i | 0.999028 | + | 0.0440814i | \(0.0140361\pi\) | ||||
−0.999028 | + | 0.0440814i | \(0.985964\pi\) | |||||||
\(152\) | −12.6572 | − | 6.37444i | −1.02663 | − | 0.517035i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.04781 | − | 5.30987i | −0.165018 | − | 0.427881i | ||||
\(155\) | 4.83728i | 0.388540i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 16.6130i | − | 1.32586i | −0.748680 | − | 0.662932i | \(-0.769312\pi\) | ||
0.748680 | − | 0.662932i | \(-0.230688\pi\) | |||||||
\(158\) | −20.1096 | + | 7.75550i | −1.59983 | + | 0.616994i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.5217 | − | 3.46050i | 0.989930 | − | 0.273577i | ||||
\(161\) | − | 3.49479i | − | 0.275428i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.4881 | 0.899818 | 0.449909 | − | 0.893074i | \(-0.351456\pi\) | ||||
0.449909 | + | 0.893074i | \(0.351456\pi\) | |||||||
\(164\) | −5.84208 | − | 6.44756i | −0.456190 | − | 0.503470i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.7480 | + | 6.84472i | −1.37751 | + | 0.531253i | ||||
\(167\) | 13.4761 | 1.04281 | 0.521405 | − | 0.853309i | \(-0.325408\pi\) | ||||
0.521405 | + | 0.853309i | \(0.325408\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.67081 | 0.743909 | ||||||||
\(170\) | −1.30443 | + | 0.503069i | −0.100045 | + | 0.0385836i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 17.8375 | − | 16.1624i | 1.36010 | − | 1.23237i | ||||
\(173\) | 4.98344 | 0.378884 | 0.189442 | − | 0.981892i | \(-0.439332\pi\) | ||||
0.189442 | + | 0.981892i | \(0.439332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.274031i | 0.0207148i | ||||||||
\(176\) | 16.0188 | + | 1.58226i | 1.20746 | + | 0.119267i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.83000 | − | 3.79106i | 0.736790 | − | 0.284152i | ||||
\(179\) | − | 3.45929i | − | 0.258559i | −0.991608 | − | 0.129280i | \(-0.958733\pi\) | ||
0.991608 | − | 0.129280i | \(-0.0412665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.1409i | − | 0.753768i | −0.926260 | − | 0.376884i | \(-0.876996\pi\) | ||
0.926260 | − | 0.376884i | \(-0.123004\pi\) | |||||||
\(182\) | −0.928498 | − | 2.40754i | −0.0688249 | − | 0.178459i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.82838 | + | 4.44616i | 0.650837 | + | 0.327775i | ||||
\(185\) | 5.04720i | 0.371078i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73230 | −0.126678 | ||||||||
\(188\) | −2.55707 | + | 2.31694i | −0.186493 | + | 0.168980i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.85546 | + | 15.1829i | 0.424800 | + | 1.10148i | ||||
\(191\) | 10.9743 | 0.794074 | 0.397037 | − | 0.917803i | \(-0.370038\pi\) | ||||
0.397037 | + | 0.917803i | \(0.370038\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.07226 | 0.149165 | 0.0745824 | − | 0.997215i | \(-0.476238\pi\) | ||||
0.0745824 | + | 0.997215i | \(0.476238\pi\) | |||||||
\(194\) | 0.859378 | + | 2.22832i | 0.0616998 | + | 0.159984i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.48209 | − | 1.34291i | 0.105864 | − | 0.0959221i | ||||
\(197\) | 4.69547 | 0.334539 | 0.167269 | − | 0.985911i | \(-0.446505\pi\) | ||||
0.167269 | + | 0.985911i | \(0.446505\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7556i | 1.18777i | 0.804549 | + | 0.593887i | \(0.202407\pi\) | ||||
−0.804549 | + | 0.593887i | \(0.797593\pi\) | |||||||
\(200\) | −0.692244 | − | 0.348629i | −0.0489490 | − | 0.0246518i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.80205 | + | 17.6373i | 0.478591 | + | 1.24096i | ||||
\(203\) | 2.16016i | 0.151613i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.99061i | 0.697775i | ||||||||
\(206\) | 6.06598 | − | 2.33942i | 0.422637 | − | 0.162995i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.26308 | + | 0.717410i | 0.503604 | + | 0.0497435i | ||||
\(209\) | 20.1631i | 1.39471i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.2955 | 1.05299 | 0.526494 | − | 0.850179i | \(-0.323506\pi\) | ||||
0.526494 | + | 0.850179i | \(0.323506\pi\) | |||||||
\(212\) | −14.9599 | + | 13.5551i | −1.02745 | + | 0.930967i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 20.7223 | − | 7.99179i | 1.41654 | − | 0.546307i | ||||
\(215\) | −27.6396 | −1.88500 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.10635 | −0.142988 | ||||||||
\(218\) | 21.1303 | − | 8.14914i | 1.43112 | − | 0.551930i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.4107 | − | 13.6970i | −0.836731 | − | 0.923450i | ||||
\(221\) | −0.785442 | −0.0528345 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.5657i | 1.57808i | 0.614343 | + | 0.789039i | \(0.289421\pi\) | ||||
−0.614343 | + | 0.789039i | \(0.710579\pi\) | |||||||
\(224\) | 1.50684 | + | 5.45247i | 0.100680 | + | 0.364308i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.93777 | + | 0.747323i | −0.128898 | + | 0.0497112i | ||||
\(227\) | − | 16.6514i | − | 1.10519i | −0.833450 | − | 0.552595i | \(-0.813638\pi\) | ||
0.833450 | − | 0.552595i | \(-0.186362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.4291i | − | 1.61432i | −0.590332 | − | 0.807161i | \(-0.701003\pi\) | ||
0.590332 | − | 0.807161i | \(-0.298997\pi\) | |||||||
\(230\) | −4.08418 | − | 10.5900i | −0.269303 | − | 0.698287i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.45688 | − | 2.74820i | −0.358262 | − | 0.180428i | ||||
\(233\) | 18.3470i | 1.20195i | 0.799268 | + | 0.600975i | \(0.205221\pi\) | ||||
−0.799268 | + | 0.600975i | \(0.794779\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.96222 | 0.258467 | ||||||||
\(236\) | −14.2583 | − | 15.7361i | −0.928138 | − | 1.02433i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.219057 | − | 0.568002i | −0.0141993 | − | 0.0368181i | ||||
\(239\) | 30.1173 | 1.94812 | 0.974062 | − | 0.226280i | \(-0.0726563\pi\) | ||||
0.974062 | + | 0.226280i | \(0.0726563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.51878 | −0.355496 | −0.177748 | − | 0.984076i | \(-0.556881\pi\) | ||||
−0.177748 | + | 0.984076i | \(0.556881\pi\) | |||||||
\(242\) | −2.64317 | − | 6.85358i | −0.169909 | − | 0.440565i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.3419 | + | 12.5174i | 0.726089 | + | 0.801342i | ||||
\(245\) | −2.29653 | −0.146720 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.14212i | 0.581699i | ||||||||
\(248\) | 2.67975 | − | 5.32095i | 0.170164 | − | 0.337881i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.52299 | − | 14.3208i | −0.349304 | − | 0.905727i | ||||
\(251\) | − | 18.2010i | − | 1.14884i | −0.818561 | − | 0.574420i | \(-0.805228\pi\) | ||
0.818561 | − | 0.574420i | \(-0.194772\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 14.0637i | − | 0.884178i | ||||||
\(254\) | 8.38601 | − | 3.23417i | 0.526185 | − | 0.202930i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6908 | − | 3.13026i | −0.980676 | − | 0.195641i | ||||
\(257\) | 5.91116i | 0.368728i | 0.982858 | + | 0.184364i | \(0.0590226\pi\) | ||||
−0.982858 | + | 0.184364i | \(0.940977\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.19775 | −0.136562 | ||||||||
\(260\) | −5.62714 | − | 6.21034i | −0.348980 | − | 0.385149i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.2330 | + | 3.94649i | −0.632199 | + | 0.243815i | ||||
\(263\) | 15.7132 | 0.968916 | 0.484458 | − | 0.874815i | \(-0.339017\pi\) | ||||
0.484458 | + | 0.874815i | \(0.339017\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.1807 | 1.42398 | ||||||||
\(266\) | −6.61124 | + | 2.54970i | −0.405361 | + | 0.156332i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 18.7273 | − | 16.9687i | 1.14395 | − | 1.03653i | ||||
\(269\) | 26.9473 | 1.64301 | 0.821504 | − | 0.570202i | \(-0.193135\pi\) | ||||
0.821504 | + | 0.570202i | \(0.193135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5.68443i | − | 0.345305i | −0.984983 | − | 0.172652i | \(-0.944766\pi\) | ||
0.984983 | − | 0.172652i | \(-0.0552337\pi\) | |||||||
\(272\) | 1.71355 | + | 0.169256i | 0.103899 | + | 0.0102626i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.08818 | − | 1.57665i | 0.246976 | − | 0.0952491i | ||||
\(275\) | 1.10275i | 0.0664985i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.86390i | 0.472496i | 0.971693 | + | 0.236248i | \(0.0759178\pi\) | ||||
−0.971693 | + | 0.236248i | \(0.924082\pi\) | |||||||
\(278\) | −1.91552 | − | 4.96683i | −0.114885 | − | 0.297891i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.92170 | − | 5.80137i | 0.174605 | − | 0.346698i | ||||
\(281\) | − | 0.186660i | − | 0.0111352i | −0.999985 | − | 0.00556760i | \(-0.998228\pi\) | ||
0.999985 | − | 0.00556760i | \(-0.00177223\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4545 | −0.740343 | −0.370171 | − | 0.928963i | \(-0.620701\pi\) | ||||
−0.370171 | + | 0.928963i | \(0.620701\pi\) | |||||||
\(284\) | −13.2726 | + | 12.0262i | −0.787584 | + | 0.713623i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.73646 | − | 9.68842i | −0.220941 | − | 0.572888i | ||||
\(287\) | −4.35032 | −0.256791 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8147 | 0.989100 | ||||||||
\(290\) | 2.52446 | + | 6.54578i | 0.148241 | + | 0.384381i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.6125 | − | 9.61592i | 0.621051 | − | 0.562729i | ||||
\(293\) | −8.52169 | −0.497843 | −0.248921 | − | 0.968524i | \(-0.580076\pi\) | ||||
−0.248921 | + | 0.968524i | \(0.580076\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.3833i | 1.41965i | ||||||||
\(296\) | 2.79604 | − | 5.55186i | 0.162516 | − | 0.322695i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.34787 | − | 8.68083i | −0.193937 | − | 0.502867i | ||||
\(299\) | − | 6.37662i | − | 0.368770i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 12.0354i | − | 0.693708i | ||||||
\(302\) | −1.42948 | + | 0.551296i | −0.0822574 | + | 0.0317235i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.97005 | − | 19.9448i | 0.112990 | − | 1.14391i | ||||
\(305\) | − | 19.3959i | − | 1.11060i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.4380 | 1.33768 | 0.668838 | − | 0.743408i | \(-0.266792\pi\) | ||||
0.668838 | + | 0.743408i | \(0.266792\pi\) | |||||||
\(308\) | 5.96422 | − | 5.40413i | 0.339843 | − | 0.307929i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.38273 | + | 2.46157i | −0.362515 | + | 0.139808i | ||||
\(311\) | −12.1365 | −0.688199 | −0.344099 | − | 0.938933i | \(-0.611816\pi\) | ||||
−0.344099 | + | 0.938933i | \(0.611816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.54204 | −0.426301 | −0.213151 | − | 0.977019i | \(-0.568372\pi\) | ||||
−0.213151 | + | 0.977019i | \(0.568372\pi\) | |||||||
\(314\) | 21.9207 | − | 8.45396i | 1.23705 | − | 0.477085i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.4666 | − | 22.5877i | −1.15133 | − | 1.27066i | ||||
\(317\) | 29.7545 | 1.67118 | 0.835590 | − | 0.549354i | \(-0.185126\pi\) | ||||
0.835590 | + | 0.549354i | \(0.185126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.69288i | 0.486708i | ||||||||
\(320\) | 10.9381 | + | 14.7613i | 0.611458 | + | 0.825182i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.61133 | − | 1.77842i | 0.256980 | − | 0.0991072i | ||||
\(323\) | 2.15686i | 0.120011i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.499998i | 0.0277349i | ||||||||
\(326\) | 5.84602 | + | 15.1584i | 0.323781 | + | 0.839547i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.53458 | − | 10.9896i | 0.305596 | − | 0.606797i | ||||
\(329\) | 1.72531i | 0.0951195i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.2670 | −0.894117 | −0.447058 | − | 0.894505i | \(-0.647528\pi\) | ||||
−0.447058 | + | 0.894505i | \(0.647528\pi\) | |||||||
\(332\) | −18.0630 | − | 19.9351i | −0.991337 | − | 1.09408i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.85765 | + | 17.7815i | 0.375234 | + | 0.972961i | ||||
\(335\) | −29.0184 | −1.58544 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.0056 | 1.74345 | 0.871727 | − | 0.489992i | \(-0.163000\pi\) | ||||
0.871727 | + | 0.489992i | \(0.163000\pi\) | |||||||
\(338\) | 4.92124 | + | 12.7605i | 0.267680 | + | 0.694080i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.32759 | − | 1.46518i | −0.0719985 | − | 0.0794605i | ||||
\(341\) | −8.47634 | −0.459020 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 30.4032 | + | 15.3117i | 1.63923 | + | 0.825553i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.53595 | + | 6.57559i | 0.136334 | + | 0.353506i | ||||
\(347\) | − | 15.3562i | − | 0.824366i | −0.911101 | − | 0.412183i | \(-0.864766\pi\) | ||
0.911101 | − | 0.412183i | \(-0.135234\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 10.7044i | − | 0.572996i | −0.958081 | − | 0.286498i | \(-0.907509\pi\) | ||
0.958081 | − | 0.286498i | \(-0.0924912\pi\) | |||||||
\(350\) | −0.361580 | + | 0.139448i | −0.0193273 | + | 0.00745379i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.06382 | + | 21.9418i | 0.323203 | + | 1.16950i | ||||
\(353\) | 17.0572i | 0.907866i | 0.891036 | + | 0.453933i | \(0.149979\pi\) | ||||
−0.891036 | + | 0.453933i | \(0.850021\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.5661 | 1.09154 | ||||||||
\(356\) | 10.0045 | + | 11.0414i | 0.530237 | + | 0.585192i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.56449 | − | 1.76035i | 0.241241 | − | 0.0930373i | ||||
\(359\) | −17.2174 | −0.908697 | −0.454349 | − | 0.890824i | \(-0.650128\pi\) | ||||
−0.454349 | + | 0.890824i | \(0.650128\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.10474 | 0.321302 | ||||||||
\(362\) | 13.3808 | − | 5.16047i | 0.703279 | − | 0.271228i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.70423 | − | 2.45028i | 0.141740 | − | 0.128430i | ||||
\(365\) | −16.4443 | −0.860734 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 25.6116i | − | 1.33692i | −0.743750 | − | 0.668458i | \(-0.766955\pi\) | ||
0.743750 | − | 0.668458i | \(-0.233045\pi\) | |||||||
\(368\) | −1.37410 | + | 13.9115i | −0.0716302 | + | 0.725186i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.65972 | + | 2.56840i | −0.346222 | + | 0.133525i | ||||
\(371\) | 10.0938i | 0.524045i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 3.99889i | − | 0.207054i | −0.994627 | − | 0.103527i | \(-0.966987\pi\) | ||
0.994627 | − | 0.103527i | \(-0.0330129\pi\) | |||||||
\(374\) | −0.881526 | − | 2.28575i | −0.0455826 | − | 0.118193i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.35840 | − | 2.19498i | −0.224767 | − | 0.113198i | ||||
\(377\) | 3.94143i | 0.202994i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.0603 | −1.08180 | −0.540898 | − | 0.841088i | \(-0.681915\pi\) | ||||
−0.540898 | + | 0.841088i | \(0.681915\pi\) | |||||||
\(380\) | −17.0539 | + | 15.4524i | −0.874847 | + | 0.792692i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 5.58457 | + | 14.4805i | 0.285731 | + | 0.740885i | ||||
\(383\) | 27.1156 | 1.38554 | 0.692771 | − | 0.721158i | \(-0.256390\pi\) | ||||
0.692771 | + | 0.721158i | \(0.256390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.24166 | −0.470999 | ||||||||
\(386\) | 1.05452 | + | 2.73432i | 0.0536739 | + | 0.139173i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.50292 | + | 2.26788i | −0.127067 | + | 0.115134i | ||||
\(389\) | −8.59148 | −0.435605 | −0.217803 | − | 0.975993i | \(-0.569889\pi\) | ||||
−0.217803 | + | 0.975993i | \(0.569889\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.50441i | − | 0.0760813i | ||||||
\(392\) | 2.52615 | + | 1.27222i | 0.127590 | + | 0.0642571i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.38941 | + | 6.19561i | 0.120377 | + | 0.312130i | ||||
\(395\) | 35.0001i | 1.76105i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 33.3145i | − | 1.67201i | −0.548725 | − | 0.836003i | \(-0.684887\pi\) | ||
0.548725 | − | 0.836003i | \(-0.315113\pi\) | |||||||
\(398\) | −22.1088 | + | 8.52653i | −1.10821 | + | 0.427396i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.107745 | − | 1.09082i | 0.00538726 | − | 0.0545408i | ||||
\(401\) | 5.42643i | 0.270983i | 0.990779 | + | 0.135491i | \(0.0432613\pi\) | ||||
−0.990779 | + | 0.135491i | \(0.956739\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.84325 | −0.191446 | ||||||||
\(404\) | −19.8108 | + | 17.9504i | −0.985626 | + | 0.893068i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.85030 | + | 1.09925i | −0.141458 | + | 0.0545549i | ||||
\(407\) | −8.84419 | −0.438390 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.1175 | 1.83534 | 0.917672 | − | 0.397339i | \(-0.130066\pi\) | ||||
0.917672 | + | 0.397339i | \(0.130066\pi\) | |||||||
\(410\) | −13.1825 | + | 5.08398i | −0.651036 | + | 0.251080i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.17366 | + | 6.81351i | 0.304155 | + | 0.335678i | ||||
\(413\) | −10.6175 | −0.522452 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.8898i | 1.51632i | ||||||||
\(416\) | 2.74939 | + | 9.94861i | 0.134800 | + | 0.487771i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −26.6049 | + | 10.2605i | −1.30129 | + | 0.501857i | ||||
\(419\) | 19.7739i | 0.966016i | 0.875616 | + | 0.483008i | \(0.160456\pi\) | ||||
−0.875616 | + | 0.483008i | \(0.839544\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4861i | 0.949692i | 0.880069 | + | 0.474846i | \(0.157496\pi\) | ||||
−0.880069 | + | 0.474846i | \(0.842504\pi\) | |||||||
\(422\) | 7.78353 | + | 20.1823i | 0.378896 | + | 0.982457i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −25.4985 | − | 12.8416i | −1.23832 | − | 0.623643i | ||||
\(425\) | 0.117963i | 0.00572202i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.44575 | 0.408718 | ||||||||
\(428\) | 21.0901 | + | 23.2759i | 1.01943 | + | 1.12508i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0651 | − | 36.4701i | −0.678280 | − | 1.75874i | ||||
\(431\) | 33.0237 | 1.59069 | 0.795347 | − | 0.606154i | \(-0.207288\pi\) | ||||
0.795347 | + | 0.606154i | \(0.207288\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −33.2428 | −1.59755 | −0.798773 | − | 0.601632i | \(-0.794517\pi\) | ||||
−0.798773 | + | 0.601632i | \(0.794517\pi\) | |||||||
\(434\) | −1.07187 | − | 2.77930i | −0.0514514 | − | 0.133411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.5054 | + | 23.7342i | 1.02992 | + | 1.13666i | ||||
\(437\) | −17.5105 | −0.837642 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 9.28199i | − | 0.443005i | −0.975160 | − | 0.221503i | \(-0.928904\pi\) | ||
0.975160 | − | 0.221503i | \(-0.0710962\pi\) | |||||||
\(440\) | 11.7575 | − | 23.3458i | 0.560516 | − | 1.11297i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.399692 | − | 1.03638i | −0.0190114 | − | 0.0492956i | ||||
\(443\) | − | 2.61270i | − | 0.124133i | −0.998072 | − | 0.0620667i | \(-0.980231\pi\) | ||
0.998072 | − | 0.0620667i | \(-0.0197691\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 17.1088i | − | 0.811035i | ||||||
\(446\) | −31.0947 | + | 11.9920i | −1.47238 | + | 0.567839i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.42767 | + | 4.76289i | −0.303679 | + | 0.225025i | ||||
\(449\) | 30.3318i | 1.43145i | 0.698384 | + | 0.715723i | \(0.253903\pi\) | ||||
−0.698384 | + | 0.715723i | \(0.746097\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.5065 | −0.824349 | ||||||||
\(452\) | −1.97217 | − | 2.17656i | −0.0927629 | − | 0.102377i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.9713 | − | 8.47348i | 1.03116 | − | 0.397680i | ||||
\(455\) | −4.19026 | −0.196442 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.64077 | 0.310642 | 0.155321 | − | 0.987864i | \(-0.450359\pi\) | ||||
0.155321 | + | 0.987864i | \(0.450359\pi\) | |||||||
\(458\) | 32.2339 | − | 12.4314i | 1.50619 | − | 0.580881i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.8951 | − | 10.7780i | 0.554611 | − | 0.502528i | ||||
\(461\) | −35.1189 | −1.63565 | −0.817826 | − | 0.575465i | \(-0.804821\pi\) | ||||
−0.817826 | + | 0.575465i | \(0.804821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.53401i | 0.117765i | 0.998265 | + | 0.0588826i | \(0.0187538\pi\) | ||||
−0.998265 | + | 0.0588826i | \(0.981246\pi\) | |||||||
\(464\) | 0.849343 | − | 8.59878i | 0.0394298 | − | 0.399188i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.2086 | + | 9.33633i | −1.12144 | + | 0.432497i | ||||
\(467\) | − | 16.0379i | − | 0.742145i | −0.928604 | − | 0.371072i | \(-0.878990\pi\) | ||
0.928604 | − | 0.371072i | \(-0.121010\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 12.6358i | − | 0.583465i | ||||||
\(470\) | 2.01628 | + | 5.22810i | 0.0930040 | + | 0.241154i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.5078 | − | 26.8214i | 0.621748 | − | 1.23455i | ||||
\(473\) | − | 48.4327i | − | 2.22694i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.37302 | 0.0629985 | ||||||||
\(476\) | 0.637998 | − | 0.578085i | 0.0292426 | − | 0.0264965i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.3260 | + | 39.7394i | 0.700993 | + | 1.81764i | ||||
\(479\) | −29.2616 | −1.33700 | −0.668498 | − | 0.743714i | \(-0.733062\pi\) | ||||
−0.668498 | + | 0.743714i | \(0.733062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.01004 | −0.182842 | ||||||||
\(482\) | −2.80837 | − | 7.28196i | −0.127918 | − | 0.331684i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.69817 | − | 6.97524i | 0.349917 | − | 0.317057i | ||||
\(485\) | 3.87832 | 0.176106 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.81399i | − | 0.127514i | −0.997965 | − | 0.0637570i | \(-0.979692\pi\) | ||
0.997965 | − | 0.0637570i | \(-0.0203083\pi\) | |||||||
\(488\) | −10.7449 | + | 21.3352i | −0.486398 | + | 0.965801i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.16865 | − | 3.03024i | −0.0527941 | − | 0.136892i | ||||
\(491\) | 19.2668i | 0.869497i | 0.900552 | + | 0.434748i | \(0.143163\pi\) | ||||
−0.900552 | + | 0.434748i | \(0.856837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.929886i | 0.0418799i | ||||||||
\(494\) | −12.0629 | + | 4.65221i | −0.542736 | + | 0.209313i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.38458 | + | 0.828187i | 0.376479 | + | 0.0371867i | ||||
\(497\) | 8.95532i | 0.401701i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.4436 | 1.76574 | 0.882869 | − | 0.469620i | \(-0.155609\pi\) | ||||
0.882869 | + | 0.469620i | \(0.155609\pi\) | |||||||
\(500\) | 16.0856 | − | 14.5750i | 0.719370 | − | 0.651815i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.0160 | − | 9.26207i | 1.07189 | − | 0.413387i | ||||
\(503\) | −33.3860 | −1.48861 | −0.744304 | − | 0.667841i | \(-0.767219\pi\) | ||||
−0.744304 | + | 0.667841i | \(0.767219\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 30.6973 | 1.36601 | ||||||||
\(506\) | 18.5569 | − | 7.15669i | 0.824954 | − | 0.318154i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.53488 | + | 9.41945i | 0.378674 | + | 0.417920i | ||||
\(509\) | 9.16584 | 0.406269 | 0.203134 | − | 0.979151i | \(-0.434887\pi\) | ||||
0.203134 | + | 0.979151i | \(0.434887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.16051i | − | 0.316762i | ||||||
\(512\) | −3.85434 | − | 22.2967i | −0.170339 | − | 0.985385i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.79970 | + | 3.00805i | −0.344030 | + | 0.132679i | ||||
\(515\) | − | 10.5577i | − | 0.465226i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.94299i | 0.305352i | ||||||||
\(518\) | −1.11838 | − | 2.89991i | −0.0491390 | − | 0.127415i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.33095 | − | 10.5852i | 0.233778 | − | 0.464193i | ||||
\(521\) | − | 1.14191i | − | 0.0500280i | −0.999687 | − | 0.0250140i | \(-0.992037\pi\) | ||
0.999687 | − | 0.0250140i | \(-0.00796304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.5606 | −0.855323 | −0.427662 | − | 0.903939i | \(-0.640663\pi\) | ||||
−0.427662 | + | 0.903939i | \(0.640663\pi\) | |||||||
\(524\) | −10.4147 | − | 11.4941i | −0.454968 | − | 0.502121i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.99605 | + | 20.7333i | 0.348645 | + | 0.904016i | ||||
\(527\) | −0.906723 | −0.0394975 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.7864 | −0.468975 | ||||||||
\(530\) | 11.7961 | + | 30.5866i | 0.512390 | + | 1.32860i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.72860 | − | 7.42596i | −0.291722 | − | 0.321956i | ||||
\(533\) | −7.93762 | −0.343816 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 36.0665i | − | 1.55929i | ||||||
\(536\) | 31.9199 | + | 16.0755i | 1.37873 | + | 0.694357i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.7129 | + | 35.5567i | 0.591203 | + | 1.53296i | ||||
\(539\) | − | 4.02419i | − | 0.173334i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.9815i | 1.54696i | 0.633818 | + | 0.773482i | \(0.281487\pi\) | ||||
−0.633818 | + | 0.773482i | \(0.718513\pi\) | |||||||
\(542\) | 7.50053 | − | 2.89267i | 0.322175 | − | 0.124251i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.648653 | + | 2.34713i | 0.0278108 | + | 0.100633i | ||||
\(545\) | − | 36.7766i | − | 1.57534i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.0634 | −0.815092 | −0.407546 | − | 0.913185i | \(-0.633615\pi\) | ||||
−0.407546 | + | 0.913185i | \(0.633615\pi\) | |||||||
\(548\) | 4.16075 | + | 4.59197i | 0.177738 | + | 0.196159i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.45507 | + | 0.561164i | −0.0620443 | + | 0.0239281i | ||||
\(551\) | 10.8234 | 0.461091 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.2405 | −0.648090 | ||||||||
\(554\) | −10.3763 | + | 4.00175i | −0.440847 | + | 0.170018i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.57891 | − | 5.05500i | 0.236598 | − | 0.214380i | ||||
\(557\) | 18.4543 | 0.781934 | 0.390967 | − | 0.920405i | \(-0.372141\pi\) | ||||
0.390967 | + | 0.920405i | \(0.372141\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.9598i | − | 0.928803i | ||||||
\(560\) | 9.14162 | + | 0.902963i | 0.386304 | + | 0.0381571i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.246295 | − | 0.0949867i | 0.0103893 | − | 0.00400677i | ||||
\(563\) | − | 31.6916i | − | 1.33564i | −0.744322 | − | 0.667821i | \(-0.767227\pi\) | ||
0.744322 | − | 0.667821i | \(-0.232773\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.37262i | 0.141887i | ||||||||
\(566\) | −6.33779 | − | 16.4335i | −0.266397 | − | 0.690753i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.6225 | − | 11.3932i | −0.949219 | − | 0.478047i | ||||
\(569\) | − | 27.5168i | − | 1.15357i | −0.816897 | − | 0.576783i | \(-0.804308\pi\) | ||
0.816897 | − | 0.576783i | \(-0.195692\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.7326 | −1.16057 | −0.580287 | − | 0.814412i | \(-0.697060\pi\) | ||||
−0.580287 | + | 0.814412i | \(0.697060\pi\) | |||||||
\(572\) | 10.8824 | − | 9.86041i | 0.455014 | − | 0.412284i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.21377 | − | 5.74018i | −0.0924010 | − | 0.239591i | ||||
\(575\) | −0.957681 | −0.0399381 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.3530 | 1.59666 | 0.798328 | − | 0.602223i | \(-0.205718\pi\) | ||||
0.798328 | + | 0.602223i | \(0.205718\pi\) | |||||||
\(578\) | 8.55659 | + | 22.1868i | 0.355907 | + | 0.922848i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.35243 | + | 6.66198i | −0.305293 | + | 0.276624i | ||||
\(581\) | −13.4507 | −0.558027 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.6194i | 1.68229i | ||||||||
\(584\) | 18.0885 | + | 9.10978i | 0.748509 | + | 0.376966i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.33648 | − | 11.2443i | −0.179138 | − | 0.464496i | ||||
\(587\) | 13.7550i | 0.567731i | 0.958864 | + | 0.283865i | \(0.0916169\pi\) | ||||
−0.958864 | + | 0.283865i | \(0.908383\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.5538i | 0.434861i | ||||||||
\(590\) | −32.1735 | + | 12.4081i | −1.32456 | + | 0.510833i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.74845 | + | 0.864127i | 0.359559 | + | 0.0355154i | ||||
\(593\) | − | 31.5293i | − | 1.29475i | −0.762171 | − | 0.647376i | \(-0.775866\pi\) | ||
0.762171 | − | 0.647376i | \(-0.224134\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.988589 | −0.0405282 | ||||||||
\(596\) | 9.75059 | − | 8.83493i | 0.399400 | − | 0.361893i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.41387 | − | 3.24491i | 0.344069 | − | 0.132694i | ||||
\(599\) | 14.6650 | 0.599196 | 0.299598 | − | 0.954066i | \(-0.403147\pi\) | ||||
0.299598 | + | 0.954066i | \(0.403147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −40.8677 | −1.66703 | −0.833515 | − | 0.552497i | \(-0.813675\pi\) | ||||
−0.833515 | + | 0.552497i | \(0.813675\pi\) | |||||||
\(602\) | 15.8805 | − | 6.12452i | 0.647242 | − | 0.249617i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.45486 | − | 1.60564i | −0.0591973 | − | 0.0653326i | ||||
\(605\) | −11.9284 | −0.484960 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.0141i | 1.62412i | 0.583572 | + | 0.812061i | \(0.301655\pi\) | ||||
−0.583572 | + | 0.812061i | \(0.698345\pi\) | |||||||
\(608\) | 27.3194 | − | 7.54997i | 1.10795 | − | 0.306192i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.5926 | − | 9.87009i | 1.03621 | − | 0.399628i | ||||
\(611\) | 3.14802i | 0.127355i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.46053i | 0.139770i | 0.997555 | + | 0.0698848i | \(0.0222632\pi\) | ||||
−0.997555 | + | 0.0698848i | \(0.977737\pi\) | |||||||
\(614\) | 11.9270 | + | 30.9261i | 0.481335 | + | 1.24808i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.1657 | + | 5.11968i | 0.409589 | + | 0.206278i | ||||
\(617\) | − | 36.6562i | − | 1.47572i | −0.674952 | − | 0.737861i | \(-0.735836\pi\) | ||
0.674952 | − | 0.737861i | \(-0.264164\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0770 | −0.405029 | −0.202514 | − | 0.979279i | \(-0.564911\pi\) | ||||
−0.202514 | + | 0.979279i | \(0.564911\pi\) | |||||||
\(620\) | −6.49603 | − | 7.16929i | −0.260887 | − | 0.287926i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.17598 | − | 16.0140i | −0.247634 | − | 0.642102i | ||||
\(623\) | 7.44987 | 0.298473 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.2951 | −1.05180 | ||||||||
\(626\) | −3.83796 | − | 9.95162i | −0.153396 | − | 0.397747i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.3098 | + | 24.6220i | 0.890257 | + | 0.982525i | ||||
\(629\) | −0.946071 | −0.0377223 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 28.1634i | − | 1.12117i | −0.828098 | − | 0.560583i | \(-0.810577\pi\) | ||
0.828098 | − | 0.560583i | \(-0.189423\pi\) | |||||||
\(632\) | 19.3893 | − | 38.4997i | 0.771264 | − | 1.53144i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.1414 | + | 39.2607i | 0.601340 | + | 1.55924i | ||||
\(635\) | − | 14.5956i | − | 0.579209i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.82461i | − | 0.0722935i | ||||||
\(638\) | −11.4701 | + | 4.42360i | −0.454107 | + | 0.175132i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.9112 | + | 21.9443i | −0.549889 | + | 0.867426i | ||||
\(641\) | − | 12.3588i | − | 0.488142i | −0.969757 | − | 0.244071i | \(-0.921517\pi\) | ||
0.969757 | − | 0.244071i | \(-0.0784830\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.0875 | 1.10766 | 0.553831 | − | 0.832629i | \(-0.313165\pi\) | ||||
0.553831 | + | 0.832629i | \(0.313165\pi\) | |||||||
\(644\) | 4.69319 | + | 5.17960i | 0.184938 | + | 0.204105i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.84595 | + | 1.09758i | −0.111972 | + | 0.0431835i | ||||
\(647\) | −43.3350 | −1.70368 | −0.851838 | − | 0.523806i | \(-0.824512\pi\) | ||||
−0.851838 | + | 0.523806i | \(0.824512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −42.7268 | −1.67717 | ||||||||
\(650\) | −0.659741 | + | 0.254437i | −0.0258772 | + | 0.00997985i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.0264 | + | 15.4275i | −0.666806 | + | 0.604187i | ||||
\(653\) | −32.0509 | −1.25425 | −0.627125 | − | 0.778919i | \(-0.715768\pi\) | ||||
−0.627125 | + | 0.778919i | \(0.715768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.8103i | 0.695905i | ||||||||
\(656\) | 17.3170 | + | 1.71048i | 0.676115 | + | 0.0667832i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.27653 | + | 0.877970i | −0.0887482 | + | 0.0342268i | ||||
\(659\) | − | 6.88401i | − | 0.268163i | −0.990970 | − | 0.134081i | \(-0.957192\pi\) | ||
0.990970 | − | 0.134081i | \(-0.0428084\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 47.2652i | − | 1.83840i | −0.393788 | − | 0.919201i | \(-0.628836\pi\) | ||
0.393788 | − | 0.919201i | \(-0.371164\pi\) | |||||||
\(662\) | −8.27790 | − | 21.4641i | −0.321730 | − | 0.834227i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.1123 | − | 33.9784i | 0.664085 | − | 1.31862i | ||||
\(665\) | 11.5067i | 0.446209i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.54929 | −0.292310 | ||||||||
\(668\) | −19.9728 | + | 18.0972i | −0.772770 | + | 0.700200i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.7667 | − | 38.2893i | −0.570489 | − | 1.47925i | ||||
\(671\) | 33.9873 | 1.31207 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.89911 | 0.265941 | 0.132971 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132971 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(674\) | 16.2869 | + | 42.2309i | 0.627346 | + | 1.62667i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.3330 | + | 12.9870i | −0.551270 | + | 0.499501i | ||||
\(677\) | 23.7479 | 0.912707 | 0.456353 | − | 0.889799i | \(-0.349155\pi\) | ||||
0.456353 | + | 0.889799i | \(0.349155\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.68878i | 0.0648094i | ||||||||
\(680\) | 1.25771 | − | 2.49733i | 0.0482309 | − | 0.0957681i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4.31341 | − | 11.1844i | −0.165169 | − | 0.428274i | ||||
\(683\) | − | 41.5546i | − | 1.59004i | −0.606583 | − | 0.795020i | \(-0.707460\pi\) | ||
0.606583 | − | 0.795020i | \(-0.292540\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7.11534i | − | 0.271863i | ||||||
\(686\) | 1.31949 | − | 0.508876i | 0.0503782 | − | 0.0194290i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.73215 | + | 47.9084i | −0.180412 | + | 1.82649i | ||||
\(689\) | 18.4172i | 0.701641i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5146 | −0.666285 | −0.333142 | − | 0.942876i | \(-0.608109\pi\) | ||||
−0.333142 | + | 0.942876i | \(0.608109\pi\) | |||||||
\(692\) | −7.38592 | + | 6.69232i | −0.280770 | + | 0.254404i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.2624 | − | 7.81442i | 0.769149 | − | 0.296631i | ||||
\(695\) | −8.64462 | −0.327909 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.87269 | −0.0709331 | ||||||||
\(698\) | 14.1244 | − | 5.44724i | 0.534616 | − | 0.206181i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.367999 | − | 0.406139i | −0.0139090 | − | 0.0153506i | ||||
\(701\) | −1.39361 | −0.0526361 | −0.0263180 | − | 0.999654i | \(-0.508378\pi\) | ||||
−0.0263180 | + | 0.999654i | \(0.508378\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.0118i | 0.415317i | ||||||||
\(704\) | −25.8662 | + | 19.1668i | −0.974868 | + | 0.722375i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.5068 | + | 8.68002i | −0.847055 | + | 0.326677i | ||||
\(707\) | 13.3668i | 0.502711i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 42.1733i | − | 1.58385i | −0.610616 | − | 0.791927i | \(-0.709078\pi\) | ||
0.610616 | − | 0.791927i | \(-0.290922\pi\) | |||||||
\(710\) | 10.4656 | + | 27.1367i | 0.392767 | + | 1.01842i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.47790 | + | 18.8195i | −0.355199 | + | 0.705290i | ||||
\(713\) | − | 7.36125i | − | 0.275681i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.8624 | −0.630618 | ||||||||
\(716\) | 4.64551 | + | 5.12698i | 0.173611 | + | 0.191604i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.76149 | − | 22.7181i | −0.326976 | − | 0.847831i | ||||
\(719\) | −11.8108 | −0.440468 | −0.220234 | − | 0.975447i | \(-0.570682\pi\) | ||||
−0.220234 | + | 0.975447i | \(0.570682\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.59723 | 0.171210 | ||||||||
\(722\) | 3.10655 | + | 8.05512i | 0.115614 | + | 0.299781i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.6183 | + | 15.0298i | 0.506121 | + | 0.558576i | ||||
\(725\) | 0.591949 | 0.0219844 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.5504i | 1.68937i | 0.535264 | + | 0.844685i | \(0.320212\pi\) | ||||
−0.535264 | + | 0.844685i | \(0.679788\pi\) | |||||||
\(728\) | 4.60923 | + | 2.32131i | 0.170830 | + | 0.0860335i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.36811 | − | 21.6980i | −0.309718 | − | 0.803081i | ||||
\(731\) | − | 5.18089i | − | 0.191622i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.4714i | 1.42097i | 0.703711 | + | 0.710487i | \(0.251525\pi\) | ||||
−0.703711 | + | 0.710487i | \(0.748475\pi\) | |||||||
\(734\) | 33.7942 | − | 13.0331i | 1.24737 | − | 0.481062i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.0553 | + | 5.26610i | −0.702386 | + | 0.194111i | ||||
\(737\) | − | 50.8487i | − | 1.87304i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1292 | 0.446179 | 0.223090 | − | 0.974798i | \(-0.428386\pi\) | ||||
0.223090 | + | 0.974798i | \(0.428386\pi\) | |||||||
\(740\) | −6.77794 | − | 7.48041i | −0.249162 | − | 0.274985i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.3186 | + | 5.13650i | −0.488943 | + | 0.188567i | ||||
\(743\) | −46.7546 | −1.71526 | −0.857630 | − | 0.514267i | \(-0.828064\pi\) | ||||
−0.857630 | + | 0.514267i | \(0.828064\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.1087 | −0.553540 | ||||||||
\(746\) | 5.27648 | − | 2.03494i | 0.193186 | − | 0.0745043i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.56743 | − | 2.32632i | 0.0938744 | − | 0.0850588i | ||||
\(749\) | 15.7048 | 0.573841 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 29.7196i | − | 1.08448i | −0.840222 | − | 0.542242i | \(-0.817576\pi\) | ||
0.840222 | − | 0.542242i | \(-0.182424\pi\) | |||||||
\(752\) | 0.678369 | − | 6.86783i | 0.0247376 | − | 0.250444i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.20067 | + | 2.00570i | −0.189397 | + | 0.0730433i | ||||
\(755\) | 2.48797i | 0.0905464i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0932i | 0.584919i | 0.956278 | + | 0.292459i | \(0.0944737\pi\) | ||||
−0.956278 | + | 0.292459i | \(0.905526\pi\) | |||||||
\(758\) | −10.7171 | − | 27.7888i | −0.389262 | − | 1.00933i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.0676 | − | 14.6391i | −1.05439 | − | 0.531014i | ||||
\(761\) | − | 5.21482i | − | 0.189037i | −0.995523 | − | 0.0945186i | \(-0.969869\pi\) | ||
0.995523 | − | 0.0945186i | \(-0.0301312\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.0140 | 0.579746 | ||||||||
\(764\) | −16.2649 | + | 14.7375i | −0.588445 | + | 0.533185i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.7985 | + | 35.7787i | 0.498559 | + | 1.29274i | ||||
\(767\) | −19.3727 | −0.699509 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.7856 | 0.641367 | 0.320683 | − | 0.947186i | \(-0.396087\pi\) | ||||
0.320683 | + | 0.947186i | \(0.396087\pi\) | |||||||
\(770\) | −4.70286 | − | 12.1943i | −0.169479 | − | 0.439450i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.07128 | + | 2.78286i | −0.110538 | + | 0.100157i | ||||
\(773\) | 19.9688 | 0.718228 | 0.359114 | − | 0.933294i | \(-0.383079\pi\) | ||||
0.359114 | + | 0.933294i | \(0.383079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.577204i | 0.0207338i | ||||||||
\(776\) | −4.26611 | − | 2.14851i | −0.153144 | − | 0.0771269i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.37200 | − | 11.3363i | −0.156744 | − | 0.406428i | ||||
\(779\) | 21.7971i | 0.780962i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0379i | 1.28954i | ||||||||
\(782\) | 1.98505 | − | 0.765558i | 0.0709852 | − | 0.0273763i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.393186 | + | 3.98063i | −0.0140424 | + | 0.142165i | ||||
\(785\) | − | 38.1522i | − | 1.36171i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.1178 | −1.14487 | −0.572437 | − | 0.819948i | \(-0.694002\pi\) | ||||
−0.572437 | + | 0.819948i | \(0.694002\pi\) | |||||||
\(788\) | −6.95912 | + | 6.30560i | −0.247908 | + | 0.224628i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −46.1822 | + | 17.8107i | −1.64309 | + | 0.633676i | ||||
\(791\) | −1.46858 | −0.0522166 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4102 | 0.547231 | ||||||||
\(794\) | 43.9580 | − | 16.9529i | 1.56001 | − | 0.601637i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.5013 | − | 24.8333i | −0.797537 | − | 0.880194i | ||||
\(797\) | −10.4964 | −0.371800 | −0.185900 | − | 0.982569i | \(-0.559520\pi\) | ||||
−0.185900 | + | 0.982569i | \(0.559520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.742698i | 0.0262748i | ||||||||
\(800\) | 1.49414 | − | 0.412921i | 0.0528260 | − | 0.0145990i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.16010 | + | 2.76138i | −0.252832 | + | 0.0975077i | ||||
\(803\) | − | 28.8153i | − | 1.01687i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 8.02588i | − | 0.282875i | ||||||
\(806\) | −1.95574 | − | 5.07112i | −0.0688880 | − | 0.178623i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −33.7666 | − | 17.0056i | −1.18791 | − | 0.598255i | ||||
\(809\) | 31.8333i | 1.11920i | 0.828763 | + | 0.559599i | \(0.189045\pi\) | ||||
−0.828763 | + | 0.559599i | \(0.810955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.39041 | −0.0488238 | −0.0244119 | − | 0.999702i | \(-0.507771\pi\) | ||||
−0.0244119 | + | 0.999702i | \(0.507771\pi\) | |||||||
\(812\) | −2.90089 | − | 3.20155i | −0.101801 | − | 0.112352i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.50059 | − | 11.6698i | −0.157746 | − | 0.409026i | ||||
\(815\) | 26.3827 | 0.924147 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −60.3029 | −2.10973 | ||||||||
\(818\) | 18.8882 | + | 48.9761i | 0.660411 | + | 1.71241i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.4165 | − | 14.8070i | −0.468524 | − | 0.517083i | ||||
\(821\) | 18.4554 | 0.644097 | 0.322048 | − | 0.946723i | \(-0.395629\pi\) | ||||
0.322048 | + | 0.946723i | \(0.395629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 41.1895i | − | 1.43578i | −0.696159 | − | 0.717888i | \(-0.745109\pi\) | ||
0.696159 | − | 0.717888i | \(-0.254891\pi\) | |||||||
\(824\) | −5.84871 | + | 11.6133i | −0.203749 | + | 0.404568i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.40298 | − | 14.0096i | −0.187994 | − | 0.487457i | ||||
\(827\) | 6.08227i | 0.211501i | 0.994393 | + | 0.105751i | \(0.0337245\pi\) | ||||
−0.994393 | + | 0.105751i | \(0.966275\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.2474i | 1.53677i | 0.639985 | + | 0.768387i | \(0.278940\pi\) | ||||
−0.639985 | + | 0.768387i | \(0.721060\pi\) | |||||||
\(830\) | −40.7587 | + | 15.7191i | −1.41475 | + | 0.545617i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −11.7280 | + | 8.69040i | −0.406594 | + | 0.301285i | ||||
\(833\) | − | 0.430472i | − | 0.0149150i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.9482 | 1.07101 | ||||||||
\(836\) | −27.0772 | − | 29.8835i | −0.936484 | − | 1.03354i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −26.0914 | + | 10.0624i | −0.901311 | + | 0.347601i | ||||
\(839\) | −45.9488 | −1.58633 | −0.793164 | − | 0.609008i | \(-0.791568\pi\) | ||||
−0.793164 | + | 0.609008i | \(0.791568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.3337 | −0.839094 | ||||||||
\(842\) | −25.7116 | + | 9.91598i | −0.886080 | + | 0.341727i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.6694 | + | 20.5405i | −0.780312 | + | 0.707034i | ||||
\(845\) | 22.2093 | 0.764022 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.19413i | − | 0.178472i | ||||||
\(848\) | 3.96875 | − | 40.1797i | 0.136287 | − | 1.37978i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.155650 | + | 0.0600283i | −0.00533875 | + | 0.00205895i | ||||
\(851\) | − | 7.68070i | − | 0.263291i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.7862i | 0.780185i | 0.920776 | + | 0.390093i | \(0.127557\pi\) | ||||
−0.920776 | + | 0.390093i | \(0.872443\pi\) | |||||||
\(854\) | 4.29784 | + | 11.1441i | 0.147069 | + | 0.381342i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −19.9800 | + | 39.6727i | −0.682903 | + | 1.35598i | ||||
\(857\) | 28.8660i | 0.986042i | 0.870017 | + | 0.493021i | \(0.164108\pi\) | ||||
−0.870017 | + | 0.493021i | \(0.835892\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.1350 | 1.81294 | 0.906471 | − | 0.422268i | \(-0.138766\pi\) | ||||
0.906471 | + | 0.422268i | \(0.138766\pi\) | |||||||
\(860\) | 40.9644 | − | 37.1175i | 1.39687 | − | 1.26569i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.8050 | + | 43.5743i | 0.572379 | + | 1.48415i | ||||
\(863\) | −27.2397 | −0.927250 | −0.463625 | − | 0.886032i | \(-0.653451\pi\) | ||||
−0.463625 | + | 0.886032i | \(0.653451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.4446 | 0.389128 | ||||||||
\(866\) | −16.9165 | − | 43.8634i | −0.574845 | − | 1.49054i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.12180 | − | 2.82863i | 0.105961 | − | 0.0960101i | ||||
\(869\) | −61.3305 | −2.08050 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 23.0553i | − | 0.781199i | ||||||
\(872\) | −20.3734 | + | 40.4538i | −0.689931 | + | 1.36994i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.91068 | − | 23.1049i | −0.301408 | − | 0.781535i | ||||
\(875\) | − | 10.8533i | − | 0.366909i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 24.5161i | 0.827850i | 0.910311 | + | 0.413925i | \(0.135842\pi\) | ||||
−0.910311 | + | 0.413925i | \(0.864158\pi\) | |||||||
\(878\) | 12.2475 | − | 4.72338i | 0.413332 | − | 0.159406i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 36.7876 | + | 3.63370i | 1.24011 | + | 0.122492i | ||||
\(881\) | 18.5560i | 0.625167i | 0.949890 | + | 0.312584i | \(0.101194\pi\) | ||||
−0.949890 | + | 0.312584i | \(0.898806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.1013 | −1.61874 | −0.809369 | − | 0.587300i | \(-0.800191\pi\) | ||||
−0.809369 | + | 0.587300i | \(0.800191\pi\) | |||||||
\(884\) | 1.16410 | − | 1.05478i | 0.0391528 | − | 0.0354760i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.44743 | − | 1.32954i | 0.115819 | − | 0.0446668i | ||||
\(887\) | 5.36841 | 0.180254 | 0.0901268 | − | 0.995930i | \(-0.471273\pi\) | ||||
0.0901268 | + | 0.995930i | \(0.471273\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.35551 | 0.213157 | ||||||||
\(890\) | 22.5748 | − | 8.70626i | 0.756711 | − | 0.291834i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −31.6467 | − | 34.9266i | −1.05961 | − | 1.16943i | ||||
\(893\) | 8.64461 | 0.289281 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.94435i | − | 0.265550i | ||||||
\(896\) | −9.55545 | − | 6.05750i | −0.319225 | − | 0.202367i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40.0224 | + | 15.4351i | −1.33556 | + | 0.515076i | ||||
\(899\) | 4.55004i | 0.151752i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.34510i | 0.144756i | ||||||||
\(902\) | −8.90864 | − | 23.0996i | −0.296625 | − | 0.769133i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.86836 | − | 3.70985i | 0.0621407 | − | 0.123388i | ||||
\(905\) | − | 23.2889i | − | 0.774148i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.80217 | 0.159453 | 0.0797267 | − | 0.996817i | \(-0.474595\pi\) | ||||
0.0797267 | + | 0.996817i | \(0.474595\pi\) | |||||||
\(908\) | 22.3613 | + | 24.6788i | 0.742085 | + | 0.818996i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.13232 | − | 5.52899i | −0.0706857 | − | 0.183284i | ||||
\(911\) | −2.79257 | −0.0925219 | −0.0462609 | − | 0.998929i | \(-0.514731\pi\) | ||||
−0.0462609 | + | 0.998929i | \(0.514731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.1280 | −1.79138 | ||||||||
\(914\) | 3.37933 | + | 8.76241i | 0.111778 | + | 0.289835i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 32.8061 | + | 36.2062i | 1.08394 | + | 1.19629i | ||||
\(917\) | −7.75532 | −0.256103 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.90433i | − | 0.260740i | −0.991465 | − | 0.130370i | \(-0.958384\pi\) | ||
0.991465 | − | 0.130370i | \(-0.0416165\pi\) | |||||||
\(920\) | 20.2746 | + | 10.2107i | 0.668434 | + | 0.336638i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.8712 | − | 46.3390i | −0.588556 | − | 1.52609i | ||||
\(923\) | 16.3399i | 0.537836i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.602253i | 0.0198019i | ||||||||
\(926\) | −3.34359 | + | 1.28949i | −0.109877 | + | 0.0423754i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.7782 | − | 3.25501i | 0.386638 | − | 0.106851i | ||||
\(929\) | 4.24927i | 0.139414i | 0.997568 | + | 0.0697070i | \(0.0222064\pi\) | ||||
−0.997568 | + | 0.0697070i | \(0.977794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.01046 | −0.164211 | ||||||||
\(932\) | −24.6383 | − | 27.1919i | −0.807055 | − | 0.890699i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 21.1618 | − | 8.16129i | 0.692434 | − | 0.267046i | ||||
\(935\) | −3.97827 | −0.130103 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.70393 | 0.0556649 | 0.0278324 | − | 0.999613i | \(-0.491140\pi\) | ||||
0.0278324 | + | 0.999613i | \(0.491140\pi\) | |||||||
\(938\) | 16.6727 | − | 6.43003i | 0.544384 | − | 0.209948i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.87237 | + | 5.32091i | −0.191536 | + | 0.173549i | ||||
\(941\) | −53.7297 | −1.75154 | −0.875769 | − | 0.482730i | \(-0.839645\pi\) | ||||
−0.875769 | + | 0.482730i | \(0.839645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 15.2035i | − | 0.495093i | ||||||
\(944\) | 42.2643 | + | 4.17465i | 1.37558 | + | 0.135873i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 63.9063 | − | 24.6462i | 2.07777 | − | 0.801318i | ||||
\(947\) | − | 48.4816i | − | 1.57544i | −0.616033 | − | 0.787720i | \(-0.711261\pi\) | ||
0.616033 | − | 0.787720i | \(-0.288739\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 13.0651i | − | 0.424112i | ||||||
\(950\) | 0.698697 | + | 1.81168i | 0.0226687 | + | 0.0587788i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.08744 | + | 0.547657i | 0.0352440 | + | 0.0177497i | ||||
\(953\) | 51.7471i | 1.67625i | 0.545476 | + | 0.838126i | \(0.316349\pi\) | ||||
−0.545476 | + | 0.838126i | \(0.683651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.2028 | 0.815544 | ||||||||
\(956\) | −44.6365 | + | 40.4448i | −1.44365 | + | 1.30808i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.8905 | − | 38.6103i | −0.481090 | − | 1.24744i | ||||
\(959\) | 3.09831 | 0.100050 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 26.5633 | 0.856881 | ||||||||
\(962\) | −2.04061 | − | 5.29119i | −0.0657920 | − | 0.170595i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.17933 | − | 7.41122i | 0.263439 | − | 0.238699i | ||||
\(965\) | 4.75901 | 0.153198 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.89472i | 0.253877i | 0.991911 | + | 0.126939i | \(0.0405151\pi\) | ||||
−0.991911 | + | 0.126939i | \(0.959485\pi\) | |||||||
\(968\) | 13.1212 | + | 6.60810i | 0.421730 | + | 0.212392i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.97358 | + | 5.11740i | 0.0633680 | + | 0.164310i | ||||
\(971\) | − | 15.1077i | − | 0.484829i | −0.970173 | − | 0.242414i | \(-0.922061\pi\) | ||
0.970173 | − | 0.242414i | \(-0.0779393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 3.76422i | − | 0.120675i | ||||||
\(974\) | 3.71302 | − | 1.43197i | 0.118973 | − | 0.0458833i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −33.6194 | − | 3.32075i | −1.07613 | − | 0.106295i | ||||
\(977\) | − | 11.3398i | − | 0.362792i | −0.983410 | − | 0.181396i | \(-0.941938\pi\) | ||
0.983410 | − | 0.181396i | \(-0.0580616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.9797 | 0.958155 | ||||||||
\(980\) | 3.40366 | − | 3.08403i | 0.108726 | − | 0.0985156i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.4222 | + | 9.80439i | −0.811256 | + | 0.312871i | ||||
\(983\) | −34.3365 | −1.09517 | −0.547583 | − | 0.836751i | \(-0.684452\pi\) | ||||
−0.547583 | + | 0.836751i | \(0.684452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.7833 | 0.343584 | ||||||||
\(986\) | −1.22697 | + | 0.473196i | −0.0390747 | + | 0.0150696i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.2770 | − | 13.5495i | −0.390585 | − | 0.431066i | ||||
\(989\) | 42.0612 | 1.33747 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 20.9504i | − | 0.665510i | −0.943013 | − | 0.332755i | \(-0.892022\pi\) | ||
0.943013 | − | 0.332755i | \(-0.107978\pi\) | |||||||
\(992\) | 3.17393 | + | 11.4848i | 0.100772 | + | 0.364643i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.8164 | + | 4.55715i | −0.374794 | + | 0.144544i | ||||
\(995\) | 38.4797i | 1.21989i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 8.15182i | − | 0.258171i | −0.991633 | − | 0.129085i | \(-0.958796\pi\) | ||
0.991633 | − | 0.129085i | \(-0.0412041\pi\) | |||||||
\(998\) | 20.0719 | + | 52.0453i | 0.635365 | + | 1.64747i | ||||
\(999\) | 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.j.d.323.30 | yes | 48 | |
3.2 | odd | 2 | inner | 1512.2.j.d.323.19 | ✓ | 48 | |
4.3 | odd | 2 | 6048.2.j.d.5615.36 | 48 | |||
8.3 | odd | 2 | inner | 1512.2.j.d.323.20 | yes | 48 | |
8.5 | even | 2 | 6048.2.j.d.5615.14 | 48 | |||
12.11 | even | 2 | 6048.2.j.d.5615.13 | 48 | |||
24.5 | odd | 2 | 6048.2.j.d.5615.35 | 48 | |||
24.11 | even | 2 | inner | 1512.2.j.d.323.29 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.j.d.323.19 | ✓ | 48 | 3.2 | odd | 2 | inner | |
1512.2.j.d.323.20 | yes | 48 | 8.3 | odd | 2 | inner | |
1512.2.j.d.323.29 | yes | 48 | 24.11 | even | 2 | inner | |
1512.2.j.d.323.30 | yes | 48 | 1.1 | even | 1 | trivial | |
6048.2.j.d.5615.13 | 48 | 12.11 | even | 2 | |||
6048.2.j.d.5615.14 | 48 | 8.5 | even | 2 | |||
6048.2.j.d.5615.35 | 48 | 24.5 | odd | 2 | |||
6048.2.j.d.5615.36 | 48 | 4.3 | odd | 2 |