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 | 757.19 | ||
Character | \(\chi\) | \(=\) | 1512.757 |
Dual form | 1512.2.c.g.757.20 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.13123 | − | 0.848721i | 0.799898 | − | 0.600136i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.559347 | − | 1.92019i | 0.279673 | − | 0.960095i | ||||
\(5\) | 0.940450i | 0.420582i | 0.977639 | + | 0.210291i | \(0.0674411\pi\) | ||||
−0.977639 | + | 0.210291i | \(0.932559\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −0.996957 | − | 2.64690i | −0.352478 | − | 0.935820i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.798179 | + | 1.06386i | 0.252406 | + | 0.336423i | ||||
\(11\) | 5.98632i | 1.80494i | 0.430749 | + | 0.902472i | \(0.358249\pi\) | ||||
−0.430749 | + | 0.902472i | \(0.641751\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.59017i | 1.82778i | 0.405957 | + | 0.913892i | \(0.366938\pi\) | ||||
−0.405957 | + | 0.913892i | \(0.633062\pi\) | |||||||
\(14\) | 1.13123 | − | 0.848721i | 0.302333 | − | 0.226830i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.37426 | − | 2.14810i | −0.843566 | − | 0.537026i | ||||
\(17\) | −2.64225 | −0.640840 | −0.320420 | − | 0.947276i | \(-0.603824\pi\) | ||||
−0.320420 | + | 0.947276i | \(0.603824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.83430i | 1.33848i | 0.743047 | + | 0.669240i | \(0.233380\pi\) | ||||
−0.743047 | + | 0.669240i | \(0.766620\pi\) | |||||||
\(20\) | 1.80584 | + | 0.526037i | 0.403799 | + | 0.117626i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.08071 | + | 6.77188i | 1.08321 | + | 1.44377i | ||||
\(23\) | 2.88452 | 0.601464 | 0.300732 | − | 0.953709i | \(-0.402769\pi\) | ||||
0.300732 | + | 0.953709i | \(0.402769\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.11555 | 0.823111 | ||||||||
\(26\) | 5.59321 | + | 7.45497i | 1.09692 | + | 1.46204i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.559347 | − | 1.92019i | 0.105707 | − | 0.362882i | ||||
\(29\) | − | 3.09794i | − | 0.575274i | −0.957740 | − | 0.287637i | \(-0.907130\pi\) | ||
0.957740 | − | 0.287637i | \(-0.0928696\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.52412 | 0.632950 | 0.316475 | − | 0.948601i | \(-0.397501\pi\) | ||||
0.316475 | + | 0.948601i | \(0.397501\pi\) | |||||||
\(32\) | −5.64020 | + | 0.433813i | −0.997055 | + | 0.0766880i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.98898 | + | 2.24253i | −0.512606 | + | 0.384591i | ||||
\(35\) | 0.940450i | 0.158965i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.213560i | 0.0351090i | 0.999846 | + | 0.0175545i | \(0.00558806\pi\) | ||||
−0.999846 | + | 0.0175545i | \(0.994412\pi\) | |||||||
\(38\) | 4.95169 | + | 6.59991i | 0.803270 | + | 1.07065i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.48928 | − | 0.937588i | 0.393589 | − | 0.148246i | ||||
\(41\) | −1.63291 | −0.255017 | −0.127509 | − | 0.991837i | \(-0.540698\pi\) | ||||
−0.127509 | + | 0.991837i | \(0.540698\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.16716i | − | 1.09298i | −0.837465 | − | 0.546491i | \(-0.815963\pi\) | ||
0.837465 | − | 0.546491i | \(-0.184037\pi\) | |||||||
\(44\) | 11.4949 | + | 3.34843i | 1.73292 | + | 0.504795i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.26304 | − | 2.44815i | 0.481110 | − | 0.360960i | ||||
\(47\) | −9.32639 | −1.36039 | −0.680197 | − | 0.733030i | \(-0.738106\pi\) | ||||
−0.680197 | + | 0.733030i | \(0.738106\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.65562 | − | 3.49296i | 0.658405 | − | 0.493979i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.6544 | + | 3.68619i | 1.75485 | + | 0.511183i | ||||
\(53\) | 7.51044i | 1.03164i | 0.856698 | + | 0.515819i | \(0.172512\pi\) | ||||
−0.856698 | + | 0.515819i | \(0.827488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.62983 | −0.759126 | ||||||||
\(56\) | −0.996957 | − | 2.64690i | −0.133224 | − | 0.353707i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.62929 | − | 3.50448i | −0.345243 | − | 0.460160i | ||||
\(59\) | − | 11.9280i | − | 1.55289i | −0.630186 | − | 0.776444i | \(-0.717021\pi\) | ||
0.630186 | − | 0.776444i | \(-0.282979\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.48304i | − | 0.189884i | −0.995483 | − | 0.0949419i | \(-0.969733\pi\) | ||
0.995483 | − | 0.0949419i | \(-0.0302665\pi\) | |||||||
\(62\) | 3.98658 | − | 2.99099i | 0.506296 | − | 0.379856i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.01215 | + | 5.27769i | −0.751519 | + | 0.659711i | ||||
\(65\) | −6.19772 | −0.768733 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.0555i | − | 1.59498i | −0.603329 | − | 0.797492i | \(-0.706160\pi\) | ||
0.603329 | − | 0.797492i | \(-0.293840\pi\) | |||||||
\(68\) | −1.47793 | + | 5.07362i | −0.179226 | + | 0.615267i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.798179 | + | 1.06386i | 0.0954006 | + | 0.127156i | ||||
\(71\) | −1.54642 | −0.183526 | −0.0917632 | − | 0.995781i | \(-0.529250\pi\) | ||||
−0.0917632 | + | 0.995781i | \(0.529250\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.96871 | −0.347461 | −0.173731 | − | 0.984793i | \(-0.555582\pi\) | ||||
−0.173731 | + | 0.984793i | \(0.555582\pi\) | |||||||
\(74\) | 0.181253 | + | 0.241584i | 0.0210702 | + | 0.0280836i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.2030 | + | 3.26339i | 1.28507 | + | 0.374337i | ||||
\(77\) | 5.98632i | 0.682204i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.9515 | 1.79468 | 0.897341 | − | 0.441338i | \(-0.145496\pi\) | ||||
0.897341 | + | 0.441338i | \(0.145496\pi\) | |||||||
\(80\) | 2.02018 | − | 3.17332i | 0.225863 | − | 0.354788i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.84719 | + | 1.38588i | −0.203988 | + | 0.153045i | ||||
\(83\) | 8.74782i | 0.960198i | 0.877214 | + | 0.480099i | \(0.159399\pi\) | ||||
−0.877214 | + | 0.480099i | \(0.840601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.48490i | − | 0.269526i | ||||||
\(86\) | −6.08291 | − | 8.10768i | −0.655937 | − | 0.874273i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 15.8452 | − | 5.96810i | 1.68910 | − | 0.636202i | ||||
\(89\) | 7.50339 | 0.795358 | 0.397679 | − | 0.917525i | \(-0.369816\pi\) | ||||
0.397679 | + | 0.917525i | \(0.369816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59017i | 0.690837i | ||||||||
\(92\) | 1.61345 | − | 5.53883i | 0.168213 | − | 0.577462i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.5503 | + | 7.91550i | −1.08818 | + | 0.816421i | ||||
\(95\) | −5.48686 | −0.562940 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7529 | 1.09179 | 0.545894 | − | 0.837854i | \(-0.316190\pi\) | ||||
0.545894 | + | 0.837854i | \(0.316190\pi\) | |||||||
\(98\) | 1.13123 | − | 0.848721i | 0.114271 | − | 0.0857337i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.30202 | − | 7.90265i | 0.230202 | − | 0.790265i | ||||
\(101\) | 3.54920i | 0.353159i | 0.984286 | + | 0.176579i | \(0.0565033\pi\) | ||||
−0.984286 | + | 0.176579i | \(0.943497\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.3303 | 1.51054 | 0.755271 | − | 0.655413i | \(-0.227505\pi\) | ||||
0.755271 | + | 0.655413i | \(0.227505\pi\) | |||||||
\(104\) | 17.4435 | − | 6.57012i | 1.71048 | − | 0.644253i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.37426 | + | 8.49601i | 0.619123 | + | 0.825205i | ||||
\(107\) | 2.41633i | 0.233596i | 0.993156 | + | 0.116798i | \(0.0372629\pi\) | ||||
−0.993156 | + | 0.116798i | \(0.962737\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.86711i | 0.657750i | 0.944373 | + | 0.328875i | \(0.106669\pi\) | ||||
−0.944373 | + | 0.328875i | \(0.893331\pi\) | |||||||
\(110\) | −6.36861 | + | 4.77815i | −0.607224 | + | 0.455579i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.37426 | − | 2.14810i | −0.318838 | − | 0.202977i | ||||
\(113\) | −15.4539 | −1.45378 | −0.726891 | − | 0.686752i | \(-0.759036\pi\) | ||||
−0.726891 | + | 0.686752i | \(0.759036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.71274i | 0.252965i | ||||||||
\(116\) | −5.94864 | − | 1.73283i | −0.552318 | − | 0.160889i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1235 | − | 13.4932i | −0.931945 | − | 1.24215i | ||||
\(119\) | −2.64225 | −0.242215 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.8360 | −2.25782 | ||||||||
\(122\) | −1.25869 | − | 1.67765i | −0.113956 | − | 0.151888i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.97120 | − | 6.76698i | 0.177019 | − | 0.607692i | ||||
\(125\) | 8.57272i | 0.766767i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.96760 | 0.707010 | 0.353505 | − | 0.935433i | \(-0.384990\pi\) | ||||
0.353505 | + | 0.935433i | \(0.384990\pi\) | |||||||
\(128\) | −2.32182 | + | 11.0729i | −0.205222 | + | 0.978715i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.01103 | + | 5.26013i | −0.614908 | + | 0.461344i | ||||
\(131\) | − | 1.53780i | − | 0.134358i | −0.997741 | − | 0.0671790i | \(-0.978600\pi\) | ||
0.997741 | − | 0.0671790i | \(-0.0213999\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.83430i | 0.505898i | ||||||||
\(134\) | −11.0805 | − | 14.7687i | −0.957208 | − | 1.27582i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.63421 | + | 6.99377i | 0.225882 | + | 0.599711i | ||||
\(137\) | 6.34042 | 0.541699 | 0.270849 | − | 0.962622i | \(-0.412695\pi\) | ||||
0.270849 | + | 0.962622i | \(0.412695\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.13659i | − | 0.690137i | −0.938578 | − | 0.345068i | \(-0.887856\pi\) | ||
0.938578 | − | 0.345068i | \(-0.112144\pi\) | |||||||
\(140\) | 1.80584 | + | 0.526037i | 0.152622 | + | 0.0444583i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.74935 | + | 1.31248i | −0.146802 | + | 0.110141i | ||||
\(143\) | −39.4509 | −3.29905 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.91346 | 0.241950 | ||||||||
\(146\) | −3.35828 | + | 2.51960i | −0.277933 | + | 0.208524i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.410075 | + | 0.119454i | 0.0337080 | + | 0.00981906i | ||||
\(149\) | − | 15.2594i | − | 1.25010i | −0.780586 | − | 0.625048i | \(-0.785079\pi\) | ||
0.780586 | − | 0.625048i | \(-0.214921\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.728441 | −0.0592797 | −0.0296398 | − | 0.999561i | \(-0.509436\pi\) | ||||
−0.0296398 | + | 0.999561i | \(0.509436\pi\) | |||||||
\(152\) | 15.4428 | − | 5.81654i | 1.25258 | − | 0.471784i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.08071 | + | 6.77188i | 0.409415 | + | 0.545694i | ||||
\(155\) | 3.31425i | 0.266207i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.1207i | 0.967337i | 0.875251 | + | 0.483669i | \(0.160696\pi\) | ||||
−0.875251 | + | 0.483669i | \(0.839304\pi\) | |||||||
\(158\) | 18.0447 | − | 13.5384i | 1.43556 | − | 1.07705i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.407979 | − | 5.30432i | −0.0322536 | − | 0.419343i | ||||
\(161\) | 2.88452 | 0.227332 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.45067i | 0.426929i | 0.976951 | + | 0.213465i | \(0.0684748\pi\) | ||||
−0.976951 | + | 0.213465i | \(0.931525\pi\) | |||||||
\(164\) | −0.913361 | + | 3.13549i | −0.0713215 | + | 0.244841i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.42446 | + | 9.89577i | 0.576250 | + | 0.768061i | ||||
\(167\) | −1.96762 | −0.152259 | −0.0761297 | − | 0.997098i | \(-0.524256\pi\) | ||||
−0.0761297 | + | 0.997098i | \(0.524256\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −30.4303 | −2.34079 | ||||||||
\(170\) | −2.10899 | − | 2.81099i | −0.161752 | − | 0.215593i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.7623 | − | 4.00893i | −1.04937 | − | 0.305678i | ||||
\(173\) | 4.48602i | 0.341066i | 0.985352 | + | 0.170533i | \(0.0545489\pi\) | ||||
−0.985352 | + | 0.170533i | \(0.945451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.11555 | 0.311107 | ||||||||
\(176\) | 12.8592 | − | 20.1994i | 0.969302 | − | 1.52259i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.48804 | − | 6.36828i | 0.636205 | − | 0.477323i | ||||
\(179\) | − | 24.8086i | − | 1.85428i | −0.374716 | − | 0.927140i | \(-0.622260\pi\) | ||
0.374716 | − | 0.927140i | \(-0.377740\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.6114i | 1.68070i | 0.542048 | + | 0.840348i | \(0.317649\pi\) | ||||
−0.542048 | + | 0.840348i | \(0.682351\pi\) | |||||||
\(182\) | 5.59321 | + | 7.45497i | 0.414596 | + | 0.552599i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.87574 | − | 7.63503i | −0.212002 | − | 0.562862i | ||||
\(185\) | −0.200842 | −0.0147662 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 15.8174i | − | 1.15668i | ||||||
\(188\) | −5.21668 | + | 17.9084i | −0.380466 | + | 1.30611i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.20688 | + | 4.65681i | −0.450295 | + | 0.337841i | ||||
\(191\) | 16.3035 | 1.17968 | 0.589838 | − | 0.807521i | \(-0.299191\pi\) | ||||
0.589838 | + | 0.807521i | \(0.299191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.98388 | 0.502711 | 0.251355 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251355 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(194\) | 12.1639 | − | 9.12617i | 0.873319 | − | 0.655221i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.559347 | − | 1.92019i | 0.0399533 | − | 0.137156i | ||||
\(197\) | − | 13.5891i | − | 0.968182i | −0.875018 | − | 0.484091i | \(-0.839150\pi\) | ||
0.875018 | − | 0.484091i | \(-0.160850\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.2305 | 1.43410 | 0.717052 | − | 0.697020i | \(-0.245491\pi\) | ||||
0.717052 | + | 0.697020i | \(0.245491\pi\) | |||||||
\(200\) | −4.10303 | − | 10.8935i | −0.290128 | − | 0.770284i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.01228 | + | 4.01495i | 0.211943 | + | 0.282491i | ||||
\(203\) | − | 3.09794i | − | 0.217433i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.53567i | − | 0.107256i | ||||||
\(206\) | 17.3421 | − | 13.0112i | 1.20828 | − | 0.906531i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.1564 | − | 22.2370i | 0.981568 | − | 1.54186i | ||||
\(209\) | −34.9260 | −2.41588 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.1090i | − | 1.31552i | −0.753230 | − | 0.657758i | \(-0.771505\pi\) | ||
0.753230 | − | 0.657758i | \(-0.228495\pi\) | |||||||
\(212\) | 14.4215 | + | 4.20094i | 0.990471 | + | 0.288522i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.05079 | + | 2.73342i | 0.140189 | + | 0.186853i | ||||
\(215\) | 6.74035 | 0.459688 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.52412 | 0.239233 | ||||||||
\(218\) | 5.82826 | + | 7.76826i | 0.394739 | + | 0.526133i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.14903 | + | 10.8103i | −0.212307 | + | 0.728833i | ||||
\(221\) | − | 17.4129i | − | 1.17132i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.9241 | −1.40118 | −0.700592 | − | 0.713562i | \(-0.747080\pi\) | ||||
−0.700592 | + | 0.713562i | \(0.747080\pi\) | |||||||
\(224\) | −5.64020 | + | 0.433813i | −0.376851 | + | 0.0289853i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.4819 | + | 13.1161i | −1.16288 | + | 0.872468i | ||||
\(227\) | − | 2.48329i | − | 0.164821i | −0.996598 | − | 0.0824107i | \(-0.973738\pi\) | ||
0.996598 | − | 0.0824107i | \(-0.0262619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.3155i | − | 0.681669i | −0.940123 | − | 0.340835i | \(-0.889290\pi\) | ||
0.940123 | − | 0.340835i | \(-0.110710\pi\) | |||||||
\(230\) | 2.30236 | + | 3.06873i | 0.151813 | + | 0.202346i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.19995 | + | 3.08852i | −0.538353 | + | 0.202771i | ||||
\(233\) | −19.5208 | −1.27885 | −0.639424 | − | 0.768855i | \(-0.720827\pi\) | ||||
−0.639424 | + | 0.768855i | \(0.720827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 8.77100i | − | 0.572157i | ||||||
\(236\) | −22.9040 | − | 6.67187i | −1.49092 | − | 0.434302i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.98898 | + | 2.24253i | −0.193747 | + | 0.145362i | ||||
\(239\) | −17.8520 | −1.15475 | −0.577376 | − | 0.816478i | \(-0.695923\pi\) | ||||
−0.577376 | + | 0.816478i | \(0.695923\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.72097 | 0.432935 | 0.216468 | − | 0.976290i | \(-0.430546\pi\) | ||||
0.216468 | + | 0.976290i | \(0.430546\pi\) | |||||||
\(242\) | −28.0952 | + | 21.0788i | −1.80603 | + | 1.35500i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.84772 | − | 0.829534i | −0.182307 | − | 0.0531054i | ||||
\(245\) | 0.940450i | 0.0600831i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −38.4490 | −2.44645 | ||||||||
\(248\) | −3.51339 | − | 9.32799i | −0.223101 | − | 0.592328i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.27584 | + | 9.69769i | 0.460165 | + | 0.613336i | ||||
\(251\) | 28.1618i | 1.77756i | 0.458336 | + | 0.888779i | \(0.348445\pi\) | ||||
−0.458336 | + | 0.888779i | \(0.651555\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.2677i | 1.08561i | ||||||||
\(254\) | 9.01316 | − | 6.76227i | 0.565536 | − | 0.424302i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.77129 | + | 14.4965i | 0.423206 | + | 0.906034i | ||||
\(257\) | 24.9286 | 1.55500 | 0.777502 | − | 0.628880i | \(-0.216486\pi\) | ||||
0.777502 | + | 0.628880i | \(0.216486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.213560i | 0.0132700i | ||||||||
\(260\) | −3.46668 | + | 11.9008i | −0.214994 | + | 0.738057i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.30516 | − | 1.73960i | −0.0806331 | − | 0.107473i | ||||
\(263\) | 19.0635 | 1.17550 | 0.587751 | − | 0.809042i | \(-0.300013\pi\) | ||||
0.587751 | + | 0.809042i | \(0.300013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.06319 | −0.433888 | ||||||||
\(266\) | 4.95169 | + | 6.59991i | 0.303607 | + | 0.404666i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.0691 | − | 7.30256i | −1.53134 | − | 0.446075i | ||||
\(269\) | 10.2410i | 0.624406i | 0.950015 | + | 0.312203i | \(0.101067\pi\) | ||||
−0.950015 | + | 0.312203i | \(0.898933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.45674 | −0.270728 | −0.135364 | − | 0.990796i | \(-0.543220\pi\) | ||||
−0.135364 | + | 0.990796i | \(0.543220\pi\) | |||||||
\(272\) | 8.91564 | + | 5.67583i | 0.540590 | + | 0.344148i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.17245 | − | 5.38125i | 0.433304 | − | 0.325093i | ||||
\(275\) | 24.6370i | 1.48567i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0596i | 0.964929i | 0.875915 | + | 0.482465i | \(0.160258\pi\) | ||||
−0.875915 | + | 0.482465i | \(0.839742\pi\) | |||||||
\(278\) | −6.90569 | − | 9.20433i | −0.414176 | − | 0.552039i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.48928 | − | 0.937588i | 0.148763 | − | 0.0560316i | ||||
\(281\) | −31.3739 | −1.87161 | −0.935806 | − | 0.352516i | \(-0.885326\pi\) | ||||
−0.935806 | + | 0.352516i | \(0.885326\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 16.4627i | − | 0.978605i | −0.872114 | − | 0.489302i | \(-0.837251\pi\) | ||
0.872114 | − | 0.489302i | \(-0.162749\pi\) | |||||||
\(284\) | −0.864985 | + | 2.96942i | −0.0513274 | + | 0.176203i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −44.6279 | + | 33.4828i | −2.63890 | + | 1.97988i | ||||
\(287\) | −1.63291 | −0.0963874 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.0185 | −0.589324 | ||||||||
\(290\) | 3.29578 | − | 2.47271i | 0.193535 | − | 0.145203i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.66054 | + | 5.70049i | −0.0971756 | + | 0.333596i | ||||
\(293\) | − | 5.78733i | − | 0.338100i | −0.985608 | − | 0.169050i | \(-0.945930\pi\) | ||
0.985608 | − | 0.169050i | \(-0.0540699\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.2177 | 0.653117 | ||||||||
\(296\) | 0.565271 | − | 0.212910i | 0.0328557 | − | 0.0123751i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.9509 | − | 17.2618i | −0.750228 | − | 0.999949i | ||||
\(299\) | 19.0095i | 1.09935i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 7.16716i | − | 0.413108i | ||||||
\(302\) | −0.824032 | + | 0.618243i | −0.0474177 | + | 0.0355759i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.5327 | − | 19.6864i | 0.718798 | − | 1.12909i | ||||
\(305\) | 1.39472 | 0.0798617 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 23.0312i | − | 1.31446i | −0.753691 | − | 0.657229i | \(-0.771728\pi\) | ||
0.753691 | − | 0.657229i | \(-0.228272\pi\) | |||||||
\(308\) | 11.4949 | + | 3.34843i | 0.654981 | + | 0.190794i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.81288 | + | 3.74917i | 0.159761 | + | 0.212939i | ||||
\(311\) | 15.7123 | 0.890964 | 0.445482 | − | 0.895291i | \(-0.353032\pi\) | ||||
0.445482 | + | 0.895291i | \(0.353032\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.53462 | −0.369358 | −0.184679 | − | 0.982799i | \(-0.559125\pi\) | ||||
−0.184679 | + | 0.982799i | \(0.559125\pi\) | |||||||
\(314\) | 10.2871 | + | 13.7113i | 0.580534 | + | 0.773771i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.92241 | − | 30.6299i | 0.501925 | − | 1.72307i | ||||
\(317\) | 19.9169i | 1.11865i | 0.828949 | + | 0.559324i | \(0.188939\pi\) | ||||
−0.828949 | + | 0.559324i | \(0.811061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.5453 | 1.03834 | ||||||||
\(320\) | −4.96340 | − | 5.65413i | −0.277463 | − | 0.316075i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.26304 | − | 2.44815i | 0.181842 | − | 0.136430i | ||||
\(323\) | − | 15.4157i | − | 0.857751i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 27.1222i | 1.50447i | ||||||||
\(326\) | 4.62610 | + | 6.16594i | 0.256216 | + | 0.341500i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.62794 | + | 4.32214i | 0.0898878 | + | 0.238650i | ||||
\(329\) | −9.32639 | −0.514180 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 21.3692i | − | 1.17456i | −0.809384 | − | 0.587280i | \(-0.800199\pi\) | ||
0.809384 | − | 0.587280i | \(-0.199801\pi\) | |||||||
\(332\) | 16.7975 | + | 4.89307i | 0.921882 | + | 0.268542i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.22583 | + | 1.66996i | −0.121792 | + | 0.0913763i | ||||
\(335\) | 12.2780 | 0.670821 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.56768 | −0.521185 | −0.260592 | − | 0.965449i | \(-0.583918\pi\) | ||||
−0.260592 | + | 0.965449i | \(0.583918\pi\) | |||||||
\(338\) | −34.4236 | + | 25.8269i | −1.87240 | + | 1.40480i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.77149 | − | 1.38992i | −0.258770 | − | 0.0753791i | ||||
\(341\) | 21.0965i | 1.14244i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −18.9707 | + | 7.14535i | −1.02283 | + | 0.385251i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.80737 | + | 5.07470i | 0.204686 | + | 0.272818i | ||||
\(347\) | − | 5.63471i | − | 0.302487i | −0.988497 | − | 0.151243i | \(-0.951672\pi\) | ||
0.988497 | − | 0.151243i | \(-0.0483278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 33.2219i | − | 1.77833i | −0.457591 | − | 0.889163i | \(-0.651287\pi\) | ||
0.457591 | − | 0.889163i | \(-0.348713\pi\) | |||||||
\(350\) | 4.65562 | − | 3.49296i | 0.248854 | − | 0.186706i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.59694 | − | 33.7640i | −0.138417 | − | 1.79963i | ||||
\(353\) | 6.20112 | 0.330052 | 0.165026 | − | 0.986289i | \(-0.447229\pi\) | ||||
0.165026 | + | 0.986289i | \(0.447229\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.45433i | − | 0.0771879i | ||||||
\(356\) | 4.19700 | − | 14.4079i | 0.222440 | − | 0.763619i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −21.0555 | − | 28.0641i | −1.11282 | − | 1.48323i | ||||
\(359\) | 1.76894 | 0.0933609 | 0.0466805 | − | 0.998910i | \(-0.485136\pi\) | ||||
0.0466805 | + | 0.998910i | \(0.485136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0390 | −0.791526 | ||||||||
\(362\) | 19.1908 | + | 25.5787i | 1.00865 | + | 1.34438i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.6544 | + | 3.68619i | 0.663270 | + | 0.193209i | ||||
\(365\) | − | 2.79192i | − | 0.146136i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.62872 | 0.502615 | 0.251308 | − | 0.967907i | \(-0.419139\pi\) | ||||
0.251308 | + | 0.967907i | \(0.419139\pi\) | |||||||
\(368\) | −9.73312 | − | 6.19625i | −0.507374 | − | 0.323002i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.227198 | + | 0.170459i | −0.0118115 | + | 0.00886173i | ||||
\(371\) | 7.51044i | 0.389922i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 19.6983i | − | 1.01994i | −0.860192 | − | 0.509970i | \(-0.829657\pi\) | ||
0.860192 | − | 0.509970i | \(-0.170343\pi\) | |||||||
\(374\) | −13.4245 | − | 17.8930i | −0.694165 | − | 0.925225i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.29801 | + | 24.6860i | 0.479508 | + | 1.27308i | ||||
\(377\) | 20.4160 | 1.05148 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.3324i | 0.838941i | 0.907769 | + | 0.419470i | \(0.137784\pi\) | ||||
−0.907769 | + | 0.419470i | \(0.862216\pi\) | |||||||
\(380\) | −3.06906 | + | 10.5358i | −0.157439 | + | 0.540476i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.4429 | − | 13.8371i | 0.943621 | − | 0.707966i | ||||
\(383\) | 17.7037 | 0.904618 | 0.452309 | − | 0.891861i | \(-0.350600\pi\) | ||||
0.452309 | + | 0.891861i | \(0.350600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.62983 | −0.286923 | ||||||||
\(386\) | 7.90035 | − | 5.92736i | 0.402117 | − | 0.301695i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.01458 | − | 20.6475i | 0.305344 | − | 1.04822i | ||||
\(389\) | − | 24.4174i | − | 1.23801i | −0.785387 | − | 0.619005i | \(-0.787536\pi\) | ||
0.785387 | − | 0.619005i | \(-0.212464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.62162 | −0.385442 | ||||||||
\(392\) | −0.996957 | − | 2.64690i | −0.0503539 | − | 0.133689i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.5333 | − | 15.3723i | −0.581041 | − | 0.774447i | ||||
\(395\) | 15.0016i | 0.754811i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.4996i | 1.07903i | 0.841975 | + | 0.539517i | \(0.181393\pi\) | ||||
−0.841975 | + | 0.539517i | \(0.818607\pi\) | |||||||
\(398\) | 22.8853 | − | 17.1701i | 1.14714 | − | 0.860657i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.8870 | − | 8.84064i | −0.694348 | − | 0.442032i | ||||
\(401\) | 29.0629 | 1.45133 | 0.725667 | − | 0.688046i | \(-0.241531\pi\) | ||||
0.725667 | + | 0.688046i | \(0.241531\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.2245i | 1.15690i | ||||||||
\(404\) | 6.81515 | + | 1.98524i | 0.339066 | + | 0.0987692i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.62929 | − | 3.50448i | −0.130489 | − | 0.173924i | ||||
\(407\) | −1.27844 | −0.0633698 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.96315 | −0.294859 | −0.147429 | − | 0.989073i | \(-0.547100\pi\) | ||||
−0.147429 | + | 0.989073i | \(0.547100\pi\) | |||||||
\(410\) | −1.30335 | − | 1.73719i | −0.0643679 | − | 0.0857935i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.57497 | − | 29.4371i | 0.422458 | − | 1.45026i | ||||
\(413\) | − | 11.9280i | − | 0.586937i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.22689 | −0.403842 | ||||||||
\(416\) | −2.85890 | − | 37.1698i | −0.140169 | − | 1.82240i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −39.5092 | + | 29.6424i | −1.93246 | + | 1.44986i | ||||
\(419\) | − | 28.8317i | − | 1.40852i | −0.709941 | − | 0.704261i | \(-0.751279\pi\) | ||
0.709941 | − | 0.704261i | \(-0.248721\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.3324i | 1.47831i | 0.673534 | + | 0.739156i | \(0.264776\pi\) | ||||
−0.673534 | + | 0.739156i | \(0.735224\pi\) | |||||||
\(422\) | −16.2182 | − | 21.6166i | −0.789488 | − | 1.05228i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.8794 | − | 7.48758i | 0.965428 | − | 0.363629i | ||||
\(425\) | −10.8743 | −0.527482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.48304i | − | 0.0717693i | ||||||
\(428\) | 4.63982 | + | 1.35157i | 0.224274 | + | 0.0653305i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.62486 | − | 5.72067i | 0.367703 | − | 0.275875i | ||||
\(431\) | 32.3775 | 1.55957 | 0.779785 | − | 0.626048i | \(-0.215329\pi\) | ||||
0.779785 | + | 0.626048i | \(0.215329\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.9777 | −1.48869 | −0.744346 | − | 0.667794i | \(-0.767239\pi\) | ||||
−0.744346 | + | 0.667794i | \(0.767239\pi\) | |||||||
\(434\) | 3.98658 | − | 2.99099i | 0.191362 | − | 0.143572i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.1862 | + | 3.84110i | 0.631502 | + | 0.183955i | ||||
\(437\) | 16.8291i | 0.805047i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.76381 | 0.418274 | 0.209137 | − | 0.977886i | \(-0.432935\pi\) | ||||
0.209137 | + | 0.977886i | \(0.432935\pi\) | |||||||
\(440\) | 5.61270 | + | 14.9016i | 0.267575 | + | 0.710406i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.7787 | − | 19.6979i | −0.702949 | − | 0.936934i | ||||
\(443\) | 7.53477i | 0.357988i | 0.983850 | + | 0.178994i | \(0.0572842\pi\) | ||||
−0.983850 | + | 0.178994i | \(0.942716\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.05656i | 0.334513i | ||||||||
\(446\) | −23.6699 | + | 17.7587i | −1.12080 | + | 0.840901i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.01215 | + | 5.27769i | −0.284048 | + | 0.249347i | ||||
\(449\) | 32.5584 | 1.53653 | 0.768263 | − | 0.640134i | \(-0.221121\pi\) | ||||
0.768263 | + | 0.640134i | \(0.221121\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.77510i | − | 0.460292i | ||||||
\(452\) | −8.64410 | + | 29.6745i | −0.406584 | + | 1.39577i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.10762 | − | 2.80916i | −0.0989153 | − | 0.131840i | ||||
\(455\) | −6.19772 | −0.290554 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.81122 | −0.178281 | −0.0891407 | − | 0.996019i | \(-0.528412\pi\) | ||||
−0.0891407 | + | 0.996019i | \(0.528412\pi\) | |||||||
\(458\) | −8.75500 | − | 11.6692i | −0.409094 | − | 0.545266i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.20899 | + | 1.51736i | 0.242870 | + | 0.0707475i | ||||
\(461\) | − | 6.29754i | − | 0.293306i | −0.989188 | − | 0.146653i | \(-0.953150\pi\) | ||
0.989188 | − | 0.146653i | \(-0.0468500\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8418 | 0.596811 | 0.298405 | − | 0.954439i | \(-0.403545\pi\) | ||||
0.298405 | + | 0.954439i | \(0.403545\pi\) | |||||||
\(464\) | −6.65471 | + | 10.4533i | −0.308937 | + | 0.485281i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.0824 | + | 16.5677i | −1.02295 | + | 0.767482i | ||||
\(467\) | − | 34.5588i | − | 1.59919i | −0.600538 | − | 0.799596i | \(-0.705047\pi\) | ||
0.600538 | − | 0.799596i | \(-0.294953\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 13.0555i | − | 0.602847i | ||||||
\(470\) | −7.44412 | − | 9.92198i | −0.343372 | − | 0.457667i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −31.5721 | + | 11.8917i | −1.45322 | + | 0.547359i | ||||
\(473\) | 42.9049 | 1.97277 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.0114i | 1.10172i | ||||||||
\(476\) | −1.47793 | + | 5.07362i | −0.0677410 | + | 0.232549i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.1947 | + | 15.1514i | −0.923684 | + | 0.693008i | ||||
\(479\) | −16.5950 | −0.758244 | −0.379122 | − | 0.925347i | \(-0.623774\pi\) | ||||
−0.379122 | + | 0.925347i | \(0.623774\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.40739 | −0.0641717 | ||||||||
\(482\) | 7.60293 | − | 5.70422i | 0.346304 | − | 0.259820i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.8919 | + | 47.6899i | −0.631452 | + | 2.16772i | ||||
\(485\) | 10.1125i | 0.459186i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.4209 | 1.19724 | 0.598622 | − | 0.801032i | \(-0.295715\pi\) | ||||
0.598622 | + | 0.801032i | \(0.295715\pi\) | |||||||
\(488\) | −3.92546 | + | 1.47853i | −0.177697 | + | 0.0669298i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.798179 | + | 1.06386i | 0.0360580 | + | 0.0480604i | ||||
\(491\) | − | 3.70049i | − | 0.167001i | −0.996508 | − | 0.0835003i | \(-0.973390\pi\) | ||
0.996508 | − | 0.0835003i | \(-0.0266100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.18554i | 0.368658i | ||||||||
\(494\) | −43.4945 | + | 32.6325i | −1.95691 | + | 1.46820i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.8913 | − | 7.57017i | −0.533935 | − | 0.339911i | ||||
\(497\) | −1.54642 | −0.0693664 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.12488i | − | 0.0951229i | −0.998868 | − | 0.0475614i | \(-0.984855\pi\) | ||
0.998868 | − | 0.0475614i | \(-0.0151450\pi\) | |||||||
\(500\) | 16.4613 | + | 4.79512i | 0.736170 | + | 0.214444i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.9015 | + | 31.8574i | 1.06678 | + | 1.42186i | ||||
\(503\) | −43.3846 | −1.93443 | −0.967213 | − | 0.253968i | \(-0.918264\pi\) | ||||
−0.967213 | + | 0.253968i | \(0.918264\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.33785 | −0.148532 | ||||||||
\(506\) | 14.6554 | + | 19.5336i | 0.651512 | + | 0.868376i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.45665 | − | 15.2993i | 0.197732 | − | 0.678797i | ||||
\(509\) | 2.34482i | 0.103932i | 0.998649 | + | 0.0519662i | \(0.0165488\pi\) | ||||
−0.998649 | + | 0.0519662i | \(0.983451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.96871 | −0.131328 | ||||||||
\(512\) | 19.9634 | + | 10.6519i | 0.882265 | + | 0.470753i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 28.1999 | − | 21.1574i | 1.24384 | − | 0.933214i | ||||
\(515\) | 14.4174i | 0.635306i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 55.8307i | − | 2.45543i | ||||||
\(518\) | 0.181253 | + | 0.241584i | 0.00796378 | + | 0.0106146i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.17886 | + | 16.4047i | 0.270961 | + | 0.719396i | ||||
\(521\) | 8.53436 | 0.373897 | 0.186949 | − | 0.982370i | \(-0.440140\pi\) | ||||
0.186949 | + | 0.982370i | \(0.440140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.8607i | 1.34944i | 0.738072 | + | 0.674722i | \(0.235736\pi\) | ||||
−0.738072 | + | 0.674722i | \(0.764264\pi\) | |||||||
\(524\) | −2.95287 | − | 0.860163i | −0.128997 | − | 0.0375764i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.5651 | − | 16.1795i | 0.940282 | − | 0.705462i | ||||
\(527\) | −9.31160 | −0.405620 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.6796 | −0.638241 | ||||||||
\(530\) | −7.99006 | + | 5.99467i | −0.347066 | + | 0.260392i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.2030 | + | 3.26339i | 0.485710 | + | 0.141486i | ||||
\(533\) | − | 10.7611i | − | 0.466116i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.27244 | −0.0982461 | ||||||||
\(536\) | −34.5566 | + | 13.0158i | −1.49262 | + | 0.562196i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8.69177 | + | 11.5849i | 0.374729 | + | 0.499461i | ||||
\(539\) | 5.98632i | 0.257849i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 15.2568i | − | 0.655940i | −0.944688 | − | 0.327970i | \(-0.893636\pi\) | ||
0.944688 | − | 0.327970i | \(-0.106364\pi\) | |||||||
\(542\) | −5.04158 | + | 3.78253i | −0.216554 | + | 0.162473i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 14.9028 | − | 1.14624i | 0.638953 | − | 0.0491447i | ||||
\(545\) | −6.45817 | −0.276638 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 35.6416i | − | 1.52393i | −0.647621 | − | 0.761963i | \(-0.724236\pi\) | ||
0.647621 | − | 0.761963i | \(-0.275764\pi\) | |||||||
\(548\) | 3.54649 | − | 12.1748i | 0.151499 | − | 0.520082i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 20.9099 | + | 27.8701i | 0.891603 | + | 1.18838i | ||||
\(551\) | 18.0743 | 0.769992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.9515 | 0.678326 | ||||||||
\(554\) | 13.6301 | + | 18.1671i | 0.579089 | + | 0.771845i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.6238 | − | 4.55118i | −0.662597 | − | 0.193013i | ||||
\(557\) | 28.3871i | 1.20280i | 0.798949 | + | 0.601399i | \(0.205390\pi\) | ||||
−0.798949 | + | 0.601399i | \(0.794610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.2328 | 1.99773 | ||||||||
\(560\) | 2.02018 | − | 3.17332i | 0.0853684 | − | 0.134097i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35.4910 | + | 26.6277i | −1.49710 | + | 1.12322i | ||||
\(563\) | − | 13.0963i | − | 0.551942i | −0.961166 | − | 0.275971i | \(-0.911001\pi\) | ||
0.961166 | − | 0.275971i | \(-0.0889993\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 14.5336i | − | 0.611435i | ||||||
\(566\) | −13.9722 | − | 18.6230i | −0.587296 | − | 0.782784i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.54172 | + | 4.09322i | 0.0646889 | + | 0.171748i | ||||
\(569\) | 20.0434 | 0.840263 | 0.420132 | − | 0.907463i | \(-0.361984\pi\) | ||||
0.420132 | + | 0.907463i | \(0.361984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 6.91621i | − | 0.289434i | −0.989473 | − | 0.144717i | \(-0.953773\pi\) | ||
0.989473 | − | 0.144717i | \(-0.0462272\pi\) | |||||||
\(572\) | −22.0667 | + | 75.7532i | −0.922656 | + | 3.16740i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.84719 | + | 1.38588i | −0.0771001 | + | 0.0578456i | ||||
\(575\) | 11.8714 | 0.495071 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.2279 | 0.966992 | 0.483496 | − | 0.875347i | \(-0.339367\pi\) | ||||
0.483496 | + | 0.875347i | \(0.339367\pi\) | |||||||
\(578\) | −11.3332 | + | 8.50292i | −0.471399 | + | 0.353675i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.62963 | − | 5.59440i | 0.0676669 | − | 0.232295i | ||||
\(581\) | 8.74782i | 0.362921i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44.9599 | −1.86205 | ||||||||
\(584\) | 2.95968 | + | 7.85787i | 0.122472 | + | 0.325161i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.91183 | − | 6.54678i | −0.202906 | − | 0.270445i | ||||
\(587\) | − | 1.76774i | − | 0.0729624i | −0.999334 | − | 0.0364812i | \(-0.988385\pi\) | ||
0.999334 | − | 0.0364812i | \(-0.0116149\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.5607i | 0.847191i | ||||||||
\(590\) | 12.6897 | − | 9.52065i | 0.522427 | − | 0.391959i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.458749 | − | 0.720607i | 0.0188545 | − | 0.0296167i | ||||
\(593\) | 14.8807 | 0.611079 | 0.305540 | − | 0.952179i | \(-0.401163\pi\) | ||||
0.305540 | + | 0.952179i | \(0.401163\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 2.48490i | − | 0.101871i | ||||||
\(596\) | −29.3009 | − | 8.53528i | −1.20021 | − | 0.349619i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.1337 | + | 21.5040i | 0.659757 | + | 0.879365i | ||||
\(599\) | 1.47561 | 0.0602916 | 0.0301458 | − | 0.999546i | \(-0.490403\pi\) | ||||
0.0301458 | + | 0.999546i | \(0.490403\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.1957 | −0.456684 | −0.228342 | − | 0.973581i | \(-0.573330\pi\) | ||||
−0.228342 | + | 0.973581i | \(0.573330\pi\) | |||||||
\(602\) | −6.08291 | − | 8.10768i | −0.247921 | − | 0.330444i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.407451 | + | 1.39875i | −0.0165790 | + | 0.0569142i | ||||
\(605\) | − | 23.3570i | − | 0.949598i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.4554 | −1.27674 | −0.638368 | − | 0.769731i | \(-0.720390\pi\) | ||||
−0.638368 | + | 0.769731i | \(0.720390\pi\) | |||||||
\(608\) | −2.53099 | − | 32.9066i | −0.102645 | − | 1.33454i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.57775 | − | 1.18373i | 0.0638812 | − | 0.0479279i | ||||
\(611\) | − | 61.4625i | − | 2.48651i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9222i | 0.764262i | 0.924108 | + | 0.382131i | \(0.124810\pi\) | ||||
−0.924108 | + | 0.382131i | \(0.875190\pi\) | |||||||
\(614\) | −19.5470 | − | 26.0535i | −0.788854 | − | 1.05143i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.8452 | − | 5.96810i | 0.638421 | − | 0.240462i | ||||
\(617\) | −12.1549 | −0.489339 | −0.244669 | − | 0.969607i | \(-0.578679\pi\) | ||||
−0.244669 | + | 0.969607i | \(0.578679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.9619i | − | 0.601371i | −0.953723 | − | 0.300686i | \(-0.902784\pi\) | ||
0.953723 | − | 0.300686i | \(-0.0972155\pi\) | |||||||
\(620\) | 6.36400 | + | 1.85382i | 0.255584 | + | 0.0744511i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.7742 | − | 13.3354i | 0.712680 | − | 0.534700i | ||||
\(623\) | 7.50339 | 0.300617 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.5156 | 0.500623 | ||||||||
\(626\) | −7.39213 | + | 5.54606i | −0.295449 | + | 0.221665i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.2741 | + | 6.77967i | 0.928736 | + | 0.270538i | ||||
\(629\) | − | 0.564278i | − | 0.0224992i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.71232 | −0.346832 | −0.173416 | − | 0.984849i | \(-0.555481\pi\) | ||||
−0.173416 | + | 0.984849i | \(0.555481\pi\) | |||||||
\(632\) | −15.9029 | − | 42.2220i | −0.632585 | − | 1.67950i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.9039 | + | 22.5306i | 0.671340 | + | 0.894803i | ||||
\(635\) | 7.49313i | 0.297356i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.59017i | 0.261112i | ||||||||
\(638\) | 20.9789 | − | 15.7398i | 0.830563 | − | 0.623143i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.4135 | − | 2.18356i | −0.411630 | − | 0.0863127i | ||||
\(641\) | 7.31021 | 0.288736 | 0.144368 | − | 0.989524i | \(-0.453885\pi\) | ||||
0.144368 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.1766i | 0.440763i | 0.975414 | + | 0.220381i | \(0.0707302\pi\) | ||||
−0.975414 | + | 0.220381i | \(0.929270\pi\) | |||||||
\(644\) | 1.61345 | − | 5.53883i | 0.0635787 | − | 0.218260i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.0836 | − | 17.4386i | −0.514767 | − | 0.686113i | ||||
\(647\) | −7.13625 | −0.280555 | −0.140277 | − | 0.990112i | \(-0.544799\pi\) | ||||
−0.140277 | + | 0.990112i | \(0.544799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 71.4046 | 2.80288 | ||||||||
\(650\) | 23.0192 | + | 30.6814i | 0.902886 | + | 1.20342i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.4663 | + | 3.04882i | 0.409893 | + | 0.119401i | ||||
\(653\) | 15.6385i | 0.611982i | 0.952034 | + | 0.305991i | \(0.0989878\pi\) | ||||
−0.952034 | + | 0.305991i | \(0.901012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.44622 | 0.0565086 | ||||||||
\(656\) | 5.50986 | + | 3.50765i | 0.215124 | + | 0.136951i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −10.5503 | + | 7.91550i | −0.411292 | + | 0.308578i | ||||
\(659\) | 1.73739i | 0.0676791i | 0.999427 | + | 0.0338395i | \(0.0107735\pi\) | ||||
−0.999427 | + | 0.0338395i | \(0.989226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.7968i | 0.886691i | 0.896351 | + | 0.443345i | \(0.146208\pi\) | ||||
−0.896351 | + | 0.443345i | \(0.853792\pi\) | |||||||
\(662\) | −18.1365 | − | 24.1735i | −0.704896 | − | 0.939528i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 23.1546 | − | 8.72121i | 0.898573 | − | 0.338448i | ||||
\(665\) | −5.48686 | −0.212771 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 8.93608i | − | 0.346006i | ||||||
\(668\) | −1.10058 | + | 3.77821i | −0.0425829 | + | 0.146183i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.8893 | − | 10.4206i | 0.536589 | − | 0.402584i | ||||
\(671\) | 8.87795 | 0.342729 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1667 | −0.507538 | −0.253769 | − | 0.967265i | \(-0.581670\pi\) | ||||
−0.253769 | + | 0.967265i | \(0.581670\pi\) | |||||||
\(674\) | −10.8232 | + | 8.12029i | −0.416895 | + | 0.312782i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.0211 | + | 58.4320i | −0.654658 | + | 2.24739i | ||||
\(677\) | − | 37.3183i | − | 1.43426i | −0.696941 | − | 0.717129i | \(-0.745456\pi\) | ||
0.696941 | − | 0.717129i | \(-0.254544\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.7529 | 0.412657 | ||||||||
\(680\) | −6.57729 | + | 2.47734i | −0.252227 | + | 0.0950017i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17.9050 | + | 23.8649i | 0.685619 | + | 0.913835i | ||||
\(683\) | 6.72259i | 0.257233i | 0.991694 | + | 0.128616i | \(0.0410536\pi\) | ||||
−0.991694 | + | 0.128616i | \(0.958946\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.96285i | 0.227829i | ||||||||
\(686\) | 1.13123 | − | 0.848721i | 0.0431904 | − | 0.0324043i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.3958 | + | 24.1839i | −0.586959 | + | 0.922001i | ||||
\(689\) | −49.4951 | −1.88561 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.18845i | − | 0.311503i | −0.987796 | − | 0.155752i | \(-0.950220\pi\) | ||
0.987796 | − | 0.155752i | \(-0.0497800\pi\) | |||||||
\(692\) | 8.61401 | + | 2.50924i | 0.327455 | + | 0.0953870i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.78229 | − | 6.37413i | −0.181533 | − | 0.241959i | ||||
\(695\) | 7.65205 | 0.290259 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.31455 | 0.163425 | ||||||||
\(698\) | −28.1961 | − | 37.5815i | −1.06724 | − | 1.42248i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.30202 | − | 7.90265i | 0.0870083 | − | 0.298692i | ||||
\(701\) | − | 5.85226i | − | 0.221037i | −0.993874 | − | 0.110518i | \(-0.964749\pi\) | ||
0.993874 | − | 0.110518i | \(-0.0352511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.24597 | −0.0469927 | ||||||||
\(704\) | −31.5939 | − | 35.9907i | −1.19074 | − | 1.35645i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.01487 | − | 5.26301i | 0.264008 | − | 0.198076i | ||||
\(707\) | 3.54920i | 0.133482i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 45.3444i | 1.70294i | 0.524399 | + | 0.851472i | \(0.324290\pi\) | ||||
−0.524399 | + | 0.851472i | \(0.675710\pi\) | |||||||
\(710\) | −1.23432 | − | 1.64518i | −0.0463232 | − | 0.0617424i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.48056 | − | 19.8607i | −0.280346 | − | 0.744312i | ||||
\(713\) | 10.1654 | 0.380697 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 37.1015i | − | 1.38752i | ||||||
\(716\) | −47.6372 | − | 13.8766i | −1.78028 | − | 0.518593i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.00107 | − | 1.50133i | 0.0746792 | − | 0.0560293i | ||||
\(719\) | 29.1182 | 1.08592 | 0.542962 | − | 0.839757i | \(-0.317303\pi\) | ||||
0.542962 | + | 0.839757i | \(0.317303\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3303 | 0.570931 | ||||||||
\(722\) | −17.0125 | + | 12.7639i | −0.633140 | + | 0.475023i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 43.4183 | + | 12.6476i | 1.61363 | + | 0.470046i | ||||
\(725\) | − | 12.7498i | − | 0.473514i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.5099 | −1.57661 | −0.788303 | − | 0.615287i | \(-0.789040\pi\) | ||||
−0.788303 | + | 0.615287i | \(0.789040\pi\) | |||||||
\(728\) | 17.4435 | − | 6.57012i | 0.646500 | − | 0.243505i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.36956 | − | 3.15829i | −0.0877014 | − | 0.116894i | ||||
\(731\) | 18.9374i | 0.700426i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.79234i | 0.103137i | 0.998669 | + | 0.0515687i | \(0.0164221\pi\) | ||||
−0.998669 | + | 0.0515687i | \(0.983578\pi\) | |||||||
\(734\) | 10.8923 | − | 8.17210i | 0.402041 | − | 0.301638i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.2693 | + | 1.25134i | −0.599693 | + | 0.0461250i | ||||
\(737\) | 78.1544 | 2.87886 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.4715i | 0.569129i | 0.958657 | + | 0.284565i | \(0.0918490\pi\) | ||||
−0.958657 | + | 0.284565i | \(0.908151\pi\) | |||||||
\(740\) | −0.112340 | + | 0.385655i | −0.00412972 | + | 0.0141770i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.37426 | + | 8.49601i | 0.234007 | + | 0.311898i | ||||
\(743\) | −18.2897 | −0.670984 | −0.335492 | − | 0.942043i | \(-0.608903\pi\) | ||||
−0.335492 | + | 0.942043i | \(0.608903\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.3507 | 0.525768 | ||||||||
\(746\) | −16.7184 | − | 22.2832i | −0.612103 | − | 0.815848i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −30.3723 | − | 8.84739i | −1.11052 | − | 0.323492i | ||||
\(749\) | 2.41633i | 0.0882908i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1167 | 0.405655 | 0.202828 | − | 0.979214i | \(-0.434987\pi\) | ||||
0.202828 | + | 0.979214i | \(0.434987\pi\) | |||||||
\(752\) | 31.4697 | + | 20.0341i | 1.14758 | + | 0.730567i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 23.0951 | − | 17.3275i | 0.841074 | − | 0.631029i | ||||
\(755\) | − | 0.685062i | − | 0.0249320i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.8173i | 0.429507i | 0.976668 | + | 0.214753i | \(0.0688948\pi\) | ||||
−0.976668 | + | 0.214753i | \(0.931105\pi\) | |||||||
\(758\) | 13.8617 | + | 18.4757i | 0.503479 | + | 0.671067i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.47016 | + | 14.5232i | 0.198424 | + | 0.526811i | ||||
\(761\) | −12.2039 | −0.442390 | −0.221195 | − | 0.975230i | \(-0.570996\pi\) | ||||
−0.221195 | + | 0.975230i | \(0.570996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.86711i | 0.248606i | ||||||||
\(764\) | 9.11929 | − | 31.3057i | 0.329924 | − | 1.13260i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.0269 | − | 15.0255i | 0.723602 | − | 0.542894i | ||||
\(767\) | 78.6073 | 2.83835 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.32578 | −0.264175 | −0.132087 | − | 0.991238i | \(-0.542168\pi\) | ||||
−0.132087 | + | 0.991238i | \(0.542168\pi\) | |||||||
\(770\) | −6.36861 | + | 4.77815i | −0.229509 | + | 0.172193i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.90641 | − | 13.4104i | 0.140595 | − | 0.482650i | ||||
\(773\) | − | 7.26470i | − | 0.261293i | −0.991429 | − | 0.130647i | \(-0.958295\pi\) | ||
0.991429 | − | 0.130647i | \(-0.0417053\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.5037 | 0.520988 | ||||||||
\(776\) | −10.7201 | − | 28.4617i | −0.384831 | − | 1.02172i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.7235 | − | 27.6216i | −0.742975 | − | 0.990282i | ||||
\(779\) | − | 9.52686i | − | 0.341335i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 9.25737i | − | 0.331255i | ||||||
\(782\) | −8.62178 | + | 6.46863i | −0.308314 | + | 0.231318i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.37426 | − | 2.14810i | −0.120509 | − | 0.0767180i | ||||
\(785\) | −11.3989 | −0.406844 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.02431i | 0.107805i | 0.998546 | + | 0.0539025i | \(0.0171660\pi\) | ||||
−0.998546 | + | 0.0539025i | \(0.982834\pi\) | |||||||
\(788\) | −26.0936 | − | 7.60101i | −0.929547 | − | 0.270775i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.7321 | + | 16.9702i | 0.452989 | + | 0.603771i | ||||
\(791\) | −15.4539 | −0.549478 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.77348 | 0.347067 | ||||||||
\(794\) | 18.2471 | + | 24.3209i | 0.647567 | + | 0.863116i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.3159 | − | 38.8464i | 0.401081 | − | 1.37688i | ||||
\(797\) | 20.6317i | 0.730813i | 0.930848 | + | 0.365406i | \(0.119070\pi\) | ||||
−0.930848 | + | 0.365406i | \(0.880930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.6426 | 0.871794 | ||||||||
\(800\) | −23.2125 | + | 1.78538i | −0.820687 | + | 0.0631227i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 32.8768 | − | 24.6663i | 1.16092 | − | 0.870998i | ||||
\(803\) | − | 17.7716i | − | 0.627148i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.71274i | 0.0956117i | ||||||||
\(806\) | 19.7111 | + | 26.2722i | 0.694295 | + | 0.925399i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.39438 | − | 3.53840i | 0.330493 | − | 0.124481i | ||||
\(809\) | 29.5889 | 1.04029 | 0.520145 | − | 0.854078i | \(-0.325878\pi\) | ||||
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.6230i | 1.49670i | 0.663307 | + | 0.748348i | \(0.269153\pi\) | ||||
−0.663307 | + | 0.748348i | \(0.730847\pi\) | |||||||
\(812\) | −5.94864 | − | 1.73283i | −0.208756 | − | 0.0608102i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.44620 | + | 1.08504i | −0.0506893 | + | 0.0380305i | ||||
\(815\) | −5.12608 | −0.179559 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.8153 | 1.46293 | ||||||||
\(818\) | −6.74567 | + | 5.06105i | −0.235857 | + | 0.176955i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.94877 | − | 0.858970i | −0.102976 | − | 0.0299965i | ||||
\(821\) | − | 48.6214i | − | 1.69690i | −0.529276 | − | 0.848450i | \(-0.677536\pi\) | ||
0.529276 | − | 0.848450i | \(-0.322464\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.7228 | 0.826924 | 0.413462 | − | 0.910521i | \(-0.364320\pi\) | ||||
0.413462 | + | 0.910521i | \(0.364320\pi\) | |||||||
\(824\) | −15.2837 | − | 40.5778i | −0.532432 | − | 1.41360i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.1235 | − | 13.4932i | −0.352242 | − | 0.469490i | ||||
\(827\) | 29.3889i | 1.02195i | 0.859595 | + | 0.510976i | \(0.170716\pi\) | ||||
−0.859595 | + | 0.510976i | \(0.829284\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 26.4785i | − | 0.919635i | −0.888013 | − | 0.459818i | \(-0.847915\pi\) | ||
0.888013 | − | 0.459818i | \(-0.152085\pi\) | |||||||
\(830\) | −9.30647 | + | 6.98233i | −0.323032 | + | 0.242360i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −34.7809 | − | 39.6211i | −1.20581 | − | 1.37361i | ||||
\(833\) | −2.64225 | −0.0915485 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.85045i | − | 0.0640375i | ||||||
\(836\) | −19.5357 | + | 67.0645i | −0.675657 | + | 2.31947i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.4701 | − | 32.6152i | −0.845305 | − | 1.12667i | ||||
\(839\) | −3.51211 | −0.121252 | −0.0606258 | − | 0.998161i | \(-0.519310\pi\) | ||||
−0.0606258 | + | 0.998161i | \(0.519310\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.4027 | 0.669060 | ||||||||
\(842\) | 25.7438 | + | 34.3129i | 0.887189 | + | 1.18250i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −36.6929 | − | 10.6885i | −1.26302 | − | 0.367915i | ||||
\(845\) | − | 28.6182i | − | 0.984496i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.8360 | −0.853376 | ||||||||
\(848\) | 16.1332 | − | 25.3422i | 0.554017 | − | 0.870254i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −12.3013 | + | 9.22926i | −0.421932 | + | 0.316561i | ||||
\(851\) | 0.616017i | 0.0211168i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 28.2378i | − | 0.966843i | −0.875388 | − | 0.483422i | \(-0.839394\pi\) | ||
0.875388 | − | 0.483422i | \(-0.160606\pi\) | |||||||
\(854\) | −1.25869 | − | 1.67765i | −0.0430714 | − | 0.0574081i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.39579 | − | 2.40898i | 0.218603 | − | 0.0823372i | ||||
\(857\) | −12.8126 | −0.437669 | −0.218834 | − | 0.975762i | \(-0.570225\pi\) | ||||
−0.218834 | + | 0.975762i | \(0.570225\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.4496i | 1.20952i | 0.796406 | + | 0.604762i | \(0.206732\pi\) | ||||
−0.796406 | + | 0.604762i | \(0.793268\pi\) | |||||||
\(860\) | 3.77019 | − | 12.9428i | 0.128562 | − | 0.441344i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.6263 | − | 27.4794i | 1.24750 | − | 0.935954i | ||||
\(863\) | −32.3418 | −1.10093 | −0.550465 | − | 0.834858i | \(-0.685549\pi\) | ||||
−0.550465 | + | 0.834858i | \(0.685549\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.21887 | −0.143446 | ||||||||
\(866\) | −35.0428 | + | 26.2914i | −1.19080 | + | 0.893418i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.97120 | − | 6.76698i | 0.0669070 | − | 0.229686i | ||||
\(869\) | 95.4907i | 3.23930i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 86.0380 | 2.91529 | ||||||||
\(872\) | 18.1765 | − | 6.84621i | 0.615536 | − | 0.231842i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.2832 | + | 19.0376i | 0.483138 | + | 0.643955i | ||||
\(875\) | 8.57272i | 0.289811i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 6.53592i | − | 0.220702i | −0.993893 | − | 0.110351i | \(-0.964802\pi\) | ||
0.993893 | − | 0.110351i | \(-0.0351976\pi\) | |||||||
\(878\) | 9.91385 | − | 7.43803i | 0.334576 | − | 0.251021i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18.9965 | + | 12.0935i | 0.640373 | + | 0.407671i | ||||
\(881\) | −53.0057 | −1.78581 | −0.892904 | − | 0.450248i | \(-0.851336\pi\) | ||||
−0.892904 | + | 0.450248i | \(0.851336\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.0481i | − | 0.943894i | −0.881627 | − | 0.471947i | \(-0.843551\pi\) | ||
0.881627 | − | 0.471947i | \(-0.156449\pi\) | |||||||
\(884\) | −33.4360 | − | 9.73984i | −1.12458 | − | 0.327586i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.39491 | + | 8.52353i | 0.214841 | + | 0.286354i | ||||
\(887\) | 4.58627 | 0.153992 | 0.0769959 | − | 0.997031i | \(-0.475467\pi\) | ||||
0.0769959 | + | 0.997031i | \(0.475467\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.96760 | 0.267225 | ||||||||
\(890\) | 5.98905 | + | 7.98257i | 0.200753 | + | 0.267576i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.7038 | + | 40.1783i | −0.391874 | + | 1.34527i | ||||
\(893\) | − | 54.4129i | − | 1.82086i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 23.3312 | 0.779876 | ||||||||
\(896\) | −2.32182 | + | 11.0729i | −0.0775666 | + | 0.369920i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.8309 | − | 27.6330i | 1.22906 | − | 0.922125i | ||||
\(899\) | − | 10.9175i | − | 0.364120i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 19.8445i | − | 0.661115i | ||||||
\(902\) | −8.29633 | − | 11.0579i | −0.276238 | − | 0.368186i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.4069 | + | 40.9050i | 0.512426 | + | 1.36048i | ||||
\(905\) | −21.2649 | −0.706870 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.8338i | 1.05703i | 0.848925 | + | 0.528513i | \(0.177250\pi\) | ||||
−0.848925 | + | 0.528513i | \(0.822750\pi\) | |||||||
\(908\) | −4.76838 | − | 1.38902i | −0.158244 | − | 0.0460962i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.01103 | + | 5.26013i | −0.232413 | + | 0.174372i | ||||
\(911\) | 55.9123 | 1.85246 | 0.926228 | − | 0.376964i | \(-0.123032\pi\) | ||||
0.926228 | + | 0.376964i | \(0.123032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.3673 | −1.73310 | ||||||||
\(914\) | −4.31135 | + | 3.23466i | −0.142607 | + | 0.106993i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.8078 | − | 5.76996i | −0.654468 | − | 0.190645i | ||||
\(917\) | − | 1.53780i | − | 0.0507826i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.6749 | −1.70460 | −0.852299 | − | 0.523055i | \(-0.824792\pi\) | ||||
−0.852299 | + | 0.523055i | \(0.824792\pi\) | |||||||
\(920\) | 7.18036 | − | 2.70449i | 0.236730 | − | 0.0891644i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.34485 | − | 7.12395i | −0.176023 | − | 0.234615i | ||||
\(923\) | − | 10.1912i | − | 0.335447i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.878917i | 0.0288986i | ||||||||
\(926\) | 14.5270 | − | 10.8991i | 0.477388 | − | 0.358168i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.34393 | + | 17.4730i | 0.0441166 | + | 0.573580i | ||||
\(929\) | 10.6988 | 0.351016 | 0.175508 | − | 0.984478i | \(-0.443843\pi\) | ||||
0.175508 | + | 0.984478i | \(0.443843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.83430i | 0.191211i | ||||||||
\(932\) | −10.9189 | + | 37.4836i | −0.357660 | + | 1.22782i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −29.3308 | − | 39.0939i | −0.959733 | − | 1.27919i | ||||
\(935\) | 14.8754 | 0.486478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.3422 | 0.958568 | 0.479284 | − | 0.877660i | \(-0.340896\pi\) | ||||
0.479284 | + | 0.877660i | \(0.340896\pi\) | |||||||
\(938\) | −11.0805 | − | 14.7687i | −0.361790 | − | 0.482216i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −16.8420 | − | 4.90603i | −0.549325 | − | 0.160017i | ||||
\(941\) | − | 37.2035i | − | 1.21280i | −0.795160 | − | 0.606399i | \(-0.792613\pi\) | ||
0.795160 | − | 0.606399i | \(-0.207387\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.71015 | −0.153384 | ||||||||
\(944\) | −25.6225 | + | 40.2481i | −0.833942 | + | 1.30996i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 48.5351 | − | 36.4143i | 1.57801 | − | 1.18393i | ||||
\(947\) | − | 25.7353i | − | 0.836283i | −0.908382 | − | 0.418142i | \(-0.862682\pi\) | ||
0.908382 | − | 0.418142i | \(-0.137318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 19.5643i | − | 0.635084i | ||||||
\(950\) | 20.3789 | + | 27.1623i | 0.661180 | + | 0.881261i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.63421 | + | 6.99377i | 0.0853752 | + | 0.226669i | ||||
\(953\) | −17.6526 | −0.571824 | −0.285912 | − | 0.958256i | \(-0.592297\pi\) | ||||
−0.285912 | + | 0.958256i | \(0.592297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.3326i | 0.496150i | ||||||||
\(956\) | −9.98548 | + | 34.2793i | −0.322953 | + | 1.10867i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −18.7727 | + | 14.0845i | −0.606518 | + | 0.455050i | ||||
\(959\) | 6.34042 | 0.204743 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.5806 | −0.599374 | ||||||||
\(962\) | −1.59208 | + | 1.19449i | −0.0513308 | + | 0.0385117i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.75935 | − | 12.9055i | 0.121081 | − | 0.415659i | ||||
\(965\) | 6.56799i | 0.211431i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.22421 | 0.296631 | 0.148315 | − | 0.988940i | \(-0.452615\pi\) | ||||
0.148315 | + | 0.988940i | \(0.452615\pi\) | |||||||
\(968\) | 24.7604 | + | 65.7384i | 0.795831 | + | 2.11291i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.58271 | + | 11.4396i | 0.275574 | + | 0.367302i | ||||
\(971\) | − | 0.945630i | − | 0.0303467i | −0.999885 | − | 0.0151734i | \(-0.995170\pi\) | ||
0.999885 | − | 0.0151734i | \(-0.00483002\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.13659i | − | 0.260847i | ||||||
\(974\) | 29.8880 | − | 22.4239i | 0.957673 | − | 0.718509i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.18572 | + | 5.00417i | −0.101973 | + | 0.160179i | ||||
\(977\) | 34.7944 | 1.11317 | 0.556585 | − | 0.830791i | \(-0.312111\pi\) | ||||
0.556585 | + | 0.830791i | \(0.312111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 44.9177i | 1.43558i | ||||||||
\(980\) | 1.80584 | + | 0.526037i | 0.0576855 | + | 0.0168036i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.14068 | − | 4.18609i | −0.100223 | − | 0.133583i | ||||
\(983\) | 23.7133 | 0.756336 | 0.378168 | − | 0.925737i | \(-0.376554\pi\) | ||||
0.378168 | + | 0.925737i | \(0.376554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.7799 | 0.407200 | ||||||||
\(986\) | 6.94724 | + | 9.25970i | 0.221245 | + | 0.294889i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.5063 | + | 73.8294i | −0.684207 | + | 2.34883i | ||||
\(989\) | − | 20.6738i | − | 0.657389i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.1109 | −0.765908 | −0.382954 | − | 0.923767i | \(-0.625093\pi\) | ||||
−0.382954 | + | 0.923767i | \(0.625093\pi\) | |||||||
\(992\) | −19.8767 | + | 1.52881i | −0.631086 | + | 0.0485397i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.74935 | + | 1.31248i | −0.0554861 | + | 0.0416293i | ||||
\(995\) | 19.0258i | 0.603158i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 30.0398i | − | 0.951371i | −0.879615 | − | 0.475685i | \(-0.842200\pi\) | ||
0.879615 | − | 0.475685i | \(-0.157800\pi\) | |||||||
\(998\) | −1.80343 | − | 2.40372i | −0.0570867 | − | 0.0760886i | ||||
\(999\) | 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.757.19 | yes | 24 | |
3.2 | odd | 2 | inner | 1512.2.c.g.757.6 | yes | 24 | |
4.3 | odd | 2 | 6048.2.c.f.3025.14 | 24 | |||
8.3 | odd | 2 | 6048.2.c.f.3025.11 | 24 | |||
8.5 | even | 2 | inner | 1512.2.c.g.757.20 | yes | 24 | |
12.11 | even | 2 | 6048.2.c.f.3025.12 | 24 | |||
24.5 | odd | 2 | inner | 1512.2.c.g.757.5 | ✓ | 24 | |
24.11 | even | 2 | 6048.2.c.f.3025.13 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.g.757.5 | ✓ | 24 | 24.5 | odd | 2 | inner | |
1512.2.c.g.757.6 | yes | 24 | 3.2 | odd | 2 | inner | |
1512.2.c.g.757.19 | yes | 24 | 1.1 | even | 1 | trivial | |
1512.2.c.g.757.20 | yes | 24 | 8.5 | even | 2 | inner | |
6048.2.c.f.3025.11 | 24 | 8.3 | odd | 2 | |||
6048.2.c.f.3025.12 | 24 | 12.11 | even | 2 | |||
6048.2.c.f.3025.13 | 24 | 24.11 | even | 2 | |||
6048.2.c.f.3025.14 | 24 | 4.3 | odd | 2 |